Environmental Organic Chemistry [3 ed.] 1118767233, 9781118767238

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Environmental Organic Chemistry

Environmental Organic Chemistry Third Edition

Ren´e P. Schwarzenbach Philip M. Gschwend Dieter M. Imboden

Copyright © 2017 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data is available. ISBN: 978-1-118-76723-5

Printed in the United States of America 10 9 8 7 6 5 4 3 2 1

v

Contents

Preface

xiii

About the Companion Website

xvii

1

General Topic and Overview 1.1 1.2 1.3 1.4

1

Introduction / 2 Assessing Organic Chemicals in the Environment / 4 What is This Book All About? / 7 Bibliography / 14

PART I Background Knowledge

17 2

Background Knowledge on Organic Chemicals 2.1 2.2 2.3 2.4

3

The Makeup of Organic Compounds / 20 Intermolecular Forces Between Uncharged Molecules / 37 Questions and Problems / 40 Bibliography / 43

The Amazing World of Anthropogenic Organic Chemicals 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12

19

Introduction / 47 A Lasting Global Problem: Persistent Organic Pollutants (POPs) / 47 Natural but Nevertheless Problematic: Petroleum Hydrocarbons / 48 Notorious Air and Groundwater Pollutants: Organic Solvents / 53 Safety First: Flame Retardants All Around Us / 56 How to Make Materials “Repellent”: Polyfluorinated Chemicals (PFCs) / 58 From Washing Machines to Surface Waters: Complexing Agents, Surfactants, Whitening Agents, and Corrosion Inhibitors / 60 Health, Well-Being, and Water Pollution: Pharmaceuticals and Personal Care Products / 63 Fighting Pests: Herbicides, Insecticides, and Fungicides / 65 Our Companion Compounds: Representative Model Chemicals / 69 Questions / 72 Bibliography / 73

45

vi

Contents

4

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

81

4.1 Important Thermodynamic Functions / 83 4.2 Using Thermodynamic Functions to Quantify Equilibrium Partitioning / 89 4.3 Organic Acids and Bases I: Acidity Constant and Speciation in Natural Waters / 98 4.4 Organic Acids and Bases II: Chemical Structure and Acidity Constant / 107 4.5 Questions and Problems / 116 4.6 Bibliography / 119 5

Earth Systems and Compartments 5.1 5.2 5.3 5.4 5.5 5.6 5.7

6

Introduction / 123 The Atmosphere / 125 Surface Waters and Sediments / 131 Soil and Groundwater / 148 Biota / 154 Questions / 155 Bibliography / 158

Environmental Systems: Physical Processes and Mathematical Modeling 6.1 6.2 6.3 6.4 6.5 6.6

165

Systems and Models / 167 Box Models: A Concept for a Simple World / 174 When Space Matters: Transport Processes / 191 Models in Space and Time / 196 Questions and Problems / 203 Bibliography / 211

PART II Equilibrium Partitioning in Well-Defined Systems 7

121

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

213

215

7.1 Introduction / 216 7.2 Molecular Interactions Governing Bulk Phase Partitioning of Organic Chemicals / 217 7.3 Quantitative Approaches to Estimate Bulk Phase Partition Constants/Coefficients: Linear Free Energy Relationships (LFERs) / 225 7.4 Questions / 232 7.5 Bibliography / 234

Contents

8

Vapor Pressure (pi ∗ ) 8.1 8.2 8.3 8.4

9

9.3 9.4

9.5 9.6 10

237

Introduction and Theoretical Background / 238 Molecular Interactions Governing Vapor Pressure and Vapor Pressure Estimation Methods / 246 Questions and Problems / 253 Bibliography / 257

( ) ( sat ) and Activity Coefficient 𝜸 sat in Water; Air–Water Solubility Ciw iw ( ) Partition Constant Kiaw 9.1 9.2

vii

259

Introduction and Thermodynamic Considerations / 261 Molecular Interactions Governing the Aqueous Activity Coefficient and the Air–Water Partition Constant / 267 LFERs for Estimating Air–Water Partition Constants and Aqueous Activity Coefficients/Aqueous Solubilities / 270 Effect of Temperature, Dissolved Salts, and pH on the Aqueous Activity Coefficient/Aqueous Solubility and on the Air–Water Partition Constant / 272 Questions and Problems / 282 Bibliography / 285

Organic Liquid–Air and Organic Liquid–Water Partitioning

289

10.1 Introduction / 291 10.2 Thermodynamic Considerations and Comparisons of Different Organic Solvents / 291 10.3 The Octanol–Water System: The Atom/Fragment Contribution Method for Estimation of the Octanol–Water Partition Constant / 298 10.4 Partitioning Involving Organic Solvent–Water Mixtures / 301 10.5 Evaporation and Dissolution of Organic Compounds from Organic Liquid Mixtures–Equilibrium Considerations / 307 10.6 Questions and Problems / 311 10.7 Bibliography / 317 11

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water 11.1 11.2 11.3 11.4 11.5

Introduction / 322 Adsorption from Air to Well-Defined Surfaces / 322 Adsorption from Water to Inorganic Surfaces / 335 Questions and Problems / 342 Bibliography / 345

321

viii

Contents

PART III Equilibrium Partitioning in Environmental Systems

349

12

351

General Introduction to Sorption Processes 12.1 Introduction / 352 12.2 Sorption Isotherms and the Solid–Water Equilibrium Distribution Coefficient (Kid ) / 354 12.3 Speciation (Sorbed versus Dissolved or Gaseous), Retardation, and Sedimentation / 360 12.4 Questions and Problems / 366 12.5 Bibliography / 368

13

Sorption from Water to Natural Organic Matter (NOM)

369

13.1 The Structural Diversity of Natural Organic Matter Present in Aquatic and Terrestrial Environments / 371 13.2 Quantifying Natural Organic Matter–Water Partitioning of Neutral Organic Compounds / 376 13.3 Sorption of Organic Acids and Bases to Natural Organic Matter / 388 13.4 Questions and Problems / 392 13.5 Bibliography / 397 14

Sorption of Ionic Organic Compounds to Charged Surfaces

405

14.1 Introduction / 407 14.2 Cation and Anion Exchange Capacities of Solids in Water / 408 14.3 Ion Exchange: Nonspecific Adsorption of Ionized Organic Chemicals from Aqueous Solutions to Charged Surfaces / 414 14.4 Surface Complexation: Specific Bonding of Organic Compounds with Solid Phases in Water / 426 14.5 Questions and Problems / 432 14.6 Bibliography / 436 15

Aerosol–Air Partitioning: Dry and Wet Deposition of Organic Pollutants 15.1 15.2 15.3 15.4 15.5

16

Origins and Properties of Atmospheric Aerosols / 442 Assessing Aerosol–Air Partition Coefficients (KiPMa ) / 445 Dry and Wet Deposition / 453 Questions and Problems / 459 Bibliography / 464

Equilibrium Partitioning From Water and Air to Biota 16.1 16.2 16.3 16.4

441

Introduction / 471 Predicting Biota–Water and Biota–Air Equilibrium Partitioning / 471 Bioaccumulation and Biomagnification in Aquatic Systems / 485 Bioaccumulation and Biomagnification in Terrestrial Systems / 498

469

Contents

ix

16.5 Baseline Toxicity (Narcosis) / 503 16.6 Questions and Problems / 507 16.7 Bibliography / 514

PART IV Mass Transfer Processes in Environmental Systems

523

17

525

Random Motion, Molecular and Turbulent Diffusivity 17.1 17.2 17.3 17.4 17.5

18

Transport at Boundaries 18.1 18.2 18.3 18.4 18.5 18.6

19

617

The Sediment–Water Interface / 618 Transport in Unsaturated Soil / 626 Questions and Problems / 630 Bibliography / 634

PART V Transformation Processes 21

581

The Air–Water Interface / 583 Air–Water Exchange Models / 585 Measurement of Air–Water Exchange Velocities / 592 Air–Water Exchange in Flowing Waters / 599 Questions and Problems / 604 Bibliography / 613

Interfaces Involving Solids 20.1 20.2 20.3 20.4

559

The Role of Boundaries in the Environment / 560 Bottleneck Boundaries / 562 Wall Boundaries / 567 Hybrid Boundaries / 572 Questions and Problems / 577 Bibliography / 580

Air–Water Exchange 19.1 19.2 19.3 19.4 19.5 19.6

20

Random Motion / 526 Molecular Diffusion / 534 Other Random Transport Processes in the Environment / 545 Questions and Problems / 550 Bibliography / 557

635 Background Knowledge on Transformation Reactions of Organic Pollutants 21.1 Identifying Reactive Sites Within Organic Molecules / 638 21.2 Thermodynamics of Transformation Reactions / 643

637

x

Contents

21.3 Kinetics of Transformation Reactions / 650 21.4 Questions and Problems / 657 21.5 Bibliography / 661 22

Hydrolysis And Reactions With Other Nucleophiles

663

22.1 Nucleophilic Substitution and Elimination Reactions Involving Primarily Saturated Carbon Atoms / 665 22.2 Hydrolytic Reactions of Carboxylic and Carbonic Acid Derivatives / 680 22.3 Enzyme-Catalyzed Hydrolysis Reactions: Hydrolases / 695 22.4 Questions and Problems / 701 22.5 Bibliography / 710 23

Redox Reactions 23.1 23.2 23.3 23.4 23.5 23.6

24

715

Introduction / 716 Evaluating the Thermodynamics of Redox Reactions / 719 Examples of Chemical Redox Reactions in Natural Systems / 730 Examples of Enzyme-Catalyzed Redox Reactions / 747 Questions and Problems / 756 Bibliography / 765

Direct Photolysis in Aquatic Systems

773

24.1 Introduction / 775 24.2 Some Basic Principles of Photochemistry / 776 24.3 Light Absorption by Organic Compounds in Natural Waters / 788 24.4 Quantum Yield and Rate of Direct Photolysis / 800 24.5 Effects of Solid Sorbents (Particles, Soil Surfaces, Ice) on Direct Photolysis / 803 24.6 Questions and Problems / 804 24.7 Bibliography / 811 25

Indirect Photolysis: Reactions with Photooxidants in Natural Waters and in the Atmosphere

815

25.1 Introduction / 816 25.2 Indirect Photolysis in Surface Waters / 817 25.3 Indirect Photolysis in the Atmosphere (Troposphere): Reaction with Hydroxyl Radical (HO∙ ) / 829 25.4 Questions and Problems / 833 25.5 Bibliography / 838 26

Biotransformations 26.1 Introduction / 847

845

Contents

xi

26.2 Some Important Concepts about Microorganisms Relevant to Biotransformations / 848 26.3 Initial Biotransformation Strategies / 858 26.4 Rates of Biotransformations / 864 26.5 Questions and Problems / 882 26.6 Bibliography / 889 27

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

897

27.1 Introduction, Methodology, and Theoretical Background / 898 27.2 Using CSIA for Assessing Organic Compound Transformations in Laboratory and Field Systems / 914 27.3 Questions and Problems / 930 27.4 Bibliography / 936

PART VI Putting Everything Together 28

945 Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

947

28.1 One-Box Model: The Universal Tool for Process Integration / 948 28.2 Assessing Equilibrium Partitioning in Simple Multimedia Systems / 952 28.3 Simple Dynamic Systems / 956 28.4 Systems Driven by Advection / 960 28.5 Bibliography / 974 Appendix

977

Index

995

xiii

Preface

“Textbooks are outdated. Don’t waste your time writing a textbook! Nowadays, teachers, students, and practitioners download whatever they need to know from the Internet. They don’t depend on textbooks anymore.” These and other similarly “encouraging” statements were made by some dear colleagues three years ago, ten years after the 2nd edition and twenty years after the 1st edition of our textbook appeared, when we announced our plan to write a 3rd edition. However, numerous others also motivated us to sit down and reflect again about the broad, interdisciplinary field of environmental organic chemistry, which has excited us during our whole scientific careers. And they won! Here it is, the 3rd edition. Also, here is why we feel that textbooks are needed more than ever: in a time in which the number of scientific publications continue to explode, there is, from time to time, a need to assess in a more holistic way the state-of-the-art in a given field, and to summarize this state-of-the-art in a didactic form, so it can be used for educational purposes. In other words, between two physical or imaginary book covers, an attempt to define a given field and to give an account where this field stands. Of course, such an attempt represents only the biased, personal view of the book’s authors, but this may be better than having no view at all. What distinguishes the 3rd edition from the previous two editions? The first important message is: our main goal and approach is still the same. We want to provide an understanding of how molecular interactions and macroscopic transport phenomena determine the distribution in space and time of organic compounds released into natural and engineered environments. We hope to do this by teaching the reader to utilize the structure of a given chemical to deduce that chemical’s physical chemical properties and intrinsic reactivities. Emphasis is placed on quantification of phase transfer, transformation, and transport processes at each level. By first considering each of the processes that act on organic chemicals one at a time, we try to build bits of knowledge and understanding that, combined in mathematical models, should enable the reader to assess organic compound behavior in the environment. The second important message is: as was the case when going from the 1st to the 2nd edition, the new edition has undergone significant changes. Old chapters have been deleted, the remaining chapters have been substantially revised, and new chapters have been added. Another important goal was to diminish the total volume of the book. Of course, for all topics, we have tried hard to give an account of the state-of-the-art and to provide access to the pertinent literature. The most drastic change made was our decision to position an introduction of mathematical modeling in Part I (Chapter 6) among other introductory chapters and, in turn, to condense the chapters on transport and mixing, and on modeling of environmental systems.

xiv

Preface

However, this does not mean that the most important physical and mathematical modeling aspects have been lost. They are now just more focused and tailor-made to the needs of environmental chemists and environmental engineers. In addition to this main change, we have added four completely new chapters, which were neither present in the 1st nor 2nd edition, and which, in our opinion, can hardly be found anywhere else: (i) A look into the vast world of anthropogenic chemicals, illustrating the great innovations made by the chemical industry in customizing chemicals that fulfill important tasks in our daily lives, but also illustrating why many of them are of environmental concern (Chapter 3); (ii) A summary of the most important physical and chemical “properties” of environmental compartments including the atmosphere, surface waters, soils, and groundwater (Chapter 5); (iii) A quantitative treatment of aerosol–air partitioning of organic pollutants and the role of aerosols in determining their residence time in the stratosphere (Chapter 15); and (iv) An introduction to compound specific isotope analysis (CSIA) and its application to assess organic pollutant transformations in laboratory and field systems (Chapter 27). Who should read and use this book, or at least keep it on their bookshelf? From our experience with the previous editions, and maybe still with a bit of wishful thinking, we are inclined to answer this question with “Everybody who has to deal with organic chemicals in the environment.” More specifically, we believe that the theoretical explanations and mathematical relationships discussed are very useful for chemistry professors and students who want both fundamental explanations and concrete applications that students can use to remember those chemical principles. Likewise, we suggest that environmental and earth science professors as well as their students can utilize the chemical property information and quantitative descriptions of chemical cycling to think about how humans are playing an increasingly important role in changing the Earth system and how we may use specific chemicals as tracers of environmental processes. Further, we believe that civil and environmental engineering professors and students will benefit from detailed understanding of the fundamental phenomena supporting existing mitigation and remedial designs, and they should gain insights that allow them to invent the engineering approaches of the future. Environmental policy and management professors as well as students can also benefit by seeing our capabilities (and limitations) in estimating chemical exposures that result from our society’s use of chemicals. Finally, chemists and chemical engineers in industry should be able to use this book’s information to help make “green chemistry” decisions, whereas governmental regulators and environmental consultants can use the book in order to better assess the chemical uses they must permit and the problem sites they must assess and manage. To meet the needs of this very diverse audience, we have tried wherever possible to present the various topics in a way to make this book useful for beginners as well as for people with more expertise. We have also incorporated a large number of references throughout the text to help those who want to follow particular topics further. Finally, by including numerous problems, we want to motivate students as well as practitioners to attempt to arrive at quantitative answers for particular cases of interest to them. For all problems, solutions are made available electronically through a web site provided by the publisher—some of them to everybody but all of them to teachers, practitioners, and others with special permission. The possibility of making

Preface

xv

materials available electronically has allowed us to turn most of the illustrative examples of the 2nd edition into problems, thus making the main text more readable. It also allows us to provide the appendices, in particular the large appendix containing properties of numerous diverse chemicals, solely in electronic form. In conclusion, this book is intended as a comprehensive text for introductory courses in environmental organic chemistry at the graduate level, as well as an important source of information for practical hazard and risk assessment of organic chemicals in the environment. We hope that with this 3rd edition, we can continue to make a useful contribution to the education of environmental scientists and engineers and, thus, to better protection of our environment. Acknowledgments. Those who have ever written a textbook know that the authors are not the only ones who play an important role in the realization of the final product. In this particular case, one person made all the difference: Jeanne Tomaszewski, who we appointed as editor and general manager for this textbook. Jeanne has not only turned our “Swiss-English” into a language that can be understood by any Englishspeaking person, she has also been a relentless critic of how we present things, and she has helped us in literature searches and in the compilation of data. Last but not least, she has managed the entire process of readying the manuscript for the publisher. THANK YOU Jeanne; without you, there would most likely not be a 3rd edition of Environmental Organic Chemistry. Many thanks to those who helped us with the numerous figures and structures in the book: above all, Werner Angst and Martin Hoffmann, but also Lauren McLean, Konstanze Schiessel, and Thierry Sollberger. Thanks as well to our professional colleagues who lent a keen eye to make sure some of our chapters are at their scientific best: Kathrin Fenner (Chapter 3), Kai-Uwe Goss (Chapter 7), Satoshi Endo (Chapters 7– 10), Hans Peter Arp (Chapter 15), Beate Escher (Chapter 16), Kristopher McNeill (Chapters 24 and 25), Fatima Hussain and Allison Perrotta (Chapter 26), and Martin Elsner, Thomas Hofstetter, Elisabeth Janssen, and Michael Sander (Chapter 27). We are also indebted to the Swiss Federal Institute of Technology in Zurich (ETH-Zurich) for significant financial support. Finally, we thank our wives Theres Schwarzenbach, Colleen Cavanaugh, and Sibyl Imboden for their continuous support during the many years of our professional lives. Ren´e P. Schwarzenbach Z¨urich, Switzerland Philip M. Gschwend Cambridge, Massachussetts, USA Dieter M. Imboden Z¨urich, Switzerland

xvii

About the Companion Website

This book is accompanied by a companion website: www.wiley.com/com/go/Schwarzenbach/EnvironmentalOrganChem3e The website includes: ! Appendices

! Selected Solutions for Students

! Additional Solutions for All Problems and Case Studies (Only Available for

Academic Adopters)

1

Chapter 1

General Topic and Overview

1.1

Introduction

1.2

Assessing Organic Chemicals in the Environment General Considerations Exposure Assessment

1.3

What is This Book All About? The Ambitious Goals of the Book A Short Guided Tour Through the Book

1.4

Bibliography

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

2

General Topic and Overview

1.1

Introduction Take a moment. Look around. Think of the plethora of natural and synthetic (manmade) organic chemicals that you use every day. Think of the various ways in which such chemicals may be released intentionally or unintentionally into the environment by our human activities. As these anthropogenic chemicals potentially accumulate in the atmosphere, in surface waters and sediments, and in soils and aquifers, we must ask, what might the diverse effects be on aquatic and terrestrial organisms, on whole ecosystems, and on human health?

Figure 1.1 Historical records of the sales/production volumes of DDT and PCBs, and the similarity of these time-varying trends to the accumulation rates of these chemicals in the sediments of Lake Ontario; adapted from Eisenreich et al. (1989). The major metabolites DDE and DDD accumulated more or less concurrently with the parent compound DDT, indicating transformation of this compound.

1980

There is no doubt that the majority of the more than 100,000 synthetic (mostly organic) chemicals commercially produced (e.g., Scheringer et al., 2012) are of great benefit and are indispensable for human society. However, as has become more and more evident in the past decades, the use of all these chemicals has its downsides. Many have been detected throughout the environment, even in remote locations far away from the point of their release (e.g., Shen et al., 2005; Lohmann et al., 2009; Scheringer, 2009; Ruggirello et al., 2010; Salamova et al., 2014). As a historical example, Fig. 1.1 shows the history of production of the insecticide DDT (along with its transformation products DDE and DDD) and polychlorinated biphenyls (PCBs), used as very stable fluids in various technical applications, as well as their accumulation in the sediments of Lake Ontario sediment ∑ (Eisenreich et al., 1989). Remarkably, ∑ cores showed that the variations in (DDT+DDE+DDD) and PCB concentrations with depth in the sediment corresponded closely to the growth and decline of their production in the United States. Clearly, a tight connection exists between production and use of these synthetic chemicals and their concentrations in the environment that result from various inputs with subsequent transport, transfer, and transformation. 1980

(a)

(b)

1970

1970

ΣPCB PCBs

1960

1960

Cl

Cl

DDT Cl

1950

Cl

Cl

Cl

Cl

1940

1940

1930

ΣDDT (DDT + DDD + DDE)

1950

0

20

40

60

80

production United States (103 tons)

100

1930

0 0

20 100

40

60 200

80

100

300

accumulation in sediments of Lake Ontario (μg

400 m–2

yr–1)

Introduction

3

Also, as was recognized more than sixty years ago, and published, for example, in 1962 by Rachel Carson in Silent Spring, chemicals like DDT or PCBs are rather persistent in the environment (i.e., resistant to abiotic or biological degradation) and may accumulate in the bodies of organisms, including humans. Such biouptake may lead to adverse effects; in the case of DDT, uptake leads birds to produce eggs with thin shells, unable to support enough weight during incubation (Carson, 1962). This effect illustrates that DDT and other biocides that are aimed with great success at particular target organisms (e.g., DDT for controlling the spread of malaria by mosquitos) also harm non-target organisms. Numerous studies show that organic chemicals designed to exhibit a particular biological effect, including pesticides and pharmaceuticals, but also many of those considered to have no effect, such as industrial chemicals like PCBs, all may pose a threat to ecosystems (e.g., stratospheric ozone depletion as shown by Molina and Rowland, 1974), human health (e.g., uptake of organochlorine and organobromine compounds into human breast milk by Noren and Meironyte 2000), or resources (e.g., water supplies by MTBE, Johnson et al., 2000). Therefore, when addressing anthropogenic organic chemicals in the environment, we now speak of “organic pollutants” or “organic contaminants.” Except for at highly contaminated sites, many of these chemicals are commonly present at rather low concentrations in the environment (e.g., ng L–1 to μg L–1 in natural waters) and referred to as “organic micropollutants.” The ubiquitous pollution of the environment by such organic micropollutants is certainly one of the key environmental problems facing humanity (e.g., Schwarzenbach et al., 2006 and 2010). So, one may ask: what needs to be done in the future to minimize the adverse impacts of anthropogenic organic chemicals on humans and the environment? Have we learned the lessons from the past? Obviously not! For example, consider compounds such as the polybrominated biphenyl ethers (PBDEs) that were produced and consumed in large quantities as flame retardants before they were restricted and then removed from the market (see short history given in Venier et al., 2015). Based on their physicochemical properties and their known persistence, one could have anticipated that they accumulate in the environment and in organisms, including humans, as has been confirmed by numerous studies (Noren and Meironyte, 2000; Hites, 2004; Frederiksen et al., 2009). Obviously, the decision to allow the use of these rather problematic chemicals in numerous consumer products for a limited time was a trade-off between (apparent) benefits for society and adverse effects on people and the environment. Likewise, methyl-t-butyl [CH3 –O–C(CH3 )3 ], an oxygenate added to gasoline to improve combustion, was introduced in the early 1980s and became one of the volumetrically largest chemicals produced in the United States before being phased out after 2000. One could have predicted that based on its high water solubility and persistence, it would become a major groundwater pollutant (Arey and Gschwend, 2005). These and other examples discussed in Chapter 3 are illustrative of conflicts of interest that exist between different stakeholders (i.e., chemical manufacturers, industrial users, governmental regulators, politicians, environmental organizations, and consumers) when introducing new chemicals, restricting chemical use, or even banning existing chemicals. It is our opinion that in the interest of human society and in the interest of the environment, such conflicts need to be better and more efficiently handled in the future. In any case, in order to make optimal decisions, we need tools that allow proper risk assessment of organic

4

General Topic and Overview

pollutants, which includes an exposure and effect assessment (van Leeuwen and Vermeire, 2007). To this end, profound knowledge and understanding is necessary of the factors that govern the input, distribution, and fate of a given chemical in the environment, as well as toxicological information on its potential impacts on ecosystems and individual organisms, including humans. Such knowledge is, of course, also critical for preventing or restricting their release into the environment, as well as for assessing already existing contamination in surface waters, sediments, soils, groundwater, and the atmosphere, and for designing innovative remediation technologies. Also, such understanding is indispensable for the advancement of “green chemistry,” which entails the design of more environmentally friendly industrial processes and benign products. To better fulfill all these tasks there is, on the one hand, an increasing need for well-trained professionals in environmental chemistry and (eco)toxicology, and, on the other hand, a need to promote these topics to a more prominent status in curricula of chemistry, environmental science and engineering, life sciences, public policy, and other areas including social sciences, such as economics and law.

1.2

Assessing Organic Chemicals in the Environment General Considerations The environmental risk assessment of organic chemicals covers two general aspects, an exposure assessment and effect assessment. Traditionally, common practice has been to divide the risk assessment into exposure and effect parts, as schematically depicted in Fig. 1.2. A predicted or measured environmental concentration of a given chemical is compared to a “no observed effect concentration (NOEC),” derived primarily from short and long-term toxicity tests or based on structure-activity considerations. One should realize, however, that on a molecular level there is considerable overlap between the two tasks since it is the same physicochemical properties of a chemical that determine how it partitions in the environment, between the environment and an organism, and within an organism (i.e., toxicokinetics). Furthermore, the intrinsic reactivity of a chemical that determines its transformation in the environment also determines its interactions and reactions with biological molecules, potentially leading to toxic effects (i.e., toxicodynamics, see Fig. 1.2). Hence, an understanding of how the structure of a chemical determines its properties and intrinsic reactivities is important in both exposure and effect assessments. In this context, we point out that each organic compound must be viewed as an individual with its own “personality.” Even structurally, closely related compounds with the same elemental composition but a different connectivity of the various atoms (referred to as isomers, see Chapter 2) may exhibit very different properties, reactivities, and toxicities. For example, the vapor pressure of ethanol (CH2 CH2 OH) is 100 times smaller than the one of its isomer dimethylether (CH3 OCH3 ). Even more dramatic differences are observed in the hydrolysis half-lives (time required for half of the molecules to be transformed by the reaction with water) of the three chlorobutane isomers, and in the toxicity of three tetrachlorodibenzodioxin (TCDDs) isomers expressed as lethal doses for rats (Table 1.1).

micropollutants Cl

F F F F F F F F F F

OH F

N

F F F F F F

N H

Br NO

ON

Br

O

O S HN

N H

Br

O Br

O

NO

N N

Br N O

O

O P

S

HN

S

S

physical chemical properties intrinsic reactivities

modeling biological systems

modeling environmental systems air

input

transformation soil

surface water sediment

Figure 1.2 Key features and commonalities of exposure and effect assessment of organic chemicals in the environment. Both assessments hinge on knowledge of the same compound properties and intrinsic reactivities. Adapted from Schwarzenbach et al. (2006).

groundwater

environmental fate

growth “dilution”

metabolic transformation

dietary uptake

digestion of diet

uptake from gastro -intestinal tract

fecal excretion

passive uptake and depuration bioavailability

toxicokinetics and -dynamics

external exposure

internal exposure effects

Table 1.1 Two Examples of the Dependency of Chemical Properties on Chemical Structure: (left) Difference in Reaction Half-lives for Three Chlorobutane Isomers in Water and (right) Variation in Toxicity of Three Tetrachlorodibenzodioxin Isomers

Compound

Hydrolysis half-lifea

Structure

Compound

LD50 rat (g kg−1 body weight)b

Structure Cl

1-chlorobutane

Cl

1 year

1,2,3,4-tetrachlorodibenzodioxin

Cl

O

Cl

O

> 10

Cl Cl

2-chlorobutane

t-butyl chloride a

Cl

Cl

1 month

30 seconds!

See Chapter 22. b Data from Kociba and Cadey (1985).

O

1,3,6,8-tetrachlorodibenzodioxin

2,3,6,7-tetrachlorodibenzodioxin

Cl

>1

Cl

O

Cl

Cl

O

Cl

Cl

O

Cl

0.00004

6

General Topic and Overview

Exposure Assessment In this book, we focus primarily on exposure assessment with some discussions on how chemicals interact with aquatic and terrestrial biota (Chapter 16). For an in-depth treatment of (eco)toxicological aspects, we refer to other textbooks (Newman and Clemens, 2008; Walker, 2012). The goal of any exposure assessment is to provide estimates of projected or actual concentrations of a given chemical in a given system. To this end, one must relate these concentrations to the input (emission) of the compound into the system. To do this, mathematical models are required that allow the user to quantitatively describe the distribution and fate of the compound in the system considered. The degree of complexity of the model required depends strongly on the system considered and on the specific questions asked (see Chapter 6). For example, if we are interested in assessing the general tendency of an organic chemical to partition between the major environmental compartments (air, surface water, sediment, soil, and groundwater) and to get an order of magnitude idea of its average residence time in each of these compartments, we can use a simple “unit world” model as depicted in Fig. 1.2. Such models are available at different levels of sophistication and are widely used in practice as screening tools for ranking existing chemicals and for evaluating new chemicals with respect to their potential to accumulate in the environment (Harvey et al., 2007; MacLeod et al, 2010; Buser et al., 2012; Hughes et al., 2012; Mackay et al., 2014). At the other extreme, if we need to know precisely how the (time dependent) input of an organic chemical translates into the temporal and spatial variations in its concentration in a “real” natural system, more complex models are needed. In such models, the compound-specific phase transfer and transformation processes as well as the systemspecific transport and mixing processes have to be taken into account. As an example, think of a lake that is used as a drinking water reservoir for which you need to predict what will happen if it gets contaminated by organic chemicals, say after a spill. For this case, you need a model that allows you to describe quantitatively the dynamic behavior of a specific organic compound in the lake. As is schematically depicted in Fig. 1.3, this includes quantification of the transport and mixing processes within the lake, the exchange between the lake and atmosphere (gas exchange) and the sediment (sedimentation/resuspension), as well as chemical, photochemical, and biological transformation reactions that the compound undergoes in the water column. Each of these processes requires knowledge about both compound-specific and systemspecific properties: (a) the molecular diffusitivity and the air–water partition constant of the compound and the turbulence at the air–water interface to describe air–water exchange; (b) the particle–water sorption coefficient of the compound and the particle composition and dynamics for sedimentation and resuspension; (c) the intrinsic chemical reactivity of the compound and the pH, temperature, and water composition for chemical transformation reactions; (d) the sunlight absorption properties of the compound and the diurnal and seasonal light regime in the water column (which is also influenced by the water composition) for direct photolysis; (e) the reactivities of the compound with photooxidants for indirect photolysis; and (f) last but not least, the biodegradability of the compound, microbial communities present, and environmental conditions such as the presence or absence of oxygen. Finally, we should point out that any persistent transformation product of an organic pollutant, which

7

What is This Book All About?

atmosphere

groundwater infiltration/exfiltration

i input by rivers, sewage effluents, etc.

wet + dry deposition

air–water exchange

hν

export by outflow i

products

i

direct + indirect photolysis products i chem. + biol. transformation

vertical and horizontal mixing

i

sorption sedimentation of particles with attached i

water i

products

i

chem. + biol. transformation

Figure 1.3 Processes that determine the distribution, residence time, and sinks of an organic chemical i in a lake. This example illustrates the various physical, chemical, and biological processes that a compound is subjected to in the environment.

sediment–water exchange (diffusion, bioturbation, resupension)

i

sediments burial

.+ hem

ucts prod tion rma nsfo a r t l.

bio

c

generally exhibits different properties and intrinsic reactivities, needs to be assessed together with the parent compound (Escher and Fenner, 2011; Fenner et al., 2013). Therefore, the challenge, but also the “beauty,” of exposure assessment is that basic organic and physical chemistry knowledge has to be intimately combined with knowledge from various fields of environmental sciences including biogeochemistry, environmental physics, microbiology, hydrology, hydrogeology, and mathematical modeling. This combination is what distinguishes environmental organic chemistry from basic chemistry and what renders it to be a particularly fascinating interdisciplinary field.

1.3

What is This Book All About? The Ambitious Goals of the Book Considering the needs and tasks previously discussed, it is obviously quite a challenge to cover such a broad topic in a single textbook. Further, besides being intended as a textbook for students in environmental sciences and engineering, earth sciences, chemistry and physics, this book also seeks to serve as a reference for practitioners who need to solve real world problems. Last but not least, we aim to provide a

8

General Topic and Overview

state-of-the-art account of the field of environmental organic chemistry, fifty years after the field developed. This all sounds utterly overambitious, and in a sense, of course, it is. Nevertheless, we strongly feel that an integral view of the whole field, from the microscopic scale of molecular interactions up to the macroscopic scale of whole environmental system dynamics is necessary for a sound exposure assessment of organic chemicals in the environment. Therefore, this book should be considered as an attempt to introduce and integrate the most important aspects of all relevant topics, but not as an exhaustive treatment of particular subjects. For readers who want to pursue certain topics in greater detail, numerous literature citations have been included, even if this is unusual for a textbook. Furthermore, basic principles are emphasized and simplified pictures are sometimes used to help the less experienced reader enhance her or his intuitive perception of a given process. Also, each chapter ends with a set of questions, which points to the chapter’s most important aspects and inspires qualitative discussions, as well as problems to allow teachers to explore the depth of their students understanding or to allow individuals who use the book to check their progress. Finally, we have chosen to write the text in a somewhat colloquial style to enhance the “palatability” of the fundamental discussions. We hope that the professionals among our readers will make an allowance for this effort to teach. A Short Guided Tour Through the Book After this introduction, the book is comprised of 27 chapters bundled into six parts. Except for Part I, the chapters within a part generally build on each other, although many chapters can also be read independently. As such, we provide a corresponding bibliography at the end of each chapter. We need to point out that to solve the case study problems in Chapter 28, as well as any practical problems arising when assessing organic chemicals in the environment, one commonly needs to go back to the knowledge and information provided throughout various chapters. Part I encompasses five chapters with quite varied content. The goal of these chapters is to provide the reader with the necessary basics in chemistry, physics, and mathematics, as well as with some knowledge about the environment required for environmental exposure assessment of organic chemicals. Some teachers might ask their students to read all these chapters before taking a course in environmental organic chemistry; others may assign individual sections of these chapters to be reviewed in association with particular topics that are discussed during the course. In Chapter 2, we review some basic chemical concepts of organic chemistry used throughout this book. For readers with rather little background in organic chemistry, it may also be useful to additionally consult the introductory chapters of an organic chemistry textbook. However, professional chemists might want to skip this chapter and continue directly to Chapter 3, where we give an overview of some groups of environmentally relevant organic chemicals that play an important role in daily life. In Chapter 4, we address some pertinent thermodynamic aspects needed throughout the book to describe partitioning and reaction equilibria. The latter is applied to an important property of organic acids and bases, that is, the acidity and basicity constants. Additional basic thermodynamic as well as kinetic considerations of transformation reactions of organic pollutants are provided later in Chapter 21. Chapter 5 is devoted to important

What is This Book All About?

9

physical and chemical “properties” of environmental compartments including the atmosphere, surface waters, soils, and groundwater. Concluding Part I, in Chapter 6, we provide the reader with basic modeling concepts and a toolkit for building simple mathematical models for quantitatively describing the environmental fate of organic compounds, both natural substances like methane and pollutants like DDT. Using the knowledge acquired in Chapters 2 and 4, in Part II, we provide a systematic treatment of equilibrium partitioning of organic chemicals between gaseous, liquid, and solid phases. Both partitioning between bulk phases and adsorption from bulk phases to surfaces are addressed. We consider well-defined systems that allow us to visualize and quantify the molecular interactions that govern partitioning. The goals are to develop an understanding of how the structure of a given chemical determines the magnitude of its partition constant and to introduce simple models for estimating such constants. The insights and methodologies provided in Part II form the basis for discussing partitioning processes in the environment in Part III (Chapters 12–16). Chapter 7 treats some general qualitative aspects of partitioning of organic chemicals between two well-defined bulk phases including air, water, and organic solvents. In addition, some simple quantitative approaches are introduced for estimating partition constants, which will be used throughout Parts II and III. Chapters 8 and 9 are devoted to the two most important compound properties governing partitioning, vapor pressure and aqueous solubility. These properties tell us how much molecules like or dislike to partition from their pure liquid or solid bulk phase into the gas or aqueous phase. We learn how to use these properties to describe the energy status of the molecules in dilute gaseous phases or aqueous solutions. For the latter case, we discuss how inorganic and organic water constituents influence this status, which is described by the aqueous activity coefficient of the compound. Chapter 9 also addresses air–water partitioning, which follows directly from the discussions on vapor pressure and aqueous solubility, since it is simply the result of how much a compound likes or dislikes being in the gas phase as compared to the aqueous phase. Chapter 10 covers partitioning between air or water and organic solvents, in particular, n-octanol, which is widely used to mimic natural organic phases and biota. By deepening our insights from Chapter 7 on how solvent characteristics determine the partitioning behavior of organic solutes, we critically evaluate under which conditions quantitative correlations between partition constants in different solvent-air or solvent-water systems can be used for predictive purposes. Chapter 11 concludes Part II by addressing partitioning of neutral organic compounds from air and water to well-defined surfaces, which is termed adsorption. The main focus is on adsorption from the gas phase to inorganic surfaces including water and ice surfaces, mineral oxide surfaces, and salt surfaces. Partitioning from the gas phase to organic surfaces including black carbon is addressed in Part III (Chapter 15). The major challenges when dealing with mass transfer processes in the environment include the heterogeneity of the various environmental phases and compartments

10

General Topic and Overview

discussed in Chapter 5, as well as the fact that, in some instances, we may not assume equilibrium between phases is established. Kinetic approaches to describe partitioning are then often needed when considering partitioning between two large compartments, such as the atmosphere and surface waters, or when mass transfer is slow as compared to other processes. These topics are addressed in Part IV. However, in Part III we need to first consider equilibrium aspects of partitioning between air or water and environmental media. The reason to first address these aspects is that knowledge of the corresponding equilibrium partition coefficients is not only important for treating situations in which one may assume partition equilibrium, but also for the quantitative description of the kinetics of mass transfer processes. For air–water partitioning, the equilibrium case is addressed in Chapter 9. In Chapters 12 to 15, our focus is on sorption equilibrium involving natural sorbents as they are encountered in colloids and larger particles in surface waters, in aerosols, and as components of sediments and soils. In addition, in Chapter 16, as a special case, we treat concepts for assessing bioaccumulation and biomagnification in aquatic and terrestrial systems. Chapter 12 provides a general introduction to sorption processes involving natural sorbents, focusing on equilibrium considerations. We discuss sorption isotherms and the related overall equilibrium sorption coefficient, Kid , which is often also referred to as a distribution coefficient (hence the subscript “d”). As several different sorbents may be present in a given natural system, we also show how one can express the overall Kid value as a composite of the different individual sorption coefficients. Finally, as an illustration, we discuss how Kid values can be used to assess the effect of sorption on the transport of organic compounds in porous media or upon sedimentation. Chapter 13 introduces sorption of organic compounds from water to organic matter present in the environment. In Part II, we learn that the majority of organic pollutants tend to partition favorably from water into organic phases. Therefore, it is not surprising that organic materials “dissolved” in water (i.e., in colloidal form) or associated with solids (e.g., suspended particles in the water column as well as constituents of sediments and soils) are often the dominant sorbents for a given organic chemical dissolved in water. In Chapter 13, we discuss approaches to quantitatively describe sorption equilibrium between such organic phases and water, with emphasis on what is referred to as “natural organic matter.” We also discuss combustion-derived materials of natural (e.g., forest fire chars) as well as anthropogenic origin (e.g., diesel engine-derived soots), which may represent important organic adsorbents for many organic compounds in the environment. Chapter 14 is devoted to those organic chemicals that may specifically interact with mineral surfaces in water. For such chemicals, appreciable adsorption can be expected for compounds that undergo electrostatic interactions or that may form surface complexes. The former group of chemicals includes primarily organic bases exhibiting amino groups (e.g., –NH2 , –NHR); the latter contains those compounds that may also form complexes with dissolved metals, for example, substituted benzenes containing two adjacent oxygen functions (e.g., –COOH, –OH). We present quantitative approaches used to describe such specific adsorption mechanisms, which may be considered an advanced topic for some readers, or simply an extension of metal-ligand complexation for others who have taken a course in Aquatic Chemistry.

What is This Book All About?

11

In Chapter 15, we address aerosol–air partitioning and its effect on the transport and residence times of organic chemicals in the atmosphere. We look at the size distribution, chemical characteristics, and sorption capacities of aerosols, and then we introduce methods to estimate aerosol–air partition coefficients. Finally, we discuss simple approaches for quantifying dry and wet deposition of aerosols and aerosol-bound organic pollutants. Finally, in Chapter 16, we discuss approaches for quantifying bioaccumulation and biomagnification along food chains or food webs in aquatic and terrestrial ecosystems. To this end, we first extend our discussion in Chapter 10 to chemical partitioning between water or air and well-defined biological materials including lipids, proteins, carbohydrates, lignin, and other plant polymers. Knowledge of the corresponding partition coefficients then allows us to derive multimedia equilibrium models for predicting bioaccumulation in organisms and plants, for interpretation of experimental data, and particularly, for assessment of the extent of equilibrium in a given system. We conclude Chapter 16 by addressing non-specific toxic effects of organic chemicals (i.e., baseline toxicity) that are primarily caused by partitioning of the compounds into membranes. In Chapter 6, mathematical models of increasing complexity are derived to describe the cycling of organic chemicals in environmental systems under the simultaneous influence of transformation and transport processes. In Part IV, further insight is gained to the physical nature of transport processes and how such processes can be quantitatively described. Box models, which are first discussed in Chapter 6, did not consider internal mixing, so the only mechanisms involving transport were the exchange of the chemical across the boundaries of the boxes, or the input and output processes, as we simply call them. In this part of the book, we treat processes that transport chemicals either within environmental compartments (e.g., within the air of a room) or between adjacent compartments (e.g., between the atmosphere over a lake and the water in the lake). Here, a distinction has to be made between advective (or directed) transport and diffusive transport, the result of random processes. Chapter 17 deals with random motion at different spatial scales. Derivations show that random motion, if averaged over time, can be described by Fick’s first law, as was introduced in Chapter 6. If the random motion originates from the thermal movement of molecules, the corresponding diffusivities that appear in Fick’s law are the molecular diffusion coefficients. Their size depends on the diffusing chemical and on the medium in which they are moving, such as air or water. Empirical expressions are derived that relate molecular diffusivities in air and water to either molar volume or molar mass of the chemical. The concept of diffusion is then extended to macroscopic random motion as it results from turbulence. Since advection in the atmosphere (wind) and in the water (water currents) is commonly turbulent, advective motion is usually accompanied by turbulent diffusion and a diffusion-like process called dispersion. Chapter 18 focuses on transport across boundaries between different environmental systems such as the atmosphere, the ocean, and the soil. As an example, we may want to know how quickly a chemical spilled into the ocean will dissipate as the result of mixing into surrounding waters and transfer to adjacent media such as the

12

General Topic and Overview

atmosphere. Such cases require us to discuss a set of environmental processes called mass transfers. If a boundary is combined with a phase change (e.g., from liquid to gas at the air–water interface or from liquid to solid at the surface of a sediment bed below a lake), we speak of an interface boundary. In contrast, non-interface boundaries occur within a single medium, for instance, the tropopause between troposphere and stratosphere or the thermocline between the epilimnion and hypolimnion in a lake. Two types of boundaries are discussed that are distinguished by the relative change of diffusivity on either side of the boundary. Bottleneck boundaries lie between systems with large diffusivities; wall boundaries separate a system with large diffusivity (e.g., water) from a system with low diffusivity (e.g., a sediment bed). Models are derived for describing rates of chemical exchanges between these two types of boundaries and between combinations of them. In the remaining two chapters of Part IV, the models derived in Chapter 18 are applied to the two most important boundaries of the environment. In Chapter 19, air–water exchange is discussed. Empirical relations are presented that relate air– water exchange to the molecular diffusivities of the chemicals in air and water and to environmental conditions, mainly to wind speed and, for the case of streams and rivers, to current velocity. In Chapter 20, models for chemical exchange between fluids (i.e., air or water) and solids (i.e., sediment beds or soils) are derived. In Part V (Chapters 21–25), we turn our attention to processes by which a compound is converted to one or several products. Therefore, we talk about processes (reactions) in which chemical bonds are broken and new bonds are formed. Before we discuss specific transformation processes in more detail, in Chapter 21, we review some general background knowledge including some thermodynamic and kinetic aspects of abiotic and biological reactions that we will need throughout the following chapters. In addition, within this chapter, we also provide an overview of the most important types of reactions that organic pollutants may undergo in the environment. By inspecting some simple molecular characteristics such as electron distribution, oxidation states of the different atoms, and the presence of acidic or basic functions that are discussed in Chapter 2, we take a first step in learning how to recognize where in an organic molecule transformation reactions may occur. For a discussion of the various transformation reactions that organic chemicals undergo in the environment, it is convenient and common to divide these processes into the three major categories of chemical, photochemical, and biologically mediated transformation reactions. The former two types of reactions are commonly referred to as abiotic transformation processes, the latter as biotransformations. Chemical reactions encompass all reactions that occur in the dark and without mediation of organisms. We subdivide these reactions into those in which there is no net electron transfer occurring between the organic compound and a reactant in the environment (Chapter 22), and into redox reactions (Chapter 23), where electrons are either transferred from (oxidation) or to (reduction) the organic chemicals. As the name indicates, photochemical reactions are reactions that are initiated by incidence of (sun)light on a waterbody, terrestrial surface, or in the atmosphere. One

What is This Book All About?

13

speaks of direct photolysis if a compound undergoes transformation as a consequence of its own direct absorption of light (Chapter 24). The term indirect photolysis (Chapter 25) is commonly used to denote (chemical) reactions of organic compounds with (short-lived) reactive species that are formed as a consequence of absorption of sunlight by other inorganic or organic species present in the system considered. The most difficult, but also most important topic in the assessment of transformations of organic chemicals in the environment, are biotransformations, which are discussed in Chapter 26. Although organic compounds may be transformed by many different organisms, including humans, the most important living actors involved in biotransformations of anthropogenic organic chemicals in the environment are microorganisms. Hence, our discussions will emphasize microbial transformation reactions. We note that biotransformations are usually the only process by which an anthropogenic compound may be completely mineralized in the environment. As such, when assessing the environmental impact of a given compound, its biodegradability is one of the key issues. Unfortunately, as we will see, because of the complexity of the factors that govern microbial transformation reactions, it is, in many cases, very difficult to make a sound prediction of the rates of such processes in a given natural system unless detailed information are available, such as growth rates of microbial populations responsible for the chemical’s biodegradation. We conclude Part V with Chapter 27 introducing compound specific isotope analysis (CSIA), which is a powerful tool for assessing whether an organic pollutant has undergone transformation in a given system, for getting hints on the mechanisms of transformation reactions and, in some cases, even for quantifying reaction rates. By discussing several case studies, this chapter acquaints the reader with an important method and allows us to deepen our insights into the abiotic and biologically mediated transformation reactions gained in Chapters 21 to 26. In Part VI, Chapter 28, we invite the reader to “put everything together,” that is, to apply her or his knowledge acquired from all other chapters covering individual transport, transfer, and transformation processes to assess the overall behavior of a specific organic chemical in a given system. We do this by providing case studies formulated as problems, complemented with hints and help, which primarily cover modeling aspects required to solve the problem. The goal of these problems is not to provide a substitute for the application of available computer models for exposure assessments, but to teach the reader how to build such a model from individual process formulations and parameterizations, and to get a first overview of a given case, helping to decide whether a more thorough investigation or more sophisticated model calculation would be worthwhile and needed. The models required to solve the problems do not need more than a simple spreadsheet, or they can even be analyzed by hand, by what are commonly referred to as “back-of-the-envelope” calculations. In addition to the various chapters, the book also provides appendices that are partly available in the printed version of the book, whereas all are available in electronic form. The appendices in the printed version include Appendix A: Mathematics and Appendix B: Physical Constants and Units. Only available in electronic form are some additional tables for Appendix A and B, plus Appendix C: Physicochemical

14

General Topic and Overview

Properties of Organic Compounds, which contains physicochemical properties and Abraham parameters of more than 400 organic chemicals covering a wide range of compound classes. Appendix D: Temperature Dependence of Equilibrium Constants and Rate Constants and Appendix E: Estimation of Gas-Phase Hydroxyl Radical Reaction Rate Constants of Organic Chemicals are also available online.

1.4

Bibliography Arey, J. S.; Gschwend, P. M., A physical-chemical screening model for anticipating widespread contamination of community water supply wells by gasoline constituents. J. Contam. Hydrol. 2005, 76(1-2), 109–138. Buser, A. M.; MacLeod, M.; Scheringer, M.; Mackay, D.; Bonnell, M.; Russell, M. H.; DePinto, J. V.; Hungerbuehler, K., Good modeling practice guidelines for applying multimedia models in chemical assessments. Integr. Environ. Assess. Manag. 2012, 8(4), 703–708. Carson, R., Silent Spring. Houghton Mifflin: Boston, 1962. Eisenreich, S. J.; Willford, W. A.; Strachan, W. M. J., The role of atmospheric deposition in organic contaminant cycling in the Great Lakes. In Intermedia Pollutant Transport: Modelling and Field Measurements, Allen, D., Ed. Plenum Press: New York, 1989; pp 19–40. Escher, B. I.; Fenner, K., Recent advances in environmental risk assessment of transformation products. Environ. Sci. Technol. 2011, 45(9), 3835–3847. Fenner, K.; Canonica, S.; Wackett, L. P.; Elsner, M., Evaluating pesticide degradation in the environment: Blind spots and emerging opportunities. Science 2013, 341(6147), 752–758. Frederiksen, M.; Vorkamp, K.; Thomsen, M.; Knudsen, L. E., Human internal and external exposure to PBDEs – A review of levels and sources. Int. J. Hyg. Environ. Health 2009, 212(2), 109–134. Harvey, C.; Mackay, D.; Webster, E., Can the unit world model concept be applied to hazard assessment of both organic chemicals and metal ions? Environ. Toxicol. Chem. 2007, 26(10), 2129– 2142. Hites, R. A., Polybrominated diphenyl ethers in the environment and in people: A meta-analysis of concentrations. Environ. Sci. Technol. 2004, 38(4), 945–956. Hughes, L.; Mackay, D.; Powell, D. E.; Kim, J., An updated state of the science EQC model for evaluating chemical fate in the environment: Application to D5 (decamethylcyclopentasiloxane). Chemosphere 2012, 87(2), 118–124. Johnson, R.; Pankow, J.; Bender, D.; Price, C.; Zogorski, J., MTBE – To what extent will past releases contaminate community water supply wells? Environ. Sci. Technol. 2000, 34(9), 210A– 217A. Kociba, R. J.; Cabey, O., Comparative toxicity and biologic activity of chlorinated dibenzop-dioxins and furans relative to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). Chemosphere 1985, 14(6-7), 649–660. Lohmann, R.; Gioia, R.; Jones, K. C.; Nizzetto, L.; Temme, C.; Xie, Z.; Schulz-Bull, D.; Hand, I.; Morgan, E.; Jantunen, L., Organochlorine pesticides and PAHs in the surface water and Atmosphere of the North Atlantic and Arctic Ocean. Environ. Sci. Technol. 2009, 43(15), 5633– 5639. Mackay, D.; Hughes, L.; Powell, D. E.; Kim, J., An updated Quantitative Water Air Sediment Interaction (QWASI) model for evaluating chemical fate and input parameter sensitivities in aquatic systems: Application to D5 (decamethylcyclopentasiloxane) and PCB-180 in two lakes. Chemosphere 2014, 111, 359–365. MacLeod, M.; Scheringer, M.; McKone, T. E.; Hungerbuhler, K., The state of multimedia massbalance modeling in environmental science and decision-making. Environ. Sci. Technol. 2010, 44(22), 8360–8364.

Bibliography

15

Molina, M. J.; Rowland, F. S., Stratospheric sink for chlorofluoromethanes: Chlorine atomiccatalysed destruction of ozone. Nature 1974, 249(5460), 810–812. Newman, M. C.; Clements, W. H., Ecotoxicology: A Comprehensive Treatment. CRC Press: Boca Raton, FL, 2008. Noren, K.; Meironyte, D., Certain organochlorine and organobromine contaminants in Swedish human milk in perspective of past 20-30 years. Chemosphere 2000, 40(9-11), 1111–1123. Ruggirello, R. M.; Hermanson, M. H.; Isaksson, E.; Teixeira, C.; Forsstrom, S.; Muir, D. C. G.; Pohjola, V.; van de Wal, R.; Meijer, H. A. J., Current use and legacy pesticide deposition to ice caps on Svalbard, Norway. J. Geophys. Res.-Atmos. 2010, 115, DOI:10.1029/2010jd014005. Salamova, A.; Hermanson, M. H.; Hites, R. A., Organophosphate and halogenated flame retardants in atmospheric particles from a European arctic site. Environ. Sci. Technol. 2014, 48(11), 6133– 6140. Scheringer, M., Long-range transport of organic chemicals in the environment. Environ. Toxicol. Chem. 2009, 28(4), 677–690. Scheringer, M.; Strempel, S.; Hukari, S.; Ng, C. A.; Blepp, M.; Hungerbuhler, K., How many persistent organic pollutants should we expect? Atmos. Pollut. Res. 2012, 3(4), 383–391. Schwarzenbach, R. P.; Egli, T.; Hofstetter, T. B.; von Gunten, U.; Wehrli, B., Global water pollution and human health. In Annual Review of Environment and Resources, Gadgil, A.; Liverman, D. M., Eds. 2010; Vol. 35, pp 109–136. Schwarzenbach, R. P.; Escher, B. I.; Fenner, K.; Hofstetter, T. B.; Johnson, C. A.; von Gunten, U.; Wehrli, B., The challenge of micropollutants in aquatic systems. Science 2006, 313(5790), 1072–1077. Shen, L.; Wania, F.; Lei, Y. D.; Teixeira, C.; Muir, D. C. G.; Bidleman, T. F., Atmospheric distribution and long-range transport behavior of organochlorine pesticides in north America. Environ. Sci. Technol. 2005, 39(2), 409–420. van Leeuwen, C. J.; Vermeire, T. G., Ed., Risk Assessment of Chemicals: An Introduction 2nd ed.; Springer: Doordrecht, The Netherlands, 2007. Venier, M.; Salamova, A.; Hites, R. A., Halogenated flame retardants in the Great Lakes environment. Acc. Chem. Res. 2015, 48(7), 1853–1861. Walker, C. H., Principles of Ecotoxicology. 4th ed.; CRC Press: Boca Raton, FL, 2012.

Part I

Background Knowledge

19

Chapter 2

Background Knowledge on Organic Chemicals

2.1

The Makeup of Organic Compounds Elemental Composition, Molecular Formula, and Molar Mass Electron Shells of Elements Present in Organic Compounds Covalent Bonding Bond Energies (Enthalpies) and Bond Lengths: The Concept of Electronegativity Oxidation State of Atoms in an Organic Molecule Box 2.1 Determining the Oxidation States of Carbon Atoms Present in Organic Molecules The Spatial Arrangement of Atoms in Organic Molecules Delocalized Electrons, Resonance, and Aromaticity Common Functional Groups

2.2

Intermolecular Forces Between Uncharged Molecules Box 2.2 Classification of Organic Compounds According to Their Ability to Undergo Particular Molecular Interactions

2.3

Questions and Problems

2.4

Bibliography

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

20

Background Knowledge on Organic Chemicals

2.1

The Makeup of Organic Compounds To understand the nature and reactivity of organic molecules, we first look at the “pieces” of such molecules, atoms and chemical bonds. Most of the millions of known natural and synthetic organic compounds are combinations of a relatively small number of elements, namely carbon (C), hydrogen (H), oxygen (O), nitrogen (N), sulfur (S), phosphorus (P), silicon (Si), as well as the halogens fluorine (F), chlorine (Cl), bromine (Br), and iodine (I). The chief reason for the almost unlimited number of stable organic molecules that can be built from this limited number of elements is the ability of carbon to form stable carbon-carbon bonds. All kinds of three-dimensional carbon skeletons can therefore be made, even when the carbon atoms are also bound to heteroatoms, elements other than carbon and hydrogen. Such parts of molecules containing heteroatoms are of particular interest because they are often the site of specific interactions and reactivities. Thus, they are commonly referred to as functional groups or functionalities. Fortunately, despite the extremely large number of existing organic chemicals containing all kinds of functional groups, knowledge of a few governing rules about the nature of the elements and chemical bonds already enable us to understand important relationships between the structure of a given compound and its properties and reactivities. In large part, these attributes then determine the compound’s behavior in the environment. Elemental Composition, Molecular Formula, and Molar Mass When describing a compound, we first specify the elements it contains, or its elemental composition. For example, butyl chloride consists of carbon, hydrogen, and chlorine. We then specify how many atoms of each of element are present in one molecule, the compound’s molecular formula. Butyl chloride contains four carbon atoms, nine hydrogen atoms, and one chlorine atom, thus its molecular formula is C4 H9 Cl. We can then calculate the molecular mass or molecular weight of the compound, which is the sum of all the atoms’ masses present in the molecule. The average atomic masses of elements of interest to us in organic molecules are given in Table 2.1 in units of mu (unified atomic mass unit). This unit is approximately equal to 1.6605 × 10−27 kg. Using these atomic mass values, we obtain an average molecular mass of 92.57 mu for butyl chloride. Complicating matters a bit is the natural occurrence of stable isotopes, atoms that have the same number of protons and electrons but different numbers of neutrons in the nucleus, thus giving rise to different atomic masses. Table 2.2 enumerates examples of common elements present in organic chemicals exhibiting stable isotopes with significant natural abundances. Thus, the atomic masses given in Table 2.1 represent averaged values of the naturally occurring isotopes of a given element (e.g., average carbon is 1.1% at 13 mu + 98.9% at 12 mu = 12.011 mu ). To find the molar mass of a pure substance, we take 1 mole, Avogadro’s number NA = 6.022 × 1023 , of identical molecules. For butyl chloride, this amount weighs 92.57 grams. Therefore, 1 mole (abbreviation 1 mol) of any pure substance always

21

The Makeup of Organic Compounds

Table 2.1 Atomic Mass, Electronic Configuration, and Typical Number of Covalent Bonds of the Most Important Elements Present in Organic Molecules Element Namea Hydrogen Helium Carbon Nitrogen Oxygen Fluorine Neon Silicon Phosphorus Sulfur Chlorine Argon Bromine Krypton Iodine Xenon

Number of Electrons in Shell

Symbol

Number

Massb (mu )

K

H He C N O F Ne Si P S Cl Ar Br Kr I Xe

1 2 6 7 8 9 10 14 15 16 17 18 35 36 53 54

1.008

1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

12.011 14.007 15.999 18.998 28.0855 30.974 32.06 35.453 79.904 126.905

L

4 5 6 7 8 8 8 8 8 8 8 8 8 8

M

4 5 6 7 8 18 18 18 18

N

7 8 18 18

O

Net Charge of Kernel

Number of Covalent Bondsc 1

7 8

1+ 0 4+ 5+ 6+ 7+ 0 4+ 5+ 6+ 7+ 0 7+ 0 7+ 0

4 3, (4)d 2, (1)e 1 4 3, 5 2, 4, 6, (1)e 1 1 1

a

The underlined elements are noble gases. Abundance-averaged mass values of the naturally occurring isotopes. c Number of covalent bonds commonly occurring in organic molecules. d Positively charged atom. e Negatively charged atom. b

contains the same amount of molecules and weighs in grams what the average molecule weighs in mu . We should point out, however, that the ensemble of individual molecules of a given compound, for example with the molecular formula C4 H9 Cl, covers a range of different masses. For butyl chloride, 95.6% of the molecules contain 4 12 C atoms, whereas 4.4% have 113 C and 3 12 C atoms. Similarly, 75.8% of all molecules contain a 35 Cl and 24.2% a 37 Cl atom. Hence, by neglecting the 2 H isotope, 72.5% have a molecular formula of 12 C4 1 H9 35 Cl, 3.3% 13 C1 H35 Cl (1 mu higher), Table 2.2 Isotope Ratios of Elements Exhibiting Stable Isotopes at Significant Abundances Present in Organic Molecules Element

Isotope Ratios = 0.00015:1

Hydrogen

2 H:1 H

Carbon Nitrogen Oxygen

13 C:12 C

= 0.011:1 = 0.0037:1 18 O:16 O = 0.0020:1 15 N:14 N

Element Silicon Sulfur Chlorine Bromine

Isotope Ratio = 0.051:1 = 0.034:1 34 S:32 S = 0.044:1 37 Cl:35 Cl = 0.32:1 81 Br:79 Br = 0.98:1 29 Si:28 Si 30 Si:28 Si

22

Background Knowledge on Organic Chemicals

23.1% 12 C1 H37 Cl (2 mu higher), and 1.1% 13 C1 H37 Cl (3 mu higher). Molecules containing different isotopes of a given element may exhibit somewhat different reactivities, particularly at positions where a reaction occurs. Therefore, measurements of the exact stable isotope composition of a given compound, referred to as compound specific stable isotope analysis (CSIA), may be very useful in assessing transformation processes in the environment (see Chapter 27). Given the molecular formula, we now describe how the different atoms are connected to each other. The description of the exact connection of the various atoms, the connectivity, is commonly referred to as the structure of the compound. Depending on the number and types of atoms, many different ways to interconnect a given set of atoms may exist, yielding different structures. Such related compounds are referred to as isomers. Furthermore, as we subsequently discuss, several compounds can have atoms connected in exactly the same order (i.e., they exhibit the same structure), but the spatial arrangement differs. Such compounds are called stereoisomers. Sometimes, the term structure is used to denote both the connectivity as well as the spatial arrangement of the atoms. The term constitution of a compound is then sometimes introduced to solely describe the connectivity. Electron Shells of Elements Present in Organic Compounds Before we can examine how many different structures exist for a given molecular formula (e.g., C4 H9 Cl), we need to recall some of the rules concerning the number and nature of bonds that each of the various elements present in organic molecules may form. To this end, we first examine the electronic configuration of the atoms involved (see also Table 2.1). The configuration of electrons of an atom is often described by the notion of electron shells of varying energies. Electrons in shells farther from the nucleus exhibit higher average energies and travel farther from the nucleus than those in inner shells. The shell closest to the nucleus (K-shell) holds two electrons (see elements in first row of periodic table). The second shell (L-shell) holds up to eight (see second row of periodic table); the third shell (M-shell) can ultimately hold eighteen, but a stable configuration is reached when the shell is filled with eight electrons (see argon structure). Electrons in the outermost shell, the valence shell, are called valence electrons, whereas the remainder of the atom is referred to as the kernel. If the outer shell is filled, as with argon and the other noble gases (helium, neon, krypton, xenon, and radon), the atom is especially nonreactive. Thus, the number of valence electrons of a particular atom chiefly determines the chemical nature of an element. Some significant differences between elements exhibiting the same number of valence electrons do exist, such as between nitrogen and phosphorus or oxygen and sulfur. The differences between such elements are due in large part to the different energetic status of the electrons in the various shells and are further addressed in subsequent discussions. Therefore, much of the chemistry of the elements present in organic molecules is understandable in terms of a simple model describing the tendencies of the atoms to attain such “filled-shell” conditions by gaining, losing, or most importantly sharing

The Makeup of Organic Compounds

23

electrons. Among the elements present in organic molecules, hydrogen requires two electrons to fill its valence shell; one it supplies, and the other it must get elsewhere. Other important atoms of organic chemistry require eight valence electrons, which is called an octet configuration (see Table 2.1). Covalent Bonding Organic molecules customarily complete the octet in their valence shell by sharing electrons with other atoms, thus forming so-called covalent bonds. Each single covalent bond is composed of a pair of electrons, in most cases one electron contributed by each of the two bonded atoms. The covalent bond may thus be characterized as a mutual deception. By contributing only one electron to the bond, each atom “feels” it has both electrons in its outer shell. Thus, we visualize the bonds in an organic compound structure as electron pairs localized between two positive atomic nuclei; the electrostatic attraction of the nuclei to the electrons holds the atoms together. The simple physical law of the attraction of opposite charges and the repulsion of like charges is the most basic force in chemistry, and it explains many chemical phenomena. Using the simple concept of electron sharing to complete an octet in a valence shell, we can now easily deduce from Table 2.1 that in a neutral organic molecule, H, F, Cl, Br, and I (monovalent atoms) should form one bond, O and S (bivalent atoms) form two bonds, N and P (trivalent atoms) form three bonds, and C and Si (tetravalent atom) form four bonds. These valency rules are valid for the majority of cases that are of interest to us. Notable exceptions are S and P (see Table 2.11 and examples given in Chapter 3). We are now ready to draw all the possible structural isomers for butyl chloride by simply applying these valency rules. Table 2.3 shows the four different possibilities. With this example, we also take the opportunity to get acquainted with some of the common conventions used to symbolize molecular structures. The first convention (type 1 in Table 2.3) differentiates shared and unshared valence electron pairs. Straight lines denote shared electrons forming covalent bonds, while pairs of dots represent the unshared electrons. This representation clearly shows the nuclei and all of the electrons we must visualize. To simplify this first convention, all lines indicating bonds to hydrogen as well as the dots for unshared (nonbonding) electrons are frequently not shown (type 2). For further convenience, we may in many cases, eliminate all the bond lines without loss of clarity, as illustrated by type 3. In this convention, parentheses indicate branching. Finally, especially when dealing with compounds exhibiting a large number of carbon atoms, another convention is simply to sketch the carbon skeleton (type 4 in Table 2.3). Each line is thus a skeletal bond and is assumed to have carbons at each end, unless another element is shown. Furthermore, no carbonhydrogen bonds are indicated but are assumed present as required to make up full bonding (four bonds) at each carbon atom. To distinguish the various carbon-carbon bonds, bond lines are placed at about 120◦ , roughly resembling the true physical bond angle (see Fig. 2.2). Finally, an approach called SMILES (Simplified Molecular-Input Line-Entry System) can be used to write out each structure in a manner normalized for computing (see U.S. EPA, 2009; Weininger, 1988).

24

Background Knowledge on Organic Chemicals

Table 2.3 Different Conventions (types 1-4 and SMILES) Symbolizing the Molecular Structures of the Four Butyl Chloride (or Chlorobutanes) Isomers type 1 H

H

H

type 2

H

H

H

H

C

C

C

C

H

H

H

H

H

H

H

H

C

C

C

C

H

H

Cl H

H

H

H

C

C

C

H

H

C

H

Cl

H 3C

H

Cl

H

type 3

CH 2 CH 2 CH 2 Cl

H 3C

CH 2 CH

CH3

Cl

H 3C

CH

CH 2 Cl

type 4

H 3CCH 2CH 2CH 2Cl

Cl

H 3CCH 2CH(Cl)CH3

CCCCCl

CCC(Cl)C

Cl

H 3CCH(CH3)CH2Cl

CH3

SMILES

Cl

CC(C)CCl

H

H

H

Cl

H

C

C

C

H

H

C

H

H

H

Cl H 3C

C

Cl (H 3C)3CCl

CH3

CC(C)(Cl)C

CH3

H

So far, we have dealt only with single bonding between two atoms. Many cases exist, however, in which atoms with more than one “missing” electron in their outer shell form double bonds or sometimes even triple bonds,when two atoms share either two or even three pairs of electrons to complete the octet in their valence shells. A few examples of compounds exhibiting double or triple bonds are given in Fig. 2.1 (using structural convention type 4). We note that a double line between the corresponding atoms indicates a double bond, and, logically, a triple bond has three parallel lines. Ring structures, with or without double bonds, are usually composed predominantly of carbon atoms, but they may also contain heteroatoms (i.e., elements other than carbon or hydrogen such as N, O, S, Si).

Cl

Cl

Cl

Cl

O

tetrachloroethene

acetone

cyclohexene

C

Figure 2.1 Some simple molecules (type 4 from Table 2.3) exhibiting double and triple bonds.

N

O furan

acrylonitrile

The Makeup of Organic Compounds

25

At this point, it is important to point out again that structural isomers may exhibit very different properties and reactivities (e.g., butyl chloride isomers in Table 1.1 and the following examples). This should remind us that even small distinctions in the arrangement of a molecule may translate into either quite similar but also very different environmental behavior. Therefore, we now review what it is about compound structure that dictates chemical nature and reactivity. Bond Energies (Enthalpies) and Bond Lengths: The Concept of Electronegativity Here we address an important aspect of chemical bonding, the strength of a chemical bond in organic molecules. We should have a general idea of the energy involved in holding atoms together in a covalent bond. The most convenient measure of bond 0 . For a diatomic molecule, energy is indicated by the bond dissociation enthalpy, ΔHAB this is defined as the heat change of the gas phase reaction: A − B → A∙ + B∙

0 ΔHAB

(2-1)

where each atom retains its original electron at constant pressure and temperature 0 (e.g., 1.013 bar and 25◦ C). Here, ΔHAB also contains the differences in translational, rotational (only AB), and vibrational (only AB) energies between educt (A–B) and products (A∙ , B∙ ). Unfortunately, it is not possible to directly measure bond dissociation (or formation) enthalpies for each of the different bonds present in a molecule containing more than one bond. They must be determined indirectly, commonly through thermochemical studies of evolved heat (calorimetric measurements) in reactions such as combustion. These studies yield only enthalpies of overall reactions, where several bonds are broken and formed. The individual bond dissociation (or formation) enthalpies have then to be deduced from this data in various ways. The results are commonly shown in tables as average strengths for a particular type of bond, valid for gas phase reactions at 25◦ C and 1.013 bar. Table 2.4 summarizes average bond enthalpies (and bond lengths) of some important covalent bonds. From these data, some general conclusions about covalent bonds in organic molecules can be drawn. Bond lengths between elements in the second row of periodic table ˚ (0.1 nm). Bonds involving larger atoms (C, N, O, F) with hydrogen are all around 1 A (S, P, Cl, Br, I) are longer and weaker. Double and triple bonds are shorter and stronger than the corresponding single bonds. We also notice that the bond enthalpies of double and triple bonds are often somewhat less than twice and three times the values of the single atom bonds. An important exception are C = O bonds. To get an appreciation of the magnitude of bond energies, it is illustrative to compare bond enthalpies to the energy of molecular motion (translational, vibrational, and rotational), which at room temperature is typically a few tens to not much more than one hundred kilojoules per mole. As can be seen in Table 2.4, most bond energies in organic molecules are much larger than this, and, therefore, organic compounds are generally stable to thermal disruption at ambient temperatures. At high temperatures, however, the energy of intramolecular motion increases and can then exceed certain

26

Background Knowledge on Organic Chemicals

Table 2.4 Average Bond Lengthsa and Bond Enthalpies of Some Important Covalent Bonds Bond

˚ Length (A)/ Enthalpy (kJ mol−1 )

H–H H–F H–Cl H–Br H–I

0.74/436 0.92/566 1.27/432 1.41/367 1.60/298 b

Single Bonds H–C 1.11/415 H–N 1.00/390 H–O 0.96/465 H–S 1.33/348 Double and triple bonds C=C 1.34/612 C=N 1.28/608 1.56/536 C=Sc

Bond

˚ Length (A)/ Enthalpy (kJ mol−1 )

Diatomic Molecules F–F 1.42/155 Cl–Cl 1.99/243 Br–Br 2.28/193 I–I 2.67/152

Bond

˚ Length (A)/ Enthalpy (kJ mol−1 )

O=O N≡N

1.21/498 1.10/946

Covalent Bonds in Organic Molecules C–C C–N C–O C–S

1.54/348 1.47/306 1.41/360 1.81/275

C–F C–Cl C–Br C–I

1.35/486 1.78/339 1.94/281 2.14/216

C=Od C=Oe C=Of

1.20/737 1.20/750 1.16/804

C≡C C≡N

1.16/838 1.16/888

˚ (1 A ˚ = 0.1 nm). Bond length in A Bond lengths are given for bonds in which none of the partner atoms is involved in a double or triple bond. If so, bond lengths are somewhat shorter. c In carbon disulfide; d in aldehydes; e in ketones; and f in carbon dioxide. a b

bond energies. This leads to a thermally induced disruption of bonds, a process that is commonly referred to as pyrolysis (heat splitting). We note here that the persistence of organic compounds in the environment is due to the relatively high activation energy needed to break bonds and not because the atoms in a given molecule are present in their lowest possible energetic state. Hence, many organic compounds are nonreactive for kinetic, not thermodynamic reasons. We discuss the energetics and kinetics of chemical reactions in Chapter 21. Here, a simple example helps to illustrate this point. From daily experience, we know that heat can be gained from burning natural gas, gasoline, or wood. We also know that all these fuels are virtually inert under environmental conditions until we light a match and provide the necessary initial activation energy to break bonds. Once the reaction has started, enough heat is liberated to keep it going. The amount of heat liberated can be estimated from the bond enthalpies given in Table 2.4. For example, when burning methane gas in a stove, the process that occurs is the reaction of the hydrocarbon, methane, with oxygen to yield CO2 and H2 O: CH4 (g) + 2O2 (g) → CO2 (g) + 2H2 O(g)

(2-2)

In this gas phase reaction, we break four C–H and two O=O “double” bonds, and we make two C=O and four O–H bonds. Therefore, when converting 1 mole of methane,

27

The Makeup of Organic Compounds

we have to invest (4 × 415) + (2 × 498) = +2656 kJ mol−1 , and we gain (2 × 804) + (4 × 465) = –3468 kJ mol−1 . The estimated heat of reaction at 25◦ C for the reaction in Eq. 2-2 is –812 kJ mol−1 (the experimental value is –802 kJ mol−1 ), an impressive amount of energy. We recall from basic chemistry that, by convention, we use a minus sign to indicate that the reaction is exothermic (from the greek exo for outside), which occurs when heat is given off to the outside. A positive sign is assigned to the heat of reaction if the reaction consumes heat by taking energy into the product structures. These reactions are called endothermic (from the greek endon for within). Electronegativity. Among the elements present in organic molecules, we intuitively and correctly predict that the smaller the atom allowing a closer approach of the bonding electrons to the positively charged nucleus, and the higher the net charge of the kernel (see Table 2.1), the greater the atom’s tendency to attract additional electrons. As indicated in Table 2.5, this attraction for the electrons, or electronegativity, increases with increasing kernel charge, as within a row in the periodic table (e.g., from C to F), and decreases with increasing kernel size, as within a column (e.g., from F to I). When visualizing a chemical bond, it is appropriate then to imagine that the “electron cloud” or averaged electron position located between the two nuclei is generally distorted toward the atom that is more electronegative. This results in the accumulation of a negative charge at one end of the bond (denoted as δ–) and, correspondingly, a deficiency at the other end (denoted as δ+):

C

δ+

X

δ–

The most commonly used quantitative scale to express electronegativity (Table 2.5) was devised by Pauling (1960). On this scale, a value of 4.0 is arbitrarily assigned to the most electronegative atom, fluorine, and a value of 1.0 to lithium. The difference in Table 2.5 Electronegativity of Atoms According to the Scale Devised by Pauling (1960) Charge of Kernel +1 H 2.2

+4

+5

+6

+7

C 2.5

N 3.0 P 2.2

O 3.5 S 2.5 Si 1.9

F 4.0 Cl 3.0 Br 2.8 I 2.5

Increasing Size of Kernel

28

Background Knowledge on Organic Chemicals

electronegativity between two atoms A and B is calculated from the extra bond energy in A–B versus the mean bond energies of A–A and B–B in which the electrons should be equally shared (see Table 2.4). The reason for deriving relative electronegativities based on bond energies is that we interpret the extra bond strength in such a bond between involving atoms of different electronegativity to be due to the attraction of the partial positive and negative charges. From Table 2.5, we can see that carbon is slightly more electronegative than hydrogen, according to Pauling’s scale. However, the electron-attracting power of an atom in isolation differs from that attached to electron-attracting or electron-donating substituents in an organic molecule. For example, many experimental observations indicate that carbon in CH3 is significantly less electronegative than hydrogen. We may rationalize this by recognizing that each additional hydrogen contributes some electron density to the carbon and successively reduces that central atom’s electronegativity. In conclusion, we should be aware that the electronegativity values in Table 2.5 represent only a rough scale of the relative electron-attracting power of the elements. Therefore, in bonds between atoms of similar electronegativity, the direction and extent of polarization also depends on the type of substitution at the two atoms. Let us further discuss the importance of charge separation in bonds involving atoms of different electronegativity, for example, C and N, O, or Cl. The extent of partial ionic character in such polar covalent bonds is a key factor in determining a compound’s partitioning behavior and reactivity in the environment. The polarization in bonds is important in directing the course of chemical reactions in which either these bonds themselves or other bonds in the vicinity are broken. For example, our earlier illustration of the combustion of methane (Eq. 2-2) demonstrates that enthalpy can be gained when nonpolar bonds, as commonly encountered in organic molecules, are broken and polar bonds are formed, such as those in carbon dioxide and water. Furthermore, the partial charge separation makes each bond between dissimilar atoms a dipole. The (vector) sum of all bond dipoles in a structure yields the total dipole moment of the molecule, an entity that can be measured. However, the dipole moments of individual bonds are most important with respect to the interactions of a given compound with its molecular surroundings. Hydrogen Bonding. One special result of the polarization of bonds to hydrogen is hydrogen bonding. As indicated in Table 2.1, hydrogen does not possess any inner electrons isolating its nucleus from the bonding electrons. Thus, in bonds of hydrogen with highly electronegative atoms, the bonding electrons are drawn strongly to the electronegative atom, leaving the proton exposed at the outer end of the covalent bond. This relatively bare proton can now attract another electron-rich center, especially heteroatoms with nonbonding electrons, and form a hydrogen bond as schematically indicated by the dotted line: −Xδ− − Hδ+ ⋅ ⋅ ⋅ Yδ− −

X, Y = N, O, …

In organic molecules, this most often occurs if X and Y represent nitrogen or oxygen. If the electron-rich center forms part of the same molecule, one speaks of an

The Makeup of Organic Compounds

29

intra-molecular hydrogen bond. If the association involves two different molecules, it is referred to as an inter-molecular hydrogen bond. Although such hydrogen bonds are relatively weak (15 to 20 kJ mol−1 ) as compared to covalent bonds, they are of enormous importance with respect to the spatial arrangements and interactions of molecules. Oxidation State of Atoms in an Organic Molecule When dealing with transformation reactions, it is important to know whether or not electrons have been transferred between the reactants. Reactions that involve the transfer of electrons between different chemical species are generally referred to as redox reactions. The terms oxidation and reduction refer, respectively, to the loss and gain of electrons at an atom or ion. To evaluate the number of electrons transferred, we conveniently examine the (formal) oxidation states of all atoms involved in the reaction. Of particular interest to us is the oxidation state of carbon, nitrogen, and sulfur in a given organic molecule, as these are the elements most frequently involved in organic redox reactions. Of particular interest to the energy production of all organisms is the oxidation state of carbon atoms. An oxidation state of zero is assigned to the uncharged element; a loss of Z electrons leads to an oxidation state of +Z. Similarly, a gain of Z electrons leads to an oxidation state of –Z. A simple example is the oxidation of sodium by chlorine, resulting in the formation of sodium chloride:

Na 0 Cl

0

+ e–

oxidation

reduction

Na+ + e– Cl

–

In ionic redox reactions, as shown in the oxidation of sodium by chlorine, a full electron transfer occurs. In covalent bonds, electrons are shared and one formally assigns possession of the electron pair to the more electronegative atom of the two bonded atoms. Therefore, to calculate the oxidation state of atoms in an organic molecule, add 0 for each bond to an identical atom, –l for each bond to a less electronegative atom or for each negative charge on the atom, and +1 for each bond to a more electronegative atom or for each positive charge. In C–S, C–I and even C–P bonds, the electrons are attributed to the heteroatom although the electronegativities of these heteroatoms are very similar to that of carbon. Finally, we should also point out that roman instead of arabic numbers are frequently used to express the oxidation state of a covalently bound atom. Recall that the elements carbon (–IV to +IV), nitrogen (–III to +V), and sulfur (–II to +VI) may be present in organic molecules in various oxidation states, while others exhibit primarily (e.g., O; –II) or exclusively only one oxidation state (e.g., H, F, Cl, Br, I; all –I). Box 2.1 illustrates how to determine the oxidation state of carbon in some organic molecules. Examples of the oxidation states of nitrogen and sulfur in various functional groups are given in Fig. 2.11.

30

Background Knowledge on Organic Chemicals

Box 2.1

Determining the Oxidation States of Carbon Atoms Present in Organic Molecules 5

CH3 1

4

CH 3 CH3 2 C H2

H3C

2-methyl-butane (iso-pentane)

O

1

H3C

C 2

O

H

acetic acid

Cl 1 C

2H

Cl

trichloroethene

H H

O

H

2

3

1 6

H

4 5

H

4-methyl-phenol (p-cresol)

(a) The carbons of the methyl groups (C1 , C4 , C5 ) are bound to three hydrogens and one carbon, hence their oxidation state is 3 (–I) + (0) = –III. The methylene group (C3 ) is bound to two hydrogens and two carbons which yields 2(– I) +2(0) = –II. Finally, the methene group (C2 ) exhibits an oxidation state of (–I) + 3(0) = –I. (b) As in (a), the oxidation state of the carbon of the methyl group (C1 ) is –III, while one of the carboxylic carbon (C2 ) is (+II) + (+I) + (0) = +III. Hence the “average oxidation state” of carbon in acetic acid is 0.

C

Cl

Determine the oxidation state of each carbon present in (a) iso-pentane, (b) acetic acid, (c) trichloroethene, and (d) 4-methylphenol (p-cresol). In organic molecules, hydrogen always assumes an oxidation state of +I, chloride of –I, and oxygen, in most cases, of –II.

7

CH3

(c) In trichloroethene, the oxidation states of the two carbons are 2(+I) + 0 = +II for (C1 ) and (–I) + (+I) + 0 = 0 for (C2 ). (d) The carbons present in the benzene ring exhibit oxidation states of (+I) + 2(0) = +I (C1 ), (–I) + 2(0) = –I for (C2 , C3 , C5 , C6 ), and 3(0) = 0 for (C4 ). The oxidation state of the methyl carbon (C7 ) is again –III.

The Spatial Arrangement of Atoms in Organic Molecules To describe the steric arrangement of the atoms in a molecule, in addition to bond lengths, we need to know something about the angles between the bonds, sizes of the atoms, and their freedom to move within the molecule (e.g., rotations about bonds). Bond Angles. A simple but very effective rule that we can apply when considering bond angles in molecules is that the electrons accept the closeness to one another because of pairing, meaning that they spin and orbit in opposite directions. However, each pair of electrons, shared or unshared, wants to stay as far as possible from other pairs of electrons. For further details on the valence shell electron pair repulsion (VSEPR) theory see Pfennig and Frock (1999). In the case of a carbon atom with four single bonds, the bonds will generally point toward the corners of a tetrahedron. In the symmetrical case, this is when a carbon is bound to four identical substituents (i.e., atoms or groups of atoms as –H in CH4 , or –Cl in CCl4 , or –CH3 in C(CH3 )4 ), the bond angles are 109.5◦ . In most cases, however, each carbon atom is bound to different substituents, which leads to minor variations in the bond angles, as illustrated in Fig. 2.2. For saturated carbon atoms, that is, carbon atoms not involved in a double or triple bond, the C–C–C bond angles are typically about 112◦ , except for ring

The Makeup of Organic Compounds

C

H H

109.5°

H

H

H

N

H C

H

C 121°

H 3C 120°

Figure 2.2 Examples of bond angles in some simple molecules. Data from Hendrickson et al. (1970) and March (1992).

Y X

Z

106°

H 106.7°

H

H 3C

H 112°

H

Cl

O

C 123°

H 3C 110°

Cl

CH3

180° 114°

H 3C

C

C

CH3

Cl

H 3C

127°

C

99.1°

N H 3C CH3 H 3C 109°

Cl C

118°

CH3

S

CH3

Cl

120°

C

N

111.7°

CH3

H

H

H

O

99.4°

S

Cl

CH3 H

CH3

112°

112° H

107°

O

S

C

H

CH3

H

92.1°

CH3

106° H

104.5°

H

112°

C

H

H O

Cl

CH3

H

31

O 123°

C

114°

H 3C

121°

O 125°

N H

systems containing less than six ring atoms, where bond angles may be considerably smaller. With respect to the heteroatoms N, O, P, and S, we see from the examples given in Fig. 2.2 that nonbonded electron pairs behave as if they point to imaginary substituents, provided that the heteroatoms are also only single-bonded to other atoms, thus giving rise to a bent or pyramidal geometry.

Stereoisomerism. The association of electrons in a single, or sigma (σ), bond allows rotation about the axis of the linkage (Fig. 2.3). Such rotation does not disrupt the Y bonding electron pair (i.e., it does not break the bond), and therefore under ambient Z temperatures, the substituents attached to two carbons bonded by a sigma bond Z are usually not “frozen” in position with respect to one another. Thus, the spatial X arrangement of groups of atoms connected by such a single bond may change from Y time to time owing to such rotation. However, such geometric distributions of the Figure 2.3 Rotation about a σ-bond leading to various spatial arrange- atoms in the structure are usually not analytically separable from one another as ments of the atoms in a molecule. the energy required for interconversion is rather small, leading to interconversions X

32

Background Knowledge on Organic Chemicals

during separation. Nevertheless, even if fast rotations about a single bond occur, stereoisomerism is possible. Stereoisomers are compounds made up of the same atoms bonded by the same sequence of bonds, but having different three-dimensional structures that are not superimposable.

COOH H C * CH3 O

When considering stereoisomerism, one commonly distinguishes between two different cases. First, molecules that are alike in every respect but are mirror images of each other are not superimposable. We refer to such molecules as being chiral. In general, any object for which the image and mirror image are distinguishable (e.g., Cl our left and right hands) is denoted to be chiral. For example, if in a molecule a carbon mecoprop atom is bound to four different substituents, as is the case in the functional group of the herbicide mecoprop (Fig. 2.4), two structural isomers are possible. In this context, one sometimes refers to such a carbon atom as a center of chirality. Mirror image HOOC COOH isomers are called enantiomers or optical isomers because they rotate the plane of H H polarized light in opposite directions. They can be analytically separated. In general, CH3 H 3C ArO OAr enantiomers have identical properties in a symmetrical molecular environment, but their behavior may differ quite significantly in a chiral environment. Most mirror (R)-form (S)-form importantly, they may react at very different rates with other chiral species. This is Figure 2.4 The two enantiomers of the reason why many compounds are biologically active, whereas their enantiomers the herbicide mecoprop. The asym- are not. For example, the “R-form” of mecoprop (see Fig. 2.4) is an active herbicide, metric carbon center is indicated by whereas the “S-form” is rather biologically inactive (Bosshardt, 1988). CH3

the asterisk; Ar denotes the aromatic substituent.

π-bond

σ-bond

The second type of stereoisomerism encompasses all other cases in which the threedimensional structures of two isomers exhibiting the same connectivity among the atoms are not superimposable. Such stereoisomers are referred to as diastereomers. They may arise due to different structural factors. One possibility is the presence of more than one chiral moiety. For example, many natural products contain two to ten asymmetric centers per molecule, and molecules of compound classes such as polysaccharides and proteins contain hundreds. Thus, organisms may build large molecules that exhibit highly stereoselective sites that are important for many biochemical reactions including the transformation of organic pollutants.

Another important form of diastereoisomerism results from restricted rotation of bonds such as those encountered with double bonds and ring structures. When considering the geometry of a double bond, we imagine a combination of two different types of bonds between two atoms. One of the bonds would be equivalent to a single bond, that is, a bond in which the pair of electrons occupies the region around the axis between the doubly bonded atoms. We can picture the second bond, which is called a π-bond (e.g., carbon–carbon, carbon–oxygen, carbon–nitrogen, carbon–sulfur, nitrogen–oxygen), by imaging the two bonding π-electrons to be π-bond present in an “electron cloud” located above and below a plane in which the axes of all other bonds, including unshaired electron pairs, lie. Figure 2.5a illustrates π-bond such electron clouds for ethylene (ethane). The atoms closest to a carbon-carbon σ-bond double bond are in a plane with bond angles of about 120◦ (see Fig. 2.2). Rotation (b) acetylene (ethyne) Figure 2.5 Simplified picture of the about the axis would mean that we would have to break this bond. In triple-bond electron clouds of the π-electrons of compounds, as in the case for acetylene (ethyne), two π-bond electron clouds exist a (a) double and (b) triple bond. orthogonal to each other, thus leading to a linear (bond angles = 180◦ ) configuration (Fig. 2.5b). (a) ethylene (ethene)

The Makeup of Organic Compounds

X

Y

H

H cis

HO

H C C

H C C

O

O

H

O

hydrogen bond maleic acid (cis) pK a1: 1.83 pK a2: 6.07

X

H

H

Y trans O

H C HO

C

C

OH

C H

O fumaric acid (trans) pK a1: 3.03 pK a2: 4.44

Let us now consider a compound XHC=CHY in which X,Y ≠ H. In this case, two isomers exist, sometimes also called geometric isomers, which are distinct and, in principle, analytically separable as no rotation occurs about the C–C bond (Fig. 2.6). To distinguish between the two isomers, one commonly uses the terms cis and trans to describe the relative position of two substituents (atoms or groups other than hydrogen). The term cis is used if the two substituents are on the same side of the double bond, and the term trans signifies they are “across” from one another. As with other types of isomerism, closely related compounds may exhibit quite different properties. For example, the boiling points of cis- and trans-1,2-dichloroethene (X=Y=Cl) are 60 and 48◦ C respectively. More pronounced differences in properties between cis/trans isomers are observed when interactions between two substituents (e.g., intramolecular hydrogen bonding) occur in the cis but not in the trans form, as is encountered with maleic and fumaric acid (Fig. 2.6). These two compounds are so different that they have been given different names. For example, their melting points differ by more than 150◦ C, and their aqueous solubilities vary by more than a factor of 100. Also, the acidity constants (pKa values in Fig. 2.6; see Section 4.3) are significantly different because the hydrogen bonding possible in maleic acid facilitates the dissociation of the first proton by stabilizing the negative charge. However, because of the hydrogen bond, dissociation of the second proton is less favorable as compared to fumaric acid. The organization of atoms into a ring containing less than ten carbons also prevents free rotation. Consequently, cis and trans isomers are also possible in such ring systems. The cis isomer has two substituents on the same side of the ring (i.e., above or below); the trans isomer exhibits a substituent on either side (Fig. 2.7). In ring systems with more than two substituted carbons, more isomers are possible. For examples, 1,2,3,4,5,6-hexachlorocyclohexane (HCH) has eight possible isomers, three of which (α-, β-, and γ-isomers) are important from an environmental point of view as they are considered Persistent Organic Pollutants (POPS; see Section 3.2).

Figure 2.6 Cis/trans isomerism at double bonds exhibiting two substituents. H

Y

H

H

Y

H

X trans

cis

Cl

H

Cl

Cl H

H H

H

Figure 2.7 Geometric isomers in ring systems with two (cis/trans) or more substituted carbons (α-, β-, γ-isomers of 1,2,3,4,5,6-hexachlorocyclohexane (HCH).

33

Cl

Cl

α-isomer

Cl

H

H

Cl

Cl

H

H Cl

Cl H

H

Cl

β-isomer

X

Cl

Cl

H

H

H

Cl

Cl Cl

H H

Cl H

H

Cl

γ -isomer

34

Background Knowledge on Organic Chemicals

At this point, we reiterate that the relative positions of atoms in many structures are continuously changing. The term “different conformations” of a molecule is used if two different three-dimensional arrangements of the atoms in a molecule are rapidly interconvertible, as is the case if free rotations about sigma bonds are possible. If rotation is not possible, we speak of different configurations, which represent isomers that can be analytically separated. Obviously, the conformations with the lowest energy, the most stable forms, are the ones in which a molecule will preferentially exist. In the case of six-membered rings such as cyclohexane, three stable conformations exist, known as the chair, twist, and boat form (Fig. 2.8).

chair

twist

Depending on the type of substituents, usually one of the forms is the most stable one. In the case of the HCH isomers (Fig. 2.7), this is the chair form. Taking a closer look at the chair form, we see that six of the bonds linking substituents to the ring are directed differently than the other six (see margin).

boat

Figure 2.8 Different possible conformations of a six-membered ring (e.g., cyclohexane). a

a e

a e e

e

a

e

e

a a

The six axial bonds (a) are directed upwards or downwards from the “plane” of the ring, while the other six equatorial bonds (e) are more within the “plane.” Conversion of one chair form into another converts all axial bonds into equatorial bonds and vice versa. In monosubstituted cyclohexanes, for steric reasons, the more stable form is usually the one with the substituent in the equatorial position. If there is more than one substituent, the situation is more complicated since we have to consider more combinations of substituents, which may interact. Often the more stable form is the one with more substituents in the equatorial positions. For example, in the α-isomer of HCH (Fig. 2.7), four chlorines are equatorial (aaeeee), and in the βisomer, all substituents are equatorial. The structural arrangement of the β-isomer also greatly inhibits degradation reactions; the steric arrangement of the chlorine atoms is unfavorable for dehydrochlorination and reductive dechlorination (see Chapter 23 and Bachmann et al., 1988). Delocalized Electrons, Resonance, and Aromaticity

propenal (acrolein)

Figure 2.9 Schematic picture of πelectron delocalization in propenal (acrolein). The blue balls represent the carbon atoms, the gray ones the hydrogen atoms, and the read one the oxygen atom.

Having reviewed the spatial orientation of different chemical bonds and the consequences on the steric arrangement of the atoms in an organic molecule, we now proceed to discuss special situations in which electrons move throughout a region covering more than two atoms. The resulting bonds are often referred to as “delocalized chemical bonds.” From an energetic point of view, this diminished constraint on the positions of these electrons in the bonds results in their having lower energy and, as a consequence, the molecule exhibits greater stability. For us, the most important case of delocalization is encountered in molecules exhibiting multiple π-bonds, spaced so they can interact with one another. We refer to such a series of π-bonds as conjugated. To effectively interact, π-bonds must be adjacent to each other, and the σ-bonds of all atoms involved must lie in one plane. In such a conjugated system, we can qualitatively visualize the π-electrons to be smeared over the whole region, as is illustrated for propenal (CH2 =CH–CHO, also known as acrolein) in Fig. 2.9. If we try to visualize propenal’s structure by indicating the extreme possible positions of these conjugated electrons, we write: O

O

O

The Makeup of Organic Compounds

35

The double-sided arrows do not signify that the three structures are interconvertible, but rather that the location of the four electrons is best thought of as a weighted average of extreme possibilities. This freedom in electron positioning results in what we call delocalization, and the visualization of a given molecule by a set of localized or “static” structures is called the resonance (from the Latin resonantia meaning echo) method for representing a structure. The relative contribution of the extremes to the overall resonance structure is determined by their relative stabilities. The stabilizing effect of delocalization is most pronounced in aromatic systems. The best-known aromatic system is that of benzene, which has three conjugated double bonds in a six-membered ring:

Again, each of the static structures alone does not represent the molecule, but the molecule is a hybrid of these structures. Thus, the electrons in the conjugated π-bonds of benzene are sometimes denoted with a circle. In substituted benzenes (i.e., benzenes in which hydrogen is substituted by another atom or group of atoms), depending on the type and position of the substituents, the different resonance forms may exhibit somewhat different stabilities and contribute differently to the overall structure. A quantitative estimate of the stabilization or resonance energy of benzene, which cannot be directly measured, may be obtained by determining the heat evolved when hydrogen is added to benzene and cyclohexene to yield cyclohexane:

+ 3 H2

ΔH0 = –208.6 kJ mol–1 cyclohexane

benzene

+ H2 cyclohexene

ΔH0 = –120.7 kJ mol–1 cyclohexane

If each of the double bonds in benzene were identical to the one in cyclohexane, the heat of hydrogenation of benzene would be three times the heat evolved during hydrogenation of cyclohexene. The values previously given show a large discrepancy between the “expected” (–120.7 × 3 = −362 kJ mol−1 ) and the measured (−208.6 kJ mol−1 ) ΔH0 value. Hence, benzene is about 150 kJ mol−1 more stable than would be expected if no resonance interactions among the π-electrons existed. Large stabilization energies are not only observed in components containing a benzene ring but, in general, in all cyclic π-bond systems with 4n + 2 (i.e., 6, 10, 14…) electrons. In the early days of organic chemistry, it was recognized that the benzene ring is particularly unreactive compared to acyclic (noncyclic) compounds containing conjugated double bonds. The quality that renders such ring systems especially stable was and

36

Background Knowledge on Organic Chemicals

still is referred to as aromaticity. Some additional examples of aromatic ring systems are given in Fig. 2.10. Aromatic compounds containing heteroatoms contribute either one (e.g., pyridine) or two electrons (e.g., furan, indole) to the conjugated π-electron systems. Also, some polycyclic compounds are referred to as polycyclic aromatic compounds, although they are not aromatic throughout their structure in a strict sense (e.g., pyrene has 16 electrons in its π-bond system).

O furan (6)

N pyridine (6)

N

As was already indicated for propenal and the five-membered heteroaromatic rings (e.g., furan, Fig. 2.10), resonance may also be important between nonbonded electrons on a single atom and a π-bond system. For example, an unshared electron pair of oxygen greatly contributes to the stabilization of the carboxylate anion, thus rendering the proton of a carboxylic acid group quite acidic (see also Fig. 2.6):

H indole (10)

O R

C

O

O O

R

C

R

O

C O

naphthalene (10)

Similarly, two unshared electrons of the nitrogen in aniline are in resonance with the aromatic π-electron system: NH2

NH2

NH2

NH2

phenanthrene (14)

aniline

pyrene (16)

Figure 2.10 Some additional examples of aromatic ring systems in organic compounds (in parentheses number of π-electrons).

This delocalization has a significant impact on the acid/base properties of anilines as compared to the aliphatic amino compounds, giving them much higher pKa values (see Chapter 4, Section 4.4). In summary, delocalization of electrons enhances stability, and we can visualize delocalized bonding by using the resonance method. In Part V, we learn more about the effects of resonance on chemical equilibrium and the kinetics of chemical reactions of organic compounds. Common Functional Groups Finally, a key feature of organic compounds involves the presence of functional groups, i.e., those parts of a molecule that exhibit one or several heteroatoms. These parts of a compound’s structure are frequently the site of specific interactions with other molecules and are points at which reactions are initiated. As we see in Chapter 3, many chemicals of particular environmental concern contain halogen atoms, that is, fluorine, chlorine, bromine and iodine. Besides the halogens, oxygen, nitrogen, and sulfur atoms are common heteroatoms present in organic molecules. Figure 2.11 provides an overview of some simple functional groups exhibiting one or several of these elements that we frequently encounter throughout the book. The oxidation states of

37

Intermolecular Forces Between Uncharged Molecules

Oxygen-containing functional groups (oxidation state of the oxygen atom is -II)

O R

R1

Ar OH phenol

R OH alcohol O H

C

R1

aldehyde

O R2 ether

O

C

R2

R

ketone

O

C

OH

R1

carboxylic acid

C

O

R2

carboxylic acid ester

Nitrogen-containing functional groups (oxidation state of the nitrogen atom) O

R2 R1

N

R1

R3

N

R1

R3

amino (amine) (-III)

N

R1

O R2

N

R2 R

azo (-I)

N

R2

carboxylic acid amid (-III)

N

O

N H

R3

R1

N

R4

carbamate (-III)

OH

hydroxyl-amine (-I)

R3

R2

urea (-III)

R

O

N

O

O

R

N O nitro (+III)

nitroso (+I)

Sulfur-containing functional groups (oxidation state of the sulfur atom) O R

R1

SH

thiol, mercaptan (-II)

Figure 2.11 Some functional groups (“functionalities”) commonly found in organic compounds.

S

R2

R1

thioether, sulfide (-II)

O R1

S

O sulfone (+II)

R

S

O OH

O sulfonic acid (+IV)

S

R2

R1

disulfide (-I)

O R2

S

R1

S

O R1

R3

O sulfonamid (+IV)

R2

sulfoxide (0)

R2 N

S

O

S

O

R2

O sulfate (+VI)

the N and S heteroatoms are indicated, and R- denotes a part of the molecule that is bound to the functional group at a carbon atom. Sometimes Ar- is used to specify that this carbon is part of an aromatic ring.

2.2

Intermolecular Forces Between Uncharged Molecules The forces between like and unlike molecules determine how a given compound is distributed in the environment. For example, such intermolecular forces strongly influence how readily a compound evaporates from its pure liquid or solid phase into the gas phase, how much it likes to be dissolved in water, or how it partitions from water

38

Background Knowledge on Organic Chemicals

or air into organic phases such as natural organic matter or biological media. Therefore, we need to understand how the chemical structure of the compound dictates what kind of molecular interactions it is capable of undergoing. In this section, we discuss qualitatively the forces that exist between uncharged molecules. If molecules carry a formal negative or positive charge, such as with acids or bases, we also need to consider electrostatic interactions. In all cases, we rely on the simple principal that opposite charges are attractive whereas like charges are repulsive. The sum of all intermolecular forces between uncharged molecules is always attractive. These affinities generally result from the electron-deficient regions in a molecule attracting electron-rich counterparts in neighboring molecules or atoms in surfaces. The total affinity of molecules for one another comes from the summation of all attractions. The resulting interactions (Fig. 2.12) can be divided into two categories: (1) “Nonspecific” interactions that exist between any kinds of molecules, no matter what chemical structure these molecules may have. These nonspecific interactions are generally referred to as van der Waals (vdW) interactions. They are a superposition of the following components: (i) Attractions between time-varying, uneven electron distributions in adjacent molecules are the origin of London dispersive forces. The intensity of such unevenness in a particular molecule or material is related to its polarizability, the tendency of its charge distribution to be distorted by an external electric field. As a result, the strength of intermolecular attraction energies arising from these time-varying dipoles is proportional to the product of the polarizabilities of each of the interacting sets of atoms. (ii) Dipole-induced dipole interactions are the source of Debye energies. Dipoles exist within chemical structures because of the juxtaposition of atoms with different electronegativities (e.g., an oxygen bonded to a carbon atom). When such a permanent dipole moment in one chemical is juxtaposed to material with a time-averaged even electron distribution, then the first molecule causes an uneven electron distribution to form in the second material. The strength of the resultant intermolecular attraction is proportional to the dipole moment’s product of the first molecule and the second molecule’s polarizability. (iii) Dipole–dipole interactions are the cause of Keesom energies. In this case, permanent dipoles in each substance cause the molecules to orient so that the two dipoles face each other in a head-to-tail fashion. The strengths of these attractions are proportional to the product of the dipole moments of the two interacting molecules and depend on the orientation of the interacting partners. (2) Specific interactions (Fig. 2.12d) result from particular molecular structures that enable relatively strong local attractions between permanently electron-poor parts of a chemical structure (e.g., the hydrogen attached to an oxygen) and corresponding permanently electron-rich sites of another molecule (e.g., the nonbonded electrons of atoms like oxygen and nitrogen). These specific interactions, which we

Intermolecular Forces Between Uncharged Molecules

Δt

locations of temporally increased electron density

δ+

δ–

δ

δ+

–

39

(a) dispersive forces

(b) dipole - induced dipole forces locations of permanently increased electron density δ+

δ–

δ– δ+

(c) dipole - dipole forces

H Figure 2.12 Illustration of the various molecular interactions arising from uneven electron distributions: (a) dispersive forces, (b) dipole– induced dipole forces, (c) dipole– dipole forces, and (d) electron acceptor-electron donor forces.

.. X

(d) H-bonding (or more generally, electron donor - acceptor interactions)

refer to as polar interactions are, of course, only possible between molecules that exhibit complementary structural moieties, which occurs if one moiety acts as an electron acceptor (often also referred to as H-donor) and the other one as an electron donor (or H-acceptor). Hence, polar interactions can be classified as electron donor–acceptor (EDA) or hydrogen donor–acceptor (HDA) interactions. The ability or inability of a given compound to undergo specific interactions can be used to divide organic chemicals into different categories of apolar, monopolar, or bipolar, which are further explained in Box 2.2. The apolar compounds interact chiefly by vdW forces. The monopolar compounds have in addition either H-donor (electron acceptor) or H-acceptor (electron donor) properties, and the bipolar compounds

40

Background Knowledge on Organic Chemicals

Box 2.2

Classification of Organic Compounds According to Their Ability to Undergo Particular Molecular Interactions

Compounds that undergo only vdW interactions (London, Debye, and Keesom interactions) are commonly referred to as apolar. Examples include alkanes, chlorinated benzenes, and PCBs. If a chemical exhibits a functionality that has either donor or acceptor characters but not both, we call such a compound monopolar. Examples include structures with an ether function, –C–O–C– (an electron donor or H-acceptor), a keto group, > C=O (an electron donor or H-acceptor), or an aromatic ring carrying electron withdrawing substituents (an electron acceptor). Some molecules contain moieties like amino (–NH2 ), hydroxyl (–OH), and carboxyl groups (–COOH) that exhibit both donor and acceptor properties. We refer to these compounds as bipolar. For large, complex compounds, it is often not obvious how the whole compound should be classified. Such compounds may exhibit functional groups that participate in locally strong polar interactions. However, due to the large size of the molecule, the overall behavior of the compound is dominated by vdW-interactions. It has, therefore, become common practice to divide the world of chemicals into only two categories, namely, polar and nonpolar compounds. The nonpolar chemicals include all those chemicals whose molecular interactions are dominated by vdW forces.

exhibit both. This classification will ultimately be useful when we want to determine whether we should include various factors for quantifying the contributions of these forces in our estimates of the energies controlling specific absorption or adsorption associations in which we are interested. Finally, we note that in the absence of electron donor-acceptor interactions, the London dispersive energy, which increases with increasing molecular size, is the dominant contributor to the overall attraction of many molecules to their surroundings. Therefore, understanding this type of intermolecular interaction and its dependency on chemical structure allows us to establish a baseline for chemical attractions. If molecules exhibit stronger attractions than expected from these interactions, other intermolecular forces are likely important. To see the superposition of these additional interactions and their effect on various partitioning phenomena, we examine the role of dispersive forces as well as of polar interactions in more detail in Chapter 7, where we derive models to quantify these interactions.

2.3

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission.

Questions and Problems

41

Questions Q 2.1 Which are the most common elements encountered in organic chemicals? What is a heteroatom in an organic molecule? Q 2.2 Explain the simplest model used to describe the tendency of the various elements present in organic chemicals to undergo covalent bonding. For which elements is this simple model not strictly applicable? Q 2.3 Which elements present in organic compounds exhibit stable isotopes. What is the relative abundance of these isotopes? Q 2.4 What does the structure of a given compound describe? What are structural isomers? Q 2.5 What types of covalent bonds exist between the atoms present in organic molecules? What factors determine the strength of covalent bonds? Give some examples of very strong and very weak bonds. Q 2.6 Which atoms present in organic molecules may exhibit different oxidation states? What are the possible oxidation states of these elements? Explain in words how you assign the oxidation states to the different atoms present in a given molecule. Q 2.7 What is stereoisomerism? What type of stereoismerism exists? Give some examples of different types of stereoisomers. Q 2.8 In what context do you use the terms, cis and trans? In what context do you use ortho, meta, and para? Q 2.9 Explain the terms “delocalized electrons,” “resonance,” and “aromaticity.” Give examples of compounds for which these terms apply. Q 2.10 What is an apolar, monopolar, and a bipolar organic compound? Give some examples of functional groups that are monopolar, and some examples that make a compound bipolar.

42

Background Knowledge on Organic Chemicals

Problems P 2.1 Determining the Oxidation State of Atoms in an Organic Molecule Determine the oxidation states of the numbered atoms in the following organic molecules: 1 NHOH 1

O

(a) 1

3

(b)

2 O

4

4

S

2

1

(c)

S3

2

4 3 OH

(d) NO 2 2

O

(e)

1 N

2 N

1 S

(f)

O

2 SO3 –

O

(g)

P

1

O

3

O 2

O S 4

P 2.2 Assessing the Number of Isomers of Substituted Benzenes Recall that di-substituted benzenes have three isomers, in that the two substituents may be in ortho-, meta-, or para-position relative to each other:

6

2

5

A 1

A

A 1

1

B

6

6

3

5

3

2

5

B

4

4

ortho or 1,2-

meta or 1,3-

2 4 B

3

para or 1,4-

Depending on the nature of the two substituents, the three isomers may have quite similar or very different properties. Write down all possible tri-substituted benzenes for the following situations (a) all substituents are the same (AAA), (b) only two of the substituents are the same (AAB), (c) all three substituents are different (ABC). P 2.3 Assessing the Number of Stereoisomers in Substituted Cyclohexanes Write down all possible stereoisomers of 1,2,3,5- and 1,2,4,5- tetrachlorocyclohexane. Which of them are chiral, that is, which ones exist as pairs of enantiomers? Cl

Cl

Cl

Cl Cl

Cl

1,2,3,5-tetrachlorocyclohexane

Cl Cl 1,2,4,5-tetrachlorocyclohexane

Bibliography

2.4

43

Bibliography Bachmann, A.; Walet, P.; Wijnen, P.; Debruin, W.; Huntjens, J. L. M.; Roelofsen, W.; Zehnder, A. J. B., Biodegradation of alpha- and beta-hexachlorocyclohexane in a soil slurry under different redox conditions. Appl. Environ. Microbiol. 1988, 54(1), 143–149. Bosshardt, H., Entwicklungstendenzen in der Bek¨ampfung von Schadorganismen in der Landwirtschaft. Vierteljahresschr. Naturforsch. Ges. Zurich 1988, 133, 225–240. Hendrickson, J. B.; Chram, D. J.; Hammond, G. S., Organic Chemistry. 3rd ed.; McGraw-Hill: New York, 1970. March, J., Advanced Organic Chemistry. 4th ed.; Wiley: New York, 1992. Pauling, L., The Nature of the Chemical Bond. Cornell University Press: New York, 1960. Pfennig, B. W.; Frock, R. L., The use of molecular modeling and VSEPR theory in the undergraduate curriculum to predict the three-dimensional structure of molecules. J. Chem. Educ. 1999, 76(7), 1018–1022. U.S. EPA, SMILES Tutorial. 2009 [accessed on September 2015]. http://www.epa.gov/med/Prods_ Pubs/smiles.htm. Weininger, D., SMILES, a chemical language and information system. 1. Introduction to methodology and encoding rules. J. Chem. Inf. Comput. Sci. 1988, 28(1), 31–36.

45

Chapter 3

The Amazing World of Anthropogenic Organic Chemicals

3.1

Introduction

3.2

A Lasting Global Problem: Persistent Organic Pollutants (POPs)

3.3

Natural but Nevertheless Problematic: Petroleum Hydrocarbons

3.4

Notorious Air and Groundwater Pollutants: Organic Solvents BTEX Compounds Tertiary Dialkyl Ethers Polychlorinated C1 – and C2 –Hydrocarbons Volatile Methylsiloxanes (VMS)

3.5

Safety First: Flame Retardants All Around Us

3.6

How to Make Materials “Repellent”: Polyfluorinated Chemicals (PFCs)

3.7

From Washing Machines to Surface Waters: Complexing Agents, Surfactants, Whitening Agents, and Corrosion Inhibitors

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

46

The Amazing World of Anthropogenic Organic Chemicals

3.8

Health, Well-Being, and Water Pollution: Pharmaceuticals and Personal Care Products Pharmaceuticals Ingredients of Personal Care Products

3.9

Fighting Pests: Herbicides, Insecticides, and Fungicides

3.10 Our Companion Compounds: Representative Model Chemicals 3.11 Questions 3.12 Bibliography

A Lasting Global Problem: Persistent Organic Pollutants (POPs)

3.1

47

Introduction In this chapter, we take a closer look at the vast world of “anthropogenic organic chemicals,” defined in Chapter 1 as organic compounds that are of interest in terms of their distribution in and effect on the environment. We also take a first glimpse at how the characteristics and properties required to make a chemical suitable for a particular purpose are related to its chemical structure and influence its environmental behavior. Obviously, anthropogenic chemicals serve certain purposes in our daily lives, and are therefore designed to persist long enough to fulfill their task. In fact, for many applications, chemicals need to be resistant to degradation even under harsh conditions. Thus, a conflict of interest often exists between the usefulness of a chemical in human society and the concern about its potential to persist in the environment. The challenge is to replace chemicals of particular concern, above all compounds that are persistent, bioaccumulative, and toxic, so-called PBT Chemicals (see Strempel et al., 2012), with more environmentally benign compounds. This undertaking is anything but trivial and requires not only profound knowledge on the use patterns and environmental behavior of chemicals, but also incorporation of economic and political constraints. The aim of this chapter is to discuss representatives of important groups of chemicals used for specific purposes in our daily lives rather than to overwhelm the reader with an endless collection of chemical structures. Key references that serve as entry points into the vast literature on the various groups of compounds are also supplied. At the end of the chapter, we choose some representative model compounds from each of these groups as our “companion compounds” throughout the book. These compounds are of interest because of their occurrence in the environment as well as their distinct properties and reactivities. They are called our companions because we frequently meet them throughout the book as we introduce new topics and concepts, and they will appear in examples and problems. But for now, let us look at some of the numerous organic chemicals that surround us.

3.2

A Lasting Global Problem: Persistent Organic Pollutants (POPs) We begin by looking at the persistent organic pollutants (POPs), a group of diverse chemicals that are not categorized by their use or structure but by their fate characteristics, which make them of particular environmental concern. POPs include high production volume chemicals that are commercially produced as well as chemicals that are primarily formed as by-products of various combustion processes. As of 2004, this group of chemicals was defined and sanctioned by the United Nations Environment Programme (UNEP) Stockholm Convention on Persistent Organic Pollutants (Secretariat of the Stockholm Convention, 2015). The goal of the Stockholm Convention is to assess the global presence of POPs (see Lohmann et al., 2007; Nizzetto et al., 2010) and to minimize, if possible, their use and release. According to this convention, all POPs share certain characteristics: (i) they persist in the environment, which means that neither abiotic nor biological transformation leads to significant removal of the chemical in any environmental compartment; (ii) they are prone to long-range transport and, thus, to global distribution, even to remote regions where the chemical

48

The Amazing World of Anthropogenic Organic Chemicals

has not been used or disposed; (iii) they bioaccumulate in the food web; and (iv) they are toxic to living organisms, including humans and wildlife. The chemical properties that favor bioaccumulation from air or water include low volatility, significant hydrophobicity (they are “water hating,” see Chapter 9), and persistence. For example, apolar compounds, such as the polychlorinated and polybrominated pollutants, travel long distances and bioaccumulate. Such compounds have also been shown to be toxic in that they may disrupt the endocrine, reproductive, or immune system or cause neurobehavioral and developmental disorders and cancer (see Li et al., 2006). Initially, the chemicals listed and regulated were the so-called “legacy POPs” or the “dirty dozen.” The legacy POPs include nine polychlorinated pesticides, such as hexachlorobenzene (HCB), DDT, aldrin, and chlordane; polychlorinated biphenyls (PCBs) used in numerous industrial and consumer applications; and the unintentionally produced polychlorinated dibenzodioxins (PCDDs) and dibenzofurans (PCDFs). As illustrated in Fig. 3.1, some of these chemicals are not single compounds but rather complex mixtures of isomers and congeners, which are related by origin, structure, or function. The Stockholm Convention also allows addition of new high production volume chemicals to the list. Chemicals already added or being considered since 2004 include alpha-, beta-, and gamma-hexachlorocyclohexane (see stereochemistry in Chapter 2); pentachlorobenzene and hexabromobiphenyl; as well as a series of other polyhalogenated, polybrominated, and polyfluorinated compounds, which we encounter in Sections 3.5 and 3.6. Although not listed in the Stockholm Convention, an additional group of compounds of considerable global concern that are commonly included in the POP category are the polycyclic aromatic hydrocarbons (PAHs). We address PAHs in Section 3.3 on petroleum hydrocarbons. Global control strategies, such as the Stockholm Convention, aim to reduce the production and use of POPs. However, as evident from the lasting ubiquitous global presence of many legacy POPs in the environment, particularly in the Arctic’s cold regions (Lohmann et al., 2009; Ruggirello et al., 2010), such strategies do not necessarily lead to an immediate reduction of detection in the environment. The presence of various old sources plus the characteristics of POPs leads to continuing emissions and lasting detection. To identify and design optimal future mitigation strategies, further developments in emission inventories, as attempted for PCBs (Breivik et al., 2007), as well as more refined chemical fate and effect models for identification and assessment of old and new POPs are necessary (Scheringer, 2009; Swackhamer et al., 2009; Strempel et al., 2012).

3.3

Natural but Nevertheless Problematic: Petroleum Hydrocarbons We now encounter another group of “classical” organic contaminants, the petroleum hydrocarbons. These compounds are everywhere in the environment. Natural

49

Natural but Nevertheless Problematic: Petroleum Hydrocarbons

Cl Cl

Cl

Cl

Cl

Cl Clm

Cl

Cl

Cln

Cl

Cl hexachlorobenzene (HCB)

H

polychlorinated biphenyls (PCBs, 209 possible congeners)

Cl

H

p,p'-DDT

Cl

Cl

Cl

Cl

Cl

H

H Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl H

Cl

H

Cl

1,2,3,4,5,6-hexachlorocyclohexane (HCH, 8 isomers, one of them exists as a pair of enantiomers)

Cl

Cl

Aldrin

Cl

Cl

Chlordan

O

Clm

O

Cln

polychlorinated dibenzop-dioxines (PCDDs, 175 possible congeners)

Figure 3.1 Some members of the so-called “legacy POPs,” the “dirty dozen.”

Clm

O

Cln

polychlorinated dibenzofurans (PCDFs, 135 possible congeners)

hydrocarbons (Fig. 3.2) range widely in size from methane (16 g mol−1 ) to β-carotene (537 g mol−1 ). Diverse branched, olefinic, cyclic, and aromatic hydrocarbons exist in fossil fuels or are derived from commercial processing of these fuels (Fig. 3.3). The global annual production of liquid petroleum products, including gasoline, kerosene, and heating oils, is more than 3 billion metric tons, so it is no surprise that processing and use of these hydrocarbons create major environmental problems. Petroleum hydrocarbons are released to the atmosphere when we pump gasoline into our cars and incompletely combust them in our engines. They are also introduced to street surfaces when our cars slowly leak engine oil. They contaminate our groundwaters from leaky gasoline underground storage tanks or heating oil tanks. Thus, not only through large oil spills, such as the wreck of the Exxon Valdez, the Gulf War oil spill, or the Deepwater Horizon disaster, do petroleum hydrocarbons pollute the environment. Although they share a common source, the various hydrocarbons in the exceedingly complex mixture that is oil certainly do not behave in the same way once released into the environment. Some constituents tend to vaporize while others clearly prefer to bind to solids. Some oil hydrocarbons are rather unreactive whereas

50

The Amazing World of Anthropogenic Organic Chemicals

H H

H H n-hexane

methane

iso-octane

n-hexadecane

2,6,10,14-tetramethyl-pentadecane (pristane)

cyclohexane H

H H H bicyclo[2.2.1]heptane

trans-bicyclo[4.4.0]decane (trans-decaline)

1,3-butadiene

1-hexene

2-methyl-1,3-butadiene (isoprene)

cis-bicyclo[4.4.0]decane (cis-decaline)

1-methyl-cyclohexene

β-carotene (orange pigment in carrots; converted to vitamin A by human liver)

Figure 3.2 Examples of aliphatic, alicyclic, and olefinic hydrocarbons.

others are easily biodegraded or interact with light; some are quite nontoxic while others are renowned for their carcinogenicity. We highlight two groups of compounds that are of particular interest to many environmental chemists, engineers, and toxicologists: the BTEX compounds (benzene, toluene, ethylbenzene, and the three xylene isomers; Fig. 3.3) and the polycyclic aromatic hydrocarbons (PAHs; Fig. 3.3). The BTEX components are important gasoline constituents and are also widely used as solvents (see Section 3.4). They are very common soil and groundwater pollutants with contamination typically occurring near petroleum and natural gas production sites, gasoline stations, and other areas with storage tanks containing gasoline or other petroleum-related products. A total of about 600,000 regulated underground storage tanks are currently operated in the United States (U.S. EPA, 2013). As a consequence of leaks or spills from storage tanks, the liquid gasoline or oil phase,

Natural but Nevertheless Problematic: Petroleum Hydrocarbons

51

benzene derivates

benzene

toluene

biphenyl

ethylbenzene

indene

o, m, p-xylene (dimethylbenzene)

styrene

1,2,3,4-tetrahydro-naphthalene (tetralin)

polycyclic aromatic hydrocarbons (PAHs)

naphthalene

pyrene

Figure 3.3 Examples of aromatic hydrocarbons.

anthracene

benzo[a]pyrene

phenanthrene

perylene

commonly referred to as NAPL (non-aqueous phase liquid), spreads in the soil. When exposed to infiltrating rainwater, the various NAPL components are dissolved according to their water solubility (Chapter 9) and may then be transported into groundwater, contaminating drinking water resources. Since the BTEX compounds are appreciably soluble in water, particularly toxic benzene, such soil and groundwater contamination often triggers monitoring programs and remediation actions (e.g., Farhadian et al., 2008). The major sources of PAHs in the environment include the combustion of fossil fuels (gasoline, oil, coal), application of asphalts and coal tars, and use of creosotes as wood preservatives. PAHs are also produced and consumed when barbecuing food

52

The Amazing World of Anthropogenic Organic Chemicals

(see Bansal and Kim, 2015). From a human health perspective, PAHs have drawn considerable interest primarily because some of them are potent carcinogens (e.g., benzo(a)pyrene; Fig. 3.3). This toxicity is the main reason why PAHs are considered to be among the most important air pollutants (see Barro et al., 2009; Kim et al., 2013). Furthermore, because of their high tendency to bioaccumulate, PAHs are of great ecotoxicological concern (see Logan, 2007) and thus are commonly considered as POPs or PBTs. Oil is a complex mixture and Fig. 3.4 illustrates how after a spill its composition may change over time due to the weathering processes. For example, between April and mid July 2010, the Deepwater Horizon disaster released about 2 × 105 metric tons of gases (C1 to C5 hydrocarbons) and 5 × 105 metric tons of oil into the Gulf of Mexico, making it the largest spill in U.S. history (Reddy et al., 2012). By comparing the gas chromatograms of the original oil with the subsequent surface slick (Fig. 3.4a and b), one sees that the more volatile fraction of the oil encompassing the molecules with less than 13 carbon atoms was almost completely lost after a relatively short time. These losses are primarily attributable to volatilization and, to a lesser extent,

(a) original oil

Figure 3.4 Gas chromatograms of (a) the original oil from the Macondo Well; (b) a surface slick taken a two months after the blow up; (c,d,e) weathered oil samples collected one year later. On the x-axes, retention times are given in n-alkane units (retention time of the sharp peaks corresponding to the elution of the respective linear alkane). The y-axes provide the relative abundances of the components within the sample analyzed. The different chromatograms cannot be compared quantitatively. Figure from Aeppli et al. (2012).

relative abundance

(b) surface slick (June 2010)

(c) sand patty (April 2011)

(d) sand patty (July 2011)

(e) rock scraping (July 2011)

n-alkane carbon number

Notorious Air and Groundwater Pollutants: Organic Solvents

53

dissolution of the more water-soluble aromatic compounds, including the BTEX compounds (Aeppli et al., 2012). An important feature of the weathering process is the increasing fraction of compounds making up what is called the unresolved complex mixture (UCM) or “hump” in the gas chromatogram (Fig. 3.6c, d, and e). In addition, we emphasize that a large number of polar compounds that are not amenable to gas chromatographic analysis, and therefore not visible in Fig. 3.4, are present in crude oil or are produced during weathering by biological and photochemical transformation reactions (McKenna et al., 2013).

3.4

Notorious Air and Groundwater Pollutants: Organic Solvents In a chemistry laboratory, solvents are needed to dissolve substances without chemically changing them. In society, we find solvents to be another group of high production volume chemicals used in industrial processes and consumer products that are released into the environment. A large variety of solvents exist on the market, with demand in the millions of metric tons in the United States alone, as different properties are necessary for different applications (Wildes, 2007). A solvent must be able to dissolve certain other compounds, but it also must exhibit advantageous properties such as viscosity, volatility, surface wetting, as well as thermal and chemical stability. Large emissions of solvents into the environment lead to exposures that may be harmful to living organisms, including humans. Of particular concern are the solvents classified as volatile organic compounds (VOCs). The term “volatile” is used because these chemicals have relatively high vapor pressures and thus evaporate quite easily under ambient conditions (see Chapter 8). Exposure to VOCs in indoor environments is more concentrated than outdoors and may lead to a variety of adverse health effects in humans, ranging from local irritation to organ damage (Wallace et al., 1986). Other VOCs are of environmental concern because they are involved in the formation of ground-level ozone (Jenkin and Clemitshaw, 2000). Here, we focus on a few solvents that are notorious such as air and groundwater pollutants, including the BTEX compounds, tertiary dialkyl ethers (methyl- and ethylt-butyl ether (MTBE, ETBE) and methyl-t-amyl ether (TAME)), along with some polychlorinated C1 – and C2 –hydrocarbons. In addition, we briefly address quite a different and perhaps less familiar group of emerging pollutants, the volatile methylsiloxanes (VMS), which are subject to long-range transport in the atmosphere, thus making them candidates for the POPs list. BTEX Compounds The BTEX compounds (benzene, toluene, ethylbenzene, and the three xylene isomers; Fig. 3.3) make up a significant fraction of gasoline, which is a major source for their emission into the environment (see Section 3.3). However, the individual BTEX compounds are also used in large quantities in industry as solvents and starting materials for the synthesis of numerous other chemicals (Moskowitz, 2010). Furthermore, except for benzene, they are used as cleaning agents and solvents for a variety of consumer-oriented applications. Hence, numerous pathways exist by which

54

The Amazing World of Anthropogenic Organic Chemicals

BTEX compounds are continuously introduced into all environmental compartments, with about 22,000 metric tons reported being directly emitted from industrial use, including about 11,000 metric tons of toluene, in the United States alone in 2011 (U.S. EPA, 2015a).

O MTBE

Tertiary Dialkyl Ethers O

Although the tertiary dialklyl ethers MTBE, ETBE, and TAME (see Fig. 3.5) are also used as solvents in industry, they are of environmental concern primarily because they are “fuel ethers,” added in large quantities as oxygenates to gasoline in the low percentage range in some parts of the world. Oxygenates improve the combustion O process and thus reduce emissions of carbon monoxide and hydrocarbons in exhaust. TAME They are produced in millions of metric tons per year (Yee et al., 2013). Besides Figure 3.5 Structures of the gaso- methanol (CH3 OH) and ethanol (CH3 CH2 OH), MTBE has been and still is the most line additives methyl-t-butyl ether important global fuel additive. ETBE

(MTBE), ethyl-t-butyl ether (ETBE), and methyl-t-amyl ether (TAME).

Cl

The release of MTBE into the subsurface causes problems because of the chemical’s high water solubility, low biodegradability, and rather low odor and flavor thresholds (van Wezel et al., 2009). MTBE has a water solubility that is about 20 times higher than that of benzene. As a consequence, MTBE is transported much faster than the BTEX compounds in the subsurface and, therefore, can potentially contaminate groundwater at a much larger scale. It comes as no surprise that MTBE is frequently detected in public drinking water supplies using groundwater as their source (e.g., Williams and Pierce, 2009). Since 2000, the two other ethers, in particular ETBE, have been increasingly used as substitutes for MTBE because of economic reasons and because they are thought to be less problematic with respect to groundwater contamination. However, these alternative ethers have similar characteristics to MTBE, perhaps making them similarly potent pollutants (Shih et al., 2004; van Wezel et al., 2009).

Cl

Polychlorinated C1 – and C2 –Hydrocarbons

Cl Cl

Cl Cl

carbon tetrachloride (CT)

Cl 1,1,1-trichloroethane (TCA) Cl Cl

Cl

trichloroethene (TCE) Cl

Cl

Cl

Cl

tetrachloroethene perchlorethene (PCE)

As PCBs are referred to as legacy POPs, one could similarly term some chlorinated solvents as legacy groundwater pollutants because they are among the most frequently detected groundwater contaminants (Moran et al., 2006). The most common pollutants include carbon tetrachloride (CT), 1,1,1-trichloroethane (TCA), trichloroethene (TCE), and tetrachloroethene (or perchloroethene; PCE) (Fig. 3.6). Because they are nonflammable, these chemicals have long been used as solvents in the dry cleaning industry or as metal degreasing agents in the automotive and other metal working industries. Carbon tetrachloride was phased out of production in the 1990s because of its role in stratospheric ozone depletion, replaced almost exclusively by PCE (Doherty, 2000). Two other widely used chlorinated solvents are trichloromethane (chloroform; CHCl3 ) and dichloromethane (methylene chloride; CH2 Cl2 ).

Similar to gasoline and other petroleum products, chlorinated solvents are introduced into the subsurface by spills, leaky storage tanks, or even illegal disposal. Compared Figure 3.6 Structures of some common polychlorinated solvents caus- to gasoline or heating oil, they have several characteristics that make them even ing major groundwater contamina- more pernicious groundwater pollutants. First, liquid polychlorinated hydrocarbons tion issues. exhibit densities greater than water and thus form DNAPLs (dense non-aqueous phase

Notorious Air and Groundwater Pollutants: Organic Solvents

55

liquids) in the subsurface. DNAPLs tend to sink through aquifers until they reach impermeable bedrock, thus producing numerous “new” contamination sources that are difficult to locate and remediate. Furthermore, under oxic conditions, these solvent chemicals are persistent and, when dissolved in water, they are quite mobile in the subsurface, leading to long-lasting contamination of large groundwater areas. Finally, under anoxic conditions, they may be transformed into less halogenated products that are more toxic than the parent compound. A classical example is the formation of vinyl chloride (CH2 =CHCl) by reductive dechlorination of PCE or TCA (see Chapters 23 and 27). Volatile Methylsiloxanes (VMS) The volatile methylsiloxanes (VMS) are a group of structurally related solvents that include various linear and cyclic oligomeric structures (Fig. 3.7). Besides being widely used in industrial applications, these solvents are present in numerous personal care and household products, including skin lotions, body washes, shampoos, cosmetics, deodorants, fragrances, and cleaning products (Horii and Kanan, 2008; Wang et al., 2009). The properties that make VMS suitable for all these applications include low surface tension, low viscosity, high thermal stability, hydrophobicity, and relatively high volatility, the last being a result of their smaller vdW interactions as compared to other organic molecules of the same size (R¨ucker and K¨ummerer, 2015). The desired properties for a specific application can be “fine-tuned” by choosing the appropriate number of dimethylsiloxane units or by using VSM mixtures. Generally, in many consumer products, the cyclic VMS (D4, D5, D6, see Fig. 3.7) are present in significantly higher quantities than the linear ones (L4 – L14) (Horii an Kanan, 2008; Wang et al., 2009). Because of their volatilities and use patterns, a large fraction of VMS used in personal care products is emitted into the atmosphere. For example, the annual atmospheric emissions of D5, the most widely used VMS, to the Northern Hemisphere have been estimated to be 30,000 metric tons (McLachlan et al., 2010). Not surprisingly, the air

Si O

Si

x

O Si

O Si n

(b) linear polydimethylsiloxanes (n = 2–12)

(a) cyclic polydimethylsiloxanes (x = 4,5,6)

O Si O Si

Si

Figure 3.7 General structures of (a) cyclic and (b) linear polydimethylsiloxanes. (c) D5 is the most common polydimethylsiloxane present in personal care and household products and is used as a dry cleaning solvent.

O

O Si

O

Si

(c) decamethylcyclopentasiloxane (D5)

56

The Amazing World of Anthropogenic Organic Chemicals

concentrations of D5 detected in the center of a city were found to be significantly higher than just outside of the city (Buser et al., 2013). Although VMS react with hydroxyl radicals in the atmosphere at appreciable rates, their half-lives in the atmosphere are long enough to permit long-range transport. Therefore, VMS have not only been detected in air near sources in highly populated areas but also in remote areas, including the Arctic (Genualdi et al., 2011; Krogseth et al., 2013). Because of their hydrophobicity and persistence in water, VMS have also been shown to bioaccumulate in aquatic organisms and aquatic food webs (Warner et al., 2010; Kierkegaard et al., 2011; Borga et al., 2012). Although the available toxicity data indicates that acceptable exposure thresholds are significantly higher than the concentration levels presently detected in environmental compartments, VMS remain a group of compounds that need to be further assessed (see Wang et al., 2013), as exemplified by the inclusion of cyclotetrasiloxane (D4) on the EU’s Priority List of Suspected Endocrine Disruptors (European Commission, 2007).

3.5

Safety First: Flame Retardants All Around Us Looking further into the world of anthropogenic organic chemicals, we encounter chemical groups commonly used and emitted from consumer products. An outbreak of fire is a scary thought, whether it be in our home or office, while traveling in cars, trains or airplanes, or while out in restaurants or theaters. In all these places, we are exposed to materials that may catch fire. In order to retard and even prevent the combustion process, “flame retardants” are added to almost every material we touch in our daily lives from furniture, textiles, electronic devices, and toys, to plastics, coatings, and foams. The amount of flame retardant added to any material is based on the desired level of fire safety, often regulated by governmental ignition test standards. Loadings in materials range from less than 1 percent by weight for organic flame retardants to more than 60 percent for inorganic compounds, such as aluminium trihydroxide (Beard, 2007). Therefore, flame retardants represent the most important group of polymer additives with a rising global consumption, estimated at about 2 million metric tons in 2008, of which about 1/3 are organic chemicals. Since a wide range of materials are loaded with flame retardants, quite a structural variety of retardant compounds are available on the market (see Beard, 2007; EFRA, 2010). These flame retardants interfere with the combustion process in different chemical and physical ways, depending on their chemical nature. Most organic flame retardants are polychlorinated or polybrominated aliphatic or aromatic compounds, some containing a phosphate ester group such as tris(2-chloroethyl)phosphate (see Fig. 3.8). In addition, as alternatives, a number of halogen-free phosphorus flame retardants are widely used (van der Veen and de Boer, 2012). Polyhalogenated compounds effectively inhibit combustion via two pathways. First, halogenated radicals formed when the flame retardant is heated, trap other highly reactive radicals formed when materials catch fire. This interrupts the gas phase

Safety First: Flame Retardants All Around Us

57

Cl Cl Cl

Cl

Cl

Cl

Cl

Cl Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl

Cl Cl

Cl

Cl Cl

Cl

Cl

Dechlorane plus (two stereoisomers syn and anti ) O Cl

O

P O

Cl

O

O Br n

Br m

Cl

polybrominated diphenyl ethers (PBDEs) (most widely used congener mixtures m+n = 5,8,10)

tris(2-chloroethyl)phosphate

Br

O O O

R1

Br

R2

Br

O O Br

O phthalates (R1, R 2 = C1 to C10; plasticizers)

O

O

bis(2-ethylhexyl)tetrabromophthalate

Br

HO

Figure 3.8 Some prominent flame retardants, plasticizers, and related compounds.

OH bisphenol A

Br

HO

OH Br

Br

tetrabromobisphenol A (TBBPA)

radical reactions generating heat that promote continued combustion. Brominated compounds are more effective at combustion suppression than chlorinated ones because the carbon-bromine bond is more easily cleaved than the carbon-chlorine bond (see bond energies in Table 2.4). Secondly, upon combustion, polyhalogenated compounds do not burn completely, thus building a char layer that shields the material from oxygen and the flame. In most cases, these retardants are only physically mixed into materials. Therefore, they are defined as additives and may diffuse out and enter the environment. Considering that many of the retardants are structurally similar to the halogenated legacy pollutants previously discussed, it comes as no surprise that they are

58

The Amazing World of Anthropogenic Organic Chemicals

ubiquitously found in the environment, just like the legacy pollutants. In fact, many that replaced polybrominated biphenyls (PBBs) in the 1970s, including polybrominated diphenyl ethers (PBDEs) (see Hites, 2004; Frederiksen et al., 2009), Dechlorane Plus, and related compounds (see Sverko et al., 2011), have already been banned or added to lists of high priority chemicals with persistence and bioaccumulation potential (e.g., Muir and Howard, 2006; Howard and Muir, 2010). Unfortunately, burning, dismantling, and recycling electronic waste results in further contamination (Eguchi et al., 2013) and formation of brominated and chlorinated dioxins and furans (see Weber and Kuch, 2003; Tue et al., 2013), especially in developing countries. The PBDEs are examples of compounds for which their accumulation in the environment and bioaccumulation in food webs could have been anticipated before they were brought onto the market because PBDEs have characteristics similar to PCBs and PBBs (see Section 3.2). New polyhalogenated aromatic compounds have emerged as substitutes for PBDEs, and many are also persistent, bioaccumulative, and already detected in the environment. Examples are a series of brominated benzenes (Venier et al., 2012), decabromodiphenyl ethane (DBDPE) (Egeback et al., 2012), brominated benzoic acid and brominated phthalic acid esters (Fig. 3.8), and tribromophenoxy compounds (Ma et al., 2012a and b). Flame retardants are often applied in combinations. Some of them also serve as plasticizers, additives that increase the plasticity or fluidity of a given material. From an environmental point of view, the most prominent plasticizers are the phthalates (phthalic acid esters, see Fig. 3.8 and Net et al., 2015). For example, by incorporating bromine atoms into the structure, an effective flame retardant is obtained, such as bis(2-ethylhexyl)tetrabromophthalate (Fig. 3.8). Other examples of compounds that serve dual purposes are the polychlorinated paraffins (see Houde et al., 2008; Friden et al., 2011) and some phosphate esters such as triphenyl phosphate. In some applications, flame retardants are covalently bound to polymer materials to minimize loss to the environment. Such compounds must exhibit functional groups that react with polymer constituents, such as, for example, the phenolic groups in tetrabromobisphenol A (TBBPA, Fig. 3.8), the most widely used brominated flame retardant. However, TBBPA is also applied as an additive and thus may be released into the environment (Howard and Muir, 2010). Looking at the structure of TBBPA, we see that it is similar to bisphenol A (Fig. 3.8), a high production volume chemical primarily used as a starting material for polymers. Bisphenol A is of considerable environmental concern because it has been shown to exhibit endocrine-disrupting effects in a variety of organisms (see Flint et al., 2012)

3.6

How to Make Materials “Repellent”: Polyfluorinated Chemicals (PFCs) All of us have probably experienced the water “repellency” of pans coated with Teflon® or textiles containing Gore-Tex® . Such products contain polytetrafluoroethylene, a widely used perfluorinated (completely fluorinated) polymer. Perfluorinated as well as other highly fluorinated compounds, all denoted as PFCs, make products

59

How to Make Materials “Repellent”: Polyfluorinated Chemicals (PFCs)

water-, and to a somewhat lesser extent, oil-, and fat-“repellent.” The term “repellent” is somewhat misleading, because on a molecular level, vdW forces always exist between water molecules and, for example, a Teflon® surface. However, the very high electronegativity of fluorine induces significantly smaller vdW interactions as compared to other organic molecules of the same size (Goss and Bronner, 2006; see also Chapter 7). Also, these forces are minor compared to the surface tension of water, thus minimizing the wetting of the surface and, therefore, leading macroscopically to the formation of water droplets. Therefore, a greasy Teflon® pan is easy to wipe clean after its use. The previously mentioned PFC polymers are not those of primary environmental concern. Instead, the thousands of lower molecular weight PFCs with four to 14 carbon atoms, mostly aliphatic, are much more notable environmental pollutants. These compounds are used in numerous industrial and consumer applications because of their “repelling” characteristics, extreme stability, and surfactant properties (Lindstrom et al., 2011; Oliaei et al., 2013). Chemically, PFCs exhibit various chain lengths and can be divided into two categories of compounds, neutral and charged (see examples in Fig. 3.9). Neutral PFCs include the fluorotelomer alcohols (FTOHs), such as 6:2 FTOH, 8:2 FTOH, and 10:2 FTOH denoting (per)fluoro hexyl, octyl, and decyl ethanol, respectively. The term telomer indicates that the chemical is a small polymer made from only two to five monomers. Another group of neutral PFCs are the perfluorosulfamides such as perfluorooctanesulfonamide (PFOSA). The most prominent strongly acidic PFCs, present as anions in water, include the perfluorocarboxylic acid (PFOAs, e.g., perfluorooctanoic acid (PFOA)) and the perfluorosulfonic acids (PFSAs, e.g., perfluorooctanesulfonic acid (PFOS)). Evidence suggests that the acidic compounds PFOA and PFOS may be formed from precursor compounds, including FTOHs, via reactions in the atmosphere (Schenker et al., 2008) and by metabolic transformations in organisms, including humans (Vestergren et al., 2008; Martin et al., 2010; Yeung et al., 2013). All of the examples that we have chosen are linear carbon chain compounds because they are the most abundant PFCs produced, although numerous isomers exist for each of these compounds. For example, 89 branched isomers are theoretically possible for PFOS. However, only a few of these have been

F

F F

F F

F F

F

F

F F

OH F

F

F F

F F

F

F

F F

F F

F

O

F F

Figure 3.9 Some prominent perfluorinated compounds.

F OH

F

F

F F

F F

F F

F F

F

O S

F

F

F F

F F

F O

NH 2

n-perfluorooctanesulfonamide (PFOSA)

n-perfluorooctylethanol (8:2 FTOH)

F

F F

F

F

n-perfluorooctanoic acid (PFOA)

F

F

F F

F F

F SO3H

F F

F F

F F

F F

F

n-perfluorooctanesulfonic acid (PFOS)

60

The Amazing World of Anthropogenic Organic Chemicals

detected in technical PFOS products at a total mass fraction of 20 to 35%, the rest being linear compounds (Houde et al., 2006; Greaves and Letcher, 2013). Although PFCs have been manufactured for more than 50 years, their occurrence in the environment was widely recognized only at the beginning of this millennium (Giesy and Kannan, 2001). The challenge of quantitative analysis of such compounds in environmental matrices, including biological samples (see Ahrens, 2011; Houde et al., 2011; Valsecchi et al., 2013), and the assumption that these compounds were not of toxicological concern contributed to delays in environmental detection. However, numerous recent studies reveal that PFCs are ubiquitous in the environment (see Ahrens, 2011; Benskin et al., 2012a and b; Zareitalabad et al., 2013) and in humans (Lindstrom et al., 2011), and accumulate in aquatic and terrestrial food chains (see Houde et al., 2006 and 2011). To date, the most widely investigated PFCs are PFOA and PFOS. These anionic PFCs strongly associate to proteins because of their charged nature and surfactant properties and, therefore, are found in the blood and liver of mammals, including humans, rather than in fatty tissue (see Chapter 16). Indoor sources, such as home furnishings and carpets, may significantly contribute to the accumulation of PFCs in humans, where some of these compounds exhibit half-lives of several years (Olsen et al., 2007; Beesoon et al., 2011; Shoeib et al., 2011). As evidence has also shown that PFCs are toxic, they are considered PBT chemicals (Lindstrom et al., 2011; Krafft and Riess, 2015).

3.7

From Washing Machines to Surface Waters: Complexing Agents, Surfactants, Whitening Agents, and Corrosion Inhibitors Expanding on the groups of chemicals found in consumer products, we now introduce laundry and dish detergents. These products include several classes of chemicals, all serving different purposes during the washing process. Because of their direct application into water, the various detergent components are introduced into wastewaters and thus enter the environment via effluents of wastewater treatment plants (WWTPs). Several of these chemicals are of concern with respect to water pollution. Among these are the builders that complex or precipitate metal ions, in particular calcium and magnesium, since these metals may interfere with the washing process by forming precipitates with soaps or surfactants. Detergents also contain surfactants or tensides, which lower the surface tension of water, thus changing its wetting properties and as a consequence improve the cleaning process at surfaces. At higher concentrations, surfactants form aggregates, called micelles, capable of keeping otherwise insoluble compounds in the aqueous phase. Other organic components present in laundry and dish detergents that should be mentioned include whitening agents, corrosion inhibitors, and fragrances. Historically, the most widely used builders, i.e., complexing agents, were phosphates and phosphonates. Because phosphorus is a key nutrient in natural waters and can cause eutrophication problems, particularly in small lakes, phosphorus salts have been replaced in many countries by other chemicals including zeolites or

From Washing Machines to Surface Waters

O

O

N

O

O OH

OH

HO

HO

61

N

O

O

N

C9H19 O

O

H n

OH

OH

HO

O

ethylenediaminetetraacetic acid (EDTA, complexing agent)

nitriloacetic acid (NTA, complexing agent)

4-nonylphenol-polyethyleneglycol-ethers (n=5–10; nonionic surfactants) O O– Na +

OH

4-nonylphenol (metabolite)

sodium stearate (soap; anionic surfactant) R O

SO3–

R

O

R

O

S

R N

O–

R=C10 –C13

R=C11 –C17

R=C12 –C18

linear alkylbenzene sulfonates (LAS; anionic surfactants)

fatty alcohol sulfates (FAS; anionic surfactants)

quarternary ammonium compounds (cationic surfactants)

O NH N –O

3S

O

N N

N

N

–O

N

3S

N

HN

SO3–

NH N

NH SO3–

4,4'-bis(2-sulfostryl)biphenyl (DSBP; fluorescent whitening agent)

N

H N N N 1H-benzotriazole (corrosion inhibitor)

Figure 3.10 Examples of laundry and dish detergent components, including complexing agents, surfactants, whitening agents, and corrosion inhibitors.

4,4'-bis(4-anilino-6-morpholino-1,3,5-triazine-2-yl) aminostilbene-2,2'-disulfonate (DAS1; fluorescent whitening agent)

N N H 5-methyl-1H-benzotriazole (corrosion inhibitor)

organic complexing agents such as NTA or EDTA (Fig. 3.10) (see Glennie et al., 2002). NTA and EDTA are also used in numerous other applications, such as pulp bleaching, textile processing, and scale removal. Whereas NTA is significantly eliminated in WWTPs, EDTA is persistent and one of the most abundant organic

62

The Amazing World of Anthropogenic Organic Chemicals

contaminants in surface waters (Reemtsma et al., 2006; Barber et al., 2013). Both NTA and EDTA are of environmental concern because of their ability to (re)mobilize heavy metals in WWTPs and in the aquatic environment (Alder et al., 1990; Nowack, 2002). Surfactants represent a group of diverse chemicals that are all built in the same general way: they contain both a hydrophobic and a hydrophilic part, thus giving them an amphiphilic character. This means, at interfaces, their hydrophilic “head” stays in aqueous solutions, whereas the hydrophobic “tail” tries to stay away. The hydrophilic head can be anionic, cationic, or neutral, whereas the hydrophobic tail usually consists of a long chain hydrocarbon moiety or, as encountered earlier, a perfluorinated alkyl chain (e.g., PFOA, PFOS, see Fig. 3.9). Surfactants are classified as high production volume chemicals with fabrication rates estimated at 15 millions metric tons per year (Reznik et al., 2010). They are not only used in detergents but also as soaps, wetting agents, dispersants, foaming agents, and emulsifiers in consumer and industrial applications. Some examples of important classes of surfactants are given in Fig. 3.10. An impressive use of surfactants that drew considerable attention was the application of about 8,000 m3 of dispersants during the Deepwater Horizon oil spill with the goal to decrease the size of oil droplets and prevent the formation of large oil emulsions or oil slicks (Kujawinski et al., 2011). A historically interesting case of surfactants as water pollutants involves 4-nonylphenol-polyethyleneglycol ethers, which are only partially biodegradable in WWTPs and transform into quite persistent endocrine disrupting products, including the potent 4-nonylphenol (Ahel et al., 1994; Sumpter and Johnson, 2008). Prominent fluorescent whitening or brightening agents include the two stilbene compounds 4,4′ -bis(2-sulfostryl)biphenyl (DSBP) and 4,4′ -bis(4-anilino-6-morpholino1,3,5-triazine-2-yl)aminostilbene-2,2′ -disulfonate (DAS1). These fluorescent compounds absorb sunlight in the UV-region and re-emit light in the visible part of the spectrum. Whitening agents adsorb to textile surfaces, making them appear more white or bright. They are also used in many other applications, such as in paper manufacturing. DSBP and DAS1 are not significantly eliminated in WWTPs because they are quite water soluble and resistant to biodegradation (Poiger et al., 1998). As a consequence, they are introduced in significant quantities into surface waters, where they are often used as markers to trace the discharge and transport of domestic wastewaters in rivers and lakes (Stoll et al., 1998; Yamaji et al., 2010). Since DSBP and DAS1 have also been shown to interact with human and rainbow trout estrogen receptors, they are of concern as water pollutants (Simmons et al., 2008). The final detergent components presented here are corrosion inhibitors, used in dishwashing for silver protection but also in many other products, including anti-icing fluids, cooling liquids, brake fluids, and additives in fracking wells. Typical inhibitors include the high production volume chemicals 1H-benzotriazole and 4- and 5-methyl1H-triazoles. As these inhibitors are widely detected in natural waters, quite persistent, and potentially toxic, they are considered important emerging water pollutants (Janna et al., 2011; Seeland et al., 2012).

Health, Well-Being, and Water Pollution

3.8

63

Health, Well-Being, and Water Pollution: Pharmaceuticals and Personal Care Products Thousands of chemicals are available on the market that support our health or help us to generally improve our well-being. Pharmaceuticals, including anti-inflammatories, antibiotics, beta-blockers, contraceptives, lipid regulators, antiepileptics, and antidepressents, are consumed daily in large amounts, as are personal care products such as soaps, shampoos, moisturizers, cosmetics, deodorants, fragrances, and sunscreens. Pharmaceuticals and ingredients of personal care products enter the environment primarily via municipal, industrial, and hospital wastewaters. Therefore, they are of primary concern as water pollutants (Hughes et al., 2013; Kaplan, 2013; Liu and Wong, 2013; Orias and Perrodin, 2013). In recent years, more wastewater and drinking water treatment plants have introduced advanced oxidation steps aimed at removing such compounds because traditional treatment plants provide insufficient removal. Sources other than WWTP outflows include runoff from agricultural fields fertilized with sewage sludge or animal manure, the latter commonly containing a variety of veterinary products including antibiotics and hormones (Metcalfe et al., 2008). The flurry of research focusing on these chemicals in the past fifteen years started primarily from the debate on endocrine disruptors. To date, although various other adverse effects are possible, they are not well understood (Corcoran et al., 2010). A compound is termed an endocrine disruptor if it imitates a natural hormone in an organism that is responsible for the maintenance of homeostasis, reproduction, development, or behavior. Possible negative effects include reproductive disorders, various cancers, and feminization, for example, as observed in fish (Tyler et al., 1998; Sumpter and Johnson, 2008). As pharmaceuticals and certain ingredients of personal care products are biologically active chemicals that are often designed to alter physiological function, they may also be biologically active in wildlife species, even at low concentrations. Because of their manner of use, these chemicals are continuously emitted, and organisms in receiving waters may be exposed throughout their lifetime to a large number of such compounds simultaneously. Here, we introduce some representative chemicals from the vast structural variety of pharmaceuticals and personal care products. We have selected them primarily based on their importance as environmental pollutants both with respect to exposure and effects (Benotti et al., 2009; Brausch and Rand, 2011; Howard and Muir, 2011). We also want to broaden the structural diversity of organic chemicals so far introduced. As we will see, these compounds are generally more polar than the chemicals we have already encountered. They exhibit various functional groups capable of hydrogen bonding, including acid and base functionalities. As a note, the common names are used for most of these chemicals instead of their lengthy systematic names. Pharmaceuticals We start with the most prominent and potent endocrine disruptors detected in wastewater and natural waters: natural estrogenics, estrone and 17β-estradiol, as well

64

The Amazing World of Anthropogenic Organic Chemicals

O

OH

OH

H

H

H

H

H

HO

H H

H

HO

H

HO

estrone (natural hormone)

17β-estradiol (natural hormone)

17α-ethinylestradiol (synthetic contaceptive) O

O O

O

S

O

F N

HN

OH

OH

O N

H 2N

O

HO

HO

O

N

HN

N O

O

O

O

O O

sulfamethoxazole (sulfonylamide antibiotic)

OH

clarithromycin (macrolide antibiotic)

ciprofloxacin (fluoroquinolone antibiotic)

Cl OH

NH Cl

OH

N

O

O

O diclofenac (anti-inflammatory)

ibuprofen (anti-inflammatory)

carbamazepine (antiepileptic and antidepressant) O

HO

O O OH

I

O

N OH

NH 2

N H I

I HN

OH OH

O O

gemfibrozil (anti-lipemic agent)

Figure 3.11 Some prominent pharmaceuticals of environmental concern, particularly with respect to water pollution.

iopromide (contrast agent)

as the synthetic contraceptive 17α-ethinylestradiol (Fig. 3.11). Historically, these hormones were the chemicals primarily blamed for the observed endocrine disruptive effects observed in aquatic organisms, particularly in fish (Corcoran, 2010). For example, exposure to 17α-ethinylestradiol at environmentally relevant

Fighting Pests: Herbicides, Insecticides, and Fungicides

65

concentrations was shown to induce feminization in fish (Tyler, 1998). Later, a variety of industrial chemicals and their transformation products were shown to also exhibit similar effects, though at much higher concentrations (Sumpter and Johnson, 2008). Such chemicals include many that we have already encountered in this chapter, such as certain POPs and bisphenol A. For example, Rutishauser et al. (2004) found that 4-nonylphenol, the surfactant transformation product, has a relative potency of 2.5 × 10−5 as compared to 17β-estradiol in yeast cells and is cytotoxic to rainbow trout hepatocytes at concentrations above 50 μM. Another group of chemicals of considerable concern are antibiotics, also often referred to as antimicrobials, which are used in large quantities in human and veterinary medicine. The toxicity of antibiotics in addition to their potential to induce bacterial resistance are issues of growing concern (Knapp et al., 2010). The vast variety of antibiotics available act by different biochemical mechanisms and can be selectively applied to optimally cure or prevent specific human or animal diseases. Consequently, antibiotics represent a group of compounds exhibiting quite different and complex chemical structures, as illustrated by sulfamethoxazole, ciprofloxacin, and clarithromycin (Fig. 3.11). We complete our short list of pharmaceuticals frequently detected in wastewater and the aquatic environment with some representative compounds that are widely consumed for a variety of ailments: non-steroidal, anti-inflammatory drugs diclofenac and ibuprofen; antiepileptic and antidepressant carbamazepine; lipid-regulating medication gemfibrozil; and the X-ray contrast agent iopromide (Fig. 3.11). Ingredients of Personal Care Products Besides solvents (see Section 3.4), personal care products contain several chemicals of environmental concern. Some prominent representatives frequently detected in surface waters (Brausch and Rand, 2011) include the biocides triclosan and triclocarban, the musks galaxolide and ketone, and the UV-filters benzophenone-3 and 4-methylbenzylidene camphor (4-MCB) (see Fig. 3.12). Pharmaceuticals and ingredients of personal care products are groups of very structurally diverse compounds (Figs. 3.11 and 3.12), most designed to exert a particular biological activity. Some of them are also transformed into products that are of environmental concern. One example is the phototransformation of triclosan to 2,8-dichlorodibenzodioxin (Kliegman et al., 2013; see Chapter 24).

3.9

Fighting Pests: Herbicides, Insecticides, and Fungicides We complete our look into the world of anthropogenic organic chemicals by introducing pesticides, a group of biologically active compounds with an even larger structural diversity than pharmaceuticals. The annual global consumption of active pesticide ingredients is estimated at about 2.5 million metric tons, of which about 40% are used as herbicides followed by insecticides and fungicides (Grube et al., 2011). The major use of pesticides is in commercial agriculture, but they are also used in our homes and public spaces for pest control measures such as weed prevention, insect control, and plant pathogen treatment.

66

The Amazing World of Anthropogenic Organic Chemicals

Cl

OH

Cl Cl

Cl

Cl

O

O N H

Cl triclosan (biocide)

O

N H

triclocarban (biocide)

galaxolide (polycyclic musk)

O OH

O2N

NO2

musk ketone (nitro musk)

Figure 3.12 Some ingredients of personal care products of environmental concern, particularly with respect to water pollution.

O

O

O

benzophenone-3 (UV-filter)

4-methylbenzylidene camphor (UV-filter)

In contrast to many other industrial chemicals, pesticides are purposely introduced into the environment. Therefore, particularly rigorous environmental assessments must be completed before regulatory agencies allow an active pesticide to be used. In principle, the assessment needs to demonstrate that the pesticide does not persist in the environment much longer than its intended use period and that its impact on nontarget organisms is minimal. However, as pesticides are directly applied to the environment, they can be immediately transported to places where degradation occurs more slowly than at the site of application. For example, depending on its physicochemical properties, a pesticide applied to an agricultural field may reach the atmosphere by volatilization, be transported by run-off into surface waters, or leach through the soil into groundwater (see Reichenberger et al., 2007; Kurt-Karakus et al., 2011). Therefore, not surprisingly, pesticides are ubiquitously found in the environment, although they are designed to persist for only a short time. In fact, several pesticides have been detected rather unexpectedly in regions far from their use, and surveys of groundwater and raw drinking water reveal the presence of certain pesticides that have long been phased out of use (Fenner et al., 2013). Obviously, pesticides are a group of compounds that highlight the conflict of interest between the usefulness of a chemical in human society and concern about its potential to contaminate the environment. This potent conflict is illustrated by the continual use in some parts of the world of polychlorinated pesticides that cause well-known environmental problems. Today, such pesticides are classified as POPs (see Section 3.2). These compounds are still favored because they are comparatively cheap and effective. For example, DDT is still the dominant insecticide used for malaria control (van den Berg et al., 2012). The structures of some representative members of important pesticide groups illustrate the chemical diversity involved (Fig. 3.13). The simplest pesticides are fumigants,

Fighting Pests: Herbicides, Insecticides, and Fungicides

Fumigants

Br H

Cl

Cl

H

Cl

Cl

H

methyl bromide

Cl

Cl

cis- and trans-1,3-dichloropropene

Herbicides N

O

chloropicrin Cl

O

OH

N

Cl

O O

Cl

N

N H

Cl 2,4-D

N

H 2N

N H

atrazine

metolachlor

Cl N

NO 2

Cl

H N N

N+

N+

N O

N H

N

de(s)ethylatrazine (metabolite)

diquat

isoproturon

Insecticides

N

N

S O

P

O

O

O

P

S

O

O S

S

HN

O O

diazinon

disulfoton

carbofuran

Cl O

Cl

O

O N cypermethrin

Miscellaneous

N

N N O

HN

O

N

O

Cl S

O Cl

aldicarb (acaricide, nematicide)

propiconazole (fungicide)

Figure 3.13 Examples of frequently used pesticides: herbicides, insecticides, and fungicides.

67

68

The Amazing World of Anthropogenic Organic Chemicals

which are broad-spectrum pesticides targeting various organisms applied as gaseous compounds into enclosed areas and then released into the atmosphere. Agricultural use is the largest source of fumigants to the atmosphere. The most prominent fumigant is methyl bromide. However, because of its high potential to deplete stratospheric ozone, methyl bromide is being phased out of agricultural use (Ristaino, 1997; U.S. EPA, 2015b). Other prominent fumigants include cis- and trans-1,3-dichloropropene, chloropicrin, and methyl iodide (CH3 I). The next group of pesticides, the herbicides, are comprised of chemicals with quite different structural characteristics. Widely used classes of herbicides include phenoxy alkanoic acids (e.g., 2,4-D and its esters and salts), chloroacetanilides (e.g., metolachlor), triazines (e.g., atrazine), bipyridyls (e.g., diquat), and urea derivatives (e.g., isoproturon). Except for the positively charged bipyridyls, which sorb strongly to soil particles (Chapters 13 and 14), many of these herbicides have been frequently detected in surface and groundwater (Reichenberger et al., 2007; Kurt-Karakus et al., 2011). Also, compounds like desethylatrazine (Fig. 3.13), a persistent and toxic metabolite of atrazine, are often found in natural waters at similar concentrations as the parent compound (Squillance et al., 2002; Loos et al., 2010). This example of desethylatrazine’s high frequency of detection in groundwater illustrates that stable transformation products of a given chemical should be included in assessments of the parent compound. Such widened assessments are of particular importance for biologically active chemicals, as their transformation products likely retain at least some of the bioactivity (Fenner et al., 2013). Many herbicides, as well as other biologically active chemicals, are chiral, meaning they exist as enantiomers or optical isomers (see Chapter 2), which usually exhibit different biological activities. An interesting example is metolachlor. This compound has an asymmetric carbon center (indicated in Fig. 3.13) much like the herbicide mecoprop, discussed earlier (Fig. 2.4). In both cases, only one of the two enantiomers has a significant herbicidal activity; the S-form in the case of metolachlor and the R-form in the case of mecoprop. Actually, a total of four metalochlor isomers exist because two geometric cis/trans isomers are also possible. Both the cis-Sform and the trans-S-form are active herbicides, whereas the corresponding R-forms are not. Prominent classes of insecticides include organophosphates (e.g., diazinon, disulfoton), carbamates (e.g., carbofuran), and pyrethroids (e.g., cypermethrin). Some organophosphates are also used as flame retardants (see Fig. 3.8’s example). However, they contain three identical alkyl or phenyl ester groups, which render them rather nontoxic. In contrast, the organophosphates used as insecticides contain one ester group with a more complex structure, making them more toxic. Furthermore, these insecticides are thionate (P=S) esters rather than oxonate (P=O) esters. The main reason for including thionate esters is to lower the mammalian toxicity. However, in most cases, these esters are converted to the more active oxonates in target organisms (Eto, 1979; Hassal, 1990). We conclude this section by adding the fungicide propiconazole and the acaricide/nematicide aldicarb, two more examples that illustrate the vast structural variety present in pesticides (Fig. 3.13).

69

Our Companion Compounds: Representative Model Chemicals

3.10

Our Companion Compounds: Representative Model Chemicals To illustrate how one may think about and evaluate various organic chemicals that occur in the environment, we chose a subset of the diverse array of synthetic compounds to serve as our “companions” or model compounds throughout the book (Table 3.1). This does not mean we will not encounter numerous other chemicals. This group of companions includes compounds of different sizes, polarities, and reactivities meant to reflect the large structural variety one comes across when assessing environmental organic chemicals. In addition to the compounds that we have already encountered in this chapter, a few new chemicals have been added as companions because they are interesting in terms of persistence and transport.

Table 3.1 Our Companion Compounds Chemical Name Bromomethane CAS: 74-83-9 Tetrachloroethene CAS: 127-18-4 Methyl-t-butyl-ether CAS: 1634-04-4 Benzene CAS: 71-43-2 Phenol CAS 108-95-2

Abbreviation/ Common Name

Molecular Formula

methyl bromide

CH3 Br

Structure Br H

PCE

C2 Cl4

MTBE

C5 H12 O

Bz

C6 H6

Ph

C6 H6 O

Uses fumigant

H H

Cl

Cl

Cl

Cl

solvent gasoline additive

O

OH

solvent, gasoline component precursor for industrial products

Cl

γ-hexachlorocyclohexane (γ-HCH) CAS: 58-89-9

lindane

C6 H6 Cl6

Cl

Cl

Cl

Cl

insecticide

Cl

Aniline CAS 62-53-3 n-Hexane CAS: 110-54-3 2-Methyl-1,3,5-trinitrobenzene CAS: 118-96-7

C6 H7 N hexane TNT

NH2

C6 H14

precursor for industrial products solvent

NO2

C7 H5 N3 O6

explosive O2N

NO2

(continued)

70

The Amazing World of Anthropogenic Organic Chemicals

Table 3.1 (Continued) Chemical Name

Abbreviation/ Common Name

Molecular Formula

Structure

Uses

Cl

Atrazine CAS: 1912-24-9

Decamethylcyclopentasiloxane CAS: 541-02-6

Az

C8 H14 ClN5

N N H

D5

′

′

2,2 ,4,4 ,5,5 Hexachlorobiphenyl CAS: 35065-27-1

N H

N O Si O

C10 H30 O5 Si5

O

O O

Cl

PCB 153

C12 H4 Cl6

solvent

Si

Si Si

′

herbicide

N

Si

Cl

industrial fluid Cl

Cl Cl

Cl

Br

2,2′ ,4,4′ ,5Pentabromodiphenyl ether CAS: 60348-60-9

PBDE 99

Br

C12 H5 Br5 O Br

flame retardant

O

Br Br OH

Cl

Triclosan CAS: 3380-34-5

TC

C12 H7 Cl3 O2

biocide

O Cl

Cl Cl

p,p′ -DDT CAS: 50-29-3

DDT

Cl

Cl

C14 H9 Cl5

insecticide Cl

Cl

Phenanthrene CAS: 85-01-8

Phe

C14 H10

combustion product

Benzo(a)pyrene CAS: 50-32-8

BaP

C20 H12

combustion product

71

Our Companion Compounds: Representative Model Chemicals

4 O Si O

3

Si

Si

D5

O

O Si

2

O

Si

hexane

1 methyl bromide

log Ki air–water (LwLa–1)

0

Br H

H H

Cl

Cl

Cl

Cl

PCE

Bz

–1

Cl

MTBE

O

–2

Cl

Cl

Cl Cl

–3

Phe aniline

Cl

NH2

–4

Cl

Cl

Cl Br

Cl

Cl

Br

Cl

Cl

Br

Cl

–5

O

Br

phenol

Br

NO2

–6

PBDE 99

BaP

TNT O2N

–7 –8

Cl

DDT

Cl

lindane

OH

Cl

PCB 153

NO2 Cl

N

Az

0

1

N H

2

Cl

N N

OH O

N H

3

Cl

4

TC Cl

5

6

7

8

9

log Ki octanol–water (LwLo–1) Figure 3.14 The air–water and octanol–water equilibrium partition constants for our companion compounds (data from Appendix C) illustrating the wide range of physical-chemical properties encountered when assessing organic pollutants in the environment.

As an illustration of the varying partitioning behavior of our chemical companions in the environment, Fig. 3.14 shows the wide range (i.e., many orders of magnitude) of air–water and octanol–water equilibrium partition constants encountered for these compounds. A key goal throughout the book is to utilize quantitative approaches that can systematically evaluate the entire array of compounds of interest. As already stated in Chapter 1, it is our goal to show that the fate of organic chemicals in the environment can be largely understood by using knowledge regarding specific environmental processes that transport and transform chemical substances as a function of the attributes that derive from their structures.

72

The Amazing World of Anthropogenic Organic Chemicals

3.11

Questions Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Q 3.1 What characteristics render an organic compound to be qualified as a POP? What are so-called “legacy POPs?” Give some examples of these compounds. What other compounds exhibit typical POP characteristics? Q 3.2 What is the composition of petroleum and what are its major components? What happens to petroleum after a spill? Q 3.3 What are the main sources of polycyclic aromatic hydrocarbons (PAHs) in the environment? Why are PAHs a problem? Q 3.4 What are the main sources of BTEX compounds in the environment? Which is the most problematic among these compounds and why? Q 3.5 When considering organic solvents as groundwater pollutants, what are the main differences between the polychlorinated C1 – and C2 –compounds and other solvents, including BTEX and dialkyl ethers such as MTBE? Q 3.6 Which characteristics make volatile methylsiloxanes (VMS) special as compared to other organic solvents? For what purposes are VMS primarily used? Q 3.7 Explain how organic flame retardants work. Why are polybrominated aromatic compounds well suited as flame retardants? Why are many of these compounds considered to be of particular environmental concern? Q 3.8 Phthalates are ubiquitous pollutants in the environment. What are they primarily used for and why do they, like many of the flame retardants, escape in large quantities into the environment? Q 3.9 In which materials that you are exposed to every day would you expect the presence of low molecular weight polyfluorinated compounds (PFCs)?

Bibliography

73

Q 3.10 Give some examples of organic chemicals present in detergents that are used in households. Explain their function and comment on why some of them are of environmental concern. How do these chemicals get into the environment? Q 3.11 What are the main routes by which pharmaceuticals are introduced into the environment? Which pharmaceuticals are of particular concern and why? Q 3.12 Why is the environmental assessment of pesticides of particular importance? What makes them different from other groups of anthropogenic compounds?

3.12

Bibliography Aeppli, C.; Carmichael, C. A.; Nelson, R. K.; Lemkau, K. L.; Graham, W. M.; Redmond, M. C.; Valentine, D. L.; Reddy, C. M., Oil weathering after the Deepwater Horizon disaster led to the formation of oxygenated residues. Environ. Sci. Technol. 2012, 46(16), 8799–8807. Ahel, M.; Giger, W.; Koch, M., Behaviour of alkylphenol polyethoxylate surfactants in the aquatic environment: I. Occurrence and transformation in sewage treatment. Water Res. 1994, 28(5), 1131–1142. Ahrens, L., Polyfluoroalkyl compounds in the aquatic environment: a review of their occurrence and fate. J. Environ. Monit. 2011, 13(1), 20–31. Alder, A. C.; Siegrist, H.; Gujer, W.; Giger, W., Behavior of NTA and EDTA in biological wastewater treatment. Water Res. 1990, 24(6), 733–742. Bansal, V.; Kim, K. H., Review of PAH contamination in food products and their health hazards. Environ. Int. 2015, 84, 26–38. Barber, L. B.; Keefe, S. H.; Brown, G. K.; Furlong, E. T.; Gray, J. L.; Kolpin, D. W.; Meyer, M. T.; Sandstrom, M. W.; Zaugg, S. D., Persistence and potential effects of complex organic contaminant mixtures in wastewater-impacted streams. Environ. Sci. Technol. 2013, 47(5), 2177–2188. Barro, R.; Regueiro, J.; Llompart, M.; Garcia-Jares, C., Analysis of industrial contaminants in indoor air: Part 1. Volatile organic compounds, carbonyl compounds, polycyclic aromatic hydrocarbons and polychlorinated biphenyls. J. Chromatogr. A 2009, 1216(3), 540–566. Beard, A., Flame Retardants: Frequently Asked Questions; European Flame Retardants Association (EFRA), 2007; p 37. www.flameretardants.eu. Beesoon, S.; Webster, G. M.; Shoeib, M.; Harner, T.; Benskin, J. P.; Martin, J. W., Isomer profiles of perfluorochemicals in matched maternal, cord, and house dust samples: Manufacturing sources and transplacental transfer. Environ. Health Perspect. 2011, 119(11), 1659–1664. Benotti, M. J.; Trenholm, R. A.; Vanderford, B. J.; Holady, J. C.; Stanford, B. D.; Snyder, S. A., Pharmaceuticals and endocrine disrupting compounds in US drinking water. Environ. Sci. Technol. 2009, 43(3), 597–603. Benskin, J. P.; Ahrens, L.; Muir, D. C. G.; Scott, B. F.; Spencer, C.; Rosenberg, B.; Tomy, G.; Kylin, H.; Lohmann, R.; Martin, J. W., Manufacturing origin of perfluorooctanoate (PFOA) in Atlantic and Canadian Arctic seawater. Environ. Sci. Technol. 2012a, 46(2), 677–685. Benskin, J. P.; Muir, D. C. G.; Scott, B. F.; Spencer, C.; De Silva, A. O.; Kylin, H.; Martin, J. W.; Morris, A.; Lohmann, R.; Tomy, G.; Rosenberg, B.; Taniyasu, S.; Yamashita, N., Perfluoroalkyl acids in the Atlantic and Canadian Arctic Oceans. Environ. Sci. Technol. 2012b, 46(11), 5815– 5823.

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Chapter 4

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

4.1

Important Thermodynamic Functions Chemical Potential Fugacity Pressure and Fugacities of a Compound in the Gas State Reference States and Standard States

4.2

Using Thermodynamic Functions to Quantify Equilibrium Partitioning Fugacities of Liquids and Solids Activity Coefficient and Chemical Potential Excess Free Energy, Excess Enthalpy, and Excess Entropy Equilibrium Partition Constants and Standard Free Energy of Transfer Effect of Temperature on Equilibrium Partitioning

4.3

Organic Acids and Bases I: Acidity Constant and Speciation in Natural Waters Thermodynamic Considerations of Acid/Base Equilibrium Effect of Temperature on Acidity Constants A Few Comments on Experimental Data Speciation in Natural Waters

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

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4.4

Organic Acids and Bases II: Chemical Structure and Acidity Constant Overview of Acid and Base Functional Groups Inductive Effects Resonance Effects Proximity Effects Estimation of Acidity Constants: The Hammett Relationship

4.5

Questions and Problems

4.6

Bibliography

Important Thermodynamic Functions

83

Whether dealing with partitioning of a given organic pollutant between two phases (e.g., between air and water) or trying to assess abiotic or biological transformation reactions of a chemical in the environment, we are always interested in the situation should it reach equilibrium. That is, we want to know what the chemical concentrations will be in the two conditions when no net changes occur anymore. From a practical point of view, we can actually assume that equilibrium is reached, or almost reached, in quite a few instances. For example, equilibrium can always be assumed for proton transfer reactions that are usually much faster than any other process. Furthermore, a partitioning process may be fast compared to a transport process or a chemical reaction in the environment. In such cases, it is appropriate to describe phase interchanges with an equilibrium approach. Furthermore, even for processes that will never reach equilibrium in the time frame considered and where kinetic approaches need to be applied, knowledge of the equilibrium situation is pivotal. For example, one uses equilibrium information to assess the direction of a chemical flux between compartments or to evaluate whether a transformation reaction may occur spontaneously or not. Also, many kinetic models describing phase interchanges assume equilibrium at the interface. The goal of this chapter is to review some important thermodynamic entities that are relevant to describe partitioning and chemical reaction equilibria, as well as to assess the extent of disequilibria: Gibbs free energy (G), enthalpy (H), entropy (S), chemical potential (𝜇), fugacity (f), activity (a), and activity coefficient (𝛾). As for the thermodynamics of chemical reactions, we focus on acid/base equilibria, which we need to take into account when treating phase transfer reactions of acids and bases. We also look at how chemical structure affects the tendency of a given acid or base function to undergo a proton transfer in aqueous solution. A further treatment of more general aspects of reaction thermodynamics will be given in Chapter 21, Section 21.2.

4.1

Important Thermodynamic Functions Chemical Potential When considering the relative energy status of the molecules of a particular compound in a given environmental system (e.g., benzene in aqueous solution), we can envision the molecules to embody both internal and external energies. Internal energies are those associated with the molecule’s chemical bonds, bond vibrations, bending, flexing, and rotations. External energies include those due to whole-molecule translations, reorientations, and interactions of the molecules with their surroundings. This energy content is dependent on the temperature, pressure, and chemical composition of the system. When we talk about the “energy content” of a given substance, we are usually not concerned with the energy status of a single molecule at any given time, but rather with an average energy status of the entire population of one type of organic molecule (e.g., benzene) in the system. To describe the (average) “energy status” of a compound, i, mixed in a milieu of substances, Gibbs (1873, 1876) introduced an entity referred to as total free energy, G, of this system, which is composed of enthalpy (H)

84

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and entropy (TS) terms (i.e., G=H-TS), where T is the absolute temperature). G can be expressed as the sum of the contributions from all of the different components present:

G(p, T, n1 , n2 , … ni , … nn ) =

n ∑

ni 𝜇 i

(4-1)

i=1

where ni is the amount of compound i (in moles) in the system containing N compounds. The entity 𝜇i , which is referred to as chemical potential of the compound i, is given by: [

∂G(J) 𝜇 i (J mol ) = ∂ni (mol) −1

] T,p,nj ≠ni

(4-2)

Hence, 𝜇 i expresses the Gibbs free energy (which we denote just as free energy) added to the system at constant T, p, and composition with each added increment of compound i. Let us now try to evaluate this important function. When adding an incremental number of molecules of i, but leaving everything else unchanged, free energy is introduced in the form of internal energies of substance i as well as by the interaction of i with other molecules in the system. As more i is added, the composition of the mixture changes and, consequently, 𝜇 i changes as a function of the amount of i. The chemical potential 𝜇i is sometimes also referred to as the partial molar free energy, Gi , of a compound. Finally, we note that Gi (J mol−1 ) is related to the partial molar enthalpy, Hi (J mol−1 ), and partial molar entropy, Si (J mol−1 K−1 ), by: 𝜇 i ≡ Gi = Hi − TSi

(4-3)

Gibbs (1876) recognized that the chemical potential could be used to assess the tendency of component i to be transferred from one system to another or to be transformed within a system, which is analogous to the use of hydrostatic head potential for identifying the direction of flow between water reservoirs (Fig. 4.1a). We know that equilibrium (no net flow in either direction) is reached when the hydrostatic head potentials of the two reservoirs are equal (Fig. 4.1b). Similarly, chemical equilibrium is characterized by equal chemical potentials for each of the constituents. As with hydrostatic head potential, chemical potential is an intensive entity, meaning it is independent of the size of the system. This in contrast to the total free energy G, which is an extensive function that at constant conditions is proportional to the size of the system. Fugacity Unfortunately, unlike hydraulic head potentials, we cannot directly observe chemical potentials. Consequently, the concept of fugacity was born. Lewis (1901) reasoned that rather than looking into a system and trying to quantify all of the chemical potential energies carried by the various components of interest, it would be more practical to assess a molecule’s urge to escape or flee that system (hence “fugacity” from Latin fugere, to flee). If one could quantify the relative tendencies of molecules to flee

Important Thermodynamic Functions

85

various situations, one could simultaneously recognize the relative chemical potentials of the compounds of interest in those situations. Based on the differences in their chemical potentials, one could quantify the direction (higher 𝜇i to lower 𝜇i ) and the extent to which a transfer or transformation process would occur. hydrostatic system gh1 ≠ gh2

(a) not at equilibrium

h2

h1

tank 1

∂m1

= gh1 < gh2 =

GL

Gg

liquid (L) benzene

tank 2

direction of flow since ∂W1

μ iL ≠ μig

W2

W1

Figure 4.1 Conceptualization of the potential functions in a hydrostatic system and in a simple chemical system. (a) In the unequilibrated hydrostatic system, water will flow from reservoir 2 of higher hydrostatic potential (=gh2 , where g is the acceleration due to gravity and h2 is the observable height of water in the tank) to reservoir 1 of lower hydrostatic potential; total water volumes (i.e., total potential energies W1 and W2 ) do not dictate flow. Similarly, benzene molecules move from liquid benzene to the headspace in the unequilibrated chemical system, not because there are more molecules in the flask containing the liquid, but because the molecules initially exhibit a higher chemical potential in the liquid than in the gas. (b) At equilibrium, the hydrostatic system is characterized by equal hydrostatic potentials in both reservoirs (not equal water volumes) and the chemical system reflects equal chemical potentials in both flasks (not equal benzene concentrations). In the hydrostatic system, m is the mass, W the weight, and gh is the hydrostatic potential. In the chemical system, ni is the number of moles of compound i, G is the Gibbs free energy, and 𝜇 i is the chemical potential.

chemical system

∂W2 ∂m2

not because W1 μ ig =

∂Gg ∂nig

not because GL>Gg

(b) at equilibrium

gh1 = gh2

air with benzene vapor (g)

μiL = μig

h2

no net flow since ∂W1 ∂ m1

= gh1 = gh2 =

note: W1>W2

∂W2 ∂ m2

no net flow since ∂ GL ∂ niL

= μiL = μig =

∂ Gg ∂ nig

note: GL>Gg

Pressure and Fugacities of a Compound in the Gas State Let us first quantify the “fleeing tendency” or fugacity of molecules in a gas since the gas phase is one of the simplest molecular systems. Imagine a certain number of moles (ni ) of a pure gaseous compound i confined to a volume, V, say in a closed beaker, at

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Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

a specific temperature, T. The molecules of the gaseous compound exert a pressure pi on the walls of the beaker (a quantity we can feel and measure) as they press upon it seeking to pass (Fig. 4.1a). It is not difficult to imagine that if the gas molecules wish to escape more “insistently” (i.e., a higher chemical potential as a result, for example, of the addition of more i molecules to the gas phase in the beaker), their impact on the walls will increase. Consequently, we measure a higher gas pressure. For an ideal gas (i.e., one in which the molecules do not interact with each other), the pressure is perfectly proportional to the amount of gaseous compound present. Stating this quantitatively, we see that at constant T, the incremental change in chemical potential of the gaseous compound i may be related to a corresponding change in pressure (deduced from the Gibbs-Duhem equation, e.g., Prausnitz, 1969): (d𝜇 ig )T =

V dp nig i

(4-4)

In this case, we can substitute V/nig with RT/pi : (d𝜇 ig )T =

RT dp pi i

(4-5)

Now we understand the reason why we cannot give an absolute value of the chemical potential. The integral of the differential expression Eq. 4-5 is only determined up to an arbitrary integration constant or, what is mathematically the same, to the (arbitrary) choice of a lower integration limit. We call this limit the “reference pressure”, p0i , or the “reference state.” In fact, every variable that is a potential, like height, potential energy, or electric potential, only involves relative values, that is, differences between different states. In order to define absolute values, a reference state is also needed for the chemical potential: 𝜇ig

∫

𝜇 0ig

pi

(d𝜇 ig )T = RT

1 dp ∫ pi i

(4-6)

p0i

Integration of Eq. 4-6 yields: 𝜇 ig = 𝜇0ig + RT ln

pi p0i

(4-7)

Let us now look at the situation in which we deal with real gases, that is, with a situation in which intermolecular forces between the molecules cannot be neglected, as is even more the case for liquids and solids. These forces influence the (partial) pressure of the gas molecules, but not the amount of the gaseous compounds. This real pressure is called fugacity. In contrast to the pressure of an ideal gas, the fugacity is not only a function of the amount of substance and temperature, but also of the composition (types and amounts of gaseous compounds present) of the gaseous system and total pressure. The fugacity

Important Thermodynamic Functions

87

of a gaseous compound is, however, closely related to its partial pressure. To account for the nonideality of the gas (due to molecule-molecule interactions), one can relate these terms by using a fugacity coefficient, θig : fig = θig pi

(4-8)

We use this result in Eq. 4-7 to obtain the correct expression for the chemical potential of a gaseous compound i so it is not based on pressure, but on fugacity: 𝜇 ig = 𝜇0ig + RT ln

fi p0i

(4-9)

Note that for the standard state, one defines ideal gas behavior as fi0 = p0i (commonly 1 bar). Under typical environmental conditions with atmospheric pressure, gas densities are very low (molecule-molecule interactions are essentially negligible) so that we set θig = 1. In other words, in all our following discussions, we assume that any compound exhibits ideal gas behavior (i.e., we use Eq. 4-7 instead of Eq. 4-9). In a mixture of gaseous compounds having a total pressure p, pi is the portion of that total pressure contributed by compound i, and it is called the partial pressure, which may be expressed as: pi = xig p

(4-10)

nig xig = ∑ njg

(4-11)

where xig is the mole fraction of i:

j

and

∑ j

njg is the total number of moles present in the gas, and p is the total pressure.

Thus, the fugacity of a gas i in a mixture is given by: fig = θig xig p ≈ pi

(4-12)

when the total pressure is near 1 bar. Reference States and Standard States Before we discuss the fugacities of compounds in liquid and solid phases, we should remember that the chemical potential, like other potentials such as potential energy or hydrostatic potential, are only defined relative to some reference condition. However, with the choice of an appropriate reference state, we can define an absolute value for the chemical potential that can then be related to other characteristics of the system such as pressure and temperature.

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Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

When we consider a change in the “energy status” of a compound of interest (e.g., the transfer of organic molecules from the pure liquid phase to the overlying gas phase or a reaction in which bonds are broken), we try to do our energy-change bookkeeping in such a way that we concern ourselves with only those energetic properties of the molecules that undergo change. During the vaporization of liquid benzene, for example, we do not worry about the internal energy content of the benzene molecules themselves, since these molecules maintain the same bonds, and practically the same bond motions, in both the gaseous and liquid states. Rather, we focus on the energy change associated with having benzene molecules in new surroundings. Benzene molecules in gas or liquid phases feel different attractions to their neighboring molecules and contain different translational, rotational, and conformational energies because in a liquid the molecules are packed fairly tightly together, whereas in the gas they are almost isolated. This focus on only the changing aspects is the guiding consideration in our choice of reference states. For each chemical species of interest, we want to pick a form (a reference state of the material) that is closely related to the situation at hand. For instance, it would be impractical, although feasible, to consider the energy status of elemental carbon and hydrogen of which the benzene molecule is composed as the reference point with which evaporating benzene should be compared. Instead, we are clever and, in this case, choose the “energy status” of pure liquid benzene as a reference state because liquid benzene includes all of the internal bonding energies common to the compound’s gaseous and liquid forms. Similarly, when dealing with simple reactions in aqueous solution such as proton transfer reactions, it would be silly to choose the pure liquid of the organic acid and base as the reference state. Rather, their “energy status” at infinite dilution in water is a better reference. Therefore, in the field of environmental organic chemistry, the most common reference states used include: (i) the pure liquid state, when we are concerned with phase transfer processes; (ii) the infinite dilution state, when we are dealing with reactions of organic chemicals in (aqueous) solution, and (iii) the elements in their naturally occurring forms (e.g., C(s), H2 , O2 , N2 , Cl2 , Br2 ), when we are interested in reactions in which many bonds are broken or formed. Certainly, other reference states may be chosen as convenience dictates, the guiding principle being that one can clearly see how the chemical species considered in a given system is related to the reference state. Once we have chosen an appropriate reference state, we also must specify the conditions of our reference state, that is, the pressure, temperature, and concentration. These conditions are referred to as standard conditions and, together with the reference state, form the standard state of a chemical species. We then refer to 𝜇 0i in Eqs. 4-7 and 4-9 as the standard chemical potential, a value that quantifies the “energy status” under these specific conditions. Since we are most often concerned with the behavior of chemicals in the earth’s near-surface ecosystems, 1 bar (105 Pa or 0.987 atm) is usually chosen as standard pressure. Furthermore, we have to indicate the temperature at which we consider the chemical potential. If not otherwise indicated, we will commonly assume a temperature of 298 K (25◦ C). In summary, as long as we are unambiguous in our choice of reference state and standard conditions, hopefully chosen so that both the starting and final states of a molecular change may be clearly related to these choices, our energy bookkeeping should be fairly straightforward to understand.

Using Thermodynamic Functions to Quantify Equilibrium Partitioning

4.2

89

Using Thermodynamic Functions to Quantify Equilibrium Partitioning Fugacities of Liquids and Solids Let us now continue with our discussion of how to relate the chemical potential to measurable quantities and how to apply the results to assess equilibrium partitioning of a given chemical i between different phases. We have already seen that the chemical potential of a gaseous compound can be related to pressure. Since substances in both the liquid and solid phases also exert vapor pressures, Lewis reasoned that these pressures likewise reflected the escaping tendencies of these materials from their condensed phases (Fig. 4.2). He thereby extended this logic by defining the fugacities of pure liquids (including subcooled and superheated liquids, hence the subscript “L”) and solids (subscript “s”) as a function of their vapor pressures, p∗iL and p∗is (see also Chapter 8): fiL = 𝛾 iL p∗iL (4-13) fis = 𝛾 is p∗is (a)

ideal gas

measured fugacity: pi

fig = pi

ideal liquid solution (c) of i ( ) in j ( ) measured fugacity: xiℓ p*iL

Figure 4.2 Conceptualization of the fugacity of a compound i (a) in an ideal gas; (b) in a pure liquid compound i; (c) in an ideal liquid mixture; and (d) in a nonideal liquid mixture (e.g., in aqueous solution). In (b), (c), and (d), the gas and liquid phases are in equilibrium with one another.

fiℓ = fig = xiℓ p*iL

pure organic liquid i ( ) (reference state) measured fugacity: piL*

(b)

fiL = fig = p*iL

nonideal liquid solution (d) of i ( ) in e.g., water ( ) measured fugacity: γiℓ xiℓ p*iL

fiℓ = fig = γiℓ xiℓ p*iL

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Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

where the activity coefficient, 𝛾 i , accounts for nonideal behavior resulting from molecule–molecule interactions. These activity coefficients are commonly set equal to 1 when we decide to take as the reference state the pure compound in the phase it naturally assumes under the conditions of interest. Thus, the molecules are viewed as “dissolved” in like molecules. This condition is defined to have “ideal” mixing behavior. If we consider, for example, compound i in a liquid mixture, such as in an organic or aqueous solution (subscript “l ”, see Fig. 4.2d), we can now relate its fugacity in the mixture to the fugacity of the pure liquid compound by: fil = 𝛾 il xil fiL∗ = 𝛾 il xil p∗iL

(4-14)

where xil is the mole fraction of i (Eq. 4-11) in the mixture or solution. For convenience, we chose the pure liquid compound (superscript ∗ ) as our reference state. If the compounds form an ideal mixture (Fig. 4.2c), implying that no nonideal behavior results from interactions among unlike molecules, 𝛾 il is equal to 1 and Eq. 4-14 represents the well-known Raoult’s Law. Activity Coefficient and Chemical Potential Using the concept of fugacity we can now, in analogy to the gas phase (Eq. 4-9), express the chemical potential of a compound i in a liquid solution by: f 𝜇 il = 𝜇 ∗iL + RT ln i∗l piL

(4-15)

where we have chosen the pure liquid compound as the reference state. The chemical potential of the pure liquid, 𝜇 ∗iL , is nearly equal to the standard free energy of formation, Δf Goi (L), of the pure liquid compound, which is commonly defined at 1 bar and not at p∗iL . Hence 𝜇 ∗iL ≅ 𝜇0iL . Substitution of Eq. 4-14 into Eq. 4-15 then yields: 𝜇 il = 𝜇 ∗iL + RT ln 𝛾 il xil

(4-16)

Generally, the expression fi ∕fref = 𝛾 i xi = ai is referred to as the activity of the compound. That is, ai is a measure of how active a compound is in a given state (e.g., in aqueous solution) compared to its reference state where activity ≡ 1 (e.g., the pure organic liquid at the same T and p). Since 𝛾 i relates ai , the “apparent concentration” of i, to the real concentration xi , it is only logical that one refers to 𝛾 i as the activity coefficient. We emphasize here that the activity of a given compound in a given phase is a relative measure and is, therefore, dependent on the reference state. The numerical value of 𝛾 i will depend on the choice of the reference state, since molecules of i in different reference states (e.g., liquid solutions) interact differently with their surroundings. Excess Free Energy, Excess Enthalpy, and Excess Entropy Before we apply Eq. 4-16 to describe the partitioning of a compound i between two phases, a few comments are necessary on the terms included in Eq. 4-16. First, we

Using Thermodynamic Functions to Quantify Equilibrium Partitioning

91

rewrite Eq. 4-16 by splitting the second term so that the first part reflects the difference in partial molar free energy of a compound i between its current solution and its situation in its reference state due to entropic differences. The second part captures any extra or “excess” differences associated with i’s actual situation in a given solution: 𝜇 il = 𝜇∗iL + RT ln xil + RT ln 𝛾 il ideal TSimix

GEil

(4-17)

As already pointed out, 𝛾 il is equal to 1 if a compound forms an ideal solution (i.e., one in which i’s interactions with its new molecular neighbors are the same as those when i was dissolved in a liquid of itself). In this rather rare case, the term RTln𝛾 il , which we denote as partial molar excess free energy of compound i in solution l , GEil , is 0. This means that the difference between the chemical potential of the compound in solution and its chemical potential in the reference state is only due to the different concentraideal expresses the partial tions of the compound i in the two states. The term Rlnxil = Simix molar entropy of ideal mixing (a purely statistical term) when diluting the compound from its pure liquid (xil = 1) into a solvent that consists of otherwise like molecules. Let us now have a closer look at the term excess free energy. For simplicity in the following sections and throughout the book, we drop the term “partial molar” and talk about the excess free energy of a given compound in a given molecular environment. To evaluate the excess free energy term, it is useful to first make some general comments on the various enthalpic and entropic contributions (Eq. 4-3) to the free energy of a given compound in a specific molecular environment. We do this in a somewhat simplistic way. In brief, the enthalpy term represents all attractions or attachments of a compound’s atoms to their surroundings. These include bonds (intramolecular forces, e.g., bond energies) as well as intermolecular interactions (see Chapter 2). Thus, the enthalpic contributions may be thought of as the “glue” holding the parts of a molecule to their surroundings. When we are only interested in the partitioning of organic compounds, we choose a reference state in a way that we only have to deal with changes in intermolecular interactions when comparing the energy of a compound in various molecular environments. The entropy term is best imagined as involving the “freedom” or latitude of orientation, configuration, and translation of the molecules involved. When molecules are forced to be organized or confined, work must be done. As a consequence, energy must be spent in the process. Conversely, the more ways the molecule can twist and turn, the more freedom the bonding electrons have in moving around in the molecular structure, the more “randomness” exists. As a result, the entropy terms are larger. This leads to a more negative free energy term (see Eq. 4-3). By analogy to Eq. 4-3, we can express the excess free energy term in Eq. 4-17 as: RT ln𝛾 il = GEil = HiEl − TSiEl

(4-18)

where HiEl and SiEl are the (partial molar) excess enthalpy and excess entropy, respectively, of the compound i in phase l . Let us now inspect the enthalpic and entropic

92

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

Table 4.1 Excess Free Energies, Enthalpies and Entropies of Hexane (apolar), Benzene (monopolar), Diethylether (monopolar) and Ethanol (bipolar) in the Ideal Gas Phase, in Hexadecane, and in Water at Infinite Dilution at 25◦ C a,b GEi phase (kJ mol−1 )

Phase Compound (i) Gas Phase Hexane Benzene Diethylether Ethanol Hexadecane Hexane Benzene Diethylether Ethanol Water Hexane Benzene Diethylether Ethanol a b

=

HiEphase (kJ mol−1 )

−

TSiEphase (kJ mol−1 )

SiEphase (J mol−1 K−1 )

4.0 5.3 0.8 6.3

= = = =

31.6 33.9 27.1 42.6

− − − −

27.6 28.6 26.3 36.3

92.6 96.0 88.2 122.0

−0.2 0.4 0.0 8.8

= = = =

0.6 3.5 1.9 26.3

− − − −

0.8 3.1 1.9 17.5

2.7 9.7 6.4 58.7

32.3 19.4 12.0 3.2

= = = =

−0.4 2.2 −19.7 −10.0

+ + + +

32.7 17.2 31.7 13.2

−109.7 −58.4 −106.3 −44.3

Data from Abraham et al. (1990) and Lide (1995). Reference state if the pure liquid organic compound.

n-hexane

benzene O diethylether OH ethanol

contributions to GEil for four simple compounds in hexadecane and in water (Table 4.1). Also shown in Table 4.1 are the corresponding values for the ideal gas phase (i.e., GEig , E ), which are identical with the free energy, enthalpy, and entropy of vaporizaHigE , Sig tion of pure liquid compounds, respectively, which we will discuss in detail in Chapter 8. Here, we note from the examples given in Table 4.1 that when considering a compound in the ideal gas state relative to the pure liquid, both enthalpy costs as well as entropy gains are important in determining the overall excess free energy. The rather high excess enthalpy and excess entropy values observed for ethanol can be fully rationalized by the ability of this compound to undergo quite strong hydrogen bonding (H-bonding, see Chapter 2) within the pure liquid (which is not the case for the other compounds). This results in a stronger “glue” among the molecules and, therefore, in a higher (positive) HigE . For the same reasons, the ethanol molecules have less freedom to move around in their own liquid phase, which leads to a larger entropy gain when transferred to the (ideal) gas phase, where freedom is maximal. A very different picture is seen when compounds move from a pure liquid into hexadecane. Here, the compounds that do not hydrogen bond with each other show almost ideal behavior (i.e., GEil ≈ 0) because in their own liquids, as well as in hexadecane, they only have van der Waals interactions (see discussion of molecular interactions in Chapters 2 and 7). In the case of ethanol, again, a significant enthalpy cost and entropy gain is found, which can be explained with the same arguments used for the

Using Thermodynamic Functions to Quantify Equilibrium Partitioning

93

gas phase. The absolute HiEl and TSiEl values are, however, smaller as compared to the gas phase, because ethanol undergoes vdW interactions with the hexadecane solvent molecules, and because the freedom to move around in hexadecane is smaller than in the gas phase. Finally, the most interesting, and maybe somewhat puzzling, case is the aqueous phase. We might not have guessed that the excess enthalpies in water are close to zero or even negative for all four compounds, even for hexane that cannot form H-bonds (see Chapter 2, Box 2.2). The very high fugacity of hexane in water is, therefore, not due to enthalpic reasons but caused by a very large negative entropy contribution. This effect is also significant for the other three compounds (see Table 4.1). This significant loss in entropy when transferring an organic molecule from one liquid phase (the pure compound) to another liquid phase (water) is, at first glance, rather surprising (compare water with hexadecane). Hence, solutions in water represent a special case, which we need to unravel if we want to understand the environmental partitioning of organic compounds. We learn more about these secrets in Chapter 9. Our next step is to demonstrate how partition constants between two different phases are linked to the corresponding excess free energy terms.

Equilibrium Partition Constants and Standard Free Energy of Transfer Let us consider a system in which two bulk phases, 1 and 2 (e.g., air and water), are in contact with each other at a given temperature and pressure. We assume that the two phases are in equilibrium with each other with respect to the amounts of all chemical species present in each. We now introduce a very small amount of a given organic compound i into phase 2 (i.e., the properties of both bulk phases are not significantly influenced by the introduction of the compound). After a short time, some molecules of compound i will have been transferred from phase 2 (reactant) to phase 1 (product) as portrayed in Eq. 4-19: i in phase 2 ⇌ i in phase 1 “reactant” “product”

(4-19)

The equilibrium situation can thus be described by an equilibrium partition constant, Ki12 , which we define as: Ki12 =

concentration of i in phase 1 concentration of i in phase 2

(4-20)

Because we have chosen i in phase l as the “product,” the abundance of i in phase 1 is in the numerator of Eq. 4-20. Furthermore, for practical purposes, we define a constant expressed as a ratio of concentrations rather than activities. Finally, we consider only situations in which the compound is present as a solute, that is, at low concentrations such that it does not significantly affect the properties of the bulk phase.

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Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

At this point, we write the chemical potentials of i in the two phases according to Eq. 4-17: 𝜇i1 = 𝜇 ∗iL + RT lnxi1 + RT ln𝛾 i1 𝜇i2 = 𝜇 ∗iL + RT lnxi2 + RT ln𝛾 i2

(4-21)

The difference between the two chemical potentials (which corresponds to the free energy of a reaction discussed in Section 4.3 and in Chapter 21) is then given as: 𝜇 i1 − 𝜇i2 = RT ln

xi1 𝛾 + RT ln i1 xi2 𝛾 i2

(4-22)

One can easily see that at the very beginning of our experiment, 𝜇i1 is smaller than 𝜇 i2 (xi1 ≪ xi2 ) and thus the difference will be negative, even if the activity coefficients of the compound in the two phases are quite different. Consequently, a net transfer of compound i from phase 2 to phase 1 will occur until equilibrium (i.e., 𝜇 i1 = 𝜇i2 ) is reached. Then, at equilibrium, we obtain after some rearrangement: ′ ln Ki12 ≡ ln

xi1 (RT ln𝛾 i1 − RT ln𝛾 i2 ) =− xi2 RT

(4-23)

which is equivalent to ′ ≡ Ki12

xi1 = e−(RT ln𝛾 i1 −RT ln𝛾 i2 )∕RT = e−Δ12 Gi ∕RT xi2

(4-24)

′ is the partition constant on a mole fraction basis. We distinguish this mole where Ki12 fraction basis from the partition constant expressed in molar concentrations by using a prime superscript. We can see now that the free energy of transfer, Δ12 G, equals the difference between the (partial molar) excess free energies of i in the two phases under specified conditions:

Δ12 G = GEi1 − GEi2

(4-25)

We now address the problem of expressing the abundance of compounds in a bulk phase. In environmental chemistry, the most common way to express concentrations is not by mole fraction, but by the number of molecules per unit volume, for example, as moles per liter of solution (mol L−1 , M). This molar concentration scale is sometimes not optimal. For example, volumes are dependent on T and p, whereas masses are not. Hence, the use of concentration data normalized per kilogram of seawater is often seen in the oceanographic literature. However, the molar scale is widely used. We can convert mole fractions to molar concentrations by: Cil =

xil (mol i (total mol)−1 ) V̄ l (L(total mol)−1 )

(4-26)

Using Thermodynamic Functions to Quantify Equilibrium Partitioning

95

where Cil is the concentration (moles per liter) of i in phase l and V̄ l is the molar volume of the mixture or solution. When we deal with a mixture of several components (e.g., organic solvent/water mixtures in Chapter 10), we generally apply Amagat’s Law as a first approximation. That is, we assume that the components of the liquid phase mix with no change in volume due to intermolecular interactions: V̄ l =

∑

xj V̄ j

(4-27)

j

where xj and V̄ j are the mole fractions and molar volumes of the pure components, j. For aqueous solutions of moderately or only sparingly soluble compounds, we can usually neglect the contribution of the organic solute to the molar volume of the mixture. This means that we set V̄ l equal to V̄ w , the molar volume of water (V̄ w = 0.0181 L mol−1 at 25◦ C). Substitution of xi by Cil V̄ l in Eq. 4-23 then yields the partition constant, Ki12 , expressed in molar concentrations (we now omit the prime superscript): lnKi12 ≡ ln

Ci1 (RT ln𝛾 i1 − RT ln𝛾 i2 ) V̄ = −RT ln 1 − Ci2 RT V̄ 2

(4-28)

Ci1 V̄ V̄ = 2 e−(RT ln𝛾 i1 −RT ln𝛾 i2 )∕RT = 2 e−Δ12 Gi ∕RT Ci2 V̄ 1 V̄ 1

(4-29)

which is equivalent to: Ki12 ≡

Using the excess free energy, enthalpy, and entropy values given for our four model compounds in Table 4.1, we can now calculate how these compounds partition between the various phases (i.e., between air and hexadecane, air and water, and hexadecane and water respectively) at equilibrium (Table 4.2). These results reflect, of course, what we have previously discussed when inspecting the excess energy terms of the compounds in various phases. In Chapters 7 to 10, we address in detail the partitioning of organic compounds between air and liquids (including water), and organic phases and water. Here, we note again the important entropy contributions to the overall excess free energy of transfer of a compound i, if water is one of the phases involved. Effect of Temperature on Equilibrium Partitioning So far, we have considered the equilibrium partitioning of an organic compound at a given temperature and pressure. Since partition constants are commonly reported for only one particular temperature (e.g., 25◦ C), we need to be able to extrapolate these values to other conditions of temperature. In most cases in environmental organic chemistry, we can neglect the effect of pressure changes on equilibrium partitioning. Exceptions might include cases of very high pressure, as for example, in the deep sea (>200 bar), deep groundwater, or in reactors operated at supercritical conditions. For these particular applications, we refer to the corresponding literature (e.g., Prausnitz, 1969; Atkins, 2014). Here, we confine our discussion to the temperature dependence

96

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

Table 4.2 Air–Hexadecane, Air–Water, and Hexadecane–Water Equilibrium Partitioning of Hexane, Benzene, Diethylether, and Ethanol: Free Energies, Enthalpies and Entropies of Transfer, as well as Partition Constants Expressed on a Molar Base (i.e., mol L−1 /mol L−1 )a phase1 phase2 Phase 1/Phase 2 Compound (i) Air/Hexadecane Hexane Benzene Diethylether Ethanol Air/Water Hexane Benzene Diethylether Ethanol Hexadecane/Water Hexane Benzene Diethylether Ethanol a

Δ12 Gi (kJ mol−1 )

=

Δ12 Hi

−

(kJ mol−1 )

TΔ12 Si

Δ12 Si

(kJ mol−1 )

(J mol−1 K−1 )

a Ki12

4.2 4.9 0.8 −2.5

= = = =

31.0 30.4 25.2 16.3

− − − −

26.8 25.5 24.4 18.8

89.9 85.6 81.9 73.3

2.2 × 10−3 1.7 × 10−3 8.7 × 10−3 3.3 × 10−2

−28.3 −14.1 −11.2 3.1

= = = =

32.0 29.7 46.8 52.6

− − − −

60.3 43.8 58.8 49.5

202.3 147.0 194.6 166.3

6.5 × 101 2.1 × 10−1 6.6 × 10−2 2.0 × 10−4

−32.5 −19.0 −12.0 5.6

= = = =

1.0 1.3 21.6 36.3

− − − −

33.5 20.3 33.6 30.7

112.4 68.1 112.8 103.0

3.0 × 104 1.3 × 102 7.7 × 100 6.4 × 10−3

Eq. 4-29: molar volumes at 25◦ C and 1 bar: V ideal gas = 24.73 L mol−1 , V̄ hexadecane = 0.293 L mol−1 , V̄ water = 0.0181 L mol−1 .

of partitioning. As a starting point, we consider the differentiation of ln Ki12 (Eq. 4-29) with respect to temperature: d ln Ki12 d ln constant 1 d(Δ12 Gi ∕T) = − dT dT R dT

(4-30)

Let us first look at the temperature dependence of the constant. Using the mole fraction ′ , this constant is equal to 1 and, therefore, temperature indepenbasis, i.e., Ki12 = Ki12 dent if mole fractions or partial pressures are used to express the abundance of i in a given liquid or in the gas phase. In contrast, when using molar concentrations, the constant is given by the ratio of the molar volumes of the two phases. These are, of course, influenced by temperature. However, as a first approximation, we may neglect this relatively small effect ( 0.999

0.57

< 0.001

0.70

< 0.001

3.33

< 0.001

6.50

0.240

10.61

>0.999

OH

1-Naphthalene-sulfonic acid

Miscellaneous Groups (AH ⇋ A− + H + ) SO3H

p-Toluenesulfonic acid SO3H

Thioacetic acid

O SH

Thiophenol SH

Ethanethiol

SH

Aliphatic alcohols a b

R

>14

OH

>> 0.999

Data from Dean (1985) and Lide (1995). Fraction in neutral (acidic) form at pH 7 (Eq. 4-59).

Here, the reaction of a neutral base with water results in the formation of a cation. Some examples of important organic bases are shown in Table 4.5. To compare acids and bases on a uniform scale, it is convenient to use the acidity constant of the conjugate acid (i = BH+ ) as a measure of the base strength: BH+ ⇌ H+ + B Kia =

(𝛾 ′H+ [H+ ])(𝛾 ′B [B]) (𝛾 ′BH+ [BH+ ])

(4-55)

Kib and Kia are quantitatively related by the ionization constant of water (ion product of water), Kw, which, at 25◦ C is: Kw = Kia Kib = (𝛾 ′H+ [H+ ])(𝛾 ′OH− [OH− ]) = 1.01 × 10−14

(4-56)

Kw is strongly temperature dependent (see Table 4.6 and Appendix D). Using our pX nomenclature: pKw = pKia − pKib

(4-57)

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Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

Table 4.5 Examples of Organic Bases Name

pKia (25◦ C) a (= pKiBH+ )

Structure

|

1–αia b (pH 7) |

Aliphatic and Aromatic Aminogroups(Ar − or R − N + −H ⇋ Ar − or R − N : + H + ) 4-Nitroaniline

|

O2N

NH 2

1-Naphthylamine

4-Chloroaniline

NH 2

Cl

NH 2

Aniline

NH 2

N,N-Dimethylaniline

N

Trimethylamine

N

n-Hexylamine

NH 2

Piperidine

NH

Heterocyclic Nitrogen 4-Nitropyridine 4-Chloropyridine

O2N

N

Cl

N

Pyridine

N

Isoquinoline

N

Benzimidazole

N

(

N H

1.01

|

< 0.999

3.92

0.999

3.99

0.999

4.63

0.996

5.12

0.987

9.81

0.002

10.64

< 0.001

11.12

< 0.001

N + H +)

1.23

> 0.999

3.83

> 0.999

5.25

0.983

5.40

0.975

5.53

0.967

7.00

0.500

8.50

0.031

N H

Imidazole

N

Benzotriazole

N

H N N N H

a b

Data from Dean (1985) and Lide (1995). Fraction in neutral (base) form at pH 7 (Eq. 4-59).

Organic Acids and Bases I: Acidity Constant and Speciation

105

Table 4.6 Acidity Constants (pKia ) of Some Organic Acids and of H2 O at Different Temperatures Acid (i) (HA,

BH+ ) a

4-Nitrobenzoic acid Acetic acid 2-Nitrophenol Imidazole 4-Aminopyridine Piperidine H2 O a b

0◦ C

10◦ C

pKia b 20◦ C

30◦ C

40◦ C

4.78 7.45 7.58 9.87 11.96 14.94

3.45 4.76 7.35 7.33 9.55 11.61 14.53

3.44 4.76 7.24 7.10 9.25 11.28 14.16

3.44 4.76 7.15 6.89 8.98 10.97 13.84

3.45 4.77 6.78 8.72 10.67 13.54

For structures see Tables 4.4 and 4.5. Data from Dean (1985) and Schwarzenbach et al. (1988).

From Eq. 4-57, it follows that the stronger an acid is (low pKia ), the weaker the basicity of its conjugate base (high pKib ), while the stronger the base (low pKib ), the weaker its conjugate acid (high pKia ). Thus, a neutral base with a pKib value < 3 (i.e., the pKia of the conjugate acid > 11 at 25◦ C) will be present in water predominantly as a cation at ambient pH values. Effect of Temperature on Acidity Constants In analogy to the temperature dependence of partition constants (Eq. 4-34), the effect of temperature on Kia over a small temperature range can be described by: Kia (T2 ) = Kia (T1 ) ⋅ e

−

Δr H 0 R

[

1 T2

− T1

1

]

(4-58)

where Δr H 0 is the standard enthalpy of reaction of the reactions in Eqs. 4-43 and 455. In general, Δr H 0 is very small for strong acids and increases with increasing pKia value. Therefore, for stronger acids we may neglect the effect of temperature on Kia , whereas for very weak acids this effect is substantial. For example, the ionization constants of piperidine and water (Kw ) change by about one order of magnitude between 0 and 30◦ C, whereas for 4-nitrobenzoic acid or acetic acid, almost no temperature dependence is observed (Table 4.6). A Few Comments on Experimental Data Acidity has long been recognized as a very important property of some organic compounds. Experimental methods for determining acidity constants are well established, and one can find quite large databases of pKia values of organic acids and bases (e.g., Kort¨um et al., 1961; Perrin, 1972; Serjeant and Dempsey, 1979; Dean, 1985; Lide, 1995). The most common procedures discussed by Kort¨um et al. (1961) include titration, determination of the concentration ratio of acid–base pairs at various pH values using conductance methods, electrometric methods, and spectrophotometric methods. The pKia values reported in the literature are often “mixed acidity constants,” commonly measured at 20 or 25◦ C, and at a given ionic strength (e.g., 0.05 – 0.1 M salt

106

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

solution). Depending on the type of measurement and the conditions chosen, reported pKia values might vary by as much as 0.3 pKa units. Also, primarily depending on the strength of an acid or base, the effect of temperature may be more or less pronounced (Table 4.6). Speciation in Natural Waters Given the pKia of an organic acid or base, we can now ask to what extent this compound is ionized in natural waters. The pH of natural water is primarily determined which are usually by various inorganic acids and bases (e.g., H2 CO3 , HCO−3 , CO2− 3 present at much higher concentrations than organic compounds of interest (see Chapter 5). These acids and bases act as hydrogen ion buffers (pH buffers), meaning that the addition of a very small quantity of an organic acid or base will not cause significant change in pH. We can easily visualize this buffering effect by the following simple example. Let us assume that of a hypothetical acid–base pair with pKia = 7.00, its undissociated and its dissociated forms are present at equal concentrations in one liter of water, say, 10−3 mol L−1 . According to Eq. 4-52, the pH of this aqueous solution will be: pH = 7.00 + log

10−3 mol L−1 = 7.00 10−3 mol L−1

If we now add 10−5 moles of a strong organic acid, (i.e., effectively, we add 10−5 moles H+ and A− each), the pH would change by less than 0.01 units: pH = 7.00 + log

0.99 × 10−3 mol L−1 = 6.991 1.01 × 10−3 mol L−1

As a first approximation, we may assume that adding a “trace” organic acid or base (where trace < 0.1 mM) to natural water will, in most cases, not substantially affect the pH of the water.

fraction in acid form (αia)

1

For a given pH, we may now express the fraction of our organic acid (denoted as HA, the same holds for BH+ ) present in the acid form in the water, αia , by:

0.8 0.6

αia =

0.4

0.2 0

–3 –2 –1 pKia +1 +2 +3 pH

Figure 4.3 Fraction in acid form as function of pH. At pH = pKia , the acid and base forms are present at equal concentrations, i.e., [HA] = [A− ]; [BH+ ] = [B].

[HA] = [HA] + [A− ]

1 1 1 = = Kia [A− ] 1 + 10(pH-pKia ) 1+ 1+ [HA] {H+ }

(4-59)

Now, αia or (1–αia ) values for various acids and bases in water at pH 7 can be readily calculated (Tables 4.4 and 4.5). One can also readily picture the fraction of the acid (or base) form of a given acid (or base) as a function of pH (Fig. 4.3). We re-emphasize that the neutral and ionic “forms” of a given neutral acid (base) behave very differently in the environment. Depending on the process considered, either the neutral or ionic species may be the dominant chemical species participating in the compound’s partitioning or reactivity, even if the relative amount of that species is very low.

107

Organic Acids and Bases II: Chemical Structure and Acidity Constant

4.4

Organic Acids and Bases II: Chemical Structure and Acidity Constant Overview of Acid and Base Functional Groups Since environmental systems typically have pH values between 4 and 9 (Fig. 5.10), we are primarily interested in compounds having pKia values in the range of 2 to 11. Therefore, the most important functional groups we have to consider include aliphatic and aromatic carboxyl groups, aromatic hydroxyl groups (e.g., phenolic compounds), aliphatic and aromatic amino groups, nitrogen atoms incorporated in aromatic compounds, and aliphatic or aromatic thiols and sulfonic acids (Tables 4.4 and 4.5). The range in pKia values for a given functional group may vary by many units because of the structural characteristics of the rest of the molecule. Depending on the type and number of substituent groups on the aromatic ring, for example, the pKia values for substituted phenols may differ by almost 10 units (Table 4.4). Therefore, it is necessary that we make an effort to understand the effects of various structural entities on the acid or base properties of a given functional group. To this end, we recall that the standard free energy, Δr G0 , for the proton dissociation reaction is given by the difference in the standard free energies of formation of the acid and conjugate base in aqueous solution (Eq. 4-48). Therefore, when comparing acidity constants of compounds exhibiting a specific acid or base functional group, the question is simply how much the rest of the molecule favors (decreases the free energy of formation) or disfavors (increases the free energy of formation) the ionic versus the neutral form of the compound in aqueous solution. Hence, we have to evaluate electronic and steric effects of substituents on the relative stability of the acid–conjugate base couple considered. Inductive Effects Let us first consider a simple example, the influence of a chloro-substituent on the pKia of butyric acid: i=

CH3CH2CH2COOH

CH2CH2CH2COOH

4.81

4.52

CH3CH2CHCOOH Cl

Cl

Cl pKia

CH3CHCH2COOH 4.05

2.86

In this example, we see that if we substitute a hydrogen atom by chlorine, which is much more electronegative than hydrogen (see Chapter 2, Table 2.5), the pKa of the carboxyl group decreases. Furthermore, the closer the electron-withdrawing chlorine substituent is to the carboxyl group, the stronger its effect in decreasing the pKia . We can intuitively explain these findings by realizing that any group that will have an electron-withdrawing effect on the carboxyl group (or any other acid function) will help to accommodate a negative charge and increase the stability of the ionized form. In the case of an organic base, an electron-withdrawing substituent will, of course, destabilize the acidic form (the cation) and also lower the pKia . This effect is called a negative inductive effect (–I). Most functional groups with which we are concerned

108

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

Table 4.7 Inductive and Resonance Effects of Some Common Substituentsa Effect b

Substituents Inductive

+I −I

O− , NH− , alkyl SO2 R, NH+3 , NO2 , CN, F, Cl, Br, COOR, I, COR, OH, OR, SR, phenyl, NR2 Resonance

+R −R a b

F, Cl, Br, I, OH, OR, NH2 , NR2 , NHCOR, O− , NH− NO2 , CN, CO2 R, CONH2 , phenyl, COR, SO2 R

Data from Clark and Perrin (1964). A plus sign means that the effect increases the pKia ; a minus sign means that the effect decreases the pKia .

have inductive electron-withdrawing (–I) effects (Table 4.7), but only a few such as alkyl groups have electron-donating (+I) effects: i= pKia

CH3COOH

CH3CH2COOH

4.75

4.87

As illustrated by the chlorobutyric acids, in saturated molecules, inductive effects usually fall off quite rapidly with distance. Resonance Effects In unsaturated chemicals, such as aromatic or olefinic compounds (i.e., compounds with “mobile” π-electrons; see Chapter 2), the inductive effect of a substituent may be felt over larger distances (i.e., more bonds). In such systems, however, another effect, the delocalization of electrons, may be of even greater importance. In Chapter 2, we learned that the delocalization of electrons (i.e., the “smearing” of π-electrons over several bonds) may significantly increase the stability of an organic species. In the case of a deprotonated organic acid, delocalization of the negative charge may lead to a considerable decrease in the pKa of a given functional group, as one can see from comparing the pKa of an aliphatic alcohol with that of phenol (Fig. 4.4).

CH3

OH

CH3

OH

O

H+ +

+ H+

pKa = 16

O

pKa = 9.92

O

Figure 4.4 Effect of delocalization on the pKia of an –OH group.

O

O

109

Organic Acids and Bases II: Chemical Structure and Acidity Constant

para-nitrophenol O

O N

OH

H+ +

HO

N

O

O

O

N

O

N

O

N

O

O

pK ia = 7.15 O

O N

O O

O

O O meta-nitrophenol OH O

N

H+ +

O O

O

N

O O

O

N O

pK ia = 8.36

O

O O

Figure 4.5 Influence of the position of a nitro substituent on the pKia of a phenolic hydrogen.

O

N O

N O

In the next step, we introduce a substituent on the aromatic ring, which through the aromatic π-electron system, may develop shared electrons (i.e., through “resonance” or “conjugation”) with the acid or base function (e.g., the –OH or –NH2 group). For example, the much lower pKia value of para-nitrophenol as compared with meta-nitrophenol may be attributed to additional resonance stabilization of the anionic species by the para-positioned nitro group (Fig. 4.5). In the meta position, only the electron-withdrawing negative inductive effect of the nitro group is felt by the –OH group. Other substituents that increase acidity (i.e., that lower the pKia through a resonance or “–R” effect) are listed in Table 4.7. All of these substituents can help to accommodate electrons. In contrast, substituents with heteroatoms having nonbinding electrons that may be in resonance with the π-electron system, have an electron-donating resonance effect (+R, Table 4.7), and, therefore, decrease acidity (i.e., increase pKa ). Many groups that have a negative inductive effect (–I) have a positive resonance effect (+R) at the same time. The overall impact of such substituents depends critically on their location in the molecule. In monoaromatic molecules, for example, resonance in the meta position is negligible, but will be significant in both the ortho and para positions.

110

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

O HO

HO

O

C

OH

O pK a = 9.32

O

O

C

O C

C OH

OH

C

O pK a = 4.48

Figure 4.6 Example of a proximity effects on the acidity constant: hydrogen bonding.

O

O

C

O

O pK a = 2.97

O

H

pK a = 13.40

O

Proximity Effects Another important group of effects are proximity effects. These effects arise from the influence of substituents that are physically close to the acid or base function under consideration. Here, two intramolecular (within the same molecule) interactions are important: hydrogen bonding and steric effects. An illustration of the effect of intramolecular hydrogen bonding can be seen by comparing para- and ortho-hydroxybenzoic acids (Fig. 4.6). The stabilization of the carboxylate anion by the hydroxyl hydrogen in ortho-hydroxy-benzoic acid (salicylic acid) leads to a much lower pKa1 value and to a much higher pKa2 value as compared with para-hydroxobenzoic acid in which no intramolelcular hydrogen bonding is possible. In some cases, steric effects may have a measurable impact on the pKia of a given acid or base. Such effects include steric constraints that inhibit optimum solvation of the ionic species by the water molecules (and thus increase the pKia ). Also, steric juxtaposition of moieties may cause groups to twist with respect to one another and thereby hinder co-planarity needed to enable resonance of the electrons of a acid or base group with other parts of the molecule. This can impact pKia . In summary, the most important factors influencing the pKia of a given acid or base function are inductive, resonance, and, sometimes, proximity effects. The impact of a substituent on the pKia depends critically on where the substituent is located in the molecule relative to the acid or base group. In one location, a given substituent may have only one of the mentioned effects, while in another location, all effects may play a role. Therefore, it is quite difficult to establish simple general rules for quantifying the effects of structural entities on the pKia of an acid or base function. Nevertheless, in certain cases, a quantification of the effects of substituents on the pKia value is possible. In the following section, we discuss one example of such an approach, the Hammett correlation for substituted aromatic compounds. Estimation of Acidity Constants: The Hammett Relationship A long time ago, Hammett (1940) recognized that for substituted benzoic acids (see Fig. 4.7) the effect of substituents in either the meta or para position on the standard free energy change of the carboxyl group’s dissociation could be expressed as the sum

Organic Acids and Bases II: Chemical Structure and Acidity Constant

111

substituted benzoic acids COOH

COOH

COOH

CH3

Cl

COOH

COOH

i=

pKia ΔpK ia

4.19 0.00

4.35 +0.16

NO 2

Cl

3.97 –0.22

3.82 –0.37

3.48 –0.71

substituted phenylacetic acids COOH

COOH

COOH

CH 2

CH 2

CH 2

H

CH3

Cl

COOH

COOH

CH 2

CH 2

i=

pKia ΔpK ia

4.28 0.00

4.36 +0.08

NO 2

Cl

4.19 –0.09

4.11 –0.17

3.90 –0.38

OH

OH

substituted phenols OH

OH

OH

H

CH3

Cl

i=

Figure 4.7 Effects of ring substituents on the pKa of benzoic acid, phenyl acetic acid, and phenol.

pKia ΔpK ia

9.90 0.00

10.25 +0.35

NO 2

Cl

9.29 –0.61

8.98 –0.92

8.36 –1.54

of the free energy change of the dissociation of the unsubstituted compound, Δr G0H , and the contributions of various substituents; Δr G0j : Δr G0 = Δr G0H +

∑ j

Δr G0j

(4-60)

To express the effect of substituent j on the pKa , Hammett introduced a constant σj , which is defined as:

σj =

−Δr G0j 2.303RT

(4-61)

Since meta and para substitutions result in different combinations of inductive and resonance effects, there are two sets of σj values, σjmeta and σjpara . Ortho substitution is excluded because as previously discussed, proximity effects, which are difficult to separate from electronic factors, may play an important role. Since Δr G0 = –2.303

112

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

Table 4.8 Hammett Constants for Some Common Substituents a Substituent j

σjmeta

σjpara

Substituent j

σjmeta

σjpara

−H − CH3 − CH2 CH3 − CH2 CH2 CH2 CH2 − C(CH3 ) 3 − CH = CH2 − C6 H5 (phenyl) − CH2 OH -− CH2 Cl − CCl3 − CF3 −F − Cl − Br −I

0.00 −0.06 −0.06 −0.07 −0.10 0.08 0.06 0.07 0.12 0.40 0.44 0.34 0.37 0.40 0.35

0.00 −0.16 −0.15 −0.16 −0.20 −0.08 0.01 0.08 0.18 0.46 0.57 0.05 0.22 0.23 0.18

− OH − OCH3 − OCOCH3 − CHO − COCH3 − COOCH3 − CN − NH2 − NHCH3 − N(CH3 ) 2 − NO2 − SH − SCH3 − SOCH3 − SO2 CH − SO−3

0.10 0.11 0.36 0.36 0.38 0.33 0.62 −0.16 −0.25 −0.15 0.73 0.25 0.13 0.50 0.68 0.05

−0.36 −0.24 0.31 0.22 0.50 0.45 0.67 −0.66 −0.84 −0.83 0.78 0.15 0.01 0.49 0.72 0.09

a

σ−jpara −0.12 1.03 0.82 0.66 0.89

1.25

Data from Dean (1985) and Shorter (1994 and 1997).

RT log Ka (Eq. 4-50), we may write Eq. 4-60 in terms of acidity constants, omitting subscript i to denote the acid function: log

∑ Ka = σj KaH j

or

pKa = pKaH −

∑

σj

(4-62)

j

Table 4.8 lists σjmeta and σjpara values for some common substituent groups. These σ values are a quantitative measurement of a given substituent’s effect on the pKa of benzoic acid. As we would expect from our previous discussion, the sign of the σj value reflects the net electron-withdrawing (positive sign) or electron-donating (positive sign) character of a given substituent in either the meta or para position. For example, we see that –NO2 and –CN are strongly electron-withdrawing in both positions, whereas the electron-providing groups, –NH2 or –N(CH3 )2 , are strongly electron-donating in the para position, but show a much weaker effect in the meta position. The differences between σjmeta and σjpara of a given substituent are due to the difference in importance between the inductive and resonance effects which, as we mentioned earlier, may have opposite signs (see Table 4.7). Let us now examine the effects of the same substituents on the pKia of another group of acids, the substituted phenyl acetic acids (Fig. 4.7). As we might have anticipated, the various substituents exert the same relative effect as in their benzoic counterparts. However, in the case of phenyl acetic acid, the greater separation between substituent and reaction site makes the impact less pronounced than in the benzoic acid. Plot∑ ting pKaH –pKa values for meta- and para-substituted phenyl acetic acids versus σj values results in a straight line with a slope, ρ, of less than 1 (Fig. 4.8). In this case, introduction of a substituent on the aromatic ring has only about half the effect on

Organic Acids and Bases II: Chemical Structure and Acidity Constant

2.25

Ka = ρΣσ j j KaH OH (ph eno ls)

log

ρ=

3

113

1. 00

2

C O O R

,X

R,X

1

KaH

OH CO CH 2 ρ = R,X

9

COOH CH 2CH 2

0

Figure 4.8 Hammett plots for meta- and para-substituted phenols, phenylacetic acids, and 3-phenylpropionic acids; data from Serjeant and Dempsey (1979).

0.4

ρ = 0.21

log

Ka

or pKaH – pKa

H

=

ρ

–1 –1

R,X

0

1

2

Σσ j j

the pKa as compared with the effect of the same substituent on the pKa of benzoic acid. Thus, ρ is a measure of how sensitive the dissociation reaction is to substitution as compared with substituted benzoic acid. It is commonly referred to as the susceptibility factor that relates one set of reactions to another. If we consider another group of acids, the substituted β-phenyl propionic acids, where the substituents are located at even greater distances from the carboxyl group, even smaller ρ values are found (ρ = 0.21, Fig. 4.8). If we express these findings in energetic terms, we obtain the classical form of the Hammett Equation: ∑ σj (4-63) Δr G0 = Δr G0H − ρ(2.303RT) j

Expressed in terms of equilibrium constants (i.e., acidity constants): ∑ logKa = logKaH + ρ σj j

or pKa = pKaH − ρ

∑ j

(4-64) σj

114

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

Table 4.9 Hammett Relationships for Quantification of Aromatic Substituent Effects on the Acidity of Various Acids a Acid CH2 CH2 COOH

pKaH (pKa of unsubstituted compound)

ρ

4.55

0.21

3.17

0.30

4.30

0.49

4.19

1.00 (by definition)

9.90

2.25 b

4.63

2.90 b

5.25

5.90 b

R,X O

CH2 COOH

R,X CH2 COOH R,X COOH R,X OH R,X NH3+ R,X NH+ R,X a Eq. 4-64; data from Williams (1984). b Use σ−jpara instead of σjpara for substituents that are in direct resonance will the acid function (Table 4.8).

pKaH and ρ values have been found for a variety of aromatic substituents on various types of aromatic acids (Table 4.9). For compound classes such as phenols, anilines, and pyridines where the acid (base) function is in resonance with the aromatic ring, the ρ values obtained are significantly greater than 1; that is, the electronic effect of the substituents is greater than in the case of benzoic acid. A simple case where the general σ constants in Table 4.8 do not succeed in correlating acidity constants occurs when the acid or base function is in direct resonance with the substituent. This may happen in cases such as substituted phenols, anilines, and pyridines. For example, owing to resonance (see Fig. 4.5), a para nitro group decreases the pKa of phenol much more than would be predicted from the σjpara constant obtained from the dissociation of p-nitrobenzoic acid (another example would be the anilines). In such “direct resonance” cases, a special set of σ values (denoted as σ−jpara ) has been derived (Table 4.8) to try to account for both inductive and direct resonance effects. If these values are employed, good correlations are obtained, as shown for meta- and para-substituted phenols in Fig. 4.8. We stated earlier that because of differential proximity effects on various acid functions, a single set of σ values for ortho substitution cannot be found for all aromatic

115

Organic Acids and Bases II: Chemical Structure and Acidity Constant

Table 4.10 Examples of Apparent Hammett Constants for ortho-Substitution in Phenols and in Anilines a phenols

Substituent j

σjortho

σanilines jortho

− CH3 − CH2 CH2 CH2 CH3 − CH2 OH −F − Cl − Br −I

−0.13 −0.18 0.04 0.54 0.68 0.70 0.63

0.10

a

0.47 0.67 0.71 0.70

Substituent j − OH − OCH3 − CHO − NH2 − NO2

phenols

σjortho

0.00 0.75 1.24

σanilines jortho −0.09 0.02 0.00 1.72

Data from Clark and Perrin (1964) and Barlin and Perrin (1966).

acids. Nevertheless, one can determine a set of σjortho values for a specific type of reaction, as for example (called “apparent” σ constants). For example, for the dissociation of substituted phenols one can find a set of σjortho values that work for other phenols (Table 4.10). Such apparent σjortho constants are used for estimating pKa values of substituted phenols and anilines. Of course, in cases of multiple substitutions, substituents may interact with one another, thereby resulting in larger deviations of experimental from predicted pKia values. In our discussion of the Hammett correlation, we confine ourselves mostly to benzene derivatives. Of course, a similar approach can be taken for other aromatic and aliphatic systems, such as for the derivatives of polycyclic aromatic hydrocarbons, heterocyclic aromatic compounds, and aliphatic acids. For a discussion of such applications, we refer to papers by Clark and Perrin (1964), Barlin and Perrin (1966), and Perrin (1980). Using the Hammett equation as a starting point, a variety of refinements using more sophisticated sets of constants have also been suggested. The interested reader can find a treatment of these approaches in various textbooks, as well as compilations of substituent constants (e.g., Taft, 1956; Hine, 1975; Lowry and Schueller-Richardson, 1981; Williams, 1984; Exner, 1988) and in data collections (e.g., Harris and Hayes, 1982; Dean, 1985; Hansch et al., 1991; Hansch et al., 1995a and b). Finally, our discussion on the Hamlett correlation is not only important for understanding the effect of structural entities on the pKia of acids and bases, but will also be very useful for evaluating what such effects have on the reactivity of organic compounds where electronic and steric effects play an important role (see Chapter 22). Furthermore, it is an example of a so-called linear free energy relationship (LFER). Such approaches for correlation are called extra-thermodynamic or outside thermodynamics. They rely on the understanding of how a portion of a molecule’s structure influences properties through incremental changes in intermolecular interactions or reactivities through inductive, resonance, and steric effects. Such extra-thermodynamic methods will allow us to link chemical structures to their properties. We will encounter more of these LFERs throughout the book (e.g., in Chapter 7).

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4.5

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Questions Q 4.1 Give at least three reasons why, in environmental organic chemistry, it is so important to understand the equilibrium partitioning behavior of a given organic compound between gaseous, liquid, and solid phases. Q 4.2 One of your friends has difficulty understanding what the chemical potential of a given compound in a given system expresses. Try to explain it in words to him or her. What do the quantities fugacity and activity describe? How are they related to the activity coefficient? Q 4.3 What are the advantages and disadvantages of choosing the pure liquid compound as reference state? When would you use a different reference state? Which one? Q 4.4 What is meant by excess free energy, excess enthalpy, and excess entropy? How are they related to each other? Q 4.5 Which thermodynamic function needs to be known for assessing the temperature dependence of equilibrium partitioning? How can this function be derived from experimental data? What caution is advised when extrapolating partition constants from one temperature to another temperature? Q 4.6 Name at least four different acid or base functional groups present in environmental organic chemicals. Which factors determine the pKa of a given acid or base function? Indicate the pKa ranges of the various functions. Q 4.7 Explain the terms inductive effect and resonance effect of substituents. What makes a substituent exhibit a negative resonance effect? Which types of substituents have a positive resonance effect? Can a given substituent exhibit a negative inductive and a positive resonance effect at the same time? If yes, give some examples of such substituents.

Questions and Problems

117

Q 4.8 How are the Hammet σjmeta and σjpara substituent constants defined? Are there cases in which the σjpara values are not applicable? If yes, give some examples. Q 4.9 For –OH and –OCH3 , the σjmeta values are positive, whereas σjpara is negative (Table 4.8). Explain these findings. Q 4.10 As indicated, 1-naphthylamine and quinoline exhibit very different susceptibility factors ρ (2.81 versus 4.90) in the corresponding Hammett equations (Dean, 1985). Explain this fact. NH2 N

X,R

X,R 1-naphthylamine

pKa = 3.84 − 2.81

∑

quinoline

σj

pKa = 4.88 − 4.90

∑

j

σj

j

Q 4.11 The two isomers 2,4,6-trichlorophenol and 3,4,5-trichlorophenol have quite different pKia values. What are the reasons for this big difference? OH Cl

OH Cl Cl

Cl

Cl

Cl

i = 2,4,6-trichlorophenol (pKia = 6.15)

i = 3,4,5-trichlorophenol (pKia = 7.73)

Q 4.12 The pKia of the herbicide sulcotrion is 3.13 (Tomlin, 1994). Would you have expected that this compound is such a strong acid? Write down the structure of the conjugate base of sulcotrion and try to explain the rather strong acidity of this herbicide. O

O

Cl

O O

S O

i = sulcotrion

118

Background Thermodynamics, Equilibrium Partitioning and Acidity Constants

Problems P 4.1∗ Assessing the Speciation of Organic Acids and Bases in Natural Waters Calculate the fraction of (a) pentachlorophenol (PCP), (b) 3,4-dimethylaniline (DMA) present at 24◦ C as neutral species in a raindrop (pH = 4.0) and in lake water (pH = 8.0). OH Cl

Cl

Cl

Cl

NH2

Cl i = 3,4-dimethylaniline (DMA) pKia = 5.28

i = pentachlorophenol (PCP) pKia = 4.75

P 4.2∗ Estimating Acidity Constants of Aromatic Acids and Bases Using the Hammett Equation Estimate the pKia values at 25◦ C of (a) pentachlorophenol (PCP), (b) 4-nitrophenol (4-NP), (c) 3,4-dimethylaniline (3,4-DMA, pKia of conjugate acid), and (d) 2,4,5-trichlorophenoxy acetic acid (2,4,5-T), Use the Hammett relationship Eq. 4-62: pKia = pKaH − ρ

∑

σj

j

to estimate the pKia values of compounds (a) – (d). Get the necessary σ, pKaH , and ρ values from Tables 4.8, 4.9, and 4.10. OH

OH Cl

Cl

Cl

Cl NO2

Cl i = PCP

i = 4-NP

NH2

O Cl

O

Cl

Cl i = 2,4,5-T

i = 3,4-DMA

OH

Bibliography

119

P 4.3 Estimation of Acidity Constants and Speciation in Water of Aromatic Organic Acids and Bases Represent graphically (as shown in Fig. 4.3) the speciation of (a) 4-methyl-2,4dinitrophenol, and (b) 3,4,5-trimethylaniline as a function of pH (pH range 2-12) at 25◦ C. Estimate, the pKia values of the compounds. OH

NH2 NO2

O2N

i = 4-methyl-2,5-dinitrophenol

4.6

i = 3,4,5-trimethylaniline

Bibliography Abraham, M. H.; Whiting, G. S.; Fuchs, R.; Chambers, E. J., Thermodynamics of solute transfer from water to hexadecane. J. Chem. Soc.-Perkin Trans. 2 1990, (2), 291–300. Atkins, P. W.; de Paula, J., Physical Chemistry. 10th ed.; Oxford University Press: Oxford, 2014. Atkinson, D.; Curthoys, G., The determination of heats of adsorption by gas-solid chromatography. J. Chem. Educ. 1978, 55(9), 564–566. Barlin, G. B.; Perrin, D. D., Prediction of the strengths of organic acids. Quart. Rev. Chem. Soc. 1966, 20(1), 75–101. Brønsted, J. N.; Pedersen, K., Die katalytische Zersetzung des Nitramids und ihre physikalischchemische Bedeutung. Z. Phys. Chem. 1924, 108, 185–235. Clark, J.; Perrin, D. D., Prediction of the strengths of organic bases. Quart. Rev. Chem. Soc. 1964, 18(3), 295–320. Dean, J. A., Ed., Lange’s Handbook of Chemistry. McGraw-Hill: New York, 1985. Demianov, P.; Destefano, C.; Gianguzza, A.; Sammartano, S., Equilibrium studies in natural waters: Speciation of phenolic compounds in synthetic seawater at different salinities. Environ. Toxicol. Chem. 1995, 14(5), 767–773. Exner, O., Correlation Analysis of Chemical Data. Plenum Press: New York and London, 1988. Gibbs, J. W., XI. Graphical methods in the thermodynamics of fluids. Trans. Conn. Acad. 1873, 2, 309–342. Gibbs, J. W., V. On the equilibrium of heterogeneous substances. Trans. Conn. Acad. 1876, 3, 108–248. Hammett, L. P., Physical Organic Chemistry. McGraw-Hill: New York, 1940. Hansch, C.; Leo, A.; Heller, S. R., Fundamentals and Applications in Chemistry and Biology. ACS: Washington, D.C., 1995a. Hansch, C.; Leo, A.; Hoekman, D., Exploring QSAR, Hydrophobic, Electronic and Steric Constants. ACS: Washington D.C., 1995b. Hansch, C.; Leo, A.; Taft, R. W., A survey of Hammett substituent constants and resonance and field parameters. Chem. Rev. 1991, 91(2), 165–195. Harris, J. C.; Hayes, M. J., Acid dissociation constant. In Handbook of Chemical Property Estimation Methods, Lyman, W. J.; Reehl, W. F.; Rosenblatt, D. H., Eds. McGraw-Hill: New York, 1982; pp. 6-1–6-28.

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Hine, J., Structural Effects on Equilibria in Organic Chemistry. John Wiley: New York, 1975; p 347. Kort¨um, G.; Vogel, W.; Andrussow, K., Dissociation Constants of Organic Acids in Aqueous Solution. Butterworths: London, 1961. Lewis, G. N., The law of physico-chemical change. Proc. Am. Acad. 1901, 37, 49–69. Lide, D. R., Ed., CRC Handbook of Chemistry and Physics. 76th ed.; CRC Press: Boca Raton, FL, 1995; Vol. 1995–1996. Lowry, T. H.; Schueller-Richardson, K., Mechansisms and Theory in Organic Chemistry. Harper and Row: New York, 1981. Perrin, D. D., Dissociation Constants of Organic Bases in Aqueous Solution: Supplement 1972. Butterworths: London, 1972. Perrin, D. D., Prediction of pKa values. In Physical Chemical Properties of Drugs, Yalkowsky, S. H.; Sinkula, A. A.; Valvani, S. C., Eds. Dekker: New York, 1980. Prausnitz, J. M., Thermodynamics of Fluid-Phase Equilibria. Prentice-Hall: Englewood Cliffs, N.J., 1969. Schwarzenbach, R. P.; Stierli, R.; Folsom, B. R.; Zeyer, J., Compound properties relevant for assessing the environmental partitioning of nitrophenols. Environ. Sci. Technol. 1988, 22(1), 83–92. Serjeant, E. P.; Dempsey, B., Ionization Constants of Organic Acids in Aqueous Solution. Pergamon: New York, 1979. Shorter, J., Values of σm and σp based on the ionization of substituted benzoic acids in water at 25C. Pure Appl. Chem. 1994, 66(12), 2451–2468. Shorter, J., Compilation and critical evaluation of structure-reactivity parameters and equations: Part 2. Extension of the Hammett sigma scale through data for the ionization of substituted benzoic acids in aqueous organic solvents at 25 degrees C. Pure Appl. Chem. 1997, 69(12), 2497–2510. Stumm, W.; Morgen, J. J., Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters. 3 ed.; Wiley: 1996. Taft, R. W., Jr., Steric Effects in Organic Chemistry. Wiley-Interscience: New York, 1956. Tomlin, C., Ed., The Pesticide Manual. The British Crop Protection Council and the Royal Society of Chemistry: Cambridge, UK, 1994. Williams, A., Free-energy correlations and reaction mechanisms. In The Chemistry of Enzyme Action, Page, M. I., Ed. Elsevier: Amsterdam, 1984; pp 127–201.

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Chapter 5

Earth Systems and Compartments

5.1

Introduction Box 5.1 Definitions of Earth Systems and Compartments

5.2

The Atmosphere Vertical Structure of the Atmosphere Box 5.2 From Partial Pressures to Concentrations Transport and Mixing Chemical Composition of the Atmosphere

5.3

Surface Waters and Sediments The Ocean and the Global Water Cycle Box 5.3 Terms and Definitions to Describe Fractions of Organic Matter in Environmental Matrices Lakes Rivers Sediments and Sedimentation Box 5.4 Porosity of Sediments, Soils, and Subsurface Strata

5.4

Soil and Groundwater Structure and Composition of Soil Groundwater in the Saturated Zone

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

122

Earth Systems and Compartments

5.5

Biota

5.6

Questions

5.7

Bibliography

Introduction

123

In the preceding chapters, we had a first look at many of the problematic organic chemicals present in the environment. We learned of their great structural variability and obtained a qualitative glimpse of how these chemicals interact with each other. In this chapter, we describe the characteristics of the natural systems in the environment where these chemicals are transported, transformed, and stored.

5.1

Introduction A major pursuit of environmental organic chemistry is to make optimal use of available information, such as chemical concentration data, to understand the behavior of chemicals in specific environments and then to extend this knowledge to anticipate behavior of other chemicals in different environments. The diversity of natural systems and the continuously growing number of organic compounds with variable properties dictate the need for a “tunable” framework that allows us to organize and understand chemical concentration data as a function of space and time. In this book, we use mass balance models to interpret such data quantitatively. These models describe the combined influences of chemical inputs and outputs on the total amount of a compound in a specific compartment. They require information of two kinds: (i) properties of the environmental compartments that affect chemical behaviors within those spatially defined locations and (ii) the chemicals’ physicochemical characteristics that determine the equilibria and dynamics of the various processes acting on those chemicals. These processes include chemical and biological transformations like hydrolysis, photolysis, and biodegradation; phase transfers like air-water exchange and sorption; and transport phenomena like advection by currents and diffusive mixing. The needed mathematical tools to develop mass balance models are introduced in Chapter 6 and developed further in later chapters.

In modeling, we use the term “compartment” to denote a physical part of the environment, like the global atmosphere, a particular lake, or the soil of an agricultural field (see Box 5.1). Although these examples may suggest a focus on the three phases: gas, liquid, and solid, this classification can be misleading. For example, the atmosphere is not just composed of gases but also contains suspended liquids (e.g., fog) and solids (e.g., dust). Likewise, one finds suspended solids in lakes and gaseous pore Condensed phases in atmosphere. space in soil. Photo: Brocken Inaglory (2008). For modeling of global-scale problems, relevant environmental compartments are the atmosphere, the oceans and their sediments, and the soil and its groundwater (Table 5.1). Often, we are concerned with more “local” problems for which non-global compartments such as a particular lake, its sediments, and its inlets and outlets are relevant. Depending on the properties of the compound under consideration, some of the local compartments may be important, others not. For example, in order to quantify the fate of chemicals discharged to a lake, the water column may be the only relevant compartment for some chemicals, whereas inclusion of the sediment bed may be necessary for other compounds.

124

Earth Systems and Compartments

Box 5.1

Definitions of Earth Systems and Compartments

Compartment: A part of the physical environment that is defined by a spatial boundary that distinguishes it from the rest of the world. Examples: atmosphere, lake sediments, Atlantic ocean, soil, Ogallala aquifer System: Used in mathematical modeling to identify the part of the world (physical, societal, political, economic…) which is the object of a model. Systems can include one or more physical compartments and/or non-physical parts of the world like the economy of a country. Examples with increasing numbers of compartments: a lake a lake + its sediments a lake + its sediments + its drainage area a lake + its sediments + its drainage area + the neighboring municipality a lake + its sediments + its drainage area + the neighboring municipality + the regional industries Phase: The physical aggregation state (gaseous, liquid, or solid) of a homogeneous material. Example: Benzene and water are two liquid phases; but benzene, dissolved in water, is a single phase. Medium: The carrier or environment in which a phase exists. Example: A calcium carbonate particle, suspended in the ocean, is a solid phase in the seawater medium. Matrix: Similar to, and sometimes interchangeable with, the term medium. It is primarily used if the surroundings are heterogeneous. Example: A calcium carbonate shell, found in a soil consisting of solids coated with aqueous films and including pore spaces filled with gases, is a solid phase in the soil matrix.

Table 5.1 Global-Scale Compartments: Mass, Volume, Area, and Density

Mass (kg) Area (m2 ) Volume (m3 ) Depth (m) Mass per area (kg m−2 ) Density (kg m−3 ) a

Earth a

Atmosphere a

Ocean

Soil b

6.0 × 1024 5.10 × 1014 1.08 × 1021

5.1 × 1018 c 5.10 × 1014 5.10 × 1018 1 × 104 1.0 × 104 1.29 d

1.4 × 1021 3.6 × 1014 1.4 × 1018 3.8 × 103 3.9 × 106 1.04 × 103

∼ 2 × 1017 1.3 × 1014 b ∼ 1.3 × 1014 ∼ 1b ∼ 1.5 × 103 ∼ 1.5 × 103 b

5.5 × 103

Data from Williams, D. R. (2013). Soil depths range widely (from 0 to more than 200 cm); here we assume a soil depth of 100 cm, have a bulk density of 1.5 g cm−3 (see Batjes, N. H., 1996), and cover 1.3 × 1014 m2 of ice-free land surface. c The troposphere contains about 80% of the total atmospheric mass. On average it extends to 10 km above the Earth’s surface (Fig. 5.1). The stratosphere (height 10 to 50 km on average) contains almost all of the remaining mass. The mass contribution from the higher layers (mesosphere, thermosphere, exosphere) is negligible. d For dry air at pressure po = 1 bar (sea level) at T = 0◦ C. b

The Atmosphere

125

The following sections introduce three major global compartments: the atmosphere (largely gaseous air), the ocean (mostly liquid seawater), and the pedosphere (chiefly solid components). Smaller compartments are discussed within the global systems with which they are most closely related. For instance, lakes and rivers are discussed in the ocean section, whereas groundwater is treated in the soil section. Finally, we mention global biota, the “compartment” consisting of all living organisms. We provide information on the typical size of each compartment, as well as the variation in their properties that may influence chemical partitioning processes and transformations. We provide typical ranges for properties like temperature, pressure, porosity, pH, ionic composition, and concentration of organic matter.

5.2

The Atmosphere The atmosphere is the only compartment that spreads over the globe’s whole surface. Global-scale transport of chemicals, both vertically and horizontally, is relatively fast (weeks to years) compared to transport in other compartments like the ocean or soils (millennia). Therefore, for many chemicals, transport in the atmosphere is the most important mechanism for global distribution. However, the atmosphere does not usually function as the major reservoir of man-made chemicals. Notable exceptions are persistent volatile chemicals like chlorofluoromethanes (freons). Vertical Structure of the Atmosphere In terms of its internal structure, the atmosphere is the least complex global compartment. In the vertical direction, the troposphere and the stratosphere (Fig. 5.1) are the

70 60 -

mesosphere

40 stratosphere

20 -

inversion

ra tur e

30 -

highest clouds

em pe

Figure 5.1 The atmosphere is divided into horizontal layers (troposphere, stratosphere, mesosphere and higher layers not shown) that are confined by heights where the temperature gradient changes sign (tropopause and stratopause). Under special weather conditions, temperature in the troposphere increases with height; such conditions, called inversions, are zones of suppressed vertical mixing.

stratopause

temperature

air t

altitude (km)

50 -

tropopause

10 troposphere 200

250

300 temperature (K)

350

126

Earth Systems and Compartments

most important layers when modeling chemical fate. The troposphere is the lowest layer, which includes 80% of the atmospheric mass and is where most of the weather phenomena occur. A narrow layer, called the tropopause, separates the troposphere from the stratosphere, and is characterized by a vertical temperature minimum and a sign change in the temperature gradient. The altitude of the tropopause occurs between 7 km (polar regions) and 17 km (equator), but these heights vary seasonally. The upper boundary of the stratosphere, the stratopause, lies at a height of about 50 km. Here, the vertical temperature gradient again changes sign. Combined the troposphere and stratosphere contain nearly 100% of the atmospheric mass. Air Pressure and Density in the Troposphere. In the troposphere, the total mean air pressure, p, decreases exponentially with height, h: p (h) = p(h = 0)e−h∕L ; with L = 8000 m

Box 5.2

(5-1)

From Partial Pressures to Concentrations

Unit Conversions for Methane in the Atmosphere The abundance of a trace molecule i in air (e.g., methane, CH4 ) is often given in partial pressure, pi (e.g., in bar), or in relative partial pressure, pi /p, i.e., in part per million by volume (ppmv), because this latter number remains approximately constant as the particular air parcel changes altitude. Using the ideal gas law, the concentration in mole per liter, Ci , or the number of molecules per cm3 can be calculated as: pi V = xi pV = xi RT ⇒ Ci =

xi p = xi (mol L−1 ); molecules per volume = Ci NA V RT

where R = 0.083145 L bar mol−1 K−1 is the gas constant; p is total pressure; pi (bar) is the partial pressure of molecule i; xi is mole fraction of molecule i; T (K) is absolute temperature; and NA = 6.02 × 1023 molecules mol−1 is Avogadro’s number. As an example, we consider air containing 1 ppmv of methane at two heights above the ground: 0 m and 10,000 m, where the air temperatures are 293 K and 223 K, respectively. Answer At 0 m altitude:

pi = 10−6 p = 10−6 bar Ci = 4.1 × 10−8 mol L−1 or 2.5 × 1016 molecules L−1

At 10,000 m:

p = 1 bar × exp(–10,000/8,000) = 0.29 bar pi = 10−6 p = 0.29 × 10−6 bar Ci = 1.6 × 10−8 mol L−1 or 9.4 × 1015 molecules L−1

Note: At 10,000 m altitude, total pressure is 29% of pressure at sea level, but due to the temperature decrease the number of methane molecules per volume is 38% of the number at sea level.

The Atmosphere

127

where p (h = 0) = 1 atm = 1.0133 bar = 1.0133 × 105 Pa is total air pressure at sea level, h is height above ground, and L is a characteristic length scale that describes how fast p decreases with height. L is the altitude at which ln [p (h)/ p (h = 0)] = e−1 = 0.37. Usually, the total air pressure at a height of 8000 m has dropped to about 0.37 × 105 Pa. A similar approximation can be used for air density; it exponentially decreases with height from its value for dry air at sea level of ρo = 1.29 kg m−3 . This exponential approximation should not be extrapolated into the stratosphere and beyond since the length scale L increases with h. That is, the exponential curve of Eq. 5-1 is only a first approximation. Nonetheless, Eq. 5-1 is very useful because it enables us to convert partial pressures of individual compounds present at various altitudes in the troposphere into corresponding concentrations like moles per liter of air or molecules per cm3 of air (Box 5.2). Transport and Mixing As all of us have experienced the wild caprices of weather, we all know that mixing in the atmosphere can be irregular, even chaotic, and difficult to forecast beyond a couple of days. Nonetheless, atmospheric mixing exhibits some general patterns when data are averaged over space and time. In the following discussion, we distinguish between vertical and horizontal mixing. Vertical mixing over the total height of the troposphere is often fairly fast (hours to a few days). An exception occurs during inversions, special weather situations where a layer of cold air lies underneath a layer of warm air, causing a strong vertical density gradient and a significant reduction in vertical exchange (see Fig. 5.1). Likewise, mixing across the tropopause (another thermally stratified layer) is slow compared to vertical mixing within the troposphere. Trans-tropopause transport mainly occurs in the spring and autumn when large storms in the troposphere temporarily destroy the vertical density gradient in the tropopause. At these times, significant volumes of air are exchanged between troposphere and stratosphere. Due to the generally minimal mixing across the tropopause, natural compounds produced in the stratosphere like ozone (O3 ), or man-made chemicals like freons (e.g., CCl2 F2 ) that do not degrade in the troposphere and hence are transported across the tropopause, can remain in the stratosphere for several years. As a result, the stratosphere serves as a significant storage compartment for these compounds. On a local scale, horizontal transport and mixing is as variable as the local wind field and impossible to predict over time scales larger than a few days. However, on a global scale, distinct horizontal wind patterns exist that are linked to the fact that solar radiation at high latitudes is smaller than at low latitudes. To reach a local thermal energy balance everywhere on the globe, heat must be transported from the surplus areas at low latitudes to the deficit areas at high latitudes. About half of the thermal energy flux is provided by ocean currents and the other half by atmospheric flow. In the atmosphere, thermal energy is transported both as sensible heat (warm air) and as latent heat (moist air). The sensible heat mechanism causes warm air at low latitudes to rise to the upper troposphere where it flows to higher latitudes. The rising warm air is replaced by cooler (and more dense) air, flowing through the lower troposphere from higher latitudes. After some time, the upper air loses much of its extra heat and sinks

128

Earth Systems and Compartments

down again. These flow patterns create three distinct circulation cells in each hemisphere, with neighboring cells circulating in opposite directions (see Hadley, Ferrel, and Polar cells in Fig. 5.2a). The boundaries between the circulation cells, especially at the Equator, are zones where air flows in north-south directions are inhibited. Sailors feared these latitudes, dubbed the equatorial doldrums, as they were often stuck in the calms.

subtropical jet polar jet

(a) tropopause polar cell North pole

60°N

30°N

generalized sketch of global atmospheric circulation

(b) vertical motion

rising airpolar front

Figure 5.2 Schematic of average atmospheric circulation. (a) In both hemispheres, large differences in surface heating by sunlight from the equator to the poles leads to three circulation cells of rising warm air and descending cold air (Hadley, Ferrel and Polar cells). Air pressure is low and cloud formation high where rising air meets another circulation cell. The boundaries between the circulation cells, especially at the equator, are zones where north-south transport is limited. Graphic: NOAA (2011). (b) The Earth’s rotation deflects air flows near the surface from the north-south axis into the latitudinal direction, thus leading to a distinct pattern of latitudes with westerly and easterly winds. Graphic: Niemi (2002).

Hadley cell

Ferrel cell

sinking airsubtropical high

surface winds 90°N polar Easterlies 60°N Westerlies 30°N Northeast trade winds

rising airequatorial low (ITCZ) sinking airsubtropical high

0° Southeast trade winds 30°S Westerlies 60°S polar Easterlies

rising airpolar front

90°S

equator

The Atmosphere

129

Actually, the global wind pattern is even more complicated (see Fig. 5.2b). The Earth’s rotation deflects latitudinal air flow to the right in the northern hemisphere and to the left in the southern hemisphere. For instance, the air flowing in the lower troposphere toward the Equator (see Hadley Cell in Fig. 5.2a) is deflected into the east-to-west direction creating “trade winds” at low latitudes (see Fig. 5.2b), and west-to-east flows in the upper troposphere. This directed air flow in the higher troposphere leads to strong winds called “jets.” One key outcome of this global air flow pattern is that latitudes between the atmospheric circulation cells act as bottlenecks inhibiting longitudinal atmospheric mixing. The most distinct of these bottlenecks is at the equator. As a result, mixing between the northern and southern hemispheres occurs on a time scale of several months to years. Therefore, we often see poor north-south mixing of persistent organic pollutants (POPs) that are mostly introduced into the environment in the northern hemisphere. As an example, Weber and Goerke (2003) observed persistent compounds like PCBs, chlordane, and mirex, all heavily used in countries north of the Equator until the 1970s and 1980s, still show increasing concentrations in fish living near Antarctica as these compounds slowly transfer from north to south through the atmosphere. Chemical Composition of the Atmosphere Concentrations of chemicals in the atmosphere are commonly given in units of parts per million by volume (ppmv), which is equivalent to relative partial pressure. This number can be converted to a mass per volume using the ideal gas law (Box 5.2). The major gaseous components in the troposphere, defined here as those present at a relative partial pressure of near or above 1%, include N2 , O2 , and Ar (Table 5.2). These major gases are rather homogeneous in concentration throughout the atmosphere. In addition, water vapor typically contributes a few percent to the total atmospheric gas pressure. For instance, at the Earth’s surface at 100% relative humidity and 20◦ C, water vapor concentration is about 17.3 mg L−1 (see Appendix B.3), corresponding to a relative partial pressure of 2.3%; at 30◦ C and 100% humidity, the concentration is 30.3 mg L−1 and partial pressure is 4.2%. Additionally, numerous minor carboncontaining components occur in the atmosphere such as CO2 , CO, CH4 , CCl2 F2 , and reactive compounds including hydrogen peroxide (H2 O2 ), ozone (O3 ), hydroxyl radical (HO∙ ), nitrogen oxides (NOx ), and nitric acid (HNO3 ). The atmosphere also always contains suspended aerosols at concentrations of about 1 to 100 μg m−3 (Table 5.2). Residence times of these aerosols are typically between 1 to 10 days, depending on size. The main removal mechanism is precipitation (“wet deposition”), and because storms are spatially and temporally variable, aerosol concentrations vary in space and time. In arid areas, “dry” deposition of aerosols can become important, and this removal mechanism occurs with vertical velocities between 0.1 and 10 cm s−1 (Chen, 1987). Since aerosols may have acids like HNO3 and bases like NH3 in them (Hand et al., 2012), they exhibit pH values ranging from about 2 (acid deposition) to about 8 (sea spray). In Chapters 9 and 15, we see how pH affects wet deposition of certain organic compounds. Aerosols also include substantial organic material (Kanakidou et al.,

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Earth Systems and Compartments

Table 5.2 Composition of the Troposphere and Stratospherea Troposphere Mean Air Pressure at Sea Level Major Components (volumetric) Nitrogen (N2 ) Oxygen (O2 ) Argon (Ar) Water (H2 O) Minor Components c Carbon dioxide Carbon monoxide (CO) Methane (CH4 ) Dichlorodifluoromethane (CCl2 F2 ) Ozone (O3 ) Hydroxyl radical (HO∙) Aerosols (solid or liquid) aerosol concentration pH organic content

Stratosphere

1.0133 × 105 Pa b 78.1% 20.9% 0.93% 0 to 4% near Earth surface near 0.01% at top of troposphere

∼78% ∼21% ∼0.9% ∼3 ppmv

∼400 ppmv (pre-industrial revolution: 280 ppmv) 0.05 – 0.2 ppmv ∼1.8 ppmv 520 pptv ∼20 pptv 0.5 to 2 × 106 molecules cm−3

averages several ppmv (< 10) less than troposphere 0.1 ppmv 0.2 – 1 ppmv 0 to 500 pptv 100 – 3000 pptv ∼107 molecules cm−3

1 to 100 μg m−3 2 – 8 tends to be more acidic for smaller aerosols and more basic for marine aerosols 20 to 90%

a

Data compiled from Winkler (1980); Ludwig and Klemm (1990); Schlatter (1999); Keene et al. (2002); Keene et al. (2004); Kanakidou et al. (2005); Quinn and Bates (2005); Pope and Dockery (2006); Seinfeld and Pandis (2006); Jimenez et al. (2009); Fouchere et al. (2011); Minschwaner et al. (2013); NOAA (2014). b 1 Pa = 1 N m−2 = 10−5 bar. c 1 ppmv = 1 part per million by volume (10−6 ); 1 ppbv = 1 part per billion (10−9 ); 1 pptv = 1 part per trillion (10−12 ); use Eq. 5-1 to get absolute partial pressure.

2005). Some of this organic matter is derived from solids such as fine soil particles, pollen, or soot blown off the surface of the Earth (Fig. 5.3). These organic components of aerosols are referred to as “primary”. But much of the aerosol organic content is formed after organic vapors in the atmosphere are oxidized and condense to form more particulate matter (Kroll et al. 2011). This aerosol organic content is referred to as “secondary”. As discussed in Chapter 15, these organic components are important for accumulating organic pollutants like PAHs, leading to the long-range transport and ultimate removal of these compounds from the atmosphere (Friedman et al., 2014). Figure 5.3 Electron micrographs (not at the same scale) of three “primary” aerosol components: (a) pollen, (b) sea salt from sea spray, and (c) soot. Primary aerosol components arise directly from the Earth surface, while secondary components are formed in the atmosphere. Micrographs from USGS, UMBC (Chere Petty), and Arizona State University (Peter Buseck) accessed at Voiland (2010).

Surface Waters and Sediments

5.3

131

Surface Waters and Sediments The Ocean and the Global Water Cycle The largest aquatic compartment on Earth by volume is the ocean (Table 5.3). The largest fresh water compartment is the polar ice, followed by groundwater (see Section 5.4). Lakes and rivers are negligible in terms of global water reservoirs, but they can be important as storage and transport media for organic chemicals as they are more directly exposed to man-made chemicals. The mean depth of the ocean, that is, the ocean volume divided by its surface area, is about 3,800 m (Table 5.3). At such a depth, the total pressure would be about 400 bar and the seawater temperature would be only 0 to 4◦ C. In contrast, if the

Table 5.3 Volumes and Flows of Water on Earth Volumes (1015 m3 )

Reservoirs Ocean Ice (expressed as volume of liquid water) Groundwatera Freshwater lakes Saline lakes and inland seas Water in living biomass Rivers (average) Global flow rates of water

1,400 29 8.3 0.125 0.104 0.003 0.001 b

Evaporation from the ocean Precipitation on the ocean Evaporation from land and from lakes Precipitation on land Runoff from land to ocean (rivers and groundwater) a

Total flux (1012 m3 yr−1 )

Flux per area c (m yr−1 )

Residence time (yr)

430

1.19

3,300 d

392 71

1.09 0.47

3,600 d 120 e

109 38

0.73 0.25

80e 220 e 37,000 f

About one half of the stock lies within a depth of 1 km. Data from Bengtsson (2010). c Per land or ocean area, respectively (see Table 5.1). d Ocean volume divided by the respective flow rate . e Residence time relative to total volume of liquid water on land, i.e., total volume of liquid water on land divided by the corresponding yearly flux. f Residence time relative to total volume of ocean, i.e., ocean volume divided by yearly runoff from land to ocean. b

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Earth Systems and Compartments

vapor transport

38

109 precipitation

392 evapo- 71 transpiration ration

evaporation

surface runoff

percolation

precipitation

430 LAKE LAND

RIVER 38 return flow OCEAN

groundwater flow

Figure 5.4 Schematic of annual global water flows in 1012 m3 yr−1 . Adapted from Bengtsson (2010).

transport [1012 m3 per year]

combined continental surface waters in lakes and rivers were evenly spread out over the part of the globe that is occupied by land, it would have a mean depth of less than 2 m. Performing the same calculation for groundwater, the depth would be about 60 m. Global Water Flows and Residence Times. Water continuously cycles from the ocean into the atmosphere and via different pathways back to the ocean. The main flow rates between the different aquatic reservoirs are listed in the lower part of Table 5.3 and illustrated in Fig. 5.4. The evaporation rate of water from the ocean is 430 × 1012 m3 yr−1 , which corresponds to an ocean water column of 1.19 m height or 0.031% of the total ocean volume (Table 5.3). The mean residence time of ocean water with respect to evaporation, which is 3,300 years, is calculated by dividing the total ocean volume by the evaporation flux per year. Most of the evaporated water falls back onto the ocean (392 × 1012 m3 yr−1 ). About 9% (38 × 1012 m3 yr−1 ) makes it to the continents and eventually flows back to the ocean via rivers or subsurface flow. While the evaporating water is fairly pure, upon rejoining the ocean, it may carry organic chemicals accumulated from the atmosphere (see Chapters 9 and 15) or the continents. The yearly runoff from the continents equals 0.45% per year of the liquid water stored on the continents, mostly as groundwater. The mean residence time of water on land is 220 years. If we disregard groundwater, the mean residence time of continental surface water with respect to runoff to the ocean (0.230 × 1015 m3 divided by 38 × 1012 m3 yr−1 ) is just 6 years. Of course, the real residence time in the different continental reservoirs varies greatly. For instance, groundwater existing in deep strata has been

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below ground for several thousand years. In turn, rainwater that does not infiltrate into the soil or pass through a large lake may be back in the ocean within a week or less. These calculations of mean residence time of water do not take into account the water stored in polar ice. The rates of freezing and melting of polar ice, relative to the stock of ice, are very low. Also, as we know from the history of the ice ages, ice volumes are not at a steady state over the “short” time scales of millennia. During the ice ages, this reservoir has been much larger; while presently, we are experiencing a distinct shrinking of the polar ice mass. Although we do not further discuss the polar ice shields, dubbed the cryosphere, we do note that the cryosphere can be a significant long-term reservoir for certain organic pollutants (see Grannas et al., 2013). Ocean Mixing. As for the atmosphere, the ocean can be vertically divided into different layers (a surface layer, an intermediate layer, and deep layers, see Fig. 5.5) as well as into different horizontal parts (e.g., Atlantic, Pacific, and Indian Oceans) and numerous smaller basins (e.g., Mediterranean, Baltic Sea, and Gulf of Mexico). The intensity of mixing and transport in the ocean varies strongly with time as well as spatially. Here, we briefly address important mechanisms of ocean mixing and their time scale. In the top several hundred meters, ocean currents are driven by the global wind field (Fig. 5.2b) which, in combination with the Coriolis effect arising from the Earth’s rotation, leads to the well-known surface currents like the Gulf Stream in the Northern Atlantic or the Kuroshio current in the Northern Pacific. At the water surface, the heating and cooling of the water column, in combination with the turbulent energy supplied from the wind field, produces a well-mixed surface layer whose depth varies with latitude (Fig. 5.5) and season. In summer, a seasonal surface layer of less than 100 m typically forms, while in winter when cooling erodes the temperature-induced density gradient (the thermocline), a layer forms to a depth of several hundred meters. Below the surface water, ocean circulation is driven by the density gradients caused by variation of temperature and salt content (salinity) of the water, called thermohaline

South

Atlantic Ocean layers and circulation 60° 30° equator 30° 60° surface water

Figure 5.5 Layers of the ocean as illustrated for the Atlantic Ocean: (1) surface layer of a few hundred meters during the winter, (2) intermediate water at about 1000 m, (3) North Atlantic Deep Water (NADW) flowing south at about 3000 m, and (4) Antarctic Bottom Water (AABW) flowing north along the ocean bottom.

intermediate water

Antarctic bottom water

North Atlantic deep water

increased nutrients & dissolved CO2 warm, low nutrients & oxygen

North

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Earth Systems and Compartments

Table 5.4 Typical Salinities of Seawater and Salty Inland Waters a Waterbody Oceans Atlantic Indian Pacific Other Seas Mediterranean Persian Gulf Red Sea Black Sea Baltic Sea Salty Inland Waters Caspian Sea Mono Lake (USA) Dead Sea Lake Aral (great basin) Lake Aral (small basin) Lake Assal (Djibouti) Don Juan Pond (Antartica)

Salinity (practical salinity units, psu) 35.4 34.8 34.5 37.4 40 40 17 to 18 8 13 73 280 (max 327) 75 20 348 (388 at 20 m depth) 442 (highest salinity on Earth surface, albeit predominantly CaCl2 instead of NaCl as in seawater)

a Definition of type of water based on salinity: fresh = 0 – 0.5 psu; brackish = 0.5 – 30 psu; saline = 30 – 50 psu; brine > 50 psu.

circulation. Salinity varies between the major oceans and, even more pronouncedly, between the main ocean and smaller basins (Mediterranean, Baltic or Black Sea) and estuaries (Table 5.4). Today, salinity is given in “practical salinity units” (psu). The units are defined so as to be close to the old salinity definition, which was “total mass of dissolved salts in g per 1 kg of sea water” (o /oo or parts per thousand). In psu units, a salinity of 35 (usually written without any units) roughly corresponds to a salinity of 35 o /oo in the old definition. Such salt content information is important for calculations involving solubilities and partition coefficients for organic chemicals (Chapters 9 and 10). Sailors have felt the effects of surface ocean currents for centuries. In contrast, only in the last few decades could oceanographers draw a quantitative picture of how the ocean circulates below the surface: where deep water is formed, where the water comes back to the surface, and how the major oceans are connected by deep and bottom water currents. Today, knowledge about the three-dimensional structure of ocean currents is extremely detailed, but the general picture is still reasonably well depicted by the “conveyor belt” model developed about 30 years ago (Fig. 5.6). Compared to the atmosphere, the global ocean circulation is not only more difficult to observe, which explains why it took so long to understand, but also more complex.

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135

Figure 5.6 The global scale transport of seawater, referred to as the “Global Conveyor Belt;” graphic from Broecker (1987, 1991). Cold, salty water sinks in the Arctic/North Atlantic, flows south (blue) until it turns east and moves toward the Indian and Pacific Oceans. The deep water flows northward until it arrives in the vicinity of India or Alaska where it rises to the ocean surface for its shallow return flow (red) back to the North Atlantic.

The vertical stability of the water column depends not only on temperature, as in the atmosphere, but also on salinity, which is the main driver of such complexity. In fact, the reason why deep water is formed in the North Atlantic (NADW: North Atlantic Deep Water, see Fig. 5.5) and in the Antarctic Ocean (AABW: Antarctic Bottom Water), but not in the North Pacific Ocean is the relatively low salinity in the North Pacific. The rates of deep water formation (in units of Sverdrups where 1 Sv = 106 m3 s−1 ) are estimated to be 15 – 20 Sv for NADW and 5 – 10 Sv for AABW. The intermediate water, as shown in Fig. 5.5, is also formed in the Antarctic and contributes another 5 – 10 Sv of flow into the Atlantic at mid-depth. Using these flow rates, the time scale for the global ocean circulation is between 500 and 1,500 yr. This rather long time explains why the deep ocean mainly acts as a sink for man-made compounds, since most of these chemicals have only been produced during the last 50 to 100 years. Either such compounds are carried to the deep ocean by the global circulation, or they are bound to particles that sink through the water column, or they repeatedly “distill” back and forth into the atmosphere moving poleward. The first two mechanisms represent mostly a one-way transport, at least on a time scale of a few hundred years; in contrast, transport to the polar regions happens on a time scale of a year or less. Chemical Composition of Seawater. The chemical composition of seawater has long been studied. In 1884, the Scottish chemist William Dittmar, based on water samples taken during the scientific Challenger expedition, found that the relative proportions of the major chemical constituents of seawater are nearly constant throughout all the oceans (“Dittmar’s law”, see Table 5.5). The composition of seawater is important for reactions such as nucleophilic substitution reactions with solutes like chloride and

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Table 5.5 Typical Chemical Components of Seawater (salinity S = 35 psu) a Components (mmol kg−1 ) 469 53 10 10 (mmol kg−1 ) 546 28 0.84 1.8 0.25 ∼8 ∼200 – 300 μM (mg C L−1 ) 0.5 – 1.5 0.1 – 0.7

Cations Na+ Mg+2 Ca+2 K+ Anions Cl− SO4 −2 Br− HCO3 − CO3 −2 pH Dissolved O2 (surface seawater) Organic Components dissolved organic carbon (DOC) particulate organic carbon (POC) a

Data from Ogawa and Tanoue (2003) and Emerson and Hedges (2008).

bromide (Chapter 22) and for processes involving bicarbonate and carbonate as well as organic matter that affect reactive oxygen species such as singlet oxygen (1 O2 ) or HO∙ radicals (Chapter 25). The pH of seawater is typically near 8, although this value can go up or down a few tenths of a pH unit in surface waters due to intense photosynthesis or heterotrophic respiration. This pH dependency can be understood by noting that protons are reactants during photosynthesis and they are products during respiration, as depicted by a stoichiometric expression using the “Redfield ratio” (Redfield, 1958):

106 CO2 + 16

NO−3

+

HPO−2 4

+ 122 H2 O + 18

photosynthesis ⇌ C106 H263 O110 N16 P + 138 O2 respiration (5-2)

H+

Deep seawater pH decreases from the surface pH near 8 down to about pH 7.5 as the water flows through the ocean (see Fig. 5.6). This pH change occurs because particulate organic matter continuously falls into the deeper layers from above, and some of this organic matter is oxidized, releasing CO2 and lowering the pH. Dissolved oxygen (O2 ) in surface seawater is usually nearly equilibrated with the atmosphere. As a result, O2 concentrations are between 200 and 300 μM, depending on the water temperature and salinity. These concentrations locally increase or decrease because of photosynthesis or respiration. While most of the ocean has some dissolved oxygen, certain locations have been found to be anoxic (O2 free). For

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137

example, seawater in the Cariaco Basin (north of Venezuela in the Caribbean Sea) is naturally anoxic below 400 m all the way to the seafloor at 1400 m. Unfortunately, large inputs of nutrients to certain parts of the ocean (e.g., “The Dead Zone” located near the mouth of the Mississippi River in the northern Gulf of Mexico) are now causing unnaturally oxygen-depleted deep water (Rabalais et al., 2002). The seawater concentration of organic carbon that passes through a glass fiber filter with about 1 μm size cutoff, called “dissolved” organic carbon or DOC (see Box 5.3), does not vary widely, almost always being near 1 mg carbon per liter of seawater (Ogawa and Tanoue, 2003). DOC concentrations are a little higher in surface waters where phytoplankton are actively photosynthesizing organic matter, but DOC concentrations generally decrease with depth below the surface layer. The chemical composition of seawater DOC is quite different from that found in freshwaters, chiefly because land plants and marine phytoplankton synthesize very different materials (see Chapter 13). Particulate organic carbon (POC), defined as organic carbon that can be filtered from water, usually occurs at somewhat lower levels than DOC in seawater, unless one is looking at a site with a plankton bloom or at a coastal location with significant resuspended solids. In contrast to DOC values, substantial concentration variations occur for trace substances that serve as nutrients for photosynthetic organisms. For example, inorganic nitrogen species, like nitrate, nitrite, and ammonia, and phosphate vary from undetectable concentrations up to micromolar levels. Box 5.3

Terms and Definitions to Describe Fractions of Organic Matter in Environmental Matrices

Matrix

Abbrev

char colloidal organic carbon coal dissolved organic carbon dissolved organic matter elemental carbon fraction black carbon

DOC DOM EC fbc

fraction organic carbon fulvic acids

foc

humic acids humic substances

Definitions carbon-rich product resulting from the pyrolysis of the surfaces of carbonaceous fuels like wood or coal carbon that passes a filter consisting of particles between sizes of about 10 nm and 1 μm and that can be oxidized to CO2 dark colored, combustible mineral substance consisting of carbonized vegetable matter carbon that passes a filter (e.g., ∼1 μm) and can be oxidized to CO2 mass that passes a filter (e.g., ∼1 μm) and whose mass is lost on combustion zero-valent, graphitic, carbon particles weight fraction of a soil or sediment’s mass that derives from pyrolysis of fossil fuels (soot) or biomass burning (chars) and can be oxidized to CO2 weight fraction of a soil or sediment’s mass that can be oxidized to CO2 natural organic compounds that can be extracted from solids (soils, sediments, or an adsorbent used on water) with strong base (pH > 12) and that remain dissolved upon lowering the pH below 2 natural organic compounds that can be extracted from solids (soils, sediments, adsorbents used on water) using strong base (pH > 12) and that precipitate upon lowering below pH 2 heterogeneous mixtures of organic compounds formed by decay and transformations of plants and microorganisms

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Earth Systems and Compartments

Matrix

Abbrev

humin kerogen lignin organic aerosols particulate organic carbon peat soil (or sediment) organic matter soot

OA POC SOM

tar total organic carbon

TOC

Definitions organic matter in soils that cannot be extracted from solids by either strong base or acid insoluble mix of organic material in sedimentary rocks complex polymer of aromatic alcohols, most commonly derived from wood, and part of the plant cell walls small atmospheric particles containing diverse organic substances carbon that is caught on a filter (e.g., ∼1 μm) and that can be oxidized to CO2 partly decomposed plant matter found in wetlands organic mass associated with soil or sediment solids that is lost on combustion black, finely divided material formed via condensation reactions during the incomplete combustion of fuels black, viscous liquid formed in pyrolytic distillation combination of dissolved and particulate carbon that can be oxidized to CO2

Note: The term natural organic matter (NOM) includes all organic matter of a natural origin and is discussed in Chapter 13.

Lakes Most of the liquid surface fresh water on Earth is found in lakes (Table 5.3). More than one million lakes exist with an area larger than 0.1 km2 (Meybeck, 1995). In total, lakes cover an estimated area of about 2,800,000 km2 (about 2% of land surface). The total lake volume is estimated to be 230,000 km3 (about 0.017% of ocean volume), a little over half of it containing fresh water (Table 5.3). Most lake water is concentrated in about 250 large lakes, including coastal lagoons, with a surface area larger than 500 km2 (Herdendorf, 1990).

Table 5.6 Global Ranking of Lakes (Data from Herdendorf (1990)) a. Per Volume Volume Rank 1 2 3 4 5 6 7 8 9 10

Lake Caspian Baikal Tanganyika Superior Nyasa (also named Malawi) Michigan Huron Victoria Great Bear Great Slave

Volume (km3 ) 78,200 23,000 18,900 12,230 6,140 4,920 3,537 2,700 2,381 2,088

Table 5.6 lists the ten largest lakes ranked by (a) volume, (b) surface area, and (c) depth. The largest in terms of volume and area is the Caspian Sea; it represents 75% of the global saline lake volume. Among the fresh water lakes, Lake Baikal has the largest volume and depth, containing nearly 20% of the total fresh water in lakes, more than all Great Laurentian Lakes combined. After the Caspian Sea, Lake Superior leads the area ranking while Lake Baikal only ranks number 8. Table 5.6d gives the largest lake per area on each continent. Australia is a special case because it has very few large lakes; Lake Eyre is its largest and is subject to large area fluctuations. Most lakes have several inlets, but only one outlet. Subsurface or groundwater inflow and outflow is important for some lakes (Townley and Trefry, 2000). The mean residence time of the water in lakes is calculated by dividing the lake volume by the discharge rate at the outlets. Typical values for lakes with volumes larger than 10 km3 lie between a few weeks to several tens of years. Lakes without surface or subsurface outlets are called terminal lakes; they keep their water balance by evaporation, like the ocean. Terminal lakes are saline or develop into saline lakes. In contrast to the

Surface Waters and Sediments

b. Per Area Area Rank

Lake

1 2 3 4 5 6 7 8 9 10

Caspian Superior Victoria Aral Huron Michigan Tanganyika Baikal Great Bear Great Slave

Area (km2 ) 374,000 82,100 68,460 64,100 59,500 57,750 32,900 31,500 31,326 28,568

c. Per Depth Depth Rank

Lake

1 2 3 4 5 6 7 8 9 10

Baikal Tanganyika Caspian Nyasa Issykkul Great Slave Matana Crater Toba Hornindalsvatnet

Depth (m) 1,741 1,471 1,025 706 702 625 590 589 529 514

d. Largest Lakes per Continent (per Area) Continent Lake Africa Asia Europe North A South A Australia

Victoria Caspian Ladoga Superior Maracaibo Eyre (large fluctuations)

Area (km2 ) 68,460 374,000 17,700 82,100 13,010 max. 9,700

density (kg m–3)

1000 999.9 999.8 999.7 999.6 999.5

0

2 4 6 8 10 12 temperature (°C)

Density of water at varying temperatures.

139

salinity of ocean water, the salt composition of saline lakes greatly varies as it reflects the different geologies of the drainage areas, where the dissolving rocks provide most of the salts. Although lakes are small compared to the ocean, they may locally be of great importance as a water resource. At the same time, small volume-to-shoreline ratios make lakes more vulnerable to man-made pollution. Flushing times of organic pollutants in lakes are in the same order as the mean residence time of the water itself. Importantly, such flushing may control the longevity of organic contaminants in lake water, especially if the chemicals are persistent and do not adsorb to particles. Mixing and Stratification of Lakes. In order to understand the processes controlling the fate of chemicals in lakes and to design effective water sampling strategies, we need to understand the phenomena that control mixing in the lakes. The seasonal change of vertical stratification in lakes is similar to that of the ocean (Fig. 5.7). At the surface, mixing is mainly due to the wind. Mixing in the horizontal direction is fairly fast, while in the vertical direction, a layer called the thermocline represents a bottleneck for vertical mixing. The thermocline is the depth zone where temperature strongly decreases, causing a density gradient that separates the surface water, or epilimnion, from the deep water called the hypolimnion. Thus, processes, like air-water exchange, only act directly on organic chemicals in a lake’s epilimnion. As in the ocean, the thermocline depth undergoes a seasonal variation, caused by the warming and cooling of the surface water and by the corresponding variation of the strength of the stratification of the water column. In lakes with total depth of less than 100 to 150 m, the thermocline depth may thus sink to the bottom of the lake, a process called total turnover. For lakes in the temperate climate zone, such turnover events commonly occur in the fall when the lake’s surface water loses heat. Turnover sometimes occurs twice per year (fall and spring) if a so-called inverse stratification (0◦ C surface water overlies 4◦ C deep water) or an ice cover develops. Inverse stratification results from the very peculiar density-to-temperature relationship of fresh water. In contrast to any other fluid, water reaches its maximum density not at its freezing point, but at 4◦ C (see figure in margin). Water with a salinity of more than 25 psu does not have such a density anomaly, thus temperature-induced inverse stratification does not occur in the ocean. Lake depth is not the only factor that controls the occurrence of turnover events. In water close to the temperature of maximum density (4◦ C), the vertical distribution of total dissolved solids may override the influence of temperature on density. We use the term total dissolved solids instead of simply “salinity” in order to avoid the erroneous conclusion that salinity effects may only be important in saline lakes. To the contrary, lakes with deep water temperatures around 4◦ C may be permanently stratified by tiny vertical gradients of calcium carbonate concentration (Imboden and W¨uest, 1995). Rivers flowing into such lakes may either trigger or inhibit vertical mixing, depending on their concentration of total dissolved solids relative to the concentration in the lake. The case of “salinity”-controlled vertical stratification, where the quotation marks are meant to remind us that even small concentrations of total dissolved solids may be

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Earth Systems and Compartments

spring

summer temperature (°C)

temperature (°C) 0

10 20

0

epilimnion

10

thermocline

20

hypolimnion

30

depth (m)

depth (m)

0

40

10 20

0

5 10 15

10 20 30 40

0

5 10 15

O2 (mg L–1)

O2 (mg L–1)

winter

autumn temperature (°C)

temperature (°C) 0

0

10 20 0

10

depth (m)

depth (m)

Figure 5.7 Typical seasonal stratification cycle of a freshwater lake. Not every lake undergoes a complete overturn. Some lakes are permanently stratified. Usually, this effect is caused by a vertical gradient in the concentration of total dissolved solids. Adapted from Campbell et al. (2002).

0

20 30 40

0

10 20

0

5 10 15

10 20 30 40

0

5 10 15

O2 (mg L–1)

O2 (mg L–1)

needed, is particularly pronounced in eutrophic lakes. Such lakes have large nutrient inputs, often resulting from human activities such as agriculture. The accumulation of dissolved salts in the deep water from the sinking and decomposition of biomass or from re-dissolution of solids at the sediment surface often leads to a permanent, dissolved solids-induced stratification, even if the lake is not very deep and thus its total water volume is exposed to the wind. As a result, in some cases, the hypolimnion in a lake may become anoxic and populated with anaerobic microorganisms. Such conditions have become common in certain lakes like Lake Erie (Conroy et al., 2011). In these lakes, one may expect organic compounds that are persistent under aerobic conditions (e.g., polychlorinated pesticides) may undergo reductive transformations (see Chapter 23). As several different factors can influence deep water mixing, simple prediction of such mixing is not possible. Instead, every lake must be taken as an individual case that must carefully be studied, especially if the deep water is around 4◦ C. The only general statement we can make is that in lakes that have deep water temperatures distinctly above 4◦ C, permanent stratification is very likely. Since water’s thermal expansion coefficient rapidly grows above 4◦ C (Appendix B, Table B.3a), above this value, the temperature has a significant effect on water density, whether dissolved salts are present or not. The two deepest freshwater lakes on Earth, Lake Baikal (1,741 m depth) and Lake Tanganyika (1,471 m), provide us with quite contrasting illustrations of mixing. In Lake

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141

Baikal, water temperature is close to the temperature of maximum density throughout the water column. Small density currents caused by water inflows at the inlets drive the vertical exchange in the lake. Water mixing is further enhanced by the fact that the temperature of maximum density decreases with pressure (i.e., with depth), leading to a very complex mixing process called cabbeling (Hohmann et al., 1997). In short, in spite of its great total depth, deep water in Lake Baikal is renewed at a typical rate of about 10% per year. In contrast, water temperature in Lake Tanganyika is about 20◦ C at all depths (Edmond et al., 1993; Verburg et al., 2003). Small vertical temperature gradients, in combination with chemical gradients, lead to a permanent stratification of this lake and to permanently anoxic deep water. To conclude, we mention a special phenomenon called the thermal bar, which was first described by F.A. Forel (1876) in Lake Geneva. A thermal bar develops in lakes that freeze over in winter or whose surface temperature drops below 4◦ C. Since in spring the water warms up faster close to the shore than at the center, such lakes develop a horizontal temperature gradient at the water surface that extends from the shore (T > 4◦ C) to the center of the lake (T < 4◦ C) where the water may still be covered by ice. Somewhere on that line from the shore to the center of the lake, the surface temperature must be 4◦ C, the temperature of maximum density. At this location, the water sinks to greater depths and thus produces a barrier (the thermal bar) that separates the shore water from the water in the middle of the lake. Due to the thermal bar, substances brought into the lake by rivers or sewers concentrate at the shore-side of the bar. Thermal bars and their effect on pollutant concentrations near the shore have been extensively studied in the Great Laurentian Lakes (Rao and Schwab, 2007). Chemical Composition of Lakes. The chemical compositions of lake waters vary widely. For example, the total dissolved salt contents can vary from 0.1 psu to about 400 psu (Livingstone, 1963). This variability largely arises from differences in the mineralogical composition of the solids surrounding the lakes. Moreover, the fact that some lakes are primarily fed by streams that quickly flow over the landscape without much chance to dissolve the surrounding rocks, while other lakes are filled by groundwater with extensive rock interactions, results in varying degrees of water equilibration with the surrounding minerals. For example, lakes in geological areas dominated by granitic rocks can have pH values as low as 4.5 or less, whereas lakes surrounded by carbonate containing rocks (e.g., calcite and dolomite) can have pHs near 8 (Baas Becking et al., 1960; Stumm and Morgen, 1996). Further, terminal salt lakes in volcanic areas can be highly alkaline with pH as high as 10 (Mono Lake) or 9.8 (Lake Van, Eastern Turkey). Diurnal variations in a lake’s surface water pH are also common. Daytime photosynthesis increases the pH (consumption of protons, Eq. 5-2), and nighttime respiration lowers the pH (Livingstone, 1963). Surface lake water usually contains dissolved oxygen at levels near saturation (i.e., 200 to 400 μM depending on the water’s temperature and salt content). The oxygen comes from the atmosphere and is made in situ by photosynthetic plankton (Eq. 5-2). Sometimes, deep lake water can be anoxic (e.g., Conroy et al., 2011). These conditions depend greatly on the time-varying mixing in lakes, as well as nutrient loadings that

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control the rate of organic matter production by algae and submerged plants. The DOC content of lake water varies from about 1 to 3 mg C L−1 for oligotrophic lakes (i.e., those with small nutrient loadings), while DOC values can be near 30 mg C L−1 for nutrient-rich or eutrophic systems (Thurman, 1985). The POC in lake water is generally much smaller (factor of 10) than the DOC (see Box 5.3 for definitions). This wide range of observed lake mixing and nutrient loading also have concomitant impacts on redox sensitive elements like iron, manganese, nitrogen, and sulfur (Wetzel, 2001). For example, dissolved iron can be present at sub-micromolar levels (Fe(III)) in oxic bottom waters in the winter and spring and then at super-micromolar concentrations (Fe(II)) when the deep water becomes anoxic in the summer and fall (e.g., Senn and Hemond, 2002). Rivers Rivers are especially important for the global water cycle because they act as the major link between the continental aqueous systems and the ocean. They bring most of the continental excess rain (precipitation minus evaporation) of 38 × 1012 m3 yr−1 back to the ocean (Fig. 5.4), carrying huge amounts of dissolved and suspended solids. Rivers also transport chemicals, sometimes carrying them over great distances. For example, after a fire destroyed a chemical storehouse in Schweizerhalle near Basel, Switzerland in 1986, great amounts of pesticides entered the Rhine River and were carried about 800 km downstream to the North Sea (Capel et al., 1988; Wanner et al., 1989). The case is further discussed in Chapter 28. The largest river in the world in terms of discharge rate is the Amazon; on average, it brings 210 × 103 m3 s−1 of water from the South American continent to the Atlantic Ocean, more than 17% of the total discharge of all rivers on Earth. The Amazon has a total length of 6,450 km and drains an area of 6.9 × 106 km2 . The second river in terms of discharge is the Congo River; it has a discharge rate of 41 × 103 m3 s−1 (3.4% of global river discharge), a length of 4,400 km, and a drainage area of 4.0 × 106 km2 . While the ratio of the discharge rates of the Amazon and Congo is 5.1, the ratio of the drainage areas is only 1.7, reflecting the difference in water flows in the two drainage areas in terms of precipitation, evaporation, infiltration, and surface runoff. Runoff per area is much smaller in the Congo than in the Amazon drainage area. An even more extreme example is given by the Nile, the longest river on Earth. The total length of the Nile of 6,650 km slightly exceeds the length of the Amazon, and its drainage area (3.4 × 106 km2 ) is about half of the Amazon. However, its discharge rate is only 2.8 × 103 m3 s−1 , which is 1.3% of the Amazon. In spite of their importance in terms of transport, rivers are negligible global reservoirs of water (Table 5.3). On a local level, the construction of dams for drinking water supply and irrigation makes rivers important for water storage, especially in arid areas. On average, the mean residence time of water in rivers is about 10 days, so pollutant resident times or “chemical memory” is generally short. However, since river water and subsurface aquifers may exchange substantial water volumes, a combined river and groundwater compartment may have significantly prolonged pollutant residence times since groundwater flows are much slower than river flows. For example, Schwarzenbach et al. (1983) reports the rapid movement of chlorinated solvents

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B

C

concentration concentration

A

concentration

XXXXXXXXXXX X X XXXXXXX X XXXX XX X XXXXXXXXXXXXXXXXXXXX XXXXX

X XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

from river water into adjacent groundwater, extending the residence time by weeks of the solvent tetrachloroethylene (PCE). Another mechanism that increases residence times in the river compartment involves chemical exchanges with the river sediments. When rivers are polluted by inputs of hydrophobic chemicals like PCBs, much of the input partitions to particles and accumulates in the sediments. After the pollutant input has been flushed from the river, the sediments slowly return the chemicals back to the river water (back-diffusion). Therefore, as observed in the Hudson River (e.g., Erickson et al., 2005), an initial input of PCBs may leave its traces in the flowing water for a long time afterwards.

A

time B

time C

time

Concentrations of pollutant cloud moving downstream.

Mixing in rivers occurs via turbulent diffusion and dispersion. Turbulent diffusion (see Section 6.3) is a random process triggered by the roughness of the riverbed. Turbulent kinetic energy is introduced into the flowing water, inducing fast turbulent mixing in all directions: vertically, laterally, and longitudinally. The process of diffusion ensues as the flow varies across the cross-section of the riverbed, generally being slower close to the river bank and faster in the middle. Thus, if a chemical is added evenly at a specific cross-section in the river, the molecules traveling in the middle of the river move downstream faster than those at the sides. This process is called dispersion (see Section 28.4). Mixing by dispersion is generally more important than turbulent diffusion in the longitudinal direction (along the main flow of the river). Therefore, downstream from the location where a single spike or chemical pulse is added, turbulent diffusion will distribute the chemical across the river downstream of the input location. Dispersion then reduces the maximal concentration and elongates the pollutant cloud while moving downstream (see margin figure). In contrast, if a chemical is continuously added to the river, its concentration will be homogeneously distributed across the river. At some point downstream of the input location, its concentration is just the added mass per unit time divided by the discharge rate of the river, provided that the chemical does not significantly react during the flow time. Chemical Compositions of Rivers. As with lakes, rivers have diverse chemical compositions that depend on the geological system through which they flow. Average composition values on a global scale (Table 5.7) are useful to estimate the amount of major ions, like sodium and calcium, delivered to the ocean, but concentrations in single rivers differ widely from these averages. For example, North American rivers have Na+ , Ca+2 , and HCO3 − concentrations ranging from 0.1 to 5 mM, 0.08 to 4 mM, and 0.2 to 5 mM, respectively (Livingstone, 1963). The average pH of rivers is generally circumneutral, but in cases like streams that have large inputs of acid mine drainage, the pH can be near 2 (Baas Becking et al., 1960). Rivers and streams also carry substantial loads of nutrients, especially in agriculturally active areas. As a result, concentrations of nutrients like nitrate are found in rivers like the Mississippi at levels between 70 and 300 uM (Sprague et al., 2011). Finally, rivers and streams can also have a wide range of DOC concentrations that depend on the type of watershed and the influences of human activities in the area (Moeller et al., 1979). Unlike lakes, rivers commonly have POC concentrations that are comparable to their DOC levels as the turbulent mixing of river flows can maintain particles in suspension. Moreover, resuspension events associated with times of high flow can temporarily increase POC concentrations.

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Table 5.7 Average Global Concentrations of Chemical Components in River Watera Components

Global Average

Cations Na+ Mg+2 Ca+2 K+ Anions Cl− SO4 −2 HCO3 − NO3 − pH Dissolved O2 Organic Components dissolved organic carbon (DOC) particulate organic carbon (POC)

(mmol kg−1 ) 0.3 0.2 0.4 0.06 (mmol kg−1 ) 0.2 0.1 1.0 0.02 2 – 10 b 0 – 300 μM (mg C L−1 ) 1 – 60 0.2 – 30

a b

Data from Livingstone (1963); Moeller et al. (1979); and Thurman (1985). Value for low pH for mine water drainage streams.

Sediments and Sedimentation Beneath most bodies of surface water, suspended solids fall through the water to form a sediment bed, that is, a matrix consisting of solids and water-filled pore spaces. Sediments are linked to overlying waters by various processes such as particle settling, molecular diffusion between pore water and open water, resuspension, and bioturbation (Chapter 20). The solids may remove chemicals from the overlying water column, particularly compounds that sorb strongly to particles (Chapter 12). Therein, sediment beds provide a potential continued source of those chemicals back to the water body. Sediment Accumulation. A large part of suspended particles in surface waters are derived from land, such as clays, silts, and sands. In situ production of organic particles (called marine snow in the ocean), fecal pellet formation and coagulation adds to the flux of particulate matter through the water column (Turner, 2002). In the deep water of the ocean, the concentrations of suspended solids are in the range of 10 to 50 × 10−6 kg m−3 , while concentrations range from 1 to 20 × 10−3 kg m−3 in lakes (Table 5.8). The sediment accumulation rate, that is, the rate at which the sediment column grows by the addition of mass at the sediment surface, is the product of the concentration of suspended particles in the open water and the effective particle settling velocity. The accumulation of solids on the seafloor results in accumulation at rates between a few millimeters per year in shallow, coastal locations to only 0.3 to 8 mm per 1000 yr in the deep ocean (Riley and Chester, 1971). The weight fraction of organic carbon of suspended solids, foc , lies between 2 and 20%; this fraction decreases by about a factor of 10 once the solids are buried in the sediment bed.

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Table 5.8 Concentration of Suspended Particles, Settling Velocities, and Sediment Accumulation Rates in Global Waters a

Ocean surface Ocean deep water Lakes

Suspended solids concentration (kg m−3 )

Particle settling velocity (m d−1 )

Sediment accumulation rate (kg m−2 yr−1 )

0.1 – 5 × 10−3 10 – 50 × 10−6 1 – 20 × 10−3

10 – 150 b 30 – 300 (up to >2000) b 0.1 – 3

1 – 10 0.1 – 1 0.1 – 10

a

Data compiled from Manheim et al. (1970); Brewer et al. (1976); Berelson (2002); Bloesch 2003; Douglas et al. (2003); Sommerfield (2006); Armstrong et al. (2009); Hodder (2009); and McDonnell and Buessler (2010). b High values for fecal pellets (Turner, 2002).

The settling velocity of suspended solids depends on the size, form, and density of the particles or their aggregates and on the viscosity of the water, which depends on temperature (Lerman, 1979). Water currents can enhance or reduce the settling velocity; if currents are strong enough, like in rivers or in shallow areas of the ocean affected by tidal movement, particle settling at the sediment surface may even temporarily become negative, a process called resuspension or sediment erosion. Field data show that settling velocities (Table 5.8) vary widely with space and time. In marine environments, typical values are between 10 and 300 m d−1 (Armstrong et al., 2009; McDonnell and Buesseler, 2010), but some particles, like fecal pellets, have settling rates over 1000 m d−1 (Turner, 2002). Settling tends to be faster close to shore than further offshore (Gustafsson et al., 1997) and also faster in the deep ocean than at the surface, since particles that reach the deep sea have had their organic contents degraded and, therefore, have larger excess densities (Berelson, 2002). In addition, compared to the more turbulent water layers closer to the surface, the absence of turbulence favors the net downward movement of these particles. A similar trend is observed in lakes (Bloesch and Sturm, 1986), although settling rates are generally smaller than in the ocean. Exceptions are the rather fast settling of particles after resuspension events due to heavy winds (Douglas et al., 2003) or resulting from in situ flocculation of particles in glacier-fed lakes (Hodder, 2009). Sediment Porosity. The porosity of sediments, as well as of soils and subsurface solids (see Section 5.4), is defined as the fraction of the total volume consisting of fluid-filled pore space. Here, we extend this definition to media that consist of all three phases: gas, liquid, and solid (Box 5.4). Typical porosities of terrestrial media lie between 10 and 60%. Freshwater sediments are very loosely packed and have a porosity of about 90% (Bloesch and Evans, 1982), with the pore space entirely water filled. This high porosity is largely due to low salt contents, as the lack of salt allows for more repulsion among the charged surfaces of particles. In contrast, typical marine sediments contain 40 to 90% water by volume (Nafe and Drake, 1963). However, even at high salinity and at a depth of several hundred meters below the sea floor, where the weight of the overlying sediments has squeezed water out, pore water may still occupy more than 40% of the volume. Deep ocean sediments are hundreds of meters thick, and their total pore water volume exceeds the groundwater reservoir below the continents. However, most of the pore

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Box 5.4

Porosity of Sediments, Soils, and Subsurface Strata

The porosity of soils and underwater sediments is defined as the fluid-filled volume, Vair + Vwater , divided by the total volume: ϕ=

Vair + Vwater Vtotal

where Vtotal includes the combined volumes of air, water, and solids that make up the soil or sediment. ϕ is expressed in percent or fraction of total volume. Typical porosities for soil and other more homogeneous materials are shown in the following: Media Marine sediments a Freshwater sediments b Soil c Clay d Sand d Gravel d Limestone d Sandstone d

Typical Porosity (%) 40 – 90 80 – 90 40 – 50 50 25 20 20 11

a

Data from Nafe and Drake (1963). Data from Bloesch and Evans (1982). c Data from Batjes (1996). d Data from Heath (1983). b

water is basically trapped, so that exchange with the overlying ocean water is limited to the near-surface sediment layers. This large volume of pore water, therefore, does not have the same importance as groundwater in the global cycling of organic pollutants. In lakes, where sediment erosion is unlikely, the sediments can act as an archive of past conditions, and so sediment cores can reveal the history of chemical pollution. In rivers, sediment accumulation is usually transitory. During flood conditions, increased current velocities lead to resuspension of particles. Interactions between Sediments and Overlying Water. Mass exchange between sediments and open water occurs via various processes, such as molecular diffusion between the pore water and the open water, particle settling, or resuspension and bioturbation of the sediment bed (see Chapters 20 and 28). Once particles become part of the sediment, transformations (e.g., organic matter decomposition) and solid–water equilibration (e.g., mineral dissolution) are intensified. Furthermore, since the contact time between the solids and their surrounding pore water is typically much greater in the sediment column than in the overlying water column, pore water concentrations of chemicals carried to the bed on particles may become higher than corresponding concentrations in the water column. Such chemicals can then

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move back into the overlying water column via back-diffusion. Further, this buildup of contaminant chemical activity in the bed implies that benthic organisms may experience greater exposure and bioaccumulation of such organic chemicals. Other important processes of mass exchange between sediment and the overlying water column include settling or resuspension of particles that carry sorbed organic chemicals. Resuspension mainly occurs via high velocities in rivers or near the shore of oceans and lakes. However, biological processes can also cause resuspension. For example, organisms living at the sediment surface can stir up sedimentary particles while searching for food. This process, by which the activities of benthic fauna move sediment solids and pore water, is generally called bioturbation. Such mixing may expand the thickness of the sediment layer from which diffusive exchange with the open water can occur. Typically, bioturbation acts to a depth of about 10 cm, although this depth can be much less (∼1 cm) in anoxic sediment beds and much greater (∼1 m) in certain sandy beds. Composition of Sediments. The mineralogical composition of oceanic sediments is highly dependent on their location (Riley and Chester, 1971). Some oceanic regions are rich in opaline silica (SiO2 ), like the belt of sediments around Antarctica, due to the deposition of particles such as diatom frustules. Other areas contain large fractions of carbonate solids (CaCO3 ) from the input of organisms with calcareous tests like foraminifera, a widespread group of marine protists. Much of the Atlantic, Southern Pacific, and Indian Oceans have such calcareous deposits. Still other regions are rich in clayey minerals from land weathering. In general, the organic carbon content of marine sediments decreases with distance from land. Typical coastal sediments have a weight fraction organic carbon (foc ) of about 1% (0.01 g organic carbon per g dry sediment), but this ranges from as low as 0.1% and up to 10% (Hyland et al., 2005). The pH of oceanic sediment pore waters varies from 6 to 9 for coastal sites and is generally between pH 6 and 8 in open ocean deposits (Baas-Becking et al., 1960). Many sites in both coastal and open ocean have pore water near the sediment bed-water interface that is oxic, but many other locations do not have dissolved O2 in the sediment bed. Anoxic conditions occur in sediments where the accumulation of organic matter is so great that aerobic organisms do not have enough O2 available to oxidize this food supply. As a consequence, anaerobic microorganisms take over, using electron acceptors like sulfate to process the organic matter. At many locations, the sediments become so depleted in inorganic electron acceptors that methanogenesis, the production of methane (CH4 ), occurs (e.g., Reeburgh, 2007). At these sites, the sediment is rich in reduced chemicals like ferrous iron (Fe+2 ) and hydrogen sulfide (H2 S), and transformations such as reductive dechlorinations requiring a supply of electrons can occur (see Chapter 23). The composition of lake sediments also widely varies. Generally, the solids’ mineralogies closely correspond to the geological deposits located nearby. The organic carbon content in lake sediments has been reported to vary from 0.1 to 10% by weight (Avnimelech et al., 2001). Typically, the organic matter’s chemical composition is similar to that of land plants, e.g., lignin-derived macromolecular material.

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5.4

Soil and Groundwater In this section, we characterize the environmental land compartment. This compartment consists of several layers (Fig. 5.8). First, we recognize an uppermost soil layer or pedosphere. This soil and the layer below it are commonly filled with air and water, and together these layers are called the unsaturated or vadose zone. Next, a narrow transitional layer called the “capillary fringe” exists, in which water is pulled up by surface tension. Finally, one reaches a “saturated” zone in which the pore spaces are entirely filled with groundwater. We focus most of our discussion on the upper soil zone and on the groundwater that flows in the saturated zone. These two subcompartments are important for problems concerning the fate of organic chemicals in the environment as soil is heavily used in agriculture and the groundwater below the water table is an important water supply. Structure and Composition of Soil Soil Horizons of the Pedosphere. The pedosphere is defined as the uppermost layer of the land compartment where the actions of plants and weathering interact with the lithosphere (Earth’s solid mineral exterior) to form soil. This sub-compartment starts at the bottom of the atmosphere and goes to the depth at which land biota have not changed the original geological materials. The overall depth of soil varies widely from location to location. For example, in the United States, the thickness of the soil zone is about 2 meters in much of the center of the country, less than 25 cm deep in mountainous and arid areas, and is nonexistent at places with exposed bedrock (COMET Program, 2006). For investigations of global carbon reservoirs, soil depths

well soil zone

unsaturated/ vadose zone

Figure 5.8 Depiction of the land compartment with the uppermost soil zone, the unsaturated or vadose zone, the capillary fridge, where groundwater seeps up via capillary action, and the saturated zone where groundwater flows. Adapted from Heath (1983).

capillary fringe groundwater

water table

Soil and Groundwater

(a)

149

(b) O horizon

A horizon

B horizon

C horizon

Figure 5.9 (a) Schematic depiction of horizons in the soil zone and (b) photograph of a corresponding soil section. (Photo: Jim Turenne accessed at Turenne, 2014.)

have been integrated for their carbon content down to 200 cm (e.g., Batjes, 1996). In contrast, those interested in the fates of pesticides used in agriculture commonly choose to consider only the uppermost 10 to 15 cm of soil that is ploughed (e.g., Mackay, 2001). By choosing a typical value of soil depth, we can make an estimate of the pedosphere compartment’s size. If one takes a 100 cm soil thickness and an average bulk density of 1.5 g cm−3 , the calculated total mass of soil on Earth is only 5 percent of the total mass of air in the atmosphere (Table 5.1). With time and the action of organisms and weather, the pedosphere evolves to have a layered nature (Fig. 5.9). The uppermost layer, or horizon, is most heavily influenced by the growth of plants, which introduces organic matter. The composition of this soil organic matter (SOM, Box 5.3) is similar to components of vascular plants like lignin, but SOM also includes decomposition products like humic substances (Box 5.3). For a detailed discussion on the present view of the structural composition of SOM, we refer to Chapter 13. In brief, SOM contains a complex mixture of aromatic and aliphatic carbon. Oxygen functionalities of SOM include carboxylic acids, phenols, and aliphatic alcohols. Nitrogen, phosphorus, and sulfur-containing functional groups are rarely present. The end result is an upper layer of soil that is organic rich and often appears dark in color (“O horizon” in Fig. 5.9). Upon reviewing data from soils collected

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Earth Systems and Compartments

around the world, Batjes (1996) reported that the uppermost 30 cm of soils has an average weight fraction of organic carbon, foc , of 1.5%. As the organic matter in the surface soil is degraded, organic acids are formed. Such products are called humic and fulvic acids (see also Chapter 13), names that refer to their solubilities in water as a function of pH (Box 5.3). Fulvic acids tend to be smaller than humic acids, and somewhat richer in oxygen functionalities. The molecular structures of these humic acids and fulvic acids bear significant similarities to the structures making up SOM as they derive from the same organisms and decomposition processes. As a result of decomposition and leaching, the foc drops to an average value of 0.7% for the layer between 0.3 and 2 m depth (Batjes, 1996). The fulvic and humic acids leach metals like iron out of the uppermost soil minerals. Subsequently, when rainfall causes water to flow downward into the soil, these organic acids and their associated metals are carried deeper into the soil. The result is a layer of metal-depleted minerals (“A” horizon in Fig. 5.9) overlaying a deeper layer in which the metals have been re-precipitated, often leading to a “rusty” coloring (“B” horizon in Fig. 5.9). Like the uppermost soil layer, these deeper horizons typically have airfilled spaces and water coatings on the mineral surfaces. However, unlike the soil near the ground surface, the deeper layers often have lower organic carbon contents, with foc of only about 0.1 to 0.5% by weight. At still greater depths, the mineral material remains largely unaltered by the soilforming processes acting close to the ground surface; this deeper zone chiefly reflects the original minerals that were deposited at the location (i.e., parent material) and is called the “C” horizon. The top of the C horizon, therefore, is the top of the “lithosphere,” the rocky outer layer of the Earth. The lithosphere acts as a large reservoir that plays vital roles for geochemical cycles (e.g., carbon dioxide) on timescales of hundreds of millions of years. The lithosphere may become relevant for anthropogenic organic compounds if methods like deep well injection, fracking for oil and gas mining, and geothermal heat exploitation become widespread; such activities will artificially connect fluids trapped in the lithosphere to those on the Earth’s surface. Soil Mineral Composition. A key outcome of soil formation is that new materials, both inorganic and organic, are formed from the parent minerals and ecosystem derived organic matter. These materials become part of the soil’s overall composition. Inorganic minerals in soils include oxyhydroxides, like ferrihydrite (Fe(OH)3 ), goethite (FeO(OH), and gibbsite (Al(OH)3 ); aluminosilicates, like kaolinite (Al2 Si2 O5 (OH)4 ); and carbonates, like calcite (CaCO3 ). The mineral mixture in any soil depends, of course, on the kinds of rocks in the area. For example, in New England, the parent rocks are igneous granites, and these lead to release quartz (SiO2 ), biotite mica (K(Mg,Fe)3 AlSi3 O10 (OH)2 ), and feldspars (e.g., NaAlSi3 O8 ). In contrast, in the Midwestern United States, the surface rocks are metamorphic carbonates. When these materials weather, they release any clayey detritus co-deposited with the original sediment deposits and carbonate fines (e.g., CaCO3 ). These solids have varying surface properties, including specific surface areas and reactive moieties that can cause surface charging. These inorganic solids, and the

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aggregates they form, have a range of pores in them, referred to as micropores ( 50 nm diameter). The term nanopores is often used to mean the sum of micropores plus mesopores (Everett, 1972). We need to understand the properties of minerals in soils in order to predict whether chemicals adsorb (see Chapters 11 and 14) or react via hydrolysis, redox processes, or photochemical transformations (see Chapters 21, 23, and 24) on their surfaces. Soil Porosity. Porosity is another important property of soil, since the volume fraction that is filled with fluids (gas and water) in soil affects the mobility and reactivity of chemicals underground (Chapters 12 and 20). Batjes (1996) found the bulk density of soils (i.e., the mass of solids divided by the sum of volumes of air plus water plus solids) varies from about 1.26 to 1.67 g cm−3 for a wide range of soil types. Assuming a mineral density of 2.6 g cm−3 , this range of bulk densities suggests soil porosities are typically 40 to 50% (Box 5.4). Therefore, about half of the total soil volume is filled with solids and the other half is filled with the soil air and water. For comparison, coarse materials like sands and gravels can have porosities that are significantly less. In general, water flows slowly through the voids below the ground surface. We can do an illustrative calculation to understand the velocity of vertical water flow in the unsaturated or vadose zone (shown as “percolation” in Fig. 5.4). If rainfall at a particular location is 0.5 m per year, but half of that water is lost back to the atmosphere via evaporation and evapotranspiration, then 0.25 m3 of water per m2 of soil surface will displace water in the unsaturated zone each year. If a soil has porosity of 50%, 20% of which is filled with water, then a cubic meter of that soil contains 0.1 m3 of water. By combining the infiltration rate and the soil water content, one finds that on average the water moves downward through the unsaturated zone at a rate of 2.5 m per year (or about 0.7 cm per day). Obviously, such a rate is highly dependent on both the timeand space-varying rain rate and the residual water held in the soil’s unsaturated zone at a particular locale. However, this example shows that water is typically not moving downward very fast. Chemical Composition of Soil Pore Water. Since soils lay directly beneath the atmosphere, their pore space is filled with water and also, often, with an air-like mix of gases including O2 . When such gases are present, the soil system is considered aerobic. However, some soils are regularly “waterlogged,” as occurs in peatlands and wetlands. In this case, O2 in the soil may be absent as its use by microorganisms exceeds it replacement from overlying air. The soil system void of O2 is said to be anaerobic. If a platinum electrode is used to assess the electron availability in waterlogged soil systems, the electrode potential (or “EH ”, see Chapter 23) would likely be near or below 0 mV. In such a “reducing” environment, minerals containing redox-sensitive metals like iron would not include Fe(+III) in solids like goethite (FeOOH), but rather Fe(+II) solids like siderite (FeCO3 ) and pyrite (FeS2 ). Conversely, in aerobic systems, oxygen can act as an electron sink, creating an “oxidizing” environment. Figure 5.10 highlights the EH of various aerobic and anaerobic soil systems. EH

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Earth Systems and Compartments

800 600

200

Figure 5.10 Typical pH and electrode potential (EH ) for a range of different types of soils. Adapted from Baas-Becking (1960).

2

4

nodu

les

us y cal care o

6

lime

–400

sligh tl

ironrich

–200

y cal care o

us

0

highl

EH (mV)

400

8

10

12

pH

values predominately lay in the range of 500 to 700 mV in aerobic soils, but drop below 200 mV in anaerobic cases (Baas-Becking, 1960; Snakin et al., 2001). As EH is related to electron availability (negative values imply high electron availability, see Chapter 23), pH is related to proton availability (low values imply high proton availability). Values of pH vary widely in different soils (see Fig. 5.10). Many soils have values in the range of 5 to 7. Those soils rich in iron often exhibit a pH of less than 5. Snakin et al. (2001) measured average pH values of 6.4 for agricultural soils and 5.4 for forest soils around the world. Groundwater in the Saturated Zone In the saturated zone of the land compartment, the groundwater completely fills all the spaces between solids (Fig. 5.8). The top of this saturated zone is called the “water table”. If a subsurface saturated volume is permeable enough to be readily pumped out, it is called an aquifer. With a total volume of 8.3 × 1015 m3 , groundwater represents by far the largest liquid fresh water reservoir on Earth (see Table 5.3). For many people, shallow aquifers provide water for drinking, irrigation, and industrial applications. Despite this immense utility, groundwater systems are among the most vulnerable to pollution since so much of our waste is disposed on the ground surface (see also Chapter 3). Deep groundwater systems have residence times of the order of 1000 to 10,000 years. The water often originates from time periods with different climate (ice age) and are

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presently not, or only slowly, replenished. Thus, the use of these deep systems for irrigation is similar to the exploitation of non-renewable resources. Groundwater Flow. The rate of groundwater flow varies widely. Groundwater seeps largely horizontally through the diverse subsurface media at rates as slow as about 0.01 cm per day to much faster rates like 30 cm per day (Alley et al., 1999). This movement of groundwater can also carry organic chemicals; numerous polluted subsurface sites have been identified in which the groundwater transported organic compounds for many kilometers over decades of travel time. Examples of pollutant transport in aquifers include studies by Barber et al. (2009), measuring PCE, dichlorobenzene, nonyl phenol, and estradiol; by Aeppli et al. (2010), measuring chlorinated ethenes; and by Roy et al. (2014), measuring artificial sweeteners. The flow rates of groundwater are calculated from Darcy’s Law, which states that the velocity of the water is directly proportional to the hydraulic conductivity and head gradient, and inversely related to the porosity. Hydraulic conductivities vary widely, depending on the “tightness” of the material through which the water is flowing. For example, the conductivity through gravel is much greater than through sand, which in turn is much higher than through metamorphic materials like sandstones and shales (Heath, 1983). Another important feature of flow in groundwater is that transport is seldom turbulent because of the small size of the pores. Therefore, molecular diffusion and dispersion along the flow are the main producers of “randomness” in the mass flux of chemical compounds. Heterogeneities exist on all spatial scales, from the micropores to the macrostructure of the aquifer (Fig. 5.11). Therefore, the description of transport in porous media strongly depends on the scale of interest (Gelhar et al., 1992). Thus, (a)

Figure 5.11 Impact of heterogeneity on transport in porous media. Three important mechanisms of transport and mixing are (a) inter-pore dispersion caused by mixing between pore channels, (b) intra-pore dispersion caused by non-uniform velocity distributions and mixing in individual channels, and (c) dispersion and retardation of solute transport by molecular diffusion between open and dead-end pores. Such effects also develop from slow exchanges between strata of differing hydraulic conductivities, such as a clay layer in a sandy aquifer.

(b)

(c)

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Table 5.9 Concentrations (mmol L−1 ) of Major Ions and pH in Four Groundwaters from Diverse Formations a

Na+ K+ Mg+2 Ca+2 Cl− HCO3 − SO4 − pH a

Limestone formation

Volcanic rocks

Springs (short residence time)

Metamorphic rocks (long residence time)

1.2 0.05 2.3 3.6 1.5 10 0.6 —

1.6 0.08 0.05 0.16 0.5 1.3 0.2 6.7

0.1 0.03 0.03 0.08 0.01 0.3 0.01 6.2

120 0.8 6.6 110 350 0.9 0.01 6.5

Data from Nelson (2002).

the quantification of transport and transformation in porous media, as deduced from measurements in laboratory systems, cannot always be accurately extrapolated to field situations. Chemical Composition of Groundwater. The chemical composition of groundwater largely depends on the nature of the minerals through which the groundwater is flowing, although inputs from humans can have a big impact. For example, the concentration of calcium in a particular groundwater measured in a limestone formation (CaCO3 (s)) was 3.6 mM, while the calcium in groundwater measured in volcanic rock was only 0.16 mM (Table 5.9). Similarly, the bicarbonate (HCO−3 ) concentrations in these two systems were 10 mM and 1.3 mM, respectively. In general, groundwater picks up an inorganic solute load that reflects dissolution of those minerals in which the groundwater occurs. Additionally, groundwater with limited contact time below ground tends to have much lower ionic concentrations (e.g., < 1 mM) than in water that has a long residence time underground, as exemplified by water measured in springs versus metamorphic rocks (Table 5.9). The pH values of 76 different shallow groundwaters, as reported by Baas Becking et al. (1960), ranged from a little below 6 to about 9. Sometimes, groundwater is somewhat more acidic than expected, assuming equilibration with the surrounding solids. This lowering of pH may be due to the buildup of CO2 in the water from microbial oxidization of the organic compounds. Finally, for unpolluted sites, investigators typically find DOC concentrations in groundwater to be near 1 to 2 mg C L−1 , although values as low as 0.1 mg C L−1 and as high as 60 mg C L−1 have also been measured (Leenheer et al., 1974; Gooddy and Hinsby, 2009).

5.5

Biota To end our discussion of Earth systems, we briefly introduce global biota, which consist of all the living organisms: animals, plants, fungi, protists, bacteria, and archaea. The biota “compartment” is commonly divided into oceanic and terrestrial parts

Questions

155

Table 5.10 Estimated Properties of the Global Biota a Marine Primary producer biomass (g C) phytoplankton land plants Prokaryotic biomass (g C) b seawater + upper 10 cm of sediment soil + upper 8 m below it Animal biomass (g C) Total biomass (g C) Total net primary production (g C yr−1 ) Areal average net primary production (g C m−2 yr−1 ) c

Terrestrial

∼0.5 – 3 × 1015 ∼1 – 2 × 1015 ∼10 – 100 × ∼10 – 100 × 1015 50 × 1015 140 1015

450 – 650 × 1015 ∼30 × 1015 ∼1 × 1015 450 – 650 × 1015 54 × 1015 410

a Data compiled from Whitman et al. (1998); Prentice et al. (2001); Zhao and Running (2010); Chavez et al. (2011); Buitenhuis et al. (2012); Buitenhuis et al. (2013); Sutton (2013); and Irigoien et al. (2014). b Much of the range in marine values results from assuming either 9 or 20 × 10−15 g C per cell. c Productivity divided by area of ocean (3.61 × 1014 m2 ) or of ice-free land (1.33 × 1014 m2 ), respectively.

(Table 5.10). The total mass of marine biota is much smaller than the mass of biota on land, particularly for photosynthetic organisms. Interestingly, the total net primary production on land and in the water is nearly equal, which is largely due to the rapid turnover of most marine primary producers (days) as compared to terrestrial primary producers (year to decades). Since the ocean is about three times larger than the land in terms of surface area, the net primary productivity per unit area on land is about three times greater than in the ocean. Another key difference is that heterotrophic microorganisms in the oceans have a biomass that is comparable to the primary producer biomass, while in the terrestrial system, the microbial mass contribution is proportionally much less. Finally, acoustic observations and ecological modeling suggest that fish contribute most of the biomass in the oceans (Sutton, 2013; Irigoien et al., 2014), while animals on land contribute about 1000 times less mass than primary producers. Importantly, these networks of organisms can act to accumulate organic chemicals from their surroundings, thereby putting their food webs (including humans) at risk of toxic exposures. The topic of bioaccumulation will be further examined as a function of chemical and organism properties in Chapter 16. Another important role of the biota with respect to organic chemicals involves their potential to transform such organic substrates, as subsequently discussed in Chapter 26.

5.6

Questions Q 5.1 (a) Explain the relation between the terms “compartment” and “system” as they are used in this book.

156

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(b) Can a system consist of several compartments? (c) Can a compartment consist of several systems? Q 5.2 On one hand, density of matter (solid, liquid, gaseous) decreases with increasing temperature (disregarding a few exceptions like water temperature between 0 and 4◦ C). On the other hand, the in situ temperature in the troposphere usually decreases with altitude (Fig. 5.1). Does this mean that air density increases with altitude, that is, the air column is physically unstable? Is there a way out of the dilemma? Q 5.3 Why is the direction of the global wind field mostly directed along the east/west axis and not along north/south? Q 5.4 Mixing in the atmosphere between the N- and S-hemisphere is slower than mixing within the hemispheres? Why? Q 5.5 Explain the difference between “primary” and “secondary” aerosols. Q 5.6 Why is the concentration of diatomic nitrogen (N2 ), on a molecule per cm3 basis, different in the troposphere and the stratosphere assuming this substance makes up 78% of the mass in both places? Q 5.7 How many molecules per cm3 would one typically find in an air sample taken at sea level in a rural area without much traffic? Q 5.8 (a) By how much would sea level rise globally if all the polar ice would melt? Note: For a precise calculation you would need a detailed map of the topography of the continents. However, as a first approximation you can calculate a lower and upper limit of sea level rise. (b) Compare the result with the effect of thermal expansion of the water column due to an overall temperature increase of the ocean by 3◦ C. Use Appendix B, Table B.3. Q 5.9 By which mechanism does the ocean mix vertically (a) in the top 200 meters; (b) or throughout the whole water column?

157

Questions

Q 5.10 Based on data provided in Tables 5.3, 5.5, and 5.7, what is the mean residence time of Na+ in the sea? Q 5.11 (a) Considering the patterns shown here in which the pH is sometimes higher in seawaters than in deep sea sediment pore waters, what processes could explain this difference? (b) Considering the patterns shown here in which the distribution of EH is somewhat narrower in seawaters than in deep sea sediment pore waters, what processes could explain this difference? 800

seawater

600

600

400

400

EH (mV)

EH (mV)

800

200 0

200 0

–200

–200

–400

–400 2

4

6

pH

8

10

12

deep sea sediment pore water

2

4

6

pH

8

10

12

Comparison of the range of (pH, EH ) conditions found for seawater and pore waters from deep sea sediments (Baas Becking et al., 1960). Q 5.12 Why is the physics of vertical mixing in a cold freshwater lake different from vertical mixing in the ocean? Q 5.13 Explain the phenomenon of the thermal bar that is observed in lakes. Q 5.14 (a) By how much does the deep sea sediment column grow in height (cm yr−1 ) given the range of sediment accumulation rates listed in Table 5.8? Assume a porosity at the sediment surface of ϕ = 0.8 and a solid density ρs = 2.5 g cm−3 . (b) Why is the long-term sediment growth of the sediment column smaller than the number calculated with the preceding data?

158

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Q 5.15 Explain the difference between evaporation and evapotranspiration. Q 5.16 (a) Why are soils in wetlands often anaerobic? (b) What is the common form of Fe in these soils? Q 5.17 Give the main characteristics of the different layers in soil (O, A, B, and C horizons, Fig. 5.10). Q 5.18 Which properties determine the flow velocity of groundwater? Explain whether each property enhances or reduces flow velocity. Q 5.19 Which processes are responsible for mixing in porous media filled with water? Q 5.20 Total net primary production on land and in the ocean is almost equal, but the biomass on land is significantly larger? Why? Note: Perhaps, calculation of “turnover rates” (net primary production per biomass) helps.

5.7

Bibliography Aeppli, C.; Hofstetter, T. B.; Amaral, H. I. F.; Kipfer, R.; Schwarzenbach, R. P.; Berg, M., Quantifying in situ transformation rates of chlorinated ethenes by combining compound-specific stable isotope analysis, groundwater dating, and carbon isotope mass balances. Environ. Sci. Technol. 2010, 44(10), 3705–3711. Alley, W. M.; Reilly, T. E.; Franke, O. L., Sustainability of Ground-Water Resources; Circular 1186. U.S. Geological Survery (USGS), Denver, CO, 1999; p 86. http://pubs.usgs.gov/circ/circ1186/. Armstrong, R. A.; Peterson, M. L.; Lee, C.; Wakeham, S. G., Settling velocity spectra and the ballast ratio hypothesis. Deep-Sea Res. Part II-Top. Stud. Oceanogr. 2009, 56(18), 1470–1478. Avnimelech, Y.; Ritvo, G.; Meijer, L. E.; Kochba, M., Water content, organic carbon and dry bulk density in flooded sediments. Aquac. Eng. 2001, 25(1), 25–33. Baas Becking, L. G. M.; Kaplan, I. R.; Moore, D., Limits of the natural environment in terms of pH and oxidation-reduction potentials. J. Geol. 1960, 68(3), 243–284. Barber, L. B.; Keefe, S. H.; Leblanc, D. R.; Bradley, P. M.; Chapelle, F. H.; Meyer, M. T.; Loftin, K. A.; Kolpin, D. W.; Rubio, F., Fate of sulfamethoxazole, 4-nonylphenol, and 17 beta-estradiol in groundwater contaminated by wastewater treatment plant effluent. Environ. Sci. Technol. 2009, 43(13), 4843–4850.

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Sutton, T. T., Vertical ecology of the pelagic ocean: classical patterns and new perspectives. J. Fish Biol. 2013, 83(6), 1508–1527. Thurman, E. M., Organic Geochemistry of Natural Waters. Martinus Nijhoff/Dr. W. Junk Publishers: Dordrecht, 1985; p 497. Townley, L. R.; Trefry, M. G., Surface water-groundwater interaction near shallow circular lakes: Flow geometry in three dimensions. Water Resour. Res. 2000, 36(4), 935–948. Turenne, J., New England Soil Profiles: Haven Series. 2014 [accessed on May 2015]. http://nesoil.com/images/haven.htm. Turner, J. T., Zooplankton fecal pellets, marine snow and sinking phytoplankton blooms. Aquat. Microb. Ecol. 2002, 27(1), 57–102. Verburg, P.; Hecky, R. E.; Kling, H., Ecological consequences of a century of warming in Lake Tanganyika. Science 2003, 301(5632), 505–507. Voiland, A., Aerosols: Tiny Particles, Big Impact. NASA Earth Observatory: 2010 [accessed on March 2015]. http://earthobservatory.nasa.gov/Features/Aerosols. Wanner, O.; Egli, T.; Fleischmann, T.; Lanz, K.; Reichert, P.; Schwarzenbach, R. P., Behavior of the insecticides disulfoton and thiometon in the Rhine River: a chemodynamic study. Environ. Sci. Technol. 1989, 23(10), 1232–1242. Weber, K.; Goerke, H., Persistent organic pollutants (POPs) in antarctic fish: levels, patterns, changes. Chemosphere 2003, 53(6), 667–678. Wetzel, R. G., Limnology 3rd ed.; Academic Press: San Diego, 2001; p 1006. Whitman, W. B.; Coleman, D. C.; Wiebe, W. J., Prokaryotes: The unseen majority. Proc. Natl. Acad. Sci. U.S.A. 1998, 95(12), 6578–6583. Williams, D. R., Earth Fact Sheet. NASA: 2013 [accessed on Need Date, 2014]. http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html. Winkler, P., Observations on acidity in continental and in marine atmospheric aerosols and in precipitation. J. Geophys. Res.-Oceans 1980, 85(NC8), 4481–4486. Zhao, M. S.; Running, S. W., Drought-induced reduction in global terrestrial net primary production from 2000 through 2009. Science 2010, 329(5994), 940–943.

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6.1

Systems and Models Mathematical Models: Definition and Role Environmental Systems and System Models Box 6.1 Terminology for Dynamic Models of Environmental Systems A Case Study: Recipes for the Model Builder

6.2

Box Models: A Concept for a Simple World Linear One-Box Model with One State Variable Box 6.2 Solution to the First-Order Linear Inhomogeneous Differential Equation (FOLIDE) From One-Box to Multi-Box Models Box 6.3 Tetrachloroethene (PCE) in Mystery Lake: One-Box Model (Model A) Box 6.4 Solution of Two Coupled First-Order Linear Homogeneous Differential Equations with a Conservation Law Box 6.5 Solution of Two Coupled First-Order Linear Inhomogeneous Differential Equations (Coupled FOLIDEs) Box 6.6 Tetrachloroethene (PCE) in Mystery Lake: Two-Box Model (Model B)

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

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6.3

When Space Matters: Transport Processes Deterministic versus Random Motion: A Thought Experiment in a Train Mathematical Description of Transport Processes Continuous Models

6.4

Models in Space and Time Gauss’ Theorem Diffusion/Advection/Reaction Modeling Box 6.7 One-Dimensional Diffusion-Advection-Reaction Equation at Steady State

6.5

Questions and Problems

6.6

Bibliography

Systems and Models

167

Chemicals in the environment experience a variety of processes. For example, they may react with other chemicals, sorb onto surfaces, be transferred from air to water, or be transported by wind and water currents. Therefore, analyzing the fate of organic chemicals in the environment requires more than studying chemicals in the laboratory; it is a multidisciplinary task that incorporates knowledge of chemical properties as well as of the characteristics of the environment in which these chemicals are found. As we proceed through the book’s chapters, our focus gradually moves from considerations of single processes acting on a chemical to more complex situations where several processes occur simultaneously. A common language is needed if we want to go beyond qualitative descriptions of the combined effects of processes like acid/base equilibrium, air–water exchange, turbulent mixing, and others. The common language is mathematics, and the translation of all these processes into that language is called mathematical modeling. As we become familiar with concepts like the acidity constant for acid/base equilibrium (Chapter 4), Henry’s law for air–water phase equilibrium (Chapter 9), or the ideal gas law, we easily forget that these simple mathematical expressions are models of phenomena that in reality are extremely complex. In environmental sciences, the expression “mathematical model” has over time acquired the meaning of something much more complicated than partitioning constants. We think of a mathematical tool that can describe a whole lake, the atmosphere, or even a combined atmosphere/ocean/land system, as in climate modeling. However, the transition from a partitioning constant to a climate model is gradual. Although the former is more fundamental than the latter, and thus often called a “law,” the same general idea is behind both models: when we describe an individual process or a whole natural system in terms of mathematical equations, we use a mathematical model by simplifying the infinite complexity of reality. This chapter provides the reader with a basic toolkit for building mathematical models. We focus on models of whole systems that themselves are built by combining individual process models. The mathematical description (the modeling) of individual processes and more refined modeling tools are introduced in later chapters, where appropriate.

6.1

Systems and Models Mathematical Models: Definition and Role We define a mathematical model as a mathematical equation or a set of mathematical equations designed to imitate or reproduce one or several selected properties of a real system. Let us briefly focus on two aspects of this rather abstract definition. First, a model is intended to be a simplified picture (imitation) of a real system. Like in a caricature, simplification exaggerates certain properties, but, in doing so, renders clearer those aspects that are important for the model’s specific purpose. Second, models are always designed to focus on a limited number of properties while all the others are overlooked. A model of everything is impossible; if one existed, it would be the real

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world, not a model. Hence, one does not build a lake model without knowing what processes and data the model should reproduce; for instance, its wave patterns, water temperature, the concentration of benzene in the surface water, or its fish stock. In short, a model is never as complex and refined as the real system that it imitates, yet this shortcoming is advantageous as it allows us to identify properties of the real system that may not become apparent without focusing on a limited number of aspects. What then are models good for in environmental sciences? Kleindorfer et al. (1993) distinguish between two fundamentally different goals of modeling, which they call inference and prediction. Inference means to bring some order to empirical data and to extract general rules from this order, that is, to develop models like the concept of the acidity constant to express the acid/base equilibrium. Once these rules have been extracted from real data by inference, the gained insight can be used to predict the outcome of a different experimental setup. Applied to environmental models, inference means to compare different models with real data to identify and quantify the major processes at work, whereas prediction means to extrapolate the development of a system into the future. Environmental Systems and System Models In order to explain what we mean with the term system, we have to highlight the difference between system and model. A system is a subunit of the world defined by the boundary that separates the system from the rest of the world (see Box 5.1 for the definitions of related terms). Examples of systems are the atmosphere, the ocean, a lake, a subsurface aquifer, and an algal cell. We can think of systems without defining a corresponding system model, but we cannot construct a model without having a system in mind, although this choice is often the consequence of an implicit, not a conscious act. A system can also include parts of the nonphysical world, like a country’s politics or economy. In this respect, the term boundary in the preceding definition is not necessarily a physical boundary. Let us now imagine a Roman architect who wants to build a new temple dedicated to Jupiter. The temple is his system. In order to better sell his idea to the Emperor, he has to build a model (modulus). When doing so, he must make several decisions: How detailed should the model be? Is it enough to represent the pillars by simple cylinders, or should the ornamentation be shown as well? Should colors be used? Should the interior of the temple also be shown and should it be furnished? Of course, the goal here is not to build a Roman temple but a mathematical model of an environmental system such as a lake. But the decisions that need to be made to build the model are similar: How detailed should we make the description of the lake? Do we need water temperature to characterize the state of the lake? If yes, is a single mean temperature value good enough, or do we need to distinguish between surface and deep water (epilimnion and hypolimnion, see Fig. 5.7) or even among every cubic meter of the water body? Which chemical parameters do we need and at what spatial resolution, and what about biological parameters such as phytoplankton, zooplankton, and fish? Do we really need to impress the Emperor, or would something less and cheaper work?

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Box 6.1 Terminology for Dynamic Models of Environmental Systems State variable

Quantity used in the model to describe the state of the system. A state variable usually depends on time t and (for some models) on one or more space coordinates x, y, z. Example: Concentration of chemical in a lake

Continuous state variable

State variable that depends on at least one space coordinate.

External force

Influence (constant or time-variable) that drives the state variables from outside. The term force is not restricted to its physical meaning. Example: Input of chemical into surface water of a lake

Output

Influence of state variables on the outside world, often a mass flux out of the system. Example: Flux of chemical from lake surface to the atmosphere

Internal process

Process occuring between state variables such as transport of a chemical or chemical transformation. Example: Vertical mixing of chemical between surface and deep water of a lake

Model parameter

Parameter used to describe modeled processes (external, output, and internal). Example: Lake volume

The answer to all these questions depends on the purpose of the model. Every lake model has its own set of properties that are used to characterize the system. Every property is represented by a mathematical variable (usually a function of time, often also of space) that we call a state variable (see Box 6.1 for terminology). The heart of the mathematical model is a set of equations that describes how these state variables are related to each other (the effect of internal processes) and how they are affected by external influences, which are influences from the world outside of the chosen system. Such external influences can be the intensity of solar radiation at the lake surface, the water discharge of the inlets into the lake and the concentrations of chemicals they carry, or the concentration of chemicals in the air. Since these influences drive the state variables, in the language of system analysis, they are called external forces (Fig. 6.1). Here, the term “force” is used more generally than a physical force, instead meaning influence. External indicates that the strength of the force is not reproduced by the model equations, like state variables are, but has to be fed into the model as a parameter such as lake volume, lake surface, or discharge rates. From a systemic point of view, the main difference between external forces and state variables is that the size and temporal change of the latter are calculated by the model while the size and temporal change of the former are known or assumed. The system is influenced (driven) by the outside world, but may also influence the outside world. For example, as the result of the chemical degradation of an organic chemical in a lake, new chemicals can form that are then carried to the outside world by the outlet of the lake. These influences are called outputs. The external forces are not

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out state variables

Figure 6.1 A mathematical model is defined by a boundary (solid line) that separates a subunit of the world (IN) from the rest of the world (OUT). The state of the system is characterized by a set of variables (state variables). The dynamics of these variables is determined by internal processes and by external forces. The impacts of the system on the rest of the world are called outputs. An essential aspect of the representation of the world as IN and OUT is that the effect of the output on the external forces is neglected. The figure gives a general view of a system with three state variables. The lines with arrows show the interactions between the components; sometimes these interactions are negligible.

external forces

internal processes

in

output

system boundary

no feedback from “output” to “external forces”

influenced by the output; external forces ignore the output. This is one of the essential simplifications of mathematical modeling. The infinite loop (everything influences everything else and is influenced by everything else) is transformed into a one-way street (driving forces influence the system state, but not vice versa) by cutting the feedback from system state to external forces (see Fig. 6.1). Model parameters are used to mathematically describe all processes that are part of the model (external, output, and internal). These parameters must be known or assumed and feed into the system. Therefore, they represent another kind of input for the model. Some model parameters can be taken from independent sources (e.g., values from chemical handbooks like a Henry’s law constant or solubility) or from scientific publications (e.g., the relation between wind speed and air–water exchange). Other parameters have to be determined indirectly by comparing model calculations with data, a process called model calibration. Incorporating all the newly defined elements, we can further refine the definition of a mathematical model: A mathematical model of a system is defined by a specific choice of state variables, by the relations among the state variables (internal processes), by the action of the outside world on the state variables (external forces), and by the action of the model on the outside world (output). The feedback from the output to the external forces is neglected. A Case Study: Recipes for the Model Builder In the following case study, we apply the defined terminology of Box 6.1 to build a concrete model. To do so, we will use a few basic recipes. The focus of the

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PCE concentration (10–9 mol L–1)

(a) 0

5

10

15

20

25

30

(b)

water temperature T (°C) 0 5 10 15 20

35

0 epilimnion

5 10

depth (m)

Figure 6.2 (a) Concentrations of tetrachloroethene (PCE) as a function of depth measured in Mystery Lake, Cleanland on two consecutive sampling dates (August 15 and September 4). Maximum depth of the lake is 35 m. The water samples in the vertical are taken every 2.5 m (15 samples). The green area represents the PCE that disappeared from the epilimnion between the two sampling dates; the brown area represents the PCE that moved into the hypolimnion. (b) Schematic view of Mystery Lake and vertical temperature profile in August/September. The thermocline (boundary between epilimnion and hypolimnion, see Fig. 5.7), is between 10 and 15 m depth.

T

15

thermocline

hypolimnion

20 25

August 15 September 4

30 35 sediment

Mystery Lake

sediment

case is the contamination of a lake with tetrachloroethene (PCE), a chlorinated solvent and one of our companion compounds (see Chapter 3). We continually refer back to this case in following sections as more complexity is introduced into our modeling. Case Study: Heidi and Paul, water chemists employed by the Public Water Authority of Cleanland, are responsible for the monitoring program conducted in Mystery Lake, located close to the capital of Cleanland. On August 15, they find dissolved tetrachloroethene (PCE) in water samples taken at several depths in the lake (Fig. 6.2). The PCE is only measured in the upper 10 m of the water column and is below the detection limit at lower depths. In water samples taken in the previous months, PCE concentrations had always been below the detection limit. Based on these new observations, Heidi and Paul decide to go to the lake again to measure another PCE concentration profile and to sample the major tributaries of Mystery Lake. The samples are taken on September 4, three weeks after the first sampling. They find that the PCE concentration in the top 10 m of the lake has dropped by about 50%, but they now detect some PCE in the lower water layers. PCE concentrations in the tributaries are below the detection limit. No indication of an accidental spill is found in drainage areas of places where PCE is used, such as dry cleaning businesses or car repair workshops. The Water Authority is alarmed by the detection of PCE in the lake. Heidi and Paul are asked to predict the future development of PCE concentrations in the lake and how long it will take until the concentration has dropped below 1 × 10−9 mol L−1 everywhere in the lake. A colleague from the Engineering Section suggests to Heidi and Paul they should use one of the many lake models published in the scientific literature (e.g., Schnoor, 1996) in order to predict the further development of PCE concentrations in Mystery Lake. Heidi and Paul quickly realize that most of these models are fairly sophisticated and include all kinds of processes such as hydrodynamics of the lake driven by the wind, tributaries, and heat exchange at the water surface; the settling of suspended particles; air-water exchange at the water surface; growth and decomposition of various groups of phyto- and zooplankton; and more. “Complexity has its price,” they say to each other. Heidi and Paul soon become aware that in order to run such a model for their lake, a large amount of information would

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be needed (meteorological data, discharge rates of inlets and outlets as well as their chemical compositions, and much more), data that is not available for Mystery Lake. Fortunately, Heidi remembers a course on modeling she took a long time ago, in particular some simple rules for the design and use of models in environmental modeling. In her notes, she finds the following “Recipes for the Model Builder” (Imboden, 1986): (1) Build the model with a hypothesis in mind and begin with the simplest model that is compatible with the measured data set and suitable to test the hypothesis. (2) Do not introduce variables like concentrations of chemical species that are not measured. (3) Move from the simple to the more complex model and alter, if necessary, the hypothesis until the field data are reasonably explained. (4) Validate the model by applying it to a set of data that was not used to build and calibrate the model. From her detailed notes during the lecture, Heidi finds that model calibration means to change the value of model parameters until optimal agreement between measured and calculated state variables is reached. Validation of a model means to run the model for another situation (e.g., further into the future) with the same parameter values that were determined by calibration and to compare the calculated state variables to an additional set of data. She remembers her teacher’s advice to proceed from the simple to the more complex model – but not vice versa – in order to check whether additional complexity would bring about an improved agreement between measurement and computation. Model complexity that goes beyond data complexity (Rule 3) could produce mathematical artifacts, that is, information that results from the mathematical structure of the model and not from the processes that are built into the model. In order to formulate a first hypothesis for the future development of PCE in Mystery Lake, Heidi and Paul consult the scientific literature for information on the physicochemical properties of PCE. They conclude that on a time-scale of weeks to months, PCE dissolved in water is fairly stable but would escape to the atmosphere at the water surface and would be flushed out of the lake at the outlet. Based on their knowledge about lake mixing (see Fig. 5.7), the scientists assume that although PCE is not homogeneously distributed in the vertical direction (Fig. 6.2), it is reasonable to assume homogeneity in the horizontal direction, so that the vertical profile measured at the center of the lake represents the vertical profile of PCE at any other location. Completing a back-of-the-envelope calculation, they conclude that the total amount of PCE in the lake has decreased by about 50% during the three weeks between the sampling dates. The scientists remember that in their survey of tributaries flowing into the lake, no PCE was found. With this information, Heidi and Paul come up with the following first hypothesis about PCE in Mystery Lake.

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173

First Hypothesis: Sometime prior to the sampling date in August, due to an accidental spill, an unknown amount of PCE has entered the surface layer of Mystery Lake. Before and after the accident, the input of PCE was not significant. The decrease of the total mass of PCE from the lake results from two processes: (1) loss through the outlet of the lake and (2) loss due to air–water exchange at the lake surface. The translation of the hypothesis into a model is shown in Figure 6.3, Model A. Upon rethinking, Heidi and Paul realize that Model A may miss an important aspect of the dynamics of PCE in the lake, that is, the concentration difference between the surface water (epilimnion) and the deep water (hypolimnion), which is clearly shown in the data (Fig. 6.2). They guess that vertical mixing between the two water layers may be important for the development of the lake’s PCE concentration since the removal processes identified in the first hypothesis, removal by flushing and air–water exchange, both probably depend on the surface concentration, not on the mean lake concentration. Thus, they formulate their second hypothesis. Second Hypothesis: Two state variables are needed to describe PCE in the lake, the mean concentrations in the epilimnion and hypolimnion, respectively. In addition to

1

2 model A

Figure 6.3 Three different models to describe tetrachloroethene (PCE) in Mystery Lake, Cleanland. Characteristic data of the models are given in Table 6.1. (a) Model A has one state variable (mean concentration of PCE in lake), (b) Model B has two state variables (mean concentrations of PCE in epilimnion and hypolimnion), and (c) Model C has 15 state variables (concentrations at 15 depths, each 2.5 m apart). The models have no external forces. Output processes are air–water exchange and flushing from the surface layer; internal processes are mixing between water layers.

model B

n state variables

model C

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Table 6.1 Characteristics of Different Models for PCE in Mystery Lake, Cleanland Model Elements

Model A

Model B

Model C

System Boundary State variable(s)

whole lake 1: mean concentration of PCE in lake

whole lake 1 to 15 mean PCE conc. at 15 depths 2.5 m apart

External force(s) a Internal processes

none none

Output

outlet flux to atmosphere

whole lake 1: mean PCE conc. in epilimnion 2: mean PCE conc. in hypolimnion none vertical mixing between epilimnion and hypolimnion outlet flux to atmosphere

a

none vertical mixing between adjacent layers outlet flux to atmosphere

No external forces are considered since the accidental spill is assumed to have occurred before the first sampling date.

processes 1 and 2, another process has to be taken into account: (3) transport of PCE between the epilimnion and the hypolimnion by vertical mixing (Fig. 6.3, Model B). Heidi is still not satisfied with the model. She points out to Paul that data from the second sampling date do not support the assumption of a completely mixed hypolimnion. She proposes to subdivide the water column into more than just two layers. Third Hypothesis: The PCE in the lake is described as a quasi-continuous vertical concentration profile by modeling the PCE concentration at 15 depths, each 2.5 m apart. This results in 15 state variables that are coupled by vertical mixing. Further, only the uppermost layer is affected by flushing and air–water exchange (Fig. 6.3, Model C). The three models are summarized in Table 6.1. The models have no external forces, since the water chemists assumed that after the accidental spill, occurring prior to the sampling on August 15, the input of PCE into the lake is zero. Now, Heidi and Paul have everything they need in order to analyze the fate of PCE in Mystery Lake and to predict how PCE concentrations in the lake will further develop. They decide to follow the advice of Rule 3 of the recipes, beginning with the simplest model and then moving step by step to the more complex models. They lack just one small detail: the mathematical equations that describe the processes and temporal change of the state variables. “No problem,” Heidi says to Paul. “Everything we need to tackle Model A can be found in my lecture notes, go ahead.” She hands here notes over to Paul, “just start reading Section 6.2.”

6.2

Box Models: A Concept for a Simple World In this section, we derive equations for describing the dynamics of the state variables of mathematical models. The basic premise of the derivation is a mass balance for

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175

one or several compartments. By adding and subtracting all processes that affect the numerical value of the state variables in each compartment, we can determine the changes of the variables per unit time. By the term compartments, we mean spatial subvolumes of the environment that are separated from their surroundings by a boundary (see Box 5.1). Examples are the troposphere, the water body of the Black Sea, the epilimnion of a lake (separated from the hypolimnion by the thermocline, see Fig. 5.7), or an algal cell. A compartment whose properties (e.g., concentrations, temperature, and density) are constant everywhere, is termed a completely mixed (homogeneous) box. The homogeneity of the box may be real or just assumed by averaging the property over the box volume. Boxes are the building blocks of many mathematical models. Every state variable is described by one single value per box. The simplest, and often most suitable, model is the onebox model. One-box models can have one or several state variables, such as the mean concentration of one or several chemicals. The box-model concept can be extended to two or more boxes (two-box or n-box model), each box being described by one or several state variables. In addition to the external forces, multi-box models contain processes describing transport between the boxes that affect the state variables (exchange fluxes). In the terminology of Box 6.1, these are internal processes. Among the models introduced for PCE in Mystery Lake (Fig. 6.3), A is a one-box model, B is a two-box model, and C is a 15-box model. For the following mathematical derivations, the starting point is the simplest version of the box-model family, the linear one-box model with one state variable. Linear One-Box Model with One State Variable

Figure 6.4 Schematic representation of a well-mixed box. A chemical is introduced into the system via the inlet and by production processes (total rate Ptot [MT−1 ]) and removed via the outlet and by internal removal processes (Rtot [MT−1 ]). Although Ptot an Rtot are in situ production and removal processes, the corresponding arrows are drawn across the system boundary to indicate that the chemical is added to or removed from the box.  [M] is the total mass of the compound in the volume V [L3 ], C and Cin [ML−3 ] are concentrations in the box and in the inlet, respectively, Q [L3 T−1 ] is the flow rate through the box. The concentration in the outlet is equal to the concentration in the box, since the box is well mixed.

Let us consider a homogeneous (completely mixed) compartment (box) that is filled with a fluid (e.g., air or water). The box is connected to the outside world by an inlet and an outlet (Fig. 6.4). The flow rate, Q, into the box is equal to the flow rate out of the box; thus the total fluid mass and, provided that the fluid density is constant, the total Q Cin

volume V

Q C

Ptot

mixing

Rtot mass  concentration C

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fluid volume, V, in the box remains constant. A chemical is added to the compartment as part of the inlet flow into the box (input concentration Cin ). We assume this input is homogeneously mixed within the box, resulting in the mean box concentration C. The chemical is removed via the outlet flow. Since the box is homogeneously mixed, the output concentration and average box concentration are equal (Cout = C). We define only one state variable, either the total mass of the chemical in the box, , or its mean concentration, C = /V. In addition to the fluid flow through the box, some in situ production and removal processes, Pj and Rk , may act on the compound while it is in the interior of the box. Their combined effects, Ptot and Rtot , are the sums of the single processes: Ptot =

∑

Pj ;

Rtot =

∑

Rm

[MT−1 ]

(6-1)

m

j

The expression in the square brackets, [MT−1 ], gives the dimension of the equation as mass per time. For every dimension, we can choose specific units, for instance, kg for mass M and s for time T. In order to arrive at an equation for the temporal change of the total mass of the compound in the box, d/dt, we take the sum of all processes that increase the mass in the box minus the sum of all the processes that decrease it (see Fig. 6.4): d = QCin + Ptot − QC − Rtot dt

[MT−1 ]

(6-2)

The first and third terms on the right-hand side of Eq. 6-2 describe the mass fluxes due to the flow of the fluid. Since the volume V is constant, we can rewrite the equation by dividing both sides by V and using /V = C, where C is the mean concentration in the box: Ptot Rtot dC = Cin kw + − kw C − dt V V

[ML−3 T−1 ]

(6-3)

The flushing or dilution rate of the box, kw , is then defined as: kw =

Q V

[T−1 ]

(6-4)

That is, kw gives the fraction per unit time of the fluid volume that enters and leaves the system. The inverse quantity, τw = 1/kw , is the mean residence time of the fluid in the box. Equations 6-2 and 6-3 are two versions of the same one-box model; they differ in the choice of the state variable on the left side,  for the former, C for the latter. On the right side of both equations are terms that we do not know how to relate to the state variable. Thus, we concentrate on Eq. 6-3 to analyze the meaning of these terms with the definitions that were introduced in Fig. 6.1 and Box 6.1. The first and second

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177

terms are external forces. They are independent of the state variable C, can be constant or time-variable, and have to be fed into the model. The third and fourth terms are output processes (negative signs). The third term describes the loss from the system via the outflow; it is proportional to C. Mathematicians call such functions linear; in chemical kinetics, they are called first order. The fourth term describes the sum of removal processes that are not via the outflow from the box. They must somehow depend on the system variable C. For now, we assume that they are proportional to C, like the loss via the outlet: ∑ ∑ ∑ Rm = km C = ktot C; ktot = km (6-5) Rtot = m

m

m

If in Eq. 6-3 we replace the first two terms by the total external force, J, given by: J = Cin kw +

Ptot V

[ML−3 T−1 ]

(6-6)

and the fourth term using Eq. 6-5, we get a first-order linear inhomogeneous differential equation (FOLIDE): ( ) dC = J − kw + ktot C = J − kC; dt

k = kw + ktot

(6-7)

The equation is first-order because it contains a first derivative of the variable C, but no higher ones; it is linear because of the term kC, and it is inhomogeneous because of the additional term J that describes the external forces. The first-order (or linear) rate constant k may be the sum of several first-order rate constants; in the specific example of Eq. 6-7, it is the sum of two such constants. Since the box has a constant volume V,  and C are linearly related, and the same procedure can be easily applied to find a FOLIDE for Eq. 6-2. The solution of Eq. 6-7 is given in Box 6.2. In the most general case, both J and k can be arbitrary functions of time. If J and k are constant and non-negative, we get: C(t) = C0 e−kt + C∞ (1 − e−kt ) = C∞ + (C0 − C∞ )e−kt

(6-8)

where C 0 is the initial value at t = 0 and C∞ = J/k is the steady-state value of C, that is, the value at which the concentration change becomes zero. The shape of C(t) for different initial values and steady states is shown in Fig. 6.5. Equation 6-8 tells us that the concentration decays from its initial value to its steadystate value at a rate given by e−kt , where for the linear one-box model k is given by kw + ktot (Eq. 6-7) and the steady-state concentration by: C∞ =

k Cin + Ptot ∕V J = w k kw + ktot

(6-9)

If the external force J is zero, C∞ is zero and the solution Eq. 6-8 is reduced to the first term on the right-hand side (Box 6.2, case a).

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Box 6.2

Solution to the First-Order Linear Inhomogeneous Differential Equation (FOLIDE) dY = J − kY dt

(1)

Y : State variable; J : inhomogeneous term; k : linear rate constant Solutions: a. Homogeneous case with constant coefficient. J = 0, k = constant Y(t) = Y 0 e−kt , Y 0 : value of variable Y at t = 0 (initial value)

(2)

b. Inhomogeneous case with constant coefficients. J, k = constant Y(t) = Y 0 e−kt + Y ∞ (1 − e−kt ) = Y ∞ + (Y 0 − Y ∞ )e−kt

(3)

For k > 0, Eq. (3) has the steady state J k

Y∞ =

(4)

c. Variable input J(t), k = constant 0 −kt

Y(t) = Y e

+

∫0

t

′

e−k(t−t ) J(t′ )dt′

(5)

d. Variable coefficients J(t) and k(t) Y(t) = Y 0 e−ϕ(t) + e−ϕ(t)

∫0

t

′

e+ϕ(t ) J(t′ )dt′

(6)

where ϕ(t) =

∫0

t

k(t′ )dt′

(7)

Time-to-Steady State. Next, we address the question of how long it takes for C to reach its steady state. Since the time dependence of C(t) is described by exponential functions of the form e−kt , strictly speaking, steady state is only reached if k > 0 and time t is infinitely large. But since exponential functions quickly become very small with the growing negative exponent (e.g., e−1 = 0.37, e−3 = 0.050, e−5 = 0.0067), we define a critical adjustment time, t5% , at which the time-dependent terms of Eq. 6-8 have dropped to 5% of their original value. Using e−kt5% = 0.05 and taking the natural logarithm on both sides, we get:

t5% =

−ln 0.05 3 = k k

(6-10)

Box Models: A Concept for a Simple World

1.0 37%

0.8 0.6

{

179

5% 14% { C0 = 0 C∞ = 1

0.4

C(t) = C∞(1 – e–kt)

0.2

state variable C(t)

0.0 1.0 0.8

C0 = 1

0.6

C∞ = 0

0.4

C(t) = C0e–kt

0.2 0.0

Figure 6.5 Solution to the firstorder linear inhomogeneous differential equation (FOLIDE) (Eq. 6.7). C 0 = initial value at t = 0, C∞ = J/k is the steady-state value. (a) Growth curve for C 0 = 0; (b) Decay curve for C 0 = 1, J = 0; (c) general case for C 0 = 0.3. The time axis is in units of 1/k. The remaining difference to steady state drops from 37% at t = 1/k to 14% and 5% for each additional time interval 1/k.

1.0 0.8

C0 = 0.3

0.6

C∞ = 1

0.4

C(t) = C∞ + (C0 – C∞)e–kt

0.2 0.0

0

1

2

3

4

5

–1

time t (in units of k )

Instead of 5% of the original value, we could choose any other adjustment criterion, for instance, 10% or 1%. Our choice only influences the numerical value in the numerator of Eq. 6-10 but does not alter the fact that the adjustment time is inversely related to the rate constant, k. For the one-box model (Eq. 6-7): t5% =

3 kw + ktot

(6-11)

The denominator consists of the sum of the flushing rate and all reaction rate constants. We can assess the relevance of the different removal processes by looking at the relative size of the different k-values. One single, large k-value is sufficient to make the response time of the system short, even if the other k-values are small or zero. If ktot (or just one single km ) is much larger than kw , time-to-steady state is primarily determined by in situ removal processes (or just by one of them) while removal through the outlet is negligible. Conversely, flushing is the dominant removal mechanism if kw >> ktot . Finally, if all the rates k are of similar size, then all the removal processes are about equally important.

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A similar analysis can be made for the size of C∞ (Eq. 6-9). If the internal production processes Ptot are zero and the input occurs exclusively via the inlet, then, J = kw Cin , and Eq. 6-9 becomes: C∞ =

kw Cin kw + ktot

(6-12)

This expression for the steady-state concentration of the linear one-box model without internal production (Eq. 6-12) is extremely useful. By comparing C∞ and Cin , we can find out whether internal removal processes exist or whether the chemical is stable (conservative) in the box. In the latter case, C∞ and Cin are equal; in the former, C∞ is smaller than Cin . In turn, C∞ > Cin points to an additional internal source (Ptot > 0 in Eq. 6-9). We should bear in mind that the concept of steady state only makes sense if J and k are constant over time. Of course, Eq. 6-9 remains valid if J or k varies with time, but then C∞ becomes a moving target for which the concept of “time-to-steady state” (Eq. 6-11) has no meaning. With the introduced equations for a one-box model, we now have everything needed to tackle Model A for tetrachloroethene (PCE) concentrations in Mystery Lake (see Table 6.1 and Fig. 6.3). Heidi and Paul decide to use the PCE concentrations measured on August 15 as initial values and assume that after this date the PCE input to the lake is zero. Box 6.3 gives the outcome of their modeling attempt. According to their approach, it takes 100 days until the mean concentration of PCE in Mystery Lake, C, has dropped below 1 × 10−9 mol L−1 . Since C is the only state variable, the model cannot tell us whether the mean concentration is indeed a good approximation or whether the real distribution of PCE is heterogeneous with areas where C remains clearly above the mean. Since Heidi and Paul do not want to run the risk that such areas exist, they decide to move one rung up the ladder of model complexity and to make a second attempt with Model B (Table 6.1 and Fig. 6.3). Model B adds a little bit of heterogeneity by treating the lake as a two-box model. Heidi must go back to her lecture notes and study the chapter dealing with multi-box models. From One-Box to Multi-Box Models When constructing multi-box models for environmental systems, we must define more than one state variable. These variables can either be added chemical species to the box or added boxes for the one selected species. For organic chemicals, the first case is only relevant for very special situations for which no additional mathematical tools are needed. Although many different organic chemicals are usually simultaneously present in natural systems, in most cases, these chemicals do not interact. They can be mathematically treated as if the other species were not present, that is, like the one-species case.

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181

Box 6.3 Tetrachloroethene (PCE) in Mystery Lake: One-Box Model (Model A) Lake characteristics 2 × 108 m3 Total Volume (Vtot ) 0.9 × 108 m3 Volume top 10 m (VE ) Surface (A) 1 × 107 m2 Water through- 10 m3 s−1 flow (Q)

In the course of a monitoring program conducted in Mystery Lake, on August 15 dissolved tetrachloroethene (PCE) was detected in water samples taken at different depths (Fig. 6.2). No PCE had been measured in the previous month. On September 4, the PCE-concentration in the top 10 m has dropped by about 50%, whereas below that depth, the concentration has increased. Use a one-box model (Fig. 6.3, Model A) to estimate how long it takes until the mean PCE concentration in the system has dropped below 1 × 10−9 mol L−1 . Mean concentration and total mass of PCE in total lake estimated from Figure 6.1

August 15 September 4

mean lake Cmean (∗)

total mass 

13.5 × 10−9 mol L−1 8.0 × 10−9 mol L−1

2,700 mol 1,600 mol

(∗) Calculated as volume-weighted mean from concentrations in surface and deep layer, respectively.

Definition of model System: Total lake volume, Vtot State variable: average PCE concentration in total lake volume, Cmean Processes to be considered: (1) removal via outlet; (2) removal by air/water exchange (Raw ) No input via inlets (Cin = 0), no in situ production (Ptot = 0). Solution Equation 6-3 is reduced to: dCmean Rtot (1) = −kw Cmean − tot dt V Assumption: Removal by air-water exchange is first-order (linear) with rate constant kaw , see Eq. 6-5 and Chapter 19. Inserting into Eq. 1 yields: dCmean (2) = −kw Cmean − kaw Cmean dt 0 = According to Box 6.2 (Eq. 2), the solution is an exponential function where Cmean −9 −1 13.5 × 10 mol L is the initial mean concentration in the total lake volume: 0 e−(k Cmean (t) = Cmean

or in logarithmic form:

w +kaw )t

( ) 0 − kw + kaw t ln Cmean (t) = ln Cmean

(3) (4)

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Environmental Systems: Physical Processes and Mathematical Modeling

If we choose t = 0 on August 15 and evaluate Eq. 4 for t = 20 d (September 4), we can solve Eq. 4 for the sum of the two first-order rate constants, kw + kaw : ] 1[ 1 0 kw + kaw = − ln Cmean (t) = (5) ln Cmean [ln 13.5 − ln 8] = 0.026d−1 t 20d The flushing rate of the total lake (Eq. 6-4) is kw = 10 m3 s−1 /2 × 108 m3 = 5 × 10−8 s−1 = 0.0043 d−1 , thus the major fraction of the removal appears to be due to air-water exchange; kaw = 0.022 d−1 (84% of total removal). The time t1 until Cmean (t) has dropped below 1 × 10−9 mol L−1 is calculated from Eq. 3 by setting Cmean (t) =1 × 10−9 mol L−1 , kw + kaw = 0.026 d−1 and by solving for t = t1 : t1 =

1 [ln 13.5 − ln 1] = 100 d 0.026d−1

(6)

If they do interact, they often do so fast compared to other processes like flushing or air-water exchange, so we can consider the reaction partners to be in equilibrium. For instance, this is usually the case for a process like sorption, so it can be assumed that the concentrations of all forms of the chemical (dissolved, sorbed on solids, and sorbed on colloids) are proportional to each other. Therefore, we can simply model one species and then calculate the concentrations of the other species by making use of the corresponding proportionality constants. Furthermore, organic chemicals in the environment can be transformed, for instance, by biological degradation (Chapters 26). Since such reactions commonly do not run backwards in a given environment, we can again model the original chemical by simply introducing the corresponding reaction rates of degradation without explicitly treating the products of the degradation process. Examples are given in Chapter 28. Therefore, we restrict the following modeling discussion to the extension of the onebox model to two or more boxes. Boxes could be the gas and water volume in a sealed glass flask, the epilimnion and hypolimnion of a lake, different basins of a lake, or the troposphere and the stratosphere. Each box can be modeled by a mass balance equation like Eq. 6-7. The boxes are coupled by mass fluxes ( 12 and  21 , if there are two boxes, see Fig. 6.6a). Examples of mass fluxes are the transport of a chemical from the water into the air and vice versa; the flux of dissolved chemicals by turbulent mixing from the surface layer into the deeper parts of a lake; the downward transport of chemicals sorbed to particles sinking to the deep-sea; and the transport of a dissolved chemical in the water of a river flowing from one lake to another lake further downstream. Without such fluxes, the differential equations would not be coupled and could be solved separately. The multi-box model would then be reduced to a couple of one-box models. Most fluxes between boxes are two-way fluxes; therefore, they are also called exchange fluxes. The equilibrium between two phases (e.g., air and water) is the result of exchange fluxes. Whether we add a chemical to the water, the air, or both, if one waits long enough, the concentrations attained in the two phases will reach a constant

Box Models: A Concept for a Simple World

external forces

external forces box 1

Figure 6.6 (a) System consisting of two boxes (two-box model) described by one state variable in each box (total mass, 1 and 2 , or mean concentration C1 and C2 ). V1 and V2 are the volumes of the boxes. In addition to the usual processes of the one-box model (external forces, outputs), mass fluxes  12 and  21 exist between the boxes. (b) Same as (a), but all processes are zero except the mass fluxes between the boxes (pure exchange model). Since there are no fluxes between the system (IN) and its environment (OUT), total mass, tot = 1 + 2 , is constant with time (Eq. 6.13), but the sum of the concentrations, C1 and C2 , is not constant, unless the box volumes are equal.

(a)

V1 C1

183

1

12 21 in

box 2 2

V2 C2

out output

V1

box 1

C1

1

(b)

output

12 21 in

box 2 2

V2 C2

out

ratio that is independent of the original concentration distribution (see Chapter 9). In contrast, if the flux occurs only in one direction (e.g.,  12 > 0,  21 = 0), one speaks of a directed flux. The examples of particles sinking and a river flowing between two lakes are directed fluxes. As we will see, directed fluxes are fundamentally different from exchange fluxes; they introduce an asymmetry into the model (Box 1 influences Box 2 but not vice versa), which is also reflected in the mathematical structure of the model equations. Exchange Fluxes and Equilibrium. In order to demonstrate how the one-box model is modified due to the interactions with another box, we utilize the case of a chemical that moves between two boxes. First, we disregard all other processes (external forces, output) and just look at the effect of the exchange fluxes between the boxes (Fig. 6.6b). For reasons soon becoming clear, we use the total mass of the chemical in Box 1 and Box 2, 1 and 2 , as the state variables. The mass transfer fluxes are described by  12 , the transfer of chemical from Box 1 to Box 2, and  21 , the transfer of chemical from Box 2 to Box 1. The mass balance equations for the two boxes are: d1 = −12 + 21 ; dt

d2 = 12 − 21 dt

[MT−1 ]

(6.13a)

d1 d2 + =0 (6.13b) dt dt where the total mass of the chemical in the two boxes, tot = 1 + 2 , is constant with time. This reflects the law of mass conservation in a two-box system that has neither inputs nor losses but only fluxes between the boxes. To relate the exchange

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Environmental Systems: Physical Processes and Mathematical Modeling

fluxes to the concentrations in the boxes, we assume that the fluxes are proportional to the concentration in the box from which the flux originates (linear exchange flux): 12 = φ1 C1 ;

21 = φ2 C2

[MT−1 ]

(6-14)

The coefficients φ1 and φ2 relate a concentration (dimension [ML−3 ]) to a mass flux [MT−1 ] and thus have the dimension of a volume flux [L3 T−1 ]. Their meaning are discussed in the following section.

If the difference between the fluxes,  12 and  21 , called the net flux,  12,net =  12 –  21 , is zero, the masses in the boxes become constant, meaning they reach a steady state. Eq. 6-14 then becomes: (

C1 C2

) = exchange equilibrium

φ2 φ1

(6-15)

Equation 6-15 is called the exchange equilibrium. In Chapter 4 we have used the same mathematical concept to describe partitioning between two or more phases of a chemical, for instance, between the concentration in air and in water, or in an organic solvent and water. Exchange Fluxes by Fluid Motion. To illustrate the meaning of the coefficient φ, we consider the special case where the exchange process is caused by the movement of a fluid (air or water) in which the chemical is embedded. As an example, consider boxes that represent the epilimnion and hypolimnion of a lake (recall Mystery Lake, Fig. 6.2). The exchange fluxes between the water layers is by turbulent motion of the water that results in the random exchange of water parcels between the upper and lower layers of the lake. Since the volumes of the epilimnion and hypolimnion are assumed to remain constant, the volumes of the downward flowing parcels per unit time must be equal to the volumes of the upward flowing parcels. Each volume carries with it the concentration of the layer from which it originates. According to the concept of completely mixed boxes, once the parcel has arrived in the other box, it is instantaneously mixed into the surrounding water. The φ’s represent the exchanged water volumes per unit time, Qex , hence the dimension [L3 T−1 ]. By replacing the φ’s by Qex , we get from Eq. 6-14: 12 = Qex C1 ;

21 = Qex C2 ;

12net ≡ 12 − 21 = Qex (C1 − C2 ) [MT−1 ] (6-16)

In other words, if the exchange fluxes are by fluid motion, φ1 and φ2 are equal, and the exchange equilibrium (Eq. 6-15) is given by C1 = C2 . Other Exchange Processes. Equation 6-16 does not always apply. If the exchange fluxes occur between different phases, for instance, between a gaseous and a liquid phase, the exchange mechanism cannot be by the exchange of fluid parcels. In fact, we have not specified the physico-chemical mechanism that drives the fluxes between the boxes, except for the specific case previously discussed. The only assumption we have made is the linear relationship between concentration and mass flux (the first-order

Box Models: A Concept for a Simple World

185

flux assumption, Eq. 6-14). In Chapters 17 to 20 of the book, different mass transfer processes are discussed such as air–water exchange and sorption between water and sediment beds or air and soils. For all of them, the first-order transport assumption (Eq. 6-14) is valid, at least as a first approximation, but the φ’s are not necessarily identical and thus the concentrations C1 and C2 are not equal at equilibrium. For instance, for air–water exchange, the concentration ratio at equilibrium, is the nondimensional Henry’s Law constant (Chapter 9). Dynamic Solution of Linear Exchange Model. We now want to derive the dynamic equations of the linear exchange model and discuss their solution. By inserting the first-order transport equations (Eq. 6-14) into Eq. 6-13, we get two coupled differential equations. In order to arrive at expressions in which the state variables on both sides are the same, we replace C by /V in both equations: d1 ex ex 1 + k22 2 = −k11 dt d2 ex ex 1 − k22 2 = k11 dt

(6-17)

ex ex The exchange rates, k11 = φ1 ∕V1 ; k22 = φ2 ∕V2 , have the dimension [T−1 ]. Equation 6-17 is a system of two coupled linear homogeneous differential equations. As for Eq. 6-13, the right-hand sides are identical except for the signs, thus the sum of the two variables, 1 + 2 , is constant with time (mass conservation).

The general solution of the homogeneous system with mass conservation (Eq. 6-17) is given in Box 6.4. By substituting the general variable Y, the masses in the two boxes as a function of time can be calculated. At this point, we highlight two properties of the solution. First, according to Eq. 6 of Box 6.4, the exchange equilibrium between the boxes is characterized by: (

1 2

) = exchange equilibrium

ex k22 ex k11

=

φ 2 V1 φ 1 V2

(6-18)

By dividing both sides by the volume ratio (V1 /V2 ), we get the expression for the corresponding concentration ratio at equilibrium that had been derived before (Eq. 6-15). Second, we note from Eq. 7 of Box 6.4 that the time to reach exchange equilibrium is characterized by the inverse of the sum of the two rate constants: t5% =

3 ex ex k11 + k22

(6-19)

As is characteristic for linear differential equations, their solutions are built from exponential functions that from a mathematical point of view need an infinite amount of time to reach steady state. So again we must choose some fractional approach to equilibration (e.g., 5%) as a practical metric of this time.

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Environmental Systems: Physical Processes and Mathematical Modeling

Box 6.4

Solution of Two Coupled First-Order Linear Homogeneous Differential Equations with a Conservation Law (see Imboden and Pfenninger, 2013, Example 5.4)

We consider two first-order linear homogeneous differential equations for the state variables Y1 and Y2 of the form: dY1 = −k11 Y1 + k22 Y2 dt dY2 = k11 Y1 − k22 Y2 dt

(1)

The sum of the two equations is zero, thus: dY1 dY2 d(Y1 + Y2 ) dYtot + = = = 0 ⇒ Ytot = Y1 + Y2 = Y10 + Y20 dt dt dt dt By replacing Y2 by Ytot – Y1 in the first Eq. 1, we get a differential equation for Y1 alone:

with the solution (Box 6.2, Eq. 3):

(2)

dY1 = k22 Ytot − (k11 + k22 )Y1 dt

(3)

( ) Y1 (t) = Y1∞ + Y10 − Y1∞ e−(k11 +k22 )t

(4)

and the steady states: Y1∞ = Note that: Y1∞

Y2∞

k22 Y0 ; k11 + k22 tot ≡

(

Y1 Y2

Y2∞ =

k11 Y0 k11 + k22 tot

) = exchange equilibrium

k22 k11

(5)

(6)

According to Eq. 6-19, time-to-steady state is characterized by: t5% =

3 k11 + k22

(7)

The Complete Linear Two-Box Model. We now derive the dynamic equations of the complete linear two-box model, that is, the model that includes external forces and outputs as well as internal fluxes. For each box, we write down the differential equation for concentration of the linear one-box model (Eq. 6-7) and then add the linear transfer fluxes (Eq. 6-14) divided by the corresponding box volumes. The results are a coupled system of two linear inhomogeneous differential equations: dC1 ex ex )C1 + k12 C2 = J1 − (kw1 + k1tot + k11 dt dC2 ex ex C1 − (kw2 + k2tot + k22 )C2 = J2 + k21 dt

(6-20)

Box Models: A Concept for a Simple World

187

where the rate constants of exchange are: ex k11 = φ1 ∕V1 ;

ex k12 = φ2 ∕V1 ;

ex k21 = φ1 ∕V2 ;

ex k22 = φ2 ∕V2

(6-21)

The terms of the first equation of Eq. 6-20 represent external input, loss through the outlet, loss by internal processes, loss by transfer to Box 1, and gain by transfer from Box 2. For the second equation, the terms mean external input, gain by transfer from Box 1, loss through the outlet, loss by internal processes, and loss by transfer to Box 2. In contrast to Eq. 6-17, all linear exchange rates (Eq. 6-21) are different. When writing the mass balance equations for concentrations instead for masses, the fluxes φ must be divided by the volume of the receiving box. If the fluxes are due to fluid motion (Eq. 6-16), then Eq. 6-21 is reduced to:

ex ex = k12 = Qex ∕V1 ; k11

ex ex k21 = k22 = Qex ∕V2

ex ⇒ k22 =

V1 ex k V2 11

(6-22)

The solution of the system of two linear, inhomogeneous differential equations is given in Box 6.5, Eq. 2. Again, it is composed of exponential functions, this time with rate constants, q1 and q2 , that are called the eigenvalues of the linear system. The time-to-steady state is determined by the smaller of the two eigenvalues (Box 6.5, Eq. 6). The temporal evolution of the state variables depends on their initial values (Box 6.5, Eqs. 2 and 5), but the steady state does not (Box 6.5, Eq. 4). The steady state of Eq. 6-20 is: (

) tot ex ex k + k + k J2 J1 + k12 w2 2 22 ∞ C1 = ( ) ex ex ex ex ) − k12 k21 kw1 + k1tot + k11 (kw2 + k2tot + k22 ) ( ex ex k21 J2 J1 + kw1 + k1tot + k11 ∞ C2 = ( ) tot ex tot ex ex ex kw1 + k1 + k11 (kw2 + k2 + k22 ) − k12 k21

(6-23)

If the rate constants are such that the denominators in the preceding equations are zero, Eq. 6-23 is not valid. This is the case if the equations have the special form of Eq. 6-17, that is, if the sum of the two state variables is constant with time (mass conversation). With these mathematical tools at hand, Heidi and Paul from the Public Water Authority of Cleanland have everything they need to develop a two-box model for PCE in Mystery Lake (Fig. 6.3, Model B). The outcome of their modeling exercise is given in Box 6.6.

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Environmental Systems: Physical Processes and Mathematical Modeling

Box 6.5

Solution of Two Coupled First-Order Linear Inhomogeneous Differential Equations (Coupled FOLIDEs) (see Imboden and Pfenninger, 2013, Appendix C and D)

Note: The following derivations are not valid if the rate constants of Eq. 1 have the special property k11 = k21 and k12 = k22 (the linear exchange model). Then the solution given in Box 6.4 applies. Any system of two first-order linear differential equations for the state variables Y1 and Y2 can be transformed to arrive at the following form: dY1 = J1 − k11 Y1 + k12 Y2 dt

(1) dY2 = J2 + k21 Y1 − k22 Y2 dt where J1 and J2 are the inhomogeneous terms, and kmn (m,n = 1 or 2) are the linear (or first-order) rate constants. If the kmn -matrix is not singular (i.e., (k11 k22 – k12 k21 ) ≠ 0), then the solutions are composed of the steady-state values, Y1∞ and Y2∞ , and of two exponential functions with rates q1 and q2 : Y1 (t) = Y1∞ + A11 e−q1 t + A12 e−q2 t Y2 (t) = Y2∞ + A21 e−q1 t + A22 e−q2 t

(2)

The rate constants, q1 and q2 , are the negative eigenvalues of the linear system. If Eq. 1 describes a mass balance model, the values of all coefficients knm and qn are positive or zero. 1 1 q1 = [k11 + k22 − r]; q2 = [k11 + k22 + r] 2 2 ] [ 1∕2 r = (k11 − k22 )2 + 4k12 k21

(3)

The steady-state values of the system are: Y1∞ =

k22 J1 + k12 J2 ; k11 k22 − k12 k21

Y2∞ =

k21 J1 + k11 J2 k11 k22 − k12 k21

The coefficients Amn introduced in Eq. 2 are: ) ( )] [ ( A11 = 1∕r − (k11 − q2 ) Y10 − Y1∞ + k12 Y20 − Y2∞ [ ( ) ( )] A21 = 1∕r (k11 − q1 ) Y10 − Y1∞ − k12 Y20 − Y2∞ ) )] [ ( ( A12 = 1∕r k21 Y10 − Y1∞ − (k22 − q2 ) Y20 − Y2∞ [ ( ) ( )] A22 = 1∕r − k21 Y10 − Y1∞ + (k22 − q1 ) Y20 − Y2∞

(4)

(5)

where Y10 and Y20 , are the initial values at t = 0. Since q1 is the smaller of the two eigenvalues, time-to-steady state is (see Eq. 6-11) t5% =

3 6 = q1 k11 + k22 − r

(6)

Box Models: A Concept for a Simple World

189

Box 6.6 Tetrachloroethene (PCE) in Mystery Lake: Two-Box Model (Model B) QC1in

epilimnion (1) hypolimnion (2)

QC1

Ra/w

QexC1

QexC2

C1 C2

Problem As an improvement of Model A (Box 6.2) a two-box model for PCE in Mystery Lake can be developed to describe the dynamics of PCE in the lake. From Fig. 6.2, the following mean can be estimated from the concentration in the two boxes, the epilimnion and the hypolimnion:

Two-Box Model of Mystery Lake

Mean PCE concentration and total mass in the epilimnion and hypolimnion of lake Lake characteristics Total Volume 2 × 108 m3 (Vtot ) 0.9 × 108 m3 Volume top 10m (V10 ) Surface (A) 1 × 107 m2 Water discharge10 m3 s−1 (Q)

Epilimnion

August 15 September 4

Hypolimnion

mean conc. CEpi

total mass Epi

mean conc. CHypo

total mass Hypo

30 × 10−9 mol L−1 13 × 10−9 mol L−1

2,700 mol 1,170 mol

0 4 × 10−9 mol L−1

0 440 mol

Solution In order to apply Eq. 6-20 and the solution of the system of differential equations given in Box 6.5, the following definitions are used: ! Box 1 = Epilimnion, V = V ; Box 2 = Hypolimnion, V = V – V 1 10 2 tot 10 ! Processes to be considered (see Eq. 6-20 for notation):

Box 1: (1) removal via outlet (kw1 = Q/V10 = 1.1 × 10−7 s−1 = 0.0096 d−1 ); (2) removal by air–water exchange (k1tot = k1aw ) ex ex (3) exchange with Box 2 by mixing (k11 , k12 ) ex ex , k22 ) Box 2: (1) exchange with Box 1 by mixing (k21

! No inputs: J , J = 0 1 2

Putting the processes into the mass balance equations for C1 and C2 yields: ( ) dC1 ex ex C1 + k12 = − kw1 + k1aw + k11 C2 dt dC2 V ex 1 (C − C2 ) = k11 dt V2 1

(1)

ex . where we have made use of Eq. 6-22 in order to express all exchange rates by k11

Since kw1 and the volumes V1 and V2 are known, only two adjustable parameters ex . Since the measurements from August 15 will be used remain in Eq. 1: k1aw and k11

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Environmental Systems: Physical Processes and Mathematical Modeling

as the initial values C10 and C20 , there are just two data points to be fitted by the model, the mean concentrations in the two subvolumes on September 4. Generally, a unique choice exists for the two model parameters to force the concentrations as a function of time exactly through the data points. Numerous procedures and computer programs are available to best-fit models to a given set of data. For didactic reasons, we rely on a simple back-of-the-envelope procedure to determine the size of the unknown model parameters. Because initially the incident PCE is confined to the epilimnion (Box 1), the back-mixing from Box 2 can at first be disregarded. The first line of Eq. 2 then reduces to: ) ( dC1 ex C1 ≈ − kw1 + k1aw + k11 dt

(2)

As for Model A (Box 6.2, Eqs. 3–5), the solution of Eq. 2 is a pure exponential function that can be used to determine the sum of the three linear rate constants from the mean concentration in the epilimnion at the two sampling dates: (

) ) 1( 1 ex = ln C10 − ln C1 (t = 20 d) = (ln 30 − ln 13) = 0.042 d−1 kw1 + k1aw + k11 t 20 d (3)

The flushing rate of the surface layer, kw1 = 0.0096 d−1 , amounts to 23% of the total removal rate. Seventy-seven percent of the removal must occur by exchange to the atmosphere and by downward mixing. The two removal rates can be further split by comparing the amount of PCE found below 10 m (440 mol) on September 4 with the total loss of PCE from the surface in this period (1530 mol). Thus, downward mixing ex = 0.29 × 0.042 d−1 = accounts for 29% of total removal from the surface layer (k11 ex ex = (V1 /V2 )k11 = 0.0100 d−1 ), and the rest (48%) must be due to 0.0122 d−1 , thus k22 ex air–water exchange (k1 = 0.0202 d−1 ). Now, we can solve the system of differential equations (Eq. 1) with the help of Box 6.5. Since the external forces, J1 and J2 , are zero, the steady-state concentrations are zero (Box 6.5, Eq. 4). The rate constants of the exponential functions appearing in the solutions (the negative eigenvalues, see Box 6.5, Eq. 3) are: q1 = 0.0066 d−1 ;

q2 = 0.0455 d−1

(4)

Inserting all these coefficients into Eq. 2 of Box 6.5 yields the numerical solution (C is in units 10−9 mol L−1 or in μmol m−3 ; t is in days): C1 (t) = 2.7e−0.0066t + 27.3e−0.0455t C2 (t) = 7.7e−0.0066t − 7.7e−0.0455t

(5)

The solution of Eq. 5 over time is shown in the figure in the margin. To test the applicability of Eq. 5, we use the data from August 15 to calculate the

PCE concentration (μmol m–3)

When Space Matters: Transport Processes

30

C1(t): Model B C2(t): Model B Ctot(t): Model A

25 20

concentrations in the two boxes for September 4 (t = 20 d) and compare them with the actual measurements (about 13 and 4 μmol m−3 , respectively): C1 (20 d) = 13.4 × 10−9 mol L−1 ;

15

191

C2 (20 d) = 3.6 × 10−9 mol L−1

(6)

10 5

Fundamental differences between the one-box model (Model A) and the two-box model (Model B) become apparent when looking at the solutions (figure in margin). For t > 50 d, in Model B, the concentration in the deep layer (C2 ) becomes larger PCB modeling results for Mystery than C and the net flux between the boxes changes sign indicating an upward flux 1 Lake. from the hypolimnion to the epilimnion. The time until the concentration has dropped below 1 × 10−9 mol L−1 (about 300 days) is much larger than calculated from Model A, since the long-term memory of the lake is in the deep water while all removal processes occur in the surface layer. Model B has its shortcomings as well, because it assumes that the sizes of the two boxes remain constant over time, which means the same degree of the lake’s stratification lasts during the whole year. During the winter, this is not the case in temperate climates (see Chapter 5, Section 5.3). 0

0

20 40 60 80 100 120 140 time (d)

So far, we have only discussed linear box models. Although natural processes are not always linear, even nonlinear phenomena can often be approximately modeled using linear equations, especially if the state variables vary only within a narrow range. Therefore, linear equations are frequently ideal tools for a first simple analysis of a system, which is why we make extensive use of them in this book. But simplicity has its price. As shown in Boxes 6.2, 6.4, and 6.5, the solutions of linear differential equations all have the same mathematical form, that is, they are exponential functions or sums of exponential functions. As a consequence, linear models always tend to the same steady state (if it exists), independently of the initial conditions. The steady states of nonlinear models may depend on the initial state of the system. An example of a nonlinear biodegration process in a reactor is given in Problem 6.8.

6.3

When Space Matters: Transport Processes Deterministic versus Random Motion: A Thought Experiment in a Train Imagine sitting in the dining car of a train that takes you through the steep mountains of eastern Switzerland to St. Moritz. While you travel uphill along the winding track, through loop-tunnels and narrow valleys, you order a cup of coffee. You add some milk and stir the coffee with your spoon. Then you lift the cup and take the first sip. Though in this wonderful setting it may seem nerdy, you ask yourself the question: How is the milk moving? You begin to analyze the situation. First, relative to the ground outside, the milk, together with the cup, your arm and the dining car, travel along the

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tracks toward St. Moritz. The motion can be described by a three-dimensional velocity vector, which is a set of three numbers comprising velocity’s components along the three axes of a Cartesian coordinate system: v = (vx , vy , vz ). The car and its content move in a common direction, like the flow of water in a river. The flow is determined by the railway tracks or by the riverbed. Therefore, this type of motion is characterized by the expressions: deterministic, directed, or advective.

A thought experiment in a train. Photo: B¨ohringer (2013).

How does the situation change when you move the cup with your arm? Most objects in the car do not experience the movement of your arm, but the movement is still directed and shared by all the fluid elements in the cup and by the cup itself. A velocity vector can still describe the movement, although the vector is not identical with the dining car’s velocity vector. The combined effect of different advective motions is described by the sum of the respective velocity vectors: vtot = vcar + vcup . How can we characterize the motion of the milk that results from stirring the coffee cup? At first glance, the motion of the fluid produced by the spoon may look like advection as well, since it sets the coffee into a rotational motion. If this were all that stirring does, we could never produce a homogeneous mix of milk and coffee. The essence of stirring is to add enough kinetic energy to the liquid to make the flow turbulent. Although the movement of the spoon is not really random, it triggers a random process called turbulent diffusion. If you could look closer, you would observe that the coffee has little eddies in it after stirring, and these work to distribute the milk throughout the coffee. This process is called turbulent diffusion. Finally, at the molecular level, if one could see it, the random motion of the molecules acts to distribute the molecules originally in the milk into the molecules that were initially in the coffee. This process is called molecular diffusion. In contrast to the deterministic nature of advective motion, these diffusive motions are random processes dependent on the relative motions of the materials. To make things even more complex, you perform another experiment in the dining car. For a moment you forget all your manners, and you put salt in the sugar bowl and mix the contents with your spoon. Not concerned about the possibility that a later customer may not be very happy about your experiment, you ask yourself whether your action is an advective or a diffusive process. After some thought, you realize that the answer depends on the scale at which you are looking. At the scale of the sugar bowl, you have randomly mixed the individual sugar and salt grains to reach a homogeneous mixture of particles of both kinds. This is a diffusive process. However, at the level of the individual grains, the picture looks different. The molecules contained in an individual crystal were advectively, or jointly, moved around. The distinction between advective and diffusive motion is scale-dependent. Environmental transport processes are composed of all the phenomena encountered in the dining car: advective motion, turbulent diffusion, and molecular diffusion. As an example, large-scale ocean currents, such as the Gulf Stream, are like the dining car. Within the Gulf Stream travel parcels of water, so-called turbulent eddies, that move relative to each other. Where eddies collide, a series of ever smaller eddies is produced until the eddies become so small that their motion dissolves in the molecular movement of the water molecules.

When Space Matters: Transport Processes

193

It is impossible to model the whole spectrum of water movement from the global scale of the Gulf Stream down to the molecular movement of the molecules. Models of fluid systems (atmosphere, ocean, lake, or river) are characterized by their scale of spatial resolution, that is, by the “grain size” of our observations and descriptions. Motion patterns that are larger than our spatial resolution are deterministically modeled by advective motion; patterns smaller than the spatial resolution are modeled as a random or diffusive process. Randomness means that the movement of an individual fluid parcel cannot be described deterministically. But the combined effect of many individual random processes results in simple macroscopic laws that depict the mean effect of the random system. In box models, the scale size below which advective transport is neglected, is determined by the size of the boxes. Since a box is assumed to be completely mixed, modeling a lake by one single box means completely disregarding the effect of internal water currents. At the same time, turbulent diffusive transport is assumed to be intense enough to keep the box well mixed. This assumption of complete diffusive mixing is an extreme method to account for transport and mixing. Sometimes such a description is not justified. In this section, we show how models can be further modified to describe systems that are not completely mixed since mixing is not fast enough or the system is too big. Mathematical Description of Transport Processes We now aim to derive mathematical expressions for diffusive and advective transport in environmental systems. To do so, we seek a mathematical description of advective and diffusive transport in a model, based on the equations derived for first-order (linear) transport by fluid motion between boxes (Eq. 6-16), in which the boxes become smaller and smaller until the boxes are replaced by continuous space coordinates. Let’s begin building the model using an illustrative example. A lake is separated into two basins linked by a shallow channel (Fig. 6.7). The modeling procedure for this system is the same as before: Two state variables are introduced and linked by an exchange flux Qex [L3 T−1 ] (Eq. 6-16). In addition to the symmetric exchange of water at the channel, we add the effect of an inlet into Basin 1 with discharge rate Qad [L3 T−1 ] and of an outlet from Basin 2 with the same discharge rate. A chemical is entering Basin 1 via the inlet (concentration Cin ). We assume that QadCin

Figure 6.7 Water exchange between two lake basins that are separated by a channel. If the channel gets long and shallow, the backward flux  21 becomes zero. The flow from Basin 1 to Basin 2 is then purely advective, the influence from Basin 2 on Basin 1 disappears and the system becomes hierarchical.

QadC2

12 = (Qad+Qex)C1 V1, C1 basin 1

21 = QexC2

V2, C2 basin 2

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Environmental Systems: Physical Processes and Mathematical Modeling

except for the outlet, no other removal or in situ transformation processes affect the concentration in the two separately mixed lake basins. The dynamic equations of the concentrations, C1 and C2 , are: ( ) dC1 ex ex C2 = k1ad Cin − k1ad + k11 C1 + k12 dt ( ) ) dC2 ( ad ex ex = k2 + k21 C1 − k2ad + k22 C2 dt

ex ex with k11 = k12 =

ex ex with k21 = k22 =

Qex ; V1 Qex ; V1

k1ad = k1ad =

Qad V1 Qad V2 (6-24)

The steady-state concentrations are C1∞ = C2∞ = Cin . As before, all rates k have dimension [T−1 ]. Imagine that the channel between the two basins gets shallower and longer. At one point, water can no longer flow back from Basin 2 (where the outlet of the lake is located) to Basin 1. The corresponding backward flux becomes zero: Qex = 0. Then, Eq. 6-24 is reduced to: dC1 = k1ad (Cin − C1 ); dt

dC2 = k2ad (C1 − C2 ) dt

(6-25)

With the elimination of the exchange flux, Qex , the mathematical structure of the two coupled differential equations (Eq. 6-24) undergoes a fundamental change. The influence from the state variable C2 on the differential equation of the state variable C1 disappears so the model becomes hierarchical. In hierarchical models, the state variables can be ordered such that the variable with the lower number influences the one with the higher number but not reversely. A series of lakes that are connected by channels in which the flow is unidirectional, that is, in which back mixing is excluded, represents a hierarchical system. The solution of such models is straightforward: First, the equation of the variable with the lowest number (the one on top of the hierarchy) is solved; the solution is inserted as an external force into the next equation and so forth. If we compare Eqs. 6-24 and 6-25 in terms of advective versus diffusive transport, Eq. 6-24 represents a system in which the coupling between the two boxes is due to both types of transport (advection and diffusion), while in Eq. 6-25, diffusion is suppressed, and transport becomes purely advective (unidirectional). A river can be modeled as a purely advective system. Although in rivers turbulence is important, turbulent transport cannot act against the current, unless the flow velocity is extremely small or the river is dammed to become a lake. Therefore, we can be rather sure that water pollution in New Orleans does not affect water quality in St. Louis upstream, but the reverse is easily possible. Continuous Models Let us now go one step further. We drop the concept of real compartments (lake basins or well-defined horizontal water layers) and subdivide the system into a large number of virtual boxes, which are boxes that do not physically exist but are just imagined. As an example, we imagine the water column of a lake or the ocean to consist of m

Fn,n+1

Δz

Fn,n–1

la ye rn

Fn–1,n

Figure 6.8 Schematic picture showing how a m-box model consisting of m horizontal layers (boxes) turns into a model with a continuous description of concentration C along the spatial axis under consideration (in this case, it is the z-axis). Fn,n+1 and Fn+1,n are the downward and upward fluxes, respectively, across the boundary between layer n and layer n+1.

195

la la ye ye rn rn +1 –1

When Space Matters: Transport Processes

Fn+1,n z

horizontal layers that are connected to their neighboring layers by vertical exchange fluxes (Fig. 6.8). We divide the total flux between the layers,  [MT−1 ], by the area A, and get the normalized flux per unit area, F =  /A [ML−2 T−1 ]. For the flux from layer n to layer n+1, we write: Fn,n+1 =

n,n+1 A

=

Qn,n+1 A

Cn = vn,n+1 Cn

[ML−2 T−1 ];

vn,n+1 ≡

Qn,n+1 A

[LT−1 ] (6-26)

The flow rate Q divided by the area across which the flow occurs is the transport velocity across the interface between layer n and layer n+1, vn,n+1 . Let us assume that vn,n+1 is larger than the reverse velocity. We split the velocities into a symmetric part = vdiff , and the excess velocity from that is the diffusive exchange velocity, vdiff n,n+1 n+1,n = vn,n+1 − vn+1,n : layer n to layer n+1 that we call the advection velocity, vad n,n+1 ad diff diff vn,n+1 = vdiff n,n+1 + vn,n+1 ; vn+1,n = vn+1,n = vn,n+1

(6-27)

For thin layers, the concentration difference between two adjacent layers can be approximated by the slope of the concentration profile, which is the vertical derivative of C(z), dC/dz, multiplied by the vertical spacing of the layers, Δz, where z is the vertical coordinate: Cn+1 − Cn ≈ Δz

dC dz

(6-28)

Let us first look at the situation of pure diffusive exchange (vad = 0). Since the diffusive velocities are equal in both directions, the net flux across the interface between layer n and n+1 is: diff,net diff diff Fn,n+1 ≡ Fn,n+1 − Fn+1,n = vdiff (C − Cn+1 ) = −vdiff Δz n,n+1 n n,n+1

dC dz

(6-29)

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Environmental Systems: Physical Processes and Mathematical Modeling

where we have approximated the concentration difference by Eq. 6-28. The product of the diffusive exchange velocity and the layer thickness is the diffusion coefficient, D: D ≡ vdiff n,n+1 Δz

[L2 T−1 ]

(6-30)

We can now drop the subscripts (n,n+1) because they refer to virtual layer numbers that were only introduced to show how one can extrapolate the concept of finite layers (or finite boxes) to the continuous space. However, we need to remember that Fdiff and D may not be constant along the chosen axis. That is, they may depend on the coordinate z, Fdiff (z) and D(z), although we do not usually explicitly write down the z-dependence. Fick’s First Law. Inserting Eq. 6-30 into Eq. 6-29 yields Fick’s first law: F diff = −D

dC dz

(6-31)

The law states that a flux resulting from a random process is proportional to the negative gradient of the concentration, that is, directed from the zone of higher concentration to the one of lower concentration. Depending on the physical nature of the flux, D either reflects molecular or turbulent diffusion. As long as the underlying process is random, the resulting flux always has the general form of Eq. 6-31. Finally, we want to calculate the net flux for the situation of pure advection (vdiff = 0). Since the backward advection velocity is zero (Eq. 6-27), the net advective flux is: ad,net = vad Fn,n+1 n,n+1 Cn

or simply F = vad C

(6-32)

Models in which space is described continuously (along one or several space coordinates) are mathematically more complex than box-models; their solutions demand partial differential equations. We come back to such models in Section 6.4.

6.4

Models in Space and Time This chapter has given us a first glimpse at mathematical modeling of environmental systems so as to fill our basic mathematical toolkit. We started with the concept of a mass balance applied to simple compartments of the environment called boxes. When moving from one- to two- and to multi-box models, we learned about how these boxes are connected by transport processes. Two distinct modes of transport were identified: diffusive transport, which we relate to random processes, and directed transport, which we relate to advective flow. By making the boxes smaller and smaller, we saw how the box models naturally develop into models in which space is described as a continuous coordinate. We learned how advective and diffusive fluxes are described in these new spatial models. For the latter, we utilized the well-known Fick’s first law (Eq. 6-31). We will now create a sketch of how these elements can be put together into continuous time-space models.

Models in Space and Time

197

Gauss’ Theorem The final mathematic tool is an equation for the local concentration changes due to the combined action of transport and reaction in a three-dimensional system (e.g., lake, ocean, atmosphere etc.). We do not fully derive this equation but make use of Gauss’ theorem. The theorem states that the mass balance in an infinitesimally small control volume can be calculated by looking at all input and output fluxes at the surface of the cube (Fig. 6.9): (

∂C ∂t

) transport

=−

∂Fxtot ∂x

−

∂Fytot ∂y

−

∂Fztot ∂z

= −divF tot

[ML−3 T−1 ]

(6-33)

Some further explanation may help to fully understand this equation. First, since concentration C now depends on four coordinates (time t, space coordinates x, y, z), the normal derivatives (i.e., dC/dt) have become partial derivatives (∂C/∂t). The notation indicates that we are looking at the change of C with time while all other coordinates (x,y,z) are held constant. Likewise, ∂C/∂x would mean the change of concentration along the x-axis while y, z and time t are kept constant. Second, in the threedimensional space, the total flux of the chemical described by concentration C is a vector Ftot (written as bold symbol) composed of the three Cartesian components Fxtot , Fytot , and Fztot . The specific ‘diagonal’ sum of the three partial derivatives in the Fzout

Fxout

Fyout δ

Fxin

Figure 6.9 A cube with dimension δ (control volume) illustrates Gauss’ theorem (Eq. 6-33). The concentration change within the cube results from the differences between input and output fluxes, Fj in – Fj out , calculated for the three Cartesian coordinates j = x, y, z.

Fyin δ

δ z

y

x

Fzin

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Environmental Systems: Physical Processes and Mathematical Modeling

middle part of Eq. 6-33 is called divergence (div). In the specific case of div F, it measures how the flux field diverges (moves apart). If the flux is constant in space, the three partial derivatives are zero and div F = 0. Thus, we can describe the essence of Gauss’ theorem as follows: The local concentration change due to a sum of fluxes is given by the divergence of the flux. For the derivation of Eq. 6-33, the physical nature of the flux did not matter, meaning whether the flux is due to diffusion, advection, or any other process. Now let us use the equation for the two types of flux that we have derived in the previous section. We restrict the discussion to just one spatial dimension (x-axis) and assume that the fluxes along the y- and z-axis are zero. For the remaining flux along the x-axis, we use Eq. 6-32 for advection and Eq. 6-31 for diffusion (Fick’s first law). The subscript x is added to v to indicate that we consider the x-component of the three-dimensional velocity vector: (

∂C ∂t

(

)

∂C ∂t

advection

) diffusion

=− =−

∂Fxadv ∂x ∂Fxdiff ∂x

=−

∂(vx C) ∂(C) = −vx if vx = constant with x ∂x ∂x

=−

( ) ∂2 (C) ∂ ∂C −D = D 2 if D = constant with x (6.34b) ∂x ∂x ∂x

(6.34a)

Equation 6-34b is called the Fick’s second law. The mathematical descriptions for either flux or change of concentration due to advection or diffusion can be summarized by a two-dimensional scheme that helps one remember these relationships (Table 6.2). In the scheme, every move to the right (from flux to concentration change) or downward (from advection to diffusion) involves a sign change as well as an additional differentiation of C with respect to x. The simple form of the scheme is helpful to qualitatively determine the direction of transport and the accompanying concentration changes due to advection and diffusion. A graphical explanation is given in Fig. 6.10.

Table 6.2 Scheme to Describe Flux and Temporal Concentration Change Due to Advection and Diffusion Flux F [ML−2 T−1 ] Advection Diffusion a

vx C −D

∂C ∂x

Concentration Change ∂C∕∂t [ML−3 T−1 ] ∂C ∂x 2 ∂C D 2 ∂x

−vx

Transport Distance L [L] vx t (Dt)1∕2 b

vx : advection velocity [LT−1 ], D: diffusivion coefficient [L2 T−1 ], C: concentration [ML−3 ], t: time [T] a The expressions for diffusion are called Fick’s first and second laws. b Relation by Einstein and Smoluchowski (Einstein, 1905), numerical factor omitted.

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Models in Space and Time

advection C

∂C >0 ∂x

C

vx > 0

∂C ∂t

∂C 0 x0

Figure 6.10 Qualitative relations between the sign of concentration change at location x0 due to advection and diffusion, respectively. C Advection (upper panels): A concentration profile along the x-axis is shifted to the right (thin line) due to advection in the positive x-direction (vx > 0). This leads to a decrease of C at x0 if the slope of C(x) is positive (left panel), and to an increase of C if the slope is negative (right panel). Diffusion (lower panels): According to the Fick’s second law (Eq. 6.34b), diffusion always shifts a concentration profile to its concave side.

∂C ∂t

vx

vx

x

x0

x

diffusion C

∂C ∂t

∂ 2C >0 ∂x 2 x0

∂ 2C 1)

L

x

CL

otherwise

v2 > Dk 2

v Ccrit ⎩0

Reactor characteristics V = 900 L Q = 100 L h−1 k = 0.5 h−1 Ccrit = 100 mg L−1 Cin = 110 mg L−1

(a) Write down the dynamic equation of the system and calculate all steady-state concentrations by setting the left-hand side of the equation zero and solve the resulting algebraic expression for C. Use the numbers of the parameters listed on the margin. Hint: Do not forget the effect of the inflow and outflow on the mass balance of the chemical in the reactor. (b) In case there are several steady states, to which steady state does the system move? Hint: Make a qualitative analysis by just looking at the size of dC/dt for different Cvalues. (c) What happens with C when the input concentration Cin is either increased to 150 mg L−1 or lowered to 50 mg L−1 ? P 6.9 Diffusive Fluxes and Concentration Changes

Consider the concentration profile C(x) = Co e−ax along the positive x-axis (0 ≤ x < ∞), where Co and a are constant positive parameters. (a) Calculate the size and direction of the diffusive flux as a function of x produced by the constant diffusivity D. (b) Calculate the corresponding in situ concentration change, ∂C/∂t, due to diffusion. Numbers:

Co = 1 mmol L−1 a = 0.02 m−1 D = 1 × 10−9 m2 s−1

Evaluate flux F and concentration change, ∂C/∂t, at x = 0, 10 m, 100 m, 1 km. P 6.10 Diffusive and Advective Fluxes Consider the same profile as in P 6.9. In addition to diffusion, an advective velocity, v, acts on the profile. (a) Calculate the corresponding additional contributions to the flux F and the concentration change, ∂C/∂t. (b) Determine the relation between v and the other parameters (D, a, Co ) such that the profile given in P 6.9 for the range 0 ≤ x < ∞ corresponds to a steady state. Is such a steady state possible if v > 0? Note: The solution to Problem 6.10b may yield a velocity v(x) that varies along the x-axis. For incompressible flow (water is hardly compressible), v(x) cannot vary with x if the flow is one-dimensional, yet in two or three dimensions this is possible. P 6.11 ∗ Diffusion and Reaction in a Lake’s Water Column The measurement of four different volatile chemicals in a lake results in distinct vertical steady-state concentration profiles (see the following figure). Based on physics and chemistry studies of the lake, the following simplifying assumptions can be made: (a)

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Environmental Systems: Physical Processes and Mathematical Modeling

C0

z= 0 aerobic zone anaerobic zone zb

1 2

3

4

vertical transport of the chemical is by turbulent diffusion with an approximate constant diffusion coefficient, D, while the mean vertical advection velocity, vz , is zero; (b) the lake consists of an oxic upper layer and an anoxic lower layer; (c) all chemicals enter the lake by air–water exchange at the water surface and are at equilibrium with the constant air concentrations; and (d) the lake bottom acts like an impermeable boundary, that is, the chemicals can neither enter the sediment column nor is there any flux out of the sediment. The four chemicals A, B, C, and D have the following specific properties: A is not reactive at all in the water; B is degraded in the anoxic part by a first-order reaction but is nonreactive in the oxic layer; C is degraded by a first-order reaction in the oxic layer but nonreactive in the anoxic layer; and D is degraded in both layers by a first-order reaction with an equal rate constant in both layers. Identify the concentration profiles of the four different volatile chemicals A to D marked in the figure (in margin) by 1, 2, 3, and 4. Derive an analytical solution for the curves of chemical A and D.

P 6.12 ∗ Tetrachloroethene (PCE) in Mystery Lake In Boxes 6.3 and 6.6, we discussed two different models to describe and interpret the PCE concentrations measured in Mystery Lake (Fig. 6.2). A third model could describe Mystery Lake as a multi-box model (Fig. 6.3, Model C). Given the number of samples taken in the vertical profile (15 samples, spaced 2.5 meters), the best we can do is to develop a 15-box model consisting of 13 layers, each 2.5 m thick, and a top and bottom layer, each only 1.25 m thick. In the following questions, you are asked to analyze the situation qualitatively. For quantitative solutions, you need a computer and the appropriate software tools. (a) Develop a 15-box model for PCE in Mystery Lake. Assume that PCE is conservative in the water column and that inlets, outlets, and air–water exchange affect the top layer only. (b) What is the problem with such a general model? What kind of additional assumptions (e.g., regarding vertical mixing) have to be made in order to get reasonable results? (c) How does the model change if it is assumed that all the inlets enter the lake at 9 m depth while the outflow occurs from the top layer? (d) Should lake bathymetry, specified by the depth-depending lake cross-section A(z), be taken into account to answer the above questions? If yes, how? P 6.13 ∗ Vertical Distribution of Dichlorodifluoromethane (CFC-12) in a Small Lake Dichlorodifluoromethane (CCl2 F2 , CFC-12) enters a small lake (surface area Ao = 2 × 104 m2 , maximum depth zm = 10 m) from the atmosphere by air–water exchange. The top 2 m of the lake are well mixed. Vertical turbulent diffusivity between 2 and 10 m is estimated to be Ez = 1 × 10–5 m2 s–1 . Groundwater infiltrates at the bottom of the lake adding fresh water at the rate of Qgw = 100 L s–1 . The only outlet of the lake is at the surface. The CFC-12 concentration in the mixed surface water is Co = 10 × 10–12 mol L–1 and below the detection limit in the infiltrating groundwater. (a) Write down the appropriate one-dimensional equation and calculate the eigenvalues λ1 and λ2 (Box 6.4, Eq. 3), the Damk¨ohler Number Da, and the Peclet Number Pe in order to sketch the shape of the vertical profile of CFC-12 between 2 and 10 m

Bibliography

211

depth at steady state provided that all relevant processes (turbulent mixing, discharge rate of groundwater, and mixed-layer concentration) remain constant. (b) Estimate how long it would take for the profile to reach steady state. (c) Somebody claims that CFC-12 might not be stable in the water column. To check this possibility, you compare your model with a vertical CFC-12 profile measured in the lake. How big would a hypothetical first-order reaction rate constant, k, have to be in order to be detected by your model? Assume that the absolute accuracy of your CFC-12 analysis is ±10%. Hint: The non-dimensional numbers Da and Pe may help. Note: Disregard the depth-dependent cross section of the lake. Assume that the area of the lake is Ao at all depths.

6.6

Bibliography Bartholomew, G. W.; Pfaender, F. K., Influence of spatial and temporal variations on organic pollutant biodegradation rates in an estuarine environment. Appl. Environ. Microbiol. 1983, 45(1), 103–109. B¨ohringer, F., Glacier Express auf Landwasserviadukt. Wikimedia Commons: 2013. https://commons.wikimedia.org/wiki/. Crank, J., The Mathematics of Diffusion. 2nd ed.; Clarendon Press: Oxford, 1975. ¨ Einstein, A., Uber die von der molekularkinetischen Theorie der W¨arme geforderte Bewegung von in ruhenden Fl¨ussigkeiten suspendierten Teilchen. Annalen der Physik 1905, 322(8), 549–560. Imboden, D. M., Mathematical Modelling of the Behaviour of Organic Micropollutants in the Aquatic Environment. In Organic Micropollutants in the Aquatic Environment, Bjørseth, A.; Angeletti, G., Eds. D. Reidel Publishing: Dordrecht, The Netherlands, 1986; pp 460-464. Imboden, D. M.; Pfenninger, S., Introduction to Systems Analysis. Springer: Berlin, 2013; p 252. Kleindorfer, P. R.; Kunreuther, H. C.; Schoemaker, P. J. H., Decision Sciences: An Integrative Perspective. Cambridge University Press: Cambridge, 1993. Larson, R. J.; Davidson, D. H., Acclimation to and biodegradation of nitrilotriacetate (NTA) at trace concentrations in natural waters. Water Res. 1982, 16(12), 1597–1604. Schnoor, J. L., Environmental Modeling. Wiley-Interscience: New York, NY, 1996; p 682. Schwarzenbach, R. P.; Gschwend, P. M.; Imboden, D. M., Models in Space and Time. In Environmental Organic Chemistry, John Wiley & Sons, Inc.: Hoboken, N.J., 2003; pp 1005–1047.

Part II

Equilibrium Partitioning in Well-Defined Systems

215

Chapter 7

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

7.1

Introduction Box 7.1 Partition Constants, Partition Coefficients, and Distribution Ratios: A Few Comments on Nomenclature

7.2

Molecular Interactions Governing Bulk Phase Partitioning of Organic Chemicals Gas–Liquid Phase Partitioning Box 7.2 Estimating Molar (Molecular) Volumes from Structures Liquid Organic Phase–Water Partitioning Some General Conclusions

7.3

Quantitative Approaches to Estimate Bulk Phase Partition Constants/Coefficients: Linear Free Energy Relationships (LFERs) Fragment Contribution Methods Single-Parameter Linear Free Energy Relationships (sp-LFERs) Poly-Parameter Linear Free Energy Relationships (pp-LFERs)

7.4

Questions

7.5

Bibliography

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

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7.1

Introduction In Section 4.2, we discussed the partitioning of a given chemical i between two bulk phases 1 and 2 (i.e., phases in which a compound may partition into as compared to adsorption onto a surface): i in phase 2 ⇋ i in phase 1 “reactant” “product”

(4-19)

and we defined its equilibrium partition constant, Ki12 , between the two phases as: Ki12 =

concentration of i in phase 1 concentration of i in phase 2

(4-20)

When considering bulk phases other than well-defined solvents, such as natural organic matter or biota (Chapters 13 and 16), one often expresses the concentration of i in mol per mass (e.g., mol kg–1 ) and not in mol per volume. If so, we refer to Ki12 as a partition coefficient and not as a partition constant (see Box 7.1 for more details on nomenclature).

Box 7.1

Partition Constants, Partition Coefficients, and Distribution Ratios: A Few Comments on Nomenclature

In the literature, one sometimes encounters a certain confused use of the terms “partition constant,” “partition coefficient,” and “distribution ratio.” Throughout this book, we use these terms in the following way: we talk of a partition constant or a partition coefficient when only one chemical species is considered in each phase. The term partition constant is reserved for those cases where we deal with the equilibrium partitioning between two well-defined phases at given conditions and where we can be sure that the proportionality factor between the concentrations in the two phases is a concentration-independent constant at given conditions. Examples include the air–water partition constant (Chapter 9), the solvent–air and the solvent–water partition constants (Chapter 10), and the air–pure surface partition constant (Chapter 11). In all other cases where this proportionality factor describes structurally varying phases, such as organic matter, black carbon, or lipids, we talk about a partition coefficient. A prominent example is the natural organic matter–water partition coefficient that we discuss in Chapter 13. Furthermore, the very general term “distribution ratio” is used for situations where we want to express the ratio of total concentrations of a given chemical in two phases. Examples include the equilibrium distribution ratio of organic acids or bases in air–water, organic solvent–water, or natural organic matter–water systems, where these compounds may be present as both neutral and charged species. Another case is the natural solid–water distribution ratio of a chemical where various different sorption mechanisms may be responsible for the presence of the compound in the solid phase. Finally, we should note that several other terms including “distribution constants,” “distribution coefficients,” and “accumulation factors” are often used in the literature to describe partitioning. We generally do not use these terms except for in our discussion on bioaccumulation, where we adopt the commonly used term “bioaccumulation factor” (BAF, Chapter 16).

217

Molecular Interactions Governing Bulk Phase Partitioning

If molar concentrations (mol L–1 ) or the same mass concentration units (e.g., ng, μg, or mg per L) are used instead of mole fractions in each phase, as used in Chapter 4, Ki12 is related to the free energy of transfer: Δ12 Gi , by: Ki12 =

V̄ 2 −Δ G ∕RT ⋅ e 12 i V̄ 1

(4-29)

where V̄ 1 and V̄ 2 are the molar volumes of the two bulk phases (e.g., in mL mol–1 or L mol–1 ). Ki12 is then not dimensionless but is expressed in units of, e.g., L2 ∕L1 or m2 3 ∕m1 3 . The ratio of the molar volumes (V̄ 2 ∕V̄ 1 ) of the two bulk phases may have a noticeable effect on the absolute value of Ki12 , particularly if the two phases have significantly different molar volumes. Such is the case for air–water partitioning at 25◦ C, as the molar volumes of air and water are 24.8 L mol–1 and 0.018 L mol–1 respectively. Hence, the air–water partition constant expressed in molar concentrations is 1378 (= 24.8/0.018) times smaller than the one expressed in partial pressure and mole fraction. However, since the molar volumes of most organic liquid phases (solvents) that we discuss do not vary much more than a factor of 2 or 3, the dissimilarities among Δ12 Gi are far more important than volume differences when comparing partition constants of organic compounds in various organic solvent–water and organic solvent–air systems. Finally, we recall that thermodynamic properties, such as partition constants or reaction constants, are independent of the transfer or reaction pathway and only depend on the starting and ending conditions. Thus, one can use known partition constants to derive unknown partition constants by thermodynamic cycles. To illustrate, one can derive the organic solvent (l )– air (a) partition constant of a compound i from the ratio of its organic solvent–water (w) and its air–water partition constants: Kil a = Kil w ∕Kiaw

(7-1)

remembering that the organic solvent phase in Kil w is water-saturated and, therefore, so is the solvent phase in Kil a . This point is in many cases unimportant, as dry and wet solvents usually have similar partition constants, but we do expand on this issue in Chapter 10 where we also discuss examples in which the water present in the organic solvent makes a difference.

7.2

Molecular Interactions Governing Bulk Phase Partitioning of Organic Chemicals Irrespective of whether we consider organic chemicals as solutes or as solvents, we can classify them according to their ability to form hydrogen bonds (H-bonds) with apolar (no H-bonding), monopolar (either H-accepting or H-donating), and bipolar (both Haccepting and H-donating) compounds (Chapter 2, Box 2.2; see also examples given in Table 7.1). In this section, we use this simple classification to gain some qualitative insights into how intermolecular interactions within a given bulk phase plus those

218

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

Table 7.1 Classification of Organic Chemicals According to Their Interaction Abilities (see Fig. 2.11 for functional groups) Compound

Interactions

Examples

Apolar Monopolar

only van der Waals van der Waals + H-accepting (e-donating)

Monopolar

van der Waals + H-donating (e-accepting) van der Waals + H-accepting + H-donating

alkanes, chlorobenzenes, PCBs alkenes, alkynes, alkylaromatic compounds, ethers, ketones, esters, aldehydes chloroform, dichloromethane

Bipolar

ideal gas (a) (no interactions)

i Step 2

insertion of i into cavity: ΔGi liquid

Step 1

formation of a cavity: ΔGcavity

primary amines, secondary amines, carboxylic acids, alcohols

between the bulk phase molecules and the molecules of a compound i determine the extent to which i partitions between two bulk phases. To attain these insights, we first consider the partitioning of an organic compound i between the gas phase (air) and a bulk liquid phase. We then discuss the partitioning of i between two liquid phases, one of which is water. For the gas phase, we assume ideal behavior, that is, we assume that no molecular interactions exist between the molecules. In the liquid phase, we assume that the compound is present in dilute solution. Therefore, we can presume that the compound’s molecules never interact with one another, but only with the solvent, thus the partition constants are independent of concentration. This section closely follows the concepts originally outlined in Goss and Schwarzenbach (2003), where further details can be obtained. Gas–Liquid Phase Partitioning

bulk liquid (ℓ ) Δa ℓ Gi = ΔGcavity + ΔGi liquid

Figure 7.1 Partitioning of a compound i from an ideal gas phase (air, subscript “a”) into a bulk liquid (subscript “l ”).

As illustrated in Fig. 7.1, when using a simple cavity model for gas–liquid partitioning, we only have to consider two free energy contributions: (1) the formation of the cavity in the liquid (ΔGcavity > 0, costing free energy), and (2) the free energy gained from the molecular interactions of the solute with the solvent molecules (ΔGiliquid < 0) upon insertion of the solute into the cavity: Δal Gi = ΔGcavity + ΔGiliquid

(7-2)

ΔGcavity is dependent on the size and the shape of the molecule to be inserted and on how strongly the bulk liquid phase molecules interact with each other, commonly referred to as cohesive energy (see Otto, 2013), especially if such interactions have to be disrupted when forming the cavity. ΔGcavity is particularly large when dealing with bipolar solvents with small solvent molecules, with water being, by far, the most extreme case (see Chapter 9). The second term in Eq. 7-2, ΔGiliquid , depends on the strength of interactions of the inserted molecule with the liquid phase molecules surrounding the cavity. Insertion of Δal Gi into Eq. 4-29 yields the air–liquid equilibrium partition constant (Kial ).

Molecular Interactions Governing Bulk Phase Partitioning

219

We can now divide both free energy terms in Eq. 7-2 into a van der Waals (vdW) component, which always occurs and includes London dispersive and, in most cases, also Debye and Keesom contributions (the latter two components being of secondary importance, for more details see Section 2.2), and into a hydrogen bonding (Hbonding) component: ) ( ) ( H vdW H + ΔG Δal Gi = ΔGvdW + ΔG + ΔG cavity cavity iliquid iliquid

(7-3)

We recall from Section 2.2 that vdW as well as H-bonding interactions are always attractive and that the former occur between all kinds of molecules. Hence, ΔGvdW cavity in Eq. 7-3 is always > 0, and ΔGvdW is always < 0. For a simple but convenient iliquid visualization of vdW interactions, we can imagine all molecules to be covered by a “glue” that has a different “stickiness” on different types of compounds. The strength of vdW attractions between a molecule i and its interaction partners then depends on the stickiness of the glues and on the size of the contact area. One should also recall from Chapter 4 that each free energy term is composed of an enthalpy and an entropy contribution (Section 4.1). When we talk about vdW and Hbonding interactions or use terms like “glue” or “vdW-stickiness” of molecules, we solely address the enthalpy contribution to free energy. Often, the contributions from enthalpy and entropy of partitioning of organic compounds are correlated. However, situations exist in which such a correlation does not hold, and we need to look at the entropy contribution to free energy to understand the differences in partitioning behavior among certain compound classes. When considering partitioning of organic compounds between air and a bulk liquid phase, one can distinguish four different possible cases: = 0; ΔGH = 0), Case I: Only vdW interactions are important (ΔGH cavity iliquid Case II: H-bonding affects only cavity formation (ΔGH = 0), iliquid Case III: H-bonding affects only interactions between i and the bulk liquid phase = 0), and (ΔGH cavity Case IV: H-bonding affects both cavity formation and interactions between i and the bulk liquid phase (all terms in Eq. 7.3 are important). In the following discussion, we briefly address each of these cases with the aim to learn how the various terms in Eq. 7-3 govern the overall partitioning of apolar, monopolar, and bipolar chemicals between air and liquid phases of different polarities. Case I. For the first case, when only vdW interactions are important, we consider the partitioning of any organic compound between air and any apolar liquid phase. Here, the apolar phase is n-hexadecane, or simply hexadecane. In Fig. 7.2a, the logarithms of hexadecane–air partition constants (log Kihexadecane–air ), of several classes of

220

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

12

12

(a)

8 6 4 2 0 –2 –4

(b)

10

log Ki octanol–air (LaLo–1)

log Ki hexadecane–air (LaLh–1)

10

8 6 4 2 0 –2

0

50

100

150

200

250

–4

300

12

0

(c)

150

200

250

300

50

100

150

200

250

300

(d) 10

8

8

log Ki octanol–water (LwLo–1)

log Ki water–air (LaLw–1)

100

12

10

6 4 2 0 –2 –4

50

6 4 2 0 –2

0

50

100

150

200

250

300

–4

0

molar volume (cm3 mol–1) aliphatic amines 1-alkanols alkanes carboxylic acid esters

Figure 7.2 Plots of the logarithms of the hexadecane–air (a), octanol– air (b), water–air (c), and octanol– water (d) partition constants of series of apolar, monopolar, and bipolar compounds (our “test set”) versus their molar volumes, Vi .

molar volume (cm3 mol–1) chlorobenzenes chlorinated phenols fluorotelomers ketones

polycyclic aromatic hydrocarbons polychlorinated biphenyls siloxanes

apolar, monopolar, and bipolar compounds are plotted against the size of the compounds expressed by their molar volumes, Vi , calculated by the McGowan method (see Box 7.2). We use these compounds, which we refer to as “our test set,” in Parts II and III to visualize relationships between different properties and parameters. Some important general observations, which also hold for partitioning to any other apolar liquid phase, can be made from hexadecane–air partitioning (Fig. 7.2a):

Molecular Interactions Governing Bulk Phase Partitioning

221

Box 7.2 Estimating Molar (Molecular) Volumes from Structures A very common way of expressing the bulk size of 1 mole of molecules of a given compound is to use the “molar volume,” Vi (mL mol–1 ), of the compound. As discussed in Chapter 4, we can derive Vi from the molar mass (g mol–1 ) and the liquid density (g mL–1 ) of the compound at a given temperature. This way of defining Vi does have certain disadvantages when we want to use it to describe the size of a compound, as in Fig. 7.2. First, because the liquid density is a bulk property, for polar compounds (e.g., alcohols) that have a network-like hydrogen-bond structure between molecules, the calculated Vi value reflects not only the intrinsic molecular volume but also the bulk structure. Second, adjustments have to be made when dealing with compounds that are solids. Therefore, various methods for estimating Vi values from the structure of a compound have been developed (for an overview see Yalkowski and Banerjee, 1992; Mackay et al., 1992–1997). Although each of these methods yields different absolute Vi values, the various data sets correlate reasonably well with each other (Mackay et al., 1992–1997). Notably, McGowan and coworkers proposed a simple method that works almost as well as the more sophisticated approaches (McGowan and Mellors, 1986; Abraham and McGowan, 1987). In this method, each element is assigned a characteristic atomic volume (see the following table), and the total volume is calculated by summing up all atomic volumes and by subtracting 6.56 cm3 mol–1 for each bond, no matter whether single, double, or triple. As an example, Vi for benzene is calculated as Vi = (6) (16.35) + (6) (8.71) – (12) (6.56) = 71.6 cm3 mol–1 , illustrating the simplicity of the calculation. Of course, by this method, identical Vi values are obtained for structural isomers, which is sufficient as a first approximation for many applications. Characteristic Atomic Volumes (cm3 mol–1 ) a C 16.35 Cl 20.95 a

H 8.71 Br 26.21

O 12.43 I 34.53

N 14.39 S 22.91

P 24.87 Si 26.83

F 12.48

Data from Abraham and McGowan (1987) and Goss et al. (2006) for the fluorine increment.

(1) Except for some are small molecules such as methane or ethane, generally, organic compounds partition favorably from air into an apolar liquid such as hexadecane (Kihexadecane–air > 1). The reason is, if only vdW forces play a role, the gain in free energy from insertion of the compound in the cavity is larger than the free energy that has to be spent to form the cavity. (2) Kihexadecane–air values of compounds with similar size may be orders of magnitude different among various compound classes. For example, the polycyclic aromatic hydrocarbon (PAH), phenanthrene (Vi = 145 cm3 mol–1 , log Kihexadecane–air = 7.68), partitions nearly three orders of magnitude more favorably from air into hexadecane as compared to an alkane of similar size, decane (Vi = 152 cm3 mol–1 , log Kihexadecane–air = 4.69), and more than five orders of magnitude more favorably than hexamethyldisiloxane (Vi = 150 cm3 mol–1 , log Kihexadecane–air = 3.12) or perfluorobutylethanol (Vi = 135 cm3 mol–1 , log Kihexadecane–air = 2.52). In general, rigid aromatic compounds, such as PAHs, exhibit significantly higher Kihexadecane–air values as compared to aliphatic compounds of similar size, regardless of whether they contain a polar functional group or not. These higher values are, on the one hand, due to the ability of aromatic compounds to undergo somewhat more intense vdW interactions than aliphatic compounds, thanks to their higher “vdW-stickiness.” This ability is

222

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

even more pronounced when comparing them to polyfluorinated aliphatic compounds (i.e., fluorotelomers) and siloxanes (Fig. 7.2), which both exhibit unusually small “vdW-stickness” (see also Chapter 3 for general characteristics of these compounds). On the other hand, the more rigid aromatic compounds also exhibit a smaller loss in entropy when being transferred from the gas phase into a bulk liquid phase as compared to the much more flexible alkanes, fluorotelomers, and siloxanes, which lose more freedom of motion. Therefore, when comparing phenanthrene with decane, perfluorobutylethanol, or hexamethylsiloxane, the differences in the entropy losses due to partitioning also contribute to the observed disparities in their Kihexadecane–air values. (3) Within a set of structurally closely related compounds, such as homologues or congeners, a linear correlation between log Kihexadecane–air and Vi is observed. The slopes of these correlations (increase of log Kihexadecane–air per increase in Vi ) are smallest for siloxanes and fluorotelomers. These small slopes can be rationalized primarily by their unusually low vdW interaction capabilities, which do not increase significantly with size as compared to other compound classes. The slope is highest for the planar PAHs because they exhibit a significant increase in “vdW-stickiness” per unit increase in size and display an entropy loss much less dependent on size, as compared to the more flexible aliphatic or alicyclic compounds. For example, our companion PAHs, phenanthrene and benzo(a)pyrene, exhibit a difference in Vi of 43 cm3 mol–1 , which translates into a variation in Kihexadecane–air of four orders of magnitude. Conversely, for siloxanes or fluorotelomers, the same difference in Vi leads to a variation of less than one order of magnitude in Kihexadecane–air . (4) Large rigid organic compounds, particularly those exhibiting a strong “vdWstickiness,” partition very strongly from air into hexadecane. Examples include two companion compounds, benzo(a)pyrene (Vi = 195 cm3 mol–1 , log Kihexadecane–air = 11.74) and PCB 153 (Vi = 206 cm3 mol–1 , log Kihexadecane–air = 9.59). Therefore, we can already see why such compounds have a high tendency to partition from air to apolar or weakly monopolar biological materials in the environment, such as waxes or lipids (see Chapter 16). Case II. To illustrate the case when H-bonding affects only cavity formation, we consider the partitioning of apolar compounds between air and a bipolar liquid phase. Compared to partitioning to an apolar phase, the partition constant of a given compound can be expected to be smaller since the energy of cavity formation is higher and no additional energy is gained from polar interactions when inserting the apolar compound. Table 7.2 summarizes the solvent–air partition constants of the apolar compound n-octane in water and various apolar and bipolar organic liquids. As is evident, the partition constant of n-octane decreases significantly with increasing cohesive energy of the liquid organic phase. However, as compared to partitioning into water, n-octane still partitions more than four orders of magnitude better into the strongly bipolar solvent, 1,2-ethanediol, highlighting the extraordinary cohesive energy of water. Case III. An example of the case when H-bonding affects only interactions of i and the bulk phase molecules is the transfer of a monopolar compound from air into a = 0 and energy is gained monopolar liquid phase of opposite polarity. Here, ΔGH cavity from additional H-bonding upon insertion of the compound into the cavity. In this

Molecular Interactions Governing Bulk Phase Partitioning

223

Table 7.2 Liquid Phase–Air Partition Constants of n-Octane for Various Organic Liquids and Water at 25◦ C Formula

Heptane Hexadecane Butanol 1,3-Propanediol 1,2-Ethanediol Water

C7 H16 C16 H34 C4 H9 OH C3 H6 (OH)2 C2 H4 (OH)2 HOH

Cohesive Energy a increasing

Liquid

Kliquid–air 8600 5000 2300 80 13 0.008

a The cohesive energy of the organic solvents increases with increasing number of bipolar OH-groups per carbon atom.

N pyridine

case, larger Kil a values can be expected as compared to partitioning of the compound into an apolar phase. Also, the activity coefficient of the compound, γil , is smaller than one (Section 4.2). For example, the partition constant of the H-acceptor pyridine (a widely used solvent and precursor substance for syntheses in chemical industry; structure in margin) between the H-donating solvent chloroform (CHCl3 ) and air is about 50 times larger as its hexadecane–air partition constant. Case IV: We conclude our qualitative discussion of air–bulk liquid partitioning by considering two examples that encompass all possible energetic combinations in Eq. 7-3, the partitioning of any kind of compound between air and a bipolar liquid. We examine the bipolar phases of n-octanol, referred to as octanol, which has a moderate term, and water, which exerts extraordinarily high cohesive energy, i.e., a ΔGH cavity . Figures 7.2b and 7.2c display the logarithms of the octanol–air and large ΔGH cavity water–air constants versus Vi of the same classes of apolar, monopolar, and bipolar compounds as seen in Fig. 7.2a. Comparison of hexadecane–air and octanol–air partitioning (Figs. 7.2a and b) shows that, for the various compound classes, very similar slopes are found when plotting the logarithms of the partition constants versus Vi . This correspondence in slopes suggests that the vdW terms in Eq. 7-3 are quite similar for partitioning from air to these two organic liquids (Goss and Schwarzenbach, 1998). However, for some compound classes, the absolute values of the partition constants are significantly different contribubetween the two systems, primarily reflecting the differences in ΔGH iliquid tions for different polar functional groups. For example, the Kihexadecane–air values of aliphatic compounds, including apolar alkanes, monopolar ketones and carboxylic acid esters, and bipolar amines and alcohols, are all in the same order of magnitude, whereas the octanol–air partition constants, Kioa , are spread over three orders of magnitude. Qualitatively, we can see that the bipolar OH- and NH2 -groups increase the magnitude of Kioa relative to Kihexadecane–air more strongly than the monopolar keto- or carboxylic ester groups. The reason is that bipolar compounds undergo much stronger H-bonding with the OH-groups of octanol as compared to the monopolar compounds. The effect of H-bonding can also be nicely seen when comparing the partition constants of the apolar chlorinated benzenes and the bipolar chlorinated phenols, which

224

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

are very similar in the hexadecane–air system but are almost two orders of magnitude different in the octanol–air system. Figure 7.2c illustrates that quite a different dependency on size is obtained for water– air partitioning than in the octanol–air system. Here, except for PAHs, an increase in size of structurally related compounds has little or even slightly disfavoring effects on partitioning into the liquid phase. In the case of PAHs, the observed increase in Kiwater–air can again be rationalized by the fact that vdW interaction abilities increase significantly with increasing size, while the entropy losses of these rigid compounds upon transfer from the gas phase do not. We discuss these entropic aspects in more detail in Chapter 9. Liquid Organic Phase–Water Partitioning We can now use the insights gained from the previous discussion on air–bulk liquid phase partitioning to evaluate the partitioning of organic chemicals between water and a bulk organic liquid. For partitioning between two bulk liquids 1 and 2, we can rewrite Eq. 7.3 as: ( ) ( ) H vdW H + Δ ΔG ΔG + Δ ΔG + Δ (7-4) Δ12 Gi = Δ12 ΔGvdW 12 12 12 cavity cavity iliquid iliquid where Δ12 ΔG = Δ1a G − Δ2a G. According to the thermodynamic cycle, Eq. 7-4 is the difference between two equations of the type Eq. 7-3 written for the respective bulk liquid–air systems. To solve the equation, we just have to consider the differences in the free energies for cavity formation (ΔΔGcavity ) and insertion of the compound (ΔΔGiliquid ), respectively, in the two bulk liquids. As in Eq. 7-1, we can then relate the organic liquid–water partition constant to the corresponding organic liquid–air and water–air partition constants. Using octanol (o) as model organic phase, we obtain: Kiow = Kioa ∕Kiwa

(7-5)

By plotting Kiow versus size (Fig. 7.2d), we see organic chemicals of increasing size increasingly favor partitioning into the octanol phase, which is similar to octanol–air partitioning (Fig. 7.2b). In fact, the slopes of the lines correlating structurally closely related compounds are very similar in both systems. This finding is expected from Eq. 7-5, since Kioa increases significantly with size (Fig. 7.2b) whereas Kiwa is much less size dependent (Fig. 7.2c). However, comparison of Figs. 7.2b and d also reveals some important differences. Comparing the absolute values of the partition constants for the various groups of compounds, one sees that polar compounds exhibit much higher octanol–air than octanol–water partition constants. For example, the Kioa values of alkyl alcohols are more than two orders of magnitude higher than the corresponding Kiow values. The contrary is found for apolar compounds, such as alkanes, for which Kiow is about two orders of magnitude larger than Kioa . This difference is due to the large free energy costs for cavity formation in water being partly compensated by inserting polar, particularly bipolar, molecules exhibiting strong H-bonding properties but not by inserting compounds that can only undergo vdW interactions.

Quantitative Approaches to Estimate Bulk Phase Partition Constants

225

Some General Conclusions In summary, from our discussions thus far, we have gained important insights into how molecular interactions determine the extent to which a neutral organic chemical partitions between two bulk phases. In particular, we have seen that: (1) With few exceptions, organic compounds generally favor bulk organic phases over air or water. The extent of partitioning is determined by the molecular size, entropic contributions, and the vdW and H-bonding properties of the compound, as well as by the characteristics of the bulk phases involved (i.e., apolar, monopolar, and bipolar). Depending on the properties of the bulk phase(s) considered, compounds exhibiting the same size but belonging to different compound classes may exhibit substantially different partition constants. (2) For both air–organic bulk phase and organic bulk phase–water partitioning of a series of structurally closely related compounds (e.g., homologues, congeners), a linear correlation between the free energy of transfer, and thus the logarithm of the corresponding partition constant or coefficient, and the size of the molecule is observed. The slopes of these correlations depend to a great extent on the vdW interaction abilities of the compounds as well as on entropic aspects. For organic phase–air partitioning, the slopes are largest for PAHs and polychlorinated and polybrominated aromatic compounds (data not shown) and smallest for siloxanes and fluorotelomers (Figs. 7.2d and b). For organic phase–water partitioning, the slopes tend to be more similar for the different compound classes (see Fig. 7.2d), which is a result of compensating vdW and, in some cases, H-bonding interactions occurring in both phases. Also, entropy contributions are significantly smaller if both phases are liquids, which is particularly important when considering rigid compounds such as the PAHs.

7.3

Quantitative Approaches to Estimate Bulk Phase Partition Constants/Coefficients: Linear Free Energy Relationships (LFERs) For many environmentally relevant matrices, experimental partition constants or coefficients required to assess quantitatively the partitioning behavior of a given compound are often not available and, therefore, have to be estimated. Examples include the partitioning from water or air to natural organic matter; to biological materials such as lipids, proteins, lignin or cellulose; or to mineral oxides or black carbon surfaces (see Part III). In the following section, we introduce some general approaches for predicting partition constants for such matrices. In all of these approaches, one tries to express the free energy of transfer, Δ12 Gi , of a given compound in the system of interest by one or several other known free energy terms in a way that they are linearly related to Δ12 Gi . Such approaches are, therefore, commonly referred to as linear free energy relationships (LFERs). They are useful for predictive purposes and also helpful for checking reported experimental data for consistency (i.e., to detect experimental errors or to discover unexpected partitioning behavior of a given compound).

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Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

Fragment Contribution Methods A common approach that is particularly suited to computer-assisted evaluations takes advantage of the assumption that the interactions of molecules with their surroundings can be estimated by summing the interactions of each of the structures’ parts. Hence, to estimate partition constants of a compound in a given two-phase system one assumes that the free energy of transfer term for the whole molecule (Δ12 Gi ) can be expressed by a linear combination of terms that describe the free energy of transfer of parts of the molecule: Δ12 Gi =

∑

Δ12 Gpart of i + special interaction terms

(7-6)

parts

Expressed in terms of partition constants, Eq. 7-6 becomes: log Ki12 =

∑

Δ log Kpart of i12 + special interaction terms

(7-7)

parts

In the extreme case, each part is an atom of the molecule. The special interaction terms are necessary to describe intramolecular interactions and stereochemical aspects between different parts of the molecule that cannot be accounted for when considering the free energy of transfer of the isolated parts. Obviously, this type of approach, dubbed the fragment contribution approach, has the advantage that it allows one to estimate a partition constant based solely on the compound’s structure. For our purposes, this approach is of interest because it provides valuable insights into how parts of a molecule contribute to the overall partition constant. Good predictions can be anticipated particularly in cases where the partition constant of a structurally closely related compound is known, and, thus, only the contributions of the parts that are different between the two compounds have to be modified. In recent years, quite sophisticated computer models based on the fragment contribution approach have become available, including Absolv (ACD/Labs), SPARC (SPARC Performs Automated Reasoning in Chemistry; see Hilal et al., 2007), and EPI Suite (Estimation Programs Interface Suite; U.S. EPA, 2012). The most widely used application based on this approach is the structural group contribution method used for estimating octanol–water partition constants (see Chapter 10, Section 10.3). Single-Parameter Linear Free Energy Relationships (sp-LFERs) The most simple and widely used approach to predict partition constants is the singleparameter linear free energy relationship (sp-LFER), in which a linear relationship is assumed between the free energies of transfer of a series of compounds in two different two-phase systems: Δ12 Gi = a′ Δ34 Gi + b′

(7-8)

227

Quantitative Approaches to Estimate Bulk Phase Partition Constants

where usually one of the phases is the same in the two systems (e.g., 2 = 4 = water or air, 1 and 3 are two different organic phases). In terms of partition constants or coefficients, Eq. 7-8 can then be written as: log Ki12 = a log Ki32 + b

(7-9)

The slope, a, and the constant, b, in Eq. 7-9 are then determined by a linear regression analysis of a set of compounds with known partition constants or coefficients in both systems.

Figure 7.3 Plot of the logarithms of (a) the hexadecane–air (Kihexadecane–air ) versus the octanol– air (Kioa ) partition constants, and (b) the logarithms of the hexadecane– water (Kihexadecane–water ) versus octanol–water (Kiow ) partition constants at 25◦ C for our test set.

Such sp-LFERs work reasonably well if certain criteria are fulfilled. First, a sp-LFER should only be applied to compounds undergoing similar intermolecular interactions during partitioning as the compounds for which the sp-LFER was derived. This means, for example, one should not expect to assemble a sp-LFER using a set of apolar compounds to predict behaviors of bipolar compounds. Also, the phases 1 and 3 (Eq. 7-9) should be comparable in terms of possible molecular interactions. As an illustration of the importance of these criteria, Fig. 7.3 shows plots of the logarithms of the hexadecane–air versus the octanol–air (Kioa ) partition constants (Fig. 7.3a) and the logarithms of the hexadecane–water versus octanol–water (Kiow ) partition constants (Fig. 7.3b) for different compound classes. As is evident from Fig. 7.3, in

12

12

8 6 4 2 0 –2 –4

1 1:

1:

10

log Ki hexadecane–water (LwLh–1)

log Ki hexadecane–air (LaLh–1)

(b)

1

(a)

10

8 6 4 2 0 –2

–4

–2

0

2

4

6

8

10

12

–4

–4

–2

log Ki octanol–air (LaLo–1)

alkanes chlorobenzenes polychlorinated biphenyls chlorinated phenols

0

2

4

6

8

10

log Ki octanol–water (LwLo–1)

ketones carboxylic acid esters aliphatic amines 1-alkanols

siloxanes fluorotelomers polycyclic aromatic hydrocarbons

12

228

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

both cases, no single sp-LFER of the type Eq. 7-9 can fit the whole data set. Good linear relationships can, however, be found for structurally closely related subsets of compounds, such as homologues series of alkanes, aliphatic ketones, esters, amines, 1-alkanols, siloxanes, and fluorotelomers. Highlighting the importance of molecular interactions, the linear relationships seen in Fig. 7.3 are quite different for bipolar compounds capable of H-bonding interactions, such as alcohols, as for apolar compounds only capable of vdW interactions in both phases, such as the n-alkanes. Therefore, sp-LFERs of the type seen in Eq. 7-9 need to be applied with necessary caution, but when used properly, they can successfully predict partition constants or coefficients of compounds from known partition constants or coefficients in one of the systems considered. Common applications include the prediction of natural organic matter–air and natural organic matter–water or biological media–air and biological media–water partition coefficients from octanol–air or octanol–water partition constants, respectively, which are discussed in Chapters 13 and 16. Poly-Parameter Linear Free Energy Relationships (pp-LFERs) A more generally applicable, yet still simple to use, set of tools for prediction of bulk phase partition constants are the poly-parameter linear free energy relationships (pp-LFERs), sometimes also referred to as the linear solvation energy relationships (LSERs). The goal of this approach is to capture the structural variety of organic compounds and bulk phase characteristics affecting intermolecular interactions in one single equation. The basic concept is to express Δ12 Gi in Eqs. 7-3 or 7-4 by a linear combination of free energy terms explicitly describing cavity formation as well as vdW and H-bonding interactions between the solute and solvent molecules. Kamlet and Taft and later Abraham and co-workers introduced this rather simple approach some decades ago (Kamlet and Taft, 1979; Taft et al., 1985; Abraham, 1993), and it has since been used successfully in numerous applications in analytical and environmental chemistry (see Endo and Goss, 2014a). The Abraham model comprises the following five terms for quantifying the logarithms of liquid–air (Eq. 7-10) and organic liquid–water (Eq. 7-11) partition constants (see Abraham et al., 2004): log Kil a = ll a Li + el a Ei + sl a Si + al a Ai + bl a Bi + c

(7-10)

log Kil w = vl w Vi + el w Ei + sl w Si + al w Ai + bl w Bi + c

(7-11)

As proposed by Goss (2005), a very similar approach can be used to describe partitioning between any bulk phase involving air, water, and organic liquids: log Ki12 = v12 Vi + l12 Li + s12 Si + a12 Ai + b12 Bi + c

(7-12)

The capital letters in Eqs. 7-10 to 7-12 are compound (solute) descriptors of i that are relevant for the partitioning process: the size of the compound (Vi ), parameters expressing the compound’s “vdW-stickiness” (the excess molar refraction (Ei ) or the log Kihexadecane–air (Li ), the latter also incorporating the size), H-donor (or electron acceptor) property (Ai ), H-acceptor (or electron donor) property (Bi ), and a “dipolarity/polarizability” parameter (Si ), which describes the ability of the compound to undergo polar interactions that are not covered by the other parameters. Often, these

Quantitative Approaches to Estimate Bulk Phase Partition Constants

229

solute descriptors are referred to as “Abraham parameters” or LSER parameters. Finally, we should point out that these descriptors describe only enthalpic aspects of partitioning with the exception of the Li term, which, as we have discussed earlier in Section 7.2, also contains an entropic contribution. The incorporation of entropic considerations is particularly important for systems where one of the phases is a gas, which is why Eq. 7-10 also uses L instead of V. The small letters in Eqs. 7-10 to 7-12 are the complementary system descriptors characterizing the bulk liquid phases involved. Hence, the first two terms in Eqs. 7-10 to 7-12 (vV, eE or lL) represent the differences between the two bulk phases with respect to the free energy contributions of cavity formation and of the vdW interactions upon introduction of the compound in the cavity. The other three terms (sS, aA, and bB) describe the differences of all polar interactions of the solute with the liquid phase molecules in the two phases. The system descriptors are derived from a multiple linear regression using known partition constants and solute descriptors of a large number (> 50) of chemicals. Because the obtained system descriptors hinge critically on the compounds used for calibration, the selected compounds should represent as wide a structural variability as possible with descriptors that are not cross-correlated. As we see throughout Parts II and III, this requirement is fortunately met for many published pp-LFERs of interest to us. Among the compound descriptors, some can be independently determined, while others cannot. The size parameter, Vi , can be calculated from the molecular structure (Box 7.2). For scaling reasons, the Vi term is expressed as the volume calculated by the McGowan method (Box 7.2) divided by 100. Nevertheless, we use the same notation, Vi . As for the vdW parameters, Li can be experimentally determined (e.g., Li et al., 2000; Stenzel et al., 2012), and Ei is related to the refractive index (Abraham et al., 1990). The other three polar parameters (Si , Ai , Bi ) cannot be independently determined but can be derived from partition constants measured in a number of well-defined air–solvent or water–solvent systems (e.g., Stenzel et al., 2013a) or from retention data in chromatographic systems using various stationary phases (e.g., Abraham et al., 2004; Poole et al., 2009; Stenzel et al., 2013b). The different solvents or stationary phases are chosen to exhibit characteristically different intermolecular interaction properties. An extensive review of this topic has been recently published by Poole et al. (2013). Currently, complete sets of compound descriptors are publicly available for about 3700 chemicals, compiled and publicly available on the UFZ-LSER database (Endo et al., 2014: http://www.ufz.de/index. php?en=31698&contentonly=1&lserd_data[mvc]=Public/start). As an illustration of the variety of descriptor values, Table 7.3 summarizes the compound descriptors for our companion compounds. More data can also be found in Appendix C. As we already pointed out in earlier discussions in Chapter 2 and in Section 7.2, inspection of Table 7.3, and of the much larger data set given in Appendix C, shows that compounds with one or more O or N atoms are strong H-acceptors, and, if they have a H-atom attached to these atoms, they are also strong H-donors. Furthermore, we note again that most monopolar compounds are H-acceptors (Ai = 0), a notable exception being CHCl3 . The dipolar/polarizability parameter Si assumes high values

230

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

Table 7.3 Solute Descriptors (Abraham parameters) for our Companion Compounds (see structures in Table 3.1)

Compound (i) Methyl bromide PCE MTBE Benzene Phenol Lindane Aniline n-Hexane TNT Atrazine D5 PCB 153 PBDE 99 Triclosan DDT Phenanthrene Benzo(a)pyrene

McGowan molar volume (cm3 mol–1 )/100 Vi

log Kihexadecane–air at 25◦ C Li

Excess molar Refraction Ei

0.42 0.84 0.87 0.72 0.78 1.58 0.82 0.95 1.38 1.62 2.93 2.06 2.26 1.87 2.22 1.45 1.95

1.63 3.58 2.38 2.79 3.77 7.57 3.93 2.67 7.27 7.78 5.24 9.59 11.71 8.96 10.02 7.58 11.47

0.37 0.64 0.02 0.61 0.81 1.45 0.96 0.00 1.57 1.22 –0.70 2.17

Dipolarity/ polarizability constant Si

H-donating parameter Ai

H-accepting parameter Bi

0.43 0.44 0.21 0.52 0.89 1.28 0.96 0.00 1.78 1.29 −0.10 1.74 1.51 1.81 1.76 1.25 1.82

0.00 0.00 0.00 0.00 0.60 0.00 0.26 0.00 0.11 0.17 0.00 0.00 0.00 0.92 0.00 0.00 0.00

0.10 0.00 0.59 0.14 0.30 0.50 0.41 0.00 0.48 1.01 0.50 0.11 0.44 0.30 0.16 0.24 0.31

1.85 1.81 1.94 3.63

(> 0.5) primarily for compounds exhibiting delocalized π-electron systems, in particular aromatic compounds. Also, the presence of chlorine, bromine, or nitro substituents leads to an increased Si value. We look further into these parameters in the following chapters, when we apply pp-LFERs to various partitioning processes. In most cases, we use Eq. 7-12, which yields comparable, and in some cases even better, results as Eqs. 7-10 and 7-11 (Goss, 2005; Endo and Goss, 2014b). Equation 7-12 has the advantage that only one equation has to be used for describing partitioning from both air and water. Also, even more importantly, Eq. 7-12 allows the direct application of the thermodynamic cycle (e.g. Eq. 7-1) to derive an equation for a two-phase system for which no or little experimental data is available. For example, a pp-LFER for organic phase–air partitioning can be derived from the corresponding pp-LFERs for organic phase–water and air–water partitioning respectively. We conclude this chapter with an illustrative application of a pp-LFER. We consider the octanol–water system for which the following two equations have been derived from experimental Kiow values of a large set of compounds representing a wide structural diversity (Goss, 2005): log Kiow = 2.41 Vi + 0.43 Li − 1.41 Si − 0.18 Ai − 3.45 Bi + 0.34 (number of chemicals = 314; r2 = 0.99; S.D. = 0.15)

(7-13)

and using Ei instead of Li (Eq. 7-11) yields: log Kiow = 3.88 Vi + 0.57 Ei − 1.06 Si − 0.05 Ai − 3.45 Bi + 0.03 (number of chemicals = 314; r2 = 0.99; S.D. = 0.15)

(7-14)

Quantitative Approaches to Estimate Bulk Phase Partition Constants

12

aliphatic amines

1: 1

predicted log Ki octanol–water (LwLo–1) Figure 7.4 Predicted (using Eq. 713) versus experimental Kiow values of our test set.

231

1-alkanols

10

alkanes

8

carboxylic acid esters

6

chlorobenzenes chlorinated phenols

4

fluorotelomers

2

ketones

0

polycyclic aromatic hydrocarbons polychlorinated biphenyls

–2 –4

siloxanes –4

–2

0

2

4

6

8

experimental log Ki octanol–water

10

12

(LwLo–1)

Comparison of the two equations shows that when using Ei instead of Li , the system descriptor for the Vi term has become more prominent, because it is the only term that describes the size of the molecule. In Eq. 7-13, the Li term represents cavity formation as well as dispersive vdW interactions. Furthermore, the H-bonding terms are virtually identical, which can be expected since substitution of Li by Ei has an influence only on how the dispersive vdW interactions are described. Finally, since Si and Ei are not completely unrelated, the relative magnitudes of the Si term in the two equations cannot be easily interpreted. In Fig. 7.4, the log Kiow values calculated from Eq. 7-13 for the set of compounds already used in Figs. 7.2 and 7.3 are plotted against their experimental log Kiow values. As is evident, compared to sp-LFERs, this conceptually simple pp-LFER is a powerful tool to predict octanol–water partition constants of a very diverse set of apolar, monopolar, and bipolar compounds. A comparable result is obtained when using Eq. 7-14 instead of Eq. 7-13 (data not shown). Predictions within a factor of 2 to 3 (0.3 to 0.5 log units) are possible (see examples in Table 7.4). Eq. 7-13 also allows us to evaluate, at least semi-quantitatively, the relative contributions of the various free energy terms to the overall free energy of partitioning. In this case, we consider partitioning between two liquid phases, and the coefficients (system descriptors) in Eq. 7-13 represent the differences in the free energy terms between the two solvents, that is, the difference in cavity formation energies and the differences in free energy gains when introducing the organic molecule in the cavity, as expressed in Eq. 7-4. Inspection of Eq. 7-13 and Table 7.4 shows that the first two terms favor partitioning into octanol, a finding attributable primarily to the hydrophobic effect (see

232

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

Table 7.4 Contribution of the Different Terms in Eq. 7-13 to the Overall Octanol–Water Partition Constant of Some Selected Compounds a Compound MTBE Benzene n-Hexane Atrazine 8:2 FTOH D5 PCB 153 PBDE 99 Triclosan Benzo(a)pyrene a

log Kiow exp.

log Kiow calc.

+2.41 Vi

+0.43 Li

–1.41 Si

–0.18 Ai

–3.45 Bi

+0.34

0.94 2.17 4.00 2.65 5.58 8.08 6.75 7.32 4.78 6.05

1.13 2.06 3.78 2.26 5.80 8.07 6.60 7.17 4.95 6.34

+2.10 +1.74 +2.29 +3.90 +5.35 +7.06 +4.96 +5.45 +4.51 +4.70

+1.02 +1.20 +1.15 +3.35 +1.49 +2.25 +4.12 +5.04 +3.85 +4.93

–0.30 –0.73 0.00 –1.82 –0.20 +0.14 –2.45 –2.13 –2.55 –2.57

0.00 0.00 0.00 –0.03 –0.11 0.00 0.00 0.00 –0.17 0.00

–2.04 –0.48 0.00 –3.48 –1.07 –1.73 –0.38 –1.52 –1.04 –1.07

+0.34 +0.34 +0.34 +0.34 +0.34 +0.34 +0.34 +0.34 +0.34 +0.34

The solute parameters of the compounds are given in Table 7.3.

Chapter 10). In particular, the volume term (vVi ) reflects the large difference in cohesion energies between octanol and water. Since Si , Ai , and Bi are all zero or positive (exception: the Si values of the siloxanes are slightly negative), the three “polar” terms are either not relevant or favor the aqueous phase. A striking feature of Eq. 7-13 is that the coefficients (system descriptors) of the terms describing H-bonding are very different (–0.18 versus –3.45). This distinction indicates that, relative to octanol, the H-donor properties of water are much more important than its H-acceptor properties when partitioning an organic molecule between these two liquids. Hence, the polar terms (sS, aA, and bB) are particularly important for compounds exhibiting high Si and/or Bi values. For example, when comparing the various terms for the three gasoline components MTBE, benzene, and n-hexane, we can see that they exhibit very similar size and vdW terms (vV and lL), but differ significantly in the polar terms. As a result, the Kiow of MTBE is three orders of magnitude smaller than that of n-hexane, which is primarily due to the strong H-accepting properties of MTBE. The two orders of magnitude smaller Kiow of benzene as compared to n-hexane is a result of benzene’s moderate polarizability/dipolarity and weak hydrogen accepting properties. A somewhat unexpected finding is that that the herbicide atrazine, and other triazines, have strong H-accepting properties but low H-donating properties, although they contain two N-H groups (Abraham et al., 2007).

7.4

Questions Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Q 7.1 What are the prerequisites for a proper application of the thermodynamic cycle to calculate a partition constant from two other partition constants, such as, for example, the octanol–air partition constant from the octanol–water and air–water partition

Questions

233

constants? Can you think of an example where the thermodynamic cycle may not be applied at all? Q 7.2 What is the difference between a partition constant, a partition coefficient, and a distribution ratio? Q 7.3 Explain the different free energy terms considered when applying the simple cavity model to describe (a) bulk liquid–air partitioning, and (b) partitioning between two bulk liquids. Which thermodynamics entities do you always have to keep in mind when talking about free energy contributions? Q 7.4 Estimate the molar volumes in cm3 mol–1 of the following companion compounds using the McGowan method described in Box 7.2: methyl-t-butyl ether (MTBE), γHCH (lindane), atrazine, decamethlycyclopentasiloxane (D5), and phenanthrene. Q 7.5 Assign the following equilibrium solvent-air partitioning processes of the following compounds to the appropriate case (cases I to IV) defined when discussing Eq. 7-3.

(a) (b) (c) (d) (e) (f) (g) (h) (i) (j)

solvent

solute

dichloromethane tetrachloroethene diethyl ether octanol ethanol toluene hexane chloroform ethyl acetate water

methyl-t-butyl ether perfluorooctylethanol (8:2 FTOH) 17α-ethinylestradiol PCB 153 atrazine PBDE 99 triclosan 4-nonylphenol phenanthrene n-decane

Q 7.6 Explain the following observations made when inspecting Fig. 7.2: (a) The organic solvent–air partition constants increase with size of the compound (Figs. 7.2a and b), whereas for the water–air partition constants (Fig. 7.2c) a much smaller, and in some cases even negative, trend is observed. (b) The organic solvent–air partition constants of the fluorotelomer alcohols and of the siloxanes increase much less with size as compared to all other compound classes (Figs. 7.2a and b).

234

Partitioning Between Bulk Phases: General Aspects and Modeling Approaches

(c) The difference between the hexadecane–air partition constants (Fig. 7.2a) of a homologues series of alkanes and the corresponding 1-alkanols is rather small, whereas for the octanol–air partition constants (Fig. 7.2b), this difference is more than two orders of magnitude. (d) The octanol–air partition constants of the 1-alkanols are more than two orders of magnitude larger than those of the n-alkanes (Fig. 7.2b), exactly the opposite is true for the octanol–water partition constants (Fig. 7.2d). Q 7.7 What is the basic concept of a linear free-energy relationships (LFERs) for estimating partition constants? What are the main differences between the fragment contribution method, single-parameter LFER, and poly-parameter LFER? List advantages and disadvantages of each of these three approaches. Q 7.8 Discuss the role of the compound descriptors used in the pp-LFERs Eqs. 7-10 to 7-12, and given for the companion compounds in Table 7.3. Which ones can be determined independently and which have to be derived experimentally? Q 7.9 How are the system parameters (small letters in Eqs. 7-10 to 7-12) determined for a given system? What determines the applicability range of a thus derived pp-LFER?

7.5

Bibliography Abraham, M. H., Scales of solute hydrogen-bonding: Their construction and application to physicochemical and biochemical processes Chem. Soc. Rev. 1993, 22(2), 73–83. Abraham, M. H.; Enomoto, K.; Clarke, E. D.; Roses, M.; Rafols, C.; Fuguet, E., Henry’s Law constants or air to water partition coefficients for 1,3,5-triazines by an LFER method. J. Environ. Monit. 2007, 9(3), 234–239. Abraham, M. H.; Ibrahim, A.; Zissimos, A. M., Determination of sets of solute descriptors from chromatographic measurements. J. Chromatogr. A 2004, 1037(1-2), 29–47. Abraham, M. H.; McGowan, J. C., The use of characteristic volumes to measure cavity terms in reversed phase lquid chromatography. Chromatographia 1987, 23(4), 243–246. Abraham, M. H.; Whiting, G. S.; Doherty, R. M.; Shuely, W. J., Hydrogen bonding. Part 13. A new method for the characterization of GLC stationary phases-The Laffort data set. J. Chem. Soc.-Perkin Trans. 2 1990, (8), 1451–1460. Endo, S.; Goss, K. U., Applications of polyparameter linear free energy relationships in environmental chemistry. Environ. Sci. Technol. 2014a, 48(21), 12477–12491. Endo, S.; Goss, K. U., Predicting Partition Coefficients of Polyfluorinated and Organosilicon Compounds using Polyparameter Linear Free Energy Relationships (PP-LFERs). Environ. Sci. Technol. 2014b, 48(5), 2776–2784. Endo, S.; Watanabe, N.; Ulrich, N.; Bronner, G.; Goss, K. U., UFZ-LSER database v 2.1 [Internet]. Helmholtz Centre for Environmental Research-UFZ: Leipzig, Germany, 2014

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Taft, R. W.; Abraham, M. H.; Famini, G. R.; Doherty, R. M.; Abboud, J. L. M.; Kamlet, M. J., Solubility properties in polymers and biological media. 5. An anaylsis of the physicochemical properties which influence octanol-water partition coefficients of aliphatic and aromatic solutes. J. Pharm. Sci. 1985, 74(8), 807–814. U.S. EPA, Estimation Programs Interface SuiteTM for Microsoft® Windows, v 4.11. United States Environmental Protection Agency: Washington, D.C., 2012. http://www.epa.gov/ opptintr/exposure/pubs/episuite.htm. Yalkowsky, S. H.; Banerjee, S., Aqueous Solubility: Methods of Estimation for Organic Compounds. Marcel Dekker: New York, 1992; p 304.

237

Chapter 8

Vapor Pressure ( pi∗) 8.1

Introduction and Theoretical Background Aggregate State and Phase Diagram: Normal Melting Point (Tm ), Normal Boiling Point (Tb ), and Critical Points (Tc , p∗ic ) Thermodynamic Description of the Vapor Pressure–Temperature Relationship

8.2

Molecular Interactions Governing Vapor Pressure and Vapor Pressure Estimation Methods Enthalpy and Entropy Contributions to the Free Energy of Vaporization: Trouton’s Rule of Constant Entropy at the Boiling Point A pp-LFER Approach for Estimating the Liquid Vapor Pressure Entropy of Fusion and Vapor Pressure of Solids Box 8.1 Parameters Used to Estimate Entropies of Phase Change Processes

8.3

Questions and Problems

8.4

Bibliography

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

238

Vapor Pressure ( pi∗ )

8.1

Introduction and Theoretical Background The quantitative description of how much a compound likes or dislikes being in the gas phase as compared to other relevant condensed phases is an important aspect of our discussion about the partitioning of organic compounds in the environment. We have already addressed such favoring of phases very generally in Chapter 7. In this chapter, we focus on a special case, the equilibrium partitioning of an organic compound between the gas phase and the pure compound itself. In contrast to Chapter 7, we do not consider the compound in a dilute solution but at the maximum concentration possible in both the air (i.e., at saturation) and condensed phase. In this particular case, the gas–pure liquid or gas–pure solid partition constant of i is commonly expressed not in molar concentrations but as the ratio of the equilibrium partial pressure in the gas phase, p∗i , to the mole fraction, xi , in the pure condensed phase. By definition, the mole fraction of a pure substance in the condensed phase is equal to one (xi = 1). Therefore, p∗i is commonly referred to as the gas phase saturation (indicated by the superscript “∗”) vapor pressure of a compound. It denotes the maximum possible partial pressure or concentration of a compound in the gas phase at a given temperature. Importantly, this vapor pressure provides direct quantitative information on the attractive forces among the compound’s molecules in its liquid or solid phase. Having such an insight into molecule-molecule interactions in the pure phase allows us to recognize how the chemical’s structure controls its fugacity and, therefore, to anticipate how placing the compound in different media affects such fugacity. This insight is main reason why the pure liquid phase is often used as reference state for the thermodynamic treatment of partitioning processes (see Section 4.1). Finally, we should note that the vapor pressure not only describes equilibrium partitioning between the gas phase and a condensed phase but also helps quantify the rate of evaporation of a compound from its pure phase or a mixture. By simple observation, we know that at ambient temperatures (e.g., 25◦ C) and pressures (e.g., 1 bar), some organic chemicals in their pure form are present as gases, some as liquids, and others as solids. We should recall that when we talk about a pure chemical, we mean that only molecules of that particular compound are present in the phase considered. Hence, in a pure gas, the partial pressure of the compound is equal to the total pressure. As already addressed in Chapter 4, a pure compound will be a liquid or a solid at ambient conditions if the forces between the molecules in the condensed phase are strong enough to overcome the tendency of the molecules to “fly” apart. In other words, if the enthalpy terms (which reflect the “glue” among the molecules in the liquid) outweigh the entropy terms (which are measures of “freedom” gained when going from the liquid phase to the gas phase), then the free energy term is positive, and the material will exist as a liquid or solid. Conversely, if this free energy term is negative, then the compound is a gas at the given conditions. This variation in phase is illustrated by the series of n-alkanes, where the C1 – to C4 –compounds are gases (p∗i > 1 bar), the C5 – to C17 –compounds are liquids, and the compounds with more than 18 carbon atoms are solids at 25◦ C and 1 bar total pressure (Fig. 8.1) This series of hydrocarbons exhibits a vapor pressure range of more than fifteen orders of magnitude ranging from 40.7 bar or 4.07×106 Pa (C2 H6 ) down to about 10−14 bar or 10−9 Pa (n-C30 H62 ). For methane, no vapor pressure is defined at 25◦ C because

Introduction and Theoretical Background

su liq perh uid ea

log pi* (bar)

0

Figure 8.1 Vapor pressure at 25 C of n-alkanes as a function of chain length. The subcooled liquid vapor pressures have been calculated by extrapolation of p∗iL values determined above the melting point (Eq. 8-7). Data from Daubert (1997) and Lide (1995).

ted

pi* = 1 bar

liq uid

C5H12

–5

su

bc liq oole uid d

C10H22

–10

◦

C20H42

–15

n-alkanes (CnH2n+2) 0

5

239

10 15 20 number of carbons

so

lid 25

30

methane cannot exist in a defined condensed form at this temperature, even at a very high pressure (see subsequent discussion). Aggregate State and Phase Diagram: Normal Melting Point (Tm ), Normal Boiling Point (Tb ), and Critical Points (Tc , p∗ic ) According to the Gibbs phase rule (number of degrees of freedom = number of chemical components – number of phases + 2; see Atkins, 2014), a system containing a single chemical distributed between two phases at equilibrium has only one degree of freedom. Therefore, by choosing a temperature of interest (i.e., defining the one degree of freedom), all other phase parameters are fixed, including the vapor pressure of the compound in the gas phase. This dependence of vapor pressure on temperature can be shown in a pressure–temperature plot (Fig. 8.2). Such a “phase diagram” allows us to assess the aggregate state (i.e., solid, liquid, gas, supercritical fluid) of the compound under various combinations of temperature and pressure. The diagram also depicts important single temperature/pressure points for the chemical of interest. Let us look at this phase diagram more closely by using four n-alkanes (Table 8.1) as illustrative examples. The points Tm , Tb , and Tc already have a subscript denoting that they are compound-specific parameters, so we omit the subscript i. First, we inspect the normal melting points (Tm ) of the compounds. Tm is the temperature at which the solid and the liquid phase are in equilibrium at 1.013 bar (= 1 atm) total external pressure. At 1 bar total pressure, we would refer to Tm as the standard melting point. As a simplification, we assume that small changes in pressure do not have a significant impact on the melting point. We also assume that Tm is equal to the triple point temperature (Tt ). This triple point temperature occurs at only one set of pressure/temperature conditions under which the solid, liquid, and gas phase of a pure substance all simultaneously coexist in equilibrium. Among our n-alkanes in Table 8.1, only n-eicosane has a Tm value that is above 25◦ C, so it is the only alkane in this group that is a solid at room temperature. The other

240

Vapor Pressure ( pi∗ )

supercritical fluid

critical point

pic* (T4)

super d e t a e h liquid

piL* (T3)

Figure 8.2 Simplified phase diagram of a pure organic chemical. The boundary between the solid and liquid phase has been drawn assuming the chemical’s melting point (Tm ) equals its triple point (Tt ), the temperature–pressure condition where all three phases coexist. In reality, Tm is a little higher than Tt for some compounds and a little lower for others.

liquid (L) e

solid (s) piL* (T2)

ur

pressure p

1.013 bar

oole subc id liqu

d

so

pis* (T1)

lid

piL* (T1)

li q

uid

va

po

r rp

es

s

gas (g)

T1 Tt ≈ Tm

Tb T3 Tc T4

T2 temperature T

three compounds have much lower melting points, which means that, in these cases, we would have to lower the temperature at least to –29.7, –138.4, and –182.5◦ C in order to “freeze” n-decane, n-butane, and methane, respectively. Let us now perform a little experiment with n-eicosane. We place pure (solid) neicosane in an open vessel (Fig. 8.3a) and in a closed vessel (Fig. 8.3b) at 25◦ C. In the open vessel, we have an ambient total pressure of 1 atm or 1.013 bar, exerted mostly by the nitrogen and oxygen molecules in the air. In contrast, in the closed vessel, we start out with a vacuum, that is, we allow no molecules other than eicosane in this Table 8.1 Normal Melting Points (Tm ), Normal Boiling Points (Tb ), and Critical Points (Tc , p∗ic ) of some n-Alkanesa

Compound

Tm (◦ C)

Tb (◦ C)

Tc (◦ C)

Methane (CH4 ) −182.5 −164.0 −82.6 −138.4 −0.5 152.0 n-Butane (C4 H10 ) n-Decane (C10 H22 ) −29.7 174.1 344.5 36.8 343.0 496.0 n-Eicosane (C20 H42 ) a

Data from Lide (1995).

p∗ic (bar) 46.04 37.84 21.04 11.60

Location of Ambient Temperature (i.e., 25◦ C) in Fig. 8.2

Aggregate State at 25◦ C

T4 T3 T2 T1

gas gas liquid solid

Introduction and Theoretical Background

vapor

ptot = 1.013 bar (a)

solid or liquid

vapor

ptot = pi* (b)

solid or liquid

Figure 8.3 Open (a) and closed (b) vessel containing a pure condensed phase and a vapor phase. In case (a), the total pressure (1 bar) is exerted by the compound’s molecules and by other gaseous species (e.g., O2 , N2 ), which do not significantly alter the composition of the condensed phase. In case (b), the total pressure is equal to the vapor pressure of the compound; that is, no other gaseous species are present.

241

vessel. Now we wait until equilibrium between the solid and vapor phase is reached, and then we measure the partial pressure of n-eicosane in the gas phase in each vessel. In the closed vessel, the total pressure will be equal to the vapor pressure, p∗is , of solid eicosane, about 10−8 bar or 10−3 Pa. In our phase diagram in Fig. 8.2, the point on the bold line at T1 represents this pressure/temperature point. Now the question is: what is the partial pressure of eicosane in the gas phase in equilibrium with the solid phase in the open vessel? Is it also equal to p∗is ? The answer is yes because, particularly in the case of a solid compound, for pressures less than about 10 bar, the total system pressure has small influence on p∗is . In general, at pressures near 1 bar we can assume that the difference in the partial pressures between the situations depicted in Figs. 8.3a and b would be less than 0.5% for most organic compounds (Atkins, 2014). However, in the open vessel, the compound would vanish because molecules could continuously leave the vessel and, thus, would have to be replenished from the condensed phase to keep a constant vapor pressure. Returning to our experiment, if we now increase the temperature, we observe that p∗is of n-eicosane increases. In our phase diagram, we move the solid line from T1 towards Tm . At Tm , the compound melts and becomes a liquid. Above Tm , a further increase in temperature leads, of course, to an increasing vapor pressure, which we now denote as p∗iL , as we are dealing with the vapor pressure of a liquid (L) compound (e.g., pressure/temperature point at T2 in Fig. 8.2). We continue to raise the temperature until p∗iL reaches 1 atm (1.013 bar), which equals the total external pressure in the open vessel. Now we have very different situations in the vessels: in the open vessel, the compound boils, whereas in vessel 2, boiling cannot occur, as there is no means of escape for the molecules. The temperature, Tb , at which p∗iL is 1 atm is referred to as the normal boiling point temperature (or standard boiling point temperature, if p∗iL is 1 bar). Historically, the standard pressure has been taken to be 1 atm (1.013 bar), which means that many Tb values are still reported as normal boiling points, which are somewhat higher than the standard boiling points. However, for practical purposes, we neglect these small differences and just refer to the boiling point, Tb . The boiling point of n-eicosane is 343◦ C (Table 8.1). We should recall that boiling means that in an open system, vaporization can occur throughout the bulk of the liquid, and the vapor can expand freely into the surroundings. Therefore, in contrast to the melting point, the boiling point of a compound depends strongly on the external pressure. A well-known example is the change in the boiling point of pure water at various pressures. At 1.013 bar, the Tb is 100◦ C, while at lower pressures, pure water boils at lower temperatures. At the summit of Mount Everest (0.357 bar external pressure), the Tb decreases to 73◦ C, making cooking pasta rather tedious. At temperatures above the boiling point (e.g., T3 ) and an external pressure of 1.013 bar, a compound exists only in the gas phase. A limited number of organic chemicals are gases at ambient temperatures. Examples are n-butane and methane, which have boiling points of –0.5 and –164◦ C respectively (Table 8.1). Other examples include some of the halogenated methanes, such as the companion compound methyl bromide (CH3 Br) and some freons (e.g., CCl2 F2 and CClF3 ). In the closed vessel (Fig. 8.3b), increasing the temperature to above the boiling point creates a situation where we have a vapor pressure, p∗iL , of greater than 1.013 bar,

242

Vapor Pressure ( pi∗ )

which cannot occur in the open vessel. We take advantage of this situation in autoclaves and pressure cookers, which use elevated water temperatures to kill bacteria and cook food quickly. In such a case, we still have both a liquid and a gas phase (e.g., pressure/temperature point on bold broken line at T3 in Fig. 8.2), and the liquid phase is referred to as a “superheated” liquid. Therefore, for compounds existing as gases at ambient temperature, we have to increase their partial pressure in the gas phase until we reach the vapor pressure of the superheated liquid to store them as liquids, for example, in a pressure bottle. For n-butane, often used as fuel for barbecues, this pressure is 2.5 bar, and for CCl2 F2 , a freon used as a propellant and foaming agent, the corresponding p∗iL value is 5.6 bar at 25◦ C. Returning to our experiment with n-eicosane in the closed vessel, if we continue to raise the temperature, more and more molecules build up in the gas phase (increasing the gas density), while the density of the liquid continuously decreases. Finally, we reach a point where the density of the vapor is equal to that of the remaining liquid, meaning that we do not have two distinguishable phases anymore. This pressure/temperature point is called the critical point of the compound (Tc , p∗ic , see Fig. 8.2). For n-eicosane, the Tc and p∗ic values are 496◦ C and 11.6 bar. Above these values, the compound exists only as one phase, which is commonly referred to as a“supercritical fluid.” Methane has a critical temperature of –82.6◦ C (Table 8.1). Hence, liquid methane will exist only below this temperature, making condensing it to a liquid at ambient temperatures impossible. In our phase diagram, this means that methane belongs to those few chemicals for which the ambient temperature is above Tc (e.g., T4 in Fig. 8.2). Other prominent examples of such chemicals are O2 (Tc = –118.6◦ C) and N2 (Tc = –147◦ C). Before we turn to a quantitative description of the dependence of vapor pressure on temperature, we need to define one important additional vapor pressure value: the subcooled liquid vapor pressure of a compound. Imagine what occurs if we cool liquid eicosane from an elevated temperature (e.g., T2 in Fig. 8.2) to a temperature below its melting (or freezing) point (e.g., T1 in Fig. 8.2). Above the melting point (Tm = 36.8◦ C), we observe a decrease in p∗iL according to the solid line describing the liquid– gas boundary. Below the melting point, we follow a different solid line now describing the solid–gas boundary until we reach p∗is (T1 ). We note that, below the melting point, the decrease in vapor pressure with decreasing temperature is steeper than in the region above the melting point, where the compound is a liquid. This increase in slope is because the energy required to transfer molecules from the solid to the gas phase is higher than transferring them from the liquid to the gas phase. Hence, if we continued to move along the liquid–gas boundary below the melting point (dashed line in Fig. 8.2), at T1 , we would reach another vapor pressure value, p∗iL , which is larger than the corresponding p∗is of the solid compound (examples in Fig. 8.1). This p∗iL value, which is referred to as the vapor pressure of the subcooled liquid, is an important entity, because it tells us something about the molecular interactions of the compound in its pure liquid form at a temperature where the compound is actually a solid. Knowledge of the properties of the subcooled liquid compound helps us understand and quantify the molecular interactions in environments in which molecules exist in a liquid state (e.g., dissolved in water), although they would be solids if pure. Our interest in situations where organic compounds are dissolved in solvents like water is a major reason

Introduction and Theoretical Background

243

why we have chosen the pure liquid compound as the reference state for describing partitioning processes. Thermodynamic Description of the Vapor Pressure–Temperature Relationship In Chapter 4, we have seen that the bulk phase equilibrium partition constant expressed on a mole fraction basis is related to the free energy of transfer by (Eqs. 4-23 to 4-25): ln Ki12 = ln(xi1 ∕xi2 ) = −Δ12 Gi ∕RT

(8-1)

/ By expressing xi1 by the equilibrium the partial pressure p∗i p0i (p0i =1 bar, standard pressure) and by setting xi2 = 1 (pure organic phase), we then obtain: ln (p∗i ∕1bar) = −Δ12 Gi ∕RT

(8-2)

For liquid (subscript “L”)-vapor equilibrium, the free energy of transfer is commonly referred to as free energy of vaporization (subscript “vap”), while for solid (suscript “s”)-vapor equilibrium, it is called the free energy of sublimation (subscript “sub”). Hence, Eq. 8-2 is simplified for liquid vapor pressure to: ln p∗iL = −Δvap Gi ∕RT

(8-3)

ln p∗is = −Δsub Gi ∕RT

(8-4)

and for solid vapor pressure:

Let us first consider the liquid vapor pressure both below and above the boiling point (Fig. 8.2). From Eq. 8-3, we can see that Δvap Gi will be positive at temperatures at which the vapor pressure is smaller than the standard pressure (i.e., 1 bar), which is, of course, the case at temperatures below the boiling point. At the boiling point, p∗iL = 1 bar, and, therefore, − RT ln 1 = 0 = Δvap Gi (Tb ) = Δvap Hi (Tb ) − Tb Δvap Si (Tb )

(8-5a)

Tb Δvap Si (Tb ) = Δvap Hi (Tb )

(8-5b)

or

Hence, at the boiling point, the compound’s molecules in the liquid state can “fly apart” because their gain in entropy upon vaporizing now matches the enthalpic attractions that are trying to hold them together. Above the boiling point, Δvap Gi will be negative (because TΔvap Si > Δvap Hi ). That is, pressures greater than 1 bar must be applied to keep a liquid phase present. As for any equilibrium partition constant, the temperature dependence of p∗iL can be described by the van’t Hoff equation (Eq. 4-33): d ln p∗iL dT

=

Δvap Hi (T) RT 2

(8-6)

244

Vapor Pressure ( pi∗ )

This equation is commonly referred to as the Clausius-Clapeyron equation. Δvap Hi is zero at the critical point, Tc . It rises rapidly at temperatures approaching the boiling point, then it rises more slowly at lower temperatures (Poling et al., 2001). Therefore, we can integrate Eq. 8.6 with the assumption that Δvap Hi is constant over the temperature range of interest (e.g., over the ambient temperature range from 0◦ C to 30◦ C). Over this narrow temperature range, we can then express the temperature dependence of p∗iL by: ln p∗iL = −

A +B T

(8-7)

where A = Δvap Hi ∕R. For liquids, plotting the observed log p∗iL (=ln p∗iL ∕2.303) versus 1/T (K) over the ambient temperature range yields practically linear relations (Fig. 8.4), as expected from Eq. 8-7. Therefore, by calculating A and B over narrow temperature ranges with known vapor pressure data, Eq. 8-7 can be used to calculate vapor pressures at any other temperature provided that the aggregate state of the compound does not change within the temperature range considered. If the temperature range is extended, the fit of experimental data may be improved by introducing a third parameter, C, in Eq. 8-7 to reflect the temperature dependence of Δvap Hi . The constant C captures the effect of changing enthalpy of vaporization over larger temperature ranges: ln p∗iL = −

A +B T +C

(8-8)

Equation 8-8 is known as the Antoine equation and has been widely used to regress experimental data. Values for A, B, and C are available for many compounds (e.g., Haynes, 2014 and Daubert, 1997). When using Eqs. 8-7 and 8-8 to extrapolate vapor pressure data below the melting point, one gets an estimate of the vapor pressure of the subcooled liquid compound at that temperature (e.g., naphthalene in Fig. 8.4). For the solid vapor pressure, p∗is , we can just substitute Δvap Hi by Δsub Hi in Eqs. 8-6 to 8-8 (i.e., A = Δsub Hi ∕R). The difference between the free energy of sublimation and the free energy of vaporization is referred to as the free energy of fusion (from the Latin, fundere meaning to melt). In other words, the energy required to convert molecules from their solid state directly to their vapor state is the same as the energy required to first melt the solid and then to vaporize them from their liquid state, even though sublimation does not involve ever having the liquid state exist. One can, therefore, obtain the free energy of fusion (melting) by rearranging then subtracting Eq. 8-3 from 8-4: Δfus Gi = Δsub Gi − Δvap Gi = RT ln

p∗iL p∗is

(8-9)

In terms of enthalpy and entropy, this means: Δfus Hi = Δsub Hi − Δvap Hi

(8-10)

Introduction and Theoretical Background

245

T (°C) 160

120

1

80

60

(sup

0 –1

40 30 20 10

erhe

ated

liqui

H 3C

d)

(liqu

(liq

)

Tm

(su

–3

id)

bco

Cl

Cl

Cl

Cl

(liquid)

ole

Cl

d li

qui

O

log pi* (bar)

Br

(liquid) uid

–2

0

Cl

d)

(liquid)

O

–4

O O

–5

(s

(liquid)

ol

id

)

–6 –7

A log pi* = – +B 2.303 T

Cl

Cl

Cl

Cl Cl

(solid)

–8 –9

(solid)

–10

Figure 8.4 Effect of temperature on vapor pressure for some organic compounds. The decadic logarithm is used, thus the factor 1/2.303 (ln p∗i = 2.303 log p∗i ).

2.5×10 –3

3.0×10 –3

3.5×10 –3

1/T (K–1)

and: Δfus Si = Δsub Si − Δvap Si

(8-11)

The thermodynamic expressions Eqs. 8-10 and 8-11 state that the intermolecular attraction forces that must be overcome to sublime the molecules of a substance are equal to the sum of the forces required to first melt and then vaporize them. Likewise, the increased randomness obtained as molecules sublime is the same as the sum of entropies associated with the sequence of melting and vaporizing. Consequently, if we can predict such thermodynamic terms for vaporization or melting, we already know the corresponding parameters for sublimation, and vice versa.

246

Vapor Pressure ( pi∗ )

Knowledge of Δfus Gi at a given temperature is useful for estimating other properties of the subcooled liquid compound, in particular, its subcooled liquid aqueous solubility (Chapter 9). As can be qualitatively seen from Fig. 8.2, Δfus Gi decreases with increasing temperature (the solid and subcooled liquid vapor pressure lines approach each other when moving towards the melting point). At the melting point, Tm , Δfus Gi becomes zero, and, by analogy to the situation at the boiling point (Eq. 8-5), we can write: Tm Δfus Si (Tm ) = Δfus Hi (Tm )

8.2

(8-12)

Molecular Interactions Governing Vapor Pressure and Vapor Pressure Estimation Methods Enthalpy and Entropy Contributions to the Free Energy of Vaporization: Trouton’s Rule of Constant Entropy at the Boiling Point We now focus on the relation between chemical structure and vapor pressure. In Fig. 8.5, the enthalpy and entropy of vaporization at 25◦ C are plotted against the free energy of vaporization for a wide variety of apolar, monopolar, and bipolar compounds. In general, we see that the enthalpic contribution is larger than the entropic one, but also that these contributions are related. We can rationalize these findings by recalling that the entropy of vaporization reflects the difference of a molecule’s freedom in the gas phase minus that in the liquid phase (Δvap Si = Sig – SiL ). At ambient pressures, the freedom of the molecules in the gas phase is generally not that different between compounds. Therefore, we may assume that differences in Δvap Si between different compounds are primarily due to differences in molecular freedom in the liquid phase. Hence, molecules that exhibit stronger intermolecular attractions (greater Δvap Hi values) have lower values of SiL , causing higher values of Δvap Si .

Figure 8.5 Plot of Δvap Hi and TΔvap Si versus Δvap Gi for a wide variety of organic compounds at 25◦ C. At the intercept (Δvap Gi = 0) the value for Δvap Hi (= TΔvap Si ) obtained from a linear regression analysis is 25.8 kJ mol−1 .

TΔvapSi

ΔvapHi

(kJ mol–1)

140 120

ΔvapHi

100 80 60 40

TΔvapSi

20 0

0

20

40

60

ΔvapGi (kJ mol ) –1

80

Molecular Interactions Governing Vapor Pressure

247

ΔvapHi (kJ mol–1)

150

Figure 8.6 Plot of Δvap Hi versus ln p∗iL for a large number of apolar, monopolar, and bipolar compounds (some bipolar outliers not included). Data from Goss and Schwarzenbach (1999).

100

50

0 –25 –20 –15 –10

–5

0

5

10

15

ln piL* (Pa)

The fact that the enthalpy and entropy terms correlate also means that Δvap Gi is proportional to Δvap Hi . We can, therefore, derive an extremely useful empirical relationship between Δvap Hi and log p∗iL (= –Δvap Gi /2.303RT; Eq. 8-3) for a given temperature, T, which allows one to estimate Δvap Hi : Δvap Hi (T) = −a log p∗iL (T) + b

(8-13)

At 25◦ C (298 K), the linear regression derived for the experimental data set of organic compounds shown in Fig. 8.6 is (Goss and Schwarzenbach, 1999): Δvap Hi (kJ mol−1 ) = −8.79(±0.07) log p∗iL (Pa) + 70.0( ± 0.2)

(8-14)

As confirmed by MacLeod et al. (2007), Eq. 8-14 holds for a very large vapor pressure range (>15 orders of magnitude), particularly, for apolar and monopolar compounds. Importantly, Eq. 8-14 applies only to the vapor pressure of the liquid compound. For solids, the difference between p∗is and p∗iL can be estimated using the melting point temperature of the compound (see Eqs. 8-21 and 8-22). Looking back at Fig. 8.5, the Δvap Hi intercept where Δvap Gi = 0 is an interesting point; it represents a compound with a boiling point Tb = 25◦ C. The corresponding Δvap Hi is 25.8 kJ mol−1 , from which the compound’s entropy of vaporization at Tb can be calculated (Eq. 8-5): Δvap Si (Tb ) =

Δvap Hi (Tb ) Tb

=

25.8 kJ mol−1 = 86.6 J mol−1 K−1 298 K

248

Vapor Pressure ( pi∗ )

This Δvap Si (Tb ) value is typical for many organic compounds that boil at very different temperatures. A long time ago, Trouton (1884) recognized that the entropy of vaporization at the boiling point for many apolar and monopolar substances is between 85 and 90 J mol−1 K−1 . This “constancy” of Δvap Si (Tb ) implies a close relationship exists between Δvap Hi (Tb ) and Tb . Kistiakowsky (1923) utilized the Clapeyron equation and the ideal gas law to derive an expression to estimate individual Δvap Si (Tb ) in which the chemical’s boiling temperature is used: Δvap Si (Tb ) = (36.6 + 8.31 ln Tb ) J mol−1 K−1

(8-15)

This expression reflects a weak relationship between the apolar or monopolar compound boiling temperature and entropy of vaporization, but substantially verifies Trouton’s empirical observation. For bipolar organic liquids, especially for H-bonding liquids such as alcohols and amines, the tendency to orient in the liquid phase is greatly increased by these highly directional intermolecular attractions. The effect is reflected in the significantly larger entropies of vaporization (between 90 and 110 J mol−1 K−1 ) of bipolar chemicals like amines and alcohols. Fishtine (1963) provided a set of empirical factors, KF , which correct the Kistiakowsky estimation for such polar interactions: Δvap Si (Tb ) = KF (36.6 + 8.31 ln Tb ) J mol−1 K−1

(8-16)

KF values are equal to 1.0 for apolar and many monopolar compounds. For compounds exhibiting a weakly bipolar character (e.g., esters, ketones, nitriles), a modest correction with a KF of about 1.04 can be made. Significant corrections are necessary for primary amines (KF = 1.1), phenols (KF = 1.15), and aliphatic alcohols (KF = 1.3). For a more comprehensive compilation of KF values, we refer to the literature (e.g., Sage and Sage, 2000). Using Eq. 8-16, and making some assumptions on the temperature dependence of Δvap Hi , Mackay et al. (1982) employed an equation to estimate the liquid vapor pressure of a compound at the temperature T solely from its boiling point: [ ( ) ] Tb Tb ∗ log piL (T)(bar) ≅ −(1∕2.303) KF (4.4 + ln Tb ) 1.8 − 1 − 0.8 ln T T (8-17) Equation 8-17 is particularly useful for prediction of vapor pressures of relatively low boiling compounds (i.e., Tb < 300◦ C). A pp-LFER Approach for Estimating the Liquid Vapor Pressure Another strategy for estimating liquid vapor pressure utilizes a pp-LFER and the compound descriptors introduced in Eqs. 7-10 to 7-12. Since in the pure liquid only identical molecules are present, we can write an equation (Eq. 8-18) in which we express the size as well as the vdW London dispersive, and the Debye and Keesom contributions by Li and Si2 respectively. We recall from Chapter 7, that Li also

8 6

apolar and monopolar compounds

249

1: 1

Molecular Interactions Governing Vapor Pressure

bipolar compounds

fitted log piL* (Pa)

4 2 0 –2 –4 –6 Figure 8.7 Fitted (Eq. 8-19) versus experimental p∗iL values for 200 apolar, monopolar, and bipolar compounds taken from Appendix C.

–8 –8

–6

–4

–2

0

2

4

6

8

experimental log piL* (Pa)

takes into account entropy changes, which is particularly important when transferring a compound between the gas phase and a condensed phase, e.g., the pure liquid. log p∗iL (T) = lvap Li + svap Si2 + hvap Ai Bi + c

(8-18)

The system descriptor, hvap , is a compounded H-bonding term. A multiple regression analysis using experimental data of a large number of apolar, monopolar, and bipolar compounds covering more than 12 orders of magnitude in p∗iL (25◦ C) yields the following equation: log p∗iL (298K) (Pa) = −0.89Li − 0.44Si2 − 5.43Ai Bi + 6.51

(8-19)

2

(number of chemicals = 199; r = 0.99; S.D. = 0.30) In Eq. 8-19, all interaction terms exhibit a negative sign, as vapor pressure is an expression of an air–organic liquid partition constant. Figure 8.7 shows that Eq. 8-19 fits the experimental data quite well over a large vapor pressure range, and provides, therefore, an attractive alternative to Eq. 8-17 for estimating p∗iL . Entropy of Fusion and Vapor Pressure of Solids As discussed in previous sections, one can obtain (subcooled) liquid vapor pressures via experimental measurements using gas chromatographic techniques (see Appendix C) or estimation methods (Eqs. 8-17 or 8-19). Now, turning to compounds that are solids at the temperature of interest, if no experimental p∗is values are available, one has to first estimate the contribution of fusion; in other words, we have to predict the

250

Vapor Pressure ( pi∗ )

solid vapor boundary below the melting point (solid line below Tm in Fig. 8.2). Since we are primarily interested in estimating the ratio p∗is ∕p∗iL , which is directly related to the free energy of fusion (Eq. 8-10), we can write the van’t Hoff equation (Eq. 4-33) as: d ln p∗is ∕p∗iL dT

=

Δfus Hi (T) RT 2

(8-20)

As a first approximation, if we assume that Δfus Hi is constant over the temperature range below the melting point and we substitute Eq. 8-12 into Eq. 8-20, we can integrate Eq. 8-20 from 1 ( p∗is = p∗iL at Tm ) to p∗is ∕p∗iL and from Tm to T respectively. We then obtain for T ≤ Tm :

ln

p∗is

p∗iL

Δ S (T ) = − fus i m R

[

Tm −1 T

] (8-21)

Now, we are left with the problem of estimating the entropy of fusion at the melting point. Unfortunately, Δfus Si (Tm ) is much more variable than Δvap Si (Tb ) since Δfus Si (Tm ) is equal to SiL (Tm ) − Sis (Tm ) and both of these entropies can vary differently with compound structure. They vary because molecular symmetry is an important determinant of the properties of a solid substance, whereas for a liquid, orientation of a molecule is not that important (Dannenfelser et al., 1993). Nevertheless, as demonstrated by Myrdal and Yalkowski (1997), a reasonable estimate of Δfus Si (Tm ) can be obtained by the empirical relationship: Δfus Si (Tm ) ≅ 56.5 + 9.2 τ − 19.2 log σ

J mol−1 K−1

(8-22)

where τ is the effective number of torsional bonds and σ is the rotational symmetry number that describes the indistinguishable orientations in which a compound may be positioned in space (see Box 8.1). For compounds exhibiting no rotational symmetry axis, σ is equal to 1, which is the case for many of the more complex environmental chemicals. For benzene, on the other hand, σ = 12 as there are six indistinguishable forms looking from the top of the ring and there are six more when the ring is flipped over. For 1,4-dichlorobenzene, σ = 4 as only two two-fold rotational axes exist. Some examples of the application of Eq. 8-22 are given in Table 8.2. For a detailed discussion of the symmetry aspects (i.e., the derivation of σ), we refer to the articles by Dannenfelser et al. (1993) and Dannenfelser and Yalkowsky (1996). Finally, we should note that Eq. 8-22 does not work well for small spherical molecules and for polar compounds for which H-bonding has a significant impact on Δfus Si (Tm ). Hence, this empirical relationship could certainly be improved.

Molecular Interactions Governing Vapor Pressure

251

Box 8.1 Parameters Used to Estimate Entropies of Phase Change Processes In phase change processes, the overall entropy change, Δ12 Si , can be understood by considering the degrees of freedom lost when molecules in one phase are introduced into a new phase. For example, when molecules in a solid state are converted into the same compound in a liquid state, one can envision the phase change process as involving three contributions to the change in molecular freedom: (1) translational, (2) conformational, and (3) rotational (Yalkowsky and Valvani, 1980; Dannenfelser and Yalkowsky, 1996): Δ12 Si = Δ12 Si translational + Δ12 Si rotational + Δ12 Si conformational When molecules in a liquid state are transferred into a gaseous state, they gain additional translational and rotational freedom. Translational freedom, reflected in Δ12 Si translational , is gained when ordered arrangements of molecules expand and become more randomized. For the process of fusion (i.e., opposite direction to freezing), the translational freedom gain involves 50 to 60 J mol−1 K−1 . For vaporization (i.e., opposite direction to condensation), the translational freedom gain is about 86 J mol−1 K−1 . Molecules in a liquid state enjoy increased rotational freedom as compared to when they were held in a solid form. The magnitude of the accompanying entropy difference, Δ12 Si rotational , can be understood by considering the “symmetry” of a molecule, meaning the more symmetrical a molecule is, the less additional freedom it gains via rotation in space. This entropy contribution may be quantified by a parameter, σ, quantifying the number of indistinguishable ways a given molecule can exist in space. The more indistinguishable orientations, the easier it is to convert the molecules to a more packed phase, hence, making the absolute value of Δ12 Si rotational smaller. One may begin by assessing whether a three dimensional view of a given molecule looks the same from above and below (i.e., is there a plane of symmetry in the plane of paper on which a molecule can be drawn?). A molecule like vinyl chloride does not look the same (σ = 1), while DDE does (σ = 2). Next, one may ask is there a way to rotate a molecule around an axis perpendicular to any plane of symmetry (e.g., perpendicular to the paper on which the molecule is drawn) and have orientations that look the same. In this sense, vinyl chloride and DDE have only one orientation that look the same, but 1,4-dichlorobenzene looks the same from above and below as well as if it is rotated 180◦ (σ = 2 × 2). Benzene looks the same from above and below and every time it is rotated 60◦ (σ = 2 × 6). The product of these numbers of indistinguishable orientations yields the symmetry number, σ. The higher a molecule’s symmetry number, the less change in rotational freedom associated with packing or unpacking of the molecules. In the case of fusion, Δ12 Si rotational = R ln σ = 19.2 log σ. When σ is 1, Δ12 Si rotational is zero; when σ is 12, the absolute value is about 20 J mol−1 K−1 . The sign depends on whether one considers unpacking (more freedom, so Δ12 Si rotational has positive sign) or the packing (e.g., freezing or condensation) direction of phase change.

Cl

Cl

Cl

Cl Cl vinyl chloride (chloroethene)

Cl DDE

Cl benzene

1,4-dichlorobenzene

252

Vapor Pressure ( pi∗ )

Finally, molecules in a liquid (or gas) state can assume different conformations due to their ability to rotate around single bonds. When a substance is packed into a liquid from a gas or into a solid from a liquid, the molecules have a reduced ability to assume various conformations. This loss of freedom is reflected in Δ12 Si conformational . For example, consider 1-bromo-2-chloro-ethane. Viewing the two carbons and the chlorine substituent as co-existing in a plane, we recognize that the bromine atom can occur in the same plane opposite the chlorine atom, above the plane, or behind the plane:

H

H

Br

Cl H

Br

H

H

Cl

H

H

Br H

H

H

Cl H

H

This amounts to rotating around the single bond connecting the two carbons. Every bond capable of such rotation offers three distinguishable orientations. Therefore, if we increased the chain length by one –CH2 – unit, 3 × 3 = 9 distinguishable conformations exist. Having only three atoms in such a chain does not enable conformation variation since three points always determine a single plane. Hence, Δ12 Si conformational increases by the number of bonds capable of rotation minus two (equivalent to number of non terminable sp3 atoms in the chain; hydrogen is not a sp3 atom). Atoms in the chain that include double bonded moieties do not offer as much conformational variety. Consider methyl ethyl ketone; rotation around the bond between the carbonyl carbon and the C3 allow two (not three) distinguishable conformers: O

CH3 CH3

H3C H

CH3

O

H

H

H

Therefore, the contribution of such atoms to Δ12 Si conformational needs to be discounted, which is done by applying a factor of 0.5 times the number of such sp2 members of a chain. This discounting also applies to ring systems. Therefore, we can estimate a parameter, τ: τ = (number of non terminable sp3 atoms) + 0.5∗ (number of non terminable sp2 atoms) + 0.5∗ (ring systems) − 1 The number of distinguishable conformers is approximately 3τ . Empirically, the observed data for the entropy of fusion at Tm are best fit using 2.85τ . With this estimate, one finds Δ12 Si conformational is approximately R ln (number of distinguishable conformers) ≈ R ln(2.85τ ) = 9.2 τ (as in Eq. 8-22). For the case of 1-bromo-2-chloro-ethane with a τ of 1, R ln(2.85τ ) = 9 J mol−1 K−1 . As chains get longer, the magnitude of the contribution of Δ12 Si conformational to Δ12 Si grows quickly (see Table 8.2).

Substitution of Eq. 8-22 into Eq. 8-21 then gives: ln

p∗is

p∗iL

[ = −(6.80 + 1.1τ − 2.3 log σ)

Tm −1 T

] (8-23)

253

Questions and Problems

Table 8.2 Comparison of Experimental and Predicted (Eq. 8-22) Entropies of Fusion at the Normal Melting Pointa Predicted (Eq. 8-22)

Experimental Compound

Tm (◦ C)

Δfus Hi (Tm ) (kJ mol−1 )

Δfus Si (Tm ) (J mol−1 K−1 )

τ

σ

Δfus Si (Tm ) (J mol−1 K−1 )

Benzene n-Butylbenzene 1,4-Dichlorobenzene Naphthalene Phenanthrene Fluoranthene Pyrene Decane Eicosane Benzoic acid 2,2′ ,4,5,5′ -Pentachlorobiphenyl p,p′ -DDT

5.5 –88.0 52.7 80.2 101.0 107.8 151.2 –29.7 36.8 122.4 77.0 109.0

10.0 11.2 17.2 18.6 18.1 18.9 17.1 28.8 69.9 18.1 18.8 27.4

35.7 60.5 52.8 52.7 48.6 49.6 40.3 118.3 225.6 45.8 53.6 71.6

0 2 0 0 0 0 0 7 17 0 0 1

12 2 4 4 2 2 4 2 2 2 1 1

35.8 69.1 45.0 45.0 50.7 50.7 45.0 115.1 207.1 50.7 56.5 65.7

a

Data from Hinckley et al. (1990) and Lide (1995).

which can be used to estimate p∗is from the subcooled liquid vapor pressure p∗iL , and vice versa. Finally, insertion of Eq. 8-23 into Eq. 8-9 yields an estimate of the free energy of fusion: Δfus Gi = +(56.5 + 9.2 τ − 19.2 log σ) [Tm − T] J mol−1

(8-24)

The entity, Δfus Gi , will be important for estimating other properties of the subcooled liquid, such as water solubility (see Chapter 9).

8.3

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Questions Q 8.1 Give at least five examples of environmentally relevant organic chemicals that are gases at 20◦ C (273K). Which of the companion compounds (Table 3.1) are liquids at both –20◦ C and +20◦ C (253K and 293K)? Q 8.2 Why are certain chemicals gases at ambient conditions of temperature and pressure?

254

Vapor Pressure ( pi∗ )

Q 8.3 Propane (Tb = –42.1◦ C, Tc = 101.2◦ C) is a gas at 25◦ C. How can you “produce” liquid propane (give two options)? Q 8.4 What is the difference between the normal and the standard boiling point of a chemical? Q 8.5 Explain in words the terms subcooled liquid, superheated liquid, and supercritical fluid. Q 8.6 How are the (subcooled) liquid and solid vapor pressures of a given compound at a given temperature related to each other? Q 8.7 Which thermodynamic entities need to be known for assessing the temperature dependence of the vapor pressure of a given compound? How can this entity be derived from experimental data? How can it be estimated? What caution is advised when extrapolating vapor pressure data from one temperature to another temperature? Q 8.8 Explain the following observations: (a) The two isomeric polycyclic aromatic hydrocarbons, phenanthrene and anthracene, are solids at 25◦ C. Although these compounds have almost the same boiling point (339◦ C and 341◦ C respectively), their vapor pressures at 25◦ C differ by more than one order of magnitude. (b) Although they have approximately the same size, n-hexane (Vi = 95 cm3 mol−1 ) exhibits a 20 times larger vapor pressure than styrene (Vi = 96 cm3 mol−1 ), and a 1000 times larger vapor pressure than 3-methylphenol (Vi = 92 cm3 mol−1 ). (c) The liquid vapor pressure of 2,6-dimethylphenol is almost one order of magnitude larger than the one of its isomer, 3,4-dimethylphenol.

Problems P 8.1∗ Basic Vapor Pressure Calculations (a) Consider the chemical 1,2,4,5-tetramethylbenzene (abbreviated TeMB and also called durene, structure in margin). In an old CRC Handbook of Chemistry and Physics, you find vapor pressure data that are given in mm Hg (see margin).

Questions and Problems

255

Estimate the vapor pressure, p∗i , of TeMB (in bar and Pa) at 20◦ C and 150◦ C using the experimental vapor pressure data given. 1,2,4,5-tetramethylbenzene

Mi = 134.2 g mol−1 Tm = 79.5◦ C Tb = 195.9◦ C Experimental vapor pressure data for TeMB T (◦ C)

p∗i (mm Hg)

45.0s 74.6s 104.2 128.1 172.1 195.9

1 10 40 100 400 760

s TeMB

is a solid at these temperatures.

(b) Estimate the free energy ( Δfus Gi , in kJ mol−1 ), the enthalpy (Δfus Hi , in kJ mol−1 ), and the entropy (Δfus Si , in kJ mol−1 K−1 ) of fusion of TeMB at 20◦ C using the vapor pressure data previously given. P 8.2 A Solvent Spill in Your Class Room You teach Environmental Organic Chemistry, and for a demonstration of partitioning processes of organic compounds, you bring a glass bottle containing 10 L of the common solvent, tetrachloroethene (PCE), into your classroom. After closing the door, you stumble, and you drop the bottle. The bottle breaks, and the solvent spills onto the floor. Soon, you can smell the solvent vapor in the air. (The odor threshold of PCE is between 8 and 30 mg m−3 ). Answer the following questions: (a) What is the maximum PCE concentration that you can expect in the air in the room (T = 20◦ C)? How much of the solvent has evaporated if you assume that the air volume is 50 m3 ? (Neglect any adsorption of PCE on the walls and furniture.) (b) If the same accident happened in your sauna (volume 15 m−3 , T = 80◦ C), what maximum PCE concentration would you and your friends be exposed to there? In an old CRC Handbook of Chemistry and Physics (Lide, 1995), you find the following vapor pressure data for PCE: T (◦ C) p∗i (kPa)

25 2.42

50 8.27

75 22.9

100 54.2

Use both the experimental data as well as Eqs. 8-19 and 8-14 to solve this problem. Compare the predicted with the experimental data. Any comments? P 8.3 How Much Freon is Left in the Old Pressure Bottle Left at a Dump Site? In a dump site, you find an old 3-liter pressure bottle with a pressure gauge that indicates a pressure of 2.7 bar. The temperature is 10◦ C. From the label, you can see that the bottle contains Freon 12 (dichlorodifluoromethane, CCl2 F2 ). You wonder how much Freon 12 is still left in bottle. Try to answer this question. In an old CRC Handbook of Chemistry and Physics (Lide, 1995), you find the following data on CCl2 F2 : T (◦ C) p∗i (kPa)

−25 123

0 308

25 651

50 1216

75 2076

Using these data, estimate the free energy (Δcond Gi ), the enthalpy (Δcond Hi ), and the entropy (Δcond Si ) of condensation of Freon 12 at 25◦ C. Note that condensation is the opposite of vaporization (watch out for the signs of the three quantities).

256

Vapor Pressure ( pi∗ )

P 8.4 What Are the Differences Between Freon 12 and its Replacement HFC-134a? (From Roberts, 1995) Hydrofluorocarbon 134a (1,1,1,2-tetrafluoroethane, F3 C–CH2 F) is used as a replacement for Freon 12 (see Problem 8.3) for refrigeration applications. Why is such a replacement necessary and what is the advantage of HFC-134a from an environmental protection point of view? Some vapor pressure data for Freon 12 is given in Problem 8.3 The vapor pressure data of HFC-134a has been determined very carefully and is as follows: T (◦ C) p∗i (kPa)

−40.0 51.6

−30.0 84.7

−20.0 132.9

−10.0 200.7

0 292.9

+10.0 414.8

(a) Determine the normal boiling points (in ◦ C) of these compounds from the data provided. (b) At what temperature (in ◦ C) will they have an equal vapor pressure? (c) Compare the enthalpies (Δvap Hi ) and entropies (Δvap Si ) of vaporization of the two compounds at ambient temperatures. Can you rationalize any differences you observe between the two compounds? (d) Automobile air conditioners commonly operate at temperatures between 30 and 50◦ C. Are the vapor pressures of the two compounds significantly (i.e., greater than 10%) different in this temperature region? P 8.5 A Public Toilet Problem Pure 1,4-dichlorobenzene (1,4-DCB) is still used as a disinfectant and air freshener in some public toilets. As an employee of the health department of a large city you are asked to evaluate whether the 1,4-DCB present in the air in such bathrooms may pose a health problem to the cleaning personnel who are exposed to this compound for several hours every day. In this context, you are interested in the maximum possible 1,4-DCB concentration in the bathroom air at 20◦ C. Calculate this concentration in g m3 air, assuming that: (a) you go online and get the vapor pressure data given below from CRC Handbook of Chemistry and Physics (Haynes, 2014: http://www.hbcpnetbase.com), (b) you have no time to look for vapor pressure data, but you know the boiling point (Tb = 174.0◦ C) and the melting point (Tm = 53.1◦ C) of 1,4-DCB, or (c) you are a pp-LFER freek. Compare the three results.

Bibliography

257

What would be the maximum 1,4-DCB concentration in the air of a public toilet located in Death Valley (Temperature 60◦ C)? Any comments?

Cl

T (◦ C) p∗i (kPa)

Cl

s

1,4-dichlorobenzene

−45.5s 0.001

−21.8s 0.01

8s 0.1

46.7s 1

99 10

173.6 100

Indicates the compound is a solid at this temperature.

P 8.6 True or False? Cl

Somebody bets you that at 60◦ C, the vapor pressure of 1,2-dichlorobenzene (1,2DCB) is smaller than that of 1,4-dichlorobenzene (1,4-DCB), but that at 20◦ C, the opposite is true. Is this person right? If yes, at what temperature do both compounds exhibit the same vapor pressure? (Try to answer these questions by using only the Tm and Tb values given in Appendix C.)

Cl 1,2-dichlorobenzene

P 8.7 Vapor pressure of Alkyl Nitriles from Biomass Burning

N

Simoneit et al. (2003) discovered that biomass burning results in the introduction of alkyl nitriles into the atmosphere. One such alkyl nitrile is dodecyl nitrile. In order to prepare to estimate the fate of dodecyl nitrile, you are asked to find its physical chemical properties. Now, estimate the vapor pressure (Pa) of dodecyl nitrile at 25◦ C.

dodecyl nitrile

M = 181.3 g mol−1 Tm = 4◦ C Tb = 277◦ C density = 0.82 g mL−1 index of refraction = 1.4361

8.4

Bibliography Atkins, P. W.; de Paula, J., Physical Chemistry. 10 ed.; Oxford University Press: Oxford, 2014. Dannenfelser, R. M.; Surendran, N.; Yalkowsky, S. H., Molecular symmetry and related properties. SAR QSAR Environ. Res. 1993, 1(4), 273–292. Dannenfelser, R. M.; Yalkowsky, S. H., Estimation of entropy of melting from molecular structure: A non-group contribution method. Ind. Eng. Chem. Res. 1996, 35(4), 1483–1486. Daubert, T. E., Physical and Thermodynamic Properties of Pure Chemicals. New Standard Reference Data System: New York, 1997. Fishtine, S. H., Reliable latent heats of vaporization. Ind. Eng. Chem. 1963, 55(6), 47–56. Goss, K. U.; Schwarzenbach, R. P., Empirical prediction of heats of vaporization and heats of adsorption of organic compounds. Environ. Sci. Technol. 1999, 33(19), 3390–3393. Haynes, W. M., Ed., CRC Handbook of Chemistry and Physics. 95th ed.; CRC Press: Boca Raton, FL, 2014; Vol. 2014–2015. Hinckley, D. A.; Bidleman, T. F.; Foreman, W. T.; Tuschall, J. R., Determination of vapor pressures for nonpolar and semipolar organic compounds from gas chromatographic retention data J. Chem. Eng. Data 1990, 35(3), 232–237. ¨ Kistiakowsky, W., Uber Verdampfungsw¨arme und einige Gleichungen, welche die Eigenschaften der unassoziierten Fl¨ussigkeiten bestimmen. Z. Phys. Chem. 1923, 107, 65–73. Lide, D. R., Ed., CRC Handbook of Chemistry and Physics. CRC Press: Boca Raton, FL, 1995; Vol. 1995-1996.

258

Vapor Pressure ( pi∗ )

Mackay, D.; Bobra, A.; Chan, D. W.; Shiu, W. Y., Vapor pressure correlations for low-volatility environmental chemicals Environ. Sci. Technol. 1982, 16(10), 645–649. MacLeod, M.; Scheringer, M.; Hungerbuhler, K., Estimating enthalpy of vaporization from vapor pressure using Trouton’s rule. Environ. Sci. Technol. 2007, 41(8), 2827–2832. Myrdal, P. B.; Yalkowsky, S. H., Estimating pure component vapor pressures of complex organic molecules. Ind. Eng. Chem. Res. 1997, 36(6), 2494–2499. Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P., The Properties of Gases and Liquids. 5th ed.; McGraw-Hill: New York, 2001. Roberts, A. L., Workbook for Environmental Organic Chemsitry. John Hopkins University: Baltimore, M.D., 1995. Sage, M. L.; Sage, G. W., Vapor Pressure. In Handbook of Property Estimation Methods for Chemicals: Environmental and Health Sciences, Mackay, D.; Boethling, R. S., Eds. CRC Press: 2000. Simoneit, B. R. T.; Rushdi, A. I.; Bin Abas, M. R.; Didyk, B. M., Alkyl amides and nitriles as novel tracers for biomass burning. Environ. Sci. Technol. 2003, 37(1), 16–21. Trouton, F., IV. On molecular latent heat. Philos. Mag. 1884, 18(110), 54–57. Yalkowsky, S. H., Estimation of entropies of fusion of organic compounds. Ind. Eng. Chem. Fundam. 1979, 18(2), 108–111. Yalkowsky, S. H.; Valvani, S. C., Solubility and partitioning I: Solubility of nonelectrolytes in water. J. Pharm. Sci. 1980, 69(8), 912–922.

259

Chapter 9

(

sat Ciw

)

(

Solubility and Activity Coefficient ( in Water; Air–Water Partition Constant Kiaw

9.1

Introduction and Thermodynamic Considerations Solubilities and Aqueous Activity Coefficients of Organic Liquids, Solids, and Gases Concentration Dependence of the Aqueous Activity Coefficient Air–Water Partitioning: “The” Henry’s Law Constant

9.2

Molecular Interactions Governing the Aqueous Activity Coefficient and the Air–Water Partition Constant Enthalpic and Entropic Contributions to the Excess Free Energy in Water and to the Free Energy of Air–Water Partitioning

9.3

LFERs for Estimating Air–Water Partition Constants and Aqueous Activity Coefficients/Aqueous Solubilities Air–Water Partition Constant

9.4

Effect of Temperature, Dissolved Salts, and pH on the Aqueous Activity Coefficient/Aqueous Solubility and on the Air–Water Partition Constant Effect of Temperature

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

)

𝜸 sat iw)

260

( sat ) ( ) ( ) Solubility Ciw and Activity Coefficient 𝜸 sat in Water; Air–Water Partition Constant Kiaw iw

Effect of Dissolved Inorganic Salts Effect of pH on Aqueous Solubility and Air–Water Partitioning of Organic Acids and Bases 9.5

Questions and Problems

9.6

Bibliography

Introduction and Thermodynamic Considerations

9.1

261

Introduction and Thermodynamic Considerations Whether an organic compound “likes” or “dislikes” being surrounded by liquid water, or alternatively, whether water “likes” or “dislikes” accommodating a given organic solute, determines the environmental behavior and toxic effects of the compound. Due to its small size and strong H-bonding characteristics, water is the most unusual solvent on the planet. Here and in Chapter 10, we discuss and try to visualize the molecular factors associated with partitioning an organic compound between a nonaqueous bulk phase (i.e., air, organic solvent) and an aqueous solution. We also consider how these factors determine a compound’s partition constants in the system considered. Fig. 9.1 summarizes the systems that concern us in our treatment of bulk phase partitioning between well-defined media. We have already briefly addressed partitioning involving organic solvents (right side of the scheme) in Chapter 7, where we have considered the compound to be in a (infinitely) diluted solution (superscript “∞”). We come back to this topic in more depth in Chapter 10. The left side of the scheme in Fig. 9.1 depicts the situation where equilibrium partitioning of the pure compound (liquid, “L” or solid, “s”) to air or water leads to a saturated vapor (Chapter 8) or a saturated aqueous solution, respectively. The latter, which is commonly referred to as the water solubility or the aqueous solubility of the compound sat (L,s)), is the main focus of this chapter. This compound property, (denoted as Ciw which has been determined experimentally for many compounds, not only tells us the maximum concentration of a given chemical that can be dissolved in pure water at a given temperature, but it also allows us to calculate the compound’s aqueous activity , and, thus, the excess free energy in saturated aqueous coefficient at saturation, 𝛾 sat iw in place of the activity coefficient of a solution. We also explore when we can use 𝛾 sat iw ∞ compound in dilute aqueous solution, 𝛾 iw , which represents a more relevant situation in the environment. Assuming ideal behavior in the gas phase, this is equivalent to ∞ , by the assessing when we can approximate the air–water partition constant, Kiaw “saturated” air–water partition constant calculated from vapor pressure and aqueous sat (see thermodynamic cycles in Fig. 9.1). Finally, we address the effect solubility, Kiaw

i (a) 8

i sat(a) p*iL,s

Kiℓ w

Ciwsat (L,s) i sat(w)

i (w)

(γ iwsat

γ iw )

8

8

Figure 9.1 Thermodynamic cycles relating partition constants between air (a), water (w), pure organic liquid (L) or solid (s), and an organic solvent (l ) at saturated (superscript “sat,” left) and (infinitely) dilute (superscript “∞,” right) conditions.

i(ℓ )

Kiaw

sat Kiaw

8

i(L,s)

Kiaℓ

262

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

of temperature, dissolved salts, and pH on the aqueous activity coefficient, and, thus, also on the air–water partition constant of a given organic compound. Solubilities and Aqueous Activity Coefficients of Organic Liquids, Solids, and Gases Let us first imagine an experiment in which we bring a pure, water-immiscible organic liquid into contact with pure water at a given temperature. What will happen? Intuitively, we know that some organic molecules will leave the organic phase and dissolve into water, while some water molecules will enter the organic liquid. After some time, so many organic molecules will have entered the water that some will begin to return to the organic phase. When the fluxes of molecules into and out of the organic phase are balanced, the system has reached a state of equilibrium. At this point, the amount of organic molecules in the water is the water solubility of that liquid organic compound. Similarly, the amount of water molecules in the organic phase reflects the solubility of water in that organic liquid. To describe this process thermodynamically, at any instant in time during our experiment, we can express the chemical potentials of the organic compound, i, in each of the two phases (Chapter 4, Section 4.2): 𝜇iL = 𝜇∗iL + RT ln 𝛾 iL xiL 𝜇iw = 𝜇 ∗iL + RT ln 𝛾 iw xiw

(9-1)

where we still use the subscript L to indicate the pure liquid organic phase, although in this case it contains some water molecules. Since in both expressions we relate chemical potential to the same reference potential, 𝜇∗iL , the difference in chemical potentials of the “product” (solutes in aqueous solution) minus the “reactant” (i in its pure liquid) molecules at any time during the experiment is given by: 𝜇 iw − 𝜇iL = RT ln 𝛾 iw xiw − RT ln 𝛾 iL xiL

(9-2)

In the beginning of our experiment, 𝜇 iL is much larger than 𝜇 iw (xiw is near zero). Therefore, a net flux of organic molecules from the organic phase (higher chemical potential) to the aqueous phase (lower chemical potential) occurs. This process continues, and xiw increases until the chemical potentials (or the fugacities) become equal in both phases. We then obtain: ln

sat xiw

xiL

=

RT ln 𝛾 iL − RT ln 𝛾 sat iw RT

(9-3)

where we now use the superscript “sat” to indicate that we are dealing with a saturated aqueous solution of the compound. In Eq. 9-3, we retain the product of the gas constant and system temperature, RT, to indicate that the ratio of concentrations in the two phases is related to a difference in free energies (i.e., each term, RT ln 𝛾 i , is a free energy term per mole of molecules in a particular state). For the majority of the compounds of interest to us, we can now make two important simplifying assumptions. First, in the organic liquid, the mole fraction of water is small compared to the mole

Introduction and Thermodynamic Considerations

263

fraction of the compound itself; that is, xiL remains approximately 1. Also, we may assume that the compound shows ideal behavior in its water-saturated liquid phase; that is, we set 𝛾 iL = 1. With these assumptions, Eq. 9-3 simplifies to: sat ln xiw

=−

RT ln 𝛾 sat iw RT

=−

sat GE, iw

(9-4)

RT

where GE,sat is the excess free energy of the compound in saturated aqueous solution iw for the case when one chooses the pure liquid (xiL = 1) as the reference state (see Chapter 4). Now we can see a key result; for an organic liquid, the aqueous activity coefficient is simply given by the inverse of its aqueous mole fraction solubility: 𝛾 sat iw =

1 sat xiw

(9-5a)

for organic liquids

(9-5b)

or in molar units (Eq. 4-26): sat Ciw (L) =

1 ̄Vw 𝛾 sat iw

where V̄ w is the molar volume of water (0.0181 L mol–1 ). When thermodynamically describing the solubility of a solid organic compound in water, conceptually, we can imagine first converting the solid to the liquid state and then proceeding as for a liquid compound. As discussed in Chapter 8, the free energy cost involved in the solid-to-liquid conversion is referred to as the free energy of fusion, Δfus Gi , which can be derived from vapor pressure data (Eq. 8-9): Δfus Gi = RT ln

p∗iL

(9-6)

p∗is

In analogy to Eq. 9-2, we can now express the difference in chemical potential as: 𝜇 iw − 𝜇is = 𝜇 iw − (𝜇 iL − Δfus Gi ) = RT ln 𝛾 iw xiw − (RT ln 𝛾 iL xiL − Δfus Gi )

(9-7)

At equilibrium, we then obtain: 𝛾 sat iw =

1 −Δfus Gi ∕RT e sat xiw (s)

or in molar units:

(9-8a) for organic solids

sat (s) = Ciw

1 e−Δfus Gi ∕RT V̄ w 𝛾 sat iw

(9-8b)

264

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

Eq. 9-8b clearly shows that the solubility of an organic solid in water is dependent on both the compatibility of the chemical with the water and the ease with which the solid is converted to a liquid. Recalling the concept of a subcooled liquid compound as one that has cooled below its freezing temperature without becoming solid (Chapter sat (L) , as: 8, Fig. 8.2), we may evaluate the solubility of such a hypothetical liquid, Ciw 1 ̄Vw Csat (L) iw

𝛾 sat iw =

(9-9)

where the liquid compound solubility is related to the actual experimental solubility of the solid compound using Eq. 9-8: sat sat Ciw (L) = Ciw (s) e+Δfus Gi ∕RT

(9-10)

The aqueous solubility of a gaseous compound is commonly reported for 1 bar (or 1 atm = 1.013 bar) partial pressure of the pure compound. One of the few exceptions is the solubility of O2 , which is generally given for equilibrium with the gas at 0.21 bar, since this value is appropriate for the earth’s atmosphere at sea level. As discussed in Chapter 4, the partial pressure of a compound in the gas phase (ideal gas) at equilibrium above a liquid solution is identical to the fugacity of the compound in the solution (see Fig. 4.2d). Therefore, by equating chemical potential or fugacity expressions for a compound in both the gas phase and an equilibrated aqueous solution phase, we have: pi = 𝛾 iw xiw p∗iL

(9-11)

We can now express the mole fraction solubility of a gaseous organic substance as a function of the partial pressure pi : p

xiwi =

pi 1 pi ⋅ ∗ 𝛾 iw piL

or in molar units:

(9-12a)

for gases p

Ciwi = p

p 1 ⋅ ∗i p i V̄ w 𝛾 iw piL

(9-12b)

The activity coefficient, 𝛾 iwi , is not necessarily constant with varying pi . In fact, evalp uation of the air–water equilibrium distribution ratio as a function of pi or Ciwi is one of the methods that can be used to assess the concentration dependence of an organic compound’s activity coefficient, regardless of whether the compound is a gas, liquid, or solid at the temperature considered. If, for sparingly soluble gases, we assume that

Introduction and Thermodynamic Considerations

265

p

𝛾 iwi is independent of concentration (even at saturation, where pi = p∗i and the compound is also present as a liquid), then we can calculate the solubility of the supersat (L) , from the actual solubility determined at pi (e.g., at heated liquid compound, Ciw 1 bar) by: p

sat (L) = Ciwi Ciw

p∗iL pi

(9-13)

Concentration Dependence of the Aqueous Activity Coefficient From an environmental point of view, knowing the activity coefficient of an organic compound in dilute aqueous solution is of the most interest as it describes a concentration at which the solute molecules do not “feel” each other. This activity coefficient is commonly denoted as 𝛾 ∞ and is referred to as the limiting activity coefficient or iw infinite dilution activity coefficient. As previously shown, an activity coefficient can be deduced from aqueous solubility (together with vapor pressure or melting data, as necessary). However, in using this “saturation” case, the activity coefficient reflects the compatibility of the organic solute with water solutions that may have been significantly modified by the presence of the solute itself. Table 9.1 shows a comparison of values obtained from solubility measurements (Eqs. 9-5 and 9-8) with 𝛾 ∞ values 𝛾 sat iw iw determined by various methods (including studies on the concentration dependence of air–water partitioning) for a series of compounds covering a very large range in activity coefficients. As is evident, even for compounds exhibiting a substantial aqueous solubility (e.g., 1-butanol, phenol), the differences between the activity coefficients in dilute solution and in saturated solution are not larger than about 30%. In fact, particularly for the more sparingly soluble compounds, the differences are well within the range of error of the experimental data. Hence, for compounds exhibiting activity coefficients larger than about 100, which represents the majority of the chemicals of interest to us, we assume that 𝛾 iw is independent of the concentration of the compound. As such, we typically omit any superscript. By making this assumption, we imply that the organic solutes do not “feel” each other in the aqueous solution even under saturation conditions. In other words, we assume that the solvation of a given organic molecule by water molecules is not influenced by the other molecules of that compound present. In Section 9.3, we introduce limited cases where this assumption is not valid. Air–Water Partitioning: “The” Henry’s Law Constant Following the previous discussion on the aqueous solubility of gases, we can now rearrange Eq. 9-12 to obtain the air–water partition constant, commonly referred to as “the” Henry’s law constant: KiH =

pi = 𝛾 iw p∗iL V̄ w Ciw

(9-14)

KiH is commonly expressed in bar Lw mol–1 or Pa Lw mol–1 . The “dimensionless” Henry constant, denoted as Kiaw , is related to KiH by: Kiaw = KiH ∕RT

(9-15)

266

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

Table 9.1 Comparison of Activity Coefficients and Corresponding of a Series of Organic ( Excess Free Energies ) Compounds in Dilute and Saturated Aqueous Solution at 25◦ C GEiw = RT ln 𝛾 iw Compound Methanol Ethanol Acetone 1-Butanol Phenol Aniline 3-Methylphenol 1-Hexanol Trichloromethane Benzene Chlorobenzene Tetrachloroethene (PCE) Naphthalene 1,2-Dichlorobenzene 1,3,5-Trimethylbenzene Phenanthrene Anthracene Hexachlorobenzene 2,4,4′ -Trichlorobiphenyl 2,2′ ,5,5′ -Tetrachlorobiphenyl Benzo(a)pyrene a b

𝛾 sat iw

a GE,sat iw (kJ mol−1 )

𝛾∞ iw

b GE,∞ iw (kJ mol−1 )

miscible miscible miscible 7.0×101 6.3×101 1.4×102 2.5×102 9.0×102 7.9×102 2.5×103 1.4×104 6.5×104 6.7×104 6.2×104 1.3×105 2.0×106 2.5×106 4.3×107 5.6×107 7.0×107 3.2×108

miscible miscible miscible 10.5 10.3 12.3 13.7 16.9 16.5 19.4 23.7 27.8 27.5 27.4 29.2 36.0 36.5 43.6 44.2 44.8 48.5

1.6 3.7 7.0 5.0×101 5.7×101 1.3×102 2.3×102 8.0×102 8.2×102 2.5×103 1.3×104 5.0×104 6.9×104 6.8×104 1.2×105 1.7×106 2.7×106 3.5×107 4.7×107 7.5×107 2.7×108

1.2 3.2 4.8 9.7 10.0 12.1 13.5 16.6 16.6 19.4 23.5 26.8 27.6 27.6 29.0 35.6 36.7 43.1 43.8 44.9 48.1

Data from Appendix C using enthalpy and entropy of fusion values given by Hinckley et al. (1990) and Lide (1995). Data from Sherman et al. (1996); Staudinger and Roberts (1996); and Mitchell and Jurs (1998).

where R has to be expressed in the respective units, i.e., 0.0831 bar Lw mol–1 K–1 or 8310 Pa Lw mol–1 K–1 . Strictly speaking, the Henry’s law constant is defined for solutes at infinite dilution. However, as discussed earlier, in most cases, we may assume that the aqueous activity coefficient is approximately independent of concentration (see Table 9.1). We may therefore replace 𝛾 iw in Eq. 9-14 by 𝛾 sat : iw KiH ≅

∗ ̄ 𝛾 sat iw piL Vw

≅

p∗iL sat Ciw (L)

(9-16)

For solid compounds: KiH ≅

p∗is sat Ciw (s)

(9-17)

Molecular Interactions Governing the Aqueous Activity Coefficient

267

because the free energy terms relating the liquid and solid vapor pressure and the liquid and solid aqueous solubility, Eqs. 9-6 and 9-10, cancel when dividing the two entities. From a practical point of view, Eqs. 9-16 and 9-17 are very useful because they tell us that we may estimate the Henry’s law constant of a compound directly from its vapor pressure and aqueous solubility. In fact, many of the KiH or Kiaw values listed in data compilations, including much of the data given in Appendix C, have been derived in this way. Comparison of calculated with experimental Kiaw values (see review and compilation of a large data set published by Sander, 2015) shows that, in most cases, Eqs. 9-16 and 9-17 yield quite satisfactory estimates with less than a factor of 2 deviation.

9.2

Molecular Interactions Governing the Aqueous Activity Coefficient and the Air–Water Partition Constant Enthalpic and Entropic Contributions to the Excess Free Energy in Water and to the Free Energy of Air–Water Partitioning As pointed out in the previous section, water is a very unusual solvent in that water molecules exhibit an extraordinary H-bonding capacity in relation to their molecular size, which is reflected in the high cohesive energy of water. In our simple cavity model of partitioning (Fig. 7.1), at least part of these H-bonds have to be disrupted when inserting an organic solute. However, since the water molecules are comparably small and, therefore, a large number of them are involved in forming the cavity, they conceivably may arrange themselves around the cavity with as little loss in Hbonding as possible. Unfortunately, even after decades of research trying to uncover the “secrets” of water, it is still unclear exactly how water molecules accommodate an organic molecule and how the size, shape, and polarity of the organic solute influence the rearrangement. To gain at least a few insights, one still relies on bulk observations that yield data such as enthalpy and entropy changes when partitioning an organic compound between air or an organic solvent and water. In the following, we compare the standard enthalpy and entropy changes observed for some of our companion chemicals and other organic compounds for the following phase transfers (see also Fig. 9.2):

Δ

Hi aw

i (w) water

,Δ

Si

aw

air i (a)

(1) from water to air (Δaw Hi , Δaw Si ), Δ

va pH i

(2) from the pure liquid to air (Δvap Hi , Δvap Si ), and

,Δ

va

pS i

i (L) HiwE , SiwE pure organic liquid

Figure 9.2 Standard enthalpy and entropy changes for the transfer of an organic compound from water to air (aw), and from the pure organic liquid to air (vap) and water (w) respectively.

E E , the excess enthalpy; Siw , the excess entropy in (3) from the pure liquid to water (Hiw water; see Chapter 4, Eqs. 4-17 and 4-18).

The corresponding values are summarized in Table 9.2. The reported data are averages from various studies and, therefore, contain quite a large error (± 5 kJ E , and mol–1 ). Also, using the thermodynamic cycle, i.e., Δaw Hi = −Δvap Hi + Hiw E Δaw Si = −Δvap Si + Siw , some of the values have been adjusted to make the data set internally consistent. Nevertheless, we can draw some important general conclusions.

pure liquid to water

−28 −28 −29 −31 0 −1 −9 −18 −12 8 8 −6 −2 −2 2 8 −13 −16 −9 5 −5 −5 −36 −36 56 60 66 72 67 75 58 60 46 50 50 51 56 52 57 42 50 55 49 59 75 116 128

28 32 37 41 67 74 49 42 32 58 58 45 54 50 59 29 34 46 54 54 70 80 92

1 4 10 16 17 22 3 9 5 18 21 20 34 36 42 58 10 18 33 35 35 47 20 26 41 50 75 70 72 90 60 65

26 32 42 52 62 71 30 40 34 58 62 58 69 68 74 31 32 42 35 37 43 40 39

25 28 32 36 45 49 27 31 29 40 41 38 35 32 32

29 32 39 47 17 23 12 27 17 10 13 26 36 38 40 50 23 34 42 30 40 52 56 62

12 16 29 16 18 20 −20 −27

−2 0 5 9 −5 −3 −19 −2 2 0 4 13 15 18 15

−104 −107 −114 −121 −74 −87 −104 −97 −57 −33 −30 −44 −70 −67 −83 −37 −60 −44 −47 −74 −107 −255 −299

−31 −32 −34 −36 −22 −26 −31 −29 −17 −10 −9 −13 −21 −20 −25 −11 −18 −13 −14 −22 −32 −76 −89

a

1

Δaw Gi = −RT ln pi ∕xi (2) Δvap Gi = −RT ln p∗iL (3) GEi = −RT ln 𝛾 iw Data compiled and averaged from Shiu et al. (1997); Goss and Schwarzenbach (1999); Bamford et al. (2000); Beyer et al. (2002); Arey et al. (2005); K¨uhne et al. (2005); Goss (2006); Mintz et al. (2007); and Lei et al. (2010).

pentane hexane octane decane 1-hexanol 1-octanol MTBE PCE benzene phenol 3-methylphenol naphthalene phenanthrene anthracene pyrene benzo(a)pyrene chlorobenzene 1,3,5-trichlorobenzene hexachlorobenzene lindane (𝛾-HCH) PCB 15 PCB 153 D5 D6

Compound

pure liquid to air

E E Hiw TSiw Δaw G(1) Δvap G(2) GE(3) SiE = Δaw Hi − TΔaw Si = Δvap Hi − TΔvap Si = − i i i (kJ mol−1 ) (kJ mol−1 ) (kJ mol−1 ) (kJ mol−1 ) (kJ mol−1 ) (kJ mol−1 ) (kJ mol−1 ) (kJ mol−1 ) (kJ mol−1 ) (J K−1 mol−1 )

water to air

Table 9.2 Standard Enthalpy and Entropy Changes for the Transfer from Water to Air (aw), and from the Pure Organic Liquid to Air (vap) or Water (w) for Some Selected Organic Compoundsa

Molecular Interactions Governing the Aqueous Activity Coefficient

269

First, let us compare the relative importance of the entropy versus enthalpy contributions to the standard free energy of the three phase transfer processes. As seen in Chapter 8 (Fig. 8.5) and as is evident from Table 9.2, for vaporization at 25◦ C, the enthalpy contribution is always larger than the entropy contribution. A similar picture is obtained for the transfer of an organic compound between an organic solvent (l ) and air (see Chapter 10). In contrast, when transferring an organic compound from water to the gas phase (air), the entropy term becomes much more important, and in most cases, is even the dominant term. This is due to the large excess entropy of organic chemicals in water, which disfavors their presence in the aqueous phase. Looking at the transfer from pure liquid to water, for some of the smaller compounds (e.g., hexane, octane, PCE, benzene, 1-hexanol, phenol, 3-methylphenol in Table 9.2), the enthalpy that has to be “spent” to isolate the molecules from their pure liquid is about equal to the enthalpy gained when inserting the compound in water; the excess enthalpy is close to zero. For the monopolar compound MTBE, the excess enthalpy is even significantly negative because the MTBE molecules may undergo H-bonding in aqueous solution but not in their pure liquid phase. For larger compounds such as the PAHs or polychlorinated aromatic compounds, the excess enthalpy becomes larger, but the entropy term is still an important factor in determining the “dislike” of the compound for the aqueous phase. This entropic effect explains what is often referred to as “hydrophobicity.” An extreme case involves the monopolar cyclic polydimethylsiloxanes (D5, D6); these compounds exhibit a negative excess enthalpy but also an extremely large negative entropy term. The net result is that they are highly hydrophobic. In summary, when transferring a compound to or from water, the entropy effect primarily determines the “dislike” of the aqueous phase (i.e., making GEi positive). The reasons for these large unfavorable entropy terms are not easy to rationalize because, as already stated, exactly how the water molecules arrange themselves around a given organic molecule is not clear. Conceivably, the water molecules forming a hydration shell around the organic compound lose some of their freedom of motion as compared to the bulk water molecules. More likely, however, the major contribution to this entropy term is the loss of freedom that the compound itself experiences when being transferred from its pure liquid into an environment that is more “rigid;” it is now surrounded by many solvent molecules that are interconnected by hydrogen bonds. Moving from a liquid to a more solid-like environment (thus losing translational, rotational, and conformational freedom, see Box 8.1) could also explain the quite substantial differences in excess entropy found between rigid E E = –44 J mol–1 K–1 ) and aliphatic (e.g., decane, Siw = aromatic (e.g., naphthalene, Siw –1 –1 –121 J mol K ) compounds of the same carbon number (Table 9.2), the latter having more degrees of conformational freedom in the gas or liquid phase. When compared to the entropies of freezing (negative entropy of fusion) of the two compounds at their melting points, one finds remarkably similar values, i.e., Δfus Si (Tm ) = −53 and –118 J mol–1 K–1 , respectively (Table 8.2). Inspecting the excess entropies of other compounds included in Table 9.2 shows the same qualitative picture, in that the more rigid compounds (i.e., PAHs, chlorobenzenes, and lindane) exhibit

270

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

distinctly lower excess entropies than the compounds with a less rigid structure (i.e., PCBs and cyclic polydimethylsiloxanes). Finally, we note that introducing a bipolar group such as an OH diminishes the excess entropy of both rigid and more flexible compounds, as is illustrated by phenol or 3-methylphenol versus benzene and by 1-hexanol and 1-octanol versus hexane and octane respectively. Due to H-bonding, the entropy of bipolar compounds in their pure liquid is lower as compared to the entropy of the structurally related apolar or monopolar compounds, thus leading to a comparably smaller loss in entropy when they transfer into water. The same reasoning explains their higher entropies of vaporization (Table 9.2), as we have already discussed in Section 8.2 when introducing the Fishtine constant (Eq. 8-16) for estimation of the entropy of vaporization of organic compounds at their boiling point.

9.3

LFERs for Estimating Air–Water Partition Constants and Aqueous Activity Coefficients/Aqueous Solubilities Air–Water Partition Constant pp-LFER. Using the pp-LFER approach described in Section 7.4, we may apply an equation published by Goss (2006) for estimating the air–water partition constant at 25◦ C: log Kiaw (298K) = 2.55Vi − 0.48Li − 2.07Si − 3.67Ai − 4.87Bi + 0.59 (number of chemicals = 390; r2 = 0.99; S.D. = 0.12)

(9-18)

From the examples given in Table 9.3 and other applications reported in the literature (e.g., Goss, 2006), we may conclude that Eq. 9-18 allows prediction of air–water partition constants within a factor of 2 to 3. Table 9.3 illustrates how the different terms in Eq. 9-18 contribute to the overall air–water partition constant of some selected compounds. Let us first compare all compounds that contain six carbon atoms (i.e., from hexane to phenol), that is, compounds of a similar size. For both the aliphatic (the first seven) as well as for the aromatic (the next three) compounds in Table 9.3, the (vVi – lLi ) term, which encompasses the free energy contributions of cavity formation, London dispersive vdW interactions, and entropy effects (see Chapter 7), is positive, thus favoring the gas phase. However, the total of these terms is larger for aliphatic as compared to aromatic compounds, which can be partly explained by the larger entropy gain when transferring a more flexible aliphatic compound from water to air as compared to transferring a more rigid aromatic compound (see Table 9.2). A much smaller or even negative (vV– lL) term is found for the larger, more rigid PAHs. In contrast, for the large, flexible telomer alcohols (e.g., 8:2 FTOH) or polydimethylsiloxanes (e.g., D5), which also exhibit weak vdW interactions, this term is very large. Looking for other terms in Table 9.3 that favor the aqueous phase, we find that the polarizability term (sS) is particularly important for PAHs. Furthermore, as we would

LFERs for Estimating Air-Water Partition Constants

271

Table 9.3 Contribution of the Different Terms in Eq. 9-18 to the Calculated Air–Water Partition Constant for Some Selected Compoundsa at 25◦ C log Kiaw b

log Kiaw = (Eq. 9-18)

+2.55Vi −0.48Li

−2.07Si

−3.67Ai

−4.87Bi

+0.59

n-hexane di-n-propyl ether 1-hexanal 2-hexanone n-hexylamine 1-hexanol n-hexanoic acid benzene aniline phenol

+1.74 −0.97 −2.06 −2.43 −2.90 −3.23 −4.56 −0.65 −4.03 −4.79

+1.73 −0.96 −2.09 −2.39 −2.77 −3.13 −4.28 −0.67 −4.14 −4.74

+1.14 +1.16 +0.86 +0.91 +0.92 +0.85 +0.85 +0.50 +0.20 +0.18

0.00 −0.52 −1.35 −1.41 −0.72 −0.87 −1.30 −1.08 −1.99 −1.84

0.00 0.00 0.00 0.00 −0.59 −1.36 −2.28 0.00 −0.95 −2.20

0.00 −2.19 −2.19 −2.48 −2.97 −2.34 −2.14 −0.68 −2.00 −1.46

+0.59 +0.59 +0.59 +0.59 +0.59 +0.59 +0.59 +0.59 +0.59 +0.59

naphthalene phenanthrene pyrene benzo(a)pyrene

−1.73 −2.76 −3.27 −4.51

−1.80 −3.11 −3.79 −5.22

+0.28 +0.06 −0.19 −0.53

−1.80 −2.59 −2.98 −3.77

0.00 0.00 0.00 0.00

−0.88 −1.17 −1.22 −1.51

+0.59 +0.59 +0.59 +0.59

8:2 FTOH D5

+0.58 +3.15

+0.51 +3.32

+4.00 +4.96

−0.29 +0.20

−2.28 0.00

−1.51 −2.44

+0.59 +0.59

Compound

a b

The solute parameters of the compounds are given in Appendix C. Experimentally derived log Kaw values given in Appendix C.

expect, the air–water partition constants of polar compounds are significantly determined by their H-bonding properties. In the case of bipolar functional groups such as hydroxyl or amino groups, we note that the relative importance of the H-donor (aA) versus H-acceptor (bB) term is quite different for aliphatic versus aromatic compounds (e.g., 1-hexanol versus phenol or n-hexylamine versus aniline). Because of resonance with the aromatic ring, the nonbonding electrons in phenol or aniline are weaker Hacceptors, whereas the H atoms bound to the oxygen or nitrogen atom, respectively, are more acidic and thus better H-donors in the aromatic versus aliphatic compounds (see also Chapter 4, Section 4.4). Bond Contribution Method. In addition to the more sophisticated pp-LFER method, we now briefly address a simple LFER approach to estimate Kiaw values that is based solely on chemical structure. The underlying idea of this LFER, which was introduced by Hine and Mookerjee (1975) and expanded by Meylan and Howard (1991), is similar to the fragment contribution method (Section 7.3, Eq. 7-6). In this method, each bond type (e.g., a C−H bond) is taken to have a substantially constant effect on Δaw Gi , regardless of the compound in which the bond occurs. This assumption is reasonably valid for simple molecules with no significant interactions between functional groups. Therefore, the method is interesting from a didactic point of view as we can directly see how certain substructural units affect air–water partitioning.

272

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

Table 9.4 summarizes bond contribution values derived by Meylan and Howard (1991) from a large data set at a temperature of 25◦ C. Some included values are for a singly bonded aliphatic carbon bound to hydrogen (C−H, 0.1197), an aromatic carbon bound to chlorine (Car −Cl, –0.3335), and an aliphatic carbon bound to a doubly bonded (olefinic) carbon (C−Cd , –0.0635). Such values can be used to calculate log Kiaw by simple addition: log Kiaw (25 ◦ C) =

∑

(number of bonds type k)(contribution of bond type k)

k

(9-19) By looking at the signs and values of each bond contribution, we readily see that units such as C−H bonds, and, particularly, C−F bonds tend to encourage molecules to partition into the air, while other units, like O−H or those groups containing oxygen or nitrogen, strongly induce molecules to remain associated with water. These tendencies correspond to the expected behaviors deduced qualitatively from our previous discussion of intermolecular interactions of organic molecules with water. For simple molecules, this contribution approach is usually accurate to within a factor of 2 or 3. One major drawback, however, is that it does not account for special intermolecular or intramolecular interactions that may be unique to the molecule in which a particular bond type occurs. Therefore, additional correction factors may have to be applied (Meylan and Howard, 1991). Furthermore, we stress the limited applicability of this simple approach for prediction of Kiaw values of more complex molecules.

9.4

Effect of Temperature, Dissolved Salts, and pH on the Aqueous Activity Coefficient/Aqueous Solubility and on the Air–Water Partition Constant So far, we have focused on how differences in molecular structure affect aqueous solubility, activity coefficients, and air–water partitioning of organic compounds in pure water at 25◦ C. The next step is to evaluate the influence of some important environmental factors on these properties. In this section, we consider three such factors: temperature, ionic strength (i.e., dissolved salts), and pH. Effect of Temperature Solubility and Aqueous Activity Coefficient. In Chapter 4 (Section 4.2), we have seen that, when assuming a constant Δ12 Hi over a narrow temperature range, the temperature dependence of any partition constant can be expressed by: ln Ki12 = −

Δ12 Hi 1 ⋅ + constant R T

(9-22)

Effect of Temperature, Dissolved Salts, and pH

273

Table 9.4 Bond Contributionsa for Estimation of log Kiaw at 25◦ C Bondb C−H C−C C − Car C − Cd C − Ct C − CO C−N C−O C−S C − Cl C − Br C−F C−I C − NO2 C − CN C–P C=S Cd − H Cd = Cd Cd − Cd Cd – CO Cd – Cl Cd – CN Cd – O Cd – F Ct – H Ct ≡ Ct Car – H Car – Car Car – Car Car – Cl a

Bond Contribution +0.1197 −0.1163 −0.1619 −0.0635 −0.5375 −1.7057 −1.3001 −1.0855 −1.1056 −0.3335 −0.8187 +0.4184 −1.0074 −3.1231 −3.2624 −0.7786 +0.0460 +0.1005 −0.0000d −0.0997 −1.9260 −0.0426 −2.5514 −0.2051 +0.3824 −0.0040 −0.0000d +0.1543 −0.2638f −0.1490g +0.0241

Bondb Car – OH Car – O Car – Nar Car – Sar Car – Oar Car – S Car – N Car – I Car – F Car – Cd Car – CN Car – CO Car – Br Car –NO2 CO – H CO – O CO – N CO – CO O–H O–P O–O O=O N–H N–N N=O N=N S–H S–S S–P S=P

Bond Contribution −0.5967c −0.3473c −1.6282 −0.3739 −0.2419 −0.6345 −0.7304 −0.4806 +0.2214 −0.4391 −1.8606 −1.2387 −0.2454 −2.2496 −1.2102 −0.0714 −2.4261 −2.4000 −3.2318 −0.3930 +0.4036 −1.6334 −1.2835 −1.0956e −1.0956e −0.1374 −0.2247 +0.1891 −0.6334 +1.0317

Data from Meylan and Howard (1991). C: single-bonded aliphatic carbon (note that for linear and branched alkanes a correction term of +0.75 has to be added to Eq. 9.19 (Meylan and Howard, 1991); Cd : olefinic carbon; Ct : triple-bonded carbon; Car : aromatic carbon; Nar : aromatic nitrogen; Sar : aromatic sulfur; Oar : aromatic oxygen; CO: carbonyl (C = O); CN: cyano (C ≡ N). Note: the carbonyl, cyano, and nitrofunctions are treated as single atoms. c Two separate types of aromatic carbon-to-oxygen bonds have been derived: (a) the oxygen is part of an –OH function, and (b) the oxygen is not connected to hydrogen. d The C = C and C ≡ C bonds are assigned a value of zero by definition (Hine and Mookerjee, 1975). e Value is specific for nitrosamines. f Intra-ring aromatic carbon to aromatic carbon. g External aromatic carbon to aromatic carbon (e.g., biphenyl). b

274

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

Recalling from Chapter 4 that we use the pure organic liquid as the reference state, we omit the Δ-notation, and we now express the temperature dependence of the aqueous solubility of liquid, solid, and gaseous compounds respectively as: sat ln Ciw (L) = −

ln 𝛾 sat iw = + sat ln Ciw (s) = −

sat (g) = − ln Ciw

E Hiw

E Hiw

1 + constant′ T

⋅

1 + constant T

E −Δvap Hi + Hiw

R

1 + constant T

⋅

R

E Δfus Hi + Hiw

R

⋅

R

⋅

1 + constant T

(9-23a) for liquids (9-23b)

for solids

for gases

(9-24)

(9-25)

In Eqs. 9-23 to 9-25, we use molar concentrations instead of mole fractions, as we assume that the molar volume of the aqueous solution is temperature-independent over the temperature range considered. Let us first consider the temperature dependence of the liquid aqueous solubility (Eq. 9-23a) and of the linked aqueous activity coefficient (Eq. 9-23b). We recall from Chapter 4 (Table 4.3) that a Δ12 Hi value of ± 30 kJ mol–1 means a factor of approximately 1.5 change in Ki12 . Inspection of Table 9.2 shows that for many compounds, E E is rather small and may even be negative. Even for very large molecules, Hiw Hiw –1 never exceeds ± 30 kJ mol . Therefore, in contrast to vaporization or air–water partitioning (see Table 9.2 and subsequent discussion), the change in liquid aqueous solubility, and thus in the aqueous activity coefficient, with increasing/decreasing E temperature is rather small. Furthermore, at temperatures above about 40◦ C, Hiw becomes increasingly more positive because the number of hydrogen bonds among E is constant the water molecules decreases. In fact, we cannot actually assume that Hiw over the ambient temperature range, which is, however, not too much of a problem for solubility approximations since the temperature effect is small anyway. If we want to E values determined at high temperatures (i.e., ≫ 40◦ C) to the ambient extrapolate Hiw temperature range, we have to be cautious. When we are interested in the solubilities of solids or gases, the effect of temperature becomes much more important. Now, we must consider the total enthalpy change when transferring a molecule from the solid or gas phase to water. This total enthalpy change includes the sum of the enthalpy of the phase change (i.e., conversion of a solid into a subcooled liquid or a gas into a superheated liquid at the temperature of interest) and the excess enthalpy of solution (Eqs. 9-24 and 9-25 respectively). In general, the resulting enthalpy change will be positive in the case of solids, due to the large positive Δfus Hi , and negative in the case of gases, from the positive Δvap Hi . Consequently, the solubility of solids increases with increasing temperature, since the “cost” of melting decreases with increasing temperature and becomes zero at the melting point. Conversely, the difficulty in condensing gaseous organic compounds increases

Effect of Temperature, Dissolved Salts, and pH

275

with increasing temperature; thus, heating an aqueous solution tends to decrease the solubility of organic gases. Air–Water Partition Constant. For the air–water partition constant, the effect of temperature is given by: ln Kiaw = −

Δaw Hi 1 ⋅ + constant R T

(9-26)

E where Δaw Hi = Δvap Hi − Hiw (Fig. 9.2). We recall from Chapter 4 that the molar volume of gases is temperature dependent and if Ki12 is expressed in molar concentrations, Δ12 Hi has to be replaced by Δ12 Hi + RTav , where Tav is the average temperature (in K) of the temperature range considered (see Atkinson and Curthoys, 1978). However, because RTav is only about 2.5 kJ mol–1 , we neglect this term. From the examples given in Table 9.2, we can see that Δaw Hi is similar or smaller than Δvap Hi E for most compounds. For compounds exhibiting a relatively large negative Hiw and a large Δvap Hi (e.g., D5, D6), the temperature effect can be as much as a factor of 3 to 4 per 10◦ C temperature change.

Mintz et al. (2008) have published a pp-LFER (Eq. 9-27) that allows one to estimate Δaw Hi values: Δaw Hi (kJ mol−1 ) = 17.3Vi + 1.4Li − 0.73Si + 33.6Ai + 43.5Bi + 8.4 (number of chemicals = 368; r2 = 0.94; S.D. = 4.7)

(9-27)

The scatter in this relation is somewhat large, which could be explained by the fact that the relative enthalpy and entropy contributions to the standard free energy of air–water partitioning differ between different compound classes (Table 9.2). A more uniform proportionality between enthalpy and entropy, which we have encountered for vaporization (Fig. 8.5), would be necessary to get a better predictive tool. Nevertheless, Eq. 9-27 allows us to predict Δaw Hi values within about ± 10 kJ mol–1 (±2 S.D.), which, for practical purposes, is often quite sufficient. Another alternative to estimate the effect of temperature on Kiaw is to use pp-LFERs, like Eq. 9-18, with the temperature-dependent system descriptors reported in Goss (2006). Effect of Dissolved Inorganic Salts When considering saline environments (e.g., seawater, salty lakes, or subsurface brines), we have to consider the effects of dissolved inorganic salts on aqueous solubilities, aqueous activity coefficients, and, consequently, on all partitioning processes involving water. Although the number of studies that have been devoted to this topic is still rather small, a few important conclusions can be drawn. Qualitatively, one observes that the presence of the predominant inorganic ionic species found in natural ) generally decreases the waters (i.e., Na+ , K+ , Mg2+ , Ca2+ , Cl– , HCO−3 HCO−3 , SO2− 4 aqueous solubility and increases the aqueous activity coefficient. Thus, the air–water partition constant, particularly of larger nonpolar or weakly polar organic compounds,

276

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

0.7

log (

9

Ciwsat s ) = Ki [salt]tot sat Ciw, salt

s

Ki s

Ki

0.5

=

0.

0.4 0.3 s

=

NaCl artifical seawater natural seawater

i

K

0.2 0.1

Figure 9.3 Effect of salt concentration on the aqueous solubility of benzene and naphthalene. Data from McDevit and Long (1952) and Gordon and Thorne (1967a).

0.1

22

0. 26

sat Ciw, salt

log (

Ciwsat

)

0.6

=

Ki

0

1

s

(mol L–1)

2

3

4

[salt]tot (mol L ) –1

is increased with increasing dissolved salt. The magnitude of this effect, which is commonly referred to as salting-out, depends on the compound and on the type of ions present. Long ago, Setschenow (1889) established an empirical formula relating organic comsat sat ) to those in pure water (Ciw ): pound solubilities in saline aqueous solutions (Ciw,salt log

sat Ciw sat Ciw,salt

= Kis [salt]tot

or

(9-28) sat sat −Ki [salt]tot Ciw,salt = Ciw 10 s

where [salt]tot is the total molar salt concentration and Kis is the Setschenow or salting constant (units M–1 ). The salting constant relates the effectiveness of a particular salt or combination of salts to change the solubility of a given compound i. As salt concentration increases, the salting-out effect exponentially increases (Fig. 9.3). For a particular salt (e.g., NaCl) or salt mixture (e.g., seawater; for composition see Table 9.5), Eq. 9-28 is valid over a wide range of salt concentrations. Kis values for a given organic solute and salt composition can be determined experimentally by linear regression of experimental solubilities measured at various salt concentrations (i.e., sat versus [salt]tot ). We assume the effect of salt on the molar volume of plots of log Ciw the solution is minor and 𝛾 iw,salt , the activity coefficient in saline solution, is valid for saturated and dilute conditions. Written in terms of activity coefficients, Eq. 9-28 is: 𝛾 iw,salt = 𝛾 iw ⋅ 10+Ki [salt]tot s

(9-29)

Effect of Temperature, Dissolved Salts, and pH

277

Table 9.5 Salt Composition of Seawater and Salting Constants for Benzene, Naphthalene, and 1-Naphthol at 25◦ C for Some Important Salts Salting constanta

Salt NaCl MgCl2 Na2 SO4 CaCl2 KCl NaHCO3 KBr CsBr (CH3 )4 NCl (CH3 )4 NBr a b

Weight (g mol–1 ) 58.5 95.3 142.0 110.0 74.5 84.0 119.0 212.8 109.6 154.1

Mole fraction in seawaterb xsalt 0.799 0.104 0.055 0.020 0.017 0.005

Kis (benzene) (L mol–1 )

Kis (naphthalene) (L mol–1 ) 0.22 0.30 0.72 0.32 0.19 0.32 0.13 0.01

0.19 0.53 0.16

−0.15

Kis (1-naphthol) (L mol–1 ) 0.21 0.33 0.35 0.18 0.13 −0.36

Data from McDevit and Long (1952); Gordon and Thorne (1967a,b); Almeida et al. (1983); and Sanemasa et al. (1984). ∑ Data from Gordon and Thorne (1967a,b). The mole fraction refers to the mole fraction of the total salt, that is, xsalt = 1.

and, similarly, for the air–water partition constant: Kiaw,salt = Kiaw ⋅ 10+Ki [salt]tot s

(9-30)

Therefore, 𝛾 iw,salt and Kiaw,salt increase exponentially with increasing salt concentration. For a given salt concentration, the standard free energy of transferring a solute from pure water to the salt solution, Δw,salt Gi , is related to Kis by: Δw,salt Gi = RT ln 𝛾 iw,salt ∕𝛾 iw = 2.303RT Kis [salt]tot

(9-31)

Before we inspect Kis values of a variety of organic compounds for seawater, we first take a look at the salting-out efficiencies of various ion combinations. Salting constants are available only for combined salts, not single ions. Nevertheless, the data in Table 9.5 illustrate that smaller ions (e.g., Na+ , Mg2+ , Ca2+ , Cl– ), which form hydration shells with more water molecules, have a bigger effect on solubility than larger ions (e.g., Cs+ , N(CH3 )4 + , Br– ) that tend to weakly bind water molecules. In fact, larger organic ions such as tetramethyl-ammonium (N(CH3 )4 + ) can even have a positive effect, a salting-in effect; that is, they promote solubility and a decrease in the activity coefficient. Such salting-in effects can also be observed for very polar compounds that may strongly interact with certain ions (Almeida et al., 1983). In a simple way, we can rationalize the salting-out of nonpolar and weakly polar compounds by imagining that the dissolved ions successfully compete with the organic compound for solvent molecules. Many environmentally relevant ions bind water molecules quite tightly in aqueous solution, which can even be seen macroscopically when the volume of the aqueous solution reduces upon dissolution. As a consequence, the number of “free” water molecules to solvate an organic molecule is changed, which depending

278

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

on the type of salt or compound present, may lead to a loss or gain in solubility. Also, the compound itself may lose further translational, rotational, and conformational freedom. In fact, the rather restricted number of studies on the thermodynamics of the transfer of organic compounds from pure water to saltwater (Eq. 9-31) report very small positive or even negative Δw,salt Hi values, thus suggesting a negative entropy effect to be primarily responsible for the salting-out effect (Gold and Rodriguez, 1989; Prak and O’Sullivan, 2009; Aria-Gonzalez et al., 2010). The small Δw,salt Hi values also mean that, over the ambient temperature range, we may assume a constant Kis . Let us now look at the effect of the various salts on the overall salting-out constant of an organic compound in seawater, the most important natural saline environment. We chose naphthalene as a model compound. First, using the data given in Table 9.5, we can make our own artificial seawater with respect to the major ion composition by dissolving an appropriate amount of the corresponding salts in water. The weight of 1 mole of “seawater salt” is given by (0.799) (58.5) + (0.104) (95.3) + (0.055) (142) + (0.02) (110) + (0.017) (74.5) + (0.005) (84) = 68.35 g. Hence, if we dissolve 34.17 g of seawater-salt in 1 L total volume, we obtain seawater with a salinity of about 34‰, which corresponds to a total molar salt concentration ([salt]tot ) of about 0.5 M. As has been demonstrated by various studies, the differences between Kis values determined in artificial and real seawater are usually only marginal (see Xie et al., 1997). Furthermore, since seawater is dominated by one salt, that is, NaCl (Table 9.5), as a first approximation, Kis values determined for sodium chloride can be used as a surrogate. s for naphthalene using the data given in Table 9.5. We Let us calculate Ki,seawater s estimate Ki,seawater by summing up the contributions of the various salts present (Gordon and Thorne, 1967a,b): s ≅ Ki,seawater

∑ k

s Ki,salt k ⋅ xk

(9-32)

s where xk is the mole fraction and Ki,saltk is the salting constant of salt k in the mixture. For naphthalene, we then obtain: s Ki,seawater = (0.799)(0.22 M−1 ) + (0.104)(0.30 M−1 ) + (0.055)(0.72 M−1 )

+(0.02)(0.32 M−1 ) + (0.017)(0.19 M−1 ) + (0.005)(0.32 M−1 ) = 0.26 M−1 which is close to the experimental value for seawater (average value 0.27 M–1 ). The Kis value of naphthalene for NaCl is 0.22 M–1 . Hence, the contribution of the other salts is only 0.04 M–1 . With insertion of the two Kis values into Eqs. 9-29 and 9-30 and assuming a [salt]tot = 0.5 M (typical seawater, see also Chapter 5), we obtain s s and 1.35 for Ki,seawater . In general, 𝛾 iw,salt ∕𝛾 iw and Kiaw,salt ∕Kiaw ratios of 1.3 for Ki,NaCl s s the error introduced when using Ki,NaCl instead of Ki,seawater is only on the order of 10%, which is often well within the experimental error of Kis measurements. Therefore, many Kis values available in the literature have been determined for NaCl, used as a reasonable surrogate for seawater. Larger compilations of Kis values can be found in Ni and Yalkowsky (2003) and Endo et al. (2012). In addition, a series of Kis values of

Effect of Temperature, Dissolved Salts, and pH

279

Table 9.6 Experimental and Estimated (Eq. 9-33) Kis values of NaCl Solutions or Seawater (sw) of Some Selected Compoundsa s Ki,NaCl = calc.

+0.21Vi – 0.013Li

−0.031Si

−0.049Ai

−0.057Bi

+0.103

0.28 0.20 0.23 0.22 0.31 0.19 0.11

0.27 0.21 0.21 0.19 0.30 0.18 0.14

+0.17 +0.16 +0.17 +0.17 +0.25 +0.11 +0.12

0.00 −0.02 −0.01 −0.02 −0.02 −0.02 −0.03

0.00 0.00 −0.02 −0.03 0.00 0.00 −0.03

0.00 −0.03 −0.03 −0.03 −0.03 −0.01 −0.02

+0.10 +0.10 +0.10 +0.10 +0.10 +0.10 +0.10

0.22 0.27 0.30 (sw) 0.32 0.30 (sw) 0.33 0.34 (sw)

0.22 0.26

+0.16 +0.21

−0.03 −0.04

0.00 0.00

−0.01 −0.01

+0.10 +0.10

0.26

+0.22

−0.04

0.00

−0.02

+0.10

0.29

+0.27

−0.06

0.00

−0.02

+0.10

0.38 n.a.

0.39 0.62

+0.34 +0.55

−0.01 +0.00

−0.03 0.00

−0.01 −0.03

+0.10 +0.10

Compound

Kis exp.b

n-hexane 2-hexanone 1-hexanol n-hexanoic acid 2-decanone benzene phenol naphthalene phenanthrene pyrene benzo(a)pyrene 6:2 FTOH D5 a b

The solute parameters of most compounds are given in Appendix C; 2-decanone parameters from UFZ-LSER database (Endo et al., 2014). Experimental Kis data from Ni and Yalkowsky (2003) and Endo et al. (2012).

a diverse set of organic compounds for ammonium sulfate ((NH4 )2 SO4 )), including a pp-LFER as given below for NaCl, is reported by Wang et al. (2014). Table 9.6 gives experimental Kis values for NaCl solutions for some representative compounds including some of our companion compounds. Also included in Table 9.6 are estimated values using a pp-LFER derived by Endo et al. (2012) and Endo (2014, personal communication): s (M−1 ) = 0.21Vi − 0.013Li − 0.031Si − 0.049Ai − 0.057Bi + 0.103 KiNaCl

(number of chemicals =

43; r2

(9-33)

= 0.84; S.D. = 0.031)

We recall that Kis is directly related to a free energy term (Eq. 9-31), and therefore, its description by a pp-LFER is feasible. We should note, however, that Eq. 9-33 has been derived from a rather small, although structurally diverse, set of compounds. Nevertheless, Eq. 9-33 is a useful tool to estimate Kis values of organic compounds, and it allows us to see how compound characteristics affect Kis . Some general trends can be seen by analyzing the data in Table 9.6. First, Kis values of organic compounds for NaCl solutions cover a range of between 0.1 and 0.6, and they tend to increase with increasing size. Second, mono- and bipolar substituents decrease Kis , most likely by diminishing the number of “free” water molecules. This is evident when comparing 2-hexanone, 1-hexanol, and n-hexanoic acid with n-hexane,

280

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

or phenol with benzene. Third, aliphatic compounds tend to have significantly higher Kis values than aromatic compounds exhibiting the same number of carbon atoms (e.g., hexane versus benzene). Similarly, with increasing size, Kis values of aliphatic compounds increase much more pronounced as compared to aromatic compounds (e.g., 2-decanone as compared to 2-hexanone versus naphthalene compared to benzene). Consequently, within a compound class, the range of Kis is larger for compounds exhibiting aliphatic moeties as compared to aromatic compounds. For example, for PAHs (Kis = 0.22–0.36) or chlorinated benzenes (Kis = 0.2–0.3), the range covers less than 0.2, whereas for the dialkyl phthalates (Kis = 0.2–0.6), the range is much larger (Endo et al., 2012). This difference between aromatic and aliphatic compounds is primarily due to the difference between the cavity formation term (+0.21Vi ), which promotes salting-out, and the vdW and polarizability terms (–0.013Li –0.031Si ). Therefore, similar to the air–water partition constant (Table 9.3), large Kis values can be expected for large compounds exhibiting weak vdW and polarizability interactions, such as the polyfluorinated telomer alcohols (e.g., 6:2 FTOH), and particularly, the polydimethylsiloxanes (e.g., D5). In summary, we can conclude that at moderate salt concentrations typical for seawater (∼ 0.5 M), salinity will affect aqueous solubility, the aqueous activity coefficient, and air– or organic solvent–water partition constants by a factor of between 1.1 (Kis = 0.1; small, rigid polar compounds) and about 2 (Kis = 0.6; large, flexible compounds exhibiting low vdW interactions). Hence, in marine environments, salting-out will not be a major factor in determining the partitioning behavior of many compounds. However, in environments exhibiting much higher salt concentrations (e.g., in the Dead Sea (5 M) or in subsurface brines near oil fields), salting-out can be substantial because of the exponential relationship (Eqs. 9-28 to 9-30). Effect of pH on Aqueous Solubility and Air–Water Partitioning of Organic Acids and Bases The water solubility of the ionic form (salt) of an organic acid or base is generally sat ) several orders of magnitude higher than the solubility of the neutral species (Ciw of the compound. The total concentration of the compound, that is, the sum of nondissociated (HA and BH+ for acids and bases, respectively) and dissociated (A– and sat , is, therefore, in contrast to neutral comB, respectively) forms at saturation, Ciw,tot pounds, strongly pH-dependent. As has been demonstrated for pentachlorophenol (Arcand et al., 1995) and as illustrated schematically for an organic acid in Fig. 9.4 (line a), at low pH, the saturation concentration is given by the solubility of the neutral sat is determined by the fraction in HA form, αia : compound. At higher pH values, Ciw,tot sat Ciw,tot

=

sat Ciw

αia

for organic acids

(9-33)

where, as we recall from Chapter 4 (Eq. 4-59): αia =

1 1 + 10pH−pKia

(4-59)

Effect of Temperature, Dissolved Salts, and pH

281

id ia

an

ic

α

ac

iw

C sa

rg

=

)o

(a

C

pKia

s iw at ,to t

t

ia

α e 1– as b c ni

ga

sat log Ciw,tot

sa

or

C iw

) (b

Figure 9.4 Schematic representation of the total aqueous solubility of (a) an organic acid and (b) an organic base as a function of pH. For simplicity, the same pKa values and maximum solubilities of the neutral and charged (salt) species have been assumed.

t = sa ,tot

C iw

t

maximum concentration determined by the solubility product of the corresponding salts

sat log Ciw,tot

sat log Ciw,tot

(a)

(b) pH

Equation 9-33 is valid only up to the solubility product of the salt of the ionized organic species, which is dependent on the type of counterions present. Unfortunately, solubility data of organic salts are rather scarce. In the case of an organic base, the situation is symmetrical to the one shown in sat Fig. 9.4 (line a), in that the BH+ form dominates at low pH. Hence, Ciw,tot is given by [Fig. 9.4 (line b)]: sat Ciw,tot =

sat Ciw

1 − αia

for organic bases

(9-34)

When considering the air–water equilibrium partitioning of an organic acid or base, we may, in general, assume that the ionized species will not be present in the gas phase. The air–water distribution ratio of an organic acid, iaw (note that we speak of a ratio and not of a partition constant since we are dealing with more than one species), is then given by: iaw =

[HA]a [HA]w + [A− ]w

(9-35)

Multiplication of Eq. 9-35 with [HA]w / [HA]w (= 1) and rearrangement shows that iaw is simply given by the product of the fraction in the HA form (αia ) and the air– water partition constant of the neutral compound (Kiaw ): iaw =

[HA]w [HA]a ⋅ = αia Kiaw − [HA]w + [A ]w [HA]w

for organic acids

(9-36)

By analogy, we obtain: iaw = (1 − αia )Kiaw

for organic bases

(9-37)

282

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

9.5

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Questions Q 9.1 What is meant by the term water solubility or aqueous solubility of a given compound? What is the range of aqueous solubilities encountered when considering environmentally relevant organic chemicals? Is there such a thing as a water insoluble compound, as often stated in handbooks? Q 9.2 How is the aqueous activity coefficient of a compound related to the aqueous solubility, if the compound is a (a) liquid, (b) solid, (c) gas under the prevailing conditions? Comment on any assumption that you make when answering this question. Q 9.3 Frequently, the air–water partition constant of a given organic compound is estimated from its vapor pressure and its aqueous solubility. What are the assumptions made when using this approximation? Are there cases in which this approach is questionable? If yes, in which cases? Q 9.4 What could be the reason why the excess enthalpy of MTBE in water is so much more negative than the excess enthalpy of 1-hexanol, which has a similar size? The values are given in Table 9.2. Q 9.5 Explain the following observations (see also Table 9.2): (a) the excess entropies in water of alkanes are generally much larger than those of aromatic compounds of similar size, and (b) the excess entropies in water of phenol and hexanol are smaller than those of benzene and hexane respectively.

Q 9.6 Explain qualitatively how the aqueous solubility of a (a) liquid, (b) solid, and (c) gaseous compound changes with temperature. Which thermodynamic quantities do you need to know to quantify this temperature dependence?

Questions and Problems

283

Q 9.7 In many cases, the temperature dependence of the air–water partition constant of a given compound has not been experimentally determined. Describe two different approaches how this temperature dependence can be estimated. Q 9.8 Explain in words how environmentally relevant inorganic dissolved salts affect the aqueous solubility of an organic compound? Is it true that the effect is linearly related to the concentration of a given salt? What is the magnitude of the effect of salt on (a) the aqueous activity coefficient, and (b) on the air–water partition constant of organic compounds in seawater? Q 9.9 Which compound characteristics primarily determine the magnitude of the salting constant (Setschenow constant) of a given compound in a sodium chloride solution? Q 9.10 Consider the air–water partitioning of an organic acid and an organic base both (neutral compound) and a pKia value of 6 (note exhibiting a Kiaw value of 0.01 Lw L−1 a that for the base this is the pKia of the conjugated acid, see Chapter 4). What is their air–water distribution ratio at pH 4 and 7, respectively? Problems P 9.1∗ Deriving Aqueous Activity Coefficients from Experimental Solubility Data and Using pp-LFERs , of the companion compounds MTBE, Calculate the aqueous activity coefficients, 𝛾 sat iw atrazine, and methyl bromide at 25◦ C from (a) experimental solubility data, and (b) using only pp-LFERs. Compare the results. All necessary data is provided in Appendix C. Comment on any assumption that you make. P 9.2∗ Estimating Air–Water Partition Constants by the Bond Contribution Method i = n-hexane

i = benzene

P 9.3∗ A Tricky Stock Solution

O i = di-n-propyl ether OH

i = phenol

Estimate the Kiaw values at 25◦ C of (a) n-hexane, (b) benzene, (c) di-n-propyl ether, and (d) phenol using the bond contribution values given in Table 9.4. Compare these values with the experimental air–water partition constants given in Table 9.3. Remember that for a linear or branched alkane (i.e., hexane) a correction factor of +0.75 log units has to be added (footnote b in Table 9.4).

You work in an analytical laboratory and are asked to prepare 250 mL of a 0.5 M stock solution of anthracene using toluene as solvent (the density of toluene is 0.87 g cm–1 at 20◦ C). You look up the molar mass of anthracene, go to the balance, weigh out 22.3 g of this compound, put it into a 250 mL volumetric flask, and then fill the flask with toluene. Although your intuition tells you that these two aromatic compounds should form a near-ideal liquid mixture, to your surprise, even after several hours of

284

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

intensive shaking, a substantial portion of the anthracene remains undissolved in the flask. What is the problem? What is anthracene’s concentration in molar units in your stock solution? Give an estimate of how much anthracene has actually been dissolved (in g). P 9.4 Evaluating the Effect of Temperature on the Aqueous Solubility and Aqueous Activity Coefficient of a Solid Compound As you live in a cold area, you want to know the aqueous solubility and aqueous sat activity coefficient of organic compounds at 1◦ C rather than at 25◦ C. Estimate Ciw sat ◦ ◦ (in molar units) and 𝛾 iw of 1,2,3,7-tetrachlorodibenzo-p-dioxin (Tm = 175 C) at 1 C using aqueous solubilities of this compound determined at more elevated temperatures by Friesen and Webster (1990). Also estimate the average excess enthalpy of the compound in water for the temperature range considered. Why are you interested in this quantity? Comment on any assumption that you make. T (◦ C)

7.0

sat Ciw ×1010 (mol L–1 )

7.56

11.5 8.12

17.0

21.0

26.0

12.5

14.9

22.6

P 9.5 Quantifying the Effect of Inorganic Salts on Aqueous Solubility and Aqueous Activity Coefficient (a) Estimate the solubility and the activity coefficient of our companion phenanthrene in (i) seawater at 25◦ C and 30‰ salinity, and (ii) a salt solution containing 117 g NaCl per liter water. (b) At oil exploitation facilities, it is common practice to add salt to the wastewater in order to decrease the solubility of the oil components, although in the wastewater treatment one then has to cope with a salt problem. Calculate how much NaCl you have to add to 1 m3 of water in order to decrease the water solubility of n-hexane by a factor of ten. How much Na2 SO4 would roughly be required to do the same job (assume a factor of 3 times larger Kis for Na2 SO4 as compared to NaCl, see Table 9.6)? P 9.6 A Small Bet with an Oceanographer An oceanography colleague bets you that both the solubility as well as the activity coefficient of naphthalene are larger in seawater (35‰ salinity) at 25◦ C than in distilled water at 5◦ C. You know that aqueous solubility and the aqueous activity coeffisat and 𝛾 sat cient are inversely related, so would you put money on the bet? Estimate Ciw iw ◦ ◦ for naphthalene in seawater at 25 C and in distilled water at 5 C. Discuss the result. Assume that the average enthalpy of solution of (solid) naphthalene is about 30 kJ mol–1 over the ambient temperature range. P 9.7 Evaluation the Direction of Air–Water Exchange at Different Temperature What is the direction of the air–water exchange (into or out of water?) of benzene in a well-mixed shallow pond located in the center of a big city in each of the following seasons: (a) summer (T = 25◦ C), and (b) winter (T = 5◦ C)? In both cases, the

Bibliography

285

concentrations detected in air and water are Cia = 0.05 mg m–3 and Ciw = 0.4 mg m–3 , respectively. Assume that the temperature of the water and the air is the same. Note: The direction of the flux can be assessed from an equilibrium consideration; the rate of air–water exchange will be discussed in Chapter 19. P 9.8 Finding the Original Concentration of Tetrachloroethene (PCE) in Water Samples You are the head of an analytical laboratory, and you check the numbers reported by one of your co-workers from the analysis of tetrachloroethene (PCE, Cl2 C=CCl2 ) in water samples of very different origins, namely (a) moderately contaminated groundwater, (b) seawater ([salt]tot ≅ 0.5 M), and (c) water from a subsurface brine ([salt]tot ≅ 5.0 M). For all samples, your laboratory reports the same PCE concentration of 10 μg L–1 . You read the report more carefully, and you realize that the sample flasks were not completely filled. The 1 L flasks were filled with only 200 mL liquid, and stored at 25◦ C before analysis. What were the original concentrations (in μg L–1 ) of PCE in the three samples? P 9.9 Raining Out of Pesticides The increasing pollution of the atmosphere by organic chemicals is creating a growing concern about the quality of rainwater. This concern makes it important to know how pesticides that are present in gaseous form in the atmosphere are scavenged by rainfall. Although for a quantitative description of this process more sophisticated models are required, some simple equilibrium calculations are already quite helpful (see also Chapter 15). Assume that the pesticides methyl bromide, atrazine, and 2,4-dinitro-6-methylphenol (DNOC) are present in the atmosphere at low concentrations. Consider now a drop of water of 0.1 mL volume and a pH of 6 in a volume of 100 L of air, which corresponds to about the air–water ratio of a cloud (Seinfeld and Pandis, 2006). Calculate the fraction of the total amount of each compound present in the water drop at 25◦ C and 5◦ C assuming equilibrium between the two phases. Comment on any assumptions that you make. What do the results tell you about the potential of the three compounds to be scavenged from the atmosphere by rain? Note: DNOC is a weak acid with a pKia value of 4.31; see Appendix C for all other data. P 9.10 Air–Water Equilibrium Distribution of Organic Acids and Bases in Fog Represent graphically the approximate fraction of (a) total 2,3,4,5-tetrachlorophenol and (b) total aniline present in the water phase of a dense fog (air–water volume ratio about 105 ) as a function of pH (pH-range 2 to 7) at 5 and 25◦ C. Neglect any adsorption to the surface of the fog droplet. Assume a Δaw Hi value of about 70 kJ mol–1 for 2,3,4,5-tetrachlorophenol, and 50 kJ mol–1 for aniline. All other data can be found in Appendix C.

9.6

Bibliography Almeida, M. B.; Alvarez, A. M.; Demiguel, E. M.; Delhoyo, E. S., Setchenow coefficients for naphthols by distribution method. Can. J. Chem.-Rev. Can. Chim. 1983, 61(2), 244–248.

286

Solubility and Activity Coefficient in Water; Air–Water Partition Constant

Arcand, Y.; Hawari, J.; Guiot, S. R., Solubility of pentachlorophenol in aqueous solutions: The pH effect. Water Res. 1995, 29(1), 131–136. Arey, J. S.; Nelson, R. K.; Xu, L.; Reddy, C. M., Using comprehensive two-dimensional gas chromatography retention indices to estimate environmental partitioning properties for a complete set of diesel fuel hydrocarbons. Anal. Chem. 2005, 77(22), 7172–7182. Arias-Gonzalez, I.; Reza, J.; Trejo, A., Temperature and sodium chloride effects on the solubility of anthracene in water. J. Chem. Thermodyn. 2010, 42(11), 1386–1392. Atkinson, D.; Curthoys, G., The determination of heats of adsorption by gas-solid chromatography. J. Chem. Educ. 1978, 55(9), 564–566. Bamford, H. A.; Poster, D. L.; Baker, J. E., Henry’s law constants of polychlorinated biphenyl congeners and their variation with temperature. J. Chem. Eng. Data 2000, 45(6), 1069–1074. Beyer, A.; Wania, F.; Gouin, T.; Mackay, D.; Matthies, M., Selecting internally consistent physicochemical properties of organic compounds. Environ. Toxicol. Chem. 2002, 21(5), 941–953. Brennan, R. A.; Nirmalakhandan, N.; Speece, R. E., Comparison of predictive methods for Henrys law coefficients of organic chemicals. Water Res. 1998, 32(6), 1901–1911. Cetin, B.; Odabasi, M., Measurement of Henry’s law constants of seven polybrominated diphenyl ether (PBDE) congeners as a function of temperature. Atmos. Environ. 2005, 39(29), 5273– 5280. Endo, S., Helmholtz Center for Environmental Research (UFZ), Leipzig, Germany. Personal Communication. February 14, 2014. Endo, S.; Pfennigsdorff, A.; Goss, K. U., Salting-out effect in aqueous NaCl solutions: Trends with size and polarity of solute molecules. Environ. Sci. Technol. 2012, 46(3), 1496–1503. Endo, S.; Watanabe, N.; Ulrich, N.; Bronner, G.; Goss, K. U., UFZ-LSER database v 2.1 [Internet]. Helmholtz Centre for Environmental Research-UFZ: Leipzig, Germany, 2014 [accessed on April 19, 2014]. http://www.ufz.de/index.php?en=31698&contentonly=1 &lserd_data[mvc]=Public/start. Friesen, K. J.; Webster, G. R. B., Temperature dependence of the aqueous solubilities of highly chlorinated dibenzo-p-dioxins. Environ. Sci. Technol. 1990, 24(1), 97–101. Gold, G.; Rodriguez, S., The effect of temperature and salinity on the Setschenow parameters of naphthalene in seawater. Can. J. Chem.-Rev. Can. Chim. 1989, 67(5), 822–826. Gordon, J. E.; Thorne, R. L., Salt effects on the activity coefficient of naphthalene in mixed aqueous electrolyte solutions. I. Mixtures of two salts. J. Phys. Chem. 1967a, 71(13), 4390–4399. Gordon, J. E.; Thorne, R. L., Salt effects on non-electrolyte activity coefficients in mixed aqueous electrolyte solutions. II. Artificial and natural sea waters. Geochim. Cosmochim. Acta 1967b, 31(12), 2433–2443. Goss, K. U., Prediction of the temperature dependency of Henry’s law constant using polyparameter linear free energy relationships. Chemosphere 2006, 64(8), 1369–1374. Goss, K. U.; Schwarzenbach, R. P., Empirical prediction of heats of vaporization and heats of adsorption of organic compounds. Environ. Sci. Technol. 1999, 33(19), 3390–3393. Hinckley, D. A.; Bidleman, T. F.; Foreman, W. T.; Tuschall, J. R., Determination of vapor pressures for nonpolar and semipolar organic compounds from gas chromatographic retention data J. Chem. Eng. Data 1990, 35(3), 232–237. Hine, J.; Mookerjee, P. K., The intrinsic hydrophilic character of organic compounds. Correlations in terms of structural contributions. J. Org. Chem. 1975, 40(3), 292–298. K¨uhne, R.; Ebert, R. U.; Sch¨uu¨ rmann, G., Prediction of the temperature dependency of Henry’s law constant from chemical structure. Environ. Sci. Technol. 2005, 39(17), 6705–6711. Lei, Y. D.; Wania, F.; Mathers, D., Temperature-dependent vapor pressure of selected cyclic and linear polydimethylsiloxane oligomers. J. Chem. Eng. Data 2010, 55(12), 5868–5873. Lide, D. R., Ed., CRC Handbook of Chemistry and Physics. 76th ed.; CRC Press: Boca Raton, FL, 1995; Vol. 1995–1996.

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McDevit, W. F.; Long, F. A., The activity coefficient of benzene in aqueous salt solutions. J. Am. Chem. Soc. 1952, 74(7), 1773–1777. Meylan, W. M.; Howard, P. H., Bond contribution method for estimating Henry’s law constants. Environ. Toxicol. Chem. 1991, 10(10), 1283–1293. Mintz, C.; Burton, K.; Ladlie, T.; Clark, M.; Acree, W. E.; Abraham, M. H., Enthalpy of solvation correlations for gaseous solutes dissolved in dibutyl ether and ethyl acetate. Thermochim. Acta 2008, 470(1–2), 67–76. Mintz, C.; Clark, M.; Acree, W. E.; Abraham, M. H., Enthalpy of solvation correlations for gaseous solutes dissolved in water and in 1-octanol based on the Abraham model. J. Chem Inf. Model. 2007, 47(1), 115–121. Mitchell, B. E.; Jurs, P. C., Prediction of infinite dilution activity coefficients of organic compounds in aqueous solution from molecular structure. J. Chem. Inf. Comput. Sci. 1998, 38(2), 200–209. Ni, N.; Yalkowsky, S. H., Prediction of Setschenow constants. Int. J. Pharm. 2003, 254(2), 167– 172. Prak, D. J. L.; O’Sullivan, D. W., Assessing the salting-out behavior of nitrobenzene, 2-nitrotoluene, and 3-nitrotoluene from solubility values in pure water and seawater at temperatures between (277 and 314) K. J. Chem. Eng. Data 2009, 54(4), 1231–1235. Sander, R., Compilation of Henry’s law constants (version 4.0) for water as solvent. Atmos. Chem. Phys. 2015, 15(8), 4399–4981. Sanemasa, I.; Arakawa, S.; Araki, M.; Deguchi, T., The effects of salts on the solubilities of benzene, toluene, ethylbenzene, and propylbenzene in water. Bull. Chem. Soc. Jpn. 1984, 57(6), 1539– 1544. Seinfeld, J. H.; Pandis, S., Atmospheric chemistry and physics: From Air Pollution to Climate Change. 2 ed.; John Wiley & Sons: Hoboken, 2006; p 1203. ¨ Setschenow, J. Z., Uber die Konstitution der Salzl¨osungen auf Grund ihres Verhaltens zu Kohlensaure. Z. Physik. Chem 1889, 4, 117–125. Sherman, S. R.; Trampe, D. B.; Bush, D. M.; Schiller, M.; Eckert, C. A.; Dallas, A. J.; Li, J. J.; Carr, P. W., Compilation and correlation of limiting activity coefficients of nonelectrolytes in water. Ind. Eng. Chem. Res. 1996, 35(4), 1044–1058. Shiu, W. Y.; Wania, F.; Hung, H.; Mackay, D., Temperature dependence of aqueous solubility of selected chlorobenzenes, polychlorinated biphenyls, and dibenzofuran. J. Chem. Eng. Data 1997, 42(2), 293–297. Staudinger, J.; Roberts, P. V., A critical review of Henry’s law constants for environmental applications. Crit. Rev. Environ. Sci. Technol. 1996, 26(3), 205–297. Wang, C.; Lei, Y. D.; Endo, S.; Wania, F., Measuring and Modeling the Salting-out Effect in Ammonium Sulfate Solutions. Environ. Sci. Technol. 2014, 48(22), 13238–13245. Xie, W. H.; Shiu, W. Y.; Mackay, D., A review of the effect of salts on the solubility of organic compounds in seawater. Mar. Environ. Res. 1997, 44(4), 429–444.

289

Chapter 10

Organic Liquid–Air and Organic Liquid–Water Partitioning

10.1 Introduction 10.2 Thermodynamic Considerations and Comparisons of Different Organic Solvents Thermodynamic Considerations LFERs for Evaluation and Prediction of Organic Solvent–Air and Organic Solvent–Water Partition Constants Effect of Temperature on the Organic Solvent–Air and Organic Solvent–Water Partition Constants 10.3 The Octanol–Water System: The Atom/Fragment Contribution Method for Estimation of the Octanol–Water Partition Constant 10.4 Partitioning Involving Organic Solvent–Water Mixtures 10.5 Evaporation and Dissolution of Organic Compounds from Organic Liquid Mixtures–Equilibrium Considerations Evaporation Dissolution Into Water

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

290

Organic Liquid–Air and Organic Liquid–Water Partitioning

Box 10.1 Estimating the Concentrations of Individual PCB Congeners in Water in Equilibrium with an Aroclor Mixture 10.6 Questions and Problems 10.7 Bibliography

Thermodynamic Considerations

10.1

291

Introduction We now extend our discussions of equilibrium bulk phase partitioning in Chapters 7 to 9 to include partitioning of organic compounds between different organic liquids and air or water. In Chapters 8 and 9, we have already introduced a special case of an organic liquid, that is, the pure liquid compound itself, which we also use as reference state in our thermodynamic treatment of partitioning equilibrium (see Section 4.2). In Section 10.2, we start out by considering some thermodynamic aspects of the partitioning of an organic compound between an organic solvent and air or an organic solvent and water. As a follow-up of our discussions in Chapter 7, we will compare some solvents that exhibit different solvent characteristics. Some emphasis will be given to 1-octanol (referred to as octanol), the most widely used solvent applied in sp-LFERs for predicting partitioning of organic chemicals in natural systems (see Section 7.3). Section 10.3 will then be devoted to a more detailed treatment of the octanol–water system, particularly to the estimation of octanol–water partition constants (Kiow ) using the fragment contribution approach. However, the main purpose of this section is not to provide another estimation method for the octanol–water partition constant. Instead, we want to visualize how structural subunits (atoms or fragments) affect the partitioning of an organic compound between water and an organic solvent, using octanol as model solvent. This visualization, which is complementary to our discussions on pp-LFERs that are based on characteristics of the entire compound, should provide the reader with important additional insights into how structural moieties determine the extent of partitioning of organic compounds. In the last two sections of this chapter, we discuss two special cases of partitioning involving mixed phases. In Section 10.4, we discuss the effect of water-miscible cosolvents on aqueous activity coefficients, and, thus, on aqueous solubility and partitioning of compounds to a mixed organic solvent–water phase. Section 10.5 focuses on the dissolution of organic compounds into water from organic liquid mixtures, such as gasoline, diesel fuel, heating oil, chlorinated solvent mixtures, or PCBs. Here, we consider the case in which the organic chemical of interest is not present in dilute concentration in the organic liquid but forms a significant part of it.

10.2

Thermodynamic Considerations and Comparisons of Different Organic Solvents Thermodynamic Considerations In analogy to air–water partitioning (Eqs. 9-14 and 9-15), we can express the solvent (l )–air partition constant, Kil a , of a compound as: Kil a =

Cil 1 = ∗ Cia (piL ∕RT)𝛾 il V̄ l

(10-1)

where p∗iL is the liquid vapor pressure of the compound, 𝛾 il is its activity coefficient in the solvent, and V̄ l is the molar volume of the solvent. When one substitutes the subscript l by w, Eq. 10-1 expresses the water–air constant, Kiwa , the reciprocal of

292

Organic Liquid–Air and Organic Liquid–Water Partitioning

10

γio = 0.1

8

γio = 10

γio = 1

γio = 100

log Kiow

6

Figure 10.1 Plot of the logarithms of the octanol–water partition constants (log Kiow ) versus the aqueous activity coefficients (log 𝛾 iw ) for a variety of apolar, monopolar, and bipolar compounds. The diagonal lines indicate where the activity coefficients in octanol (𝛾 io ) (calculated from Eq. 10-2) equal 0.1, 1, 10, or 100.

alcohols alkanes alkylbenzenes amines carboxylic acids chloroalkanes chlorobenzenes

4 2 0 –2 –2

0

2

4

6

8

esters ethers ketones nitrobenzenes phenols phthalates polycyclic aromatic hydrocarbons

10

log γiw

air–water constant in Eq. 9-15. Dividing Kil a by Kiwa then yields the solvent–water partition constant, Kil w : Kil w =

𝛾 V̄ Cil = iw w Ciw 𝛾 il V̄ l

(10-2)

The dominant factor determining the magnitude of any organic solvent–water partition constant is, for most compounds, the large aqueous activity coefficient, 𝛾 iw . As an example, Fig. 10.1 illustrates the partition constant, log Kiow (Eq. 10-2, l = o), for a large number of diverse organic compounds in the octanol–water system. Activity coefficients in octanol, 𝛾 io , lie only between 0.1 (bipolar small molecules) and about 50 (large apolar and weakly polar compounds), whereas 𝛾 iw values span a range of ten orders of magnitude (see also Table 9.1). Therefore, the tendency of the compound to leave the aqueous phase (its “hydrophobicity”) primarily drives partitioning into an organic bulk phase. When using the thermodynamic cycle to calculate a partition constant from two others, such as Eq. 10-2, one should distinguish, in principle, whether one considers the organic solvent “dry” (no water dissolved in the solvent) or “wet” (saturated with water). Hence, when using experimental solvent–air partition constants determined for dry solvents, we would get hypothetical dry solvent–water partition coefficients. Conversely, when using experimental solvent–water partition constants, we would derive water-saturated organic solvent–air partition constants. Table 10.1 shows that, at water saturation, apolar or weakly polar organic solvents contain very small amounts of water. Therefore, the distinction between dry and wet

293

Thermodynamic Considerations

Table 10.1 Mole Fraction of Some Common Organic Solvents Saturated with Watera Organic Solvent “l ”

xl

n-Pentane n-Hexane n-Heptane n-Octane n-Decane n-Hexadecane

0.9995 0.9995 0.9993 0.9994 0.9994 0.9994

Trichloromethane Tetrachloromethane Trichloroethene Tetrachloroethene Benzene Toluene 1,3-Dimethylbenzene 1,3,5-Trimethylbenzene n-Propylbenzene

0.9948 0.9993 0.9977 0.9993 0.9975 0.9976 0.9978 0.9978 0.9958

a

Organic Solvent “l ”

xl

Chlorobenzene Nitrobenzene Aminobenzene

0.9981 0.9860 0.9787

Diethylether Methoxybenzene Ethyl acetate Butyl acetate 2-Butanone 2-Pentanone 2-Hexanone 1-Butanol 1-Pentanol 1-Hexanol 1-Octanol

0.9501 0.9924 0.8620 0.9000 0.6580 0.8600 0.8930 0.4980 0.6580 0.7100 0.8060

Data from Demond and Lindner (1993).

is generally not important. In contrast, some smaller, polar solvents contain significant amounts of water. In these cases, 𝛾 il ,dry may be significantly different from 𝛾 il ,wet . Moreover, the molar volume of the solvent may be somewhat different, leading to differences in the corresponding partition constants (Abraham and Acree, 2008; Abraham et al., 2009). For example, in the case of octanol, at equilibrium, there will be roughly one water molecule per four octanol molecules in the organic phase (xl ≅ 0.8, Table 10.1). The molar volume of “dry” octanol (V̄ l = 0.16 L mol–1 ) is, therefore, about 20% larger than that of “wet” octanol (V̄ l ≅ 0.13 L mol–1 , see Section 10.3 for calculation of molar volumes of organic solvent–water mixtures). Conversely, only about one octanol molecule will be present per 10,000 water molecules in octanol– saturated water. Neither the aqueous activity coefficient of the compound nor the molar volume of the aqueous phase is, therefore, significantly impacted by such a small amount of octanol in the water. LFERs for Evaluation and Prediction of Organic Solvent–Air and Organic Solvent–Water Partition Constants As for many other two-phase systems, pp-LFERs have been developed for estimating solvent–air and solvent–water partition constants. Table 10.2 lists pp-LFERs for a few common organic liquids; additional pp-LFERs for other liquids are compiled in the UFZ-LSER database (Endo et al., 2014). With the exception of octanol, one equation is valid for both the wet and dry solvent, since these organic liquids contain only a small fraction of water at saturation (e.g., chloroform and olive oil: xl > 0.99; diethylether: xl = 0.95).

294

Organic Liquid–Air and Organic Liquid–Water Partitioning

Table 10.2 pp-LFERs for Some Organic Solvent–Air (log Kil a = vl a Vi + ll a Li + sl a Si + al a Ai + bl a Bi + c) and Organic Solvent–Water (log Kil w = vl w Vi + ll w Li + sl w Si + al w Ai + bl w Bi + c) Systems at 25◦ Ca,b Solvent–air system solvents

Equation

vl a

ll a

sl a

al a

bl a

c

Diethylether (wet/dry) Chloroform (wet/dry) Octanol (wet) Octanol (dry) Olive oil (wet/dry)

10-3 10-4 10-5 10-6 10-7

+0.87 +0.89 −0.04 +0.07 +0.35

+0.74 +0.69 +0.91 +0.90 +0.80

+0.93 +1.33 +0.66 +0.47 +1.01

+3.21 +0.28 +3.49 +3.52 +1.76

0.00 +1.42 +1.42 +0.82 +0.01

+0.03 −0.01 −0.25 −0.14 −0.38

Water (l = w )

9-18

−2.55

+0.48

+2.07

+3.67

+4.87

−0.59

vl w

ll w

sl w

al w

bl w

c

+3.42 +3.44 +2.41 +2.90

+0.26 +0.21 +0.43 +0.32

−1.14 −0.70 −1.41 −1.06

−0.46 −3.39 −0.18 −1.91

−4.87 −3.38 −3.45 −4.87

+0.62 +0.58 +0.34 +0.21

Solvent–water system solvents Diethylether (wet/dry) Chloroform (wet/dry) Octanol (wet) Olive oil (wet/dry)

10-8 10-9 10-10 10-11

a

Data from Goss (2005) and UFZ-LSER Database (Endo et al. 2014). ppLFER expressions contain solute descriptors for the size of the compound (Vi ), the log Kihexadecane–air (Li ), the H-donor property (Ai ), the H-acceptor property (Bi ), and a “dipolarity/polarizability” parameter (Si ), plus the complementary fitted system descriptors characterizing the bulk liquid phases involved (lower case letters). b

First, let us directly compare the different solvent characteristics by inspecting the ppLFERs for solvent–air partitioning. For example, the monopolar solvents diethylether (H-acceptor) and chloroform (H-donor), which exhibit very similar molar volumes and vdW properties, only significantly differ, as expected, in their al a and bl a system descriptors (Eqs. 10-3 and 10-4). The solvent–air partition constants of apolar compounds in the two monopolar solvents or any apolar solvent are thus very similar. In contrast to monopolar solvents, the bipolar solvent octanol differs significantly in the vl a system descriptor, which encompasses the larger free energy contribution of cavity formation, and in the al a or bl a descriptors (Eqs. 10-5 and 10-6). We can also see that the water present in wet octanol has an influence primarily on the bl a descriptor, makO COR O COR ing wet octanol a somewhat better H-donor. However, as is evident from Fig. 10.2, for O COR the majority of our test set of apolar, monopolar, and bipolar compounds (introduced General structure of olive oil, R1 , in Chapter 7, in the following referred to as “test set”), the differences between the R2 , R3 = C14 , C16 , C18 saturated or wet octanol–air and the dry octanol–air partition constants are within a factor of two. unsaturated chains (for details see Therefore, if no experimental dry octanol–air partition constants are available, the Hui, 1996). estimated wet octanol–air partition constants are very reasonable surrogates. Finally, comparison of the two monopolar H-accepting solvents diethylether (Eq. 10-3) and olive oil (Eq. 10-7, structure in margin) shows that olive oil has a significantly smaller al a descriptor, which is due to its 2.5 times smaller carbon to oxygen ratio. As already pointed out in Chapter 7 (Section 7.3), a common approach used to predict partition coefficients between natural organic matter or biological media and air or water is based on sp-LFERs using octanol as reference solvent: log Kil a = a log Kioa + b log Kil w = c log Kiow + d

(10-12) (10-13)

Thermodynamic Considerations

14

predicted log Ki octanol (dry)–air (LaLo–1)

1: 1

aliphatic amines 1-alkanols

12

alkanes carboxylic acid esters

10

chlorobenzenes chlorinated phenols

8

fluorotelomers ketones

6

phthalates

4

polycyclic aromatic hydrocarbons polychlorinated biphenyls

2 Figure 10.2 Dry versus wet octanol– air partition constants for our test set. The values have been calculated using Eqs.10-6 and 10.5, respectively.

295

siloxanes 2

4

6

8

10

12

14

predicted log Ki octanol (wet)–air (LaLo–1)

The underlying idea is that octanol offers solutes a similar set of intermolecular interactions as they would experience in organic matter or biological media. Therefore, one might expect the free energies of partitioning into like media (e.g., octanol and biological media) from air or water to correlate with one another. Using olive oil as an example of a biological material, the calculated logarithms of the olive oil–air (Eq. 10-7) and olive oil–water (Eq. 10-11) partition constants of our test set are plotted against the corresponding calculated logarithms of the octanol–air (Eq. 10-6) and octanol–water (Eq. 10-10) partition constants, respectively, in Figs. 10.3a and b. Similar to our findings in Chapter 7 when plotting the logarithms of hexadecane–air versus octanol–air as well as the hexadecane–water versus octanol–water partition constants (Fig. 7.3), no single sp-LFER of the type in Eqs. 10-12 and 10-13 is capable of fitting the entire data set. Good linear relationships can, however, be found for subsets of compounds, in particular for structurally related compounds, such as homologous series of alkanes, aliphatic ketones, esters, amines, alcohols, siloxanes, and fluorotelomers. Hence, we point out again that an sp-LFER of the type Eqs. 10-12 and 10-13 using octanol (or any other organic liquid) as a reference solvent needs to be applied with caution, especially if the training set of solutes exhibits different intermolecular interactions than the compounds of interest. However, when used properly, they can be quite useful, as we see in Chapters 13 and 16. Effect of Temperature on the Organic Solvent–Air and Organic Solvent–Water Partition Constants As discussed in Chapter 4 (Eq. 4-33), for a narrow temperature range (e.g., the ambient temperature range, –20 to 40◦ C), the temperature dependence of the organic

296

Organic Liquid–Air and Organic Liquid–Water Partitioning

12

12

6 4 2 0

–2

0

2

4

6

8

10

12

1

10 8 6 4 2 0 –2

predicted log Ki octanol–air (LaLo–1)

aliphatic amines 1-alkanols alkanes carboxylic acid esters

1:

1: 1

8

–2

(b)

predicted log Ki olive oil–water (LwLoo–1)

predicted log Ki olive oil–air (LaLoo–1)

(a) 10

–2

0

2

4

6

8

10

12

predicted log Ki octanol–water (LwLo–1)

chlorobenzenes chlorinated phenols fluorotelomers ketones

phthalates polycyclic aromatic hydrocarbons polychlorinated biphenyls siloxanes

Figure 10.3 Calculated (a) olive oil–air (Eq. 10-7) versus octanol–air (Eq. 10-6) and (b) olive oil–water (Eq. 10-11) versus octanol–water (Eq. 10-10) partition constants for our test set.

solvent–air (Eq. 10-14) and organic solvent–water (Eq. 10-15) partition constants is given by the familiar van’t Hoff relationships: Δ H 1 ln Kil a = − l a i ⋅ + constant R T Δl w Hi 1 ln Kil w = − ⋅ + constant R T

(10-14) (10-15)

We also recall from Chapter 4 that, if one of the phases considered is the gas phase and the partition constant is expressed in molar concentrations, due to the temperature dependence of the molar volume of gases, Δl a Hi has to be replaced by Δl a Hi + RTav where Tav is the average temperature (in K) of the temperature range considered (Atkinson and Curthoys, 1978). However, because RTav is equal to only about 2.5 kJ mol–1 , we neglect this term, just like we did when discussing air–water partitioning (Eq. 9-25). Finally, using the thermodynamic cycle, we can relate the enthalpies in Eqs. 10-14 and 10-15 with the enthalpy of water–air exchange, Δwa Hi (see Table 9.2 for some examples; note that the table gives Δaw Hi = −Δwa Hi values) by: Δl w Hi = Δl a Hi − Δwa Hi (10-16) For l = octanol and l = hexadecane, Table 10.3 summarizes the Δl a Hi and Δl w Hi values of some apolar, monopolar, and bipolar compounds, together with their enthalpies

297

Thermodynamic Considerations

Table 10.3 Examples of Experimental or Calculated Enthalpies of Condensation, Water–Air Partitioning, Octanol–Air and Octanol–Water Partitioning, and Hexadecane–Air and Hexadecane–Water Partitioning Solvent system

Solute Compound

pure liquid–aira Δcond Hi (kJ mol–1 )

water–aira Δwa Hi (kJ mol–1 )

octanol– airb Δoa Hi (kJ mol–1 )

hexadecane– airc Δha Hi (kJ mol–1 )

octanol– waterb Δow Hi (kJ mol–1 )

hexadecane– waterd Δhw Hi (kJ mol–1 )

n-Hexane MTBE PCE Benzene Phenol 1-Hexanol Phenanthrene Pyrene Lindane (𝛾-HCH) PCB 153 D5

−32 −30 −40 −34 −58 −62 −69 −74 −70 −90 −60

−32 −49 −42 −32 −58 −67 −54 −59 −54 −70 −80

−30 −28 −38 −31 −65 −61 −75 −76 −74 −88 −58

−32 −28 −38 −31 −40 −40 −77 −85 −74 −96 −69

2 16 4 1 −7 6 −21 −17 −20 −18 22

1 21 4 1 18 27 −23 −26 −20 −26 11

a c

Data from Table 9.2. b Data from Beyer et al. (2002) and Mintz et al. (2007) or calculated using Eq. 10-17. Calculated using pp-LFER for Δha Hi published by Mintz et al. (2008). d Calculated using Eq. 10-16.

of condensation (negative enthalpies of vaporization) and of air–water partitioning at 25◦ C. For octanol–air partitioning, some of the Δoa Hi values have been calculated using the pp-LFER published by Mintz et al. (2008): Δoa Hi (kJ mol−1 ) = +1.6Vi − 9.7Li + 6.0Si − 53.7Ai − 9.2Bi − 6.7 (10-17) (number of chemicals = 138; r2 = 0.99; S.D. = 2.6) From Table 10.3, we can draw some general conclusions. First, for all compounds, the enthalpy of octanol–air partitioning is quite similar to the enthalpy of condensation. The same holds for partitioning between the apolar solvent hexadecane and air, with the exception that bipolar compounds exhibit somewhat smaller enthalpies because they cannot undergo H-bonding in the apolar solvent. Therefore, Kil a is very sensitive to temperature (recall from Chapter 4 (Table 4.3) that a Δa Hi value of 50 kJ mol–1 means a factor of two change in Kil a per 10 degree change in temperature and a factor of 4 if Δl a Hi is 100 kJ mol–1 ). We also highlight that, because all these enthalpies are negative, an increase in temperature favors the gas phase; that is, Kil a decreases with increasing temperature. In contrast to solvent–air partitioning, partitioning between organic solvents and water is significantly less temperature dependent. That is, the corresponding enthalpies are much smaller (Table 10.3), which is not surprising since the enthalpy of partitioning is given by the difference of the excess enthalpies of the compound in the organic solvent E . Typically, HiEl for organic compounds in organic soland water, Δl w Hi = HiEl − Hiw vents is small and does not exceed ±10 kJ mol–1 ; the excess enthalpy of a compound

298

Organic Liquid–Air and Organic Liquid–Water Partitioning

in a solvent is given by HiEl = Δl a Hi − Δcond Hi , and the liquid–air term is commonly close to the condensation term. Also, the excess enthalpies in water are fairly small E values that are not much larger than ± 20 to 30 kJ mol–1 , (Table 9.2), leading to Hiw meaning less than a factor of 1.5 change in Kil w per 10 degree change in temperature. Finally, if needed, to estimate the enthalpy for octanol–water partitioning, we may derive a pp-LFER combining Eq. 10-17 and the pp-LFER reported for air–water partitioning (Chapter 9, Eq. 9-27) using the thermodynamic cycle (Eq. 10-16): Δow Hi (kJ mol−1 ) = +18.9Vi − 8.3Li + 5.3Si − 20.1Ai + 34.3Bi + 1.7

10.3

(10-18)

The Octanol–Water System: The Atom/Fragment Contribution Method for Estimation of the Octanol–Water Partition Constant The classical fragment or group contribution method for estimating log Kiow was originally introduced by Rekker and co-workers (Rekker, 1977) and Hansch and Leo (Hansch and Leo, 1979; Hansch and Leo, 1995; Hansch et al., 1995). A computerized version of this method (known as the CLOGP program; note that P is often used to denote Kiow ) was initially established by Chou and Jurs, (1979) and later modified and extended by Hansch and Leo (1995). The method estimates log Kiow by using single atom “fundamental” fragments consisting of isolated types of carbons, hydrogen, and various heteroatoms, plus some multiple atom “fundamental” fragments (e.g., –OH, –COOH, –NH2 , –CN, –NO2 ). These fundamental fragments were derived from a limited number of rather simple compounds assuming that one can cut up molecules into parts that interact somewhat independently with the surrounding media. The values of each fragment are summed together to estimate a log Kiow . Since the extent of these interactions are not independent in more complex molecules due to stereochemical factors or inductive effects, the method also uses a large number of correction factors for unsaturation and conjugation, branching, multiple halogenation, proximity of polar groups, and more (Hansch et al., 1995). Meylan and Howard (1995) also developed a simple atom/fragment contribution method derived from multiple linear regressions of experimental log Kiow values. To estimate the log Kiow of a given compound at 25◦ C, one simply adds up the fragment coefficients, fk , and correction factors, cj , according to the equation: log Kiow =

∑ k

nk ⋅ f k +

∑

nj ⋅ cj + 0.23

(10-19)

k

where nk and nj are the frequency of each type of fragment or specific interaction, respectively, occurring in the compound of interest. Tables 10.4 and 10.5 give selected values of fragment coefficients and correction factors; for a more comprehensive collection, see Meylan and Howard (1995). An updated collection is used in the KOWWIN program (v1.66: n(fk ) = 186, n(cj ) = 322) in EPI Suite (Estimation Programs Interface Suite; U.S. EPA, (2012).

299

The Octanol–Water System

Table 10.4 Selected Atom/Fragment Coefficients, fk , for log Kiow Estimation at 25◦ C (Eqs. 10-19 and 10-20)a Atom/Fragmentb

fk

Carbon −CH3 −CH2 – −CH< >C< =CH2 =CH– or =C< Car

0.55 0.49 0.36 0.27 0.52 0.38 0.29

Halogens al–F ar–F al–Cl ol–Cl ar–Cl al–Br ar–Br al–I ar–I

0.00 0.20 0.31 0.49 0.64 0.40 0.89 0.81 1.17

Atom/Fragmentb Carbonyls al–CHO ar–CHO al–CO–al ol–CO–al ar–CO–al ar–CO–a—r al–COO– (ester) ar–COO– (ester) al–CON< (amide) ar–CON< (amide) >N–COO– (carbamate) >N–CO–N< (urea) al–COOH ar–COOH

−0.94 −0.28 −1.56 −1.27 −0.87 −0.20 −0.95 −0.71 −0.52 0.16 0.13 1.05 −0.69 −0.12

Nitrogen Containing Groups al–NH2 al–NH– al–N< ar–NH2 , ar–NH–, ar–N< al–NO2 ar–NO2 ar–N=N–ar al–C ≡ N ar–C ≡ N

−1.41 −1.50 −1.83 −0.92 −0.81 −0.18 0.35 −0.92 −0.45 −0.40 0.05 −2.55 −2.11 −2.43 −1.98 −0.44 −0.21 −3.16

Aliphatic Oxygen al–O–al al–O–ar ar–O–ar al–OH ol–OH ar–OH al–O–(P) ar–O–(P)

−1.26 −0.47 0.29 −1.41 −0.89 −0.48 −0.02 0.53

Heteroatoms in Aromatic Systems Oxygen Nitrogen in five-member ring Nitrogen in six-member ring Nitrogen in fused ring Sulfur

−0.04 −0.53 −0.73 0.00 0.41

Sulfur Containing Groups al–S–al ar–S–al al–SO–al ar–SO–al al–SO2 –al ar–SO2 –al al–SO2 N< ar–SO2 N< ar–SO3 H

Phosphorus →P=O →P=S

−2.42 −0.66

Silicon Containing Groups al–Si–al ar–Si– or O–Si–

a b

fk

Data from Meylan and Howard (1995); total n(fk ) = 130. al: aliphatic attachment, ol: olefinic attachment; ar: aromatic attachment.

0.30 0.68

300

Organic Liquid–Air and Organic Liquid–Water Partitioning

Table 10.5 Examples of Correction Factors, cj , for log Kiow Estimation at 25◦ C (Eqs. 10-19 and 10-20)a Functional Groupb

cj

Functional Groupb

Factors Involving Aromatic Ring Substituent Positions o–OH/–COOH 1.19 o–N factor 2), the cosolvent volume fraction needs to be greater than 5 to 10%, depending on the solvent. Below 1%, the effect can be neglected, even for very hydrophobic compounds. Therefore, when conducting experiments, we do not have to worry about significant changes in the activities of organic solutes in an aqueous phase when adding a small amount of a CMOS, as is, for example, common practice when spiking an aqueous solution with a sparingly soluble organic compound dissolved in an organic solvent such as methanol.

Partitioning Involving Organic Solvent–Water Mixtures

7

2,4,6-trichlorobiphenyl (PCB 30) methanol

6 log γ iw,CMOS

303

5

ethanol

4 3 2

n-propanol

1

Figure 10.4 Effect of different CMOSs (methanol, ethanol, and propanol) on the activity coefficient, 𝛾 iw,CMOS , of 2,4,6-trichlorobiphenyl (PCB 30) in water/CMOS mixtures. Data from Li and Andren (1994).

0

0

0.2 0.4 0.6 0.8 volume fraction cosolvent, fv,CMOS

1

The magnitude of the cosolvent effect, as well as its dependence on the amount of cosolvent present, is a function of both the type of cosolvent (see examples given in Fig. 10.4 and in Table 10.6) and the type of organic solute considered (see Fig. 10.5). In general, CMOSs are relatively small molecules with strong H-acceptor and/or Hdonor properties. When mixed with water, they are able to break up some of the hydrogen bonds between the water molecules and thus form a new H-bonded “mixed solvent” that changes its nature as a function of the properties and the relative amount of the cosolvent. We can see in Table 10.6 that, qualitatively, the more “water-like” solvents such as glycerol, ethylene glycol, and methanol have a much smaller impact on the activity coefficient of an organic solute as compared to organic solvents for which hydrogen bonding plus vdW interactions are important for partitioning. For example, the activity coefficient of naphthalene decreases by a factor of about 5 when going from pure water to a 40% glycerol/60% water mixture, while the effect is about 10 or 20 times larger when ethanol or acetone, respectively, are the cosolvents. The 8 7 log γiw,CMOS

6

Figure 10.5 Illustration of the effect of a CMOS (methanol) on the activity coefficient of organic compounds in different water–methanol mixtures. Data calculated from measurements in Dickhut et al. (1989); Jayasinghe et al. (1992); Li and Andren (1994); Fan and Jafvert (1997).

2,4,6-trichlorobiphenyl (PCB 30)

5

4-chlorobiphenyl (PCB 4) naphthalene 2,4,5-trimethylaniline

4 3 2

aniline

1 0

0

0.2

0.4

0.6

0.8

volume fraction methanol, fv,MeOH

1

304

Organic Liquid–Air and Organic Liquid–Water Partitioning

Table 10.6 Effect of Various CMOSs on the Activity Coefficient, 𝛾 iw.CMOS , of Naphthalene at Two Different CMOS/Water Ratios (fv,CMOS = 0.2 and 0.4) Naphthalene Activity Coefficienta 𝛾 iw ∕𝛾 iw,CMOS = xiw,CMOS ∕xiw Cosolvent Glycerol

36.2

2.5 (2.0)

34.9

3 (2.4)

9

29.7

3.5 (2.7)

14

26.7

5.5 (3.7)

36

26.1

7 (4.2)

48

OH

24.9

17 (6.2)

180

N

24.8

14 (5.7)

140

24.8

15 (5.9)

130

20.7

14 (5.7)

180

19.7

20 (6.5)

270

HO HO

Methanol

H 3C

OH OH OH

O

Dimethylsulfoxide (DMSO)

S

Ethanol

OH

Propanol

Dimethylformamide

fv,CMOS = 0.2 (σci )c

OH

Ethylene glycol

Acetonitrile

Solubility Parameter δ (MPa1/2 )b

Structure

H 3C

C

O N

fv,CMOS = 0.4 5.5

H

1,4-Dioxane Acetone

O O O

a Data from Dickhut et al. (1989); Li et al. (1996); Fan and Jafvert (1997). b Hildebrand solubility parameter from Barton (1991) in units of megapascal1/2 . c Cosolvency power, σci , for the range 0 < fv,solv < 0.2; see Eq. 10-22.

Hildebrand solubility parameter, δ, given in Table 10.6, is a measure of the cohesive forces among the molecules in the pure solvent, l ; it is defined as the square root of the cohesive energy density (Barton, 1991): ( δ=

Δvap Hl − RT V̄ l

)1∕2 (10-21)

The solvents exhibiting higher cohesive forces in their pure liquid (larger δ) tend to have a smaller cosolvent effect in water. Generally, the cosolvent effect is largest for large apolar solutes like PCBs and smallest for small, polar solutes line aniline (Fig. 10.5). Since the changes in excess

Partitioning Involving Organic Solvent–Water Mixtures

305

enthalpy and entropy with changing cosolvent–water composition are not generally linearly correlated with each other, a strictly linear relationship between excess free energy (or log 𝛾 iw,CSOM ) and fv,CSOM cannot be expected over the whole water/CMOS mixture range (see Figs. 10.4 and 10.5). Considering the rather complex factors that determine the excess free energy of an organic solute in a CMOS/water mixture, it is not surprising that any simple quantitative models developed for describing cosolvent effects all have somewhat limited predictive capabilities. Such models are, however, quite well-suited for fitting experimental data and for estimating activity coefficients of structurally closely related compounds in a given water/CMOS system for which experimental data are available. As we subsequently discuss, an alternative to these classical experimental approaches is to use pp-LFERs to describe activity coefficients in water/CMOS mixtures. For a discussion of the various approaches taken to quantify cosolvent effects, we refer to the literature (e.g., Li and Andren, 1995; Li et al., 1996; Fan and Jafvert, 1997; Millard et al., 2002; Machatha and Yalkowski, 2005). For our purposes, as a first approximation, we adopt the simplest empirical approach where we assume a log-linear relationship between activity coefficient (or mole fraction solubility) of a given compound and volume fraction of the CMOS for a restricted cosolvent range. 1 2 ≤ fv,CSOM ≤ fv,CSOM we may write: For example, for the cosolvent range fv,CSOM [ ] 1 1 log 𝛾 iw,CSOM (fv,CSOM ) = log 𝛾 iw,CSOM (fv,CSOM ) − σci fv,CSOM − fv,CSOM

(10-22)

1 2 ) − log𝛾 iw,CSOM (fv,CSOM )]∕ with the cosolvency power σci = [log 𝛾 iw,CSOM (fv,CSOM 1 2 [fv,CSOM − fv,CSOM ]. 1 If we consider a fv,CSOM range starting with pure water, that is, fv,CSOM = c 1 2 2 0, 𝛾 iw,CSOM (fv,CSOM ) = 𝛾 iw , and σi = [log𝛾 iw,CSOM (fv,CSOM ) − log𝛾 iw ]∕fv,CSOM , Eq. 10-22 can also be written as:

𝛾 iw,CSOM (fv,CSOM ) = 𝛾 iw 10−σi ⋅fv,CSOM c

(10-23)

This approach is very similar to the one used for describing the effect of salt on the aqueous activity coefficient (Eq. 9-28) and thus also on the effect of salt on the organic solvent-water partition constant, only with the opposite sign in the exponent. Finally, for calculating molar volumes of CMOS/water mixtures, we use Amagat’s Law (Eq. 4-27), with the mole fractions of two solvents in a binary mixture (subscripts 1 and 2) related to the volume fractions by: x1 =

1 1 − fv1 V 1 1+ ⋅ fv1 V2

and x2 = 1 − x1

(10-24)

As previously mentioned, an alternative to the classic log-linear approach is to apply pp-LFERs to estimate activity coefficients in water/CMOS mixtures. Abraham and Acree (2011) have determined the solubilities of 73 organic compounds in water and

306

Organic Liquid–Air and Organic Liquid–Water Partitioning

Table 10.7 pp-LFERs Describing the Effect of the Cosolvent Ethanol on the Activity Coefficient of Organic 𝛾 iw Solutes in Ethanol/Water Mixtures (log = vw,ETOH Vi + ew,ETOH Ei + sw,ETOH Si + aw,ETOH Ai + bw,ETOH Bi + c) 𝛾 iw,ETOH at 25◦ Ca fv,ETOH 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a b

V w,ETOH (L mol–1 )

vw,ETOH

ew,ETOH

sw,ETOH

aw,ETOH

bw,ETOH

cb

0.019 0.021 0.023 0.025 0.027 0.031 0.035 0.040 0.048 0.058

+0.45 +0.92 +1.41 +1.92 +2.42 +2.81 +3.10 +3.32 +3.55 +3.86

−0.02 +0.04 +0.11 +0.13 +0.12 +0.14 +0.09 +0.18 +0.21 +0.47

0.00 −0.04 −0.10 −0.16 −0.25 −0.33 −0.37 −0.47 −0.58 −1.04

+0.07 +0.10 +0.13 +0.17 +0.25 +0.29 +0.31 +0.26 +0.26 +0.33

−0.37 −0.82 −1.32 −1.81 −2.28 −2.68 −2.94 −3.21 −3.45 −3.60

−0.23 −0.18 −0.16 −0.08 +0.04 +0.20 +0.35 +0.52 +0.67 +0.73

Data from Abraham and Acree (2011). Note: the constants deviate from the original published equation by the term log V w,ETOH ∕V w .

in ten different ethanol/water mixtures ranging from pure ethanol (volume fraction of ethanol, fv,EtOH = 1) down to 10% ethanol/90% water (fv,EtOH = 0.1). We use the ethanol/water system as an example as it has been extensively investigated because of its importance in the pharmaceutical industry. Using these solubilities, Abraham and Acree (2011) derived the ten pp-LFERs given in Table 10.7 for quantifying “partition constants” between the ten ethanol/water mixtures and water. We note that they used the E-term (excess molar refraction) instead of the L-term (log Kihexadecane–air ) (Eq. 711 instead of Eq. 7-12). We recall that the standard free energy of transferring a solute from pure water (w) to another liquid (l ) is given by: Δw,l Gi = −2.302RT log 𝛾 iw ∕𝛾 il

(10-25)

where, in this case, 𝛾 il is 𝛾 iw,ETOH (fv,ETOH ). Inspection of Table 10.7 shows that two terms in the pp-LFERs are dominating the overall effect of the cosolvent ethanol on the activity coefficient of the compound: the volume term (vw,ETOH ) representing the difference in cavity formation costs as well as the size term in the dispersive vdW interactions and the H-donor term (bw,ETOH ) expressing the difference in the H-donor properties between water and the ethanol/water mixture. We already made a similar observation when discussing the partitioning of organic compounds between another bipolar solvent, octanol, and water (Eq. 10-10). As a consequence, we may expect large cosolvent effects for large, apolar compounds and much smaller effects for small, polar compounds. We already noted these effects when discussing Fig. 10.5, and Fig. 10.6 shows predicted log 𝛾 iw ∕𝛾 iw,ETOH values of some of our companion compounds. We can also see that for a restricted cosolvent range, particularly between 0 and 50% EtOH, a log-linear relationship (Eq. 10-22) describes the dependency of log 𝛾 iw ∕𝛾 iw,ETOH on fv,EtOH reasonably well.

307

Evaporation and Dissolution of Organic Compounds

10

predicted log (γiw/γiw,EtOH)

8

atrazine benzene D5

6

1-hexanol methylbromide n-hexane

4

PCB 153 phenanthrene

2

Figure 10.6 Calculated log 𝛾 iw ∕ 𝛾 iw,ETOH plotted as a function of the ethanol fraction for several of our companion compounds, using the equations given in Table 10.7.

0 0.0

0.2

0.4

0.6

0.8

1.0

volume fraction ethanol, fv,EtOH

In conclusion, any partition constant or coefficient between air or another (organic) bulk phase, including the pure compound and water, Kibulkw , is modified by a cosolvent present in the aqueous phase by: Kibulkw,CSOM (fv,CSOM ) = Kibulkw

𝛾 iw,CSOM 𝛾 iw

(10-26)

We neglect the change in molar volume due to added cosolvent as it is minimal as compared to the change in the activity coefficient. For example, when considering a 50% ethanol/50% water mixture, the bulk phase–ethanol/water partition coefficient of PCB 153 would be about 50,000 times smaller as compared to the bulk phase–water coefficient (see log 𝛾 iw ∕𝛾 iw,ETOH in Fig. 10.6).

10.5

Evaporation and Dissolution of Organic Compounds from Organic Liquid Mixtures–Equilibrium Considerations Liquid organic mixtures are commonly divided into so-called light non-aqueous phase liquids (“LNAPLs”, e.g., gasoline, diesel fuel, and heating oil) or dense non-aqueous phase liquids (DNAPLs”, e.g., coal tars, creosotes, chlorinated solvent mixtures, and PCBs). The density distinction is made when considering dissolution into water, because if the liquid mixture’s density is greater than that of water, then the mixture tends to “fall” through water bodies and reside at loci like bedrock underlying aquifers or river bottoms. In contrast, LNAPLs float on water tables or at the air– water interface. To assess such environmental contamination, we need to know how

308

Organic Liquid–Air and Organic Liquid–Water Partitioning

organic compounds present in liquid organic mixtures partition into air (evaporation) or into an aqueous phase (dissolution). In this section, we discuss the factors that determine the concentration of a given component of a LNAPL or DNAPL in an adjacent gaseous or aqueous phase that is in equilibrium with the organic mixture. Therefore, we consider a “snapshot” of the situation where we assume a constant composition of the liquid organic mixture. In reality, when exposed continuously to air or “clean” water, the composition of a LNAPL or DNAPL may change significantly with time, as more volatile or water-soluble compounds, respectively, become depleted (e.g., Lemkau et al., 2010). Depending on the contact time and contact area between the organic phase and air or water, equilibrium may not be established. Thus, a mass transfer approach has to be taken to describe the evaporation or dissolution process. However, even for modeling the evaporation or dissolution kinetics, the equilibrium partitioning of a given compound needs to be known to quantify the mass transfer gradient (see Part IV). Evaporation We recall from Chapter 4 (Eq. 4-14) that, when assuming ideal gas behavior, the partial pressure of a compound above a liquid mixture (subscript “mix”) is given by: pi = 𝛾 imix ximix p∗iL

(10-27)

Let us now evaluate in which cases we may, as a first approximation, assume that Raoult’s Law (𝛾 imix = 1) is valid. From our earlier discussions concerning the molecular factors causing deviations from ideal behavior (Section 4.2), we would expect 𝛾 imix values not too different from 1 when either apolar compounds or monopolar compounds are in mixtures in which the major components undergo primarily vdW interactions, with the added restriction for monopolar compounds that no major constituents have complementary polarity. As confirmed by experimental data and by model calculations (e.g., Peters et al., 1999a), examples meeting the above criteria include aliphatic hydrocarbons and BTEX compounds present in most gasolines and in other fuels (Cline et al., 1991; de Hemptinne et al., 1998; Heermann and Powers, 1998; Garg and Rixey, 1999); the components of mixtures of chlorinated solvents (Broholm and Feenstra, 1995); PAHs present in diesel fuels, coal tars, and creosotes (Lane and Loehr, 1992; Lee et al., 1992a, b); and PCB congeners present in pure PCB mixtures (e.g., Aroclor 1242) or in hydraulic oils consisting of other types of compounds (e.g., trialkylphenylphosphates; Luthy et al., 1997). In all these cases, the 𝛾 imix values determined were found to meet the Raoult’s law criteria within less than a factor of 2 to 3, and, therefore, for practical purposes, 𝛾 imix can be set to 1. Dissolution Into Water As a starting point for describing the equilibrium partitioning of a given compound, i, between a liquid organic mixture and an aqueous phase (subscript “w”), we rearrange Eq. 10-2: Ciw 𝛾 iw V̄ w = Cimix 𝛾 imix V̄ mix

(10-28)

Evaporation and Dissolution of Organic Compounds

309

With ximix = Cimix V̄ mix , we obtain: Ciw =

ximix 𝛾 imix 𝛾 iw V̄ w

(10-29)

Hence, in order to calculate the aqueous concentration of compound i at equilibrium, one needs to know its mole fraction in the mixture, ximix (or Cimix and V̄ mix ), as well as its activity coefficients in the organic (𝛾 imix ) and the aqueous (𝛾 iw ) phases. Very often when dealing with complex mixtures, V̄ mix is not known and has to be estimated. As a first approximation, this can be done from the density of the liquid mixture, ρmix , and ̄ mix , of the mixture components: by assuming an average molar mass, M V̄ mix ≅

̄ mix M ρmix

(10-30)

For example, the average molar masses of gasoline and coal tar have been estimated as 105 g mol–1 and 150 g mol–1 , respectively (Cline et al., 1991; Picel et al., 1988). Let us now consider the various factors that may influence the equilibrium partitioning of an organic compound between a liquid organic mixture and water. First, the organic mixture may originally contain a significant amount of a highly water-soluble compound, which can cause a cosolvent effect in the water phase, as discussed in Section 10.3. Prominent examples include the oxygenated compounds such as methyl-tbutyl ether (MBTE), methanol, or ethanol that are added to gasoline (Cline et al., 1991; Poulsen et al., 1992; Heermann and Powers, 1998). We recall from Section 10.4 that we can neglect the cosolvent effect in the water if the volume fraction of the organic solvent does not exceed 0.01 (1%). However, in some countries, such polar compounds may make up 10 to 20 % of the gasoline. In these cases, cosolvent effects in the “aqueous” phase (now water-CMOS phase) may be significant (e.g., Heermann and Powers, 1998). In the following, we will focus on those cases for which we may assume that the effect on the aqueous activity coefficient of a given compound by other dissolved mixture constituents is minimal. Furthermore, we also neglect the effect of salts on 𝛾 iw (which has the opposite effect of a cosolvent, see Section 9.4, Eq. 9-28); we would need to consider salting-out when dealing with the pollution of the marine (Section 9.1, environment or groundwater brines. Thus, if we assume that 𝛾 iw ≈ 𝛾 sat iw ̄ Table 9.1), we may substitute the term 𝛾 iw Vw in Eq. 10-28 by the inverse of the liquid sat (L), of the compound: aqueous solubility, 1∕Ciw sat Ciw = Cimix V̄ mix 𝛾 imix Ciw (L)

(10-31)

With ximix = Cimix V̄ mix , we obtain: sat Ciw = ximix 𝛾 imix Ciw (L)

(10-32)

By rearranging Eq. 10-31, we may then also express the liquid organic mixture–water partition coefficient, Kimixw = Cimix ∕Ciw , as: Kimixw =

1 ̄Vmix 𝛾 imix Csat (L) iw

(10-33)

310

Organic Liquid–Air and Organic Liquid–Water Partitioning

As previously mentioned, we usually apply Raoult’s Law and assume 𝛾 imix is 1. Box 10.1 provides an illustrative application of Eq. 10-32. We should note, however, that particularly for bipolar compounds, such as certain minor constituents in gasoline (e.g., phenolic compounds and aromatic amines), larger deviations from ideal behavior have to be expected. In addition, in mixtures containing large quantities of polar compounds, the activity coefficients of the various mixture compounds may change with time, if these polar constituents are depleted during the dissolution process. Furthermore, changes in the molar volume of the mixture as a consequence of the preferential dissolution of the more water-soluble components may have to

Box 10.1

Estimating the Concentrations of Individual PCB Congeners in Water in Equilibrium with an Aroclor Mixture

̄ Aroclor , Aroclor 1242 is a commercial PCB mixture with an average chlorine content of 42%, an average molar mass M –1 –3 of about 265 g mol and a density, ρAroclor , of 1.39 g cm . Luthy et al. (1997) have determined the composition of a pure Aroclor 1242 mixture, and they have measured the aqueous concentrations of some individual congeners at 25◦ C in equilibrium with the Aroclor 1242 mixture. Among the congeners investigated was 2,2′ ,5,5′ -tetrachlorobiphenyl (PCB 52), which was determined to be present in the Aroclor 1242 mixture at about 3.2 mass percent (i.e., mass ). The measured aqueous concentration for this compound was 1.11 μg L–1 . Is this fraction miAroclor = 0.032 gi g−1 Aroclor concentration reasonable? What aqueous PCB 52 concentration would you have predicted from the above information, when assuming that Raoult’s Law is valid? Convert the mass fraction (miAroclor = 0.032) of PCB 52 in the Aroclor 1242 mixture into the mole fraction by using ̄ Arcolor , of 265 g mol–1 : the average molar mass, M xiAroclor = miAroclor

̄ Aroclor M (265) = (0.032) = 0.029 Mi (292)

Estimate the liquid aqueous solubility of PCB 52 from its aqueous solubility using Tm (Eqs. 9-10 and 8-24). The sat (L) value is 3.5×10–7 mol L–1 . Insert this value, together with the previously calculated xiAroclor value resulting Ciw and 𝛾 iAroclor = 1, into Eq. 10-32 to get the estimated aqueous concentration of PCB 52: Ciw = (0.029)(1)(3.5×10−7 mol L−1 ) = 1.0×10−8 mol L−1 or about 3 μg L–1 . This value is three times higher than the measured one, but it is within the same order of magnitude. Since apolar PCB 52 probably has an 𝛾 iAroclor value near 1, the discrepancy is more likely due to uncertainties in the measured mole fraction in the Aroclor. Cl

Cl

Cl

Mi = 292 g cm–3 Tm = 86.5◦ C sat (s) = 10–7 mol L–1 Ciw Cl

2,2′,5,5′-tetrachlorobiphenyl (PCB 52)

Questions and Problems

311

be considered. Finally, we should be aware that the preferential dissolution of more soluble compounds in a mixture leads to a higher concentration of the less soluble compounds, and thus to increasing concentrations, in the aqueous phase. The same holds for the preferential evaporation of more volatile compounds leading to higher partial pressures of the less volatile constituents. These issues have to be taken into account when evaluating the long-term dynamics of complex organic mixtures in the environment (e.g., Mackay et al., 1996; Peters et al., 1999b; Arey et al., 2007).

10.6

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Questions Q 10.1 Give several reasons why it is important to an environmental scientist to be able to predict the partitioning behavior of a given compound between organic solvents and air or water. Q 10.2 Imagine a hypothetical compound for which Δl w Gi is equal to zero (GEil = GEiw ) in each of the solvent–water systems: trichloromethane (chloroform)–water, noctanol–water, and n-hexadecane–water. A colleague of yours claims that the Kil w (= Cil ∕Ciw ) values of such a compound are 0.22, 0.11, and 0.06, respectively, for the three solvent–water systems. Another colleague disagrees and claims that the Kil w values are all equal to 1. Who is right and why? Q 10.3 What are the dominant factors determining the magnitude of organic solvent–air and organic solvent–water partitioning of the majority of organic compounds of environmental concern? In which cases would you expect significant differences between “wet” and “dry” solvents?

NH2 i = amphetamine (2-aminopropylbenzene)

Q 10.4 The Kil w values of the stimulant amphetamine (see structure in margin) for the solvents trichloromethane (chloroform, log Kicw = 2.20), n-octanol (log Kiow = 1.80), and nheptane (log Kihw = 0.40) differ quite substantially. Explain why these values differ. Q 10.5 Why in many cases is the effect of temperature on organic solvent–water partitioning of organic compounds not very significant in contrast to organic solvent–air partitioning? What maximum |Δl w Hi | values would you expect? Give examples of solutes and organic solvents for which you would expect (a) a substantial positive (i.e., > 10 kJ mol–1 ) and (b) a substantial negative (i.e., < –10 kJ mol–1 ) Δl w Hi value?

312

Organic Liquid–Air and Organic Liquid–Water Partitioning

Q 10.6 How do dissolved salts in the aqueous phase affect the organic solvent–water partition constant, Kil w ? Write an analogues quantitative expression as derived for air–water partitioning (Chapter 9, Section 9.4). Q 10.7 What are the major difficulties of any atom/fragment contribution method for estimation of solvent–water partition constants from structure? Q 10.8 Which compound and cosolvent characteristics determine the effect of a cosolvent on the activity coefficient of the compound in an organic solvent–water mixture? In which cases is the effect particularly large? Q 10.9 The air–water partition constant of decamethylcyclopentasiloxane (D5) is about 25 times larger than the one for n-hexane (see Appendix C). A colleague claims that when comparing the partition constant of the two compounds between air and a 30% ethanol/water mixture, the situation is very different, in that the air–ethanol/water mixture partition constant of n-hexane is now about a factor of 5 larger than that of D5. Is your colleague correct? Why or why not? Q 10.10 What are the major factors determining the aqueous concentration of a constituent of a liquid organic mixture (LNAPL, DNAPL) that is in equilibrium with an aqueous phase? Explain Raoult’s Law and give some practical examples of (a) cases in which you can apply it to estimate the concentration of a given LNAPL or DNAPL constituent in water that is in equilibrium with the organic liquid, and (b) cases in which Raoult’s Law does not hold. Q 10.11 When flushing a gasoline contaminated soil in a laboratory column with clean water, Mackay et al., (1996) observed that after 5 pore volumes (i.e., after 5 times replacing the water in the column), the benzene concentration in the effluent decreased from 370 to about 75 μg L–1 , while the 1,2-dimethylbenzene (o-xylene) concentration increased from 1200 to 1400 μg L–1 . Explain these findings. Problems P 10.1∗ How Much is the Olive Oil on your Balcony Contaminated by Air Pollutants You live in a town where air pollution, primarily from traffic, is quite substantial. From a recent article in the local newspaper, you learn that the benzene concentration in your area’s air may reach up to 10 parts per billion on a volume base (i.e., 10 ppbv). You wonder to what extent the olive oil that you use for your salad, which you left in an open bottle on the table on your balcony, is contaminated with this rather toxic compound. Calculate the maximum concentration of benzene in the olive oil assuming

Questions and Problems

313

an average temperature of 15◦ C and a total pressure of 1 bar. Use the ideal gas law to convert ppbv to molar concentrations. What is the situation with respect to another notorious air pollutant, benzo(a)pyrene, that is present at an average gaseous concentration of about 10 pg m–3 ? Comment on the results by comparing the calculated concentrations with the WHO drinking water standards for benzene and benzo(a)pyrene, which are 10 μg L–1 and 0.7 μg L–1 respectively. Hint: Use Eq. 10-7 to estimate the olive oil–air partition constants and make some assumptions on the temperature dependence of these constants. P 10.2∗ A Small Accident in Your Kitchen In your kitchen (T = 25◦ C) you drop a small bottle with 20 mL of the solvent 1,1,1trichloroethane (methyl chloroform), which you use for cleaning purposes. The bottle breaks and the solvent starts to evaporate. The doors and the windows are closed. On your stove sits an open pan containing 2 L of cold olive oil. Furthermore, on the floor there is a large bucket filled with 50 L of water. The air volume of the kitchen is 30 m3 . Calculate the concentration of methyl chloroform in the air, the water in the bucket, and in the olive oil at equilibrium. Assume that the adsorption of methyl chloroform to any other phases/surfaces present in the kitchen can be neglected. Comment on any other assumptions that you can make. P 10.3 Extraction of Neutral Organic Pollutants from Water Samples For analyzing organic pollutants in water samples, compounds are commonly concentrated by adsorption, purging with gas bubbles, or extraction with an organic solvent. You have the job to determine the concentration of 1-naphthol in contaminated groundwater by using gas chromatography. You want to extract 20 mL water samples with a convenient solvent. In the literature (Hansch and Leo, 1979), you find the following log Kil w values for 1-naphthol for a series of solvents: Solvent l n-hexane benzene trichloromethane (chloroform) ethyl acetate (acetic acid ethyl ester) n-octanol

log Kil w 0.52 1.89 1.82 2.60 2.90

Are you surprised to find such large differences in the Kil w values of 1-naphtol for the various solvents? If not, try to explain these differences. You decide to use ethyl acetate as the solvent for the extraction. Why would you not pick n-octanol?

OH

1-naphthol

Now you wonder how much ethyl acetate you should use. Calculate the volume of ethyl acetate that you need at minimum if you want to extract at least 99% of the total 1-naphthol present in the water sample. Are you happy with this concentration step? A colleague tells you that it would be much wiser to extract the sample twice with the goal to get 90% of the total compound each time out of the water (which would also amount to 99%), and then pool the two extracts. How much total ethyl acetate would you need in this case?

314

Organic Liquid–Air and Organic Liquid–Water Partitioning

Finally, another colleague suggests you add 3.56 g NaCl to the 20 mL sample in order to improve the extraction efficiency. How much less ethyl acetate would be required in the presence of the salt (Kis = 0.21, Table 9.4)? Is there any other effect that the addition of NaCl would have on the extraction, and is this effect favorable for the analytical procedure chosen? P 10.4 Extraction of Organic Acids and Bases from Water Samples OH Cl

Cl

Cl i = 2,4,6-trichlorophenol (2,4,6-TCP) log Kibw = 3.60 pKia = 6.15

You have the job of determining the concentrations of 2,4,6-trichlorophenol (2,4,6TCP) and 4-ethyl-2,6-dimethylpyridine (EDMP) in wastewater samples from an industrial site. You decide to extract the compounds first into an organic solvent, and then analyze them by liquid chromatography. From the Kil w values reported for the two compounds for various solvent–water systems, you conclude that there seems to be no single solvent that is optimally suited to extract the two compounds simultaneously. Would this be wise anyway? If there were such a solvent, at what pH would you carry out the extraction? What would be the problem? Regardless, you decide to extract first 2,4,6-TCP with butyl acetate (subscript b) and then EDMP with trichloromethane (chloroform, subscript c). Give the pH-conditions at which you perform the extractions and calculate how much solvent you need at a minimum in each case if you want to extract at least 98% of the compounds present in a 100 mL water sample. P 10.5 Evaluating Partition Constants of Chlorinated Phenols in Two Different Organic Solvent–Water Systems

N i = 4-ethyl-2,6-dimethyl pyridine (EDMP) log Kicw = 3.70 pKia = 7.43

Kishino and Kobayashi (1994) determined the n-octane–water (Kioctanew ) and noctanol–water (Kiow ) partition constants of a series of chlorinated phenols. Plot the log Kioctanew values versus the log Kiow values of the 13 compounds. Inspect the data and try to derive meaningful sp-LFERs of the type Eq. 10-13 for subsets of compounds. Discuss your findings in terms of the molecular interactions that govern the partitioning of the chlorinated phenols in the two different solvent–water systems. Partitioning constants for chlorinated phenols

OH 6

2 Cln

5

3 4

chlorinated phenols

Compound 1 2 3 4 5 6 7 8 9 10 11 12 13

Phenol 2-Chlorophenol 3-Chlorophenol 4-Chlorophenol 2,3-Dichlorophenol 2,4-Dichlorophenol 2,5-Dichloropehol 2,6-Dichlorophenol 3,5-Dichlorophenol 2,4,5-Trichlorophenol 2,4,6-Trichlorophenol 2,3,4,6-Tetrachlorophenol Pentachlorophenol

log Kioctanew

log Kiow a

−0.99 0.74 −0.31 −0.41 1.27 1.21 1.31 1.48 0.41 1.76 2.05 2.58 3.18

1.57 2.29 2.64 2.53 3.26 3.20 3.36 2.92 3.60 4.02 3.67 4.24 5.02

a Values given in the Appendix may differ somewhat from the ones determined by Kishino and Kobayashi (1994).

315

Questions and Problems

P 10.6∗ Estimating Octanol–Water Partition Constants Using the Atom/Fragment Contribution Method Estimate the Kiow values at 25◦ C of (a) ethyl acetate, (b) 2,3,7,8-tetrachlorodibenzodioxin, (c) the herbicide 2-s-butyl-4,6-dinitrophenol (Dinoseb), (d) the insecticide parathion, and (e) the hormone testosterone using solely the fragment coefficients and correction factors given in Tables 10.4 and 10.5 (Eq.10-19). Compare the estimated values with the experimental Kiow values that you can find in Appendix C. Comment on the results. OH NO2 O O ethyl acetate

Cl

O

Cl

Cl

O

Cl

NO2 2-s-butyl-4,6-dinitrophenol (Dinoseb)

2,3,7,8-tetrachlorobenzodioxin

NO2 OH

O O

P

S

O O testosterone

parathion

P 10.7 Estimating Octanol–Water Partition Constants from Known Values of Structurally Closely Related Compounds Using the Atom/Fragment Contribution Method Estimate the Kiow values of the following four compounds by using the Kiow value of a structurally related compound (Eq. 10-20) that you choose from Appendix C. Are the estimates different than the indicated experimental Kiow values? If so, why? O

OH

O O

Cl

n-pentyl acetate (exp. log K iow = 2.23)

H N

3,5-dichloro benzoic acid (exp. log K iow = 3.00)

Cl

N O

Cl

S O

P

O

O Cl chlortoluron (exp. log K iow = 2.41)

Cl toldofus-methyl (exp. log K iow = 4.56)

316

Organic Liquid–Air and Organic Liquid–Water Partitioning

P 10.8 Estimating the Solubilities and the Activity Coefficients of Organic Pollutants in Organic Solvent (CMOS)/Water Mixtures Estimate the solubility and the activity coefficient of naphthalene in a 30% methanol/70% water (v:v) mixture at 25◦ C. naphthalene

sat Ciw (25◦ C) = 2.5×10−4 mol L−1 Tm = 80.2◦ C 𝛾 sat (25◦ C) = 6.7×104 iw (see Table 9.1)

P 10.9 Assessing the Dissolution Behavior of Gasoline Components Gasoline is a mixture of primarily aliphatic (>50%) and aromatic (∼30%) hydrocar̄ gas , of about 105 g mol–1 and a density of about bons with an average molar mass, M 0.75 g cm–3 (Cline et al., 1991). In addition, it contains a variety of additives, including oxygenates, anti-oxidants, corrosion inhibitors, detergents, anti-freezing agents, and dyes (see Chapter 3). You are asked to investigate a gasoline spill underneath a gas station. Compounds that are among those of great concern with respect to groundwater pollution are benzene and 3,4-dimethylaniline (DMA). You know that the spilled gasoline contains 2 volume percent benzene and 10 mg L–1 DMA. Furthermore, in the literature, you find experimental gasoline–water partition coefficients (Eq. 10-33) of 300 Lw L−1 gasoline for benzene (Cline et al., 1991) and 30 Lw L−1 gasoline for DMA (Schmidt et al., 2002; at pH 8 where DMA is present primarily as neutral species). These coefficients have been determined for other brands of gasoline. With this information, answer the following questions: (a) Using the gasoline–water partition coefficients reported in the literature, calculate the activity coefficients of benzene and DMA in the gasoline mixture of interest. Which of the two values do you trust more? (b) What benzene and DMA concentration would you expect in groundwater that is in equilibrium with a large pool of the spilled gasoline at 25◦ C (i.e., assume that the gasoline composition is not altered significantly by the dissolution of the components in the aqueous phase)? (c) In the aqueous phase that is in equilibrium with the spilled gasoline, you measure a naphthalene concentration of 1 mg L–1 . How much naphthalene does the gasoline contain? Comment on any assumptions that you make. Hint: To estimate the mole fraction of a given gasoline component from its volume fraction, use Eq. 10-24 by assuming a binary mixture of the component with a solvent that has the average molar volume of the whole gasoline mixture. P 10.10 Estimating the Concentrations of Individual PCB Congeners in Water that is in Equilibrium with an Aroclor/Hydraulic Oil Mixture. Aroclor 1242 is a commercial PCB mixture with an average chlorine content of ̄ Aroclor , of about 265 g mol–1 and a density, ρAroclor , of 42%, an average molar mass M

Bibliography

O

R O

P

R O

O

R Fyrquel 220 hydraulic oil (R is primarily n-butyl)

10.7

317

1.39 g cm–3 . Luthy et al., (1997) have determined the composition of a pure Aroclor 1242 mixture, and they have measured the aqueous concentrations of some individual congeners at 25◦ C in equilibrium with the real Aroclor 1242 mixture (see Box 10.1) and a mixture of 5% (v/v) Aroclor 1242 in a hydraulic oil (Fyrquel 220) consisting of trialkyl-phenyl phosphates (see structure in margin), with an average molar ̄ Aroclor , of about 380 g mol–1 and a density, ρFyrquel , of 1.14 g cm–3 at 25◦ C. mass, M Among the congeners investigated was 2,2′ ,5,5′ -tetrachlorobiphenyl (PCB 52), which was determined to be present in the Aroclor 1242 mixture at about 3.2 mass percent ). The measured aqueous concentrations (i.e., mass fraction miAroclor = 0.032 gi g−1 Aroclor for this compound in equilibrium with Fyrquel was 0.10 μg L–1 . Is this concentration reasonable? What aqueous PCB 52 concentrations would you have predicted from the preceding information, when assuming that Raoult’s Law is valid?

Bibliography Abraham, M. H.; Acree, W. E., Comparison of solubility of gases and vapours in wet and dry alcohols, especially octan-1-ol. J. Phys. Org. Chem. 2008, 21(10), 823–832. Abraham, M. H.; Acree, W. E., Partition coefficients and solubilities of compounds in the waterethanol solvent system. J. Solut. Chem. 2011, 40(7), 1279–1290. Abraham, M. H.; Acree, W. E.; Leo, A. J.; Hoekman, D., The partition of compounds from water and from air into wet and dry ketones. New J. Chem. 2009, 33(3), 568–573. Arey, J. S.; Nelson, R. K.; Reddy, C. M., Disentangling oil weathering using GCxGC. 1. Chromatogram analysis. Environ. Sci. Technol. 2007, 41(16), 5738–5746. Atkinson, D.; Curthoys, G., The determination of heats of adsorption by gas-solid chromatography. J. Chem. Educ. 1978, 55(9), 564-566. Augustijn, D. C. M.; Jessup, R. E.; Rao, P. S. C.; Wood, A. L., Remediation of contaminated soils by solvent flushing. J. Environ. Eng.-ASCE 1994, 120(1), 42–57. Barton, A. F. M., Ed., CRC Handbook of Solubility Parameters and Other Cohesion Parameters. 2 ed.; CRC Press: Boca Raton, FL, 1991. Beyer, A.; Wania, F.; Gouin, T.; Mackay, D.; Matthies, M., Selecting internally consistent physicochemical properties of organic compounds. Environ. Toxicol. Chem. 2002, 21(5), 941–953. Broholm, K.; Feenstra, S., Laboratory measurements of the aqueous solubility of mixtures of chlorinated solvents. Environ. Toxicol. Chem. 1995, 14(1), 9–15. Chou, J. T.; Jurs, P. C., Computer-assisted computation of partition coefficients from molecular structures using fragment constants. J. Chem. Inf. Comput. Sci. 1979, 19(3), 172–178. Cline, P. V.; Delfino, J. J.; Rao, P. S. C., Partitioning of aromatic constituents into water from gasoline and other complex solvent mixtures. Environ. Sci. Technol. 1991, 25(5), 914–920. Coyle, G. T.; Harmon, T. C.; Suffet, I. H., Aqueous solubility depression for hydrophobic organic chemicals in the presence of partially miscible organic solvents. Environ. Sci. Technol. 1997, 31(2), 384–389. de Hemptinne, J. C.; Delepine, H.; Jose, C.; Jose, J., Aqueous solubility of hydrocarbon mixtures. Rev. Inst. Fr. Pet. 1998, 53(4), 409–419. Demond, A. H.; Lindner, A. S., Estimation of interfacial tension between organic liquids and water. Environ. Sci. Technol. 1993, 27(12), 2318–2331. Dickhut, R. M.; Andren, A. W.; Armstrong, D. E., Naphthalene solubility in selected organic solvent/water mixtures. J. Chem. Eng. Data 1989, 34(4), 438–443. Endo, S.; Watanabe, N.; Ulrich, N.; Bronner, G.; Goss, K. U., UFZ-LSER database v 2.1 [Internet]. Helmholtz Centre for Environmental Research-UFZ: Leipzig, Germany,

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2014 [accessed on April 19, 2014]. http://www.ufz.de/index.php?en=31698&contentonly= 1&lserd data[mvc]=Public/start. Fan, C. H.; Jafvert, C. T., Margules equations applied to PAH solubilities in alcohol-water mixtures. Environ. Sci. Technol. 1997, 31(12), 3516–3522. Garg, S.; Rixey, W. G., The dissolution of benzene, toluene, m-xylene and naphthalene from a residually trapped non-aqueous phase liquid under mass transfer limited conditions. J. Contam. Hydrol. 1999, 36(3-4), 313–331. Ghosh, R. S.; Saigal, S.; Dzombak, D. A., Assessment of in situ solvent extraction with interrupted pumping for remediation of subsurface coal tar contamination. Water Environ. Res. 1997, 69(3), 295–304. Goss, K. U., Predicting the equilibrium partitioning of organic compounds using just one linear solvation energy relationship (LSER). Fluid Phase Equilib. 2005, 233(1), 19–22. Groves, F. R., Effect of cosolvents on the solubility of hydrocarbons in water. Environ. Sci. Technol. 1988, 22(3), 282–286. Hansch, C.; Leo, A., Substituent Constants for Correlation Analysis in Chemistry and Biology. Wiley: New York, 1979; p 178. Hansch, C.; Leo, A., Exploring QSAR: Fundamentals and Applications in Chemistry and Biology. American Chemical Society: Washington, D.C., 1995; Vol. 1, p 557. Hansch, C.; Leo, A.; Hoekman, D., Exploring QSAR: Hydrophobic, Electronic and Steric Constants. American Chemical Society: Washington, D.C., 1995; Vol. 2, p 348. Heermann, S. E.; Powers, S. E., Modeling the partitioning of BTEX in water-reformulated gasoline systems containing ethanol. J. Contam. Hydrol. 1998, 34(4), 315–341. Hui, Y. M., Ed., Bailey’s Industrial Oil and Fat Products, Edible Oil and Fat Products: General Applications Wiley: New York, 1996; Vol. 1, p 560. Jayasinghe, D. S.; Brownawell, B. J.; Hua, C.; Westall, J. C., Determination of Henry’s constants of organic compounds of low volatility: Methylanilines in methanol-water. Environ. Sci. Technol. 1992, 26(11), 2275–2281. Khossravi, D.; Connors, K. A., Solvent effects on chemical processes. I: Solubility of aromatic and heterocyclic compounds in binary aqueous-organic solvents. J. Pharm. Sci. 1992, 81(4), 371–379. Kishino, T.; Kobayashi, K., Relation between the chemical structures of chlorophenols and their dissociation constants and partition coefficients in several solvent-water systems. Water Res. 1994, 28(7), 1547–1552. Lane, W. F.; Loehr, R. C., Estimating the equilibrium aqueous concentrations of polynuclear aromatic hydrocarbons in complex mixtures. Environ. Sci. Technol. 1992, 26(5), 983– 990. Lee, L. S.; Hagwall, M.; Delfino, J. J.; Rao, P. S. C., Partitioning of polycyclic aromatic hydrocarbons from diesel fuel into water. Environ. Sci. Technol. 1992a, 26(11), 2104–2110. Lee, L. S.; Rao, P. S. C.; Okuda, I., Equilibrium partitioning of polycyclic aromatic hydrocarbons from coal tar into water. Environ. Sci. Technol. 1992b, 26(11), 2110–2115. Lemkau, K. L.; Peacock, E. E.; Nelson, R. K.; Ventura, G. T.; Kovecses, J. L.; Reddy, C. M., The M/V Cosco Busan spill: Source identification and short-term fate. Mar. Pollut. Bull. 2010, 60(11), 2123–2129. Li, A.; Andren, A. W., Solubility of polychlorinated biphenyls in water/alcohol mixtures. 1. Experimental data. Environ. Sci. Technol. 1994, 28(1), 47–52. Li, A.; Andren, A. W., Solubility of polychlorinated biphenyls in water/alcohol mixtures. 2. Predictive methods. Environ. Sci. Technol. 1995, 29(12), 3001–3006. Li, A.; Andren, A. W.; Yalkowsky, S. H., Choosing a cosolvent: Solubilization of naphthalene and cosolvent property. Environ. Toxicol. Chem. 1996, 15(12), 2233–2239.

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Luthy, R. G.; Dzombak, D. A.; Shannon, M. J. R.; Unterman, R.; Smith, J. R., Dissolution of PCB congeners from an Aroclor and an Aroclor/hydraulic oil mixture. Water Res. 1997, 31(3), 561– 573. Machatha, S. G.; Yalkowsky, S. H., Bilinear model for the prediction of drug solubility in ethanol/water mixtures. J. Pharm. Sci. 2005, 94(12), 2731–2734. Mackay, A. A.; Chin, Y. P.; MacFarlane, J. K.; Gschwend, P. M., Laboratory assessment of BTEX soil flushing. Environ. Sci. Technol. 1996, 30(11), 3223–3231. Meylan, W. M.; Howard, P. H., Atom/fragment contribution method for estimating octanol–water partition coefficients. J. Pharm. Sci. 1995, 84(1), 83–92. Millard, J. W.; Alvarez-Nunez, F. A.; Yalkowsky, S. H., Solubilization by cosolvents - Establishing useful constants for the log-linear model. Int. J. Pharm. 2002, 245(1-2), 153–166. Mintz, C.; Burton, K.; Ladlie, T.; Clark, M.; Acree, W. E.; Abraham, M. H., Enthalpy of solvation correlations for gaseous solutes dissolved in dibutyl ether and ethyl acetate. Thermochim. Acta 2008, 470(1–2), 67–76. Mintz, C.; Clark, M.; Acree, W. E.; Abraham, M. H., Enthalpy of solvation correlations for gaseous solutes dissolved in water and in 1-octanol based on the abraham model. J. Chem Inf. Model. 2007, 47(1), 115–121. Morris, K. R.; Abramowitz, R.; Pinal, R.; Davis, P.; Yalkowsky, S. H., Solubility of aromatic pollutants in mixed solvents. Chemosphere 1988, 17(2), 285–298. Munz, C.; Roberts, P. V., Effects of solute concentration and cosolvents on the aqueous activity coefficient of halogenated hydrocarbons. Environ. Sci. Technol. 1986, 20(8), 830–836. Peters, C. A.; Knightes, C. D.; Brown, D. G., Long-term composition dynamics of PAH-containing NAPLs and implications for risk assessment. Environ. Sci. Technol. 1999b, 33(24), 4499–4507. Peters, C. A.; Mukherji, S.; Weber, W. J., UNIFAC modeling of multicomponent nonaqueous phase liquids containing polycyclic aromatic hydrocarbons. Environ. Toxicol. Chem. 1999a, 18(3), 426–429. Picel, K. C.; Stamoudis, V. C.; Simmons, M. S., Distribution coefficients for chemical components of a coal-oil/water system. Water Res. 1988, 22(9), 1189–1199. Pinal, R.; Lee, L. S.; Rao, P. S. C., Prediction of the solubility of hydrophobic compounds in nonideal solvent mixtures. Chemosphere 1991, 22(9–10), 939–951. Pinal, R.; Rao, P. S. C.; Lee, L. S.; Cline, P. V.; Yalkowsky, S. H., Cosolvency of partially miscible organic solvents on the solubility of hydrophobic organic chemicals. Environ. Sci. Technol. 1990, 24(5), 639–647. Poulsen, M.; Lemon, L.; Barker, J. F., Dissolution of monoaromatic hydrocarbons into groundwater from gasoline-oxygenate mixtures. Environ. Sci. Technol. 1992, 26(12), 2483–2489. Rekker, R. F., The Hydrophobic Fragmental Constant: Its Derivation and Application with a Means of Characterizing Membrane Systems. Elsevier: Amsterdam, 1977; p 390. Schmidt, T. C.; Kleinert, P.; Stengel, C.; Goss, K. U.; Haderlein, S. B., Polar fuel constituents: Compound identification and equilibrium partitioning between nonaqueous phase liquids and water. Environ. Sci. Technol. 2002, 36(19), 4074–4080. U.S. EPA, Estimation Programs Interface SuiteTM for Microsoft® Windows, v 4.11. United States Environmental Protection Agency: Washington, DC, 2012. http://www.epa.gov/opptintr/ exposure/pubs/episuite.htm.

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Chapter 11

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

11.1 Introduction 11.2 Adsorption from Air to Well-Defined Surfaces Characteristics of Mineral Surfaces Surface–Air Partition Constants: Definition and Temperature Dependence sp-LFER Modeling Approach to Estimate Surface–Air Partitioning pp-LFER Modeling Approach to Estimate Surface–Air Partitioning Box 11.1 Estimating the Fraction of Phenanthrene in the Gas Phase and Sorbed to the Walls of a Vessel 11.3 Adsorption from Water to Inorganic Surfaces Nonspecific Adsorption of Nonionic Organic Compounds to Mineral Surfaces Specific Adsorption of Nonionic Organic Compounds to Mineral Surfaces 11.4 Questions and Problems 11.5 Bibliography

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

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Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

11.1

Introduction In the previous chapters on equilibrium partitioning, our discussions focused on molecules penetrating into bulk phases, such as benzene dissolving in water, which is referred to as absorption into a phase. We assumed that (1) the presence of the compound of interest did not influence the properties of the phases considered and (2) the partition constant was independent of solute concentration, with the case of liquid organic mixtures (Section 10.4) being an exception. In this chapter, we focus on the partitioning of organic compounds to solid and liquid surfaces, a process termed adsorption. Such two-dimensional surfaces only have a limited number of sites available for adsorption. Hence, the partition “constant” may change with increasing compound (sorbate) concentration in the bulk phase due to the corresponding increasing surface coverage. In this chapter, we are primarily interested in understanding and quantifying the molecular interactions governing adsorption to well-defined surfaces. Therefore, we consider only cases in which compound concentrations are small enough so we can assume a concentration-independent partitioning (adsorption) constant, as we did for absorption processes. We also limit the discussion to neutral compounds that do not interact specifically with charged surface species via complexation or electrostatic interactions. Ionic interactions, which are particularly important in aquatic systems, are addressed in Chapter 14. The main focus of this chapter is on adsorption of such nonionic compounds from the gas phase (i.e., air) to inorganic surfaces including water and ice surfaces, mineral surfaces, and salt surfaces. We also briefly address some organic surfaces for comparison; partitioning to organic surfaces, in particular to carbonaceous materials, is discussed in Chapter 13.

11.2

Adsorption from Air to Well-Defined Surfaces In the environmental assessment of nonionic organic chemicals, transfer processes between air and natural surfaces are frequently neglected. Absorption of such chemicals from air into bulk phases such as water or organic phases is assumed to be the dominant partitioning process. However, adsorption, particularly to inorganic surfaces, may be more important than absorption in situations such as transfer from air to snow or ice surfaces; to the surfaces of small water droplets (< 10 μm) in fog; to inorganic aerosols as encountered above the sea (i.e., salts), above deserts (i.e., mineral dust), or in urban areas (e.g., carbonaceous materials); and, last but not least, to abundant soil minerals such as quartz and clays, particularly at low humidity. Knowledge of the adsorption behavior of organic chemicals from air onto surfaces of solids or liquids is also important for indoor and outdoor air quality assessments and the design of engineered systems including air purification systems (e.g., filters). Unfortunately, to date, rather few studies have systematically investigated the exchange of organic chemicals between the gas phase and environmentally important inorganic surfaces. Nevertheless, since from a molecular interaction point of view, adsorption from the air to a surface of a condensed phase (Fig. 11.1) is somewhat easier to treat than absorption processes involving bulk phases where cavity formation has to be

Adsorption from Air to Well-Defined Surfaces

air (a)

i

adsorption to surface of condensed phase: ΔGisurface

323

taken into account (see Fig. 7.1), some important general insights into this process are possible with the limited experimental data available. Characteristics of Mineral Surfaces

Among the inorganic surfaces, mineral surfaces are the most significant for adsorption processes involving gaseous organic compounds in the environment. Many common minerals expose a surface to the exterior that consists of hydroxyl groups protruding surface (surf) into the medium from a “checker board” plane of electron-deficient metals (e.g., Si, Figure 11.1 Adsorption of a com- Al, Fe) and electron-rich ligands (e.g., hydroxyl, carbonate) (Fig. 11.2a). Like water pound i from air (assuming an ideal molecules, these surface groups typically include a combination of hydrogen donors gas phase) to a surface of a con- (e.g., –OH, –C(=O)OH) and acceptors (–OH, –C(=O)OH, and –O–). Therefore, such densed phase. bipolar surfaces interact with molecules adjacent to the mineral surface via vdW, Hdonor, and H-acceptor interactions. We can use data of pure liquid:silica solid attractions (Fowkes, 1964) to understand the relative contributions of such molecule:surface interactions (Fig. 11.2b). While all sorbates are attracted to all surfaces by vdW forces, stronger attractions per unit surface area of silica are observed as complementary functional groups are included on the surface and the sorbate that are capable of H-bonding (note that the free energies of adsorption, Δsurfa Gi , are in mJ m−2 ). This surface attraction energy is very strong for an H-donor and H-acceptor sorbate like water (−460 mJ m−2 ), as compared to other small nonionic organic compounds (Fig. 11.2b). Thus, such surfaces strongly prefer to bind water, and the overall energy change resulting from adsorption of organic chemicals directly to water-wet solids would have to include the high “cost” of desorption of water from the same surface. i

ΔsurfaGi = ΔGisurface

In the environment, minerals are almost always exposed to water vapor, and one may reasonably expect these natural polar surfaces are water-wet. The extent of the water coverage, however, can vary. The amount of water at a mineral surface is proportional to the activity of water in the atmosphere (i.e., the ratio of water’s partial pressure to its saturation pressure at the particular temperature); the saturation vapor pressure of water at ambient temperatures corresponds to about 1 mol of water per m3 of air. Commonly, such water activity is quantified in terms of “relative humidity” (RH) where 100% RH implies the air is equilibrated with pure water liquid, thus the activity of the water in the atmosphere is equal to 1. Therefore, the extent of water coverage at a surface can be related to RH (Fig. 11.3a). The first monolayer of water (a one water molecule-thick layer everywhere) occurs at RH conditions much less than 100%. For example, many pure mineral oxides exhibit monolayer coverage at about 30% RH (Goss and Schwarzenbach, 1999a; Goss, 2004). Compositionally heterogeneous soils have been reported to have monolayer quantities of water at less than 20% RH (Chiou and Shoup, 1985). At greater RH, this layer of water on which other sorbates adsorb grows thicker and thicker (see Fig. 11.3b). For example, Chiou and Shoup (1985) observed that adsorbed water on a soil equaled about three times monolayer coverage at 80% RH. As the water coverage at a mineral surface changes with RH, so does the affinity for organic compounds adsorbing from the gas phase. At lower water coverage, vdW and H-bonding interactions directly with the mineral surface drive attraction. Once water coverage at a mineral surface reaches about five to six monolayers, the

324

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

Figure 11.2 (a) A schematic view of a mineral surface exhibiting loci of partial positive charges where metal atoms occur (Mδ+ ) and partial negative charges where linking anions occur (Oδ− ) and hydroxyls extending to the exterior. (b) Interactions of organic chemicals wetting silica surfaces and estimates of the Δsurfa Gi values derived from surface tension data (Fowkes, 1964).

Adsorption from Air to Well-Defined Surfaces

Figure 11.3 (a) Typical increase of adsorbed water on a mineral oxide surface as function of relative humidity. (b) Illustration of adsorption of neutral organic compounds to polar mineral surface with varying water surface coverage (related to RH).

adsorbed water (mg m−2)

4

(a)

(b)

6 molecular layers

3

10% rel. humidity i

40% rel. humidity i

5 molecular layers

2

80% rel. humidity i

monolayer coverage 1

0

325

90% rel. humidity i

0

20

40 60 relative humidity (%)

80

100

adsorbed water mineral surface

surface properties of the water film, particularly those describing vdW interactions, resemble those of pure water. As such, much weaker molecular interactions, as compared to a “dryer” mineral surface (at low RH), drive attraction of organic pollutants. This decrease in attraction is illustrated by Fig. 11.4, which shows the adsorption of 1,3-dichlorobenzene to a soil at different RH. At 0% RH, adsorption is strongest and decreases with increasing RH; at 90% RH, adsorption is minimal. In conclusion, as we continue our discussion of adsorption, we need to remember that partially water-wet mineral surfaces, not completely dry surfaces, must be considered as adsorbents of organic chemicals from air and that the amount of water coverage is important.

0.3

Cis (mol kg−1)

Cl

Figure 11.4 Adsorption of 1,3-dichlorobenzene on Woodburn soil at 20◦ C at different relative humidities. Data from Chiou and Shoup (1985).

0.2

Cl

on soil

0% RH 50% RH 90% RH

0.1

0

0

5.0×10 –5 Cia (mol L−1)

1.0×10 –4

326

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

Surface–Air Partition Constants: Definition and Temperature Dependence Since adsorption to a surface is proportional to the available surface area of the condensed phase, we define the equilibrium partition coefficient, Kisurfa , as the concentration of the compound on the surface per unit surface area of the condensed phase divided by the concentration in air:

Kisurfa (e.g., m) =

Cisurf (e.g., mol m−2 surf) Cia (e.g., mol m−3 a )

(11-1)

Hence, Kisurfa is expressed, for example, in m3a m−2 surface which we denote in Eq. 11-1 simply as m. If the surface area is not known, the partition constant is normalized to the mass of the solid (subscript s): Kisa (e.g., La kg−1 solid) =

Cis (e.g., mol kg−1 solid) Cia (e.g., mol L−1 a )

(11-2)

As the adsorption process, however, is a surface process, the normalized Kisa derived for a particular inorganic solid is not directly applicable to the same material from another source. We assume that Kisurfa or Kisa is not dependent on the concentration of the compound at the surface; that is, we assume that the sorbing compound molecules, i, do not “feel each other” at the solid surface as the surface is far from saturated. All sites at the surface are assumed to be equally interactive with respect to intermolecular interactions, leading to a “linear adsorption isotherm” (see Chapter 12). With respect to the effect of temperature on Kisurfa , as for all other partition processes discussed so far, we need to know the enthalpy of the phase transfer, in this case Δsurfa Hi . As stated in Chapter 4 (Section 4.2), the molar volume of gases is temperature dependent, and so if the partition constant is expressed in molar concentrations, Δsurfa Hi has to be replaced by Δsurfa Hi + RTav , where Tav is the average temperature (in K) of the temperature range considered (Atkinson and Curthoys, 1978). However, because RTav is only about 2.5 kJ mol−1 , we neglect this term. Hence, we write: ln Kisurfa (T) = −

Δsurfa Hi 1 + const R T

(11-3)

Similar to the prediction of enthalpies of vaporization from vapor pressure data (Eq. 8-14), Goss and Schwarzenbach (1999b) derived an empirical relationship to estimate Δsurfa Hi from Kisurfa at 15◦ C (288K): Δsurfa Hi (kJ mol−1 ) = −9.83 log Kisurfa (m) − 90.5

(11-4)

As verified by Arp et al. (2006a), Eq. 11-4 predicts Δsurfa Hi with a standard error of less than ±15 kJ mol−1 , which, for most practical applications, is sufficient. Hence,

Adsorption from Air to Well-Defined Surfaces

327

assuming Δsurfa Hi is constant over the ambient temperature range, we can estimate the surface–air partition constant at any other temperature by: Kisurfa (T) = Kisurfa (288K) e

−

Δsurfa Hi (288K) R

(

1 − 1 T 288

)

(11-5)

sp-LFER Modeling Approach to Estimate Surface–Air Partitioning The traditional and still most widely used approach to estimate surface–air partition constants is to apply simple single-parameter LFERs (sp-LFERs) relating Kisurfa to the liquid vapor pressure, p∗iL , of the compound: log Kisurfa (T)(m) = −a log p∗iL (T)(Pa) + b

(11-6)

Similar to the sp-LFERs applied earlier to estimate bulk phase–air and bulk phase– water partition constants or coefficients using, for example, octanol–air or octanol– water partition constants (see Chapters 7 and 10), the slope, a, and the intercept, b, in Eq. 11-6 are determined by a linear regression analysis of a set of compounds with known Kisurfa values. We use a minus sign for the term log p∗iL since we use the surface–air and not the air–surface partition constant. Figure 11.5 shows the application of Eq. 11-6 to adsorption from air to a quartz surface at 90% RH; good relations are restricted to structurally related compounds, particularly for mono- and bipolar compounds adsorbing to this polar surface. Furthermore, as previously discussed (Figs. 11.3 and 11.4), even when considering the same surface, the system’s RH may have a large impact on Kisurfa . Thus, for a given surface, one has to derive not only different sp-LFERs for different groups of compounds but also for different RHs. Since a 0 apolar compounds

experimental log Kisurfa (m3m–2)

–1

monopolar compounds

–2

bipolar compounds

–3

–4

–5 Figure 11.5 Experimental Kisurfa values for different apolar, monopolar, and bipolar compounds on a quartz surface at 90% RH versus liquid vapor pressure, p∗iL , of the compound. Data from Arp et al. (2006a).

–6 –6

–5

–4

–3 –log piL* (Pa)

–2

–1

0

328

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

model that incorporates both compound and surface variability in one equation would be highly advantageous, we now turn to pp-LFERs. pp-LFER Modeling Approach to Estimate Surface–Air Partitioning As depicted in Fig. 11.1, adsorption to a surface, including water-wet mineral surfaces, does not involve any cavity formation. As a consequence, we do not need to consider such a contribution when describing the free energy of surface–air partitioning as we have done for bulk phase–air partitioning (see Chapter 7, Fig. 7.1). Therefore, the surface–air partition constant can be simply related to the free energy of transfer from the gas phase to the surface: log Kisurfa = −Δsurfa Gi ∕2.303RT + constant

(11-7)

The constant in Eq. 11-7 depends on the units of Kisurfa , and the chosen air and surface standard states. As proposed by Goss (2004), when only considering interactions of the compound with the surface (vdW and H-bonding), using the units defined in Eq. 11-1, and defining the surface standard state as proposed by de Boer (1968), Eq. 11-7 can be written as: ( ) H (11-8) log Kisurfa (m) = − ΔvdW isurf Gi + Δisurf Gi ∕2.302RT − 8.47 or as expressed by introducing corresponding vdW and H-bonding pp-LFER terms: log Kisurfa (m) = a1 (vdWi )(vdWsurf ) + a2 (HDi )(HAsurf ) + a3 (HAi )(HDsurf ) − 8.47 (11-9) In contrast to pp-LFERs used for bulk phase partitioning introduced in Chapter 7 (Eq. 7-12) then used throughout Chapters 8 to 10, we only need three terms to describe adsorption from air to surfaces, and we explicitly express the corresponding surface parameters. The coefficients a1 , a2 , and a3 are scaling factors that depend on the specific parameters used for the description of the vdW and H-bonding terms and, of course, on temperature. In bulk partitioning, the system descriptors (i.e., v, e, l, s, a, b) include scaling and characterization of the bulk phases involved. Using the same solute descriptors as for bulk phase partitioning (Li , Ai , and Bi ), Eq. 11-9 can be expressed as: log Kisurfa (m) = a1 (vdWsurf )Li + a2 (HAsurf )Ai + a3 (HDsurf )Bi − 8.47

(11-10)

We now need to define the parameters for vdW and H-bonding interactions (vdWsurf , HAsurf , and HDsurf ) for a surface in order to solve Eq. 11-10 and apply it to specific surfaces. Parameters for vdW and H-Bonding Interactions for Surfaces. The first parameter in Eq. 11-10, the vdW surface parameter vdWsurf , may √be expressed by the square root

of the vdW component of the surface free energy, 𝛾 vdW , which can be determined surf √ independently (Goss, 2004). For water, 𝛾 vdW is 4.7 (mJ m−2 )0.5 ; values for various surf

Adsorption from Air to Well-Defined Surfaces

329

Table 11.1 Van der Waals (vdWsurf ), H-Acceptor (Electron Donor) (HAsurf ), and H-Donor (Electron Acceptor) (HDsurf ) Values for Some Condensed Phases at 15◦ C (or as stated)a

Surface Inorganic Surfaces Water Water (0◦ C) Ice (0◦ C) Quartz (SiO2 ) Ca-kaolinite Hematite (Fe2 O3 ) Limestone (CaCO3 ) Corundum (Al2 O3 ) KNO3 (NH4 )2 SO4 NH4 Cl NaCl Organic Surfaces Paraffin wax (H–(CH2 )n –H) Teflon (F–(CF2 )n –F) Nylon 6,6 Activated carbon Graphite

Relative Humidity (RH, %)b

vdWsurf c (mJ m−2 )0.5

HAsurf d

HDsurf d

100 100 100 45 90 30 90 30 90 40 90 40 90 35 60 35 70 35 60 35 60

4.7 4.7 5.4 6.8 5.3 7.0 4.7 6.5 4.8 5.4 4.9 5.4 4.8 7.1 6.8 6.6 6.3 6.8 6.3 6.2 6.0

1.0 n.a. n.a. 0.89 0.88 n.a. n.a. n.a. n.a. 1.20 1.01 1.13 1.05 0.99 1.00 1.08 1.34 1.19 1.21 1.11 1.06

1.0 n.a. n.a. 1.06 0.85 1.12 0.75 0.92 0.76 0.96 0.91 1.00 0.89 0.75 0.70 0.73 0.53 0.75 0.69 0.79 0.77

n.r. n.r. n.a n.r. n.a.

5.0 4.2 6.0 ∼11 10.7–11.5

0 0

0 0

a

Data from Goss (1997), Goss and Schwarzenbach (1999a and 2002), and Goss et al. (2003). n.r. = not relevant, n.a. = not available. c Square root of the van der Waals component of the surface free energy. d Relative to the H-acceptor and H-donor properties of water. b

√ for the other surfaces at different RH are shown in Table 11.1. Values for 𝛾 vdW surf mineral surfaces, salts, and organic surfaces vary significantly from about 4 (Teflon) to almost 12 (graphite). An interesting observation can be made when comparing the vdWsurf value of the bulk water surface with those of a series of representative mineral surfaces (i.e., quartz, kaolinite, hematite, limestone, corundum). As evident in Fig. 11.6a, in all cases, vdWsurf decreases significantly with increasing relative humidity (RH) and approaches

330

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

the bulk water surface value when approaching water vapor saturation. As discussed earlier, most organic molecules cannot compete well with water for the sorption sites at mineral surfaces. In the presence of water, organic molecules can only adsorb on top of the adsorbed water film (as pictured in Fig. 11.3b). With increasing numbers of water layers, the vdW interactions at the surface of the adsorbed water films become more and more independent of the surface type that is underneath the water molecules. Thus, at 90% RH which corresponds to an average of about 5 to 9 molecular layers of adsorbed water (Fig. 11.3a), an apolar compound cannot tell the difference between a quartz (SiO2 ) and a corrundum (Al2 O3 ) surface, while at 20% RH the differences are significant.

10

(a)

vdWsurf (mJ m–2)0.5

8 6 bulk water surface

4 2 0

0

1.4

20

40

60

80

100

(b)

HDsurf

1.0

bulk water surface

0.8 0.6 0.4 0.2 0

NaCl NH4Cl (NH4)2SO4 quartz

1.2

Figure 11.6 (a) van der Waals parameter vdWsurf and (b) H-donor parameters HDsurf of various surfaces as a function of relative humidity (RH) at 15 to 20◦ C. The corresponding values for a bulk water surface are indicated. Data from Goss and Schwarzenbach (1999a and 2002); values between 30 and 90% RH are estimated from linear interpolation.

Al2O3 CaCO3 hematite kaolinite KNO3

0

20

40 60 relative humidity (% RH)

80

100

Adsorption from Air to Well-Defined Surfaces

331

The H-bonding parameters in Eq. 11-10 are not independently measured, but HAsurf and HDsurf are rather determined according to a scale with water set equal to 1.0 and alkanes set to 0.0 (Goss, 2004). Values for other surfaces, therefore, are relative to a water surface (Table 11.1). For mineral surfaces, the HDsurf values decrease with increasing RH and become somewhat more similar among the various surfaces (Fig. 11.6b). However, in contrast to the vdW parameter, the values of HDsurf at 90% RH (0.65-0.91) are smaller than that of the bulk water surface (1.0). HAsurf values for the same surfaces at 90% are often quite similar to the water surface (Table 11.1). These deviations from a water surface may be due to the orientation of the water molecules caused by the nearby solid surface, but a definitive explanation is still missing. Between 90 and 100% RH, when the thickness of the adsorbed water layer rapidly grows, one can expect that these deviations disappear. Salt surfaces are particularly important when considering partitioning to aerosols in the marine environment. Compared to mineral surfaces, the salt surface parameters exhibit a considerably weaker dependence on RH (Figs. 11.6a and b and Table 11.1); this weaker dependence is because all four salts considered are hygroscopic and, therefore, adsorb water in significant amounts at low RH. However, the type of underlying salt still has a strong influence on the surface water layer because one can assume that this layer represents a saturated solution of the salt. It is not surprising then that the vdW, the HAsurf and the HDsurf values of the different salts do not become similar at high RH and that they do not match the values of the pure bulk water surface. Values above 60 or 70% RH are not currently available, but one can assume that they do not change at higher humidity (Goss and Schwarzenbach, 1999a). Finally, for organic hydrophobic surfaces (e.g., paraffin wax, polyethylene, polyvinylchloride, polystyrene, Teflon) to which water molecules only weakly adsorb, the effect of humidity can most likely be neglected for all the surface parameters. As a final note on the surface parameters provided in Table 11.1, we should say that, in general, solid surfaces exhibit chemical and morphological heterogeneities. In this case, different surface sites would have to be described by different surface parameter values. However, on hydrophilic surfaces, the adsorbed water film that is always found at ambient conditions levels out these heterogeneities. Hence, the minerals and salt surfaces in Table 11.1 can be characterized by single values, just like homogenous surfaces. Applying pp-LFERs to Various Surfaces at Different Relative Humidity. We have now defined the parameters for vdW and H-bonding interactions and can solve Eq. 11-10 using a reference surface and organic sorbents with known solute descriptors (Li , Ai , and Bi ). Roth et al. (2002) used a water surface as a reference, deriving the pp-LFER for adsorption from air to the water surface at 15◦ C: log Kiwsurfa (288K)(m) = 0.635Li + 3.60Ai + 5.11Bi − 8.47 (number of chemicals = 60; r2 = 0.932)

(11-11)

The fitted Eq. 11-11 for adsorption on a water surface provides the scaling factors a1 , a2 , and a3 introduced in Eq. 11-10. As these fitted coefficients depend only on

332

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

temperature and the scales used to describe the interactions, they can be applied to any surface at 15◦ C. Thus, for any surface: √ log Kisurfa (288K)(m) = 0.135 𝛾 vdW L + 3.60(HAsurf )Ai + 5.11(HDsurf )Bi − 8.47 surf i (11-12) Using Eq. 11-12, one can quickly see that an apolar compound (Ai = Bi = 0) exhibiting an Li value of about 10 (e.g., PCB 153) will adsorb more than 10 orders of magnitude more strongly from air to graphite than to Teflon. To apply Eq. 11-12 at different RH, one must simply insert the corresponding surface parameters give in Table 11.1. For example, for the quartz surface (qsurf) at RH = 45% and 90%, Eq. 11-12 yields: log Kiqsurfa (288K, RH = 45%)(m) = 0.92Li + 3.20Ai + 5.42Bi − 8.47

(11-13)

log Kiqsurfa (288K, RH = 90%)(m) = 0.72Li + 3.17Ai + 4.34Bi − 8.47

(11-14)

and

A comparison of Eqs. 11-13 and 11-14 shows that for the quartz surface, the main effect of RH is on the vdW interaction term, and to a somewhat lesser extent on the H-donating term, since Bi usually has values < 1. The H-accepting properties of the quartz surface show, however, almost no effect with change in RH. As an example of the use of these equations, one finds the Kiqsurfa value of an apolar compound exhibiting an Li value of about 3 (e.g., tetrachloroethene, PCE) is about 4 times larger at 45% RH than at 90% RH, while for a compound with Li of about 10 (e.g., PCB 153) the difference is a factor of 100. Figure 11.7 shows log Kiqsurfa values predicted with Eq. 11-14 versus experimental data; the pp-LFER equation fits the data quite well. We should point out, however, that Eq. 11-12 has been derived using primarily rather simple, monofunctional compounds covering a rather narrow range in log Kiqsurfa (−3 to −6 m). For such compounds, predictions within a factor of 2 to 3 are possible (Goss and Schwarzenbach, 2002). However, when applying Eq. 11-12 to more complex, multifunctional compounds, even larger deviations must be expected. Also, application of Eq. 11-12 to compounds exhibiting weak vdW properties, such as the polyfluorinated compounds (HFCs) and the siloxanes, is not optimal as the Li value does not adequately describe the vdW interactions with surfaces. The reason is that Li depends, not only on vdW interactions, but also the size of the cavity that has to be formed in hexadecane (see Chapter 7). For almost all other organic compounds, both vdW interactions and cavity formation energy in hexadecane exhibit a similar proportionality to the molecular volume, which is not the case for the HFCs and the siloxanes. Whereas this non-proportionality of the HFCs and the siloxanes cancels out when considering bulk phase partitioning, for adsorption to surfaces, equations using the molar refraction of the compound (i.e., a measure of its polarizability) yield significantly better results (Arp et al., 2006b).

Adsorption from Air to Well-Defined Surfaces

333

predicted log Kiqsurfa (m3 m–2)

1: 1

0 –1

apolar compounds

–2

monopolar compounds

–3

bipolar compounds

–4 –5 –6

Figure 11.7 Calculated (Eq. 11-14) logKiqsurfa (288K, RH = 90%)(m) versus experimental values for a set of 103 apolar, monopolar, and bipolar compounds. Data from Arp et al. (2006a).

–7

–7

–6

–5

–4

–3

–2

–1

0

experimental log Kiqsurfa (m3 m–2)

In conclusion, as is illustrated by two examples in Box 11.1, the pp-LFER model Eq. 11-12 using the surface parameters given in Table 11.1 enables us to make calculations concerning the partitioning of organic pollutants between air and well-defined surfaces. However, we should point out that various difficulties exist when applying this model to real-world problems. For example, when we encounter the partitioning of organic compounds between air and aerosols or soils (see Chapter 15), we need to know the types and, particularly, the areas of the dominating (accessible) surfaces present in a given system. To date, experimental data are often reported on a per mass, and not on a per surface area basis, because surface areas are not very well known. Furthermore, surface areas and surface properties may change significantly with changing conditions (e.g., with changing humidity). In addition, the overall partitioning process may be strongly dominated by absorption of a compound into a bulk phase (e.g., water, natural organic material), so that adsorption to a surface is not important anymore (see Chapter 15).

Box 11.1 Estimating the Fraction of Phenanthrene in the Gas Phase and Sorbed to the Walls of a Vessel Consider two closed air-sampling vessels made out of Teflon and glass (quartz) with an air volume Va = 10−3 m3 (1 L) and an inner surface area of Asurf = 6×10−2 m2 (600 cm2 ). In these vessels, you capture air samples that you want to analyze for phenanthrene, which is present at low concentrations. Calculate the fraction of the total phenanthrene present in the air in the two vessels after adsorption equilibrium between the gas phase and the walls of the vessel, which has been established at 15◦ C (288 K) and 50% relative humidity. Assume that only adsorption at the surface of the walls is important and that the surface is not saturated with phenanthrene. (In reality, absorption could also be important for Teflon, and actually is if one is using “soft” Teflon.)

334

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

Teflon is an apolar sorbent that undergoes only vdW interactions. Insert the vdWsurf parameter of Teflon (4.2, independent of RH, see Table 11.1) into Eq. 11-12 to obtain: log Kiteflona (288K)∕m = 0.135(4.4)(7.58) − 8.47 = −3.97 or: Kiteflona (288K) = 1.2 × 10−4 m The fraction of phenanthrene present at equilibrium in the gas phase (air) is given by: fia =

Cia Va = Cia Va + Citeflon Ateflon

1 1 = A Citeflon Ateflon 1+ 1 + Kiteflona teflon Cia Va Va

where Citeflon is the concentration of phenanthrene per unit surface area. Insert the values of Ateflon and Va , together with the estimated Kiteflona value into the previous equation to get: fia =

1 = 0.993 1 + (0.00012 m)(60 m−1 )

Thus, virtually all phenanthrene is still present in the gas phase. Quartz, on the other hand, is a bipolar sorbent that exhibits quite strong H-donor and H-acceptor properties. Phenanthrene is monopolar with Ai = 0.0 and Bi = 0.24 (see Appendix C). Interpolating linearly, the vdWsurf and HDsurf values given in Table 11.1 can be found for quartz to obtain the appropriate values for 50% RH: vdWquartz (50%) = 6.8 − (5∕45)(1.5) = 6.6 HDquartz (50%) = 1.06 − (5∕45)(0.21) = 1.04 Inserting these values, together with the phenanthrene’s parameters, into Eq. 11-12 yields: log Kiqsurfa (288K)∕m = 0.135(6.6)(7.58) + 5.11(1.04)(0.24) − 8.47 = −0.44 or Kiqsurfa (288K) = 0.36 m The fraction of phenanthrene in the air is in this case: fia =

1 = 0.04 1 + (0.36 m)(60 m−1 )

which means that in the glass vessel, 96% of the compound would be lost to the quartz surface.

Adsorption from Water to Inorganic Surfaces

11.3

335

Adsorption from Water to Inorganic Surfaces Although sorption from water to organic matter is commonly dominating the overall sorption of organic compounds in aquatic environments (see Chapter 13), adsorption to inorganic surfaces may prove to be significant under certain conditions. One example is when aquifer solids are derived from sand and gravel beach deposits and contain small organic contents (Schwarzenbach and Westall, 1981; Banerjee et al., 1985; Piwoni and Banerjee, 1989; Ball and Roberts, 1991; Hundal et al., 2001). Additionally, engineered systems such as clay liners are often used to isolate organic wastes buried below ground. While we may be interested in the impact of these low-permeability materials on the subsurface hydraulics, we also need to consider the possibility that those aluminosilicates sorb nonionic organic pollutants and inhibit offsite transport (Boyd et al., 1988). Also, sorption to certain mineral surfaces, even if it is insignificant from a mass balance point of view, may be critical to quantify when dealing with surface-catalyzed transformations (Ulrich and Stone, 1989; Burris et al, 1995). Finally, laboratory glass surfaces may sorb nonionic compounds from aqueous solutions (e.g., Qian et al., 2011), hampering experimental data interpretation. Nonspecific Adsorption of Nonionic Organic Compounds to Mineral Surfaces Experimental Findings. Numerous investigators have observed adsorption of apolar and weakly monopolar organic compounds in water to water-wet inorganic surfaces. Generally, adsorption from water to mineral surfaces can be reasonably well described by a concentration-independent partitioning (adsorption) constant, as reported for adsorption of chlorinated compounds like lindane and trichlorobenzene on silica or PAHs on quartz and goethite-covered quartz (Su et al., 2006; Muller et al., 2007). Hence, as for surface–air partitioning, we may define a surface-normalized solid– water adsorption coefficient, Kisurfw : Kisurfw (e.g., m) =

Cisurf (e.g., mol m−2 ) Ciw (e.g., mol m−3 )

(11-15)

If we chose length (in m) as the dimension, we have actually divided a solid surface area by a volume of water. If the surface area is not known, we may also define a solid–water partition coefficient based on mass, Kisw : Kisw (e.g., Lw kg−1 s )=

) Cis (e.g., mol kg−1 s Ciw (e.g., mol L−1 w )

(11-16)

We should point out that, particularly when considering highly porous materials exhibiting surface areas of 500 m2 g−1 and more, the amount of this surface area actually available for adsorption of organic compounds is often unclear (Schwarzenbach and Westall, 1981; Su et al., 2006). Also, nanopores (< 50 nm, see Chapter 5) may play a particularly important role in the adsorption (see Cheng et al., 2012). Therefore, the significant differences observed for surface normalized partition constants of a given compound to the same type of mineral oxide may be, at least partly, due

336

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

–4

Al2O3 surface Fe2O3 surface

–5

SiO2 surface chlorinated benzenes

log Kisurfw (m)

–6

Figure 11.8 Adsorption of chlorinated benzenes, PAHs and NACs (highlighted with red circle) to various mineral oxide surfaces; surfacenormalized adsorption constants as a function of the aqueous activity coefficient of the solutes derived from their liquid aqueous solubilities (see Chapter 9; Eqs. 9-5 and 9-8). Data from Schwarzenbach and Westall (1981); Mader et al. (1997); Su et al. (2006); and Muller et al. (2007).

PAHs NACs

–7

–8

–9

–10

2

4

6 log

8

10

iw

to an erroneous assumption of the actual surface area available for adsorption, leading to a smaller apparent Kisurfw value. Conversely, traces of strongly sorbing organic materials on minerals may lead to a higher apparent adsorption constant. The absolute values of sorption enthalpies are small (between −15 and −25 kJ mol−1 ; e.g., Mader et al., 1997; Su et al., 2006). We recall that the excess enthalpies of solution of PAHs and chlorinated benzenes in water are positive, but they exhibit very similar absolute values (Table 9.2). Since we may reasonably anticipate that some of this energy yield of mineral sorption came from the removal of those chemicals from aqueous solution, after accounting for enthalpies of solution, the remaining steps in mineral binding of nonpolar sorbates comes out to be energetically neutral or even slightly endothermic. Increasing the temperature generally results in diminished adsorption of neutral apolar and weakly monopolar compounds to mineral oxide surfaces; the dependence, however, is rather weak, corresponding with the small values of sorption enthalpy. Also, pH and ionic strength do not significantly affect adsorption (Mader et al., 1997; Su et al., 2006). Further, the presence of competing neutral sorbates does not affect mineral surface adsorption, implying that the sorbates do not compete for specific sorption sites (e.g., Boucher and Lee, 1972; Mader et al., 1997; Su et al., 2006). From Fig. 11.8, one sees that for adsorption of a given class of compounds (e.g., chlorinated benzenes, PAHs) to a particular mineral surface, the area-normalized sorption coefficient (e.g., log Kisurfw in units of m) tends to correlate quite well with the sorbate’s aqueous activity coefficient. Indeed, the higher the log γiw (the sorbate’s

Adsorption from Water to Inorganic Surfaces

337

“dislike” of water), the greater the affinity of the compound for the mineral surface. We also note that the dependence of log Kisurfw on γiw is somewhat more pronounced for the PAHs as compared to the chlorinated benzenes. Finally, we should point out that the nitroaromatic compounds adsorb significantly more strongly than would be expected from their aqueous activity coefficients, suggesting the increased polarity of these nitro- substituted substances may enable favorable near-surface interactions which, in addition to their desire to escape aqueous solution, enhance their adsorption. Mechanistic Considerations. All the aforementioned experimental observations suggest that significant specific interactions between the sorbate molecules and the mineral surface do not drive adsorption. As previously discussed for surface–air partitioning, actual adsorption of nonionic organic compounds directly on waterwet hydrophilic inorganic surfaces would require that these organic sorbates displace water molecules already adhering to the polar surface. However, water has much stronger interaction energies on mineral surfaces per unit area than apolar and monopolar compounds (see Fig. 11.3), so surface adsorption from bulk water onto fully water-wet hydrophilic solids probably does not explain the sorption of apolar and monopolar organic compounds on minerals. Instead, the observations suggest the process simply involves partitioning of the neutral sorbates between the bulk water and the “special” water immediately adjacent to solid surfaces and inside the nanometer-sized pores of these solids. Water molecules near inorganic surfaces are more organized than corresponding molecules located in the bulk solution because of their interactions with the solid. Such “special” surfaceordered water films are called vicinal water (Fig. 11.9b). Being located in this layer of vicinal water may be energetically more favorable for the sorbate. The volume of this vicinal water per mass of sorbent is related to the mineral particle’s porosity and surface area. Consequently, the amount of such special near-surface water per mass of solid is greater for fine, porous silica (∼ 0.5 mL g−1 ) than for quartzite sand (< 0.001 mL g−1 ), and greater for expandable montmorillonite (∼ 0.5 mL g−1 ) than for the two-layer clay, kaolinite ( O− : K+ +

δ+

NACδ− ⇋ (Si, Al) > O :δ+ NACδ− : K+

(11-18)

where the surface species involves electron delivery to the NAC from the siloxane oxygen and/or from the NAC to adsorbed cations like potassium (Eq. 11-18) or ammonium or cesium (Weissmahr et al., 1997). With this exchange in mind and assuming that we are in the linear part of the isotherm, we may define a thermodynamic equilibrium constant: KNAC,EDA (L mol−1 sites) =

[(Si, Al) > O− :NAC : K+ ] [ (Si, Al) > O− :K+ ][NAC]

(11-19)

where this sorption coefficient has the subscript EDA to remind us that it reflects electron donor-acceptor surface interactions; it has the units that result from the ratio: (mol NAC kg−1 solid) (mol sites kg−1 solid)−1 (mol NAC L−1 )−1 = L mol−1 sites.

OH NO2

NO2 2,4-dinitro-6-methylphenol (DNOC) OH NO2

NO2 2,4-dinitro-6-sec-butylphenol (Dinoseb)

Values of KNAC,EDA have been measured for a large number of NACs and other aromatic derivatives (Table 11.2; Haderlein and Schwarzenbach, 1993; Haderlein et al., 1996). Generally, the values increase as more electron-withdrawing nitro substituents occur on a sorbate (e.g., compare 4-nitrotoluene at 820 versus 2,4-dinitrotoluene at 120,000 versus 2,4,6-trinitrotoluene at 300,000 L mol−1 sites). Also, ring substituents that prevent close approach of the ring system to the siloxane face (e.g., the secbutyl in Dinoseb) lower the value of the KNAC,EDA significantly (compare Dinoseb with DNOC). The extent of complexation with any particular clay mineral also depends on the abundance of siloxane sites per mass of clay. This surface area factor is defined as 1 for a two-layer clay like kaolinite, is higher for a three-layer clay like illite (about 6 times more than kaolinite), and is greatest for an expandable clay like montmorillonite (about 12 times more than kaolinite). The KNAC,EDA values provided in Table 11.2 are normalized to the kaolinite case, but these values have to be increased by the appropriate factors to handle sorption to aluminosilicate clays like illite and montmorillonite. Recognizing that any given clay has a finite number of sites per unit surface area, we can assume the sites are partially filled with NACs and partially filled with competitors, e.g., hydrated K+ : [total sites] = [(Si, Al) > O− : NAC : K+ (H2 O)m ] + [(Si, Al) > O− :K+ (H2 O)n ] (11-20)

341

Adsorption from Water to Inorganic Surfaces

Table 11.2 Adsorption of Nonionic Nitroaromatic Compounds (NACs) to Aluminosilicate Clays: (a) Surface Area Factors, fsaf , for Different Clays Expressing Maximum Sorption Sites Relative to Kaolinite, and (b) KNAC,EDA Values (L mol−1 sites) Measured for Several NACs on K+ -Kaolinite (a) Aluminosilicate Clay

Surface Area Factor (fsaf )

Kaolinite Illite Montmorillonite

1 6 12 KNAC , EDA (L mol−1 sites)a

(b) Compound Nitrobenzene 1,2-Dinitrobenzene 1,4-Dinitrobenzene 2-Nitrotoluene 3-Nitrotoluene 4-Nitrotoluene 2,4-Dinitrotoluene 2,6-Dinitrotoluene 2,4,6-Trinitrotoluene (TNT) 2-Amine-4,6-dinitrotoluene 4-Amino-2,6-dinitrotoluene 2,6-Diamino-4-nitrotoluene 2,4-Dinitro-6-methyl-phenol (DNOC) 2,4-Dinitro-6-sec-butyl-phenol (Dinoseb) a

100 70 31,000 50 420 820 120,000 1,700 300,000 50,000 1,800 180 450,000 1,100

Data from Haderlein et al. (1996)

where the subscripts, m and n on the water reflect changed degrees of cation hydration when an NAC is present. Now we can substitute for the NAC-free site term in Eq. 11-20, and after rearranging find: [(Si, Al) > O:NAC:K+ (H2 O)m ] =

[total sites]KNAC,EDA [NAC] 1+KNAC,EDA [NAC]

(11-21)

or KNACclayw =

[(Si, Al) > O:NAC:K+ (H2 O)m ] [total sites]KNAC,EDA = [NAC] 1+KNAC,EDA [NAC]

(11-22)

In most aquatic systems where Na+ , K+ , Mg2+ , and Ca2+ serve as the predominant cations, it is only the fraction of the siloxane surface covered by potassium counterions that proves to be accessible to NACs. Therefore, for natural solids in a real world

342

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

soil or sediment, the total available sites for such EDA interactions can be approximated by the product: [total sites] = fclay × fK+ clay × fsaf × (6×10−3 mol sites kg−1 K+ -kaolinite) (11-23) where fclay is the clay mineral (not clay size) content of the solids (kg clay kg−1 solid), fK+ clay is the fraction of cationic counterion charges contributed by weakly hydrated cations like potassium (kg K+ clay kg−1 clay), fsaf is the average surface area factor reflecting the ratio of siloxane surface availability of the clay minerals present versus kaolinite, and 6×10−3 mol sites kg−1 K+ -kaolinite is the typical value for the maximum site density on kaolinite. Finally, combining the expression for the total sites with Eq. 11-22, we have: −1

KNACclayw (L kg

solid) =

fclay ⋅ fK+ clay ⋅ fsaf (6×10−3 )KNAC,EDA 1 + KNAC,EDA [NAC]

(11-24)

For the sake of simplicity, we assume that fK+ clay and KNAC,EDA are linearly related, which is not necessarily the case (see Weissmahr et al., 1999). Equation 11-24 indicates that KNACclayw is constant at low concentrations (i.e., [NAC] ≪ 1/KNAC,EDA ) and declines at higher levels. Now, one may apply knowledge of the clay mineralogy of natural solids and the cationic composition of the aqueous solutions in which they are bathed to estimate the sorption of NACs. Often, this sorption mechanism is even more important than absorption to NOM for NACs with fairly large KNAC,EDA values (Weissmahr et al., 1999). Finally, we should note that when present in mixtures, competition for sites between different NACs may strongly influence the transport of these contaminants (Haderlein and Schwarzenbach, 1993; Fesch et al., 1998).

11.4

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Questions Q 11.1 Give examples of environmentally relevant situations in which adsorption of organic vapors on inorganic surfaces is an important partitioning process. Q 11.2 What intermolecular interactions and corresponding free energy contributions would you suspect to be important for the following sorbate:medium:sorbent combinations:

Questions and Problems

343

(a) tetrachloroethene (PCE) partitioning between air and quartz sand? (b) atrazine partitioning between air and Teflon? (c) methyl-t-butyl ether (MTBE) partitioning between air and quartz sand? (d) perfluoro octylethanol (8:2 FTOH) partitioning between air and quartz sand? (e) 2,2′ ,4,4′ ,5,5′ -hexachlorobiphenyl (PCB 153) partitioning between water and quartz sand? (f) phenanthrene partitioning between water and quartz sand? (g) phenol partitioning between water and quartz sand? Q 11.3 Why does the sorption of nonpolar organic vapors to polar inorganic surfaces generally decrease with increasing humidity? What about polar compounds? Why does the relative humidity have a negligible influence on sorption of organic vapors to apolar surfaces? Q 11.4 Storey et al., (1995) reported Kisurfa values for the adsorption of n-alkanes and PAHs from air to quartz at 25 to 30% RH and 70 to 75% RH, respectively. When plotting Kisurfa versus ln p∗iL (Eq. 11-12) for the various data sets, the following slopes “a” are obtained:

a (25-30% RH) a (70-75% RH)

n-alkanes

PAHs

1.04 0.96

1.22 1.18

Would you have expected to find steeper slopes for the PAHs as compared to the n-alkanes? If yes, why? Why are the slopes at low RH somewhat steeper than the ones corresponding to high relative humidities? Q 11.5 Consider two apolar compounds exhibiting a factor of ten difference in their hexadecane–air partition constant. What differences do you expect for the two compounds in their (a) Teflon–air, and (b) graphite–air adsorption coefficients? Q 11.6 Why is adsorption of nonionic organic compounds from water to mineral surfaces generally rather weak? Are there any exceptions? In what cases may even weak adsorption become relevant?

344

Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

Q 11.7 Explain why the following sorbate pairs exhibit the relative KNAC,EDA ’s indicated for adsorption from water to a siloxane surface (Table 11.2): (a) KNAC,EDA (2,4-dinitrotoluene) ≫ KNAC,EDA (2-nitrotoluene) (b) KNAC,EDA (1,4-dinitrobenzene) ≫ KNAC,EDA (1,2-dinitrobenzene) (c) KNAC,EDA (DNOC) ≫ KNAC,EDA (Dinoseb)

Problems P 11.1 Using the Thermodynamic Cycle to Estimate Solid Surface–Water Partition Constants Experimentally determined quartz surface–water partition constants of phenanthrene, Kiqsurfw , are in the order of 10−7 to 10−8 m at 25◦ C (Muller et al., 2007; Su et al., 2006). Assume that the thermodynamic cycle is applicable and calculate Kiqsurfw at 25◦ C using the air–water partition constant of phenanthrene given in Appendix C and the Kiqsurfa (288K, 90% RH) value estimated from Eq. 11-14. Comment on the result. P 11.2 Assessing the Speciation of Bromomethane and of Atrazine in a Quartz Sand Consider a confined volume of pure quartz sand exposed to air (RH = 45%), with a porosity ϕ = 0.5 (see Box 5.4), a density of 2.65 g cm−3 and a surface area A = 1 m2 g−1 . What fraction fia of (a) the fumigant bromomethane and (b) the herbicide atrazine will be present in the pore air at 15◦ C and at 35◦ C assuming a linear adsorption isotherm? Comment on the result. Hint: Consult Box 11.1. Use Eq. 11.4 for estimation of the adsorption enthalpy of the two compounds. P 11.3 Designing a Sorption Treatment to Remove 1,1,2,2-Tetrachloroethane (CHCl2 -CHCl2 ) from a Waste Gas Stream A process in your company generates waste gases that need to be vented to the outside at a rate of 1 m3 per hour. In particular, you must be sure that the 1,1,2,2tetrachloroethane present at 100 ppmv (i.e., 100×10−6 m3 of 1,1,2,2-tetrachloroethane vapor per m3 of total gas) must be removed from the gas stream before discharge. A colleague suggests that you construct an adsorbent column filled with alumina (Al2 O3 ) and run the gas through that column to capture the 1,1,2,2-tetrachloroethane. (a) If the waste gas stream is somewhat dry (i.e., 60% RH) and warm (30◦ C), how many hours of waste gas can you treat with a 10 m3 tank of alumina (packed bed porosity 0.3, density 4 g mL−1 , with a specific surface area of 10 m2 g−1 , and assumed surface properties like those measured for corundum, see Table 11.1). Assume the 1,1,2,2-tetrachloroethane “breaks through” at a volume equal to the tank’s void volume (i.e., number of cubic meters in tank that are filled with gas) divided by the venting

Bibliography

345

gas flow rate and by the equilibrium fraction of 1,1,2,2-tetrachloroethane in the gas phase. (b) If you could construct a tank with the same void volume and surface area of silica, would it be more effective? What about activated carbon? Explain your reasoning. Hint: See Box 11.1 for calculating the fraction in the gaseous and adsorbed phase. P 11.4 Where do Organic Compounds Sit in a Fog Droplet? Inside or at the Surface? Several studies have shown that the concentrations of many organic pollutants in fog water are much higher than would be expected from the compound’s equilibrium air/water partition constant Kiaw . In order to describe the observed enrichment of compounds in fog water, an enrichment factor EF can be defined (see, e.g., Goss, 1994 and references cited therein): K EF = iaw Diaw where iaw = total concentration of i in the gas phase/total concentration of i in the fog droplet (iaw = Cia /Ciwtot ). One possible cause for an enrichment (i.e., iaw < Kiaw ) is the presence of colloidal organic material in the fog droplet, with which the organic compounds may associate (see Chapters 13 and 15). Another possibility suggested by several authors (e.g., Perona, 1992; Valsaraj et al., 1993; Goss, 1994) is enrichment by adsorption at the air–water interface, that is, at the surface of the fog droplet. Is this a reasonable assumption for any organic compound? Estimate the enrichment factor due to surface adsorption at equilibrium for a fog droplet (consisting of pure water) of 8 μm diameter with a surface area (Ad ) to volume (Vd ) ratio, rsv , of 7500 cm2 cm−3 for (a) tetrachloroethene, (b) phenanthrene and (c) benzo(a)pyrene at 15◦ C. Neglect the fact that the surface is curved. Hint: Express the total concentration, Ciwt , in the fog droplet by (Ad Cisurf + Vd Ciw )/Vd where Ad /Vd = rsv and Cisurf = Cia Kisurfa . Cisurf , Ciw , and Cia are the surface concentration, the bulk water concentration, and the bulk air concentration of i, respectively. Kisurfa can be estimated by Eq. 11-11.

11.5

Bibliography Arp, H. P. H.; Goss, K. U.; Schwarzenbach, R. P., Evaluation of a predictive model for air/surface adsorption equilibrium constants and enthalpies. Environ. Toxicol. Chem. 2006a, 25(1), 45–51. Arp, H. P. H.; Niederer, C.; Goss, K. U., Predicting the partitioning behavior of various highly fluorinated compounds. Environ. Sci. Technol. 2006b, 40(23), 7298–7304. Atkinson, D.; Curthoys, G., The determination of heats of adsorption by gas-solid chromatography. J. Chem. Educ. 1978, 55(9), 564–566. Ball, W. P.; Roberts, P. V., Long-term sorption of halogenated organic chemicals by aquifer material. 1. Equilibrium. Environ. Sci. Technol. 1991, 25(7), 1223–1237. Banerjee, P.; Piwoni, M. D.; Ebeid, K., Sorption of organic contaminants to a low carbon subsurface core. Chemosphere 1985, 14(8), 1057–1067.

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Partitioning of Nonionic Organic Compounds Between Well-Defined Surfaces and Air or Water

Bhatnagar, N.; Kamath, G.; Potoff, J. J., Prediction of 1-octanol-water and air-water partition coefficients for nitro-aromatic compounds from molecular dynamics simulations. Phys. Chem. Chem. Phys. 2013, 15(17), 6467–6474. Boucher, F. R.; Lee, G. F., Adsorption of lindane and dieldrin pesticides on unconsolidated aquifer sands. Environ. Sci. Technol. 1972, 6(6), 538–543. Boyd, S. A.; Mortland, M. M.; Chiou, C. T., Sorption characteristics of organic compounds on hexadecyltrimethylammonium-smectite. Soil Sci. Soc. Am. J. 1988, 52(3), 652–657. Burris, D. R.; Campbell, T. J.; Manoranjan, V. S., Sorption of trichloroethylene and tetrachloroethylene in a batch reactive metallic iron-water system. Environ. Sci. Technol. 1995, 29(11), 2850– 2855. Cheng, H. F.; Hu, E. D.; Hu, Y. A., Impact of mineral micropores on transport and fate of organic contaminants: A review. J. Contam. Hydrol. 2012, 129, 80–90. Chiou, C. T.; Shoup, T. D., Soil sorption of organic vapors and effects of humidity on sorptive mechanism and capacity. Environ. Sci. Technol. 1985, 19(12), 1196–1200. de Boer, J. H., The Dynamical Character of Adsorption. 2nd ed.; Clarendon Press: Oxford, 1968; p 240. Fesch, C.; Simon, W.; Haderlein, S. B.; Reichert, P.; Schwarzenbach, R. P., Nonlinear sorption and nonequilibrium solute transport in aggregated porous media: Experiments, process identification and modeling. J. Contam. Hydrol. 1998, 31(3-4), 373–407. Fowkes, F. M., Attractive forces at interfaces. Ind. Eng. Chem. 1964, 56(12), 40–52. Goss, K. U., Predicting the enrichment of organic compounds in fog caused by adsorption on the water surface. Atmos. Environ. 1994, 28(21), 3513–3517. Goss, K. U., Conceptual model for the adsorption of organic compounds from the gas phase to liquid and solid surfaces. Environ. Sci. Technol. 1997, 31(12), 3600–3605. Goss, K. U., The air/surface adsorption equilibrium of organic compounds under ambient conditions. Crit. Rev. Environ. Sci. Technol. 2004, 34(4), 339–389. Goss, K. U.; Buschmann, J.; Schwarzenbach, R. P., Determination of the surface sorption properties of talc, different salts, and clay minerals at various relative humidities using adsorption data of a diverse set of organic vapors. Environ. Toxicol. Chem. 2003, 22(11), 2667–2672. Goss, K. U.; Schwarzenbach, R. P., Quantification of the effect of humidity on the gas/mineral oxide and gas/salt adsorption of organic compounds. Environ. Sci. Technol. 1999a, 33(22), 4073– 4078. Goss, K. U.; Schwarzenbach, R. P., Empirical prediction of heats of vaporization and heats of adsorption of organic compounds. Environ. Sci. Technol. 1999b, 33(19), 3390–3393. Goss, K. U.; Schwarzenbach, R. P., Adsorption of a diverse set of organic vapors on quartz, CaCO3 , and alpha-Al2 O3 at different relative humidities. J. Colloid Interface Sci. 2002, 252(1), 31–41. Haderlein, S. B.; Schwarzenbach, R. P., Adsorption of substituted nitrobenzenes and nitrophenols to mineral surfaces. Environ. Sci. Technol. 1993, 27(2), 316–326. Haderlein, S. B.; Weissmahr, K. W.; Schwarzenbach, R. P., Specific adsorption of nitroaromatic: explosives and pesticides to clay minerals. Environ. Sci. Technol. 1996, 30(2), 612–622. Hundal, L. S.; Thompson, M. L.; Laird, D. A.; Carmo, A. M., Sorption of phenanthrene by reference smectities. Environ. Sci. Technol. 2001, 35(17), 3456–3461. Li, H.; Teppen, B. J.; Johnston, C. T.; Boyd, S. A., Thermodynamics of nitroaromatic compound adsorption from water by smectite clay. Environ. Sci. Technol. 2004, 38(20), 5433–5442. Mader, B. T.; Goss, K. U.; Eisenreich, S. J., Sorption of nonionic, hydrophobic organic chemicals to mineral surfaces. Environ. Sci. Technol. 1997, 31(4), 1079–1086. Mikhail, R. S.; Brunauer, S.; Bodor, E. E., Investigations of a complete pore structure analysis. I. Analysis of micropores. J. Colloid Interface Sci. 1968a, 26(1), 45–53. Mikhail, R. S.; Brunauer, S.; Bodor, E. E., Investigations of a complete pore structure analysis. 2. Analysis of four silica gels. J. Colloid Interface Sci. 1968b, 26(1), 54–61.

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Muller, S.; Totsche, K. U.; Kogel-Knabner, I., Sorption of polycyclic aromatic hydrocarbons to mineral surfaces. Eur. J. Soil Sci. 2007, 58(4), 918–931. Ogram, A. V.; Jessup, R. E.; Ou, L. T.; Rao, P. S. C., Effects of sorption on biological degradation rates of (2,4-dichlorophenoxy) acetic acid in soils. Appl. Environ. Microbiol. 1985, 49(3), 582– 587. Perona, M. J., The solubility of hydrophobic compounds in aqueous droplets. Atmos. Environ. Part A Gen. Topics 1992, 26(14), 2549–2553. Piwoni, M. D.; Banerjee, P., Sorption of volatile organic solvents from aqueous solution onto subsurface solids. J. Contam. Hydrol. 1989, 4(2), 163–179. Qian, Y. A.; Posch, T.; Schmidt, T. C., Sorption of polycyclic aromatic hydrocarbons (PAHs) on glass surfaces. Chemosphere 2011, 82(6), 859–865. Qu, X. L.; Zhang, Y. J.; Li, H.; Zheng, S. R.; Zhu, D. Q., Probing the specific sorption sites on montmorillonite using nitroaromatic compounds and hexafluorobenzene. Environ. Sci. Technol. 2011, 45(6), 2209–2216. Roth, C. M.; Goss, K. U.; Schwarzenbach, R. P., Adsorption of a diverse set of organic vapors on the bulk water surface. J. Colloid Interface Sci. 2002, 252(1), 21–30. Schwarzenbach, R. P.; Westall, J., Transport of nonpolar organic compounds from surface water to groundwater. Laboratory sorption studies. Environ. Sci. Technol. 1981, 15(11), 1360–1367. Storey, J. M. E.; Luo, W.; Isabelle, L. M.; Pankow, J. F., Gas/solid partitioning of semivolatile organic compounds to model atmospheric solid surfaces as a function of relative humidity. 1. Clean quartz. Environ. Sci. Technol. 1995, 29(9), 2420–2428. Su, Y. H.; Zhu, Y. G.; Sheng, G.; Chiou, C. T., Linear adsorption of nonionic organic compounds from water onto hydrophilic minerals: Silica and alumina. Environ. Sci. Technol. 2006, 40(22), 6949–6954. Ulrich, H. J.; Stone, A. T., The oxidation of chlorophenols adsorbed to manganese oxide surfaces. Environ. Sci. Technol. 1989, 23(4), 421–428. Valsaraj, K. T.; Thoma, G. J.; Reible, D. D.; Thibodeaux, L. J., On the enrichment of hydrophobic organic compounds in fog droplets. Atmos. Environ. Part A Gen. Topics 1993, 27(2), 203–210. Weissmahr, K. W.; Haderlein, S. B.; Schwarzenbach, R. P.; Hany, R.; Nuesch, R., In situ spectroscopic investigations of adsorption mechanisms of nitroaromatic compounds at clay minerals. Environ. Sci. Technol. 1997, 31(1), 240–247. Weissmahr, K. W.; Hildenbrand, M.; Schwarzenbach, R. P.; Haderlein, S. B., Laboratory and field scale evaluation of geochemical controls on groundwater transport of nitroaromatic ammunition residues. Environ. Sci. Technol. 1999, 33(15), 2593–2600.

Part III

Equilibrium Partitioning in Environmental Systems

351

Chapter 12

General Introduction to Sorption Processes

12.1 Introduction 12.2 Sorption Isotherms and the Solid–Water Equilibrium Distribution Coefficient (Kid ) Qualitative Considerations Quantitative Description of Sorption Isotherms The Solid–Water Distribution Coefficient, Kid 12.3 Speciation (Sorbed versus Dissolved or Gaseous), Retardation, and Sedimentation Dissolved (fiw ), Gaseous (fia ), and Sorbed Fractions (fis ) of a Compound in a Given System Box 12.1 Definition of Concentrations in an Aqueous System with Solids Retardation in Porous Media Sedimentation 12.4 Questions and Problems 12.5 Bibliography

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

352

General Introduction to Sorption Processes

12.1

Introduction Based on our previous discussions of how molecular interactions affect partitioning, it makes sense that structurally identical molecules behave very differently if they are in the gas phase or surrounded by water molecules and ions, as opposed to clinging onto the exterior of solids or buried within a solid matrix. Therefore, sorption to condensed phases from water or air is extremely important because it can dramatically affect the fate and impacts of chemicals in the environment (see Fig. 12.1). For example, the environmental transport of water-borne molecules obviously differs from the movements of the same kind of molecules attached to particles that settle. Also, transport of a given compound in porous media such as soils, sediments, and aquifers is strongly influenced by the compound’s tendency to sorb to the various components of the solid matrix. Additionally, only dissolved molecules are available to collide with the interfaces of other environmental compartments, such as the atmosphere; thus, phase transfers are controlled by the dissolved species of a chemical (Chapter 19). Similarly, since molecular transfer is a prerequisite for the uptake of organic pollutants by organisms, the bioavailability of a given compound and thus its rate of biotransformation or its toxic effect(s) are affected by sorption processes (Chapter 16). Furthermore, some sorbed molecules are substantially shaded from incident light. Therefore, these molecules may not experience direct photolysis processes (Chapter 24). Moreover, when present inside solid matrices, they may never come in contact with short-lived, solution-phase photooxidants like OH-radicals. Finally, since the chemical nature of aqueous solutions and solid environments differ greatly (e.g., pH, redox conditions), various chemical reactions including hydrolysis or redox reactions may occur at very

(a) air water

Figure 12.1 Examples of environmental partitioning and reaction processes that depend on the phase in which the organic molecule is present. (a) Dissolved species may participate directly in air–water exchange while sorbed species may settle with solids. (b) Dissolved species may react at different rates as compared to their sorbed counterparts due to differential access of other dissolved and solid phase “reactants.”

i

i

dissolved organic molecules colliding with air-water interface and volatilizing

sorbed organic molecules settling with particles

(b) air water

i

i . Cl –, Br–, HO–, HS–, HO , ...

dissolved organic molecules are more accessible to light, to other dissolved chemicals, and to microorganisms than sorbed molecules

Introduction

acid-base equilibrium in solution

+ NH3

NH2

reactive O surface groups desorption

OH ionizable surface groups

Figure 12.2 Various sorbent–sorbate interactions possibly controlling the association of a chemical (3,4-dimethylaniline) with natural solids present in an aquatic system.

natural organic matter

reactive moiety of sorbate covalently bounds to surface group N

sorption

– O

353

charged sorbate electrostatically attracted to oppositely charged surface sites + – O H3N OH NH2

solid phase

sorbate adsorbs to mineral surface

NH2

solution phase natural sorbate escapes water into natural organic matter

different rates in the sorbed and dissolved states. Hence, we must understand solid– solution and solid–gas phase exchange phenomena before we can quantify virtually any other process affecting the fates of organic chemicals in the environment. Unfortunately, when we are dealing with natural environments, sorption is often not an exchange between one homogeneous solution or vapor phase and a single, well-defined condensed medium, as we discussed in Part II. Rather, in a given environmental system, some combination of interactions governs the association of a particular chemical (called the sorbate) with any particular solid or mixture of solids (called the sorbent(s)). Consider the case of 3,4-dimethylaniline in an aquatic system (Fig. 12.2). This compound is a weak base with pKia = 5.28. As such, it reacts in aqueous solution to form some 3,4-dimethyl ammonium cations. For the fraction of molecules that remain uncharged, this organic compound may escape the water by penetrating the natural organic matter present in the system. Additionally, such a nonionic molecule may displace water molecules from the region near a mineral surface to a minor extent and be held there by London dispersive and polar interactions (see Chapter 11). These two types of sorption mechanisms are non-specific and will operate for any organic chemical and any natural solid. Additionally, since the sorbate is ionizable in the aqueous solution, then electrostatic attraction to specific surface sites exhibiting the opposite charge will promote sorption of the ionic species (Chapter 14). Finally, should the sorbate and the sorbent exhibit mutually reactive moieties (e.g., in Fig. 12.2 a carbonyl group on the sorbent and an amino group on the sorbate), some portion of the chemical may actually become bonded to the solid. All of these interaction mechanisms operate simultaneously, and the combination that dominates the overall solution–solid distribution depends on the structural properties of the organic sorbate and the solid sorbent of interest.

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12.2

Sorption Isotherms and the Solid–Water Equilibrium Distribution Coefficient (Kid ) Qualitative Considerations When we are interested in describing the equilibrium distribution of a chemical among the solids and solution present in any particular volume of an aquatic environment, we begin by considering how the total sorbed concentration of the chemical, Cis (e.g., mol kg–1 solid), depends on its concentration in the solution, Ciw (e.g., mol L–1 ). The relationship of these two concentrations is commonly referred to as a sorption isotherm. The name “isotherm” indicates this sorption relationship only applies at a constant temperature. In the following discussion, we only consider sorption from aqueous solution, but we note that the same general considerations also hold for sorption from the gas phase, i.e., from air (one can just substitute the subscript “w” by “a”).

(a)

(b)

Experimentally determined sorption isotherms exhibit a variety of shapes for different combinations of sorbates and sorbents (Fig. 12.3). As used in Chapter 11 when discussing adsorption to surfaces, the simplest case (Fig. 12.3a) is the one in which the affinity of the sorbate for the sorbent remains the same over the observed concentration range; thus, it is called the linear isotherm case. This case applies to situations where partitioning into a homogeneous organic phase is dominating the overall sorption or concentrations are sufficiently low so that the strongest adsorption sites are far from being saturated. The second type of isotherm behavior (Figs. 12.3b and c) reflects those situations in which at higher sorbate concentrations, less additional molecules sorb to the sorbent, such as when binding sites become filled or the remaining sites are less attractive to the sorbate molecules. In the extreme case (Fig. 12.3c), above some maximum Cis value, all sites are “saturated,” and no more additional sorption is possible. Isotherms of the type shown in Figs. 12.3b and c describe experimental studies of adsorption processes to organic (e.g., activated carbon) and inorganic (e.g., clay mineral) surfaces. Of course, in a soil or sediment, more than one important sorbent may be present. Therefore, the overall sorption isotherm may reflect the superposition of several individual isotherms that are characteristic for each specific type of sorbent. When such a mixed case involves an adsorbent exhibiting a limited number of sites with a high affinity for the sorbate that dominates the overall sorption at low concentrations (e.g., soot, clay mineral; type (c) isotherm), plus a partitioning process predominating at higher concentrations (e.g., into natural organic matter; type (a) isotherm), then a mixed isotherm best describes the data (Figs. 12.3b or d).

Cis (e.g., mol kg–1 solid)

(c)

(d)

(e)

(f)

Ciw (e.g., mol L–1)

Figure 12.3 Various types of observed relationships between concentrations of a chemical in the sorbed state, Cis , and the dissolved state, Ciw . Similar relationships apply to the sorption of gaseous compounds to solid sorbents (substitute Ciw by Cia ).

Another case encountered less frequently in experimental studies involves the situation in which previously sorbed molecules lead to a modification of the sorbent, which favors further sorption (Fig. 12.3e). Studies reporting such sorbent modifications usually involve anionic or cationic surfactants as sorbates. In some of these cases, a sigmoidal isotherm shape (Fig. 12.3f) has been observed, indicating that the sorption promoting effect only starts after a certain loading of the sorbent. In summary, depending on the composition of a natural bulk sorbent and on the chemical nature of the sorbate, multiple sorption mechanisms can act simultaneously, and the

Sorption Isotherms and Equilibrium Distribution Coefficient

355

resulting isotherms may have a variety of different shapes. However, it is not possible to prove a particular sorption mechanism applies from the shape of the isotherm. Instead, the isotherm type and its degree of nonlinearity must be consistent with the sorption mechanism(s) prevailing in a given situation. Quantitative Description of Sorption Isotherms A very common mathematical approach for fitting experimentally determined sorption data using a minimum of adjustable parameters employs an empirical relationship known as the Freundlich isotherm: n

Cis = KiF Ciwi

(12-1)

where KiF is the Freundlich constant or capacity factor (e.g., with units in Eq. 12-1 of (mol kg−1 )(mol L−1 )−ni and ni is the Freundlich exponent. For a correct thermodynamic treatment of Eq. 12-1, we would always have to use dimensionless partitioning constants of compound i in both the sorbed and aqueous phase in order to obtain a dimensionless KiF . However, in practice, Cis and Ciw are expressed in a variety of concentration units. Therefore, KiF is commonly reported in the corresponding units, which also means that for ni ≠ 1, KiF depends nonlinearly on the units in which Ciw is expressed. The relationship in Eq. 12-1 assumes that multiple types of sorption sites act in parallel, with each site type exhibiting a different sorption free energy and total site abundance. The Freundlich exponent is an index of the diversity of the free energies associated with the sorption of the solute by multiple components of a heterogeneous sorbent (Weber and Digiano, 1996). For the special case of ni = 1, the isotherm is linear (Fig. 12.3a), and we denote constant sorption free energies at all sorbate concentrations with a concentration-independent distribution coefficient Kid (which is often also referred to as the partition coefficient and denoted as Kip ): Cis = Kid Ciw = Kip Ciw

ni > 1

log Cis

ni = 1

ni < 1

0

(12-2)

When ni < 1, the isotherm is concave downward, and one infers that added sorbates are bound with weaker and weaker free energies (Fig. 12.3b). When ni > 1, the isotherm is convex upward, and we infer that more sorbate present in the sorbent actually enhances the free energies of further sorption (Fig. 12.3e). KiF and ni can be deduced from experimental data by linear regression of the logarithmic form of Eq. 12-1 (Fig. 12.4):

log Ciw

Figure 12.4 Graphic representation of the Freundlich isotherm Eq. 12-3 for the three cases ni > 1, ni = 1, and ni < 1. ni and log KiF are obtained from the slope (ni ) and intercept (log KiF indicated by the points at log Ciw = 0) of the regression line.

logCis = ni logCiw + logKiF

(12-3)

The units of KiF again depend on the units of Ciw and on the exponent ni (Eq. 12-1). If a given isotherm is not well described by Eq. 12-3, then some assumption behind the Freundlich multi-site conceptualization is not valid. For example, if only a limited number of the total sorption sites become saturated (as in Fig. 12.3c), then Cis cannot

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General Introduction to Sorption Processes

increase indefinitely with increasing Ciw . In this case, the Langmuir isotherm may be a more appropriate model: Cis =

Γmax KiL Ciw 1 + KiL Ciw

(12-4)

where Γmax represents the total number of surface sites per mass of sorbent. In the ideal case, Γmax would be equal for all sorbates. However, in reality, Γmax may vary somewhat between different compounds (e.g., because of differences in sorbate size). Therefore, it usually represents the maximum achievable surface concentration of a given compound i (i.e., Γmax = Cis,max , and thus has the same units). The constant KiL , which is commonly referred to as the Langmuir constant, is defined as the equilibrium constant of the sorption reaction: surface site + sorbate in aqueous solution ⇋ sorbed sorbate This approach using a constant KiL implies a constant sorbate affinity for all surface sites exists. To derive KiL and Cis,max from experimental data, one can fit 1/Ciw versus 1/Cis : 1 = Cis

(

1 Cis,max KiL

)

1 1 + Ciw Cis,max

(12-5)

and use the slope and intercept to extract estimates of the isotherm constants (Fig. 12.5). 1/Cis

Many cases exist, such as type (d) and (f) isotherms in Fig. 12.3, in which the relationship between sorbed concentrations and dissolved concentrations covering a large concentration range cannot be described solely by a linear, a Freundlich, or even a Langmuir equation. In these cases, a combination of equations may need to be applied –1 Cis,max (e.g., Weber et al., 1992; Xia and Ball, 1999; Xing and Pignatello, 1997). Among these distributed reactivity models, the simplest case involves a pair of sorption mechanisms 1/Ciw involving absorption (e.g., linear isotherm with partition coefficient, Kip ) and siteFigure 12.5 Graphic represenlimited adsorption (e.g., Langmuir isotherm), and the resultant combined equation is: tation of the Langmuir isotherm (Cis,max KiL)–1

Eq. 12-5. Cis,max and KiL can be derived from the slope and intercept of the regression line.

Cis = Kip Ciw +

Cis,max KiL Ciw 1 + KiL Ciw

(12-6)

Another equation that fits data from sediments known to contain black carbon (e.g., soot) uses a combination of a linear and a Freundlich isotherm (Accardi-Dey and Gschwend, 2002): n

Cis = Kip Ciw + KiF Ciwi

(12-7)

These dual-mode models have been found to be quite good at fitting experimental data for natural sorbents that contain components exhibiting a limited number of

Sorption Isotherms and Equilibrium Distribution Coefficient

357

highly active adsorption sites in addition to components into which organic compounds may absorb (Huang et al., 1997; Xia and Ball, 1999; Xing and Pignatello, 1997). At low concentrations, the Langmuir or the Freundlich term may dominate the overall isotherm, while at high concentrations (e.g., KiL Ciw ≫ 1), the absorption term dominates. The Solid–Water Distribution Coefficient, Kid To assess the extent to which a compound is associated with solid phases in a given system at equilibrium, we need to know the ratio of the compound’s total equilibrium concentrations in the solids and in the aqueous solution. As mentioned earlier, we denote this solid–water “distribution” coefficient as Kid (e.g., in L kg–1 solid): Kid =

Cis Ciw

(12-8)

When writing these natural solid–water distribution or partition coefficients (Kip ), we use a somewhat different subscript terminology than we introduced for air–water or organic solvent–water partitioning; that is, we do not indicate the involvement of a water or air phase by using a subscript “w” or “a”, respectively. When dealing with nonlinear isotherms (i.e., if ni in Eq. 12-1 is substantially different from 1), the value of this ratio may only apply at the given solute concentration. Inserting Eq. 12-1 into Eq. 12-8, we can see how Kid varies with the sorbate concentration: n −1

Kid = KiF Ciwi

(12-9)

For practical applications, one often assumes that Kid is constant over some concentration range. To examine how reasonable such a simplification is, we can differentiate Kid with respect to Ciw in Eq. 12-8 and rearrange the result to find: dKid dC = (ni − 1) iw Kid Ciw

(12-10)

Therefore, the assumption that Kid is constant is equivalent to presuming: (1) the overall process is either described by a linear isotherm (ni – 1 = 0), or (2) the relative concentration variation, (dCiw /Ciw ), is sufficiently small, so that when multiplied by (ni – 1), the relative Kid variation, (dKid /Kid ), is also small. For example, if the sorbate concentration range is less than a factor of 10, when multiplied by (ni – 1) with an ni value of 0.7, then the solid–water distribution coefficient would vary by less than a factor of 3. The Complex Nature of Kid . The prediction of Kid for any particular combination of organic chemical and solids in the environment can be quite complicated, but, fortunately, many situations can be reduced to fairly simple limiting cases. We begin by emphasizing that the way we defined Kid means that we may have lumped together

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General Introduction to Sorption Processes

several different “forms” of a given compound i in each phase. For example, referring again to Fig. 12.2, we recognize that the total concentration of the 3,4-dimethylaniline in the sorbed phase must combine the contributions of molecules in many different sorbed forms. Additionally, the solution even contains both a neutral and a charged species of this chemical. In a conceptual way, the distribution ratio for this case would have to be written as: Kid = where Cioc

Cioc foc + Cimin Asurf + Ciex σsurf ex Asurf + Cirxn σsurf rxn Asurf Ciw,neut + Ciw,ion

(12-11)

is the concentration of sorbate i associated with the natural organic matter (expressed as organic carbon) present (mol kg−1 oc),

foc

is the weight fraction of solid which is natural organic matter (expressed as organic carbon, i.e., kg oc kg−1 solid),

Cimin

is the concentration of sorbate i associated with the mineral surface (mol m−2 ),

Asurf

is the specific surface area of the relevant solid (m2 kg−1 solid),

Ciex

is the concentration of ionized sorbate drawn towards positions of opposite charge on the solid surface (mol mol−1 surface charges),

σsurf ex is the net concentration of suitably charged sites on the solid surface (mol surface charges m–2 ) for ion exchange, Cirxn

is the concentration of sorbate i bonded in a reversible reaction to the solid (mol mol–1 reaction sites),

σsurf rxn is the concentration of reactive sites on the solid surface (mol reaction sites m–2 ), Ciw, neut is the concentration of uncharged chemical i in solution (mol L–1 ), and Ciw, ion is the concentration of the charged chemical i in solution (mol L–1 ). All terms in Eq. 12-11 may also warrant further subdivision. For example, Cioc foc may reflect the sum of adsorption and absorption mechanisms acting to associate the chemical to a variety of different forms of organic matter (e.g., living biomass of microorganisms, partially degraded organic matter from plants, plastic debris from humans, etc.; see Chapter 13). Similarly, Cimin Asurf may reflect a linear combination of the interactions of several mineral surfaces present in a particular soil or sediment with a single sorbate (Chapters 11 and 14). Thus, a soil consisting of montmorillonite, kaolinite, iron oxide, and quartz mineral components may actually have Cimin Asurf = Cimont aAsurf + Cikao bAsurf + Ciiron ox cAsurf + Ciquartz dAsurf where the parameters a, b, c, and d are the area fractions exhibited by each mineral type. Similarly, Cirxn σsurf rxn Asurf may reflect bonding to several different kinds of surface moieties, each with its

Sorption Isotherms and Equilibrium Distribution Coefficient

359

own reactivity with the sorbate (e.g., 3,4-dimethylaniline). For now, we work from the simplified expression of Eq. 12-11 primarily because little data is available allowing rational subdivisions of soil or sediment that differentially sorb organic chemicals beyond that reflected in this equation. To properly apply Eq. 12-11, it is very important to realize that any one exchange process only involves particular combinations of species in the numerator and denominator. For example, in the case of sorption of dimethylaniline (DMA) to natural sorbents (Fig. 12.2), exchanges between the solution and the solid-phase organic matter reflect establishing the same chemical potential of the uncharged DMA species in the water and in the particulate natural organic phase: NH 2

NH 2

water

organic matter

(12-12)

As a result, a single free energy change and associated equilibrium constant applies to the sorption reaction depicted by Eq. 12-12. Similarly, the combination: NH 2

NH 2

water

min surf

(12-13)

would indicate a simultaneously occurring exchange of uncharged aniline molecules from aqueous solution to the available mineral surfaces. Again, this exchange is characterized by a unique free energy difference reflecting the equilibria shown in Eq. 12-13. Likewise, the exchange of:

NH 2

N

(12-14) water

rxn site

should be considered if it is the neutral sorbate which can react with components of the solid. Such specific binding to a particular solid phase moiety may prevent rapid desorption, and, therefore, such sorbate–solid associations may cause part or all of the sorption process to appear irreversible on some time scale of interest.

360

General Introduction to Sorption Processes

In addition to sorptive interactions in which only the uncharged DMA species is directly involved, the charged DMA species (i.e., anilinium ions) is involved in processes such as ion exchange: NH 3

NH 3

water

ion exchange site

(12-15)

Of course, the anilinium ion in solution is quantitatively related to the neutral aniline species via an acid-base reaction having its own equilibrium constant (see Chapter 4, Section 4.3). However, we emphasize that the solution–solid exchange shown in Eq. 12-15 has to be described using the appropriate equilibrium expression relating corresponding species in each phase. The influence of each sorption mechanism is ultimately reflected by all these equilibria in the overall Kid expression, and each is weighted by the availability of the respective sorbent properties in the heterogeneous solid (i.e., foc , σsurf ex , σsurf rxn or the various A values). By combining information on the individual equilibria (e.g., Eqs. 12-12 through 12-15) with these sorbent properties, we can develop versions of the complex Kd expression (Eq. 12-11) that take into account the structure of the chemical we are considering. In Chapters 13 to 15, we discuss these individual equilibrium relationships. Here, we strive to provide a first look at the effects of sorption on the speciation (sorbed versus dissolved or gaseous) and thus on some transport processes, including retardation in porous media and sedimentation from a water or air column.

12.3

Speciation (Sorbed versus Dissolved or Gaseous), Retardation, and Sedimentation Dissolved (fiw ), Gaseous (fia ), and Sorbed Fractions (fis ) of a Compound in a Given System Let us start out by considering the speciation of a neutral organic compound in an environmental aqueous system containing only solids and water. We may evaluate what fraction of the compound is dissolved in the water, fiw , for any volume: fiw =

Ciw Vw Ciw Vw + Cis Ms

(12-16)

where Vw is the volume of water (L) in the total volume Vt , and Ms is the mass of solids (kg) present in that same total volume. Now, if we substitute the product Kid Ciw from Eq. 12-8 for Cis in Eq. 12-16, we have: fiw =

Ciw Vw Vw = Ciw Vw + Kid Ciw Ms Vw + Kid Ms

(12-17)

Speciation, Retardation, and Sedimentation

361

Finally, if we refer to the quotient, Ms /Vw , as the solid-to-water phase ratio, rsw (e.g., kg L–1 ) in the environmental compartment of interest, we may describe the fraction of chemical in solution as a function of Kid and this ratio: fiw =

1 1 = 1 + (Ms ∕Vw ) Kid 1 + rsw Kid

(12-18)

Such an expression clearly indicates that for substances exhibiting a great affinity for solids (and hence a large value of Kid ) or in situations having large amounts of solids per volume of water (large value of rsw ), we predict that small fractions of the chemical remain dissolved in the water. Correspondingly, the fraction present in particulate form, fip , must be given by: fip = (1 − fiw )

(12-19)

since we assume that no other phases are present (e.g., air, other immiscible liquids). The fraction of the total volume, Vt , that is not occupied by solids, the so-called porosity ϕ (see also Box 5.4), is often used instead of rsw to characterize the solid to water phase ratio in environmental systems like sediment beds or aquifers. In the absence of any gas phase, ϕ is related to parameters previously discussed by: ϕ=

Vw Vw = Vt Vw + Vs

(12-20)

where, Vs , the volume occupied by particles, can be calculated from Ms /ρs , (where ρs is the density of the solids and is typically near 2.5 kg L–1 for many natural minerals). Thus, we find the porosity is also given by: ϕ=

Vw 1 = Vw + Ms ∕ ρs 1 + rsw ∕ ρs

(12-21)

Some representative porosities encountered in the aquatic and terrestrial environment are given in Box 5.4. Solving for rsw yields the relation: rsw = ρs

1−ϕ ϕ

(12-22)

The definitions of the relevant quantitites that are used to describe solid-water mixtures are summarized in Box 12.1, together with the approximations valid for ‘dilute’ systems such as the open water column in lakes and oceans. In the soil and groundwater literature, a third parameter, the bulk density ρb , is commonly used to describe systems: ρb =

Ms = ρs (1 − ϕ) Vt

(12-23)

Thus, rsw is simply equal to ρb /ϕ. It is a matter of convenience whether rsw , ϕ, or ρb is used in discussions.

362

Box 12.1 Css

General Introduction to Sorption Processes

Definition of Concentrations in an Aqueous System with Solids ( ) kgs mtot –3 Concentration of (suspended) solids per bulk volume

ρs

( ) kgs ms –3

ϕ

( –3 ) mw mtot –3 Porosity

rsw

( ) kgs mw –3

Kid = Cis /Ciw

( –1 3) kgs mw Solid–water distribution coefficient

fiw

(−)

Fraction dissolved: fiw =

(1 – fiw )

(−)

Fraction particulate: 1 − fiw =

Cit

( ) mol mtot –3 Total (dissolved and particulate) concentration per bulk volume

Cid = fiw Cit

( ) mol mtot –3 Dissolved concentration per bulk volume

Cip = (1–fiw ) Cit

( ) mol mtot –3 Particulate concentration per bulk volume; Cit = Cid + Cis

Ciw

( ) mol mw –3 Dissolved concentration per water volume

Cis

( ) mol kgs –3 Concentration sorbed on solids

Density of solids

Solid-to-water phase ratio: rsw = ρs

1−ϕ ϕ

1 1 + rsw Kid rsw Kid 1 + rsw Kid

Approximations for small rsw (‘open water’) rsw ∼ Css ; ϕ ∼ 1; fiw ∼ 1; (1 – fiw ) ∼ rsw Kid ; Cid ∼ Ciw

As compared to soils, aquifers, or sediments, rsw in surface waters is much smaller (i.e., 10–5 to 10–7 kg L–1 ), and, therefore, Vw ≈ Vt . The same holds for the atmosphere (Va ≈ Vt ), where particle (aerosol) concentrations are even smaller, i.e., 10–10 to 10–12 kg L–1 (Table 5.2). In these cases, rsw is simply given by the particle concentration, which is sometimes also denoted as Sw or Sa respectively.

Retardation in Porous Media Let us now consider a typical groundwater situation: a chemical is released into flowing groundwater. The aquifer solids have a ρs of about 2.5 kg L–1 (e.g., quartz

Speciation, Retardation, and Sedimentation

363

density is 2.65 kg L–1 ), and ϕ of such porous media is often between 0.2 and 0.4. If in our particular groundwater situation ϕ is 0.2, insertion of these values into Eq. 12-22 yields an rsw value of 10 kg L–1 . Thus, fiw as a function of Kid expressed in L kg–1 (Eq. 12-18) is:

fiw =

1 1 + (10 kg L−1 )Kid

(12-24)

We now apply this speciation information to a release of one of our companion compounds, the solvent tetrachloroethene (PCE, Chapter 3), into flowing groundwater. From experience, we know that the Kid value for PCE in this case happens to be in the order of 1 L kg–1 since the aquifer materials usually contain only very little organic matter, which is the main sorbent for this kind of compounds (see Chapter 13). Insertion of this Kid value into Eq. 12-24 then yields a fiw of about 0.09. Therefore, we deduce that only one PCE molecule out of 11 will be in the moving groundwater at any instant (Fig. 12.6). This result has implications for the fate of the PCE in the subsurface environment. If PCE sorptive exchange between the aquifer solids and the water is fast relative to the groundwater flow and if sorption is reversible, we can conclude that all the PCE molecules move at one eleventh the rate of the water. The phenomenon of diminished chemical transport speed relative to the water seepage velocity is referred to as retardation. It is commonly described by the retardation factor, Rfi , which is simply equal to the reciprocal of the fraction of molecules capable

groundwater level

i Figure 12.6 Illustration of the retardation of the transport of an organic compound i in groundwater due to: (1) reversible sorptive exchange between water and solids, and (2) limiting transport of i to that fraction remaining in the flowing water. As dissolved molecules move ahead, they become sorbed and stop, while molecules sorbed at the rear return to the water and catch up. Thus, overall transport of i is slower than that of the water itself.

(1)

i

i (2)

v = groundwater flow in response to sloping watertable v . fiw = average speed of molecules

364

General Introduction to Sorption Processes

−1 of moving with the flow at any instant, fiw : −1 Rfi = fiw = 1 + rsw Kid

(12-25)

Hence, Rf PCE = 11. Sedimentation As already mentioned, in the water column of surface waters, for example in lakes, rsw is in the order of 10–6 kg L–1 . In this case, fiw is given by: fiw =

1+

(10−6

1 kg L−1 )Kid

(12-26)

Since in lakes the organic matter content of the solids is commonly significantly higher than in aquifers (Chapter 5), for our companion compound PCE we may assume a Kid value of as large as 100 L kg–1 (see Chapter 13). However, even with this much larger Kid , fiw is 1/1.0001 = 0.99990; that is, virtually all PCE is present in a dissolved form in the water column of a lake. Only 0.1‰ will be sorbed to particles. From Eq. 12-26, we can easily see that we need a Kid of 106 in order to have 50% of the PCE molecules in a sorbed or particulate form (fip = 1 – fiw = 0.5). Sedimentation, that is, the removal by sinking particles, can be an important process for a given organic pollutant in a water column. However, how large must the fraction of said pollutant be in particulate form, fip , in order for sedimentation to be of importance? To answer this question, we consider a well-mixed waterbody, such as the epilimnion of a lake, which can be described by the one-box model introduced in Chapter 6 (Section 6.2). We recall that, in this simple approach, we express all processes as first-order reactions characterized by a first-order reaction constant. By doing so, we can compare the different first-order rate constants to assess the relative importance of each process. Firstly, we note that a process that is equally important for all compounds is flushing or dilution, which we denote by the flushing rate constant kw : kw =

Q −1 [T ] V

(6-4)

where Q is the water flow rate (e.g., in m3 d–1 ) and V is the volume or the wellmixed waterbody (e.g., in m3 ). Here, we only further consider the first-order removal rate constant of sedimentation of the compound, ksed , which we compare to kw (see Fig. 12.7). We address all other processes in other respective chapters. For our simple back-of-the-envelope calculation, we assume that we have a constant steady-state concentration of particles in the epilimnion, denoted as Sw (e.g., in kg–3 ), and an average particle sinking velocity vs (e.g., in m d–1 ). The flux Fs per unit area (e.g., in kg m–2 d–1 ) of particles out of our box (i.e., the epilimnion of the lake) is then

Speciation, Retardation, and Sedimentation

365

QCt

QC in

epilimnion

Ct ksed dCt = Cinkw − (kw + ksed)Ct dt

Figure 12.7 Box model for Mystery Lake, Cleanland (see Chapter 6, Section 6.1) including removal of contaminant via the outlet (kw ) and sedimentation (ksed ). The model is used for some simple calculations assuming no water exchange between the epilimnion and the hypolimnion and all removal processes can be expressed as first-order reactions.

given by Fs = vs Sw , which multiplied by the total surface area, A, of our waterbody yields the total flux of particles: total flux = AFs = Avs Sw

(12-27)

which, divided by the volume, yields the first-order particle removal rate constant, ks (e.g., in d–1 ): ks =

v A vs = s V h

(12-28)

where h = A/V (e.g., in m) is the mean depth of the epilimnion. To now obtain the first-order removal rate constant of the compound, ksed , we simply have to multiply Eq. 12-28 by the fraction in particulate form (note that we omit the subscript i): ksed = ks (1 − fiw ) =

vs (1 − fiw ) h

(12-29)

For illustration, let us apply these equations to the epilimnion of Mystery Lake, Cleanland (Fig. 12.7), introduced in Chapter 6, Section 6.1. We assume a mean epilimnion depth h = 10 m and a mean particle settling rate vs = 1 m d–1 , which yields a ksed = 0.1 (1 – fiw ) d–1 . The flushing rate constant of the epilimnion of Mystery Lake, kw , is 0.01 d–1 . Therefore, in order to make sedimentation equally or more important than flushing (ksed ≥ kw ), the value of (1 – fiw ) has to be at least 0.1, that is, at least 10% of the compound has to be sorbed. When assuming a typical particle concentration of 5 × 10–6 kg L–1 in a lake, only for compounds with Kid values equal or greater than 22,000 L kg–1 does sedimentation become an important process. Thus, for PCE with its Kid of 100 L kg–1 , sedimentation in the epilimnion can be completely neglected. In contrast, gas exchange with the atmosphere cannot be neglected, which we already predicted for PCE in Chapter 6 and which we further discuss in Chapter 19.

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General Introduction to Sorption Processes

12.4

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Questions Q 12.1 Give five reasons why it is important to know to what extent a given chemical is present in the sorbed form in a natural or engineered system. Q 12.2 What are the most important natural sorbents and sorption mechanisms for (a) apolar compounds, (b) polar compounds, and (c) ionized compounds? Q 12.3 What is a sorption isotherm? Which types of sorption isotherms may be encountered when dealing with sorption of organic compounds to natural sorbents? Does the shape of a sorption isotherm tell you anything about the sorption mechanism(s)? If yes, what? If no, why not? Q 12.4 Write down the most common mathematical expressions used to describe sorption isotherms. Discuss the meaning of the various parameters and describe how they can be derived from experimental data. Q 12.5 Which environmental parameters and compound properties determine the fraction in dissolved form of (a) a neutral organic compound and (b) an ionizable organic compound in an aquifer? How is the retardation factor of a compound in an aquifer defined, and what does it exactly describe? Q 12.6 Which environmental parameters and compound properties determine the rate at which a compound is removed from a waterbody by sedimentation? Q 12.7 Explain more explicitly how one gets from Eq. 12-28 to Eq. 12-29 and under which assumptions Eq. 12-29 may be used to describe sedimentation of organic chemicals in the water column. Problems P 12.1∗ Determining Kid Values from Experimental Data A common way to measure Kid values is to measure isotherms in batch experiments. To this end, the equilibrium concentrations of a given compound in the solid

Questions and Problems

NO 2 1,4-dinitrobenzene

Ciw (μmol L–1 )

Cis (μmol kg–1 )

0.06 0.17 0.24 0.34 0.51 0.85 1.8 2.8 3.6 7.6 19.5 26.5

97 241 363 483 633 915 1640 2160 2850 4240 6100 7060

phase (Cis ) and in the aqueous phase (Ciw ) are determined at various compound concentrations and/or solid/water ratios. Consider the adsorption of 1,4-dinitrobenzene (1,4-DNB) to the homoionic clay mineral, K+ -illite. 1,4-DNB forms electron donoracceptor complexes with clay minerals. In a series of batch experiments, Haderlein et al., (1996) measured the data at pH 7.0 and 20◦ C given in the margin and plotted in the figure. Using this data, estimate the Kid values for 1,4-DNB for equilibrium concentrations of 1,4-DNB in the aqueous phase of 0.20 μM and of 15 μM respectively. Derive appropriate isotherms for estimating these Kid values. 8000

6000 Cis (μmol kg–1)

NO 2

367

4000

500 400 300 200

2000

100 0

0

0

10

0

Ciw (μM)

0.1

0.2

0.3

20

30

Figure. Adsorption of 1,4-DNB to K+ -illite

P 12.2 Retardation of Phenanthrene in an Aquifer Containing Very Little Organic Material

mineral quartz kaolinite iron oxides a Data

log Kidsurf w (m)a –7.2 –7.8 –7.3

from the literature cited in Chapter 11, Fig. 11.8. Values measured at 20◦ C.

Due to runoff from streets, a series of PAHs have been detected in drinking water originating from an aquifer containing very little organic carbon. Therefore, it can be assumed that primarily adsorption to mineral surfaces determines how fast these compounds are transported in the aquifer. Using the surface normalized Kisurfw values (Chapter 11, Eq. 11-15) given in the margin, estimate the retardation factor of our companion compound phenanthrene in this aquifer from which you have the following information: the average porosity is 0.3; the aquifer solids consist of 95% quartz (density 2.65 g mL–1 ; surface area 1 m2 g–1 ), 4% kaolinite (density 2.6 g mL–1 ; surface area 10 m2 g–1 ), and 1% iron oxides (density 3.5 g mL–1 ; the surface area is 50 m2 g–1 ; and organic carbon content is ≪ 0.1%. The average temperature is 10◦ C, and the pH is 7.0. P 12.3 Elimination of PCB 153 from the Epilimnion of a Lake After an accident in early summer, an unknown amount of our companion compound PCB 153 was introduced into the epilimnion of our model Mystery Lake, Cleanland. As the owner of an environmental analytical lab, you were offered the job to monitor the concentrations of this compound in the epilimnion of Mystery Lake during the summer. At the end of August, you look at your data and realize that after 46 days, the total concentration of PCB 153 had dropped to one fourth of its initial total concentration. A colleague of yours claims that the elimination of the compound was

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General Introduction to Sorption Processes

only due to flushing. Is this person correct? If not, are there other significant elimination processes, and how important are they as compared to flushing? Since you have already read Chapter 6, you know that, unlike for PCE, gas exchange is not a major removal mechanism for this compound from the epilimnion of Mystery Lake. You also assume that, under the oxic conditions prevailing in the epilimnion, PCB 153 is quite persistent to any transformation reaction. Hence, only elimination by sedimentation could be important. Is this a reasonable assumption? Calculate the Kid value that would be necessary to account for the additional elimination by assuming the lake parameters used earlier (mean epilimnion depth h = 10 m, flushing rate constant kw = 0.01 d–1 , and mean particle settling rate vs = 1 m d–1 ). Compare your result with an estimate of your colleague who has read Chapter 13 and who tells you that, for PCB 153, you should expect a Kid between 104 and 5 × 104 L kg–1 . Hint: You are dealing with case a in Box 6.2.

12.5

Bibliography Accardi-Dey, A.; Gschwend, P. M., Assessing the combined roles of natural organic matter and black carbon as sorbents in sediments. Environ. Sci. Technol. 2002, 36(1), 21–29. Haderlein, S. B.; Weissmahr, K. W.; Schwarzenbach, R. P., Specific adsorption of nitroaromatic: Explosives and pesticides to clay minerals. Environ. Sci. Technol. 1996, 30(2), 612–622. Huang, W. L.; Young, T. M.; Schlautman, M. A.; Yu, H.; Weber, W. J., A distributed reactivity model for sorption by soils and sediments. 9. General isotherm nonlinearity and applicability of the dual reactive domain model. Environ. Sci. Technol. 1997, 31(6), 1703–1710. Weber, J. W. J.; DiGiano, F. A., Process Dynamics in Environmental Systems. Wiley: New York, 1996; p 968. Weber, W. J.; McGinley, P. M.; Katz, L. E., A distributed reactivity model for sorption by soils and sediments. 1. Conceptual basis and equilibrium assessments. Environ. Sci. Technol. 1992, 26(10), 1955–1962. Xia, G. S.; Ball, W. P., Adsorption-partitioning uptake of nine low-polarity organic chemicals on a natural sorbent. Environ. Sci. Technol. 1999, 33(2), 262–269. Xing, B. S.; Pignatello, J. J., Dual-mode sorption of low-polarity compounds in glassy poly(vinyl chloride) and soil organic matter. Environ. Sci. Technol. 1997, 31(3), 792–799.

369

Chapter 13

Sorption from Water to Natural Organic Matter (NOM)

13.1 The Structural Diversity of Natural Organic Matter Present in Aquatic and Terrestrial Environments The Complex Nature of Natural Organic Matter (NOM) Black Carbon and Other Organic Sorbents 13.2 Quantifying Natural Organic Matter–Water Partitioning of Neutral Organic Compounds The Organic Carbon–Water Partition Coefficient (Kiocw ) LFER Modeling Approaches to Estimate Organic Carbon–Water Coefficients Effect of Temperature and Solution Composition on Kiocw Nonlinearity of Sorption Isotherms Due to the Presence of Black Carbon (BC) in Soils and Sediments 13.3 Sorption of Organic Acids and Bases to Natural Organic Matter Effect of Charged Moieties on Sorption: General Considerations Sorption to NOM of Compounds Forming Anionic Species (Organic Acids)

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

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Sorption to NOM of Compounds Forming Cationic Species (Organic Bases) 13.4 Questions and Problems 13.5 Bibliography

The Structural Diversity of Natural Organic Matter

371

In Part II, we learned that the majority of nonionic organic pollutants tend to favorably partition from water into organic phases. The driving force of this partitioning is the tendency of the compound to leave the aqueous phase (its “hydrophobicity”), that is, the free energy gain associated with removing a compound from aqueous solution. Therefore, it makes sense that organic materials “dissolved” in water (i.e., truly dissolved or in colloidal form) or associated with solids (e.g., particles in the water column as well as constituents of sediments, soils, and aquifer materials) are often the dominating sorbents for organic chemicals dissolved in natural waters. In this chapter, we discuss quantitative approaches for describing sorption equilibrium between such organic materials and water, with an emphasis on what is referred to as “natural organic matter” (NOM), which refers to all organic materials of natural origin. We also address the role of carbon-rich, combustion-derived materials from natural (e.g., forest fire chars) or anthropogenic (e.g., diesel soots) origins. These “black” carbon materials are important additional organic adsorbents, particularly for compounds such as PAHs and planar PCBs.

13.1

The Structural Diversity of Natural Organic Matter Present in Aquatic and Terrestrial Environments The Complex Nature of Natural Organic Matter (NOM) The Operational Size Fractions of NOM. In a given environmental system, the NOM present is commonly operationally divided into a fraction that passes through a filter having a pore size near 1 μm (see also Chapter 5, Box 5.3), referred to as “dissolved” organic matter (DOM), and a “particulate” fraction (POM), sometimes also referred to as soil and sediment organic matter (SOM), which is withheld by the filter. DOM often represents a more diverse set of constituents than POM, as DOM encompasses small molecules (< 200 Da), aggregates of small and larger molecules, micelles, and colloids. Thus, the commonly studied NOM components of fulvic and humic acids (see Table 13.1) are considered part of DOM. Some of these “dissolved” organic water constituents may act as sorbents, while others are simply co-solutes or are too small to significantly sorb pollutants. For example, Remucal et al. (2012) showed that a significant fraction (36%) of Suwanee River fulvic acid (SRFA), which is frequently used as model DOM, is made up of constituents that pass a 100–500 molecular weight cutoff dialysis membrane. The common analytical methods for determining the total organic carbon (TOC) present in a sample involve combusting (oxidizing) the sample and measuring the evolved CO2 ; the abundance of DOM in aqueous solution is usually expressed by the aqueous concentration of reduced carbon [DOC]:

[DOC] =

mass of organic carbon (e.g., kg oc) total volume (e.g., L )

(13-1)

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Sorption from Water to Natural Organic Matter (NOM)

Table 13.1 Properties of Organic Components that May Act as Sorbents of Organic Compounds in the Environmenta Mole Ratio Component

C

H

N

O

% Aromaticity

Biogenic Molecules Proteins Collagen (protein) Cellulose (polysaccharide) Chitin (polysaccharide) Lignin (alkaline extract) Lignin (org. solvent extract)

1.0 1.0 1.0 1.0 1.0 1.0

1.6 1.7 1.7 1.8 1.1 0.98

0.4 0.19 < 0.01 0.13 < 0.01 < 0.01

0.2 0.31 0.84 0.64 0.40 0.33

< 10 < 10 < 10 < 10 28 34

Diagenetic Materials Fulvic acids soil leachate brown lake water river water groundwater Suwannee River

1.0 1.0 1.0 1.0 1.0

1.04 0.88 1.62 1.04 1.0

< 0.1 < 0.1 < 0.1 < 0.1 < 0.1

0.53 0.55 1.09 0.51 0.62

36 35 29 24 24

Humic acids brown lake water river water “average” soil Aldrich (AHA) Suwannee River Pahokee peat Humin

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.80 1.48 1.15 0.78 0.90 1.9 1.0 0.4 to 1

< 0.1 < 0.1 0.07 0.01 0.02 0.02 0.06

0.54 0.91 0.50 0.44 0.40 1.1 0.48 0.05 to 0.3

40 38

Combustion-Derived Materials NIST diesel soot BCb from Boston Harbor sediment

1.0 1.0

0.1 1.0

0.016 0.07

41 45 31 47

∼100

a

Data from Oser (1965); Brownlow (1979); Chin et al. (1994); Xing et al. (1994); Zhou et al. (1995); Schulten and Schnitzer (1997); Arnold et al. (1998); Haitzer et al. (1999); Accardi-Dey and Gschwend (2002); Niederer et al. (2007); Bronner and Goss (2011a). b BC = black carbon.

The abundance of POM (or SOM) is described by the weight fraction of organic carbon present in a given solid matrix, foc : foc =

mass of organic carbon (e.g., kg oc) total mass of solid sorbent (e.g., kg solid)

(13-2)

Since NOM is typically made up of about half (40 to 60%) carbon, [DOM] (e.g., kg om L–1 water) equals approximately 2 [DOC], and fom is approximately 2 foc .

The Structural Diversity of Natural Organic Matter

373

This purely operationally size division of the total organic matter present in a sample into DOM and POM is often misleading from a process-oriented point of view. For example, if we consider a porous medium such as lake sediment or aquifer stratum, we may be interested in the fraction of NOM that is mobile and thus may transport sorbed organic pollutants. This mobile fraction is not necessarily represented by a DOM measurement; POM may also be mobile. Conversely, POM may not include all the organic material settling in the water column of a lake or in the ocean. Finally, when we consider the bioavailability of a compound in aqueous solution, both POM and DOM may be important sorbents, but not all of the DOM may represent a “separate phase” that can act as a sorbent. The Structural Composition of NOM. In the past 10 years, the number of studies focused on determining the structural composition of NOM and its dynamics in aquatic and terrestrial environments has grown exponentially. The growth stems from increased interest in local, regional, and global carbon cycles coupled with increasingly powerful analytical tools such as modern spectroscopy (see Simpson and Simpson, 2012; Nebbioso and Piccolo, 2013; Abdulla and Hatcher, 2014; Minor et al., 2014). However, despite these enormous research efforts, only modest progress has been made in characterizing NOM from various origins, especially with respect to its properties as a sorbent for organic pollutants. What we do know, from work conducted many years ago (e.g., Thurman, 1985; Schulten and Schnitzer, 1997; Hayes, 1998), is that NOM present in soils, sediments, groundwater, surface waters, atmospheric aerosols, and wastewater comprises recognizable biochemicals like proteins, nucleic acids, lipids, cellulose, and lignin (addressed in more detail in Chapter 16; structures in Fig. 16.2). NOM also contains a menagerie of micro- and macromolecular residues generated by diagenesis, i.e., the reactions of partial degradation, rearrangement, and recombination of the original molecules formed in biogenesis (see Table 13.1). In the past, this mixture of residues in NOM was postulated to exist in high molecular weight polymeric structures, particularly in the “persistent” fractions (e.g., Schulten and Schnitzer, 1997). The current view of the structural composition of NOM is that of a supramolecular association of a diversity of much smaller molecules (schematically depicted in Fig. 13.1, see Sutton and Sposito, 2005; Kleber and Johnson, 2010; Schmidt et al., 2011; Nebbioso and Piccolo, 2013; Drosos et al., 2014; Lehmann and Kleber, 2015). These supramolecular associations are characteristic in both the DOM and POM fractions of NOM and can form structurally distinct sorptive phases. In solution, dissolved (macro)molecules may form organic phases relevant for sorption by aggregation facilitated by complexing cations (e.g., Ca2+ , Al3+ , Fe3+ ), which act as intermolecular bridges. The formation and stability of such aggregates is dependent on the concentration of the respective metal cation and on pH (Mouvenchery et al., 2012; Kloster et al., 2013). At mineral surfaces, molecules exhibiting numerous bipolar groups such as polyphenols (Bentley and Payne, 2013), sugars (Petridis et al., 2014), or fulvic acids (Armanious et al., 2014) tend to form self-assembled organic layers. Subsequently, other molecules may adsorb to these layers, thus forming a stable supramolecular assembly held together by electrostatic, H-bonding, and vdW interactions (Petridis

374

Sorption from Water to Natural Organic Matter (NOM)

i

i

Figure 13.1 Schematic picture of the supramolecular associations of a diversity of “small” biogenic molecules and their breakdown products that form natural organic matter.

et al., 2014). Such POM assemblies formed in soils can persist because of the impenetrability of light and microbes (see Mayer, 2004; Schmidt et al, 2011). However, when these assemblies reach surface waters, photochemical and microbial processes can readily degrade or transform them (Rossel et al., 2013; Guenet et al., 2014; Hotchkiss et al., 2014; Marin-Spiotta et al., 2014). Particularly NOM exposed to photochemical transformation processes tends to exhibit smaller aromaticities as compared to the source material, which was observed in the terrestrially-derived components of marine NOM (Bianchi, 2011). Whether we consider DOM or POM as the bulk sorbent or “solvent” for organic pollutants in a given system, we are faced with a spatially and structurally heterogeneous matrix; a variety of organic phases of different sizes (volumes) exhibit different polar (reflected primarily by the O/C ratio) and apolar (reflected by the H/C ratio and the % aromaticity) moieties, creating different microenvironments into which organic compounds may partition. Depending on the organic material considered, the number of polar groups might vary quite significantly. Highly polar fulvic acids may have O/C ratios of near 0.5 (Table 13.1), while more mature organic matter

The Structural Diversity of Natural Organic Matter

375

have ratios of around 0.2 to 0.3; these evolve towards coal values below 0.1 (Brownlow, 1996). Furthermore, evidence exists that some NOM consists of both flexible (“rubbery”) molecules and materials with more rigid (“glassy”) character. Rigid domains are often present in the POM of soils and sediments, and contain nanopores that are accessible only by diffusion (Leboeuf and Weber, 1997; Xing and Pignatello, 1997; Xia and Ball, 1999; Cornelissen et al., 2000; Latao et al., 2012; Pignatello, 2012). In summary, the chemical composition and the physical characteristics of this complex mixture of organic phases in a given environmental setting depend on the types of the biological source materials and on the physical, chemical, and biological processes to which they have been exposed. From a process-oriented point of view, we should envision NOM as a continuum of dissolved, colloidal, particulate, and solid surface-bound organic phases of different sizes (volumes) and chemical compositions.

Black Carbon and Other Organic Sorbents In addition to the NOM found in the environment due to biogenesis and diagenesis, other identifiable organic sorbents, mostly derived from human activities, can be present and so be included in a TOC measurement. Examples include combustion products (soots, fly ash, biochars), tars and asphalt, plastics and rubbers, wood, and nonaqueous phase liquids. The most important among these sorbents are the various forms of “black” carbon (BC) engendered from incomplete combustion (Goldberg, 1985). The myriad descriptors of these materials, such as soot, smoke, black carbon, carbon black, charcoal, spheroidal carbonaceous particles, elemental carbon, graphitic carbon, charred particles, high surface area carbonaceous material, reflect either the formation processes or the operational techniques employed for their characterization. BC particles are ubiquitous in sediments and soils, often contributing up to 10% or even more of TOC (Gustafsson and Gschwend, 1998; Cornelissen et al., 2005; Lohmann et al., 2005; Koelmans et al., 2006). Such particles can be quite porous and exhibit a rather apolar and aromatic surface (Table 13.1). Consequently, BC has a high affinity for many organic pollutants, particularly for planar aromatic compounds. Therefore, at low pollutant concentrations where these sorptive sites are not saturated, significantly higher apparent partition coefficient values may be observed as compared to values that would be predicted from simple partitioning models considering only NOM (Gustafsson et al., 1997; Naes et al., 1998; Karapanagioti et al., 2000; Lohmann et al., 2005; Koelmans et al., 2006). Capitalizing on this high sorptive affinity, activated carbon or biochars are increasingly used to amend soils and sediments as a means of remediation via immobilization of pollutants (see Ghosh et al., 2011; Oen et al., 2012; Ahmad et al., 2014). Another identifiable organic sorbent in natural systems are synthetic polymers, such as plastics (Andrady, 2011; Lambert et al., 2014); rubber (Kim et al., 1997); and wood, as found in the wood chips or sawdust used as fills at industrial sites (Severton and Banerjee, 1996; Mackay and Gschwend, 2000). If such materials are present in a soil, sediment, or waste of interest, then they will serve as part of the organic sorbent mix. We further discuss sorption to such sorbents when addressing bioaccumulation in Chapter 16.

376

Sorption from Water to Natural Organic Matter (NOM)

Finally, special organic sorbents that may be of importance, particularly when dealing with contamination in the subsurface, are nonaqueous phase liquids (NAPLs, see also Section 10.4). These liquids may be immobilized in porous media and serve as absorbents for passing nonionic organic compounds (Mackay et al., 1996). In such cases, we may apply partition coefficients as discussed in Chapter 10 for organic solvents; in the special case of phases such as coal tar, one may describe sorption equilibrium using the data reported by Endo et al. (2008a). We should keep in mind, however, that the chemical composition of the absorbing NAPL evolves with time.

13.2

Quantifying Natural Organic Matter–Water Partitioning of Neutral Organic Compounds The Organic Carbon–Water Partition Coefficient (Kiocw ) Sorption of neutral organic chemicals to the organic matter present in a given environmental system may involve partitioning into, as well as adsorption onto, a wide variety of different organic substances. Thus, in general, we cannot expect linear isotherms over the whole concentration range, and we should be aware that predictions of overall organic matter–water partition coefficients may have rather large errors if some of the important organic materials present are not recognized (Kleineidam et al., 1999; Lohmann et al., 2005; Koelmans et al., 2006). Conversely, with appropriate site-specific information, reasonable estimates of representative, generally applicable organic carbon–water partition coefficients, Kiocw , are often possible using:

Kiocw (e.g., L kg

−1

oc) =

Cioc (e.g., mol kg−1 oc) Ciw (e.g., mol L−1 )

(13-3)

where Cioc and Ciw are the concentations of i per mass organic carbon and per volume of water respectively. Historically, the vast majority of Kiocw values were determined for soil and sediment organic matter (SOM), primarily by equilibrium batch experiments with slurries or in columns (Chiou et al., 1979; Karickhoff et al., 1979; Schwarzenbach and Westall, 1981). Kiocw is calculated by dividing the experimentally determined Kid (= Cis ∕Ciw ) value by the fraction of organic carbon, foc , of the sorbent investigated: Kiocw (e.g., L kg−1 oc) =

Kid (e.g., L kg−1 solid) foc (e.g., kg oc kg−1 solid)

(13-4)

Of course, a meaningful Kiocw value is only obtained if sorption to the natural organic material is the dominant process. This may be particularly problematic for sorbents exhibiting very low organic carbon contents (i.e., foc < 0.001) (Schwarzenbach and Westall, 1981). Also, care must be taken to ensure that equilibrium is established and the analyzed aqueous phase does not contain any colloids (Gschwend and Wu, 1985).

Quantifying Natural Organic Matter–Water Partitioning

377

Various techniques have been developed to measure DOM–water partition coefficients, as the organic phase cannot be easily separated from the aqueous phase. Examples include dialysis techniques (e.g., Aeschbacher et al., 2012), solubility enhancement measurements (e.g., Wei-Haas et al., 2014), fluorescence quenching techniques (e.g., Hur et al., 2009), direct solid–phase microextraction (SPME) (e.g., Doll et al., 1999), and passive dosing (e.g., Gouliarmou et al., 2012). However, despite all these method developments, compared to SOM, the available data for DOM–water partitioning is still rather scarce, particularly with respect to the range of compounds investigated. By far, the most studies have been conducted with PAHs (e.g., ter Lak et al., 2005; Hafka et al., 2010; Kim and Kwon, 2010;) and, to a lesser extent, with polyhalogenated aromatic compounds, including PCBs (e.g., Durjava et al., 2007) and PBDEs (Wei-Haas et al., 2014), as model pollutants. Let us now look at the variability in Kiocw values reported for a given compound for partitioning to SOM and DOM of different origins. For most organic compounds, organic carbon–water partition constants are primarily determined by the “desire” of the compound to escape the water. In thermodynamic terms, Kiocw mostly depends on the aqueous activity coefficient (Chapter 10, Eq. 10.2 and Fig. 10.1). When considering soil or sediment organic matter (SOM) from different origins, the variability in Kiocw of a given compound is not too large, often being within a factor of 2 to 3, as shown for our companion compound atrazine in Fig. 13.2 (see other examples in Gerstl, 1990; Nguyen et al., 2005; Bronner and Goss, 2011a). Larger variability of up to an order of magnitude or even more in reported SOM Kiocw values, also seen in Fig. 13.2, are likely due to experimental artifacts or the nonlinearity of isotherms (Endo et al., 2008b). As DOM often contains a more diverse set of materials as compared to SOM, we may expect that the differences in DOM-Kiocw of a given compound between DOM of different origins will be larger than SOM-Kiocw . For example, for sorption to Aldrich humic acid as compared to Suwannee River fulvic acid, 5 and 10 times higher Kiocw

Figure 13.2 Frequency diagram illustrating the variability in the log Kiocw values determined for our companion atrazine for 217 different soil and sediment samples. The majority of log Kiocw values are within 0.3-0.5 log units. Data compiled by Gerstl (1990).

number of experimental values

40 35 30 25 20 15 10 5 0 1.3

1.7

2.1 2.5 2.9 3.3 −1 log Kiocw (L kg oc)

3.7

378

Sorption from Water to Natural Organic Matter (NOM)

values have been reported for phenanthrene and benzo(a)pyrene respectively (Kim and Kwon, 2010). Also, as not all of the components of DOM are large enough to act as sorbents, DOM-Kiocw values are often smaller than those of SOM-Kiocw . Suwannee River fulvic acid, for instance, is a poorer sorbent as compared to average values reported for SOM. LFER Modeling Approaches to Estimate Organic Carbon–Water Coefficients sp-LFER Approach to Estimate Kiocw . The most widely used method for estimating Kiocw of a given compound is still to estimate it from its octanol–water partition constant, Kiow , using the sp-LFER: log Kiocw = a log Kiow + b

(13-5)

As discussed in Chapters 7 and 10, such sp-LFERs work best for structurally closely related compounds. Severe limitations are seen when pooling compounds exhibiting different molecular interactions, particularly when pooling apolar with bipolar compounds (Nguyen et al., 2005). Furthermore, they are strictly applicable only for the range of Kiow values for which they were derived. Table 13.2 summarizes some sp-LFERs derived from experimental NOM-Kiocw values for various compound classes. As can be seen from the r2 values, good Table 13.2 sp-LFERs (Eq. 13-5) Relating NOM–Water Partition Coefficients, Kiocw and Octanol–Water Partition Constants, Kiow , at 20 to 25◦ C for Some Sets of Neutral Organic Compoundsa NOM Type

Set of Compoundsb

SOM SOM SOM

Alkylated benzenes PAHs Chlorinated benzenes and PCBs Chlorinated phenols (neutral species) All phenylureas Only alkylated and halogenated phenylureas, phenyl-methylureas, and phenyl-dimethylurea Only alkylated and halogenated phenylureas PAHs Chlorinated benzenes and PCBs

SOM SOM SOM

SOM Aldrich humic acid Suwannee River fulvic acid

a

b

log Kiow rangec

r2

nd

0.81 1.12 0.94

−0.22 −0.86 −0.43

2.2 – 4.0 3.4 – 6.1 2.8 – 7.2

0.96 0.95 0.98

10 11 24

0.89

−0.15

2.2 – 5.3

0.97

10

0.49 0.59

1.05 0.78

0.5 – 4.2 0.8 – 2.9

0.62 0.87

52 27

0.62

0.84

0.8 – 2.8

0.98

13

1.20 0.82

−0.81 0.31

4.6 – 6.8 4.6 – 6.8

0.98 0.93

7 8

Kioc in L kg–1 oc: slopes (a) and intercepts (b) of Eq. 13-5. Data compiled from Schellenberg et al. (1984); Sabljic et al. (1995); Chiou et al. (1998); Poole and Poole (1999); Nguyen et al. (2005); Durjava et al. (2007); Kim and Kwon (2010); Gouliarmou et al. (2012). c Range of experimental values for which LFER has been established. d Number of compounds used for LFER. a b

Quantifying Natural Organic Matter–Water Partitioning

379

correlations are found for structurally closely related sets of compounds, except for the group of 52 phenylureas. For the alkylated benzenes, chlorinated benzenes, PCBs, PAHs, and chlorinated phenols, the sp-LFERs were derived from averaged Kiocw values representing, in general, quite a large number of measurements. For these classes of compounds, predictions within a factor of 2 to 3 should be possible (Nguyen et al., 2005). Since the 52 phenylureas represent quite a different structural diversity, the correlation is much weaker but improves significantly for subsets of structurally more similar compounds (Table 13.2). From the differences in the various sp-LFERs given in Table 13.2, it is, however, difficult to draw any mechanistic conclusions. What can be seen is that, compared to octanol, partitioning from water to SOM increases somewhat more with size for the PAHs (slope > 1), whereas, for the substituted benzenes and PCBs, the increase is somewhat smaller (slope < 1), and is smallest for the bipolar phenylureas (slope ≪ 1). A final insight from Table 13.2 is that Aldrich humic acid represents a sorbent that is much more similar to SOM as compared to most DOM in the environment, which is reflected in very similar or even larger Kiocw found for Aldrich humic acid as compared to average values reported for SOM (e.g., for PAHs). pp-LFER Approach to Estimate Kiocw . As with predicting partition constants for organic solvent–water partitioning (Chapter 10), pp-LFERs are generally applicable tools for predicting Kiocw values. Few pp-LFERs derived from experimental NOM– water partitioning data have been reported in the literature to date. However, these still provide some important insights into the variability of NOM and the prominent intermolecular interactions at play during sorption. As discussed in Chapter 7, two types of pp-LFERs are commonly used that differ primarily in the way in which the vdW-interactions are expressed. Thus, pp-LFERs for NOM–water partitioning may also take two forms, one using the solute descriptor of the excess molar refraction (Ei ) and the other using log Kihexadecane–air (Li ), which incorporates size (Eqs. 13-6 and 13-7). Table 13.3 summarizes the coefficients of the pp-LFERs, as compiled in the UFZ-LSER database (Endo et al., 2014). log Kiocw = vocw Vi + eocw Ei + socw Si + aocw Ai + bocw Bi + c

(13-6)

log Kiocw = vocw Vi + locw Li + socw Si + aocw Ai + bocw Bi + c

(13-7)

Both Eqs. 13-6 and 13-7 are well suited to fit the reported experimental data (Bronner and Goss, 2011b; Neale et al., 2012). However, as with all pp-LFERs, one must use caution when applying these equations to solutes exhibiting different intermolecular interactions than the compounds used for the calibration regression. For example, the data sets used to calibrate the pp-LFERs in Table 13.3 did not contain groups of compounds that exhibit unusually small vdW properties, such as polyfluorinated compounds or siloxanes (see Chapter 7). Additionally, because of the heterogeneity of NOM (Section 13.1), the coefficients derived from a multiparameter regression analysis of the experimental data depend on, to even greater degree than well-defined organic solvents, the range and structural diversity of the set of calibration compounds used. Therefore, a mechanistic interpretation of the system

380

Sorption from Water to Natural Organic Matter (NOM)

Table 13.3 pp-LFERs for Some NOM–Water Systems (logKiocw (Lkg−1 oc ) = vocw Vi + eocw Ei + socw Si + aocw Ai + −1 bocw Bi + c and logKiocw (Lkgoc ) = vocw Vi + locw Li + socw Si + aocw Ai + bocw Bi + c) at 25◦ C or 15◦ Ca NOM Type SOMc Pahokee peatd Pahokee peat(low conc)e Pahokee peat (high conc)e Aldrich humic acidf Suwannee River fulvic acidf Pahokee peatd Aldrich humic acid f Aldrich humic acid(dry)g Suwannee River fulvic acidf Suwannee River fulvic acid(dry)g

eocw

socw

aocw

bocw

c

r2

nb

S.D.

+2.28 +2.99 +3.71

+1.10 +0.81 +0.31

−0.72 −0.61 +1.27

+0.15 −0.21 −0.10

−1.98 −3.44 −3.94

+0.14 −0.29 −1.04

0.98 0.92 0.91

75 79 51

0.25 0.34

13-11

+3.51

+0.43

+0.19

+0.02

−3.83

−0.82

0.90

51

0.34

13-12 13-13

+3.94 +2.86

+0.29 +0.63

−0.52 −0.63

+0.36 +0.05

−3.40 −2.48

−0.85 −1.21

0.97 0.85

52 34

0.29 0.24

13-14 13-15

+1.20 +2.65

+0.54 +0.40

−0.98 −0.72

−0.42 +0.49

−3.34 −3.42

+0.02 −0.92

0.93 0.97

79 51

0.24 0.32

13-16

+1.81

+0.45

−1.25

−0.40

−2.31

−0.16

13-17

+1.54

+0.34

−0.69

+0.02

−2.43

−0.82

13-18

+3.68

+0.05

−0.96

−0.11

−3.51

−0.79

Eq.

vocw

13-8 13-9 13-10

locw

74 0.82

34

0.26

87

a

Contain solute descriptors for the size of the compound (Vi ), the excess molar refraction (Ei ) or the log Kihexadecane–air (Li ), the H-donor property (Ai ), the H-acceptor property (Bi ), and a “dipolarity/polarizability” parameter (Si ), plus the complementary fitted system descriptors characterizing the NOM phases involved (lower case letters). b Number of compounds used for LFER. c Data from Nguyen et al. (2005); log Kiocw range: 1 to 7. d Data from Bronner and Goss (2011b); log Kiocw range: 1 to 4.5. e Data from Endo et al. (2009); log Kiocw range: 1 to 6. low conc = 4.3 mg kg–1 oc, high conc = 430 mg kg–1 oc. f Data from Neale et al. (2012); Aldrich: log Kiocw range: 2 to 7; Suwannee River: log Kiocw range: 1 to 4. g Kiocw calculated at 15◦ C using Eq. 13-19 with pp-LFER for OC–air partitioning from Niederer et al. (2007) and pp-LFER for air–water partitioning from Goss (2006). dry = partially hydrated state (RH = 98%).

descriptors in Eqs. 13-8 through 13-18 is rather difficult. The only general conclusions are that, similar to the octanol–water system (Chapters 7 and 10), aocw is commonly rather small, implying NOM is “electron rich” and thus a good H-acceptor, and that bocw is strongly favoring the aqueous phase, suggesting NOM does not supply protons as well as bulk water. Finally, we should note that, as for the sp-LFERs previously discussed, the pp-LFERs are strictly applicable for the range of Kiocw values for which they were derived (see Table 13.3). As the equations for different types of NOM depend significantly on the set of calibration compounds from which they were derived, we compare them instead by calculating the respective partition coefficients of our test set of apolar, monopolar, and bipolar compounds (introduced in Chapter 7 and in the following referred to as test set). Looking at the Pahokee peat data, Endo et al. (2009) used two concentrations of solute to probe for high affinity sorption sites leading to nonlinearity of isotherms at low concentrations. Figure 13.3a shows that, particularly for the highly hydrophobic

381

8

6

4

2

0

–2 –2

0

2

4

6

8

10

10 (b) 8

6

4

2

0

–2 –2

–1

log Kiocw Pahokee peat (high conc)-water (L kg oc) aliphatic amines 1-alkanols alkanes

1: 1

(a)

log Kiocw Pahokee peat (low conc)–water (L kg–1 oc)

10

1: 1

log Kiocw Pahokee peat (low conc)-water (L kg–1 oc)

Quantifying Natural Organic Matter–Water Partitioning

carboxylic acid esters chlorobenzenes chlorinated phenols

0

2

4

6

8

10 –1

log Kiocw Pahokee peat (high conc)-water (L kg oc) ketones polycyclic aromatic hydrocarbons polychlorinated biphenyls

Figure 13.3 Plots of calculated log Kiocw values for our test set (without polyfluorinated compounds and siloxanes) for Pahokee peat (a) at different solute concentrations; Pahokee peat (low conc) (Eq. 13-10) versus Pahohee peat (high conc) (Eq. 13-11) (Endo et al., 2009) and (b) derived using a wider sorbate concentration range (Eq. 13-9) than Pahokee peat (high conc) (Eq. 13-11).

planar PAHs and PCBs, much higher Kiocw values (more than an order of magnitude) are predicted for low solute concentrations (Eq. 13-10), which is in line with experimental evidence. Hence, Eq. 13-10 reflects both sorption to high affinity sites and partitioning, whereas Eq. 13-11 can be assumed to describe primarily partitioning. Figure 13.3b shows that Kiocw values calculated for Pahokee peat with Eq. 13-11 are in good agreement with those using Eq. 13-9 derived by Bronner and Goss (2011b), even below and somewhat above the Kiocw range for which they were derived. Only for the highly hydrophobic compounds are there noticeable deviations, in that Eq. 13-11 predicts significantly larger Kiocw values. In subsequent discussions, we use Pahokee peat (Eqs. 13-9 or 13-14, respectively) as a representative SOM for estimating SOM–water partition coefficients for several reasons. First, as shown by Fig. 13.4, Pahokee peat seems to be reasonably representative for SOM originating from different soil environments (factor of 2 for log Koc ranging from 1 to 4). Also, compared to all other reported pp-LFERs, the calibration data set used to derive Eq. 13-9 for Pahokee peat represents a much larger structural diversity than in Eq. 13-8 for SOM. Furthermore, Eq. 13-8 and earlier data by Poole and Poole (1999; data not shown) represent composites of literature values of quite varying quality. Finally, Eq. 13-9 and the equivalent Eq. 13-14, respectively, have been validated for a large number of complex molecules, including pesticides and pharmaceuticals.

382

Sorption from Water to Natural Organic Matter (NOM)

4

Eurosoils exp. log Kiocw (L kg–1 oc)

3

1:

1

Eurosoil 1, n=4 Eurosoil 2, n=4 Eurosoil 3, n=38 Eurosoil 4, n=39 Eurosoil 5, n=33

2

1

Figure 13.4 Comparison of experimental Kiocw values for standard soils (Eurosoil 1-5) to experimental Kiocw values for Pahokee peat at 25◦ C. Data from Bronner and Goss (2011a).

0

0

1

2

3

4

–1

exp. log Kiocw (L kg oc) Pahokee peat

For DOM–water partitioning, to date, only two pp-LFERs are available that are based on direct measurements: Eqs. 13-12 and 13-15 for Aldrich humic acid and Eqs. 13-13 and 13-17 for Suwannee River fulvic acid, both from Neale et al. (2012). However, for DOM–air partitioning, Niederer et al. (2007) have reported pp-LFERs for 10 fulvic and humic acids at 98% relative humidity. These DOMs cover a wide range of sorbents exhibiting different polarities and aromaticities. Among these DOMs, the strongest sorbents for partitioning from air are the least polar humic acids tested, including Leonardite and Aldrich humic acid (C/O ratio > 1.7; aromaticity > 45%). These sorbents exhibit Kioca values that are up to one order of magnitude larger than the weakest sorbents, including the most polar fulvic acids such as Suwannee River, Elliot Soil, and Wakish Peat fulvic acids (C/O ratio < 1.3; aromaticity < 36%). Assuming that the thermodynamic cycle approach (Section 7.1) is valid, from these data, we can calculate the corresponding DOM–water partition coefficient by multiplying Kioca with the air–water partition constant, Kiaw : Kiocw = Kioca Kiaw

(13-19)

In the same vein, we can predict Kiocw values using a pp-LFER derived by adding the one reported for air-water partitioning (Eq. 9-18) to the corresponding one for DOM–air. Comparison of the resulting equations for Aldrich humic acid (Eq. 13-16) and Suwannee River fulvic acid (Eq. 13-18) with the ones for the immersed acids, Eqs. 13-15 and 13-17, shows that quite different system descriptors parameters are

383

Quantifying Natural Organic Matter–Water Partitioning

log Kiocw Pahokee peat–water (L kg–1 oc)

1: 1

10

Figure 13.5 Plot of calculated log Kiocw values for our test set (without polyfluorinated compounds and siloxanes) for Pahokee peat versus Suwannee River fulvic acid.

alkanes

8

chlorobenzenes polychlorinated biphenyls

6

chlorinated phenols

4

ketones carboxylic acid esters

2

aliphatic amines 1-alkanols

0

polycyclic aromatic hydrocarbons –2 –2

0

2

4

6

8

10

log Kiocw Suwanee River fulvic acid–water (L kg–1 oc)

obtained. Again, a mechanistic interpretation of these differences is ambiguous. However, we would expect that the characteristics of any NOM sorbent would be different in a partially hydrated state (“dry”state, RH = 98%) as compared to being completely immersed (“dissolved”) in water. We conclude that using Eq. 13-19 to calculate Kiocw from Kioca or vice versa may lead to significant under- or overestimation of these values, and should therefore be applied with caution. Instead, we can use NOM–air partitioning data to assess upper and lower limits for the Kiocw of a given compound. In other words, we can identify those NOMs that we can expect to be the strongest and weakest sorbents. The strongest sorbents include humic materials such as the lignite derived Leonardite humic acid, and also Pahokee peat, which we use as a representative SOM. The weakest bulk sorbents are surface water DOMs including fulvic acids, such as Suwannee River fulvic acid, which we use to estimate the lower limit of Kiocw values. Figure 13.5 shows the differences that we may expect between SOM-Kiocw and DOM-Kiocw values typical for surface waters. The disparity grows with increasing hydrophobicity of the compounds and may become larger than one order of magnitude. Effect of Temperature and Solution Composition on Kiocw Temperature. As with organic solvent–water partition constants (Eqs. 10-15 and 1018), we may express the temperature dependence of Kiocw by: ln Kiocw = −

Δocw Hi 1 ⋅ + constant R T

(13-20)

384

Sorption from Water to Natural Organic Matter (NOM)

with the change in enthalpy as: E E Δocw Hi = Hioc − Hiw

(13-21)

E E Hioc and Hiw are the excess enthalpies of the compound in the NOM considered and in water respectively. A negative Δocw Hi means that Kiocw decreases with increasing E values are in the order temperature. As we have seen in Chapter 9 (Table 9.2), Hiw –1 –1 between –20 kJ mol and, at maximum, +30 kJ mol . Furthermore, as is the case E can be assumed to be with organic solvents, for NOM–water partitioning, Hioc –1 generally rather small (i.e., ±10 kJ mol ). For example, Haftka et al. (2010) reported Δocw Hi values of between –15 and –25 kJ mol–1 for partitioning of a series of PAHs to DOMs of various origins. E However, since Hioc represents the average excess enthalpy of the compound for the various organic sorbents present, it may, in some cases, depend on the concentration range considered. Particularly for SOM, where at low concentrations sorption to E may be somewhat larger as comspecific sites may dominate the overall Kiocw , Hioc pared to higher concentrations where partitioning is the major process. This affect is E was found to prinot so significant for apolar and weakly polar compounds as Hiw marily determine Δocw Hi for adsorption to hydrophobic surfaces, including surfaces of black carbon materials (Bucheli and Gustafsson, 2000). For polar compounds that may undergo H-bond interactions with specific sites present in SOM, however, Δocw Hi may be concentration dependent. For example, for sorption of diuron and other phenylurea herbicides to soils, Δocw Hi is between –50 and –60 kJ mol–1 at very low concentrations and between –20 and 0 kJ mol–1 at high concentrations (Spurlok, 1995). Hence, as for organic solvent–water partition constants (see Table 10.3), NOM–water partition coefficients are usually rather insensitive to temperature, whereas adsorption coefficients may vary by about a factor of two with a ten degree change in temperature.

pH and Ionic Strength. For sorption of neutral compounds to SOM over the ambient pH range, we may assume, in general, that pH will not have a significant altering effect, as has been demonstrated for Pahokee peat (Bronner and Goss, 2011a). We may also assume that the sorbent properties of SOM will not be heavily influenced by ionic strength (Means, 1995), but we may have to take into account the effect of salt on the activity coefficient of the compound in the aqueous phase (see Section 9.4) and thus on Kiocw . Similar to air–water or organic solvent–water partitioning, we may quantify this effect simply by: Kiocw, salt = Kiocw 10+Ki [salt]tot s

(13-22)

Kis values can be estimated using Eq. 9-33. For example, for the companion compound phenanthrene, Kis = 0.3 (Table 9.6) and [salt]tot = 0.5 M for seawater, meaning that the presence of the salt from seawater will increase Kiocw by a factor of about 1.4. Because particularly polar DOMs such as Suwannee River fulvic acid exhibit a rather large number of acidic (e.g., carboxylic, phenolic; see Table 13.1) and other polar

Quantifying Natural Organic Matter–Water Partitioning

385

groups that may dissociate or form complexes with metal ions (e.g., Mg2+ , Ca2+ , Al3+ ), pH and major ion composition of the solution may affect their sorption characteristics. When carboxyl groups are ionized, their electrostatic repulsions cause the DOM to spread out in solution. When divalent cations like calcium are bound to such functional groups, they enable bridging of like-charged groups and, therefore, cause the macromolecules to coil. The results of the limited number of relatively old studies on this subject demonstrate that these effects may be quite complex (Schlautman and Morgan, 1993; Ragle et al., 1997). Depending on the nature of the DOM constituents, changes in pH and ion composition may or may not have a significant impact on the number of hydrophobic and hydrophilic domains that are relevant for sorption of a given neutral organic compound. Consequently, based on the still very limited data available, it is not possible to predict quantitatively the effect of solution composition on the Kiocw value of a given compound for such DOMs. Nevertheless, a few general comments on trends and magnitudes of such effects can be made. First, when considering the effect of pH, Kiocw values of apolar and weakly polar compounds exhibit a general decreasing trend with increasing pH, with the trend more pronounced for larger as compared to smaller compounds. For DOMs, the largest effects of pH are found for those consisting primarily of smaller sized, highly polar constituents, such as fulvic acids. For example, Kiocw values for large PAHs and such DOMs vary up to a factor of 2 to 3 between pH 4 and 10 (Schlautman and Morgan, 1993). We can rationalize these findings by envisioning an increase in the number of negatively charged functional groups with increasing pH; these may lead to the destruction of hydrophobic DOM domains (e.g., by uncoiling of macromolecules or by disaggregation of DOM components). However, since these effects are particularly pronounced at low pH ( 7), when virtually all of the quinoline is in its nonionic form, the overall sorption is primarily determined by partitioning of this neutral species (Q) to Aldrich humic acid: qocw ≅

N H pKia = 4.90

+ H+ N quinoline

[Q]oc = Kqocw [Q]w

at high pHs

(13-28)

With decreasing pH, the fraction of the cationic form of quinoline (QH+ ) increases and the sorbed cations increase too. However, at the same time, the number of negatively charged moieties in Aldrich humic acid decreases, leading to the observed sorption maximum at pH 5. Now, the partitioning reflects: qocw ≅

[Q]oc + [QH+ ]oc [Q]w + [QH+ ]w

at pH below 7

(13-29)

In this case, due to electrostatic interactions, the maximum qocw is about a factor of 4 larger than the Kqocw for partitioning of the neutral species. An even more pronounced case of pH-dependence involves the sorption to Aldrich humic acid of the two biocides, tributyltin (TBT) and triphenyltin (TPT). Because

392

Sorption from Water to Natural Organic Matter (NOM)

OH2 R R

of their high toxicity to aquatic organisms, TBT and TPT are of considerable environmental concern (Fent, 1996). Again, sorption varies strongly with pH (Fig.13.9b). As the pH increases, the iocw increases by more than a factor of 10 as compared to the neutral species (TBTOH, TPTOH). In fact, even at pH 8, where the abundance of TBT+ or TPT+ is very small, sorption of the cation was still found to dominate the overall sorption (Arnold et al., 1998).

Sn R OH2

OH2 R R

Sn R + H + OH

R = n-C4H9: TBT pKia = 6.3 R = n-C6H5: TBT pKia = 5.2

13.4

These findings concerning the sorption of triorganotin biocides on NOM can be rationalized by postulating the formation of an inner sphere complex (i.e., by ligand exchange of a water molecule) between the tin atom of the charged species and negatively charged ligands (i.e., carboxylate, phenolate groups) present in the humic acid. For more details, we refer to Arnold et al. (1998). Other examples illustrating the domination of cation binding to NOM include the sorption of the antimicrobials clarithromycin to Elliot humic acid (Sibley and Pedersen, 2008) and sulfathiazole to Leonardite humic acid (Richter et al., 2009). We conclude this section by noting that sorption of charged species to NOM is generally fast and reversible, provided that no real chemical reactions take place that lead to the formation of covalent bonds (i.e., to “bound residues”). This conclusion is based on experimental data and on the assumption that in aqueous solution more polar sites on NOM are more easily accessible as compared to more hydrophobic domains. Therefore, for charged species we may assume that equilibrium is established within relatively short time periods. Hence, in the case of TBT and TPT, contaminated sediments may represent an important source for these highly toxic compounds in the overlying water column (Berg et al., 2001).

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Questions Q 13.1 (a) Why is natural organic matter (NOM) such an important sorbent for the majority of organic pollutants in aquatic as well as in terrestrial systems? (b) What is the general make-up of NOM and what are its most important properties with respect to the sorption of organic compounds? What is (are) the driving force(s) for sorption to NOM from water? From air? (c) What is the difference between dissolved organic matter (DOM) and particulate organic matter (POM), e.g., soil and sediment organic matter (SOM)? Does it make sense to strictly distinguish between POM and DOM? (d) What properties of NOM may lead to nonlinear sorption isotherms?

Questions and Problems

393

Q 13.2 Besides NOM, which other organic sorbents may play an important role in soils and sediments? aquifers? surface waters? Which of these sorbents may lead to nonlinear sorption isotherms? Why? Q 13.3 How is the Kiocw value of a given neutral organic compound defined? How large is the variability its Kiocw for (a) different SOMs and (b) different DOMs? Which are the major (structural) factors of SOM or DOM that cause this variability? Which NOM can be used as a representative SOM when discussing sorption properties? Q 13.4 Kile et al. (1995) reported numerous Kiocw values of 1,2-dichlorobenzene determined for uncontaminated soil–water and sediment–water partitioning in the range between 300 and 500 L kg–1 oc. However, for heavily contaminated soils and sediments, these authors found significantly higher Kiocw values (700 – 3000 L kg–1 oc), although isotherms were linear over a wide concentration range. Try to explain these findings. Q 13.5 How do (a) pH, (b) ionic strength, and (c) temperature affect the sorption of neutral organic compounds to dissolved and particulate organic matter? Give examples of compound–organic phase combinations in which you expect (i) a minimum and (ii) a maximum effect. Q 13.6 Why is it more difficult to interpret the coefficients of the pp-LFERs derived for NOM–water partitioning (Table 13.3) as compared to organic solvent–water partitioning discussed in Chapter 10? Q 13.7 What is the major difference between the sorption of neutral and the sorption of charged organic species to NOM? Describe qualitatively the pH-dependence of the NOM–water partitioning of (a) an organic acid and (b) and organic base.

Problems P 13.1 Estimating the Kiocw Value of Isoproturon from Kiocw ’s of Structurally Related Compounds Urea-based herbicides are widely used despite the concern that they may contaminate groundwater of agricultural regions (Johnson et al., 1998). You have been asked to evaluate the sorption behavior of the herbicide Isoproturon (Vi = 1.78, Ei =1.20, Si = 1.54, Ai = 0.39, Bi = 0.88) in soils.

394

Sorption from Water to Natural Organic Matter (NOM)

H N

As you are unable to find the Kiocw of this specific compound, you collect data on some structurally related compounds:

N O

H N

3

isoproturon

N O

4 5

4-methyl 3,5-dimethyl 4-chloro 3,4-dichloro 3-fluoro 4-methoxy

log Kiow

log Kiocw (L kg–1 oc)

1.33 1.90 1.94 2.68 1.37 0.83

1.51 1.73 1.95 2.40 1.73 1.40

Using the collected data, estimate a Kiocw for Isoproturon. Did you use all the compounds for deriving an sp-LFER? Why or why not? Compare this value with the one estimated by using the pp-LFER Eq. 13-9 in Table 13.3. P 13.2 ∗ What Fraction of Atrazine is Present in Dissolved Form? Our companion compound atrazine is still one of the most widely used herbicides. Estimate the fraction of total atrazine present in truly dissolved form (a) in lake water exhibiting 2 mg POC L–1 , (b) in marsh water containing 100 mg solids L–1 , if the solid’s organic carbon content is 20%, and (c) in an aquifer exhibiting a porosity of 0.2 by volume, a density of the minerals present of 2.5 kg L–1 , and an organic carbon content of 0.5%. Assume that partitioning to NOM is the major sorption mechanism. You can find Kiocw values for atrazine in Fig. 13.2. Comment on which values you select for your calculations. P 13.3 Is Sorption to Dissolved Organic Matter Important for the Environmental Behavior of Phenanthrene and Benzo(a)pyrene? Somebody claims that for our companion compounds phenanthrene and benzo(a)pyrene (see structures in Table 3.1 and Abraham parameters in Table 7.3 or Appendix C), sorption to DOM is generally unimportant in the environment. Is this statement correct? Use Eq. 13-17 (Table 13.3) to estimate Kiocw for sorption to DOM. Comment on your assumptions. P 13.4 Assessing the Speciation of a PCB-Congener in a Sediment–Pore Water System

Cl Cl

Cl Cl 2,2',4,4'-tetrachlorobiphenyl (PCB 47)

Consider a surface sediment exhibiting a porosity ϕ = 0.8, solids with average density ρs = 2.0 kg L–1 solid, a particulate organic carbon content of 5%, and a DOC concentration in the pore water of 20 mg DOC L–1 . Estimate the fractions of the total 2,2′ ,4,4′ -tetrachlorobiphenyl (PCB 47, Vi = 1.81, Li = 8.23, Si = 1.48, Ai = 0, Bi = 0.15) present in truly dissolved form in the porewater and associated with the

Questions and Problems

395

pore water DOM. Assume that absorption into the organic material is the major sorption mechanism. Estimate the Kiocw values using the respective pp-LFER given in Table 13.3, i.e., Eqs. 13-14 (SOM) and 13-17 (DOM). P 13.5 Evaluating the Transport of 1,2-Dichloropropane in Groundwater

Cl

Cl

1,2-dichloropropane

A group of investigators from the USGS recently discovered a large plume of the soil fumigant 1,2-dichloropropane (DCP) (log Kiow = 2.28; Montgomery, 1997; Vi = 0.776, Li = 2.84, Si = 0.63, Ai = 0, Bi = 0.17) in the groundwater flowing away from an airfield. The aquifer through which the DCP plume is passing has been found to have a porosity of 0.3. The aquifer solids consist of 95% quartz (density 2.65 g mL–1 ; surface area 0.1 m2 g–1 ), 4% kaolinite (density 2.6 g mL–1 ; surface area 10 m2 g–1 ), 1% iron oxides (density 3.5 g mL–1 ; surface area 50 m2 g–1 ), and organic carbon content −1 , see Eq. 12-18)] do you expect at minimum of 0.2%. What retardation factor [(Rfi (fiw (assumption that only SOM is responsible for sorption) for DCP transport in the plume assuming that sorptive exchanges are always at equilibrium? P 13.6 Estimating the Retardation of Organic Compounds in an Aquifer from Breakthrough Data of Tracer Compounds −1 , see Using tritiated water as conservative tracer, an average retardation factor, Rfi (fiw Eq.12-18) of about 10 was determined for chlorobenzene in an aquifer. (a) Assuming this retardation factor only reflects absorption to the aquifer solids’ POM, what is the average organic carbon content (foc ) of the aquifer material if its minerals have a density of 2.5 kg L–1 and if the porosity is 0.33? (b) Estimate the Rfi values of 1,3,5trichlorobenzene (1,3,5-TCB) and 2,4,6-trichlorophenol (2,4,6-TCP) in this aquifer (pH = 7.5, T = 10◦ C) by assuming that absorption into the SOM present is the major sorption mechanism. Why can you expect to make a better prediction of Rfi for 1,3,5TCB compared to 2,4,6-TCP? You can find all relevant information in Appendix C (website). Comment on all assumptions that you make.

OH Cl

Cl

Cl

Cl

Cl

Cl

Cl

chlorobenzene

1,3,5-trichlorobenzene (1,3,5-TCB)

2,4,6-trichlorophenol (2,4,6-TCP)

P 13.7 ∗ Evaluating the Concentration Dependence of Phenantrene Sorption to Soils and Sediments Containing Black Carbon (BC) Huang et al. (1997) measured sorption isotherms for our companion phenanthrene (Kiow = 4.57; use sp-LFER in Table 13.2 to estimate Kiocw ) for 21 soils and sediments. All isotherms were nonlinear with Freundlich exponents ni between 0.65 and 0.9. For example, for a top soil (Chelsea I) and for a lake sediment (EPA-23), interpolating their isotherm data yields the following “observed” sorbed concentrations,

396

Sorption from Water to Natural Organic Matter (NOM)

Cis , in equilibrium with dissolved concentrations, Ciw , of 1 μg L–1 and 100 μg L–1 , respectively:

Cis (μg kg–1 solid) Ciw (μg L–1 ) 1 100

Chelsea-I

EPA-23

3,200 91,000

1,700 51,000

For Chelsea I soil, foc was measured as 0.056 kg oc kg–1 solid, and for the EPA-23 lake sediment as 0.026 kg oc kg–1 solid. The fbc values were not measured, but in sediment samples, it is typically between 1 and 10% of the foc (Gustafsson and Gschwend, 1998). Use the full range of 1 to 10% for both cases to see the possible impact of adsorption to black carbon, i.e., fbc = 0.00056 to 0.0056 kg bc kg–1 solid. Use an ni value of 0.7 in Eq. 13-25. Finally, for estimating Kibcw values for planar compounds use the relationship that can be derived from data published by Xia and Ball, (1999) and Bucheli and Gustafsson, (2000): logKibcw (L kg−1 bc) ≈ 1.6 logKiow -1.4

(r2 = 0.98; n = 9)

P 13.8 Evaluating the Concentration Dependence of Equilibrium Sorption of 1,2,4,5-Tetrachlorobenzene (TeCB) to an Aquitard Material Xia and Ball (1999) measured sorption isotherms for a series of chlorinated benzenes and PAHs for an aquitard material (foc = 0.015 kg oc kg–1 solid) from a formation believed to date from the middle to late Miocene. Therefore, compared to soils or recent sediment POM, the organic matter present in this aquitard material can be assumed to be fairly mature and/or contain char particles from prehistoric fires. A nonlinear isotherm was found for TeCB (fitting Eq. 12-3) and the following Freundlich parameters were reported: KTeCBF = 128 (mg g–1 solid)(mg mL–1 )–nTeCB and nTeCB = 0.80. For partitioning of TeCB to this material (linear part of the isotherm at higher concentrations), the authors found a KTECBocw value of 4.2×104 L kg–1 oc. (a) Calculate the apparent KTECBocw values of TeCB for the aquitard material for aqueous TeCB concentrations of Ciw = 1, 10, and 100 μg L–1 using the Freundlich isotherm previously given. Compare these value of the KTECBocw values previously given for POM–water partitioning. Comment on the result. (b) At what aqueous TeCB concentration (μg L–1 ) would the contribution of adsorption to the overall KTECBocw be equal to the contribution of absorption, (partitioning)? Note: When using Freundlich isotherms, be aware that the numerical value of KTECB F depends nonlinearly on the unit in which the concentration in the aqueous phase is expressed. Hence for solving this problem, you may first convert μg L–1 to mg mL–1

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Cl

Cl

Cl

Cl

397

or you may express the Freundlich equation using, for example, μg kg–1 and μg L–1 , respectively: KTeCBF = 128(106 μg kg−1 )(106 μg L−1 )−0.8 = 128×106 ×104.8 (μg kg−1 )(μg L−1 )−0.8

1,2,4,5-tetrachlorobenzene (TeCB)

13.5

= 2030(μg kg−1 )(μg L−1 )−0.8

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405

Chapter 14

Sorption of Ionic Organic Compounds to Charged Surfaces

14.1 Introduction 14.2 Cation and Anion Exchange Capacities of Solids in Water Oxides/Oxyhydroxides Solids with Other Surface Potential Determining Ions Aluminosilicate Clays Natural Organic Matter 14.3 Ion Exchange: Nonspecific Adsorption of Ionized Organic Chemicals from Aqueous Solutions to Charged Surfaces Adsorption via Ion Exchange “Reactions” Box 14.1 Derivation of Ion Exchange Isotherms for a Cationic Organic Compound (i = BH+ ) Competing with Monovalent Inorganic Cations (e.g., Na+ ) Effects of the Ionic Organic Sorbate’s Structure Natural Organic Matter and Ion Exchange Box 14.2 Estimation of Kid for an Organic Amine Adsorbing to Kaolinite Adsorption of Organic Ions at High Sorbate Concentrations Impacts of Multiple Sorption Mechanisms on Isotherms of Ionic Organic Sorbates

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

406

Sorption of Ionic Organic Compounds to Charged Surfaces

14.4 Surface Complexation: Specific Bonding of Organic Compounds with Solid Phases in Water Organic Sorbate-Natural Organic Matter Reactions Organic Sorbate-lnorganic Solid Surface Reactions 14.5 Questions and Problems 14.6 Bibliography

407

Introduction

14.1

Introduction Many organic compounds exhibit acid or base functionalities and can, therefore, exist as anions or cations in aqueous solutions (Chapter. 4, Section 4.3). As illustrated by Fig. 14.1, despite the fact that charged moieties encourage those ions to stay dissolved in water, one still finds that these organic ions adsorb to natural solids. Since most natural surfaces are charged when they are submerged in water, this implies we must consider how electrostatic interactions affect adsorption of these charged substances. In this chapter, sorption arising from nonspecific electrostatic attractions to charged surfaces will be referred to as “ion exchange” (Fig. 14.2a). In addition, ionic organic compounds can bond directly with specific atoms exposed on solid surfaces. This adsorptive interaction is called “surface complexation” (Fig. 14.2b). In Chapter 12, we have already included “ion exchange” in the Kid expression:

Kid =

Cioc foc + Cimin Asurf + Ciex σsurf ex Asurf + Cirxn σsurf rxn Asurf Ciw,neut + Ciw,ion

(12-11)

where Asurf is the specific surface area of the relevant solid (m2 kg−1 solid), Ciex is the concentration of ionized sorbate drawn towards positions of opposite charge on the solid surface (mol mol−1 surface charges), and σsurf ex is the net concentration of suitably charged sites on the solid surface (mol surface charges m−2 ) for ion exchange. Likewise, complexation between a sorbate acting as a ligand and surface metals was already included through the product Cirxn σsurf rxn Asurf in Eq. 12-11, where Cirxn is the concentration of sorbate i bonded in a reversible reaction to the solid (mol mol−1 reaction sites) and σsurf rxn is the concentration of reactive sites on the solid surface (mol reaction sites m−2 ). In both cases, we need to consider how the structure of the organic sorbate, the nature of the surface, and the pH and ionic composition of the solution affect the extent of adsorption.

500

H

300 Kid = 49 L kg–1

200 100

0

O O

80

Cl

20

Ciw (µmol L ) –1

Cl

Kid = 4 L kg–1

40

Kid = 4 L kg–1 Kid = 5 L kg–1

0

10

Kid = 4 L kg–1

O–

60

20

Kid = 100 L kg–1 Kid = 680 L kg–1

0

(b)

100

Kid = 29 L kg–1

N+

Cis (µmol kg–1)

Cis (µmol kg–1)

400

Figure 14.1 Sorption isotherms for some charged organic compounds interacting with natural solids: (a) quinolinium cation on a subsoil of foc = 0.0024 and cation exchange capacity of 84 mmol kg−1 (data from Zachara et al. 1986), and (b) sorption of 4-(2,4-dichlorophenoxy)-butyrate anion on a sediment with foc = 0.015 and unknown anion exchange capacity (data from Jafvert 1990).

120

(a)

0

10

20 Ciw (µmol L ) –1

30

408

Sorption of Ionic Organic Compounds to Charged Surfaces

(a)

OH O– OH O–

Figure 14.2 Schematic view of two ways in which an ionic organic chemical i may sorb to natural (b) inorganic solids: (a) adsorption of charged molecules from aqueous solution to complementarily charged surfaces due to electrostatic attractions, and (b) chemisorption due to surface bonding or inner sphere complex formation.

i+

adsorption to charged surface sites of opposite charge

i+

OH diffuse double layer

bulk water

OH O

i

OH inner sphere complexes, reactive surface sites

O–

i

adsorption to surface moieties capable of forming (inner sphere) bond with sorbate

bulk water

In this chapter, we first examine the extent to which various solids become charged in natural water (Section 14.2). Then we consider adsorption of ionized compounds largely arising from electrostatic attractions to charged mineral surfaces (Section 14.3). We conclude with surface interactions involving sorbate-sorbent bonding or surface complexation (Section 14.4). As we proceed, we identify solid properties like surface area (Asurf ), surface charge (σsurf ex ), and reactive surface sites (σsurf rxn ) that are the key sorbent factors used to “tune” the intensity of each interaction for solids of interest. Also, we develop our understanding of how the structures of sorbates dictate their sorption behavior in environments of interest.

14.2

Cation and Anion Exchange Capacities of Solids in Water Almost all particles are charged in natural waters. If this surface charge is of opposite sign to that of an organic compound, then there will be electrostatic attraction between the organic sorbate in the bulk solution and the particle surface. This is the same interaction energy drawing inorganic cations like Na+ and Ca2+ near a negatively charged surface in water. Therefore, organic ions will accumulate in the thin film of water surrounding the particle as part of the population of charged ions in solution balancing the charges on the solid surface (Fig. 14.3). Conversely, organic molecules with charges of like sign as the surface will be repulsed from the adsorbed near-surface water. These electrostatic effects act similarly for all charged sorbates. To evaluate the importance of such nonspecific charge-derived interactions, we need to know the “concentration of charges” on the surfaces of solids, called the cation exchange capacity (CEC) if the surface is negatively charged, or the anion exchange capacity (AEC) if the surface is positively charged. In Eq. 12-11, these ion exchange capacities are quantified using the product of the surface charge density, σsurf ex (e.g., mol charges m−2 solid), multiplied by the solid’s specific surface area, Asurf (e.g., m2 kg−1 ). To maintain charge balance, the adjacent layer of water must contain an excess of ions called counter ions (e.g., Cl− and i− to balance M-OH2 + in Fig. 14.3) that carry charge equal in magnitude and opposite in sign to that exhibited by the particle surface. The thickness of this ion-rich water layer varies inversely with the ionic strength of the solution (Morel, 1983; Whitehead et al., 2015). For typical ionic compositions of natural waters (ranging from 10−3 to 0.5 M), most

409

Cation and Anion Exchange Capacities of Solids in Water

near-surface water

oxide solid

+

OH2

M

OH

M

Na+ (1) double layer counterion

Cl–

i

OH

M

Figure 14.3 A positively charged oxide particle in water attracts anionic species including organic ones (e.g., i− ) to the adsorbed near-surface water (arrow 1). M in the solid refers to atoms like Si, Al, or Fe. Binding of the organic chemical to the surface (Section 14.4) is also shown (arrow 2).

i–

bulk water

i–

Na+

Na+

–

Na+

i–

co-ion for i

i

M M

Cl–

+

OH2

Cl

Na+

–

charged surface group

Cl– Na+ Cl–

Na+

(2) surface bound organic sorbate competing ion

Na+

i–

(> 63%) of the counterions are packed into a layer of water between 0.4 and 9 nm thick. This range is very similar to the 1–10 nm range postulated to reflect ordered vicinal water (Drost-Hansen, 1969; Etzler and Fagundus, 1987; Bowen and Yousef, 2003). Therefore, this is a very special microscopic water environment having different properties than the bulk water. The abundance of charges on particles depends on the surface chemistry of the solid and the nature of the aqueous solution in which it occurs. Several important kinds of surfaces are common in the environment (Table 14.1). Here, we discuss: (1) oxides and oxyhydroxides, (2) aluminosilicates and clay minerals, and (3) carbonates. While absorption into natural organic matter (NOM) was previously discussed in Chapter 13 (Section 13.3), in this chapter NOM is also discussed as an ion exchange sorbent and as a surface reactant. Table 14.1 Sorbent Properties of “Pure Solids” Commonly Present in Aquatic Environmentsa Composition

Specific surface area (m2 g−1 )

CEC (pH 7)b (mol m−2 )

Oxides Quartz Amorphous silica Goethite Amorphous iron hydroxide

SiO2 SiO2 α-FeOOH Fe(OH)3

0.2 (10 μm)b 2 (1 μm)b 100–300 600

0.6 to 5×10−4 1 to 4×10−4

Gibbsite

Al(OH)3

80–200

Na3 Al7 Si11 O30 (OH)6 Al2 Si2 O5 (OH)2 KAl3 Si3 O10 (OH)2

600–800 5–30 65–100

CaCO3

1

Sorbent

Aluminosilicates Montmorillonite Kaolinite Illite Carbonate Calcite a

0.9 to 2×10−6 3 to 20×10−6 1 to 6×10−6

AEC (pH 7)b (mol m−2 )

1 to 4×10−7 0.6×10−7 (I = 10−3 M)b 5×10−7 (I = 10−1 M)b 2 to 5×10−7

int int pKa1 pKa2 pHzpc

(–3) (–3) 6 7.4

7 7 9 8.6

2 2 7.5 8

5

8

6.5

3 to 4×10−7 0.6 to 2×10−5 3×10−7

2.5 4.6

9×10−6

8–9.5

Data from Carroll (1959); Parks (1965); Somasundaran and Agar (1967); Grim (1968); Mikhail et al. (1968a, b); Tipping (1981); Davis (1982); Schindler and Stumm (1987); Zullig and Morse (1988); Dzombak and Morel (1990); Kraepiel et al. (1998); Brady and Weil (2002). b Assumed particle size, pH or ionic strength shown in parentheses.

410

Sorption of Ionic Organic Compounds to Charged Surfaces

Oxides/Oxyhydroxides Hydroxyl groups cover the water-wet surface of natural solids that are oxides or oxyhydroxides (e.g., quartz with M = Si, goethite with M = Fe, and gibbsite with M = Al, see Fig. 14.3). These hydroxyl moieties can undergo proton-exchange reactions with the aqueous solution much like dissolved acids and bases: M − OH+2 ⇌

M − OH + H+

(14-1)

M − OH ⇌

M − O− + H+

(14-2)

We may define acid-base equilibrium constants for those acid-base surface reactions (neglecting activity coefficients here): Ka1 =

[ M − OH][H+ ] [ M − OH+2 ]

(14-3)

Ka2 =

[ M − O− ][H+ ] [ M − OH]

(14-4)

These equilibrium constants differ from their solution counterparts in that they reflect both an intrinsic reactivity of the particular O-H bond (Kaint ) and an electrostatic free energy, Δelect Gi = zi FΨo , derived from moving the charged ion, H+ , to/from a charged surface with electrical potential, Ψo (V), as compared to far from the surface: int zFΨo ∕RT e Ka1 = Ka1

(14-5)

int zFΨo ∕RT e Ka2 = Ka2

(14-6)

where z = +1 for the exchanging ion, H+ , in this case; F is the Faraday constant (96,485 C mol−1 ); Ψo is the surface potential relative to the bulk solution (V or J C−1 ) (see Fig. 14.4); R is the gas constant (8.31 J mol−1 K−1 ); and T is the absolute temperature (K). At acidic pHs, [ M − OH+2 ] > [ M − O− ], and so the surface has a net positive charge and Ψo is positive. In this case, the term ezFΨo ∕RT , mathematically reflects the extra energy associated with moving protons from the bulk solution to the particle surface. At higher and higher pH’s, attached protons are lost from the surface and Ψo becomes less and less positive as Eq. 14-1 is pushed to the right; Ψo eventually becomes negative as Eq. 14-2 continues to the right. This shift in surface charge (from a net positive surface where [ M − OH+2 ] > [ M − O− ] to a net negative one where [ M − O− ] > [ M − OH+2 ]) makes it electrostatically more difficult to move H+ away from the charged oxide surface as solution pH is increased. Depending on the environmental conditions, it is also possible for some inorganic ) to bond to atoms on solid surfaces. In such a case, these species (e.g., Fe3+ or PO3− 4 inorganic ions, along with H+ and OH− , are responsible for establishing the extent of charging on the solid surface. The combination of ions that are responsible for this charge formation are called “potential (Ψo ) determining” ions. For more information on the effect of such surface reactions on surface charge, the interested reader

Cation and Anion Exchange Capacities of Solids in Water

411

+

+ + + - + + + - ++ + - + + + ++ + solid

+

charged ions in water

+

-

+ +

solid

+

+

+

+

+

+ -

Figure 14.4 Simple model of electrostatic potential (mV) as a function of distance from a surface in water. Ψo is the surface potential at the solid surface, and this electrostatic potential falls off through the layers of accumulated counter ions. The potential just outside the layer of ions immediately adjacent to the surface is the “Stern potential,” and the so-called “zeta potential” is the value measured by observing particle movement in an electric field recognizing that all ions inside the “slipping plane” are moving with the particle. The measured zeta potential only gives an estimate of the true surface potential, Ψo .

potential measured with electrophoresis

surface potential, Ψo mV

surface-water interface

“slipping plane” ions inside stay with particle

far from surface

is referred to the literature (e.g., Dzombak and Morel, 1990, for effects of specific adsorption and its impact on surface charge for hydrous ferric oxide). Focusing now on surface acid-base reactions, it is easy to see that the abundance of [ M − OH+2 ] and [ M − O− ] species on the oxide/oxyhydroxide’s surface affects the surface charge. The surface area normalized concentration of this excess surface charge, σsurf ex (mol charges m−2 ) is: σsurf ex = [ M − OH+2 ] − [ M − O− ]

(14-7)

When these two surface species are present in equal concentrations, the surface exhibits zero net charge (or Ψo = 0). We call the solution pH that establishes this condition, the pH of zero point of charge or pHzpc . This pHzpc can be calculated if we know the intrinsic acidities of M–OH2 + and MOH since: [ M − OH+2 ] = [ M − O− ] at pHzpc

(14-8)

Substituting from Eqs. 14-3 to 14-6 and recalling Ψo = 0 at pHzpc , we have: [ M − OH][H+ ]zpc int Ka1

=

int [ M − OH] Ka2

[H+ ]zpc

(14-9)

int int Ka2 [H+ ]2zpc = Ka1

(14-10)

int int pHzpc = 0.5(pKa1 + pKa2 )

(14-11)

412

Sorption of Ionic Organic Compounds to Charged Surfaces

Eq. 14-11 shows that an oxyhydroxide’s pHzpc is midway between the intrinsic pKa ’s of its surface groups. Table 14.1 shows such intrinsic pKa ’s and the corresponding pHzpc values for oxyhydroxides that are common in the environment. At neutral pHs, we see that silicon oxyhydroxides are negatively charged, iron oxyhydroxides are positively charged, and the aluminum oxyhydroxide called gibbsite is nearly uncharged. Now, when the aqueous solution pH is below the pHzpc , we have the condition [ M − OH+2 ] > [ M − O− ], and the solid exhibits a net positive surface charge and is electrostatically attractive to anions from solution. The concentration of such positive surface charges is called the solid’s anion exchange capacity (or AEC). Conversely, when we are above the solid’s pHzpc , then [ M − O− ] > [ M − OH+2 ], and the surface is negatively charged. It has a cation exchange capacity (or CEC), and this capacity grows at higher and higher pH. In light of their pHzpc values, we can now understand why siliceous surfaces present in natural systems exhibit a net negative charge and therefore have a pH-dependent CEC, while Fe oxyhydroxides are positively charged and have a pH-dependent AEC (Table 14.1). Typically, surface charge densities in the range of 10−4 to 10−8 mol m−2 are seen for oxides at circumneutral pHs (Table 14.1). This implies that 10−4 to 10−8 moles of counter ions, including some charged organic molecules, must accumulate in a thin layer of water opposite each meter squared of surface due to electrostatic attractions. While general values for CECs and AECs for oxyhydroxides are given in Table 14.1 for pH 7, one may need values that correspond to other conditions. To estimate the concentration of excess surface charge for solid oxides as a function of pH (and if necessary considering other solution constituents that chemically bond to oxyhydroxides like CO3 −2 or PO4 −3 ), one can use two approaches. First, computer models (e.g., FITEQL; Westall, 1982) can be used to simultaneously solve for all the surface and solution species in a solution of interest using knowledge of the solid’s acid–base site density (e.g., [ Fe − OH+2 ] + [ Fe − OH] + [ Fe − O− ] = 2×10−6 mol m−2 ; Dzombak and Morel, 1990), the solution pH and solid’s intrinsic acidity coefficients, and the concentrations of any specifically adsorbing ions and their intrinsic complexation coefficients. Alternatively, one can measure the total CEC or AEC for representative solid specimens at conditions of interest (e.g., pH). To do this, one saturates a solid with a measurable ion that is not a component of the solids (e.g., ammonium for cations or nitrate for anions), displaces this ion with acid or base, quantifies it, and then normalizes it by the mass or area of solids (e.g., Gillman and Sumpter, 1986; Hendershot and Duquette, 1986).

Solids with Other Surface Potential Determining Ions Other solid phases like calcium carbonates are also common in nature. One widespread form, calcite (CaCO3 ), exhibits surface charging due to either excess Ca2+ or CO2− on the solid’s surface. At circumneutral pHs, carbonate (CO2− ) is typically 3 3 present at μM levels while calcium concentrations are usually in the millimolar range (see Chapter 5). Hence, such solids typically have calcium in excess on their surfaces

Cation and Anion Exchange Capacities of Solids in Water

413

making them positively charged in natural waters. This implies such solids will act as anion exchangers (Table 14.1). Aluminosilicate Clays

edge HO OH O

Al

O

HO O O face

OH

Si

Si

O

O

Si

O

Al

O

O

O

HO

Mg

OH

O

Al

O

Si

Si

O O

O Si O O

O

Si O Si O VVVVVVVVVVVVVVVVVVVVVVVVVVVV continuing

Example of a clay mineral.

Clay minerals present a different case with regard to assessing their surface charge. These mixed aluminum oxides and silicon oxides (thus aluminosilicates) expose two kinds of surface to the external media, and therefore the same particles may exhibit both a CEC and an AEC at the same time (Table 14.1). First, the edges of these flake-shaped minerals act like aluminum oxyhydroxides ( Al–OH) and respond to pH changes in the solution much like pure aluminum oxyhydroxides (e.g., pHzpc of kaolinite edge ∼7; Williams and Williams, 1978). The consequent anion exchange capacity observed empirically for clay minerals is up to 0.1 mol kg−1 for a wide variety of clays (Grim, 1968), but this value changes with solution pH and ionic strength. In contrast, the faces of these particles have a “siloxane” structure (–Si-O–Si–), which does not have free hydroxyl groups ( Si–OH) to participate in proton exchange reactions with the bulk solution. Instead, the faces exhibit a charge due to cation substitutions of the aluminum or silicon atoms within the internal structure. These substitutions do not change the overall crystal structure, so they are called “isomorphic.” They typically involve cations of lower total positive charge (e.g., Al3+ for Si4+ or Mg2+ for Al3+ ). The result is a fixed permanent charge deficiency that looks like a negative surface charge to the surrounding solution. As was the case for oxyhydroxides, the overall exchange capacity of aluminosilicate minerals is a function of solution properties like pH and ionic strength, but computational approaches can be employed to deduce how such environmental conditions affect ion exchange capacities (Kraepiel et al., 1998). Empirical measures of this negative surface charge or CEC are made by assessing the maximum concentrations of weakly bound cations such as ammonium, NH+4 , which can be sorbed. Table 14.1 shows the results of such cation exchange capacity tests on three common clays, montmorillonite, illite, and kaolinite. Three-layer clays like montmorillonite exhibit the highest CEC’s near 1 mol kg−1 or 1.4×10−6 moles of charged sites per meter squared (assuming a specific surface area of 700 m2 g−1 ; Grim, 1968). On the other extreme, two-layer kaolinite clays exhibit the lowest CEC’s of about 0.1 mol kg−1 (Grim, 1968). This is chiefly due to their much smaller specific surface areas as compared to the three-layer clays, since per unit area kaolinites actually have greater charge density, ∼ 10−5 mol m−2 . Natural Organic Matter As we pointed out in Chapter 13 (Section 13.3), natural organic matter (DOM, POM, SOM) is also charged in water. This is mostly due to ionization reactions of carboxyl groups (–COOH; see Cabaniss, 1991; Leenheer et al., 1995; Richie and Perdue, 2003). Such acidic moieties occur at about l to 10 mmol per gram of natural organic matter. Carboxyl moieties exhibit pKa ’s ranging from about 3 to 6 (Chapter 4, Section 4.3), and so the extent of charging is dependent on the solution pH. However, in general, particulate organic matter is anionic and acts as a cation exchanger. Realizing there will almost always be charges on inorganic and organic particle surfaces submerged

414

Sorption of Ionic Organic Compounds to Charged Surfaces

in water, we can now examine their impact with regard to sorbing ionized organic chemicals from solution.

14.3

Ion Exchange: Nonspecific Adsorption of Ionized Organic Chemicals from Aqueous Solutions to Charged Surfaces Adsorption via Ion Exchange “Reactions” Due to charging of particles in water, ions from solution must accumulate in the film of water adjacent to those surfaces to balance the excess charges (Fig. 14.2a). As solution conditions change, the composition of the ion mixture in the near-surface water also changes via ion exchange “reactions” (e.g., exchanging i− for Cl− in Fig. 14.3). Since this water layer remains tightly associated with the solid, any organic ions contained within the layer are “sorbed.” This nonspecific surface association is sometimes termed “physisorption” as no bonding or complexation with atoms on the surface is involved. As previously noted for protons moving between bulk aqueous solution and solid surfaces, ionized organic chemicals are electrostatically attracted (or repulsed) to (from) charged solid surfaces, in addition to any difference in van der Waals and electron donor/acceptor interactions with the surface compared to the bulk aqueous solution. Here, we call this electrostatic interaction energy Δelect Gi , and it has the magnitude: Δelect Gi = zi FΨo

(14-12)

where zi is the charge of the organic sorbate. Additionally, as we saw for nonionic organic compounds (Chapter 11, Section 11.3), the hydrophobic part of an organic sorbate’s structure encourages its transfer from bulk aqueous solution into the nearsurface water. We will term this free energy contribution Δhydrophobic Gi . Together, these interactions promote an ion exchange “reaction” (Fig. 14.3): i + competing ion:surf ⇌ i:surf + competing ion

(14-13)

where i is the organic ion participating in the exchange, “surf” represents the charged surface of the solid in water, “competing ion” is the inorganic ion with the same type of charge (positive or negative) as i and thus also attracted to the charged surface. The colons indicate surface association without bonding or complexation. At low concentrations, the accumulation of organic ions at the surface relative to their concentration in the bulk solution is due to a free energy increment: Δsurf water Gi = zi FΨo + Δhydrophobic Gi

(14-14)

= −RT ln ([i:surf]∕[i])

(14-15)

= −RT ln Kidex

(14-16)

Ion Exchange

415

where Kidex (L kg−1 ) is the distribution ratio of the ionic organic compound accumulated due to ion exchange, and we note that we have substituted chemical concentrations for chemical activities (i.e., assumed activity coefficients are 1). Since the displacement of the competing ion results in the “recovery” of its Δelect Gcompeting ion , the overall ion exchange process (i.e., Eq. 14-13) involves an overall free energy change (indicated by subscript, ex): Δex Gi = (zi FΨo + Δhydrophobic Gi ) − zcompeting ion FΨo

(14-17)

Assuming the charged parts of the two competing ions approach the surface to the same extent (since Ψ varies with distance from the solid surface), then the two electrostatic energies are the same, and we have: Δex Gi ≅ Δhydrophobic Gi

(14-18)

= −RT ln([i:surf][competing ion]∕[i][competing ion:surf])

(14-19)

= −RT lnKiex

(14-20)

Kiex is dimensionless for two monovalent ions exchanging, but it does not equal the organic sorbate’s sorption coefficient, Kid (L kg−1 ). Rather, it is the ratio of the sorption coefficients of the organic ion and the competing ion: Kiex = Kid ∕Kcompeting ion d

(14-21)

In Box 14.1, we derive an expression that relates the concentration of a sorbed organic cation in the near-surface water adjacent to a negatively charged particle’s surface at “low” concentrations to its concentration in the bulk aqueous solution.

Box 14.1

Derivation of Ion Exchange Isotherms for a Cationic Organic Compound (i = BH+ ) Competing with Monovalent Inorganic Cations (e.g., Na+ )

1. “Ion exchange reaction” at low concentrations: i+ + Na:surf ⇌ Na+ + i:surf

(14-22)

/ Kiex = [i:surf][Na+ ] [i+ ][Na:surf]

(14-23)

2. Corresponding equilibrium constant:

3. Sum of cations must equal cation exchange capacity (CEC): CEC = [i:surf] + [Na:surf]

(14-24)

416

Sorption of Ionic Organic Compounds to Charged Surfaces

4. Substituting for [Na:surf] in Eq. 14-23: [i:surf][Na+ ] [i+ ](CEC − [i:surf])

Kiex =

(14-25)

5. And rearranging one finds a hyperbolic or Langmuir isotherm: [i:surf] =

(CEC)Kiex

[Na+ ] + Kiex [i+ ]

[i+ ]

(14-26)

6. At low concentrations of [i+ ](≪[Na+ ]/Kiex ), this implies a linear isotherm behavior: Kid =

[i:surf] (CEC)Kiex ≅ [i+ ] [Na+ ]

(14-27)

7. At high concentrations, that is where Kiex [i+ ] > [competing ion], continued sorption of [i+ ] may be encouraged by interactions between i+ sorbates. Consequently, the Langmuir isotherm (Eq. 14-26) may no longer be followed. Let us complete this theoretical treatment by considering some sorption observations for a small organic cation, ethyl ammonium (i = EA; pKia ∼ 10), associating with a single charged solid surface, Na-saturated montmorillonite (Fig. 14.5). Before any EA is added to the montmorillonite suspension, the negative charges on the surface of the clay are balanced by sodium cations accumulated in the thin film of water surrounding the particles. When a small quantity of EA is added to the suspension, an ion exchange reaction occurs resulting in some of the EA+ cations exchanging with Na+ near the solid’s surface. This ion exchange can be expressed: EA+ + Na:surf ⇌ EA:surf + Na+

Cis (mol kg–1)

1

Figure 14.5 Ion exchange of ethyl ammonium (EA) to montmorillonite (CEC measured to be 0.96 mol kg−1 ) from a 10 mM aqueous NaCl solution; a Langmuir isotherm with best fit KEAex = 2 matches the experimental data well (data from Cowan and White, 1958).

(14-28)

CEC = 0.96 mol kg–1

0.5

CEC × Kiex [Na+] 0

0

0.02

= KEAex (at low EA concentration)

0.04

0.06

Ciw (mol L–1)

0.08

0.1

Ion Exchange

417

where again the colons in the bound reactant and product indicate association without specific bond formation. The sorbed concentration of the EA changes as a function of the dissolved EA+ concentration, the concentration of the competing ion (Na+ ), and the CEC of the solid. At low organic cation concentrations, that is where KEAex [EA+ ] ≪ [Na+ ], typical in many environmental situations, the bound-to-dissolved ratio is constant (Fig. 14.4): / Kid (L kg−1 ) = CEC × Kiex [Na+ ]

(14-29)

In this particular case (Cowan and White, 1958), the observed slope of the isotherm (i.e., KEAd ) at low [EA+ ] was about 200 L kg−1 . With the CEC = 0.96 mol kg−1 and [Na+ ] = 0.01 mol L−1 , one can deduce that KEAex was about 2. This implies EA+ enjoys a small Δhydrophobic GEA (see Eqs. 14-18 to 14-20). From this example, we can see the important factors dictating the extent of accumulation of organic ions near the charged particle surface. First, the greater the ion exchange capacity, the larger is the maximum extent of sorption. Further, KEAex is near one for EA since its R– group (CH3 CH2 –) is not very hydrophobic (low Δhydrophobic GEA ). At elevated EA+ levels, the isotherm is hyperbolic and the boundversus-dissolved distribution ratio (KEAd ) declines. We also deduce that for EA+ concentrations less than about 10−2 M (i.e., less than the Na+ concentration), we have a constant KEAd of about 200 (mol kg–1 )/(mol L–1 ) for this montmorillonite in a 10 mM Na+ solution. Effects of the Ionic Organic Sorbate’s Structure The remaining problem involves the question of how the rest of the structure of a charged organic sorbate influences its sorption (i.e., the magnitude of Kiex ). Presumably, the sorbate’s chemical structure contributes to the Δhydrophobic Gi , which dictates the preference of the ionic sorbate for the near-particle water region versus the bulk solution. Cowan and White (1958) also investigated the sorption of a series of alkyl ammonium ions to the same Na-montmorillonite (Fig. 14.6). A very clear pattern emerged: the longer the alkyl chain, the steeper was the initial isotherm slope. Exactly parallel results have been seen for sorption of other amphiphiles, such as negatively charged n-alkyl benzene sulfonates binding to positively charged alumina particles (Somasundaran et al., 1984), phenyl alkenoates sorbing to goethite (Evanko and Dzombak, 1999), and cationic surfactants associating with negatively charged silica (Atkin et al., 2003). Such effects are due to the increasing hydrophobicity of the “R–” groups involved (i.e., Δhydrophobic Gi ). By favoring chemical partitioning to the near surface from the bulk solution, hydrophobic effects augment the electrostatic forces and thereby enhance the tendency of the sorbates to collect near the particle surface (Somasundaran et al., 1984; Droge and Goss, 2013a). This effect has been captured using a pp-LFER analysis of sorption data. Droge and Goss (2013a) measured the Kid (L kg−1 ) values of a large set of organic ammonium cations sorbing to three clays: kaolinite, illite, and bentonite. For many of these sorbates, they found similar values of the ratio, Kid /CEC, for all three clays. These ratios

418

Sorption of Ionic Organic Compounds to Charged Surfaces

1.6

NH 3+

+

1.4

Cis (mol kg–1)

1.2 1

NH 3+

+ NH 3+

+

NH 3+

CEC = 0.96 mol kg–1 x

x

0.8

NH 3+

x x

0.6

NH 4+

x

x

0.4 Figure 14.6 Adsorption isotherms for a series of alkyl ammonium compounds on sodium montmorillonite (adapted from Cowan and White, 1958). The horizontal line indicates the cation exchange capacity of the clay, which is exceeded for the longer chain alkyl ammonium compounds.

0.2 0 0

0.02

0.04

0.06

0.08

0.1

0.12

Ciw (mol L–1)

could be converted to Kiex values by multiplying by the corresponding competing ion concentrations (see Eq. 14-27 in Box 14.1). Finally, one can use Abraham solute parameters (Abraham and Acree, 2010) for organic ions given in Appendix Table C.2 to elucidate which chemical interactions are controlling this partitioning of the organic ions (see Section 7.3 for more information about individual solute parameters). The Vi values of the ionized organic compounds are assumed to be nearly the same as their nonionic counterparts since protonation/deprotonation does not change molecular size much. Not surprisingly, when one protonates an amine, the Bi value decreases. It is also worth noting that the ionic organic species now include a new term reflecting their charging (i.e., J+ for organic cations and J− for organic anions). Since an ion exchange reaction involves adsorbing the organic cation and desorbing the competing ion (e.g., Na+ ), one may write: / log Kiex = log([i:surf][Na+ ] [i+ ][Na:surf]) = log Kid − log KNad

(14-30)

and then use the corresponding Abraham parameters for each Kid term: log Kiex = v(Vi − VNa+ ) + e(Ei − ENa+ ) + s(Si − SNa+ ) + a(Ai − ANa+ ) + +b(Bi − BNa+ ) + j(Ji+ − JNa + ) + (constanti − constantNa+ )

(14-31)

419

Ion Exchange

1: 1

4.5 4.0 primary amines

estimated log Kiex,clays

3.5

Figure 14.7 Comparison of the average log Kiex,clays values found for organic ammonium compounds sorbing to kaolinite, illite, and bentonite from 15 mM NaCl solutions (data from Droge and Goss, 2013b) with estimates of these values made using Eq. 14-33.

secondary amines

3.0

tertiary amines

2.5 2.0 1.5 1.0 0.5 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

average measured log Kiex,clays

or: log Kiex = v(ΔV) + e(ΔE) + s(ΔS) + a(ΔA) + b(ΔB) + j(ΔJ + ) + (Δconstant) (14-32) Using the subset of data from Droge and Goss (2013a) for which ion exchange of organic ammonium compounds to all three clays was consistent on a CEC-normalized basis, and the Abraham parameters for the corresponding organic ions and sodium ion (Appendix Table C.2), one finds a best-fit pp-LFER (Fig. 14.7), which is: log Kiex,clays = 1.08(±0.07)ΔV − 0.56(±0.23)ΔB (number of chemicals = 18; r2 = 0.97; S.D. = 0.30)

(14-33)

This means that the ΔJ+ term is not important, implying that the Δelect Gi − Δelect GNa+ is not very far from zero, as previously assumed. As was noted by Droge and Goss (2013a), the greater the organic ion’s Vi term, the stronger the organic ammonium compounds affinity for the near surface environment over the bulk aqueous solution. Conversely, a larger Bi term discourages surface association. Presumably, this implies breaking hydrogen bonds with water is not fully replaced by making new bonds with electron acceptors in the environment near a charged particle’s surface. An illustrating application of this approach is given in Box 14.2. Natural Organic Matter and Ion Exchange Natural organic matter is also commonly negatively charged at circumneutral pHs due to the ionization of carboxyl groups. As a result, this material is attractive to cations, while also absorbing the nonionic amine. Droge and Goss (2012; 2013b) reported Kid values for organic ammonium compounds for the well-characterized Pahokee peat (see Section 13.2). For primary ammonium sorbates, the Kiex values (= Kid [competing ion]/CEC) were similar to average values found for clays (Fig. 14.8). However,

420

Box 14.2

Sorption of Ionic Organic Compounds to Charged Surfaces

Estimation of Kid for an Organic Amine Adsorbing to Kaolinite

We consider the sorption of naphthyl-methyl-amine (NMA) from water at pH 6 and having an ionic composition of 15 mM NaCl to kaolinite (CEC = 40 mmol kg−1 ). The following data can be found for this compound: pKNMAH+ a = 9.05; Vi = 1.35 and Bi = 0.08. NH 2

naphthyl-methyl-amine (NMA)

To estimate the sorption coefficient, you assume the cation near the charged kaolinite surface is the only sorbed species, while both protonated NMA and its conjugate base are in the aqueous solution. This leads to a sorption coefficient expression: KNMA d =

[NMAH+ :surf] [NMAH+ ] + [NMA]

where [NMAH:surf] is the sorbed concentration (mol kg−1 kaolinite), [NMAH+ ] is the dissolved concentration of the protonated amine (mol L−1 water), and [NMA] is the dissolved concentration of the nonionic amine (mol L−1 water). Dividing both the numerator and denominator by [NMAH+ ], one finds: KNMA d =

[NMAH+ :surf] 1 + [NMAH ] 1 + [NMA]∕[NMAH+ ]

The first term reflects the ion exchange process and can be estimated using Eq. 14-27. The second term reflects the dissolved phase acid-base equilibrium of the NMA and its conjugate acid, NMAH+ , and thus can be found from the solution pH and this acid’s pKNMAH+ a : KNMAd =

(CEC)(KNMAH+ ex )

1

[Na ]

−pKNMAH+a

+

1 + 10

∕10−pH

1. First, you find the ratio of [NMA]/[NMAH+ ] = 10(pH−pKNMAH+ a ) = 0.0089, so the right-hand term is equal to 0.999. This, of course, tells you that at pH 6, the nonionic [NMA] ≪ [NMAH+ ] and can be neglected here. 2. Next, you use Eq. 14-33 to estimate Kiex fro NMAH+ using the competing ion’s values of VNa = 0.033 and BNa = 0.00: log Kiex = 1.08(1.35 − 0.033) − 0.56(0.08 − 0.00) = 1.38; Kiex = 24 3. Finally, combining everything: KNMAd ≈ (40 mmol kg−1 )(24)(0.999)∕(15 mmol L−1 ) = 64 L kg−1 We note that testing by Droge and Goss (2013a) found KNMAd = 40 L kg−1 .

421

Ion Exchange

1: 1

3.5 3.0 primary amines

log Kiex,peat

2.5

secondary amines tertiary amines

2.0

quarternary amines

1.5 1.0 0.5

Figure 14.8 Comparison of ion exchange coefficients for aluminosilicate clays with those for Pahokee peat; data from Droge and Goss (2012; 2013a).

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

log Kiex,clay

secondary amines had about a factor of 3 lower Kiex,clays than Kiex,OM , and tertiary and quaternary amines were still lower by an order of magnitude or greater. This may mean that the more heavily substituted organic cations cannot get as near to the charged sites in organic matter as they can for aluminosilicates (i.e., thereby invalidating the assumption that counterions like Na+ and organic ions experience the same surface potential Ψ value). Nonetheless, the data suggest that natural organic matter should be seen as both an absorbent (“foc model”) and as an ion exchanger (“CEC model”). This expanded role implies that Kid estimates for ionizable organic compounds should consider (1) acid-base equilibria, (2) nonionic species uptake into the organic matter, plus (3) ion exchange of cationic species: Kid (L kg−1 ) = [(B in OM) + (BH+ near charged OM + BH+ near charged clay)]∕ ([B]w + [BH+ ]w ) or: foc Kioc [B]w + {(CECoc + CECclay )Kiex [BH+ ]w ∕[Na+ ]} [B]w + [BH+ ]w

(14-34)

Therefore, the result depends on sorbate properties (Kioc , pKia , Kiex ), solution properties (pH, competing ions), and sorbent properties (foc , CEC). Adsorption of Organic Ions at High Sorbate Concentrations One does not usually have especially high concentrations of organic ions in the environment, but sometimes these conditions occur, for example, at spills. Also, high concentrations are found in some engineered situations. For example, such conditions may apply in applications like surfactant-mediated particle floatation (Zhang and Somasundaran, 2006) or subsurface remediation (Paria, 2008). Under these conditions, the sorption process for charged organic sorbates can change dramatically as

422

Sorption of Ionic Organic Compounds to Charged Surfaces

a result of the organic sorbates interacting with one another on the sorbent surface. For example, at about eight methylenes (–CH2 –) in a hydrophobic chain, the extent of sorption for alkyl amines can far exceed a clay’s cation exchange capacity (Cowan and White, 1958, Fig. 14.6). Likewise, Vasudevan et al., (2013) found that aromatic amines can adsorb beyond a clay’s CEC. Moreover, one finds that the isotherms no longer conform to the Langmuir model (recall Box 14.1). These observations imply the sorption mechanism must be changing as the hydrophobic portions of the sorbates get larger. This “extra” transfer to the solid surface occurs because the hydrophobic portion of the organic ion strongly prefers to escape the bulk water and move into the near surface water, particularly when like hydrophobic molecules are already abundant there. Such partitioning causes “co-ions” (i.e., oppositely charged inorganic ions like Cl− ) to also move from aqueous solution, and this has also been seen for partitioning of very hydrophobic organic ions into organic solvents (Jafvert et al., 1990). Thus, we may anticipate little difference in sorption for ionic organic chemicals due to moieties of like charge (e.g., –COO− versus −SO−3 ), so long as these charged functional groups do not react with the surface, since the electrostatic attraction to a surface is fairly nonselective. However, we do expect substantial variations between sorbates if they differ in the hydrophobicity of their nonpolar parts. This sorption behavior is not surprising if one considers the large enrichment of ions near a charged surface due to the Δelect Gi . In addition, the hydrophobic free energy advantage of the organic sorbate (Δhydrophobic Gi ) causes the local concentration of the organic sorbate i in the solution adjacent to the particle surface to be very high. At high concentrations near the surface, two phenomena influence the organic sorbate’s continued partitioning to the surface. First, there is a negative feedback associated with the limited number of ion exchange sites attracting counterions. This tends to cause the isotherm to level out at the CEC for cations or AEC for anions. Secondly, for organic ions with substantial hydrophobic parts in their structures (i.e., large Δhydrophobic Gi ), the association with the particle surface can exceed the particle’s ion exchange capacity (Fig. 14.9). In fact, so much i can accumulate at the surface that the macroscopic properties of the surface change. A classic observation is that so much organic ion accumulation occurs at the surface that one sees the surface charge of the particle “reverse” (Fig. 14.9, Fuerstenau, 1971). It should be noted that electroneutrality requires no net charge build up in the nearsurface area. Thus additional organic ion sorption requires the co-transfer of a “coion” of opposite charge to i (e.g., Na+ combined with i− in Fig. 14.9). Since the transfer of these oppositely charged co-ions against the electrostatic potential requires –zi FΨo (note that zco-ion = –zi ), their accumulation in the near-surface water is given by (focusing on the monovalent case here): [co-ion:surf] = [co-ion] exp(−zi FΨo∕RT) = [co-ion]exp(Δhydrophobic Gi ∕RT) (14-35) This means, in the case of the sorption of the alkyl ammonium ions to Namontmorillonite (Fig. 14.6), the charge balance equation in the near surface region must be: RNH3 :surf + Na:surf = CEC + Cl:surf

(14-36)

423

Ion Exchange

O O

PZC

S

–30

O-

10–10 region 1

region 2

region 3

–20

Cis (mol cm–2)

charge 0

10–11 sorbed concentration

+10

+20

Figure 14.9 The sorption isotherm of dodecyl sulfonate (circles) on αalumina (15 m2 g−1 ) suspended in water at pH 7.2 and 2 mM NaCl. Electrophoretic mobilities (squares), a measure reflecting Ψ, show the corresponding changes in the particles’ zeta potential from positive 50 mV with only Na+ sorbed to –30 mV when the sorbed ions are predominantly dodecyl sulfonate. Adapted from Wakamatsu and Fuerstenau (1968) and Fuerstenau (1971).

10–12

zeta potential ≈ Ψo (mV)

–10

+30

+40

10–13

10–5

10–4

10–3

+50

Ciw (mol L–1)

This model explains why the total sorbed concentrations of organic ions can exceed the solid’s CEC (Fig. 14.6) and why the isotherms of all the alkyl amines are not well fit with a series of simple Langmuir isotherms. To provide an estimate of Kiex for use in these cases, let us try to isolate the contribution of the sorbate’s hydrophobicity using some available data. For the alkyl ammonium ions exchanging with sodium cations in the data of Cowan and White (1958), one has: − RT ln Kid = +zi FΨo + Δhydrophobic Gi

(14-37)

− RT ln Kid = +zi FΨo − RT ln Kiex

(14-38)

implying:

Thus, if we examine the variation in –RT ln Kid for a series of alkyl amines participating in ion exchange, we should see how R– groups affect the value of –RT ln Kiex while the product, zi FΨo , remains constant. Since this hydrophobic effect appears to regularly increase with the size of the nonpolar part of the chemical structure (Cowan and White, 1958; Somasundaran et al., 1984, Teppen and Aggarwal, 2007; Samaraweera

424

Sorption of Ionic Organic Compounds to Charged Surfaces

et al., 2014), we may reasonably propose this energy term is composed of “excess free energy of solution in water” contributions from each of the nonpolar parts of the structure. Consequently, we expect for the alkyl ammonium ions: − RT ln Kiex = Δhydrophobic Gi ≈ mΔhydrophobic GCH2

(14-39)

and together with the electrostatic term, we have: − RT ln Kid = +zi FΨo + (mΔhydrophobic GCH2 )

(14-40)

where m is the number of methylene (–CH2 –) groups in each sorbate’s alkyl chain, and Δhydrophobic GCH2 is the hydrophobic contribution made by each methylene driving these sorbates into the near surface water layer. Using Cowan and White’s (1958) observed variation of –RT ln Kid for the alkyl ammonium ions, when these organic sorbates are present at levels much less than Na+ , as a function of the number of methylenes in the alkyl chains, one can examine the hydrophobic and electrostatic energy effects. A least-squares correlation line through the Kid data yields: − RT ln Kid = −10.9 − m(0.75 kJ mol−1 )

(14-41)

The intercept in this fitted result implies that the alkyl ammonium ions experienced an electrostatic attraction to the clay surface corresponding to: zi FΨo ≈ −11 kJ mol−1

(14-42)

which corresponds to Ψo ≈ –0.11 V, a typical surface potential. Also, we see Δhydrophobic GCH2 = –0.75 kJ mol−1 . Somasundaran et al. (1984) noted that inclusion of the phenyl group in alkyl aryl sulfonates increases the ion exchange sorption tendency of these amphiphiles to a degree corresponding to lengthening the alkyl chain by 3-4 methylene groups. This is consistent with increasing the nonpolar structure’s hydrophobicity to the same extent [i.e., Δlog Kow (phenyl) ∼ 1.68 and Δlog Kow (3-4 methylenes] ∼ 1.59 to 2.12). Thus, there is little doubt that hydrophobic phenomena are playing an important role in determining the extent of amphiphilic sorption. Notably, the phenomena described occurs in cases involving ionic organic compounds that form micelles/hemimicelles (Fuerstenau, 1956; Somasundaran et al., 1964; Chandar et al., 1983, 1987; Atkin et al., 2003) and inorganic salt precipitates (Jafvert and Heath, 1991). Micelle/hemimicelle formation plays a critical role in amphiphile “sorption” to minerals when the organic ions are present at relatively high dissolved concentrations, about 0.001-0.01 of their critical micelle concentrations (CMC, i.e., the level at which they self-associate in the bulk solution). When the organic sorbate levels are low, the sorption mechanism is like the discussed ion exchange mechanism (Fig. 14.10). However, at some point in the isotherm, micelles form in the near surface, presumably due to both electrostatic and hydrophobic effects enhancing the near-surface concentrations. This in turn allows rapid coagulation of the resultant micelle with the oppositely charged particle surface. Such aggregation smothers that subarea of the particle’s surface charge with what have been called hemimicelles. Electrophoretic mobility measurements clearly demonstrate the neutralization of the particle’s charges in this steep portion of the isotherm, even going so far as

Ion Exchange

425

III

Cis

II

I Ciw Figure 14.10 Relationship between sorbed and dissolved amphiphile concentrations (upper isotherm plot). These different parts of the isotherm reflect changes in the solid surface as sorption proceeds, possibly explainable by the following: in portion (I) with low dissolved concentrations, sorption occurs via ion exchange and related mechanisms. At some point, sufficient near-surface concentration enhancement occurs that micelles form (IIa) and rapid coagulation between oppositely charged micelles and the surface follows (IIb). When the surface becomes fully coated with such micelles, additional sorption is stopped (III). In portion III, the solid surface charge is converted from one sign to the other, implying sorbates must become physically associated with the particle surface, as opposed to simply being present in the diffuse double layer or the vicinal water layer.

I ion exchange

III surface fully covered; charge reversed

solid

Cl–

Cl–

Na

+

Na+ solution + Na+ Na

Na+

solution solid

Na+ Na+

Cl

solid

Cl–

Cl– Na

Cl–

solution Cl–

solid

Na+ Na+

solution

Na+

Na+

Na+

Cl–

+

Cl– Na+

Na

IIa micelle formation in near surface layer

Na+

Na+

Na+ Na+

Na+

–

Na+

Na+

Na+

Cl– +

Na+ Na

+

Na+

Na+ Na

+

IIb hemimicelle attachment to particle surface

to reverse the surface charge (e.g., Chander et al., 1987; Atkin et al., 2003). The onset of this particle coating by hemimicelles occurs at different dissolved concentrations for various amphiphiles, but is near millimolar levels (∼100 mg L−1 ) for decylsubstituted amphiphiles and is near micromolar levels (∼100 μg L−1 ) for octadecyl derivatives. Elevated near-surface concentrations, derived from accumulation of these amphiphiles in the thin film of water near the particle surface by factors of 100 or more, are compensating just enough to achieve critical micelle concentrations in this near-surface water layer. Finally, the entire particle surface is covered with a bilayer of amphiphile molecules; the particle’s surface charge is now that of the surfactant, and the addition of still more amphiphile to the solution does not yield any higher sorbed loads. This especially extensive degree of sorption may cause macroscopic phenomena such as dispersion of coagulated colloids and particle flotation. Impacts of Multiple Sorption Mechanisms on Isotherms of Ionic Organic Sorbates Finally, we note that work performed using the mix of solids that occur in “real world” soils and sediments suggests the heterogeneity of the natural sorbents is very

426

Sorption of Ionic Organic Compounds to Charged Surfaces

0 N+

Figure 14.11 Observed sorption of dodecylpyridinium on a soil exhibiting an overall cation exchange capacity of 0.135 mol kg−1 . Two Langmuir isotherms are placed on the data to illustrate how different portions of the observed isotherm may reflect the influence of different materials in the complex soil sorbent or possibly different mechanisms (data from Brownawell et al. 1990).

Cis (mol kg–1)

–1 Na+ = 10–2 M K = 102

–2

capacity = 10–1 mol kg–1

–3

K = 105 capacity = 10–3 mol kg–1

–4 –5

–9

–8

–7

–6

–5

–4

–3

–2

Ciw (mol L–1)

important to charged organic species (Brownawell et al., 1990; Droge and Goss, 2013c). It appears that one sees the influence of more than one solid surface type at the same time. Thus, fitting sorption isotherms for real world solids may require using combinations of isotherms. For example, two Langmuir isotherms may be superimposed to fit the experimental data (Fig. 14.11). Presumably, each isotherm reflects the association of the organic sorbate with different solid materials that make up the complex medium we simply call a soil, subsoil, or sediment.

14.4

Surface Complexation: Specific Bonding of Organic Compounds with Solid Phases in Water In contrast to nonspecific ion exchange, ions sometimes bond to specific atoms on a solid surface, displacing other ligands. This “chemisorption” or “surface complexation” forms a sorbed species, which is distinct from organic ions simply dissolved in the near-surface water (i.e., M–i is not the same as M–OH2 + with i− nearby in the diffuse double layer, Fig. 14.3, path 1). One or both of these sorbed species may co-exist in significant proportions (Stone et al., 1993; Whitehead et al., 2015). Some organic substances form covalent bonds with the NOM in a sediment or soil; other organic sorbates serve as ligands for metals on the surfaces of inorganic solids. Organic Sorbate-Natural Organic Matter Reactions First, some organic sorbates can react with organic moieties contained within the natural organic matter of a particulate phase. Especially prominent in this regard are organic bases like substituted anilines (Hsu and Bartha, 1974, 1976; Fabrega-Duque et al., 2000; Li et al., 2000; Weber et al., 2001; Chen and Nyman 2007; Gulkowska et al., 2012). When compounds like 3,3′ -dichlorobenzidine are mixed with sediment, they become irretrievable using organic solvents that are capable of recovering them from absorbed positions within natural organic matter or using salt solutions that should displace them from ion exchange sites (Appleton et al., 1980; Weber et al.,

Surface Complexation: Specific Bonding of Organic Compounds

427

2001, Chen and Nyman 2009). Conditions that promote hydrolysis (see Chapter 22) do release much of the sorbed amines. Thus, it appears that reactions between the basic amine and carbonyl functionalities in the natural organic matter explain the strong sorption seen (Stevenson, 1976; Chen and Nyman, 2009). Cl H 2N

NH2 Cl 3,3’-dichlorobenzidine

Due to their low pKia values (∼ 5), the aromatic amines can be largely deprotonated at natural water pH’s. Thus, the nitrogen’s nonbonded electrons can nucleophilically attack carbonyl moieties or carbon double bonds in β-unsaturated carbonyls such as present in quinone moieties: OH R

HN

R1

H

O

N

R2 R1

R2

H

R

R

OH HN

H

R1

O

N H

1,2 nucleophilic addition at carbonyls

R1

1,4 nucleophilic addition at β-unsaturated carbonyls (Michael addition)

(14-43)

R

Observations indicate that the importance of such reactions increases with pH, and modeling suggests such reactive carbonyls occur at tens of millimoles per kg of organic carbon (Chen and Nyman, 2009). These reactions often proceed slowly over hours, days, and even years, so the extent of this chemisorption is difficult to predict as it may be kinetically controlled. Furthermore, such bond-forming sorption is sometimes irreversible on the timescales of interest, and we might not wish to include these effects in a Kid expression reflecting sorption equilibrium. Nevertheless, this condensation-type sorption is very important to reducing the mobility and bioavailability of such compounds (Li et al., 2000; Weber et al., 2001). Organic Sorbate-lnorganic Solid Surface Reactions A second type of surface reaction involves bonding of organic sorbates with metals exposed on the surface of the solid. This process is often referred to as formation of “inner sphere complexes,” in contract to cases in which the organic ion is separated from the metals by other ligands or water (see Fig. 14.12). In these cases, the organic sorbate bonds to one or two metals (i.e., mononuclear or binuclear) using either one or two functional groups (i.e., monodentate or bidentate). In these sorption reactions, we may consider that a ligand such as a hydroxyl bound to a metal on the solid is displaced by the organic sorbate: M − OH + i− ⇌

M − i + OH−

(14-44)

Based on spectral evidence, such surface bonding (or inner sphere complexation) reactions occur on oxyhydoxides of metals like Fe, Al, and Ti (Boily et al., 2000;

428

Sorption of Ionic Organic Compounds to Charged Surfaces

O

O H HO HO O H

O

M M

O M

O

O outer sphere complex

O

inner sphere, mononuclear, bidentate complex

O

O M

Figure 14.12 Illustration of possible adsorption mechanisms of organic acids to mineral surfaces illustrated by phthalate. Adapted from Hwang and Lennart (2009).

M

O

O H O H O inner sphere, mononuclear, monodentate complex

M

O

M

O O

inner sphere, binuclear, bidentate complex

Roddick-Lanzilotta and McQuillan, 2000; Sverjensky et al., 2008; Hwang and Lenhart, 2009; Lindegren et al., 2009; Hanna et al., 2014). Carboxylic acids and phenols are common reactive moieties of such sorbates. Often, the resultant bound species is not known with certainty, but is only assumed as part of a modeling fit. Surface complexation modeling is used to interpret sorption as a function of solution properties like pH and ionic strength, and these efforts suggest unique surface-associated species. However, at the present time, it is difficult to clearly distinguish the continuum from inner sphere bound sorbates to outer sphere hydrogenbonded sorbates to outer sphere diffuse double layer counter ions. Given such additional sorption mechanisms, multiple sorption equilibria may need to be modeled (Stone et al., 1993; Evanko and Dzomback, 1999; Whitehead et al., 2015). The sorption coefficient may include ionic species held near the solid surface by outer sphere interactions and also by inner sphere bonding: [ K id,ion exchange = and surface reaction

] [ ] organic counterion organic ion bound + near the surface to the surface [ ] [ ] neutral organic Hi organic ion i− + in solution in solution

(14-45)

The denominator in this expression can be simplified by using an acid-base relation relating Hi in solution to its conjugate base, i− , to give (Hi + i− ) = (10−pH ∕ 10−pKia + 1)(i− ), so that Eq. 14-45 becomes: [ ] [ ] ⎛ organic organic ion bound ⎞ ⎜ counterion ⎟ to surface ⎟ (10−pH ∕10−pKia + 1)−1 K id,ion exchange = ⎜ − + − in solution] ⎜ ⎟ [i in solution] [i and surface reaction ⎜ ⎟ ⎝ ⎠ (14-46)

Surface Complexation: Specific Bonding of Organic Compounds

429

For low sorbate levels, we can use Eq. 14-26 to estimate the first term on the right hand side of Eq. 14-46. Now our task is to develop an expression to predict the last term. To do this, we begin by writing the reaction involved: i:surface + L − M

⇌ i−M

+ L:surface

(14-47)

where i−M and L − M represent species in which an organic compound and an inorganic ligand are directly bonded to at least one metal atom on the surface of the solid. One should note that such inner sphere bonding could involve monodentate or bidentate bonding, as well as association with one or two metals (see Fig. 14.12). Such surface complexation reflects a free energy change that we refer to as Δrxn Gi and a corresponding equilibrium expression: Kirxn =

[i−M ][L:surface] [i:surface][L − M ]

(14-48)

The species L:surface and i:surface represent near-surface ions already accumulated in the water near the solid surface. Recalling Eq. 12-11, we can assume that there are a finite number of key reactive sites on the solid, σsurf rxn (mol m−2 ), so we have: σsurf rxn Asurf = [i−M ] + [L − M ]

(14-49)

with Asurf equal to the specific particle surface area (m2 kg−1 ). Therefore, we can rewrite Eq. 14-48: Kirxn =

[i−M ][L:surface] [i:surface](σsurf rxn Asurf − [i−M ])

(14-50)

As discussed in Section 14.3, the concentrations of ions in the layer of water next to the particle surface can be related to the corresponding species in the bulk solution: [L:surface] = [L− ]bulk e−Δelect Gi ∕RT

(14-51)

[i:surface] = [i]bulk e−Δelect Gi ∕RT e−Δhydrophobic Gi ∕RT

(14-52)

and:

Using these relations in Eq. 14-50, we have: Kirxn =

[i−M ][L− ]bulk ⋅ e−Δelect Gi ∕RT

(σsurf ex Asurf − [i−M ])[i]bulk ⋅ e−Δelect Gi ∕RT ⋅ e−Δhydrophobic Gi ∕RT [i−M ][L− ]bulk = (14-53) (σsurf ex Asurf − [i−M ])[i− ]bulk Kiex

430

Sorption of Ionic Organic Compounds to Charged Surfaces

where Kiex is equal to exp(–Δhydrophobic Gi /RT), as discussed in Section 14.3. Rearranging, we then find: [i−M ] =

σsurf rxn Asurf Kiex Kirxn [i− ]bulk [L− ]bulk + Kiex Kirxn [i− ]bulk

(14-54)

Thus, another Langmuir isotherm is expected with the maximum bound concentrations equal to σsurf rxn Asurf . Returning to our overall Kid expression for organic ions (Eq. 14-46), we can now write: K id,ionexchange = andsurface reaction

σsurf ex Asurf Kiex σsurf rxn Asurf Kiex Kirxn + − [comp.ion] + Kiex [i ] [comp.ligand] + Kiex Kirxn [i− ]

(14-55)

As for nonreacting organic ions, we need information on the ion exchange tendency of the chemical of interest (Kiex or Δhydrophobic Gi ), and we need to assess Kirxn or Δrxn Gi . Various investigators have utilized surface complexation modeling along with reasonable hypotheses concerning the surface species formed (and hence the adsorption reaction stoichiometry) to extract values of the product, Kiex Kirxn , for cases of interest (e.g., Mesuere and Fish, 1992; Ali and Dzombak, 1996; Vasudevan and Stone, 1996; Evanko and Dzombak, 1998, 1999). For example, Evanko and Dzombak (1999) fitted data for carboxylic acids and phenols sorbing to goethite from 10 mM NaCl solutions. They considered a sorption reaction of the form: Fe − OH + i− + H + ⇌

Fe − i + H2 O

(14-56)

and fitted an “intrinsic” equilibrium constant, K1int , after accounting for electrostatic contributions: K1int =

[ Fe − i] Fe − OH]

𝛾 ′i [i− ]𝛾 ′H+ [H+ ][

(14-57)

Adding the reaction, H2 O = H+ + OH− with Kw = 10−14 , this sorption reaction is equivalent to a ligand exchange with OH- being replaced by i− : Fe − OH + i− ⇌

Fe − i + OH−

(14-58)

For this reaction, the equilibrium constant is the product, Kiex Kirxn , since i− must partition from bulk solution into the near-surface water and then undergo the complexation reaction. Thus, this product (Kiex Kirxn ) is related to the previous “intrinsic” constant from reaction 14-56: Kiex Kirxn = 10−14 K1int

(14-59)

Kiex Kirxn values depend on the sorbate’s structure (see examples given in Table 14.2). First, Kiex Kirxn values increase with the addition of moieties like carboxyl groups (compare hemimellitate to phthalate to benzoate). Also, functional groups positioned to allow multiple bonds with surface metals enhance the equilibrium values (compare

431

Surface Complexation: Specific Bonding of Organic Compounds

Table 14.2 Examples of Equilibrium Coefficients for Non-Charged Surface Species Binding to Goethitea,b Organic sorbate (i)

pKia

benzoic acid

4.12

Structure

Sorption reaction COOH

phthalic acid

2.87 5.23

COOH

log (Kiex Kirxn )c

Fe − i + OH−

10−6.1

Fe − OH + Hi− ⇌

Fe − iH + OH−

10−3.75

Fe − OH + H2 i− ⇌

Fe − iH2 + OH−

10−2.97

Fe − OH + Hi− ⇌

Fe − iH + OH−

100.12

Fe − OH + Hi− ⇌

Fe − iH + OH−

10−5.45

Fe − OH + Hi− ⇌

Fe − iH + OH−

10−4.54

Fe − OH + i− ⇌

COOH

hemimellitic acid

2.79 4.49 6.95

COOH COOH COOH

catechol

9.34 13.24

OH OH

salicylic acid

2.88 13.56

3-hydroxy-2naphthoic acid

2.65 12.72

COOH OH COOH OH

a

Deduced from data and complexation modeling in Evanko and Dzombak (1999). Note that one cannot assume the surface species are inner sphere “surface complexes.” c Equation 14-54 with L− = OH− . b

COOH

1-naphthoic acid COOH HO OH

salicylate to benzoate). Values of Kiex Kirxn increase for ligands with greater pKia values (Vasudevan and Stone, 1996). This may be interpreted as the greater the tendency to “hold” a proton (i.e., greater pKia ), the greater will be the affinity for bonding to a metal on an oxide surface. For the four mono carboxylic acids (benzoic acid, 1-naphthoic acid, 3,5-dihydroxy benzoic acid, and 6-phenyl hexnoic acid) also investigated by Evanko and Dzombak (1998, 1999), a value of Kiex Kirxn ≈ 10−6 was always found. The product was a little higher for the acids with larger “R-” groups (ranging from benzoic acid at 10−6.1 to phenyl hexanoate at 10−5.32 ). This range is consistent with our expectations from the Kiex contribution, since Kiex (benzoic acid) should be about 10 times less than Kiex (phenyl hexanoate) given the latter’s five methylenes (–CH2 –) (see Eq. 14-39).

3,5-dihydroxybenzoic acid

(CH 2)5COOH phenyl hexanoic acid

Returning to our effort to anticipate the overall sorption of organic compounds that may act both as counter ions and surface ligands, we can recognize all the terms in the second half of Eq. 14-55: σsurf rxn Asurf = [ Fe − OH]

(14-60)

432

Sorption of Ionic Organic Compounds to Charged Surfaces

and: [comp.ligand] = [OH− ]

(14-61)

With the empirical measures of K1int reported in the literature and understandings of the “stoichiometries” of both the ion exchange and ligand exchange processes, we can now estimate the solid–water distribution ratios of such ionic organic sorbates. We should point out that many organic sorbates, and especially bidentate ones like phthalate and salicylate, can apparently form more than one bound surface species. The relative importance of these surface species varies greatly as a function of pH. Hence, accurate predictions of the sorption of such organic ligands on mineral oxides requires applying more than one empirical surface reaction equilibrium constant to calculate the contributes of each bound species (see Evanko and Dzombak, 1999). Finally, we can also evaluate Kirxn recognizing that the tendency to form chemical linkages to solid surface atoms correlates with the likelihood of forming comparable complexes in solution (Stumm et al., 1980; Schindler and Stumm, 1987; Dzombak and Morel, 1990). That is, the free energy change associated with the exchange shown by Eq. 14-48 appears energetically similar to that for a process occurring between two dissolved components: +

+

M − Lz + i− ⇌ M − iz + L−

(14-62)

where z+1 would be the charge of the free metal in aqueous solution. This entirely solution-phase exchange reaction is characterized by an equilibrium constant: +

K iligand exchange = in solution

[M − iz ][L− ] +

[M − Lz ][i− ]

(14-63)

A substantial database is available to quantify such solution equilibria (e.g., Martell and Smith, 1997; Morel, 1983). The procedure for other charged organic chemicals is analogous. By using such complexation results in Eq. 14-56, we begin to build an overall estimate of charged organic chemical sorption to minerals. We may now anticipate even a small degree of adsorption, which can be important (e.g., to the rate of heterogeneous transformations, Ulrich and Stone, 1989).

14.5

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission.

Questions and Problems

433

Questions Q 14.1 For what kind of compounds and in which environmentally relevant cases is adsorption of organic chemicals to inorganic surfaces in water important? Give five examples.

CH 2NH 3+

Q 14.2

benzyl ammonium pK ia = 9.33

What intermolecular interactions and corresponding free energy contributions (ΔGi ) would you suspect to be important for the following sorbate:sorbent:solution combinations:

O OH

(a) benzyl ammonium between water and quartz sand? See structure in margin.

OH

(b) ortho-phthalic acid between water and quartz sand? See structure in margin.

O ortho-phthalic acid pK ia1 = 2.89 pK ia2 = 5.51

Indicate in each case the intermolecular interaction forces, key structural features of the sorbate, and the environmental parameters influencing sorption. Q 14.3 Why do minerals have charges when they are submerged in water? Q 14.4

pyrene

Indicate whether the following solids are positively charged, neutral, or negatively charged when they occur in water at pH 7 (neglect specific adsorbates like phosphate or ferric iron species):

SO3 –

(a) quartz (SiO2 ) (b) natural organic matter pyrene sulfonate

(c) goethite (FeOOH) (d) gibbsite (Al(OH)3 )

NH 3+ butyl ammonium

(e) kaolinite

O

Q 14.5

O–

Which of the two compounds do you think would sorb more to kaolinite in water at pH 6? See structures in margin.

butyrate NH 3+

(a) pyrene or pyrene sulfonate?

propyl ammonium NH 3+ octyl ammonium

(b) butyl ammonium or butyrate? (c) propyl ammonium or octyl ammonium?

434

Sorption of Ionic Organic Compounds to Charged Surfaces

Q 14.6 How can organic ions accumulate in excess of the ion exchange capacity near a pure mineral solid submerged in water? Q 14.7 If organic ions are not bonded to a mineral’s surface, why do they still not migrate past the minerals in a groundwater flow? Problems P 14.1 Evaluating the Sorption of an Organic Anion, 2,4-DichlorophenoxyButyrate, to Negatively Charged Natural Solids In Fig. 14.1b, a sorption isotherm shows that an organic anion, 2,4-dichlorophenoxybutyrate (DB− ), will sorb to a sediment from water of pH 7.9, despite the sediment’s overall negative charge (as evidenced by its CEC of about 140 mmol kg−1 ; Jafvert, 1990). DB characteristics Mi = 246 g mol−1 pKia = 4.95 Kiow = 2.5×103

(a) The sediment also contained 1.5% organic carbon (foc = 0 .015). Given a pKia of 4.95 for this acid, can you account for the observed Kid values near 4 to 5 L kg−1 , assuming the neutral DB species partitioned into the NOM of the sediment? What Kid value (L kg−1 ) do you expect from such absorption? (b) You suspect the hydrophobicity of this organic anion also causes it to accumulate near the mineral surface against the electrostatic repulsion it feels: DB− + Na+ ⇌ DB:surf + Na:surf KDBex (L kg−1 ) (i) Write a charge balance equation for the near-surface water assuming a solution composition of 20 mM NaC1. (ii) Write an equilibrium equation (i.e., relating KDBex to chemical concentrations) for the exchange reaction shown above. (iii) Derive an isotherm equation describing [DB:surfl as a function of [DB− ] by combining the equilibrium quotient relation with your near-surface charge balance equation. (iv) What value of KDBex would be necessary to account for the observed KDBd values (i.e., [DB:surf]/ [DB− ]) if the solution composition was 20 mM NaCl? (v) Would such a KDBex be “reasonable”? Explain your reasoning in light of electrostatic and hydrophobic energies required. P 14.2 Designing a Reactor to Remove Aniline from a Wastewater You have been charged with removing the aniline present at 100 ppm in the water of a 100 m3 tank. (a) One colleague suggests you add alum (A12 (SO4 )3 ) and NaOH to make a 100 mg L−1 suspension of negatively charged amorphous aluminum hydroxide (Al(OH)3 )

Questions and Problems

435

particles at pH 10 and 10 mM Na2 S04 . Assume the surface density of Al–OH is int int = 7 and pKa2 = 9. 6×10−6 mol m−2 , a specific surface area of 800 m2 g−1 , and pKa1 Will the aniline sorb to these negatively charged aluminum hydroxide particles and be carried to the bottom of the tank? Calculate the fraction of aniline sorbed to the particles before settling. NH 2

NH 3+

aniline

pK a = 4.6

(b) Another colleague suggests you add Na:montmorillonite clay and HC1 to make a 100 mg L−1 suspension of clay particles at pH 3 and 10 mM NaC1. Assume a CEC of 1×10−6 mol m−2 and AEC of 5×10−7 mol m−2 at pH 3, a specific surface area of 7×105 m2 kg−1 , and a pHzpc = 2.5. Will the aniline sorb to these mixed-charge clay particles and be carried to the bottom of the tank? Calculate the fraction of aniline sorbed to the particles before settling. P 14.3 Transport of Di-Isopropanol-Amine (DIPA) in Ground Water from a Sour Gas Processing Plant Di-isopropanol-amine (DIPA) was used to remove hydrogen sulfide from natural gas supplies (Goar, 1971). Unfortunately, this compound has been found as a groundwater contaminant at a total concentration of about 1 mM levels near such a sour gas processing plant. Estimate the retardation factor for DIPA the nearby aquifer. Aquifer characteristics mineralogy: 70% quartz, 5% calcite, 25% montmorillonite, 0.2% organic matter cation exchange capacity: CEC = 90 mmol kg−1 density of aquifer material: ρs = 2.6 kg L−1 total aquifer porosity: ϕ = 0.40 groundwater composition: pH = 8.0; [Na+ ] = 20 mM; [Ca+2 ] = 1 mM; [Cl− ] = 20 mM; [HCO−3 ] = 1 mM

N OH

H

OH

di-isopropanol-amine (DIPA) pKDIPAH+a = 8.88

P 14.4 What Mechanism Accounts for the Benzidine Sorption in Sediments and Soils? Zierath et al. (1980) measured sorption isotherm data for benzidine on sediments and H 2N

NH 2

soils. Using Missouri River sediment with foc = 0.023 kg oc kg−1 solid, CEC = 190 mmol kg−1 , and a specific surface area Asurf = 131 m2 g−1 , they obtained the following sorption data:

benzidine

Benzidine Sorption to Missouri River Sedimenta Ciw (μmol L−1 ) 20 30 120 200 340 a

Data from Zierath et al. (1980).

Cis (μmol kg−1 ) 1500 3000 5300 7600 9300

436

Sorption of Ionic Organic Compounds to Charged Surfaces

You are interested in discerning what mechanism or mechanisms were responsible for the benzidene sorption observed with Missouri River sediment. To examine this question, you assume the tests used 1 g of soil per 10 mL of water and had a pH of 6 and a salt content of 1 mM NaCl. Given these assumptions, what sorption mechanism would predominate? Justify your answer using estimates of Kid (a) first assuming absorption into organic matter predominates and (b) then assuming adsorption to ion exchange sites predominates. P 14.5 Impact of Diquat Sorption on Its Biodegradation The presence of montmorillonite in microbial cultures has been seen to reduce the rate of diquat (D) biodegradation (Weber and Coble, 1968). It has been hypothesized that this is due to significant diquat adsorption to the clay. What fraction (%) of the diquat in 1 μM diquat solutions would be adsorbed to a 10 mg L−1 montmorillonite suspension (assume CEC = 1 mol kg−1 ) at pH 7 and 10−2 M NaCl and assuming KDex = [D:surf2 ] [Na+ ]2 / [D2+ ] [Na:surf]2 = 3 kg L−1 . (Hint: (1 – ε )0.5 ≈ 1 – ε /2 for small values of ε).

N+ N+ diquat

O

P 14.6 Adsorption of Organic Ions to Iron Oxides from Seawater OH OH

O ortho-phthalic acid pKia1 = 2.89 pKia2 = 5.51

Balistrieri and Murray (1987) evaluated the sorption of organic acids to positively charged goethite (FeOOH) particles suspended at 6.6 g L−1 in 0.53 M NaCl solutions to mimic seawater salt. They observed the adsorption trend for ortho-phthalic acid added at 200 μM as shown in the table. Why is the extent of adsorption largest near pH 4? Ortho-phthalic Acid Sorption to Goethitea pH 3 4 5 6 7 8

% adsorbed 60 65 50 25 5 5

a

Data from Balistrieri and Murray (1987).

14.6

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Parks, G. A., The isoelectric points of solid oxides, solid hydroxides, and aqueous hydroxo complex systems. Chem. Rev. 1965, 65, 177–198. Ritchie, J. D.; Perdue, E. M., Proton-binding study of standard and reference fulvic acids, humic acids, and natural organic matter. Geochim. Cosmochim. Acta 2003, 67(1), 85–96. Roddick-Lanzilotta, A. D.; McQuillan, A. J., An in situ infrared spectroscopic study of glutamic acid and of aspartic acid adsorbed on TiO2: Implications for the biocompatibility of titanium. J. Colloid Interface Sci. 2000, 227(1), 48–54. Samaraweera, M.; Jolin, W.; Vasudevan, D.; MacKay, A. A.; Gascon, J. A., Atomistic prediction of sorption free energies of cationic aromatic amines on montmorillonite: A linear interaction energy method. Environ. Sci. Technol. Lett. 2014, 1(6), 284–289. Schindler, P. W.; Stumm, W., The surface chemistry of oxides, hydroxides, and oxide minerals. In Aquatic Surface Chemistry, Stumm, W., Ed. Wiley-Interscience: New York, 1987; pp 83– 110. Somasundaran, P.; Agar, G. E., The zero point of charge of calcite. J. Colloid Interface Sci. 1967, 24, 433–440. Somasundaran, P.; Healy, T. W.; Fuerstenau, D. W., Surfactant adsorption at the solid–liquid interface – Dependence of mechanism on chain length. J. Phys. Chem. 1964, 68, 3562–3566. Somasundaran, P.; Middleton, R.; Viswanathan, K. V., Relationship between surfactant structure and adsorption. In Structure/Performance Relationship in Surfactants, Rosen, M. J., Ed. American Chemical Society: Washington, DC, 1984. Stevenson, F. J., Organic matter reactions involving pesticides in soil. In Bound and Conjugated Pesticide Residues, Kaufman, D. D.; Still, G. G.; Paulson, G. D.; Bandal, S. K., Eds. American Chemical Society: Washington, DC, 1976; pp 180–207. Stone, A. T.; Torrents, A.; Smolen, J.; Vasudevan, D.; Hadley, J., Adsorption of organic compounds possessing ligand donor groups at the oxide/water interface. Environ. Sci. Technol. 1993, 27(5), 895–909. Stumm, W.; Kummert, R.; Sigg, L., A ligand exchange model for adsorption of inorganic and organic ligands at hydrous oxide interfaces. Croat. Chem. Acta 1980, 53(2), 291–312. Sverjensky, D. A.; Jonsson, C. M.; Jonsson, C. L.; Cleaves, H. J.; Hazen, R. M., Glutamate surface speciation on amorphous titanium dioxide and hydrous ferric oxide. Environ. Sci. Technol. 2008, 42(16), 6034–6039. Teppen, B. J.; Aggarwal, V., Thermodynamics of organic cation exchange selectivity in smectites. Clay Clay Min. 2007, 55(2), 119–130. Tipping, E., The adsorption of aquatic humic substances by iron oxides. Geochim. Cosmochim. Acta 1981, 45, 191–199. Ulrich, H. J.; Stone, A. T., The oxidation of chlorophenols adsorbed to manganese oxide surfaces. Environ. Sci. Technol. 1989, 23(4), 421–428. Vasudevan, D.; Arey, T. A.; Dickstein, D. R.; Newman, M. H.; Zhang, T. Y.; Kinnear, H. M.; Bader, M. M., Nonlinearity of cationic aromatic amine sorption to aluminosilicates and soils: Role of intermolecular cation-pi interactions. Environ. Sci. Technol. 2013, 47(24), 14119–14127. Vasudevan, D.; Stone, A. T., Adsorption of catechols, 2-aminophenols, and 1,2-phenylenediamines at the metal (hydr)oxide/water interface: Effect of ring substituents on the adsorption onto TiO2 . Environ. Sci. Technol. 1996, 30(5), 1604–1613. Wakamatsu, T.; Fuerstenau, D. W., The effect of hydrocarbon chain length on the adsorption of sulfonates at the solid/water interface. In Adsorption From Aqueous Solution, Weber, W. J., Ed. American Chemical Society: Washington, DC, 1968; pp 161–172. Weber, E. J.; Colon, D.; Baughman, G. L., Sediment-associated reactions of aromatic amines. 1. Elucidation of sorption mechanisms. Environ. Sci. Technol. 2001, 35(12), 2470–2475. Weber, J. B.; Coble, H. D., Microbial decomposition of diquat adsorbed on montmorillonite and kaolinite clays. J. Agric. Food Chem. 1968, 16(3), 475–478.

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Sorption of Ionic Organic Compounds to Charged Surfaces

Westall, J. C., FITEQL: A Program for the Determination of Chemical Equilibrium Constants from Experimental Data. Department of Chemistry, Oregon State Univ.: Corvallis, OR, 1982. Whitehead, C. F.; Carbonaro, R. F.; Stone, A. T., Adsorption of benzoic acid and related carboxylic acids onto FeOOH(goethite): The low ionic strength regime. Aquat. Geochem. 2015, 21(2–4), 99–121. Williams, D. J. A.; Williams, K. P., Electrophoresis and zeta potential of kaolinite. J. Colloid Int. Sci. 1978, 65, 79–87. Zachara, J. M.; Ainsworth, C. C.; Felice, L. J.; Resch, C. T., Quinoline sorption to subsurface materials: Role of pH and retention of the organic cation. Environ. Sci. Technol. 1986, 20(6), 620–627. Zhang, R.; Somasundaran, P., Advances in adsorption of surfactants and their mixtures at solid/solution interfaces. Adv. Colloid Interface Sci. 2006, 123, 213–229. Zierath, D. L.; Hassett, J. J.; Banwart, W. L.; Wood, S. G.; Means, J. C., Sorption of benzidine by sediments and soils. Soil Sci. 1980, 129(5), 277–281. Zullig, J. J.; Morse, J. W., Interaction of organic acids with carbonate mineral surfaces in seawater and related solutions. I. Fatty acid adsorption. Geochim. Cosmochim. Acta 1988, 52, 1667– 1678.

441

Chapter 15

Aerosol–Air Partitioning: Dry and Wet Deposition of Organic Pollutants

15.1 Origins and Properties of Atmospheric Aerosols Origins, Size Fractions, Concentrations, and Residence Times of Aerosols in the Atmosphere Chemical Composition of Aerosols 15.2 Assessing Aerosol–Air Partition Coefficients (KiPMa ) Field Data A Simple Quantitative Model for Describing Aerosol–Air Equilibrium Partitioning pp-LFERs for Estimating KiPMa Two Case Studies: Organic Pollutants in Urban Air 15.3 Dry and Wet Deposition Dry Deposition of Particle-Bound Compounds Wet Deposition of Gaseous and Particle Bound Compounds by Rainfall Dry versus Wet Deposition of Particle-Bound Compounds 15.4 Questions and Problems 15.5 Bibliography

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

442

Aerosol–Air Partitioning: Dry and Wet Deposition of Organic Pollutants

Atmospheric aerosol particles, commonly referred to plainly as aerosols, play a key role in various important processes occurring in the atmosphere. They affect climate by absorbing and scattering solar radiation and by acting as nuclei for cloud and ice formation. Aerosols are also the locus of heterogeneous chemical and photochemical reactions, as they reduce visibility and contribute significantly to air pollution, particularly in urban regions (see Seinfeld and Pandis, 2006; Matthias, 2011; Calvo et al., 2013). Furthermore, as highlighted in this chapter, association of organic pollutants, particularly semi-volatile chemicals (SVOCs), with aerosols may strongly affect their long-range transport, distribution, and fate in the environment (see Bidleman, 1988). Particularly small aerosols (2.5 μm). The size of a particle is expressed as its aerodynamic diameter, which is the diameter calculated from its mass assuming a sphere with a density of 1 g cm−1 . In practice, however, when collecting aerosols by fibers, filters, denuders, electrostatic precipitators, or combinations thereof, the measurements often only provide information on the total mass of particulate matter (PM) smaller than a given size, most commonly 8). But in general, kN will be too small to be of environmental significance. For the more reactive N–monoalkyl carbamates, however, the neutral reaction might have to be considered. From the few compounds for which kN values have been reported (Table 22.9), and by using our chemical intuition, we may conclude that the relative importance of the neutral reaction increases (i.e., the INB value decreases) with increasing reactivity.

Hydrolytic Reactions of Carboxylic and Carbonic Acid Derivatives

691

From our discussion of neutral ester hydrolysis, we recall that the relative importance (relative to addition of the nucleophile) of the dissociation of the alcohol moiety decreases with decreasing pKa of the corresponding alcohol. Therefore, since in the elimination step the dissociation of – O–R3 is always rate limiting, the kN /kB ratio will decrease with increasing goodness of the leaving group (i.e., decreasing pKa ). Furthermore, any group or substituent that increases the acidity of the N–H proton will have a much greater impact on kB than on kN (only electronic effect). From Table 22.9, we see that for moderately reactive carbamates, INB values around 7 are found. Consequently, for these and for less reactive compounds, neutral hydrolysis has to be considered at ambient pH values. Finally, we point out that activation energies for the base-catalyzed hydrolysis of carbamates span a wide range of between 50 and 100 kJ mol–1 (Christenson, 1964). Quantitative Structure-Reactivity Considerations: Hammett and Brønsted Relationships In order to understand available kinetic data better and potentially allow estimation of reaction rates of new compounds within a compound class, it is useful to develop quantitative relationships between the structures of individual compounds and their reactivities. Such relationships are particularly suited for situations in which the standard free energies of activation, Δ‡ G0 , vary systematically with chemical structure changes. In these cases, we may try to apply linear free-energy relationships (LFERs) similarly to what we have done to evaluate or estimate equilibrium constants (e.g., acidity constants in Chapter 4). The use of such LFERs to relate kinetic data for a given reaction of a series of structurally related compounds hinges on the ability to express quantitatively the electronic and steric effects of structural moieties of the reactants on Δ‡ G0 . When dealing with hydrolytic reactions of carboxylic and carbonic acid derivatives, in general, both types of effects have to be taken into account. In this context, it has to be pointed out that quantification of steric effects is much more difficult as compared to electronic effects (see Exner, 1988). In the following discussion, we confine ourselves to cases in which electronic effects predominate. For approaches in which steric effects are included, particularly the approach introduced by Taft and co-workers, we refer to the literature (Taft, 1956; Pavelich and Taft, 1957; MacPhee et al., 1978; Williams, 1984). Hammett Relationship. In our first example, we evaluate the influence of meta and para ring substituents on the base-catalyzed hydrolysis of substituted benzoic acid ethyl esters. In this case, structural changes associated with adding a substituent –X are made at points in the structure that are well away from the reaction site. As discussed earlier (Fig. 22.6), in this case, we can assume a tetrahedral activated complex exhibiting a negative charge that is not significantly delocalized into the ring system:

O

HO

O

O

OC2H5

+ HO– X

– ǂ

O

OC2H5

+ C2H5OH

X

X

692

Hydrolysis And Reactions With Other Nucleophiles

Thus, intuitively, we expect that through an inductive effect, electron-withdrawing ring substituents (–X) will stabilize the negatively charged activated complex relative to the uncharged ground state; that is, they will decrease Δ‡ G0 as compared to the unsubstituted compound and, therefore, increase k relative to kH (X = H). Conversely, an electron-donating substituent exerts the opposite effect. As discussed in Chapter 4, the inductive effect of aromatic substituents in meta or para positions may be quantitatively expressed by the Hammett σjmeta and σjpara substituent constants (see Table 4.8). It comes as no surprise that, in this case, where we deal primarily with inductive effects, the rate constants of the base-catalyzed hydrolysis of meta- and para-monosubstituted benzoic acid ethyl esters can be related successfully by the Hammett equation: ( log

k kH

) = ρ σjm,p

(22-27)

For compounds with more than one substituent, the Hammett equation has the form: ( log

k kH

) =ρ

∑

σjm,p

(22-28)

j

From the linear fit of the data shown in Fig. 22.8, a ρ value of 2.55 (Exner, 1988) is obtained at 25◦ C, indicating a substantial influence of the substituents on the reaction rate. For example, a nitro group in the meta or para position increases the rate of hydrolysis by a factor of 100. It should be pointed out that the data shown in Fig. 22.8 were not obtained in pure water, but in a mixture of ethanol and water (85:15), for which the most complete data set is available. A quite similar value (ρ = 2.47) is 2.0

p–NO2 m–NO2

log ( k ) = 2.55 σ j kH

log ( k ) kH

1.0 p–Br p–I

0

m–CH3

m–Br m–Cl p–Cl

m–OCH3 O

p–CH3

C

OC2H 5

p–OCH3 H=

–1.0 Figure 22.8 Effects of substituents on the base-catalyzed hydrolysis of benzoic acid ethyl esters in ethanol: water (85:15) at 25◦ C. Relative reaction rates are correlated with Hammet σj constants. Data from Tinsley (1979).

p–NH2

–0.8

–0.4

p 0 0.4 σ j-constant

m 0.8

Hydrolytic Reactions of Carboxylic and Carbonic Acid Derivatives

693

found for the same reaction in acetone/water (3:2, Exner, 1988), but a significantly smaller value (ρ = 1.77) is derived in pure water (Drossman et al., 1988). These findings are consistent with the results obtained for the base-catalyzed hydrolysis of meta and para substituted benzoic acid methyl esters (R = CH3 , instead of CH2 CH3 , in Fig. 22.6), for which at 25◦ C, the corresponding ρ values are 2.38 in acetone/water (3:2, Exner, 1988) and 1.67 in pure water (Smith and Menger, 1969; Steinberg and Lena, 1995), respectively. The fact that ρ is much smaller in water as compared to organic solvent/water mixtures can be rationalized by the better ability of the solvent, water, to polarize the carboxyl bond, which leads to a reduction of the substituent effect. As already pointed out in Chapter 21 (Table 21.1), one has to be very careful when trying to extrapolate hydrolysis rate data from nonaqueous to aqueous solutions. Furthermore, we should note that ρ is also a function of temperature since, as implied by Eq. 21-40 (Chapter 21), the effect of temperature on the rate constant is different for compounds exhibiting different Δ‡ H0 (or Ea ) values, the relative size of which is determined by the type of substituent(s) present. For example, in the case of the hydrolysis of the benzoic acid ethyl esters in ethanol/water (85:15), ρ decreases from 2.55 at 25◦ C to 2.13 at 50◦ C (Exner, 1988).

O O

X

III

O O

X IV

Since in the case of the benzoic acid methyl and ethyl esters, we left the alcohol moiety (–O–R) invariant, ρ primarily reflects a structural effect on the kB1 term in Eq. 22-26. Although the dissociation of the leaving group may also determine the overall kB term, it is the same within a series considered. For substituted benzoic acid phenyl esters (III) and acetic acid phenyl esters (IV), however, the situation is somewhat different, since the substituents exhibit effects on kB1 as well as on kB3 . These effects are paralleling each other. For example, an electron-withdrawing substituent increases kB1 by an inductive effect and, at the same time, it renders the alcohol moiety a better leaving group (it decreases the pKa of the alcohol). If the dissociation of the leaving group (i.e., the phenolate species) is rate determining, we would expect a ρ value similar to or even greater than that found for the benzoic acid ethyl esters previously discussed (although there is an oxygen between the phenyl group and the carbonyl carbon which renders the electronic effect of substituents on kB1 smaller as compared to the benzoic acid ethyl esters). However, the observed ρ value derived from kB values of some substituted phenyl acetic acid esters (IV) in aqueous solution is modest, being on the order of 1 (Drossman et al., 1988). This result implies that the effect of electron-withdrawing substituents in enhancing the combined kB expression (Eq. 22-26) is even less than the impact of the same substituents on kB1 rates for benzoic acid methyl and ethyl esters. This suggests that for the phenyl esters, the rate of dissociation of the leaving group is not significant in determining the overall reaction rate. This example nicely demonstrates how LFERs may be useful for prediction of rate constants and may also give valuable hints regarding rate-determining steps. Brønsted Relationship. As seen, the Hammett equation can, in principle, be applied to both equilibria and rate data. This implies that in certain cases it is feasible to relate rate constants to equilibrium constants when both reflect similar effects of a given structural moiety. In a general form, a rate-equilibrium relationship can be written in terms of the corresponding changes in free energies of activation and of equilibriation: ΔΔ‡ G0 = β ΔΔr G0

(22-29)

694

Hydrolysis And Reactions With Other Nucleophiles

where the first Δ indicates the incremental differences between the Δ‡ G0 and Δr G0 values, respectively, of a series of structurally related compounds. In terms of rate and equilibrium constants, Eq. 22-29 can be expressed as: K k = β log kH KH

log

(22-30)

where the subscript H denotes a reference compound (e.g., the unsubstituted compound). A very common application of Eq. 22-30 is the use of acidity constants (Ka ) of a (sub)structural (sub)unit (e.g., the Ka of a leaving group) to relate rate constants for hydrolytic reactions of a series of compounds. In this case, Eq. 22-30 is commonly referred to as a Brønsted relationship and can be written as: log k = −β pKa + C

(22-31)

where C is the logarithm of the rate constant of the compound for which the corresponding pKa value is zero. An example in which rate constants are related to equilibrium constants involves the base-catalyzed hydrolysis of N-phenyl carbamates (Fig. 22.9). As previously discussed, these compounds hydrolyze by an elimination mechanism with the dissociation of the alcohol moiety being the rate-determining step. As shown in Fig. 22.9, by using the pKa ’s of the leaving groups (phenols and aliphatic alcohols), we find a nice relationship to the rates of these reactions which covers almost 10 orders of magnitude.

+6

4–NO2 4–CHO 4–CN 3–NO2 3–Cl 3–CHO 4–Cl H 4–Me 4–OCH3

R

+4

H N

=

om ar

R

ic

up

o gr

0

6

2

5

3 X, R′

)

–CH2–CH2Cl

ic

at

4

ph ali

(

–CH2–CCl3 –CH2–CF3 –CH2–CHCl2

=

R=

–2

R

log kB (M–1 s–1)

O

at

+2

gr

–4

ou p

Figure 22.9 Correlation (Brønsted plot) of base-catalyzed hydrolysis rates (log kB ) of carbamates as a function of the pKa of the alcohol moiety for a series of N-phenyl carbamates. Data from references given in Table 22.9.

O

–CH3 –CH2–CH3

log kB = – 1.15 pKa + 13.6

–6 6

8

10

12

14

pKa of alcohol moiety

16

Enzyme-Catalyzed Hydrolysis Reactions: Hydrolases

22.3

695

Enzyme-Catalyzed Hydrolysis Reactions: Hydrolases We conclude this chapter with a brief qualitative look at the strategies that microorganisms use to hydrolytically break down organic pollutants. A more detailed discussion and a more quantitative treatment of microbially mediated transformation reactions are given in Chapter 26. The goal of this section is to illustrate that microorganisms perform the same type of hydrolysis reactions that we have discussed in this chapter. The only difference is that they use special proteins (enzymes), in this case referred to as hydrolases, to promote reactant interactions and thereby lower the free energy of activation that determines the transformation rate (see Chapter 26, Fig. 26.6). Generally, an enzymatically catalyzed reaction is initialized by the formation of an enzyme:substrates complex, followed by the reaction (here the hydrolysis) to form an enzyme:products complex, which then detaches to the products including the regenerated enzyme. Hydrolases can lower the activation energy of reactions by several tens of kJ per mole, thereby speeding reaction rates by many orders of magnitude. Therefore, they can make hydrolysis reactions occur that, purely chemically, would be much too slow to lead to a significant transformation of a given compound under ambient conditions. Some of this reaction rate enhancement arises because hydrolases (and in general enzymes) form complexes with substrates. By holding the reacting chemical species in an advantageous orientation with respect to one another, the hydrolases facilitate substrate interaction (i.e., they lower the entropy of activation). Additionally, enzymes may include polar and charged structural components that can alter the electron densities of the bound reactants. This lowers the enthalpy of activation in that barriers are lowered to break existing bonds, and formation of new bonds is encouraged. Since hydrolysis is an important metabolic approach used by microorganisms to initiate transformations of natural and xenobiotic compounds under any environmental conditions, hydrolases are typically constitutive (i.e., always present), although their activity levels may be regulated. Hence, we can expect microbial hydrolysis to generally occur if a compound exhibits one or several hydrolyzable functional groups. For example, Wanner et al. (1989) were not surprised to see immediate biodegradation of some hydrolyzable insecticides with no lag period, after these compounds were spilled into the Rhine River.

H

H COOH

N

H2N O

Hydrolases Reacting by SN 2 Mechanisms

O N

H HS

glutathione (GSH)

COOH

H critical thiol moiety

Let us now have a look at a few representative examples of the large number of enzymes that catalyze hydrolysis reactions. We start out with two cases that induce SN 2 reactions. Our first example is the glutathione transferase, which facilitates the encounter of the tripeptide gluthatione (γ-glutamic acid-cysteine-glycine, GSH) with a compound with which GSH may react (Mannervik, 1985; Vuilleumier, 1997; Allocati et al., 2009). GSH contains a thiol moiety which, like other reduced sulfur species (Table 22.4), is a strong (soft) nucleophile which undergoes SN 2 reactions primarily with (soft) electrophiles such as saturated carbon atoms bound to good leaving groups (Section 22.1). For example, a series of alkyl halides and epoxides have been found to be

696

Hydrolysis And Reactions With Other Nucleophiles

transformed by GSH in the first step of biodegradation (Vuilleumier, 1997). This is the case for dichloromethane (Stucki et al., 1981; Kohler-Staub and Leisinger, 1985), which chemically hydrolyzes at an extremely slow rate (Table 22.2):

G SH

H

H

SN2

C Cl

G

Cl

S

Cl

CH 2

+ H + + Cl –

Here the hydrolase is also referred to as dehalogenase (Copley, 1998; de Jong and Dijkstra, 2003; Koudelakova et al., 2013). Formation of the GSH adduct (i.e., the compound formed when the two reactants are attached to one another) permits the attack of water on the previously chlorinated carbon, and since the resulting intermediate is not particularly stable in this case, it decomposes, releasing formaldehyde and regenerating glutathione in a reaction much like the dehydration of geminal diols:

G

S

CH 2

Cl

G

S

CH 2

H 2O

Cl –

"adduct"

G

S

H+

CH 2

OH

H+ G

S

CH 2

O

H

G SH

O

+

H

C

H

The overall result is equivalent to the hydrolysis of both of the original carbon– chlorine bonds: CH2 Cl2 + H2 O → CH2 O + 2H+ + 2Cl− In sum, the excellent bionucleophile, GSH, is used to get the reaction started, and subsequent hydrolysis steps cause it to go to completion. The process works well enough that some bacterial species (e.g., a Hyphomicrobium isolate) can grow on methylene chloride as its sole source of carbon (Stucki et al., 1981). This microorganism is also capable of degrading other dihalomethanes, CH2 BrCl, CH2 Br2 , and CH2 I2 (KohlerStaub and Leisinger, 1985). Other dehalogenases rely on moieties of amino acids like cysteine (Keuning et al., 1985; Scholtz et al., 1987a and b) or aspartic acid (Li et al., 1998; Copley 1998; Janssen et al., 2001) contained within the protein structure. Like GSH-transferases, these enzymes first form the enzyme adduct: Enz−Nu:− +

R−X → Enz−Nu−R + X− “adduct”

In a subsequent step, the enzyme adduct then detaches the alkyl group as an alcohol product. Sometimes, monohalogenated compounds act as growth inhibitors because the adduct formed is difficult to hydrolyze and thereby incapacitates the enzyme. However, assuming the adduct can be hydrolyzed, then the enzyme is prepared to serve again.

697

Enzyme-Catalyzed Hydrolysis Reactions: Hydrolases

L

H 2O O Zn2+

O

L

Zn2+

H

H

Zn2+

O Zn2+

Zn2+

Asp 301 H

H

L–

H N

O

O

O

H 2O O

P

H

O

H N

O

O

H

O

O

Figure 22.10 Proposed mechanism for the hydrolysis of phosphoric acid esters by phosphotriesterase. Adapted from Bigley and Raushel (2013).

Zn2+

P OR OR O

RO OR

OR OR

P

Asp 301 O

N H

Asp 301 O

A second example of a hydrolase initiating an SN 2 reaction, this time at a (hard) phosphorus atom (Eq. 22.13, case II), is the phosphotriesterase (PTE), one of several enzymes that hydrolyze phosphate and thiophosphate (thio)esters (Bigley and Raushel, 2013). As is the case for the base-catalyzed abiotic hydrolysis of phosphate esters, the attacking (hard) nucleophile is an OH– species coordinated to two Zn2+ . As shown shematically in Fig. 22.10, the reaction is additionally facilitated by the two Zn2+ species, one decreasing the electron density at the P-atom, the other one putting the carboxylate moiety of the aspartate amino acid in the right position. Carboxylic and Carbonic Acid Ester Hydrolases

hydroxyl group OH H N H

O

serine in a peptide chain mercapto group (thiol group) SH H N H

O

cysteine in a peptide chain

Anthropogenic compounds containing carboxylic or carbonic acid esters or other acid derivatives in their structures (e.g., amides, carbamates, ureas, see Fig. 22.4) are often readily hydrolyzed by microorganisms. To understand how enzymatic steps can be used to transform these substances, it is instructive to consider the hydrolases used by organisms to split naturally occurring analogs (e.g., fatty acid esters in lipids or amides in proteins). The same chemical processes, and possibly even some of the same enzymes themselves, are involved in the hydrolysis of xenobiotic substrates. In the following, we consider two illustrative examples, one where organisms use a hydroxy functionality of an amino acid as nucleophile operating in a similar way as the base-catalyzed hydrolysis discussed earlier (Fig. 22.6), and one where a metal ion plays a pivotal role.

We begin by considering the enzymes using the hydroxyl group of serine (Fersht, 1985) or, analogeously, the thiol of cysteine to initiate hydrolysis. The general process proceeds by the following steps (Fig. 22.11). First, the substrate associates with the free enzyme (I) in a position suited for nucleophilic attack. To improve the ability of the nucleophile to form a bond with the electron-deficient atom, other amino acids (e.g., histidine and aspartic acid) may assist in this and subsequent steps by proton transfers (this group of amino acids is often referred to as the “charge relay system”). This amounts to converting the serine or the cysteine to the more nucleophilic conjugate bases, RO– or RS– , respectively (see II in Fig. 22.11).

698

Hydrolysis And Reactions With Other Nucleophiles

Asp C

O "charge relay" system

O

H O

N N

His

O

H

O

R1 Ser

R1

binding

OH carboxylic acid

O

H 2O

I

deacylation

Asp

Asp

C

C

O

N

N

O

O

HO

H H

II

VI

R1

O

O R1

H N

O

OR2

N H

His

His

OR2

O Ser

Ser

acylation

O

Asp

Asp

C

C

O

N His

O H O N

O

H

V

R1

H

O

H

III

O R 2O

N

O

N

H

His

Ser

Ser

IV

H 2O

Asp O

C

O

N

Figure 22.11 Schematized reaction sequence showing the hydrolysis of an ester by a serine hydrolase (Fersht, 1985).

His

R2

O N

H

R1

O Ser

R1

O

OH

alcohol release

Enzyme-Catalyzed Hydrolysis Reactions: Hydrolases

699

Subsequently, the nucleophile attacks to form a tetrahedral intermediate (III), similar to what we saw previously in the chemical hydrolysis process (Section 22.2). Decomposition of this intermediate leads to the release of an alcohol, an amine, or another leaving group from the original compound. Continued processing involves enzymeassisted attack of water on the enzyme adduct (IV, again with the help of the charge relay system) and release of the acid compound. Experience with various carboxylic acid esters and amides shows that either initial attack (the “acylation” step shown from II → IV) or release of the acid compound (the “deacylation” step shown from IV → I) can be rate limiting, depending on the kind of compound hydrolyzed. For amides, the initial attack and release of an amine is often the slow step (Fersht, 1985), since these nitrogen compounds are very strong bases and thus poor leaving groups. In contrast, esters often have the deacylation steps as the bottleneck to reaction completion (Fersht, 1985). Since ionizable groups of various amino acids play critical roles in these hydrolysis reactions, such hydrolases exhibit some sensitivity to the medium pH. Generally, these enzymes operate best at nearneutral pHs, since more acidic conditions protonate the histidine and thereby negate its involvement. Another approach for hydrolysis of acid derivatives utilizes metal-containing hydrolases (see I in Fig. 22.12). In these enzymes, a metal, for example a zinc atom, is included in the active site of the enzyme (Fersht, 1985). The process begins with the association of the carbonyl oxygen (or its equivalent in other compounds) with a ligand position on this metal (II). This association with an electropositive metal atom causes the central atom (e.g., a carbonyl carbon in an ester) to be even more electron deficient. The result is a very susceptible position for attack by nucleophilic moieties, such as the carboxylate of a nearby glutamate. An anhydride-type tetrahedral intermediate is formed (III), resulting in the release of the alcohol portion of the original ester (IV). The new enzyme-acid complex is more suited to attack by water than the original compound. Thus attack by water on (V) ultimately leads to the severance of the acid’s covalent linkage to the glutamate (VI). Ligand exchange at the zinc permits the release of the acid product. As a result, this overall biological hydrolysis operates analogously to an acid-catalyzed abiotic reaction. Now recognizing that hydrolases use mechanisms parallel to abiotic “base” and “acid” catalysis mechanisms, we can anticipate how the rates of transformations of related xenobiotic compounds will vary. This may help us understand and/or develop predictive relationships between the rates of biological and comparable chemical hydrolyses as long as these processes are rate limited by similar mechanisms. Empirically, it is found that enzymes that catalyze hydrolysis are not always very selective within a structurally related group of xenobiotic compounds. This was noted for enzymes induced by various kinds of substrates including halides (Keuning et al., 1985; Scholtz et al., 1987a and b; Li et al., 1998), phenyl amides and ureas (Englehar et al., 1973), and phosphoric and thiophosphoric esters (Munnecke, 1976; Rosenberg and Alexander, 1979). With these remarks on enzyme catalyzed hydrolysis reactions, we conclude our discussion of hydrolytic reactions and other reactions involving nucleophilic species.

700

Hydrolysis And Reactions With Other Nucleophiles

H Zn2+

O H O

O C

R1

O

O

OH

Glu

C

R1

OR2

I H 2O

H 2O

OH

Zn2+

Zn2+

C

O

C

O

O O

OR2

R1

II

VI

R1

O

O

Glu

Glu

H+ acylation step

Zn2+

OH O

C

Zn2+

III

V

R1

OR2 O

O O Glu

IV

H+

H 2O R1 O

R 2OH

C O

O

Figure 22.12 Reaction sequence for hydrolysis of an ester by a zinccontaining hydrolase (Fersht, 1985).

R1

O

O

Zn2+

C

Glu

Glu

Questions and Problems

701

We should point out that we only took a close look at a few representative structural moieties that may undergo these types of reactions in the environment. Nevertheless, the general knowledge that we acquired in this chapter should put us in a much better position to evaluate the importance of such reactions for other functional groups that form part of environmental organic chemicals. Some additional examples of such functional groups are included in the following problem section.

22.4

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission.

Questions Q 22.1 Explain in words what a nucleophilic substitution reaction is. At what kind of atoms do such reactions primarily occur? What are the mechanisms and the corresponding rate laws of such reactions? Q 22.2 What are the major factors determining the rates of nucleophilic substitution reactions? In this context, Scott (2005) reports a pretty good LFER relating the neutral first-order hydrolysis rate constants (Eq. 21-2) between 1-adamantyl-X (1-Ad-X) and t-butyl-X ((CH3 )3 C-X): X

H

log kN (1-Ad-X) = 0.96 log kN (t-butyl-X) − 1.86 (number of chemicals = 6; including all halides; r2 = 0.99) H

H 1-adamantyl-X

Although one can assume that both types of compounds hydrolyze by an SN 1 mechanism, the 1-Ad-X compounds react about 2 orders of magnitude more slowly. Rationalize this finding. Q 22.3 Explain in words what a β-elimination reaction is. What is the difference between an E1- and an E2-mechanism? What is an E1CB mechanism? Give examples of compounds that react by E1-, E2-, and E1CB mechanisms. Q 22.4 Explain the terms hard and soft Lewis acids and bases.

702

Hydrolysis And Reactions With Other Nucleophiles

Q 22.5 Rank the following inorganic water constituents in order of increasing nucleophilicity with respect to substitution reactions at a saturated carbon atom. Comment on your sequence. Br− , OH− , NO−3 , CN− , CIO−4 , S2 O2− 3 , H2 O Q 22.6 Explain in words what the Swain-Scott relationship describes and discuss in which cases it may be applied. Q 22.7 Give four examples of good leaving groups. Q 22.8 Which structural and environmental factors favor an elimination mechanism over a nucleophilic substitution mechanism? Q 22.9 Inspection of Table 22.6 shows that the INB values for hydrolysis of trimethyl- and triethylphosphate are ≥ 10, whereas INB of triphenylphosphate is < 6. Explain these findings. Q 22.10 As can also be seen from Table 22.6, acid-catalyzed hydrolysis is unimportant for many phosphoric and triophosphoric acid triesters. Among the exceptions are diaxonon and diazinon (IAN = 6.4 and 5.7, respectively). Explain why. Q 22.11 When comparing the hydrolysis rate constants of a series of carboxylic acid esters (Table 22.7), it can be seen that the values for the acid-catalyzed reactions are all of the same magnitude, whereas the rate constants for the base-catalyzed reactions vary by several orders of magnitude. Explain these findings. Q 22.12 What do the terms IAN , IAB , and INB express? Q 22.13 How can dissolved metal species accelerate the hydrolysis of acid derivatives? Q 22.14 Rank the carbamates I – VI in order of increasing reactivity with respect to basecatalyzed hydrolysis. Comment on your order.

703

Questions and Problems

O N

O CH 3

O

H

CH 3

N CH 3

CH 3

I

II

O

O N

CH 3

O

N

O

O

H

H

NO 2

III

O2 N

IV

O N

O O

H

NO 2

N

O

NO 2

H V

VI

Q 22.15 Which strategies do microorganisms use to hydrolytically break down organic pollutants? What are the main differences compared to abiotic (chemical) hydrolysis reactions? Q 22.16 Ethylene dibromide (EDB, also 1,2-dibromoethane, BrCH2 CH2 Br) is a chemical that was used as a gasoline additive and a soil fumigant. What initial biodegradation product would you expect from this compound? Problems P 22.1∗ Some More Reactions Involving Methyl Bromide Estimate the half-life in days (with respect to chemical transformation) of methyl bromide (CH3 Br) present at low concentration (i.e., < 1 μM) in a homogeneous aqueous solution (pH = 7.0, T = 25◦ C) containing 100 mM Cl– , 2 mM NO−3 , 1 mM HCO−3 , and 0.1 mM CN– . In pure water at pH 7.0 and 25◦ C, the half-life of CH3 Br is 20 days (Table 22.3). P 22.2 What Happens to Trimethylphosphate in Seawater? The hydrolysis half-life of trimethylphosphate (CH3 O)3 PO, TMP) in pure water is 1.2 yr at 25◦ C and pH 7.0 (Table 22.6). A colleague in oceanography claims that

704

Hydrolysis And Reactions With Other Nucleophiles

in sterile seawater, he observed a half-life for TMP of only about 80 days at 25◦ C and pH 8. Is this result reasonable? What are the major initial products of the abiotic transformation of TMP in seawater? The major ion composition of seawater is given in Table 5.5. P 22.3 1,2-Dibromoethane in the Hypolimnion of the Lower Mystic Lake, Massachusetts Various studies suggest that in pure water, the major transformation reaction of the widely used pesticide, 1,2-dibromoethane (1,2-DBE, BrCH2 –CH2 Br), is neutral hydrolysis to yield the final product ethylene glycol (Roberts et al., 1993). Based on measurements at high temperatures, Jeffers and Wolfe (1996) have estimated a hydrolysis half-life of 6.4 years for 1,2-DBE at 25◦ C, corresponding to a kN value of 3.5×10–9 s–1 . The reported Arrhenius activation∑energy for this reaction is: Ea = 108 kJ – – – – – mol–1 . Estimate how large the concentration of [S2− n ](= [ S–S ] + [ S–S–S ] + [ S– – 2− S–S–S ]) species expressed as [Sn ] would have to be in the anoxic hypolimnion of Mystic Lake, Massachusetts at 10◦ C (Miller et al., 1998) in order to lower the half-life of 1,2-DBE by a factor of 100 as compared to the half-life determined by hydrolysis alone. Compare this calculated concentration with the actual measured concentration of S2− n given below.

Lower Mystic Lake characteristics pH = 6.8 [Cl– ] = 0.4 M [HS– ] = 3×10–3 ∑ [ S2− ] = 9×10–5 n

Assume that the initial reaction with the reduced sulfur species (HS− , S2− n ) present is an SN 2 reaction at one of the carbon atoms and not reductive debromination (a process that we discuss in Chapter 23). What products would you expect from the reaction of 1,2-DBE with the polysulfide species. P 22.4 Nucleophilic Substitution Reactions of Phosphate and Phosphorothionate Triesters under Sulfate Reducing Conditions Jans et al. (Gan and Jans, 2006 and 2007; Guo and Jans, 2006; Wu et al., 2006; SaintHilaire et al., 2011) investigated the abiotic transformation of a series of phosphate and phosphorothionate triesters in the presence of hydrogen sulfide (H2 S/HS– ) and of polysulfides (S2− n ) as they are found under sulfate-reducing conditions (see also Problem 22.3). For fenchlorphos, Wu et al. (2006) reported the following second– ◦ order rate constants for the reaction with HO– , HS– , and S2− n at 25 C: Cl

S (CH3O)2P

O

Cl Cl

fenchlorphos

kHO– = 1.6×10–2 M–1 s–1 kHS– = 1.3×10–3 M–1 s–1 kS2− = 1.6×10–2 M–1 s–1 n The rate constant for the neutral reaction (which was not reported) can be assumed to be similar and on the order of 1×10–7 s–1 . Is this a reasonable assumption? Calculate the half-life of fenchlorphos at pH 8 and 25◦ C (a) in the absence, and (b) in the presence of the sulfur species, assuming HS– and Sn2− concentrations of 1 and 0.1 mM, respectively. What product distribution would you predict in the two cases? Would you expect the same product distribution at 5◦ C? P 22.5 Hydrolysis of 2-Trifluoromethylphenol at Ambient pH and Temperature Many agrochemicals capable of enzyme inhibition are fluorine-stabilized analogues of the natural enzyme substrate (e.g., they exhibit a CF3 – instead of a CH3 – group,

705

Questions and Problems

see Key et al., 1997). Commonly, carbon-fluorine bonds are assumed to hydrolyze only very slowly under ambient conditions. One exception seems to be aromatic trifluoromethyl groups that are located in ortho-position to a phenol group such as in 2-trifluoromethylphenol. Reinscheid et al. (2006) evaluated the hydrolysis of 2-trifluoromethylphenol (2-TFMP, pKia = 8.95) in the temperature range 34 to 69◦ C. They also determined the pH-dependence in the pH-range between pH 5 and 9. They found that 2-TFMP hydrolyzed quantitatively to salicylic acid (no intermediates detected): OH

OH CF3

COO

H 2O / HO

2-trifluoromethyl-phenol (2-TFMP)

salicylate

At a given pH they observed first-order kinetics, and they found that log kobs increased linearly with pH up to pH 8 and then leveled off somewhat. At pH 7.4 and 37◦ C, they obtained a hydrolysis half-live of 6.9 h. The activation energy, Ea , determined at pH 7.4 was 105 kJ mol–1 . (a) Estimate the half-life of TFMP in groundwater at pH 6.4 and 7◦ C. Assume that the dissociated species, i.e., 2-trifluorophenolate, is formed instantly (see Section 4.3), and then slowly reacts in a unimolecular reaction as the rate-limiting step. Neglect the temperature dependence of the pKia value (Chapter 4.3) (b) What mechanism do you propose for the first step of the reaction (dissociation of the first fluorine atom)? Would you expect the other two isomers 3- and 4-TFMP to hydrolyze in the same manner? Explain your reasoning. P 22.6∗ Deriving Kinetic Parameters for Hydrolysis Reactions from Experimental Data Consider the hydrolysis of 2,4-dinitrophenyl acetate (DNPA), a compound for which the acid-catalyzed reaction is unimportant at pH > 2 (see Fig. 22.5). O O(H)

O

+

+ H2O / HO– NO2 2,4-dinitrophenyl acetate (2,4-DNPA)

O

NO2

NO2

(H)O

NO2 2,4-dinitrophenol

acetate

In a laboratory class, the time course of the change in concentration of DNPA in homogeneous aqueous solution has been followed at various conditions of pH and temperature using an HPLC method (Klausen et al., 1997). The concentrations determined as a function of time were:

706

Hydrolysis And Reactions With Other Nucleophiles

pH 5.0 a , T = 22.5◦ C Time (min) 0 11.0 21.5 33.1 42.6 51.4 60.4 68.9 75.5 a

pH 8.5, T = 22.5◦ C

[DNPA (μM)]

Time (min)

[DNPA (μM)]

100.0 97.1 95.2 90.6 90.1 88.5 85.0 83.6 81.5

0 4.9 10.1 15.4 25.2 30.2 35.1 44.0 57.6

100.0 88.1 74.3 63.6 47.7 41.2 33.8 26.6 17.3

Very similar results were also found at pH 4.0 and 22.5◦ C.

At pH 5, the following temperature dependence (Table below) was observed for kh : T (◦ C) 17.7 22.5 25.0 30.0

kh / s–1 3.1×10–5 4.4×10–5 5.2×10–5 7.5×10–5

(a) Determine the (pseudo-)first-order reaction rate constants, kh , for this reaction at pH 5 and pH 8.5, respectively, at 22.5◦ C. (b) Derive the rate constants for the neutral (kN ) and base-catalyzed (kB ) hydrolysis of DNPA at 22.5◦ C. (c) Derive the Arrhenius activation energy, Ea , for the hydrolysis of DNPA at pH 5. Is this Ea value also valid for pH 8? Explain your reasoning. P 22.7 Assessing the Hydrolysis Half-Life of the MTBE Transformation Product, tert-Butyl Formate Various studies on the fate of our companion, the gasoline additive methyl-t-butyl ether (MTBE), have shown that it can be oxidized to t-butyl-formate, which happens particularily in the atmosphere: CH3 –O–C(CH3 )3 → H–C(= O)–O–C(CH3 )3 MTBE TBF Church et al. (1999) have investigated the hydrolysis of TBF as a function of pH and temperature. The rate constants for the acid-catalyzed, neutral, and base-catalyzed reactions are given in Table 22.7 (R1 =H, R2 =C(CH3 )3 ). The corresponding Ea values are 60, 80, and 90 kJ mol–3 , respectively. Calculate the hydrolysis half-lives of TBF

Questions and Problems

707

(a) in an acidic rain drop (pH = 2.5, 5◦ C), (b) in surface water (pH = 8, 15◦ C), and (c) in an alkaline solution at pH 12 and 25◦ C. P 22.8 Neutral Hydrolysis of Substituted Benzyl Chlorides: Evaluating the Reaction Mechanism(s) Using the Hammett Relationship Among many other experimental data concerning hydrolysis reactions of alkyl halides, Scott (2005) reported the neutral hydrolysis rate constants given below for a series of substituted benzyl chlorides at 25◦ C. 3

2 1

4

X,R 5

3

Cl

2 1

+ H2O

4

X,R

6

5

OH + Cl– + H+

6

You wonder whether an analysis of the rate constants using a Hammett relationship (Eq. 22-28) would provide you with some hints on whether the reaction occurs by an SN 1 or SN 2 mechanism. Besides the “regular” Hammett constants given in Chapter 4 (Table 4.8) that are used to evaluate the electronic effects of substituents on the stabilization/destabilization of negative charges, you find a set of Hammett constants σ+j that have been derived to express substituent effects on the stabilization of radicals or positive charges. (a) For which substituents (type, position) are the σj - and σ+j -values significantly different? (b) Which set of σj -values do you use to evaluate the rate data given below? Plot the rate data against these σj -values. Discuss the result. Substituent (X,R)

σj

σ+j

log kh (s–1 )

H (unsubstituted) 3–CH3 4–CH3 4–C(CH3 )3 4–OCH3 3–Cl 4–Cl 3–NO2 4–NO2

0 –0.06 –0.16 –0.20 –0.24 0.37 0.22 0.73 0.78

0 –0.07 –0.31 –0.26 –0.78 0.40 0.11 0.67 0.79

–4.88 –4.74 –3.34 –4.00 +0.45 –5.71 –5.15 –6.36 –6.57

P 22.9 Base-Catalyzed Hydrolysis of Diethyl Phenylphosphates: Mechanistic Considerations Using the Hammett and Brønsted Relationships It is commonly assumed that the base-catalyzed hydrolysis of substituted dialkyl (i.e., dimethyl or diethyl) phenyl phosphates occurs by nucleophilic attack of OH– at the phosphorus with the phenolate being the leaving group (Eq. 22-14):

708

Hydrolysis And Reactions With Other Nucleophiles

–

2

O (RO)2P

O

O

3

1

4 6

5

–

+ HO

kB

O (RO)2P

–

O

+

X

1

6 5

X

2

+ H+

3 4

Furthermore, it has been postulated that, when considering a series of such compounds, the relative reactivity (i.e., the relative magnitude of the kB values) is determined primarily by the relative electrophilicity of the phosphorus atom and not by the relative “goodness” of the leaving group (i.e., the phenolates). Is this hypothesis correct? Try to answer this question by evaluating the Hammett (Eq. 22-28) and Brønsted (Eq. 22-31) relationships that you can derive from the kB values reported by van Hooidonk and Ginjaar (1967) for a series of meta- and para-substituted diethyl phenyl phosphates. Do you include all compounds in the Brønsted relationship? If not, which ones do you exclude and why? Second-Order Rates Constants, kB , and pKia Values of the Phenol Moieties for a Series of Monosubstituted Diethyl (R=C2 H5 ) Phenyl Phosphates at 25◦ C. The Hammett constants are given in Table 4.8. Substituent X (and position) 4–OCH3 4–C2 H5 3–CH3 H 3–OCH3 4–Cl 4–Br

log kB a (kB in M–1 s–1 )

pKia b (0.1 M KCl)

–3.55 –3.49 –3.45 –3.33 –3.21 –2.94 –2.90

10.12 10.18 10.09 9.89 9.65 9.35 9.27

Substituent X (and position) 3–Cl 3–Br 4–COCH3 3–NO2 4–CN 4–NO2

log kB a (kB in M–1 s–1 )

pKia b (0.1 M KCl)

–2.81 –2.78 –2.49 –2.19 –2.19 –1.96

9.13 9.06 8.01 8.39 7.85 6.99

a

Data from van Hooidonk and Ginjaar (1967). Experimental values in 0.1 M KCl determined by van Hooidonk and Ginjaar (1967). These values differ somewhat from the values given for some of the compounds in the Appendix C. b

P 22.10 Synthesizing the “Right” Carbamates You work in the chemical industry and you are asked to synthesize two different carbamates of either Type I or Type II (see margin). One carbamate (compound A) should have a hydrolysis half-life of approximately 1 month at 25◦ C and pH 8.0, while the hydrolysis half-life of the other one (compound B) should be about 10 months at 25◦ C and pH 9.0. You assume that only the base-catalyzed reaction (Fig. 22.7) is important at the pH’s of interest, and you search the literature for kB values for these type of compounds. For some Type I compounds, as well as for some Type II compounds, you find the following data. Why are the effects of substituents on kB so much larger for Type I as compared to Type II compounds? What are the structures of the molecules that you are going to synthesize in order to get the desired half-lives?

Questions and Problems

3

3

2

O

4

R, X

1

H

N

5

O

709

2

O H3C

6

4

R, X

1

N

5

O

6

type II

type I

Carbamates of Type I and Type II and Hammett substituent constants σj (Table 4.8)

Substituents (R,X) –H (unsubstituted) 4–OCH3 4–CH3 3–NH2 4–Cl 3–Cl 3–NO2 4–NO2 3–N+ (CH3 )3 3–CH3 –4–NO2 a

Type II kB (M–1 s–1 )

Type I kB (M–1 s–1)

0 –0.24 –0.16 –0.16 0.22 0.37 0.73 0.78/1.25 a 0.88

7.5×10–5

2.5×101 3.0×101

2.8×10–5

4.2×102 1.8×103 1.3×104 2.7×105

3.9×10–4 2.5×10–4 3.3×10–4

σ−j

P 22.11 Estimating the Hydrolysis Half-Life of Methyl-3,4-Dichlorobenzenesulfonate in Homogeneous Aqueous Solution A colleague of yours who investigates the fate of benzene sulfonates and benzene sulfonate esters in natural waters is interested in the stability of methyl-3,4dichlorobenzene sulfonate (MDCBS) in aqueous solution. Because he has not read Chapter 22 of Environmental Organic Chemistry, he asks you to help him estimate the hydrolysis half-life of this compound at pH 7 in water at 25◦ C and at 5◦ C. In the literature you find rate constants for the neutral hydrolysis of some substituted methyl benzene sulfonates at 25◦ C, and you learn that the activation energies of these reactions are on the order of 85 kJ mol–1 (Robertson, 1967). Using the following data, estimate the neutral hydrolysis half-life of MDCBS at 25◦ C and 5◦ C. Postulate the most likely reaction mechanism for the hydrolysis of MDCBS. Do you expect that the reaction will be pH dependent in natural waters? Cl

O S X

O

O O

CH3

Cl

S O MDCBS

O CH3

710

Hydrolysis And Reactions With Other Nucleophiles

First-Order Rate Constants for the Neutral Hydrolysis of Some Substituted Methyl Benzenesulfonates in Aqueous Solution at 25◦ C a

Substituent(s)

kN ×106 (s–1 )

4–CH3 4–OCH3 3–CH3 –4–CH3

8.0 6.0 6.6

a

4

R,X

Data from Robertson (1967).

Kim et al. (2010 and 2011) reported kB values determined for the base-catalyzed hydrolysis of a series of substituted phenyl benzoates (I), phenyl phenyl carbonates (II), and phenyl phenyl thiocarbonates (III) in 80 mol % H2 O/ 20 mol % DMSO. Some rate constants are given in the following table.

O

I 3 4

O

R,X O

O II

3 4

S O

9.4 52.7 62.5

4–Br 3–NO2 4–NO2

P 22.12 Evaluating the Base-Catalyzed Hydrolysis of Phenyl Benzoates, Phenyl Phenyl Carbonates, and Phenyl Phenyl Thiocarbonates

3

O

Substituent(s)

kN ×106 (s–1 )

R,X

Substituent(s)

Σσj /Σσ−j

type I log kB (M–1 s–1 )

type II log kB (M–1 s–1 )

type III log kB (M–1 s–1 )

H 4–Cl 3–COCH3 4–COOC2 H5 4–NO2 3–NO2 , 4–NO2

0 0.22 0.38 0.45/0.66 0.78/1.25 1.51/1.98

–0.35 n.d. 0.26 0.49 1.13 2.00

0.86 1.32 1.33 1.54 2.15 2.90

–0.28 0.11 0.15 0.23 0.67 1.38

O

(a) Rationalize the differences in reactivity between the three different compound classes.

III

(b) Establish the Hammett relationships for the three compound classes and discuss your findings in light of the rate-limiting steps of the base-catalyzed hydrolysis of this type of acid derivatives (Eq. 22-26).

22.5

Bibliography Allocati, N.; Federici, L.; Masulli, M.; Di Ilio, C., Glutathione transferases in bacteria. Febs J. 2009, 276(1), 58–75. Barnard, P. W.; Vernon, C. A.; Llewellyn, D. R.; Welch, V. A.; Bunton, C. A., The reactions of organic phosphates. Part V. The hydrolysis of triphenyl and trimethyl phosphates. J. Chem. Soc. 1961, (JUL), 2670–2676. Bender, M. L.; Homer, R. B., Mechanism of alkaline hydrolysis of p-nitrophenol Nmethylcarbamate. J. Org. Chem. 1965, 30(11), 3975–3978.

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715

Chapter 23

Redox Reactions 23.1 Introduction 23.2 Evaluating the Thermodynamics of Redox Reactions Processes Determining the Redox Conditions in the Environment Evaluating the Thermodynamics of Redox Reactions of Organic Pollutants One-Electron Reduction Potentials of Organic Compounds Box 23.1 Calculating the Reduction Potential of an Aqueous Hydrogen Sulfide (H2 S) Solution as a Function of pH and Total Hydrogen Concentration Box 23.2 Calculating Free Energies of Reaction Using Half-Reaction Potentials EH0 (W) 23.3 Examples of Chemical Redox Reactions in Natural Systems Factors Determining the Rate of Redox Reactions Reduction of Nitroaromatic Compounds (NACs) Reduction of Polyhalogenated C1 – and C2 –Alkanes Oxidation of Phenols and Anilines 23.4 Examples of Enzyme-Catalyzed Redox Reactions Enzyme-Catalyzed Oxidations Using Oxygen as a Co-Substrate Initial Transformation by Addition of a Carbon-Containing Moiety Reductions Involving Nucleophilic Electron-Rich Bioreactants 23.5 Questions and Problems 23.6 Bibliography Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

716

Redox Reactions

23.1

Introduction Many major pathways by which organic chemicals are transformed in the environment include oxidative and reductive steps, especially when we consider photochemical and biologically mediated transformation processes (Chapters 24 to 26). Several of these reactions may, however, also occur abiotically in the dark. We should note that some of the reactions we discuss in this chapter may be catalyzed by biological molecules (e.g., iron porphyrins, quinoid compounds) released from organisms (e.g., after cell lysis). This has led to a certain confusion with respect to the use of the term “abiotic” for such reactions. For the following discussion, we adopt the definition of Macalady et al. (1986), who suggest that a reaction is abiotic if it does not directly involve the participation of metabolically active organisms. Of course, this does not imply that “abiotic” redox reactions are not heavily influenced by biological (particularly microbial) activity, since the availability of suitable reactants for electron transfer reactions is determined largely by biological processes. At this point, we should first ask ourselves how we can recognize whether an organic compound has been oxidized or reduced during a reaction. As we briefly discussed in Chapter 21 (Fig. 21.3), the easiest way to do that is to check whether there has been a net change in the oxidation state(s) of the elements involved in the reaction, particularly the elements C, N, or S. For example, if a chlorine atom in a trichloromethyl substitutent is replaced by a hydrogen atom, as is observed in the transformation of DDT to DDD: (+I)

(+III)

H CHCl 2

H CCl3 (–I)

Cl

Cl DDT

+ Cl–

(–I)

+ H + + 2 e– Cl

(23-1)

Cl DDD

then the oxidation state of the carbon atom at which the reaction occurs changes from +III to +I. The oxidation states of all other atoms remain the same. Hence, conversion of DDT to DDD requires a total of two electrons and one proton (charge balance) to be transferred from an electron donor to DDT. This type of reaction is termed a reductive dechlorination. We note that the species that donates the electrons is oxidized during this process. Thus, in any electron transfer reaction, one of the reactants is oxidized while the other one is reduced. We, therefore, term such reactions redox reactions. Since our focus is on the organic pollutant, we speak of an oxidation reaction if the pollutant is oxidized or of a reduction reaction if the pollutant is reduced. Let us now compare the reaction previously discussed (Eq. 23-1) with another reaction that we discussed in Section 22.1, dehydrochlorination. Here, as is illustrated by the transformation of DDT to DDE (Eq. 23-2), the change in oxidation state of one of the carbon atoms involved in the reaction is compensated by the change in oxidation state of the adjacent carbon atom.

Introduction

Cl

(+III)

(+II)

717

Cl

H CCl3 (–I)

(0)

+ HO –

Cl

+ H 2O + Cl–

Cl

Cl

(23-2)

Cl DDE

DDT

Hence, dehydrochlorination requires no net electron transfer from or to the compound, and therefore, we shall not consider this reaction to be a redox reaction. However, another elimination reaction, the dihalo-elimination, is a redox reaction. As an example, we consider the dichloro-elimination of hexachloroethane (HCA) to tetrachloroethene (perchloroethylene, PCE), a reaction that has been observed to occur in groundwater systems (e.g., Roberts and Gschwend, 1994): Cl Cl Cl

(+III)

C C (+III)

HCA

Cl Cl Cl

+ 2 e–

Cl

(+II)

Cl

C C Cl

(+II)

Cl

+ 2 Cl–

(23-3)

PCE

We realize that during this reaction, the oxidation states of both carbon atoms are altered by –1. Hence, as in our first example (Eq. 23-1), the reduction of HCA to PCE requires two electrons to be transformed from an electron donor to HCA. Let us now take a brief look at some important redox reactions of organic pollutants that may occur abiotically in the environment. We first note that rather few functional groups are oxidized or reduced abiotically. This contrasts with biologically mediated redox processes by which organic pollutants may be completely mineralized to CO2 , H2 O, and so on. Table 23.1 gives some examples of functional groups that may be involved in chemical redox reactions. We discuss some of these reactions in detail later in this chapter. In Table 23.1, only overall reactions are indicated, and the species that act as a sink or source of the electrons (i.e., the oxidants or reductants, respectively) are not specified. Therefore, no information about the actual reaction mechanisms are given that may consist of several reaction steps. Furthermore, in the environment, it is often not known which species actually act as electron donors or acceptors in an observed redox reaction of a given organic pollutant. Such reactions may involve electron transfer mediators that are present only at low concentrations, but that are continuously regenerated by chemical and/or biological processes controlling the actual bulk electron donors present in the system (Fig. 23.1, e.g., Schwarzenbach et al., 1997; Van der Zee and Cervantes, 2009; Sposito, 2011; Zhang and Weber, 2013; Kl¨upfel et al., 2014; Sander et al., 2015). In contrast to the reactions discussed in Chapter 22, we are in a much more difficult position with respect to quantification of reaction rates. Consequently, when treating redox reactions we frequently have to content ourselves with a rather qualitative description of such processes. This may include an assessment of the environmental (redox) conditions allowing a reaction to occur spontaneously, and of the relative reactivities of a series of related compounds in a given system.

718

Redox Reactions

Table 23.1 Examples of Some Simple Redox Reactions that May Occur Chemically in the Environment a reduction oxidized species

oxidation

reduced species

Eq. number

Change in Oxidation State of Carbon Atom(s) R COOH

+ 2 H+ + 2 e–

R CHO + H2O

(23-4)

O

O + 2 H+ + 2 e–

HO

(23-5)

C X (X=Cl,Br,I) + H+ + 2e–

C C

C H

(X=Cl,Br,I) + 2e–

C C

OH

+ X–

(23-6)

+ 2 X–

(23-7)

X X

2 X C

(X=Cl,Br,I)+ 2e–

C C

+ 2 X–

(23-8)

Change in Oxidation State of Nitrogen Atom(s) R

+ 6 H+ + 6 e–

NO2

X R X

R X

NH

NH2 + 2 H2O

X

N N

R

R

NH

X

+ 2H+ + 2e–

R X

+ 2H+ + 2e–

R

NH

NH

X

2

R X

(23-9)

R

(23-10)

X

NH2

(23-11)

Change in Oxidation State of Sulfur Atom(s) R S S R + 2 H+ + 2 e–

2 R SH

(23-12)

R S R' + H2O

(23-13)

O R S R' + 2 H+ + 2 e–

a

Some reactions are reversible (indicated by double arrows), whereas others are irreversible under environmental conditions. The dotted arrow indicates that, in principle, a reaction is possible but that there is no indication that it occurs abiotically in the dark.

Evaluating the Thermodynamics of Redox Reactions

e.g. CCl4

e.g. HO Fe(II)porph "Surf-Fe(II)" Cob(I)alamin

Cl2C=CCl2 ArNO2 oxidized organic pollutant

Figure 23.1 Schematic representation depicting the importance of electron transfer mediators as well as the concurrence of microbial and abiotic processes for reductive transformations of organic pollutants. Adapted from Schwarzenbach et al. (1997).

23.2

e.g.

reduced

OH SH OH

Cl2C=CHCl CHCl3 ArNH2 abiotic

e.g. CO2

H+ S(s) FeOOH(s) SO2– 4

reduced

oxidized

mediator

bulk electron donor

oxidized e.g. OH O Fe(III)porph "Surf-Fe(III)" Cob(II,III)alamin O

SH

719

reduced e.g. {CH2O} H2 FeCO3(s) HS– FeS Fe(s)

abiotic or biological

Evaluating the Thermodynamics of Redox Reactions For many of the reactions discussed in Chapter 22 (e.g., hydrolysis), the free energy change, Δr G (Eq. 21-8), of the reaction considered is negative under typical environmental conditions. These reactions occur spontaneously. Therefore, we did not discuss the thermodynamics of such reactions extensively. As already pointed out in Chapter 21, when looking at redox reactions of organic pollutants, the situation is quite different. Here, depending on the redox conditions prevailing in a given (micro)environment, an electron transfer to or from an organic compound may be thermodynamically feasible or not. In other words, depending on the redox conditions (which are predominantly determined by microbially mediated processes), electron acceptors (oxidants) or donors (reductants) that may react abiotically in a thermodynamically favorable reaction with a given organic chemical may or may not be present in sufficient abundance. Furthermore, as seen when discussing hydrolysis reactions, a reaction may also not occur at a significant rate for kinetic reasons. Nevertheless, thermodynamic considerations are very helpful as a first step in evaluating the redox conditions under which a given organic compound might undergo an oxidation or reduction reaction. Furthermore, since most of the redox reactions in the environment are biologically mediated, the evaluation of how much energy an organism may derive from a given reaction may provide very useful insights to the sequences in which important biological redox reactions occur in the environment, and the kinds of organisms expected under given conditions (see Thauer et al., 1977; Hanselmann, 1991; Schink, 1997). Processes Determining the Redox Conditions in the Environment Before we proceed to evaluate the thermodynamics of redox reactions of organic pollutants under environmental conditions, we need to make a few remarks about microbial processes that determine the redox conditions in the environment. We can get a general idea about the maximum free energies that microorganisms could gain from catalyzing specific redox reactions under various (standard) conditions by inspecting the standard reduction potentials, EH0 of the half-reactions given in

720

Redox Reactions

Table 23.2 Standard Reduction Potentials and Average Standard Free Energies of Reaction (per Electron Transferred) at 25◦ C of Some Redox Couples that Are Important in Natural Redox Processes (the reactions are ordered in decreasing EH0 (W) values) a Half-reaction Oxidized Species (1a) (1b) (2) (3) (4) (5) (6) (7) (8a) (8b) (9) (10) (11a) (11b) (12)

EH0 (V)

Reduced Species O2 (g) + 4 H+ + 4 e− = 2 H2 O O2 (aq) + 4 H+ + 4 e− = 2 H2 O 2 NO−3 + 12 H+ + 10 e− = N2 (g) + 6 H2 O MnO2 (s) + HCO−3 (10−3 ) + 3 H+ + 2 e− = MnCO3 (s) + 2 H2 O NO−3 + 2 H+ + 2 e– = NO−2 + H2 O NO−3 + 10 H+ + 8 e– = NH+4 + 3 H2 O FeOOH(s) + HCO−3 (10–3 M) + 2 H+ + e– = FeCO3 (s) + 2 H2 O CH3 COCOO– (pyruvate) + 2 H+ + 2 e– = CH3 CHOHCOO– (lactate) HCO−3 + 9 H+ + 8 e– = CH4 (aq) + 3 H2 O CO2 (g) + 8 H+ + 8 e– = CH4 (g) + 2 H2 O + – – SO2− 4 + 9 H + 8 e = HS + 4 H2 O S(s) + 2 H+ + 2 e– = H2 S(aq) 2 H+ + 2 e– = H2 (aq) 2 H+ + 2 e– = H2 (g) 6 CO2 (g) + 24 H+ + 24 e– = C6 H12 O6 (glucose) + 6 H2 O

EH0 (W) (V)

+1.23 +0.81 +1.19 +0.77 +1.24 +0.74 +0.53 b +0.85 +0.43 +0.88 +0.36 −0.05 b −0.19 +0.21 −0.20 +0.17 −0.24 +0.25 −0.22 +0.14 −0.27 +0.08 −0.33 0.00 −0.41 −0.01 −0.43

Δr G0 (W)∕n c (kJ mol–1) −78.3 −74.3 −72.1 −50.7 b −41.6 −35.0 +4.8 b +17.8 +19.3 +23.6 +20.9 +26.0 +31.8 +40.0 +41.0

a

Most of the electron transfer reactions involving these redox couples are biologically mediated. Data from Thauer et al. (1977) and Stumm and Morgan (1995). b These values correspond to [HCO−3 ] = 10–3 M. c n = number of electrons transferred.

Table 23.2. We recall from Chapter 21 (Eqs. 21-17 to 21-21) that these standard reduction potentials actually reflect the free energies of the given reaction with molecular hydrogen (pH2 = 1 bar) as the electron donor or proton ({H+ } = 1) as the electron acceptor, respectively; that is, they are expressed relative to the standard hydrogen electrode (SHE, see also Fig. 21.4). Furthermore, using the Nernst equation (Eq. 2120), we can calculate (standard) reduction potentials at environmentally more realistic conditions (i.e., pH 7, [HCO−3 ] = 1 mM, [Cl− ] = 1 mM, etc.), which we denote as EH0 (W). Finally, we can calculate the standard free energy of the half-reaction per electron transferred by (Eq. 21-18): Δr G0 (W)∕n = −FEH0 (W)

(23-14)

On earth, photosynthetic harvesting of solar energy is the main cause of nonequilibrium redox conditions. In the process of photosynthesis, organic compounds exhibiting reduced states of carbon, nitrogen, and sulfur are synthesized, and at the same time, oxidized species including O2 (oxic photosynthesis) or oxidized sulfur species (anoxic photosynthesis), are produced. Using glucose as a model organic compound, we can express oxic photosynthesis by combining Eqs. (12) and (1) in Table 23.2. Since, by convention, all reactions are expressed as reductions (see Chapter 21), we have to take the reversed form of Eq. (1). Furthermore, because we are looking at the

Evaluating the Thermodynamics of Redox Reactions

721

overall process, it is convenient to write the reaction with a stoichiometry corresponding to the transfer of one electron: 1∕4 CO2 (g) + 1∕4 H2 O ⇌ 1∕24 C6 H12 O6 + 1∕4 O2 (g) The standard free energy change per electron transferred, Δr G0 (W)/n, of the above photosynthesis reaction can now be simply derived from Table 23.2 by adding the Δr G0 (W)/n value of reaction (12) (+41.0 kJ mol−1 ) and reversed reaction (1) (+78.3 kJ mol−1 ): Δr G0 (W)/n = +119.3 kJ mol−1 . Thus, on a “per electron basis”, under standard conditions (pH 7), we have to invest 119.3 kJ mol−1 to (photo)synthesize glucose from CO2 and H2 O. In our standard redox potential picture using EH0 (W) values, this is equivalent to promoting one mole of electrons from a potential of +0.81 to −0.43 V (see Table 23.2). The chemical energy stored in reduced chemical species (including organic pollutants) can be utilized by organisms that are capable of catalyzing energy yielding redox reactions. For example, from Table 23.2 we can deduce that in the oxidation of glucose [reversed reaction (12)], oxygen is the most favorable oxidant (i.e., electron acceptor) from an energetic point of view, at least if O2 is reduced all the way to H2 O (which is commonly the case in biologically mediated processes). The Δr G(W)/n value for the reaction of glucose with O2 (reversed photosynthesis reaction) is, of course, −119.3 kJ mol−1 . The next “best” electron acceptors would be NO−3 (if converted to N2 ), then MnO2 (s), and so on, going down the list in Table 23.2. Amazingly, the chemical reaction sequence given in Table 23.2 (which is based on standard free energy considerations) is, in essence, paralleled by a spatial and/or temporal succession of different microorganisms in the environment. In other words, in a given (micro)environment, the organisms that tend to be dominant are those capable of utilizing the “best” electron acceptors available, where the “best” electron acceptor is the one exhibiting the highest reduction potential. These microorganisms then in turn determine the redox conditions in that (micro)environment. This sequential utilization of electron acceptors can be seen if we look at the dynamics of some dissolved redox species along the flow path of a confined contaminant plume in the ground (Fig. 23.2). For simplicity, we assume a situation where we have a constant input of reduced (e.g., organic compounds, NH+4 ) and oxidized species (e.g., O2 , NO−3 , SO2− 4 ). As is shown in Fig. 23.2, natural or synthetic organic compounds (the major electron donors) are degraded over the whole length of the plume. As long as there is molecular oxygen present, aerobic respiration takes place. This includes the oxidation of organic compounds and NH+4 (to NO−3 ) and the consumption of O2 . We should point out that in aerobic respiration, oxygen not only plays the role of a terminal electron acceptor, but it is also a co-substrate in many important biologically catalyzed reactions (see Section 23.4). This is the reason why one usually makes such a sharp distinction between oxic, suboxic and anoxic conditions (see also Chapter 26). Once the oxygen is consumed, denitrification is observed until nitrate is virtually absent. In the region where denitrification occurs, one often observes the reductive dissolution of oxidized manganese phases [e.g., MnO2 (s), MnOOH(s)], which may

722

Redox Reactions

dump site waste soil

contaminant plume

groundwater flow concentration

organic compounds, NH4+ SO42– O2

H 2S NO

aerobic Figure 23.2 Variation in concentrations of important dissolved redox species along the flow path of a contaminant plume in groundwater. This sequence results in several zones of characteristic microbial metabolism and corresponding redox conditions.

aerobic respiration

O2

CH4

anaerobic conditions denitrification

H2O NO–3

in addition:

– 3

MnO2

sulfate reduction 2–

N2 SO4

methanogenesis

H2S CO2 CH4

Mn2+ FeOOH

Fe2+

or may not be biologically catalyzed. Under those conditions, iron is still present in oxidized forms [e.g., FeOOH(s)]. Then, a marked decrease in redox potential occurs when only electron acceptors are left in significant abundance that exhibit low reduction potentials (see Table 23.2). This redox sequence has led to a somewhat different terminology in that one speaks of the oxic (aerobic), suboxic (denitrification, manganese reduction), and anoxic conditions. Processes involving electron acceptors exhibiting a low redox potential include, in sequence: iron reduction, sulfate reduction, fermentation, and methanogenesis. The temporal or spatial succession of redox processes illustrated in Fig. 23.2 for a groundwater case is also observed in other environments in which access to oxygen and other electron acceptors is limited. Examples include sediment beds and poorly mixed lakes and ocean basins. Finally, we should point out that, in certain cases, the apparent redox sequence may be reversed when following, for example, a plume because the availability of stronger oxidants may increase with increasing distance from a landfill or hazardous waste site. For a more detailed discussion of the biogeochemical processes that determine the redox conditions in natural systems, we refer to the literature (e.g., Tratnyek et al., 2011). Evaluating the Thermodynamics of Redox Reactions of Organic Pollutants Let us now come back to the question of how to assess whether or not a given organic compound may, in principle, undergo a redox reaction in a given environmental

Evaluating the Thermodynamics of Redox Reactions

723

system. For such an assessment, we need to know the standard reduction potentials of the half-reactions involving the compound of interest and its oxidized or reduced transformation product, and of the environmental oxidant/reductant couple involved. The standard reduction potentials of some organic redox couples are given in Table 23.3. As is the case for the reduction potentials given in Table 23.2, many of the half-reactions involving organic pollutants do not occur reversibly at an electrode surface, so that we would not be able to measure the corresponding EH values using a galvanic cell as depicted in Fig. 21.4. Hence most of the reduction potentials given in Table 23.3 are calculated from thermodynamic data, such as (estimated) standard free energies of formation (Δf G0 (aq)) of the various species involved in the half-reaction (see Chapter 21). Since we often do not know the oxidant or reductant, we need to assign an EH value to the environmental system we are considering. Unfortunately, unlike the situation with proton transfer reactions where we may use pH as a master variable, it is usually not possible to assign an unequivocal EH value to a given natural water (Stumm and Morgan, 1996). Many environmentally significant redox processes are slow and, therefore, we cannot assume equilibrium between all redox couples present. That also means that measurements of redox potentials of natural waters using an inert electrode and a reference electrode are often difficult to interpret, inasmuch as many important redox pairs do not show reversible electrochemical behavior at the electrode surface. This is particularly true for more oxidizing environments (aerobic conditions, denitrifying conditions) since the electrode does not respond to redox couples involving oxygen or inorganic nitrogen species. Under more reducing conditions, EH measurements may be of some value, because there are often certain redox couples present to which the electrode does respond. Such couples include manganese species (MnIII , MnIV /MnII ), iron species (FeIII /FeII ), and certain organic compounds (e.g., quinones/hydroquinones). When measuring redox potentials in the field as well as in the laboratory, the SHE is often not used as a reference electrode for practical reasons. The most common reference electrodes are the saturated calomel electrode (SCE, EH0 = +0.24 V at 25◦ C) and the silver–silver chloride electrode (EH0 = +0.22 V at 25◦ C). The measured EH0 potentials are, however, easily converted to the hydrogen scale by adding the appropriate value of the reference electrode (e.g., +0.24 V in the case of SCE) to the measured value. Owing to the difficulties in assigning a meaningful EH value to a given natural system, it is helpful to use the EH0 (W) values of the most important biogeochemical redox processes (Table 23.2 and Fig. 23.3) as a framework for evaluating under which general redox conditions a given organic compound might undergo a certain redox reaction. Let us illustrate this point with a few examples. By inspecting Fig. 23.3, we can see that hexachloroethane may be reduced to tetrachloroethene [reaction 1 in Table 23.3] under any environmental redox conditions. The reduction of nitrobenzene to aniline [reaction 9 in Table 23.3] is only possible at redox conditions typical for environments in which iron reduction, sulfate reduction, or fermentation occurs. Aniline may be oxidized to azobenzene [reverse reaction 12 in Table 23.3] under aerobic, denitrifying, and manganese reducing conditions. In the subsurface where pollutants may be transported through various redox zones, nitrobenzenes may first get reduced to the corresponding anilines, and then may be converted to azobenzenes upon reaching more oxidizing environments. Finally, as already pointed out earlier (Fig. 23.1), some

724

Redox Reactions

Table 23.3 Standard Reduction Potentials and Average Standard Free Energies of Reaction (per Electron Transferred) at 25◦ C of Some Organic Redox Couples in Aqueous Solution with Reactions Ordered by Decreasing EH (W) values a half-reaction 0

oxidized species

reduced species

EH (V)

EH (W) (V)

0

ΔrG0 (W) / n (kJ mol–1)

(1)

Cl3C CCl3 + 2 e–

=

Cl2C CCl2 + 2 Cl–

+0.95

+1.13

–109.0

(2)

CBr4 + H+ + 2e–

=

CHBr3 + Br–

+0.89

+0.83

–80.1

(3)

CCl4 + H+ + 2e–

=

CHCl3 + Cl–

+0.79

+0.67

–64.7

(4)

CHBr3 + H+ + 2e–

=

CH2Br2 + Br–

+0.67

+0.61

–58.9

(5)

Cl2C

=

Cl2C CHCl + Cl–

+0.70

+0.58

–56.0

(6)

CHCl3 + H+ + 2e–

=

CH2Cl2 + Cl–

+0.68

+0.56

–54.0

+0.68

+0.56

–54.0

CCl2 + H+ + 2e–

Cl6

Cl5

+ H+ + 2e–

=

(8)

Cl + H+ + 2e–

=

+ Cl–

+0.54

+0.42

–40.5

(9)

NO2 + 6H+ + 6e–

=

NH2 + 2H2O

+0.83

+0.42

–40.5

+0.70

+0.28

–27.0

(7)

(10)

O

O

+ 2H+ + 2e–

+ Cl–

=

HO

OH

=

H3C S CH3 + H2O

+ 0.57

+ 0.16

– 15.4

2

+ 0.31

– 0.10

+ 9.7

O (11)

H3C S CH3 + 2H+ + 2e–

(12)

N N

+ 4H+ + 4e– =

O

NH2 O

(13)

CH3 S CH3 + 2H+ + 2e– O

=

H3C S CH3 + H2O

+ 0.17

– 0.24

+ 23.2

(14)

R S S R + 2H+ + 2e– (cystine)

=

2 R SH (cysteine)

+ 0.02

– 0.39

+ 37.6

a b c

Estimated from thermodynamic data of Dean (1985), Vogel et al. (1987), Roberts et al. (1996), and Totten and Roberts (2001). [H+ ] = 10–7 , {Cl– } = 10–3 , {Br– } = 10–5 . n = number of electrons transferred.

Evaluating the Thermodynamics of Redox Reactions

a EH0(w)

organic compounds

(volt)

Ox Cl3C–CCl3

electron transfer (ET)–mediators

Red

Ox

Red

Cl2C=CCl2

725

oxidants / reductants Ox

Red

HS•

HS–

O2

H2O

1.0

CBr4

CHBr3

–

2 NO3 CCl4 Cl2C=CCl2 0.5

CHCl3

N2

CHCl3 Cl2C=CHCl CH2Cl2

MnO2 (s)

NO2

NH2

O H3C–S–CH3

H3C–S–CH3

–

NH4

NO3

FeIIIPorph

–

NO2

NO3

Cob(III)alamin

MnCO3 (s)

–

+

Cob(II)alamin FeIIPorph

0.0

N=N

2

NH2

NOMOX

α–FeOOH(s) α–Fe2O3(s) Cl2C=CCl2 –0.5

NO2

Cl2C=CCl + Cl– NO2

–

Cob(II)alamin

FeOOH (s)

NOMred

Fe2+ (10–5 M) Fe2+ (10–5 M)

O2

O2. -

2–

HS–

S(s)

HS–

SO4

R-S-S-R (cystine) Fe3O4 (s) – HCO3 Cob(I)alamin

FeCO3 (s)

Fe2+ (10–5 M)

2 R-SH (cysteine) Fe2SiO4 (s) CH2O Fe0 (s)

Figure 23.3 Selection of environmentally relevant redox couples including organic pollutants such as nitroaromatic and halogenated compounds, as well as examples of electron transfer mediators and important natural bulk reductants. The values given represent reduction potentials at pH 7 at equal (except otherwise indicated) concentrations of the redox partners, but at environmental concentrations of the major anions involved: [HCO−3 ] = [Cl– ] = 10–3 M; [Br– ] = 10–5 M; Porph = porphyrin.

naturally occurring chemical species may act as electron transfer mediators (middle bar in Fig. 23.3). Of primary importance are complexed (e.g., Strathmann, 2011), adsorbed (e.g., Gorski and Scherrer, 2011; Luan et al., 2013; Zhang and Weber, 2013) and structural iron species present in clay minerals (e.g., Neumann et al., 2011; Gorski et al., 2013; Sander et al., 2015), as well as natural organic matter constituents (primarily quinone/hydroquinone couples, Uchimiya and Stone, 2009; Aeschbach et al., 2011; Zhang and Weber, 2013; Kluepfel et al., 2014). Among all redox couples, the

726

Redox Reactions

Fe(III)/Fe(II) couple is particularly interesting, since depending on the chemical environment (i.e., type of ligand(s)), it may assume almost any redox potential between − 0.5 and + 0.8 V (Strathmann, 2011). Thus, depending on its chemical speciation, iron may serve as an oxidant or as a reductant. This is also one of the reasons why iron is such an important metal in mediating electron transfers in biological systems. At this point, we might wonder how reasonable it is to use EH0 (W) values as given in Tables 23.2 and 23.3 for assessing whether or not a reaction will occur spontaneously in a given natural system. The species involved will, of course, not be present at standard concentrations. To evaluate this problem, let us compare the EH value of a 10−4 M aqueous hydrogen sulfide (H2 S) solution at pH 8 with the EH0 (W) value of reaction 10 in Table 23.2 (−0.27 V). The calculated value (see Box 23.1) is −0.18 V, which is still in the same “ball park”. Of course, if we want to evaluate the free energy of reaction of a redox reaction involving redox couples that exhibit very similar EH0 (W) values, we need to take into account the actual concentrations (activities) of the species involved. An example demonstrating how to calculate the free energy of reaction, Δr G, of a redox reaction from the corresponding half reaction reduction potentials is given in Box 23.1. One-Electron Reduction Potentials of Organic Compounds Except for the iron(III)/iron(II) couple [reaction (6) in Table 23.2], so far we have considered reduction potentials of half reactions with an overall transfer of an even number of electrons (i.e., 2, 4, 6, etc.). However, in many abiotic multi-electron redox processes, particularly if organic compounds are involved, the actual electron transfer occurs by a sequence of one-electron transfer steps (Eberson, 1987). The resulting intermediates formed are often very reactive, and they are not stable under environmental conditions. In our benzoquinone example used in Chapter 21 (Eq. 21-11), BQ is first reduced to the corresponding semiquinone (SQ), which is then reduced to HQ:

O

O

+ H+ + e–

HO

BQ

O

+ H+ + e–

HO

SQ

OH

(23-15)

HQ

Each of these subsequent one-electron steps has its own EH0 (W) value. We denote the reduction potential for the transfer of the first electron by EH1 (W) and for the transfer of the second electron by EH2 (W): BQ + H+ + e− ⇌ SQ; +

−

SQ + H + e ⇌ HQ;

EH1 (W) = +0.10 V

(23-16)

EH2 (W)

(23-17)

= +0.46 V

1 2 (W) and Em7 (W) for We note that in the literature one often finds the notation Em7 1 2 EH (W) and EH (W).

From these values, we see that the free energy change is much less negative [smaller EH0 (W) value] for the transfer of the first electron to BQ as compared to the transfer of the second electron to SQ.

Evaluating the Thermodynamics of Redox Reactions

727

Box 23.1 Calculating the Reduction Potential of an Aqueous Hydrogen Sulfide (H2 S) Solution as a Function of pH and Total Hydrogen Concentration The Nernst equation for reaction 10 in Table 23.2 is: EH = EH0 −

{H S} 0.059 V log 2+ 2 2 {H }

(1)

where EH0 = 0.14 V. Since H2 S dissociates in aqueous solution: H2 S ⇌ HS− + H+ ;

pKa1 = 7.0 at 25◦ C

(2)

Neglecting {S2− } since pKa2 is >14, the H2 S concentration at a given pH is (see Chapter 4, Eq. 4-59): {H2 S} =

1 {H S} 1+Ka1 ∕{H+ } 2 tot

(3)

Substitution of EH0 = 0.14 V and Eq. 3 into Eq. 1 yields the desired Nernst equation: EH ({H2 S}tot , pH, 25◦ C) = +0.14 V−

{H2 S}tot 0.059 V log + 2 {H }[{H+ } + Ka1 ]

(4)

By setting {H2 S}tot = 10–4 , {H+ } = 10–8 , and Ka1 = 10–7 , one obtains an EH value of – 0.18 V. For describing the EH value of a hydrogen sulfide solution, instead of reaction 10 in Table 23.2, we could also use the redox couple involving S(s) and HS– (instead of H2 S): S(s) + H+ + 2e− = HS− ;

EH0 = −0.06 V

(5)

The corresponding Nernst equation is then: EH ({H2 S}tot , pH, 25◦ C) = −0.06 V−

Ka1 {H2 S}tot 0.059 V log + 2 {H }[{H+ } + Ka1 ]

(6)

The results from Eq. 4 and Eq. 6 must be identical if H2 S, HS– , and S(s) are all at equilibrium with one another. We can see that this is true by noting that [(–0.059 V)/2] log Ka1 = +0.20 V. Using this in Eq. 6, we transform it to Eq. 4: EH ({H2 S}tot , pH, 25◦ C) = (−0.06 +0.20) V− = + 0.14 V−

{H2 S}tot 0.059 V log + 2 {H }[{H+ } + Ka1 ]

{H2 S}tot 0.059 V log + 2 {H }[{H+ } + Ka1 ]

728

Box 23.2

Redox Reactions

Calculating Free Energies of Reaction Using Half-Reaction Potentials EH0 (W)

Evaluate whether the reduction of azobenzene (AzB) to aniline [reaction 12 in Table 23.3] by H2 S (assuming that S(s) is formed) occurs spontaneously under (a) standard environmental conditions (“W” conditions), and (b) at pH 9 and {H2 S}tot = 10–4 and with {AzB} = 10–8 and {An} = 10–6 . Calculate the corresponding Δr G values. What would be the {An}/{AzB} ratio at equilibrium at pH 9 and 10–4 M H2 S assuming an initial azobenzene concentration of 5×10–7 M? The Δr G of a reaction is related to the difference, EH , of the reduction potentials of the corresponding half reactions by Eq. 21-16 (Chapter 21): Δr G = −nFΔEH

(1)

where ΔEH = EH (oxidant) – EH (reductant). Thus, if ΔEH is positive, then Δr G is negative, and the reaction may occur spontaneously. Using the EH0 (W) values, the Nernst equations for the two half reactions are (see also Box 23.1): {An}2 0.059 V log 4 {AzB}({H+ }∕10−7 )4

(2)

{H2 S}tot 0.059 V log + −7 2 ({H }∕10 )[({H+ }∕10−7 ) + Ka1 ∕10−7 ]

(3)

EH (AzB∕An) = −0.10 V − EH (S(s)∕H2 S) = −0.27 V −

Setting the activity of H+ in the standard state to 10–7 , Ka1 also has to be divided by 10–7 in Eq. 3. Ka1 /10–7 = ({H+ }/10–7 ){HS– }/{H2 S}. (a) At standard environmental conditions, ΔEH is given by the difference of the EH0 (W) values, that is: ΔEH (W) = EH0 (W) (AzB∕An) − EH0 (W)(S(s)∕H2 S) = ( − 0.10) − ( − 0.27) = +0.17 V Therefore, the reaction: AzB + 2H2 S ⇌ 2 An + 2 S(s)

(4)

occurs spontaneously from left to right at standard environmental conditions. The Δr G0 (W) value at these conditions is (4 electrons are transferred): Δr G0 (W) = −(0.17 V)(4)(96.5 kJ mol−1 V−1 ) = −65.6 kJ mol−1 (b) Insertion of the corresponding activities of the various species into Eqs. 2 and 3 yields the EH values for the conditions previously specified: (10−6 )2 0.059 V = −0.16 V log −8 4 (10 )(10−9 ∕10−7 )4 (10−4 ) 0.059 V log −9 EH (S(s)∕H2 S) = −0.27− = −0.21 V 2 (10 ∕10−7 )(10−9 ∕10−7 + 10−7 ∕10−7 ) EH (AzB∕An) = −0.10 −

(5) (6)

Evaluating the Thermodynamics of Redox Reactions

729

In this case, ΔEH = EH (AzB/An) – EH (S(s)/H2 S), and we find: ΔEH = ( − 0.16) − ( − 0.21) = +0.05 V Therefore: Δr G = (0.05 V) (4) (96.5 kJ mol−1 V−1 ) = −19.3 kJ mol−1 Hence, the reaction Eq. 4 still occurs from left to right, although it is much closer to equilibrium as compared to standard environmental conditions. Since the H2 S concentration is much higher than the AzB concentration, it remains more or less constant during the reaction. The EH value of the system is therefore determined by EH (S(s)/H2 S) = –0.21 V (see Eq. 6). At equilibrium, EH (AzB/An) has to be equal to –0.21 V (i.e., ΔEH = 0). Insertion of this value and {H+ } = 10–9 into Eq. 2 above yields after some rearrangement: log

{An}2 ≅ 0, {AzB}

i.e.,

{An}2 ≅1 {AzB}

By denoting the equilibrium concentration of An as x, and with an initial AzB concentration of 5×10–7 M, we may write (one AzB produces two An): x2 −7

(5×10 ) −

1 x 2

= 1 or

x2 + 12 x − 5×10−7 = 0

Solving this equation yields about 10–6 for {An} and about 10–12 for {AzB}. Therefore, virtually all AzB is reduced to An.

Conversely, there is more energy required to oxidize HQ to SQ as compared to the oxidation of SQ to BQ. In general, we can assume that the formation of an organic radical is much less favorable from an energetic point of view, as compared to the formation of an organic species exhibiting an even number of electrons. From this, we may conclude that the first one-electron transfer between an organic chemical and an electron donor or acceptor is frequently the rate-limiting step. Thus, when we are interested in relating thermodynamic and kinetic data (e.g., through LFERs), we need to consider primarily the EH values of this rate-limiting step, that is, the EH value of the first one-electron transfer (see Section 23.3). We should be aware that if this first step is endergonic (i.e., positive Δr G value for 1 e– -transfer), the overall reaction may still be exergonic (i.e., negative Δr G value for 2 e– -transfer), and the whole reaction may proceed spontaneously (Eberson, 1987). Therefore, for our evaluation, regardless of whether or not a given redox reaction is possible under given conditions, we need to consider the EH values of the overall reaction.

730

Redox Reactions

Finally, we should note that the value of a multi-electron transfer half reaction is given by the average of the respective standard one-electron reduction potentials. This is easy to rationalize when recalling that the overall standard free energy of reaction of a sequence of reaction steps is given by the sum of the Δr G0 (or Δr G0 (W)) values of each step. Hence, we may write: Δr G0 = Δr G1 + Δr G2 + ....... + Δr Gn =

n ∑

Δr G k

(23-18)

k=1

Substitution of Δr G0 by – nFEH0 and Δr Gk by – nFEHk into Eq. 23-18 and rearrangement yields: n

EH0 =

1∑ k E n k=1 H

(23-19)

and, similarly: n

EH0 (W) =

1∑ k E (W) n k=1 H

(23-20)

Thus, the EH0 (W) value of the overall reaction Eq. 23-15 (BQ + 2 H+ + 2 e– = HQ) is (0.10 V + 0.46 V)/2 = 0.28 V.

23.3

Examples of Chemical Redox Reactions in Natural Systems Factors Determining the Rate of Redox Reactions Having considered the reduction potentials of “overall” half reactions, we have learned how to assess whether, from a thermodynamic point of view, a given compound may undergo oxidation or reduction to yield a specific product in a given environment. We now have to tackle the more difficult part, the kinetics of such reactions. As pointed out earlier, a compound may react with several different electron acceptors (oxidants) or electron donors (reductants), and the relative importance of such species present in a given system may be strongly influenced by complex biogeochemical processes. Furthermore, depending on the type of compounds and the oxidants or reductants involved, various reaction steps, sorption/desorption to/from unreactive sorbents (e.g., NOM), adsorption to a reactive surface, actual electron transfer, or regeneration of oxidants or reductants, may determine the overall transformation rate. Thus, in different systems, not only the absolute rates but also the relative rates of oxidation or reduction of a series of compounds may be quite different, even if the compounds are structurally closely related. Therefore, in contrast to the reactions discussed in Chapter 22, prediction of rates of redox reactions in natural systems is rather difficult. Nevertheless, knowledge from studies in well-defined model systems may help us to develop a framework for assessing pathways and rates of redox reactions of organic chemicals in more complex systems. Before we illustrate this approach by some examples, we first need to make some general remarks on the factors that determine the kinetics of redox reactions. As already pointed out in Section 23.2, the oxidative or reductive transformation of an organic compound very often occurs in sequential one-electron transfer steps

Examples of Chemical Redox Reactions in Natural Systems

731

(Eberson, 1987), where the transfer of the first electron determines the overall transformation rate. Therefore, we should be particularly interested in those compound-specific properties that are relevant for this first one-electron reaction. In a very simple way, we may picture a one-electron transfer reaction (e.g., the transfer of the first electron from a reductant R to an organic compound (e.g., an organic pollutant P) schematically as: P +R

(P + R)

starting materials

precursor complex

PR

P

R

transition state

P

+ R

(23-21)

products

In this context, one often speaks of an inner-sphere mechanism if there is a strong electronic coupling between R and P in the transition state, and conversely, of an outer-sphere mechanism, if the interaction is weak (Eberson, 1987). Furthermore, we point out that by exchanging P and R, Eq. 23-21 would describe an oxidation of the organic pollutant. From Eq. 23-21, we see that we may divide a one-electron transfer into a series of steps (maybe somewhat artificially). First, a precursor complex (PR) has to be formed; that is, the reactants have to meet and interact. Therefore, electronic as well as steric factors determine the rate and extent at which this precursor complex formation occurs. Furthermore, in many cases, redox reactions take place at surfaces, and therefore, the sorption behavior of the compound may also be important for determining the rate of transformation. In the next step, the actual electron transfer between P and R occurs. The activation energy required to allow this electron transfer to happen depends strongly on the “willingness” of the two reactants to lose and gain, respectively, an electron. Finally, in the last steps of reaction sequence Eq. 23-21, a successor complex may be postulated which decays into the products. In the following, we try to illustrate these general points by discussing two specific types of reduction reactions, namely the reduction of aromatic nitro groups (Eq. 9 in Table 23.3) and the reductive dehalogenation of polyhalogenated C1 – and C2 – compounds (Eqs. 1 to 6 in Table 23.3). These two cases represent two very different types of reactions. In the first case, the transfer of the first electron is reversible, whereas in the second case, it is irreversible and involves the breaking of a bond. In the latter case, therefore, one speaks of a dissociative electron transfer. Furthermore, compounds undergoing reductive dehalogenation may also react by a two electron transfer mechanism which may yield different products as compared to the one-electron transfer reaction. We have chosen two examples representing reductive transformations of organic pollutants, since chemical oxidations involving oxidants other than reactive species formed by photochemical processes (Chapter 25) or reactions involving enzymes (Section 23.4), are somewhat less important in natural systems in contrast to “engineered” systems (e.g., in water treatment, see, e.g., Crittenden et al., 2012; von Sonntag and von Gunten, 2012). We will, however, come back to some chemical oxidation reactions occurring in natural systems. Reduction of Nitroaromatic Compounds (NACs) Aromatic nitro groups (ArNO2 ) are present in many environmentally relevant chemicals including pesticides, dyes, and explosives (Chapter 3). As is illustrated

732

Redox Reactions

by nitrobenzene (Table 23.3, Fig. 23.3), reduction to the corresponding amino compounds is thermodynamically feasible under redox conditions below about +0.4 V. Hence, it is not surprising that reduction of NACs has been observed in many anaerobic soils and sediments (see Zhang and Weber, 2013). In most cases, the corresponding amino compounds (IV in Eq. 23-22) were found as the major reduction products, although stable intermediates (i.e., the nitroso(II) and the hydroxylamine(III) compounds) are formed during reduction of an aromatic nitro group: ArNO2 I

+ 2e – + 2H+

ArNO

– H2O

+ 2e – + 2H+

II

ArNHOH

+ 2e – + 2H+

III

– H2O

ArNH2

(23-22)

IV

In laboratory model systems using reduced DOM constituents (Dunnivant et al., 1992), Fe(II) adsorbed to iron (hydr)oxides (Klausen et al., 1995), or zero-valent iron metal (Agrawal and Tratnyek, 1996) as reductants, the nitroso- and, particularly, the hydroxylamino compounds have been observed as reaction intermediates, but were ultimately also converted to the corresponding amino-compounds. From a practical point of view, reduction of NACs is of great interest for two reasons. First, the amino compounds formed may exhibit a considerable (eco)toxicity, and, therefore, may be of even greater concern as compared to the parent compounds. Additionally, the reduced products may react further with natural matrices, in particular, with natural organic matter, thus leading to “bound residues” (see section on oxidations below). Let us now turn to some kinetic considerations of NAC reduction. As an illustrative example, we consider the time courses of nitrobenzene (NB) concentration in 5 mM aqueous hydrogen sulfide (H2 S) solution in the absence and presence of natural organic matter (Fig. 23.4). As is evident, although reduction of NB by H2 S to nitrosobenzene and further to aniline (Eq. 23-22) is very favorable from a thermodynamic point of view (see Fig. 23.3), it seems to be an extremely slow process. However, when dissolved organic matter (DOM) is added to the solution, reduction occurs

5 mM H2S blank

Figure 23.4 Reduction of nitrobenzene (NB) in 5 mM aqueous hydrogen sulfide solution in the absence (▴) and presence ( !) of DOM (Hyde County, 66 mg DOC L–1 ) at pH 7.2 and 25◦ C: Plot of ln ([NB]/[NB]0 ) versus times. [NB]0 and [NB] are the concentrations at time zero and t, respectively. Adapted from Dunnivant et al. (1992).

ln ([NB] / [NB]0)

0.0

slope = –kR

–1.0

5 mM H2S + DOM

NO2 –2.0 NB –3.0

0

100

200 300 time t (h)

400

500

733

Examples of Chemical Redox Reactions in Natural Systems

at an appreciable rate. In order to understand these findings, some general kinetic aspects of redox reactions using NACs as model compounds should be recognized. First, the transfer of the first electron is in many cases the rate-limiting process in the overall reduction or oxidation of an organic pollutant. In the case of NACs at ambient pH (i.e., pH 6 – 9), the transfer of the first electron yields a nitroaromatic radical anion ∙− ArNO∙− 2 (the pKa values of ArNO2 radicals are well below 5; Neta and Meisel, 1976): ArNO2 + e− ⇌ ArNO−2 ;

EH1 (ArNO2 )

(23-23)

where EH1 (ArNO2 ) denotes the one-electron standard reduction potential of the halfreaction Eq. 23-23 at pH ≥ 6. Since for NACs, the formation of the radical anion is reversible, values of EH1 (ArNO2 ) can be measured, for example by pulse radiolysis, and are available for a variety of such compounds (see examples given in Table 23.4; more values can be found in Bylaska et al., 2011). Inspection of Table 23.4 shows that substituents that stabilize the nitroradical anion make the reduction potential more positive whereas electron donating groups lead to more negative potentials relative Table 23.4 Names, Abbreviations, and One-Electron Reduction Potentials (EH1 (ArNO2 ); Eq. 22-23) of a Series of Substituted Nitrobenzenes Compound

Abbreviation

2,4,6-Trinitrotoluene 2-Amino-4,6-dinitrotoluene 4-Amino-2,6-dinitrotoluene 2,4-Diamino-6-nitrotoluene 2,6-Diamino-4-nitrotoluene 2,4-Dinitrotoluene 2,6-Dinitrotoluene Nitrobenzene 2-Methylnitrobenzene 3-Methylnitrobenzene 4-Methylnitrobenzene 2-Chloronitrobenzene 3-Chloronitrobenzene 4-Chloronitrobenzene 2-Acetylnitrobenzene 3-Acetylnitrobenzene 4-Acetylnitrobenzene 1,2-Dinitrobenzene 1,3-Dinitrobenzene 1,4-Dinitrobenzene 3-Aminonitrobenzene 4-Aminonitrobenzene

TNT 2-A-4,6-DNT 4-A-2,6-DNT 2,4-DA-6-NT 2,6-DA-4-NT 2,4-DNT 2,6-DNT NB 2-CH3 -NB 3-CH3 -NB 4-CH3 -NB 2-Cl-NB 3-Cl-NB 4-Cl-NB 2-Ac-NB 3-Ac-NB 4-Ac-NB 1,2-DNB 1,3-DNB 1,4-DNB 3-NH2 -NB 4-NH2 -NB

a b

Values from references cited in Hofstetter et al. (1999). Values from Hofstetter et al. (1999) and Riefler and Smets (2000).

EH1 (ArNO2 ) a (mV) –280 b –400 b –440 b –505 b –495 b –380 –400 –485 –590 –475 –500 –485 –405 –450 –470 –505 –360 –290 –345 –260 –500 < –560

734

Redox Reactions

NAC +

R

reactants

NAC

NAC

R

precursor complex (PC)

R

NAC

R

NAC

actual electron transfer (transition state) (ET)

(a)

(b)

G ET

NAC

successor complex (SC)

PC

G

+

R

products

ET

SC

SC

PC Δ‡G10

R

products

Δ‡G10

products

ΔrG10

ΔrG10 reactants

reactants reaction coordinate

reaction coordinate

Figure 23.5 Simplified scheme for the transfer of the first electron from a reductant R to a NAC (adapted from Eberson, 1987). Panels (a) and (b) show free energy profiles of reactions where the actual electron transfer (a) or other steps such as precursor formation (b) are rate determining. The subscript 1 is used to denote transfer of one electron to the NAC.

to the unsubstituted compound (nitrobenzene). Furthermore, ortho-substituents have a significant steric effect in that they hinder the co-planarity of the nitro group with the aromatic ring thus diminishing delocalization, and, therefore stabilization of the negative charge. We can envision a simple reaction scheme for the various steps that may determine the overall rate of a one-electron transfer reaction between a reductant R and a NAC (Fig. 23.5). Depending on the reductant(s) involved in the reaction, the actual transfer of the electron and/or other steps such as precursor complex formation or successor complex dissociation may be rate-determining for the formation of the nitroaromatic radical anion, ArNO∙− 2 . Figure 23.5a depicts the situation in which the actual electron transfer is the rate-determining step. The transition state in such a reaction is energetically closer to the radical products than to the precursor complex. The standard free energy of activation, Δ‡ G01 , can then be assumed to be proportional to the standard free energy change, Δr G01 , of the reaction (we use a subscript 1 to denote transfer of the first electron to the NAC): Δ‡ G01 = a′ Δr G01 + constant′

(23-24)

Since log kR is proportional to Δ‡ G01 /2.3 RT (Chapter 21, Eq. 21-39), where kR denotes the reaction rate constant, we may also write this linear free energy relationship as: log kR = a

Δr G01 2.3RT

+ constant

(23-25)

735

Examples of Chemical Redox Reactions in Natural Systems

From Chapter 21 (Eq. 21-16), we recall that: [ ] Δr G01 = −F EH1 (ArNO2 ) − EH1 (R∙+ )

(23-26)

where n = 1 and EH1 (R∙+ ) is the one-electron standard reduction potential of the halfreaction R∙+ + e– = R. Insertion of Eq. 23-26 into Eq. 23-25 then yields: logkR = −a

[ 1 ] EH (ArNO2 ) − EH1 (R∙+ ) 2.3RT∕F

+ constant

(23-27)

We should emphasize that we expect Eq. 23-27 to hold only if the actual electron transfer is rate limiting. If other steps in the reaction sequence are partially or fully rate limiting (e.g., precursor formation, Fig. 23.5b), other factors have to be taken into account for evaluating and/or interpreting reduction rates. Now we are in the position to rationalize the observations made in Fig. 23.4 by looking at the energetics of the reduction of nitrobenzene to nitrosobenzene by hydrogen sulfide in homogeneous aqueous solution (Fig. 23.6; Ar = C6 H5 ): ArNO2 + HS− + H+ ⇌ ArNO + S(s) + H2 O

(23-28)

In this case, we may assume that the actual electron transfer is significantly rate limiting (Dunnivant et al., 1992). As is evident from Fig. 23.6, although the overall reaction is strongly exergonic (i.e., Δr G0 = –101 kJ mol–1), the transfer of the first electron is highly endergonic (i.e., Δr G01 = +154 kJ mol–1 ), suggesting a large Δ‡ G01 value. Consequently, nitrobenzene, as well as other nitroaromatic compounds (Dunnivant et al., 1992), reacts only very slowly with hydrogen sulfide under these conditions. Upon addition of natural organic matter to an H2 S solution, reduced DOM constituents may be formed that exhibit more negative reduction potentials than HS∙ (see range E 0(W) (volt)

E 0(W) (volt)

H

H

•

ArNO2 + HS• + H+ 0.5

Δ rG10(W) = +154 kJ mol –1

ArNO2 + 2 H+ + 2 e– = ArNO + H2O

Figure 23.6 Energetic considerations for the reduction of nitrobenzene to nitrosobenzene (Ar = C6 H5 ) with HS– as electron donor at environ0.0 mental (“W”) standard conditions. 0 0 0 Δr G = –nFEH (W). Δr G1 is the Δ‡G10 Δ rG10(W) Δ rG0(W) standard free energy of reaction for ArNO2 + HS – + H+ ArNO + S(s) + H2O the transfer of the first electron; Δr G0 is the overall standard free energy of reaction for the transfer of both –0.5 ArNO2 + e– = ArNO2 electrons.

Δ rG0(W) = –101 kJ mol –1 per e–

HS • + e– = HS–

1.0

1.0

0.5 DOM ox + e– = DOM red 0.0

S(s) + H + + 2e– = HS– –0.5

736

Redox Reactions

of EH0 (W) values of DOMred/ox couples, dashed line in Fig. 23.6). Such DOM species (e.g., hydroquinone and, particularly, mercaptohydroquinone moieties that are formed by addition of HS− to quinone moieties; Dunnivant et al., 1992; Perlinger et al., 1996) may reduce NACs at a much faster rate as is illustrated by Fig. 23.4. Because such species may be re-reduced continuously and at higher rates by the bulk reductant H2 S, they may act as electron-transfer mediators (Fig. 23.1). The rapid regeneration of these species yields a steady-state concentration of reduced DOM constituents, which explains the pseudo-first order kinetics observed for the disappearance of nitrobenzene and of other NACs. For evaluating the reduction kinetics of NACs in a given natural system, the relative reaction rates of a series of NACs with known EH1 (ArNO2 ) values can be used to probe whether the actual electron transfer is significantly rate limiting. To this end, the rate constants observed for the reduction of the NACs can be analyzed using the LFER Eq. 23-27 with EH1 (R∙+ ) = constant and 2.3 RT/F = 0.059V at 25◦ C: logkR = a

EH1 (ArNO2 ) 0.059 V

+b

(23-29)

If a significant correlation is found between log kR and EH1 (ArNO2 )∕0.059V with a slope of close to 1.0, it can be concluded that, for the series of NACs (or any other compound class) considered, the actual transfer of the electron from the reductant to the compounds is dominating the overall rate (Eberson, 1987), although other factors co-correlating with EH1 (ArNO2 ) cannot always completely be ruled out. We should emphasize that such LFERs relating thermodynamic properties to reaction rates do not say anything about the detailed reaction mechanism (e.g., Hofstetter et al., 2008; Hartenbach et al., 2008; see also Chapter 27). If a much weaker dependency of log kR on EH1 (ArNO2 ) (i.e., a slope of a 10 M may not only be an important removal process for such compounds in natural waters, particularly in waters with high nitrate/nitrite concentrations, but also in engineered systems such as drinking water or wastewater treatment plants, where, for example, HO∙ is formed during ozonation. Significantly slower rates are found only for compounds that do not exhibit any aromatic ring or carbon–carbon double bond, and for aliphatic compounds with no easily abstractable H-atoms. Such H-atoms include those that are bound to carbon atoms carrying one or several electronegative heteroatoms or groups. (We recall that the stabilization of a carbon radical (R∙ ) is similar to that of a carbocation.) Finally, we ′ note that several methods have been developed to predict kip,HO ∙ values including, for example, a group contribution method (Minakata et al., 2009) or, more recently, more sophisticated computational models (e.g., Minakata et al., 2014). Reaction With Singlet Oxygen (1 O2 ) is formed primarily by energy transfer from 3 CDOM∗ to 3 O2 (Fig. 25.2, Zepp et al., 1977). The most important consumption mechanism for 1 O2 is physical quenching by water, and to a lesser extent by DOM moieties. The near-surface steady-state concentration of 1 O2 in a natural water is more or less proportional to the DOM concentration, at least for [DOC] < 20 mg oc L−1 . However, different types of aquatic DOM may exhibit quite different overall quantum yields for 1 O2 production, which is due to the different light absorption characteristics of different DOM (e.g., Dalrymple et al., 2010; Coelho et al., 2011; Peterson et al., 2012). Thus, DOM normalized singlet oxygen steady state concentrations, [1 O2 ]0ss /DOC, have been found to vary up to a factor of 5 between different surface waters (Peterson et al., 2012). Finally, as has been demonstrated by Latch and McNeill (2006), using a hydrophobic singlet oxygen trap, 1 O2 concentrations within the CDOM phase may be more than two orders of magnitude higher than in the surrounding aqueous phase. This means that particularly highly hydrophobic organic pollutants that are appreciably associated with CDOM (e.g. fiCDOM > 0.01), will be exposed to a higher apparent singlet oxygen steady-state concentration, [1 O2 ]0ss,app , which is given by: 1O 2

[1 O2 ]0ss,app = fiCDOM [1 O2 ]0ss,CDOM + fiaq [1 O2 ]0ss,aq

(25-14)

where [1 O2 ]0ss,CDOM and [O2 ]0ss,aq are the 1 O2 steady state concentrations in the CDOM and aqueous phase, and fiCDOM and fiaq are the fractions of the compound associated with CDOM and in dissolved form, respectively. In contrast to hydroxyl radical, 1 O2 is a more specific transient oxidant. As is illustrated by the reaction with FFA (a probe compound used to determine 1 O2 concentrations, Eq. 25-15), it may undergo a so-called Diels-Alder-reaction forming an

824

Indirect Photolysis: Reactions with Photooxidants in Natural Waters and in the Atmosphere

endoperoxide intermediate that further reacts to yield various products (Haag et al., 1984a):

OH

+

O

1O

OH O

2

O O

(25-15) O

OH

O

O

O

OH OH

O

≤ 10%

85%

O

OH

≤ 10%

1010

109

108

107

DMF (ef)

1

FFA (ef) H 3C

CH3

H 3C

CH3 S

OH

10

(er) (et)

(so)

CH3

(pKa = 10.2)

OH

k’ip,

Figure 25.4 Second-order rate constants [multiplied by (1 –αia ) for phenols] for reactions of several compounds with 1 O2 (left scale) as a function of pH. The abbreviations in parentheses indicate the reaction type: ef = endoperoxide formation (Eq. 25-15); er = ene reaction; et = electron transfer; so = sulfur oxidation. The scale on the right indicates the half-lives of the compounds in the epilimnion of Greifensee on a clear summer day (data from Scully and Hoign´e, 1987).

or (1 – αia) k’A–p,

(M–1 s–1)

range of epilimnion pH in Greifensee during summer

OH

Cl

(et)

106

(pKa = 7.8)

6

(et)

Cl

(pKa = 7.2)

7

102

8 pH

9

NO 2

10

103

t1/2 in epilimnion of Greifensee (summer, 47,5°N latitude) (days)

Besides its properties as a reactant in addition reactions, 1 O2 is also a significantly better electron acceptor (oxidant) than 3 O2 . However, because of its low steady-state concentration in natural waters (Fig. 25.1), it is an important photooxidant for only a few very reactive types of organic compounds. Such compounds include those exhibiting structural moieties that may undergo Diels-Alder reactions, those containing electron-rich double bonds (i.e., double bonds that are substituted with electrondonating groups), or compounds exhibiting functional groups that are easily oxidized, including reduced sulfur groups (e.g., sulfides), anilines, and phenols (see also Section 23.3). Figure 25.4 summarizes some kinetic data for reactions of organic compounds with 1 O2 in water. As can be seen, for phenolic compounds the transformation

Indirect Photolysis in Surface Waters

825

rate is pH dependent, since the phenolate species (A– ) is much more reactive toward oxidation by 1 O2 as compared to the neutral phenol (HA) [i.e., k′ 1 ≪ kA′ − p,1 O ]. HAp, O2

2

Since 1 O2 behaves as an electrophile, one can assume that electron-donating substituents on an organic compound will, in general, increase its reactivity, while electron-withdrawing substituents will have the opposite effect. In the case of phenolic compounds, the effect(s) of the substituent(s) on the pKa (see Chapter 4), and thus on the abundance of the reactive phenolate species present at a given pH, may be more important than the effect(s) of the substituent(s) on kip,1 O2 . In this case, the overall transformation rate is dominated by the rate of transformation of the anionic species (i=A– ): ( rate =

dCit dt

) 1O 2

≅ −(1 − αia )kA′ − p,1 O [1 O2 ]ss Cit

(25-16)

2

where Cit is the total phenol concentration ([A– ] + [HA]) and (1 –αia ) is the fraction in the dissociated (anionic) form (Section 4.3). This effect is illustrated in Fig. 25.4, where for the phenolic compounds, (1 –αia ) kA′ − p,1 O is plotted as a function of pH. At 2 lower pH-values the contribution of the nondissociated phenol may become important (e.g., for 4-methylphenol, Fig. 25.4). In these cases, the overall rate of transformation is given by: ( rate =

dCit dt

[

) 1O 2

′

]

′

= − αia kHAp,1 O + (1 − αia )kA− p,1 O− 2

[1

2

O2

] ss

Cit

(25-17)

The right-hand scale in Fig. 25.4 gives the calculated half-lives for indirect photolysis involving 1 O2 for the various compounds in the well-mixed epilimnion of Greifensee (zmix = 5 m) on a clear summer day. The half-lives are based on a measured [1 O2 ]0ss (noon) value of 8×10–14 M, corresponding to a [1 O2 ]0ss (24 h) value of about 3.5×10–14 M (factor 0.44, Section 24.3). When assuming that virtually all light is absorbed within the epilimnion {i.e., S(λm ) = [2.3 (1.2) α(λm ) zmix ]–1 }, and taking the α value at 410 nm [α(410 nm) = 0.005 cm–1 ; see Table 24.6], a depth-averaged 1 O concentration [1 O ]ss(24 h) = 4×10–15 M is calculated (Eq. 25-11). The choice 2 2 of 410 nm is based on the findings by Haag et al. (1984b) that some humic and fulvic materials exhibit a maximum in 1 O2 production around this wavelength. With the [1 O2 ]0ss (24 h) value previously calculated, the half-life of a compound with respect to photooxidation by 1 O2 in the epilimnion of Greifensee is then given by: t1∕2 =

ln 2 2 × 109 days sec = ′ kip, × 10−15 ) 1O

′ kip, 1 O (4 2

(25-18)

2

From the half-lives indicated in Fig. 25.4, it can be seen that for most pollutants, the assumption of a well-mixed epilimnion (typical mixing rates 1 – 10 d–1 , see Chapter 5) with respect to indirect photolysis with 1 O2 is a reasonable assumption. Further′ ′ more, for compounds exhibiting kip, 1 O values [or (1 –αia ) kA− p,1 O values for phenolate 2

2

826

Indirect Photolysis: Reactions with Photooxidants in Natural Waters and in the Atmosphere

species] greater than 107 M–1 s–1 , during the summer, photooxidation by 1 O2 is equal to, or more important than, depletion of the concentration by dilution with inflowing water [t1/2 (dilution) in the epilimnion of Greifensee on the order of 70 days]. We ′ should recall, however, that only a few compound classes exhibit such large kip, 1O 2

values, and that, therefore, 1 O2 must be considered to be a rather selective photooxidant. Reactions with Reactive DOM Constituents (3 CDOM∗ )

We conclude our discussion of indirect photolysis in water by briefly addressing an example in which the “photo-reactant” is not well defined and not easily quantifiable as in the case of HO∙ or 1 O2 . As has been shown more than three decades ago (see Canonica, 2007), excited CDOM constituents (e.g., quinones, ketones; Golanoski et al., 2012), that are commonly denoted as 3 CDOM∗ , may directly react with organic pollutants. These reactions, which are often also referred to as photosensitized reactions, may be classified as energy, electron- or hydrogen-transfer reactions. Energy transfer may cause, for example, cis-trans-isomerization of double bonds (Zepp et al., 1985; Grebel et al., 2011) or, more seldomly, even promote the pollutant into an excited state, much as occurs by direct photolysis (Porras et al., 2014). The other two mechanisms lead to an oxidation of the organic pollutant. Again, reaction rates are fastest with easily oxidizable compounds such as electron-rich phenolic compounds or aromatic amines (Canonica, 2007) as we have already encountered in Section 23.3 when discussing chemical oxidations. However, also less reactive compounds such as, for example, the phenylurea herbicides (Gerecke et al., 2001; Canonica et al., 2006) or sulfonamide antibiotics (Boreen et al., 2005; Guerard et al., 2009; Bahnm¨uller et al., 2014) may be oxidized by 3 CDOM∗ . As can be easily rationalized for reactions involving 3 CDOM∗ , a priori predictions of absolute reaction rates are rather difficult since the different types of excited chromophores present in a given DOM may exhibit different reactivities towards an organic pollutant (e.g., Guerard et al., 2009). Furthermore, as has been demonstrated in several studies, antioxidant moieties, such as electron-rich phenolic groups present in DOM, may “inhibit” oxidation of pollutants by 3 CDOM∗ by re-reducing oxidation intermediates back to their parent compounds (Canonica and Laubscher, 2008; Wenk et al., 2011; Wenk and Canonica, 2012; Janssen et al., 2014). This “inhibitory” effect of DOM may also occur with pollutants excited by direct photolysis (Janssen et al., 2014), but apparently not for intermediates formed by reactions with 1 O2 (Janssen et al., 2014) and HO∙ (Wenk et al., 2011). In order to estimate rate data for 3 CDOM∗ sensitized photolysis of a pollutant of interest in a given system under given conditions, it may, however, be possible derive such data if transformation rates are available for structurally related compounds. In such cases, LFERs such as the Hammett relationship (Chapter 22, Eq. 22-28), or using oxidation potentials of the compounds as molecular descriptors (Chapter 23, Eq. 23-33; Canonica et al., 2000; Arnold, 2014) may be helpful. Figure 25.5 illustrates 0 , determined by Gerecke that the observed pseudo first-order rate constants, kip,sens

Indirect Photolysis in Surface Waters

827

0.0 1 2

–0.2

3

0 log kip,sens (h–1)

–0.4 5

–0.6

4

6 8 7

–0.8

9

–1.0

Figure 25.5 Hammett plot for the oxidation of a series of substituted phenylurea herbicides by 3 CDOM∗ . The linear regression line is given in Eq. 25-20. The compound names and structures as well as the corresponding σ+jpara , σ+jmeta (= σjmeta ), and 0 kip,sens values are given in Table 25.1. Adapted from Gerecke et al. (2001).

–1.2

11

10

–1.4

–0.6

–0.4

–0.2 σ

0.0 + jpara

0.2

0.4

0.6

+σ

+ jmeta

et al. (2001) for 3 CDOM∗ sensitized photooxidation of a series of structurally related phenyl urea herbicides (Eq. 25-19)

H R2

N

O

O N R3

R1

R4

3CDOM*

–H

R2

N

N R3

R4

(25-19)

R1

were found to correlate quite well with the σ+ - Hammett substituent constants of the ring substituents (Table 25.1) yielding the relationship: 0 log kip,sens (h−1 ) = −1.16 Σσ+j − 0.72

(25-20)

0 where kip,sens is the observed pseudo-first-order rate constant determined for the photosensitized reaction of a compound in a solution of 2.5 mg oc L−1 Suwanee River fulvic acid (SRFA) at pH 8 exposed to broadband irradiation (λ > 320 nm) in a photoreactor (for details see Gerecke et al., 2001). In analogy to using σ−jpara for delocalization of a negative charge (Chapter 4), σ+jpara instead of σjpara values have to be used in the Hammett equation in cases where a positive charge or a radical is delocalized, as is, for example, the case for radical formation upon the oxidation of anilines, phenols, and phenylureas (for more details and a comprehensive compilation of σ+jpara constants, see Hansch et al., 1995a and b).

828

Indirect Photolysis: Reactions with Photooxidants in Natural Waters and in the Atmosphere

Table 25.1 Chemical Structure, Hammett Constants, and Pseudo-First-Order Rate Constants for Suwanee River Fulvic Acid (SRFA) Sensitized Photolysis of a Series of Phenyl Urea Herbicides (PUHs) H R2

N

O N R3

R1

Compound Metoxuron CGA 24482 GGA 16519 IPU CGA 17767 CGA 17092 Fenuron Chlorotoluron GCA 18414 Fluometuron Diuron a c

Hammett Constants a

Substituents No. c 1 2 3 4 5 6 7 8 9 10 11

−R1

−R3

σ+jpara

σ+jmeta

σ+jpara + σ+jmeta

0 kip,sens (h−1 ) b

−CH3 −CH3 −CH3 −CH3 −CH2 CH3 −CH3 −CH3 −CH3 −CH2 CH3 −CH3 −CH3

−0.78 −0.30 d −0.30 −0.28 −0.28 −0.26 0 −0.31 −0.28 0 0.11

0.37 −0.07 d 0 0 0 0 0 0.37 0.37 0.43 0.37

−0.41 −0.37 −0.30 −0.28 −0.28 −0.26 0 0.06 0.09 0.43 0.48

0.63 0.52 0.47 0.44 0.32 0.31 0.18 0.22 0.16 0.051 0.055

−R2

−OCH3 −Cl 3,4-tetramethylene −H −CH2 CH3 −H −CH(CH3 )2 −H −CH(CH3 )2 −H −C(CH3 )3 −H −H −Cl −CH3 −Cl −CH(CH3 )2 −H −CF3 −Cl −Cl

Values from Hansch et al. (1995a and b). b SRFA: 2.5 mg oc L–1 , l > 320 nm; data from Gerecke et al. (2001). Numbers in Fig. 25.5. d Hammett constant for 3,4-tetramethylene assumed to correspond to –R1 = –R2 = –CH2 CH3 .

Concluding Remarks As already pointed out in the introduction to this section, depending on the water −∙ ∙− composition, some additional transient photoreactants (e.g., CO∙− 3 , SO4 , Br2 ) may become relevant for the transformation of certain pollutants. We should also be aware that, depending on the structure of the compound, and on the steady-state concentrations of all transient photoreactants present in a given sunlit water, not only one but several different reactions including direct photolysis (Chapter 24) may take place simultaneously, potentially leading to a variety of different transformation products. Therefore, the total “photochemical elimination” of a given pollutant can be expressed as the sum of direct photolysis and the reactions with the various transient oxidants (see e.g., Zeng and Arnold, 2013): ( rate =

dCi dt

) p

= −kip,obs Ci ∙ ′ ′ = − (kip,direct + kip,HO [1 O2 ]ss ∙ [HO ]ss + k 1 ip, O

(25-21)

2

∗ ∙− ′ ′ 3 + kip, 3 CDOM∗ [ CDOM ]ss + kip,CO∙− [CO3 ]ss + kip,other )Ci 3

′ where kip, 3 CDOM∗ is the apparent average second-order rate constant for reac∗

tion with 3 CDOM . As shown by Zeng and Arnold (2013), for a given system, ∗ ′ 3 kip, 3 CDOM∗ [ CDOM ]ss can be estimated from experimental data.

829

Indirect Photolysis in the Atmosphere (Troposphere)

percentage of kobs

100%

direct 1O 2

CO3•− 3DOM*

•

OH other

100%

80%

80%

60%

60%

40%

40%

20%

20%

0%

0%

percentage of kobs

Figure 25.6 Percent calculated con, tribution of direct photolysis, CO∙− 3 HO∙ , 1 O2 , and 3 CDOM∗ and other processes to the photodegradation of pesticides in water from a prairie hole under simulated sunlight. A very similar picture was obtained for natural sunlight. Figure from Zeng and Arnold (2013).

NO2 N F3C

e e or or or e n n n n lid os le lin lin lin zin azin chl chl chl trion iuro turo xuro tazo yra yrif azo ura tha ura a o a a r d ro to n op rp on lfl e rifl at yan cet al tol eso p e be cl lo ic ha im t e m c a iso m ch rop et end m p p

NO2 trifluralin

Cl O O

Cl N

N

N propiconazole Cl

O H3C

N

N

CH3

H

Cl

diuron O Cl

N

OH Cl

Using Eq. 25-21, Zeng and Arnold (2013) estimated the relative contributions of the different photochemical reactions to the overall photolytic eliminations determined for 16 common pesticides under simulated and natural sunlight in water samples derived from various prairie potholes. An illustrative example is given in Fig. 25.6. As can be seen, the relative contributions (which do not say anything about the absolute rates) of the various processes may differ substantially between different compounds. For example, the dinitroaniline derivatives trifluralin, pendimethalin, and ethafluralin that significantly absorb sunlight between 290 and 500 nm (Perez et al., 2008; n → π∙ transition, see Section 24.2), undergo primarily direct photolysis. Under the conditions used, the half-life of trifluralin was about 0.5 h. In contrast, propiconazole (halflife ≅ 50 h) reacted primarily with 1 O2 (possibly by a Diels-Alder reaction, Eq. 2515), and diuron (half-life ≅ 5 h) primarily with 3 CDOM∗ , as previously discussed (Table 25.1) and also postulated by Gerecke et al. (2001) for lake water. Finally, for the rather unreactive clopyralid (half-life > 150 h) several different processes including the reaction with HO∙ seem to be important. Other examples illustrating the relative contributions of the various processes in Eq. 25-21 to the overall photolytic transformation of a variety of different organic pollutants in water can be found in Chowdhury et al. (2010) for 17β-estradiol, Xu et al. (2011) for ibuprofen and octylphenol, Dell’Arciprete et al. (2012) for various insecticides, Wang et al. (2012) for various beta-blockers, and Bahnm¨uller et al. (2014) for sulfonamide antibiotics.

clopyralid

25.3

Indirect Photolysis in the Atmosphere (Troposphere): Reaction with Hydroxyl Radical (HO∙ ) Long-range transport of an organic pollutant in the environment occurs when the compound has a sufficiently long tropospheric lifetime. This lifetime is partially

830

Indirect Photolysis: Reactions with Photooxidants in Natural Waters and in the Atmosphere

determined by wet or dry deposition and/or by vapor transfers into surface waters (see Chapters 15 and 19). Additionally, the tropospheric lifetime of a pollutant strongly depends on its reactivity with photooxidants and, to a lesser extent, on direct photolysis. Since light absorption rates and reaction quantum yields are very difficult to quantify for direct photolysis reactions of organic chemicals in the atmosphere (Atkinson et al., 1999), we confine our discussion of photolytic transformations to reactions with photooxidants, in particular, HO∙ in the gas phase. For reactions in atmospheric water phases, we refer to the literature (see Herrmann et al., 2015). As we have already noted in Section 25.2, when discussing reactions of organic chemicals with ROS in the aqueous phase, HO∙ is a very reactive, rather nonselective oxidant. Other important photooxidants present in the troposphere include ozone (O3 ) and ∙ the nitrate radical (NO3 ). Although, in the troposphere, some of these species (e.g., O3 ) are generally present in significantly higher concentrations as compared to HO∙ (see Fig. 25.1), they are rather selective oxidants, and are, therefore, only important reactants for chemicals exhibiting specific functionalities. O3 reacts primarily with compounds containing one or several electron-rich carbon–carbon double bonds such as alkenes (Atkinson, 1994; Atkinson et al., 1995; Grosjean et al., 1996a and b). The nitrate radical, which is particularly important at night when HO∙ radicals are less abundant (Atkinson et al., 1999), also reacts with compounds exhibiting electron-rich ∙ carbon–carbon double bonds. In addition, NO3 undergoes reactions with polycyclic aromatic hydrocarbons (PAHs) and with compounds exhibiting reduced sulfur and/or nitrogen functionalities (Atkinson, 1994). In the case of PAHs, such reactions yield rather toxic nitroaromatic compounds, such as 1- and 2-nitronaphthalene from the ∙ reaction of naphthalene with NO3 (Sasaki et al., 1997). Therefore, reactions beside that with HO∙ should be considered in such cases. Sources and Typical Concentrations of HO∙ in the Troposphere The presence of low levels of O3 in the troposphere is important because photolysis of O3 in the troposphere occurs in the wavelength region of 290–335 nm to form the excited oxygen atom, O(1 D). O(1 D) atoms are either deactivated to ground-state oxygen atoms, O(3 P), or react with water vapor to generate HO∙ radicals. O3 + hv → O2 + O(1 D)

(290 > λ ≤ 335 nm)

O(1 D) + N2 , O2 → O(3 P) + N2 , O2 O( D) + H2 O → 2HO 1

(25-22)

∙

At 298 K and atmospheric pressure with 50% relative humidity, about 0.2 HO∙ are produced per O(1 D) atom formed. Photolysis of O3 in the presence of water vapor is the major tropospheric source of HO∙ , particularly in the lower troposphere where water vapor mixing ratios are high (for an explanation of the term “mixing ratio” see the following discussion). Other sources of HO∙ in the troposphere include the photolysis of nitrous acid (HONO), the photolysis of formaldehyde and other carbonyls in the presence of NO, and the dark reactions of O3 with alkanes. All these processes involve quite complicated reaction schemes. For a discussion of these reaction schemes we refer to the literature (e.g., Atkinson, 2000).

Indirect Photolysis in the Atmosphere (Troposphere)

831

At this point, we need to recall how gaseous concentrations of chemical species in the atmosphere are commonly expressed (see also Chapter 5, Box 5.2). A widely used approach is to give the fraction of the total volume that is occupied by the gaseous species i considered. This is referred to as the (volume) mixing ratio. Mixing ratios are frequently expressed as ppmv (= 10–6 ), ppbv (= 10–9 ), or pptv (10–12 ). When assuming ideal gas behavior, for given p and T, mixing ratios are proportional to partial pressures (mixing ratio = xi ptot = pi where xi is the mole fraction of i, see Box 5.2). Thus, they can be easily converted to molar concentrations by: concentration in mol L−1 =

p mixing ratio ptot = i RT RT

(25-23)

where ptot is the total pressure. For atmospheric gas-phase reactions, one commonly expresses concentrations of reactive species not in mol L–1 but in molecule cm–3 . Thus, at 298 K and ptot = 1 bar, concentration and mixing ratio are related by: mixing ratio (6.022×1023 )(1) (0.0831)(103 )(298) = (mixing ratio)(2.43×1019 )

concentration in molecule cm−3 =

(25-24)

Direct spectroscopic measurements of HO∙ close to ground level show peak daytime HO∙ concentrations in the range of 2 to 10×106 molecule cm–3 for mid-latitude northern hemisphere sites in the summer (Atkinson et al., 1999). These measurements show a distinct diurnal profile, with a maximum HO∙ concentration around solar noon. Model calculations suggest that, in addition to exhibiting a diurnal profile, the HO∙ concentration depends on season and latitude. For example, the mean monthly surface HO∙ concentrations (24 h averages) at 35◦ N latitude are estimated to be in the order of 2×105 molecule cm–3 in January and 2×106 molecule cm–3 in July, compared to about 1.2×106 molecule cm–3 during the whole year at the Equator. The summer/winter HO∙ concentration ratio increases with increasing latitude because of the increasing light differences (see Atkinson et al., 1999). For practical purposes (e.g., for use in environmental fate models), it is reasonable to assume a diurnally, seasonally, and annually averaged global tropospheric HO∙ concentration of 1×106 molecule cm–3 . Rate Constants and Tropospheric Half-Lives for Reactions with HO∙ ′ Figure 25.7 summarizes second-order rate constants, kiHO ∙ , for some environmentally relevant organic compounds. These rate constants allow us to estimate those compounds tropospheric half-lives t1/2,HO∙ :

t1∕2,HO∙ =

ln 2

∙ ′ kiHO ∙ [HO ]ss

(25-25)

′ –3 –1 s–1 , and the t The units of kiHO ∙ are (molecule cm ) 1/2,HO∙ values given in Fig. 25.7 have been calculated for an average global tropospheric HO∙ concentration of 1×106 molecule cm–3 at 25◦ C. We should also note that, as a first approximation, we ′ neglect the effect of temperature on kiHO ∙ , because over the temperature range of the

832

Indirect Photolysis: Reactions with Photooxidants in Natural Waters and in the Atmosphere

diffusion-controlled reaction

2×10-10

S

S

NH 2

1h 10–10

OH

5×10–11

OH

O

10–11 H 2C

CH 2

OH

Cl

5×10–12 k'i HO· (molecule cm –3) –1 s –1

O

H

O

10–12

H

H

1d Cl O

Cl Cl

Cl

Cl

H O

5×10–13

O

O

Cl

O Cl

Cl

Cl

Cl

O2N

OH

O

2×10–13

Cl

O

Cl

Cl

Cl Br

Cl

Cl

Cl Cl

CH 2Cl 2

Cl

Cl

N

Cl

Cl

10 d

Cl

Br

Cl

O

Cl

CH3

Cl

Cl

OH

OH

H 3C

10–13

H

10 h

S OH

2×10–12

OCH3

N

t1/2,HO • (assumption [OH •]ss = 10 6 molecule cm –3)

2×10–11

NO 2

CHCl3

100 d

5×10–14 Cl CHFCl 2

Br

1 yr

2×10–14 Cl

10–14

5x10–15

CH 4

Cl

F

H

Cl Cl

Cl

F F

∙ ′ Figure 25.7 Second-order rate constants (kiHO ∙ ) and half-lives (t1∕2,HO∙ ) for reaction of HO radicals in the troposphere at 298 K for organic compounds as vapors in air. For calculation of the half-lives, a steady-state HO∙ concentration of 10−6 molecule cm−3 has been assumed. Data from Atkinson (1986); Atkinson (1994); Anderson and Hites (1996); and Brubaker and Hites (1997).

Questions and Problems

833

lower troposphere (–40◦ to 30◦ C), this effect is less than a factor of 2 to 3 for many compounds of interest to us (Atkinson, 1986 and 1994). Comparison of Figs. 25.7 and 25.3 shows that relative reaction rates of organic chemicals with HO∙ follow more or less the same general pattern in air and in water; that is, compounds containing electron-rich double bonds or aromatic systems and/or easily abstractable H-atoms react faster as compared to compounds exhibiting no such functionalities. However, the differences in absolute rates are much more pronounced in the gas phase (about a range of 104 for the compounds considered) as compared to the solution phase (about a range of 102 for the same scope of compounds). The major reason is that in the aqueous phase, particularly for addition reactions of HO∙ to double bonds or aromatic systems, there is a rapid release of energy from the intermediate adduct to the solvent molecules. This stabilizes the intermediate as compared to the gas phase, where the reaction is much more reversible. Therefore, in the gas phase, such reactions are more selective, and this is reflected in larger differences in reactivity between compounds. Finally, we note that gas-phase second-order rate constants for reactions of HO∙ with organic pollutants can be estimated with reasonable accuracy from structure-reactivity relationships using fragment methods (Kwok and Atkinson, 1995). A short description and some applications can be found Appendix ′ using E, available online. Examples of more advanced methods for prediction of kHO∙ ¨ other molecular descriptors are discussed in Oberg (2005), Wang et al. (2009), and Li et al. (2014a and b).

25.4

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission. Questions Q 25.1 What is meant by the terms indirect photolysis and sensitized photolysis? What types of reactions do indirect photolyses of organic pollutants include in natural waters? In the atmosphere? Q 25.2 Why does one speak of transient photooxidants? Give examples of such species. What are their major sources and sinks in natural waters? In the atmosphere? Q 25.3 Describe the general kinetic approach that can be used to quantify indirect photolysis involving well-defined photooxidants in: (a) the water column of surface waters and (b) the atmosphere.

834

Indirect Photolysis: Reactions with Photooxidants in Natural Waters and in the Atmosphere

Q 25.4 Why is the hydroxyl radical (HO∙ ) a more important photooxidant in the atmosphere as compared to surface waters? What kind of reactions do organic pollutants undergo with HO∙ ? How structure-specific are these reactions? Q 25.5 Somebody claims that the volume-averaged steady-state concentration of singlet oxygen ([1 O2 ]ss ) in a well-mixed epilimnion of 5 m depth is more or less independent of the DOM concentration, whereas at the surface it is proportional to [DOM], at least for [DOC] < 20 mg oc L−1 . Could this person be correct, and if yes, why?

O O Cl

H3C

OH H

(R)-(+)-mecoprop pKia = 3.8 OH

Q 25.6 Why is 1 O2 a more selective photooxidant than HO∙ ? With what type of organic pollutants does 1 O2 primarily react? Q 25.7 Why is it difficult to quantify DOM-mediated photolysis of organic pollutants? What type of reactions do 3 CDOM∗ species undergo with organic chemicals? Q 25.8

2,4,6-trimethylphenol (TMP) OH

Halladja et al. (2009) investigated the fulvic acid-mediated phototransformation of the herbicide, mecoprop, as a function of pH. They found that at pH 2 mecoprop reacted about 10 times faster than at pH 6.5, while the transformation of 2,4,6-trimethylphenol (TMP) and FFA (Eq. 25.15) showed no pH-dependence. (a) Rationalize these findings.

Cl 2-methyl-4-chlorophenol (MCP)

(b) One of the main transformation products of mecoprop was identified as 2-methyl4-chlorophenol (MCP). What could be the initial reaction leading to this product? Problems P 25.1 Estimating the Hydroxyl Radical Steady-State Concentrations at the Surface and in the Epilimnion of a Lake

[NO−3 ] = 150 μM [NO−2 ] = 1.5 μM [DOC] = 4 mg oc L–1 [HCO−3 ] = 1.2 mM [CO2− ] = 0.014 mM 3

Estimate (a) the near-surface and (b) the well-mixed epilimnion (hmix = 5 m) hydroxyl radical steady-state concentration at noon ([HO∙ ]0ss (noon)) and averaged over a day ([HO∙ ]0ss (24 h)) in Greifensee (47.5◦ N) on a clear summer day. Assume that photolysis of nitrate (NO−3 ) and nitrite (NO−2 ) are the major sources, and that DOM, HCO−3 , and CO2− are the major sinks for HO∙ in Greifensee. The concentrations of the various 3 species are given in the margin. Using the decadic molar extinction coefficients, εi (λ), for nitrate (Gaffney et al., 1992) and nitrite (Fischer and Warneck, 1996), a good friend of yours working at Eawag in Switzerland has calculated the summer mid-day near-surface light absorption rates (Eq. 24-25, see example given for PNAP in Fig. 24.10 and Table 24.5) of nitrate and nitrite in Greifensee:

Questions and Problems

835

0 −5 mol photons (mol NO− )−1 s−1 ka,NO − (noon) = 2.0×10 3 3

0 −4 mol photons (mol NO− )−1 s−1 ka,NO − (noon) = 6.0×10 2 2

NO−3 absorbs light between 290 and 340 nm with a maximum light absorption rate at 320 nm(λmax ). For NO−2 the range is much wider, 290–400 nm with λmax = 360 nm. In the literature, you also find the quantum yields for HO∙ photoproduction from nitrate and nitrite at the corresponding λmax (Jankowski et al., 1999): Φr,NO−3 = 0.007 (mol HO∙ )(mol photons)−1 Φr,NO−2 = 0.028 (mol HO∙ )(mol photons)−1 Finally, with respect to the consumption of HO∙ , you find the corresponding second′ ′ [j]) in the literature. For reaction order rate constants kHO ∙ (Eq. 25-5 with kox,j = k ox,j ,j ′ of HO⋅ with DOM, an average rate constant kHO∙ ,DOC = 4×104 L (mg oc)−1 s−1 can be used (Mostofa et al. (2013). For reactions with HCO−3 and CO2− 3 , the rate constants ′ 7 M−1 s−1 and k′ 8 M−1 s−1 (Larson and Zepp, = 1.0×10 = 4.0×10 are kHO ∙ ∙ 2− ,HCO− 1988).

HO ,CO3

3

P 25.2 How Important Are Reactions of Phenols with HO∙ and 1 O2 in a Shallow Pond? Consider a shallow well-mixed pond (average depth = 2 m, T = 25◦ C; pH = 8.5; α(λ) take values given in Table 24.5; mean residence time of the water: 35 d). In this pond, a midday, near-surface steady-state concentration of 1 O2 ([1 O2 ]0ss (noon)) of 8×10–14 M has been determined using FFA as probe molecule (see Eq. 25-15). Recall that maximum 1 O2 production occurs at 410 nm. The steady-state HO∙ concentration in this pond has been estimated to be 10−16 M. Calculate the 24 h-averaged photolysis half-life of 4-methoxy- and 2-chlorophenol in this pond by assuming that only the reactions with HO∙ and 1 O2 are important (note that for 4-methoxyphenol reactions with 3 CDOM∗ may also be relevant). What is the relative importance of the two oxidants? How important are they compared to flushing? (see Chapter 6, Section 6.2). In the literature you find the following data (Tratnyek et al., 1991):

OH

OH

Cl

H3CO 4-methoxyphenol

pKia = 10.2 kA′ − p,1 O−

−1 −1

= 7 × 10 M s 8

2

′ 7 −1 s−1 kHAp, 1 O = 3 × 10 M 2

2-chlorophenol

pKia = 8.5 kA′ − p,1 O− = 2 × 108 M−1 s−1 2

′ 6 −1 s−1 kHAp, 1 O = 5 × 10 M 2

836

Indirect Photolysis: Reactions with Photooxidants in Natural Waters and in the Atmosphere

For the reaction with HO∙ , assume that both compounds react with a nearly diffusion controlled rate constant of 1×1010 M–1 s–1 (see Fig. 25.3). P 25.3 Evaluating Reactions of Organic Pollutants with the Carbonate Radical (CO∙− 3 ) ∙−

As pointed out in Section 25.2 (Eq. 25-2), the major source for CO3 radicals in surface ∙ water is the reaction of HCO−3 and CO2− 3 with hydroxyl radical (HO ), although under certain conditions, other reactions may also be important (Canonica et al., 2005). ∙− The major sink for CO3 is regarded to be DOM. The rate constant for reaction of ∙− ′ CO3 with DOM is about kCO = 3×102 L (mg oc)−1 s−1 (Canonica et al., 2005), ∙− 3 ,DOC which is about 100 times smaller than for the reaction of HO∙ with DOM constituents ′ = 4×104 L (mg oc)−1 s−1 , Mostofa et al. (2013). (kHO ∙ ,DOC (a) Estimate the near-surface carbonate radical steady-state concentration at noon ∙− ∙− ([CO3 ]0ss (noon)) and averaged over a day ([CO3 ]0ss (24 h)) in Greifensee (47.5◦ N) on a clear summer day. The concentrations of the relevant water constituents as well as other important data are given in Problem 25.1. Hint: About 15% of the HO∙ produced is consumed by HCO−3 /CO2− 3 . Compare the ∙ carbonate radical concentrations with the [HO ]0ss (noon) = 2.5×10−16 M estimated by a colleague working at Eawag. (b) For reactions of meta- and para-substituted anilines, Canonica et al. (2005) reported the following QSAR: ′ −1 s−1 ) = −1.05 ∑ σ+ + 8.82 kip,CO ∙− (M j 3

(number of chemicals = 9; r2 = 0.90; S.D. = 0.16) Calculate the 24 h-averaged near-surface half-lives of 3,4-dimethylaniline and 4-nitroaniline with respect to reaction with CO∙3− . How important are these reactions relative to the reactions of the two compounds with HO∙ ? Recall that in analogy to using σ−jpara for delocalization of a negative charge, σ+jpara values have to be used in cases where a positive charge or a radical is delocalized (σ+j values from Hansch et al., 1995a and b). NH2

NH2

NO2 3,4-dimethylaniline + σCH ,para = −0.37 3 σ+CH ,meta = −0.06 3

4-nitroaniline

σ+NO ,para 2

= 0.79

Questions and Problems

837

P 25.4 Assessing the Fate of Ibuprofen in Surface Waters – Is Photolytic Transformation Important?

OH O ibuprofen pKa = 4.5 (Babic et al., 2007)

Ibuprofen is one of the most widely used analgesic and anti-inflammatory drug. It exists in two enatiomeric forms (see Chapter 2 for stereochemistry) of which only one is an active drug (see refs cited in Jacobs et al., 2011). Like many other pharmaceuticals, it has been detected in surface waters including our test lake, Greifensee (Tixier et al., 2003). From the data of their field study, Tixier et al. (2003) concluded that photochemical transformation, in particular, direct photolysis was negligible for the elimination of ibuprofen in Greifensee. The conclusion that direct photolysis is a rather unimportant process for this compound has also been drawn from laboratory experiments carried out by Packer et al. (2003), Lin and Reinhard (2005), Yamamoto et al. (2009), and Jacobs et al. (2011). (In some of the cited literature, you find data for many other pharmaceuticals.) In contrast, Vione et al. (2011) and Li et al. (2015) using a polychromatic UVB lamp and a mercury lamp, respectively, and a quartz cuvette as photoreactor, consider direct photolysis as an important process in surface waters. In fact, Vione et al. (2011) report a large quantum yield, Φ, of 0.33 for direct UVB photolysis. In addition, in all laboratory studies it was found, that the presence of DOM and, in some cases, also nitrate enhanced the rate of photolysis. Hence, indirect photolysis primarily involving HO∙ , 1 O2 , and 3 CDOM∗ as potential oxidants has been postulated for ibuprofen; the carbonate radical has been considered to be unimportant. Furthermore, only partial quenching of indirect photolysis by adding isopropanol has been reported (Jacobs et al., 2011). Finally, in the literature, you find the second-order rate ′ 9 −1 s−1 , Huber constants for the reactions of ibuprofen with HO∙ (kip,HO ∙ = 7.4×10 M et al., 2003) and 1 O2 (kip,1 O2 = 6.0×104 M−1 s−1 , Vione et al., 2011). (a) From inspecting the structure of ibuprofen, which photolytic reactions would you consider to be important for its elimination in surface waters? Where in the molecule would you expect that a particular reaction is initiated by the various transient oxidants? Would you expect that the two enatiomers react differently with these transient oxidants? (b) Lin and Reinhard (2005) reported a near-surface photolytic half-life of 15 h for ibuprofen in river water (pH 7.5; [DOC] = 4.6 mg oc L−1 ; [NO−3 ] = 350 μM) for simulated middday-midsummer sunlight conditions that corresponded quite well with the conditions encountered in Greifensee (Problem 25.1). Therefore, you can use the data given in Problem 25.1 to estimate the (near-surface) HO∙ concentration in the river water by assuming that NO−3 is the main source and DOM is the main sink for HO∙ . Based on this estimate, what is the contribution of the reaction with HO∙ to the overall photolytic transformation of ibuprofen? (c) Assuming the same (i.e., half-life of 15 h) near-surface photolytic transformation rate constants of ipuprofen with the relevant transient oxidants in the epilimnion of Greifensee, and that only DOM and NO−3 are the relevant water constituents, would photolysis be an important removal mechanism for this compound in the epilimnion of Greifensee on a midsummer day? Assume an average αaverage = 0.026 cm–1 (Table 24.5, Fig. 24.12) for the light absorption by both NO−3 and DOM.

838

Indirect Photolysis: Reactions with Photooxidants in Natural Waters and in the Atmosphere

The flushing rate of the epilimnion of Greifensee is 0.01 d−1 . You can find all other pertinent information in Problem 25.1.

25.5

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845

Chapter 26

Biotransformations

26.1 Introduction 26.2 Some Important Concepts about Microorganisms Relevant to Biotransformations Limits of Environmental Conditions Microorganisms Working Together: Syntrophy Sharing Genetic Codes Biocatalysts: Enzymes 26.3 Initial Biotransformation Strategies Hydrolyses Oxidations Reductions Additions 26.4 Rates of Biotransformations Bioavailability Biouptake Kinetics Michaelis-Menten Enzyme Kinetics Box 26.1 Kinetic Expressions for Enzymatic Hydrolysis of R–L Under Simplifying Assumptions Monod Population Growth Kinetics

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

846

Biotransformations

Box 26.2 Monod Limiting-Substrate Models of Microbial Population Growth 26.5 Questions and Problems 26.6 Bibliography

Introduction

26.1

847

Introduction Reactions mediated by organisms constitute a very important set of transformations affecting the fates of almost all organic compounds in both natural and engineered systems. One major goal of this chapter is to characterize the rates of such biotransformations. By changing the structure of the organic chemical of interest, these transformations remove the particular compound from an environmental system. The resulting products, often referred to as metabolites, may also be of environmental concern (e.g., Berggren et al., 2013; Fenner et al., 2013). They exhibit their own partitioning properties, reactivities, overall fates, and effects. Therefore, the appearance of toxic metabolites may inspire new mass balance and toxicity considerations. When we speak of biotransformations of organic compounds, we do not necessarily mean that the compounds are fully mineralized. Mineralization is defined as the complete conversion of an organic chemical to stable inorganic forms of C, H, N, P like CO2 , H2 O, NO−3 or NH+4 , and PO3− 4 . Consequently, mineralization generally entails several successive biotransformations. As a result, experimental observations relying on the appearance of CO2 to quantify the rate of loss of a specific organic chemical place a lower limit on the initial biotransformation rate since the time rate of CO2 appearance (d[CO2 ]/dt) must be less than or equal to the time rate of change quantifying an organic substrate’s disappearance (–d[i]/dt). Biotransformations of organic compounds are especially important because many reactions, although thermodynamically feasible, occur extremely slowly or not at all via abiotic mechanisms for kinetic reasons. Organisms enable such reactions by using catalytic enzymes and co-substrates (see Chapters 22 and 23). Hence, we may only begin to assess the question of whether benzene can be biodegraded under naturally occurring methanogenic conditions by calculating whether such natural attenuation of this toxic substance is thermodynamically feasible under these conditions (see Chapter 21). However, even if this benzene transformation proves to be thermodynamically feasible, the rates of abiotic mechanisms may be extremely slow. But if a suitable microorganism species or cooperative combination of microbial species are present, they may catalyze the biotransformation of benzene in the environment of interest. However, in the environment, often such biotransformations can only be detected via techniques like compound-specific isotope analysis (CSIA, see Chapter 27). In this chapter, we focus on biotransformations of organic compounds carried out by microorganisms since they are metabolically very diverse and environmentally ubiquitous (Madigan et al., 2015). We first describe a few general principles pertaining to the ecology and enzymatic capabilities of microorganisms, especially insofar as these characteristics influence what we can expect these organisms to do to anthropogenic compounds (Section 26.2). Next, recalling the nature of reactions catalyzed by enzymes (see Sections 22.3 and 23.4), we note some factors that may affect the rates of these enzymatically catalyzed biotransformations in environmental settings (Section 26.3). Finally, in Section 26.4, we review mathematical formulations with which rates of the biotransformations in environmental settings may be described and discuss how we might approach quantifying the overall rate of any particular biodegradation.

848

Biotransformations

In this chapter, we do not attempt to review the immense literature on biotransformations, nor deal with the complete metabolic pathways that can be found on the web for many xenobiotic (foreign to organisms) substances (Eawag, 2016). Although biotransformation rates are probably the least well understood inputs to overall chemical fate modeling, we try to find generalities to better anticipate biologically mediated reactions in environmental systems.

26.2

Some Important Concepts about Microorganisms Relevant to Biotransformations Although plants and animals can biotransform many xenobiotic organic chemicals, from an environmental system mass balance point of view, microorganisms generally play the most important roles. Microorganisms include metabolically diverse bacteria, archaea, protists, and fungi. Representatives are present virtually everywhere in nature, even under extreme conditions of temperature, pressure, pH, salinity, oxygen, nutrients, and water content. In the following section, topics are discussed that pertain to judging whether a biotransformation will proceed under specific chemical and biological conditions in order to gain a sense of what factors may be limiting. Limits of Environmental Conditions Even when present, microorganisms are not necessarily metabolically active in a particular environment. As an example, the biodegradation of hydrocarbons in oxic (O2 present) settings is well known. However, in anoxic conditions (O2 absent), these compounds are often much more persistent (Fig. 26.1). Another example is the transformation of some chlorinated solvents (e.g., CCl4 ) under reducing (low or negative EH ) conditions (see Table 23.2), while in oxic situations these compounds are persistent (Bouwer and McCarty, 1983; Wilson and Wilson, 1985; Fogel et al., 1986; Aulenta et al., 2006). Often such effects are chemically reasonable (e.g., hydrocarbon degradation when O2 is present is thermodynamically favorable, and polychlorinated solvents are thermodynamically unstable under reducing conditions). But even under chemically suitable conditions for biotransformations, other considerations may supersede and limit degradation. For example, while tetrachloroethene (PCE) is thermodynamically unstable at EH (W) less than 0.5 V (see Fig. 23.3), it does not always degrade at the same rate under anoxic conditions. PCE may be more persistent if sulfate (SO2− 4 ) is present (Aulenta et al., 2006; Berggren et al., 2013). This may be due to the presence of sulfate-reducing bacteria that outcompete PCE reducers for a key reductant (e.g., H2 ) or that grow faster than PCE reducers (Yang and McCarty, 1998). In addition, since factors like temperature, pH, and oxygen concentration affect the composition, growth rate, and enzymatic expression of the microbial community, it is not surprising that such environmental conditions influence the rates of biologically mediated transformations and they may dictate whether these processes operate at all. Microorganisms Working Together: Syntrophy Another important aspect to consider when dealing with biotransformations is how different microorganisms can form associations that “enable” one another. It has long been recognized that “cooperating” microbial species, termed consortia, may

Some Important Concepts about Microorganisms

849

60

50

naphthalene (µM)

40

30

20

with O2 without O2

10 Figure 26.1 Variation in time courses of naphthalene degradation by microorganisms in laboratory soil–water incubations with O2 present (filled circles) or no O2 present (open circles). Data from Mihelcic and Luthy (1988).

0 20

10

0

40

30

50

time (days)

be required to execute a particular sequence of transformations in order to render the overall transformation thermodynamically feasible (Gray and Thornton, 1928). Classical examples of this involve the cooperation of sulfate-reducing bacteria with anaerobic methane oxidizers (Boetius et al., 2000), or the cooperation of two methanogenic microorganisms (see Chapter 21, Problem 21.3). With respect to biotransformations of anthropogenic chemicals, 3-chlorobenzoate has been found to be degraded by a consortium of microorganisms (Dolfing and Tiedje, 1986; Becker et al., 2005). The first species uses H2 and reductively removes the chlorine from the aromatic ring converting the carbon to which the Cl was initially attached from redox state C(+I) to C(−I): O

O

O

O

+ H2

+ Cl – + H+

Cl 3-chlorobenzoate

benzoate

(26-1)

850

Biotransformations

The degradation is continued by a second species that converts the benzoate product to acetate and carbon dioxide: O

O O 3

+ 6 H 2O benzoate

H 3C

O

+ CO 2 + 3 H2 + 2 H+

(26-2)

acetate

The H2 produced by this second species is subsequently used by the first microorganism, as well as by another organism, to make methane from CO2 . Finally, yet another species utilizes the acetate to producing methane and carbon dioxide: O H 3C

O

acetate

+ H+

CH 4 + CO2

(26-3)

methane

Since the build-ups of the products, benzoate, H2 , and acetate, are prevented, the catalytic removal of 3-chlorobenzoate by the first microorganism can continue. This example of syntrophy illustrates how cooperation of different microorganisms, each exhibiting specific enzymatic capabilities, may enable the continued biotransformation of a compound that would not have been performed by a single organism. Sharing Genetic Codes Microorganisms can also exchange genetic material between different microbial species via horizontal gene transfers. This sharing of genetic material allows for increased metabolic flexibility that can enable biotransformations of xenobiotic compounds (Springael and Top, 2004; Liang et al., 2012). One way in which horizontal gene transfer occurs is via plasmids, which are relatively short lengths of DNA that occur in many microbial species and have been found to code for a variety of degradative enzymes (Davison, 1999). Unlike the way we normally think of genetic inheritance in which DNA is passed “vertically” from mother to daughter during cell multiplication, plasmid DNA can be exchanged “horizontally” between non-progeny organisms. Such exchange allows for additional metabolic tools, or combinations of tools, to be acquired and utilized by a particular microbial species. An example of the effect of such horizontal genetic sharing was found in Alcaligenes spp. that were able to transfer genes encoding for pesticide degradation via a plasmid to a variety of distantly related species such as Escherichia coli (Don and Pemberton, 1981). Also plasmids encoding for the enzymes enabling complete degradation of the herbicide, 2,4-D, have been found widely in other microbial species (Kim et al., 2013). If the resulting metabolic capability proves beneficial, for example by providing a new energy or carbon source or by eliminating a critical toxicant, the newly enhanced microorganism will maintain the genetic code and the derived enzymatic facility since it confers a competitive advantage. However, should the extra tools prove not very

Some Important Concepts about Microorganisms

851

worthwhile (i.e., not helping confer competitive advantage), then the newly acquired genes, and the functions they confer, will probably be discarded. Through an amazing balance of metabolic and genetic cooperation, the microbial communities in the environment maximize their ability to adapt to changing conditions. Since the introduction of xenobiotic organic chemicals could present new nutritional opportunities (source of C, N, P…) or toxic threats, it is reasonable to expect microorganisms and their community structure to change in response to unfamiliar compounds in their milieu. Biocatalysts: Enzymes Finally, microorganisms facilitate biotransformations via two important approaches. The first approach involves the use of special proteins, called enzymes, which serve as catalysts. These “biological tools” promote substrate interactions and thereby lower the free energy of activation that determines the transformation rate (see Section 6.4, Fig. 26.6). Enzymes can lower the activation energy of reactions by several tens of kJ per mole, thereby speeding the transformations by factors of 109 or more; for example, one may use the Arrhenius equation (Eq. 21-30, Chapter 21) for a case of Ea of 80 kJ mol−1 decreased to 30 kJ mol−1 by an enzyme, thereby causing the rate to increase by about 6×108 times. Some of this reaction rate enhancement arises because enzymes hold the reacting compounds in an advantageous orientation with respect to one another. As a result, the enzymes facilitate substrate interaction, thereby lowering the entropy barrier for the reaction as compared to depending on diffusive collisions with the right reactant orientations. Additionally, enzymes include polar and charged structural components that can alter the electron densities of the bound reactants (e.g., see the use of zinc by hydrolases in Figs. 22.10 and 22.12). This lowers the barriers to breaking existing bonds and encourages new bonds to be made. Second, organisms may invest metabolic energy to synthesize reactive species. For example, before it is used to oxidize hydrocarbons, O2 is converted to a much more reactive oxidant by enzymatic complexation and reduction, the latter requiring the organisms to spend energy in the form of NAD(P)H (see Chapter 23, Fig. 23.14). This scheme is similar to one previously discussed in photochemical transformations where, through the boost in energy provided by the absorption of light, an activated species (e.g., 1 O2 , HO∙ , 3 CDOM∗ ) is formed that is much more reactive (Chapter 25).

R H

COOH

HOOC

NH2

D-amino acid mirror plane

H 2N

R H

L-amino acid

In light of these insights, some principles controlling the types of enzymatic tools that microorganisms maintain can be inferred. First, since organisms developed to continuously deal with biochemicals like amino acids, sugars, and fatty acids, and the corresponding proteins, carbohydrates, and lipids, we should expect much of their enzymatic apparatus is suited to performing the metabolic job of synthesizing (anabolism) and degrading (catabolism) such compounds. The corollary of this point is that recently invented chemicals, which are also often referred to as “xenobiotic compounds” (foreign to organisms), with structures that differ from those usually processed by organisms are sometimes not met with suitable enzymatic tools when microorganisms first encounter them. This applies to humans too; our catabolic capabilities are specialized for handling L-amino acids (see structures in margin).

852

Biotransformations

5-phenyl-pentanoic acid

stearic acid (a common fatty acid) O

O

OH

OH ATP + HSCoA (CoA = coenzyme A)

H2O + AMP + 2 Pi O

O

SCoA

SCoA oxidant (FAD)

reductant (FADH2) O

O

SCoA

SCoA H2O H OH O

H OH O

SCoA

SCoA oxidant (NAD+) O

O

reductant + H + (NADH)

O

O SCoA

SCoA HSCoA

SCoA

O

Figure 26.2 Parallel “beta oxidation” pathways for a xenobiotic substituted benzene, 5-phenyl pentanoic acid, and a naturally occurring fatty acid, stearic acid (Nelson and Cox, 2000).

O O

SCoA

3-phenyl-propanoic acid

SCoA

palmitic acid

Synthetic D-amino acids made of the same atoms, but linked together so as to make the mirror image of L-amino acids, do not add to our caloric intake since we cannot readily metabolize them. Thus, one might expect that structurally unusual chemicals will be somewhat persistent in the environment with respect to microbial transformations. A second key principle is that enzymes do not have perfect substrate specificity. Enzymes, although “designed” for binding and catalyzing reactions of particular chemicals, may also have some ability to bind and induce reactions in structurally similar compounds. This imperfect enzyme specificity suggests that xenobiotic chemicals, exhibiting some structural part very like those of common substrates, may undergo “fortuitous” biotransformation. For example, 5-phenyl pentanoic acid may become involved with the enzymatic apparatus designed to handle fatty acids since parts of their structures are the same (Fig. 26.2). Thus, a certain level of biodegradation may occur for xenobiotic chemicals with structural similarities to naturally occurring

853

Some Important Concepts about Microorganisms

organic compounds. This is part of the basis for a phenomenon often referred to as co-metabolism (Horvath, 1972; Alexander, 1981; Van Eerd et al., 2003; Nzila, 2013; Frascari et al., 2015), in which non-target compounds are biotransformed by enzyme systems, but these compounds do not serve as a growth substrate. This imperfect binding specificity principle also helps us to understand why chemicals called competitive inhibitors may block the active sites of enzymes (i.e., the locations within the macromolecular enzymes where chemical bond changes occur). These inhibitors are structurally like the enzyme’s appropriate substrate, enabling them to bind to the enzyme’s active site. But these compounds may be somewhat, or even completely, unreactive, and as a result they “gum up the works”. Such enzyme inhibition appears to explain the limited microbial dehalogenation of 3chlorobenzoate in the presence of 3,5-dichlorobenzoate (Suflita et al., 1983). In this case, 3,5-dichlorobenzoate is initially transformed to 3-chlorobenzoate: O

O

O

O

O

2e – + H+ Cl

Cl

3,5-dichlorobenzoate

+ Cl –

O

2e – + H+

+ Cl –

Cl 3-chlorobenzoate

benzoate

(26-4) Subsequent degradation of the 3-chlorobenzoate does not proceed until most of the original 3,5-dichlorobenzoate is transformed. The explanation for this finding is that the dichloro aromatic substrate competes with the monochloro-compound for the same enzyme active site. As a result, 3,5-dichlorobenzoate acts as a competitive inhibitor of the biochemical removal of 3-chlorobenzoate. Once nearly all the dichloro-compound is degraded, 3-chlorobenzoate molecules can increasingly access the enzyme site and transformation to benzoate proceeds. This type of substrate–substrate interaction may be especially important for contaminants introduced as mixtures in the environment. One example is the mix of polycyclic aromatic hydrocarbons co-introduced in coal tar wastes. Laboratory observations of the biodegradation of such hydrocarbons show that some of these components can inhibit the removal of other compounds in the mix (Guha et al., 1999). Such results indicate that the rate of a particular chemical’s biotransformation may be a function of factors such as the presence of competing substrates interacting with the same enzyme systems. A third generality regarding the metabolic aptitude of organisms is that they always seem to have some relatively nonspecific enzymes available just for the purpose of attacking unexpected or unwanted compounds (Schlichting et al., 2000; Denisov et al., 2005; Urban et al., 2015). This may be analogous to our carrying a Swiss Army knife so as to be able to pry, pick at, slice, uncork, punch, and tweeze as the occasion requires. Organisms have long been bombarded with chemicals made by other

854

Biotransformations

species, and consequently, they have always needed to eliminate some of this chemical “noise.” The strategy for many bacteria often entails an initial oxidative step, converting the insulting chemical signal into something more polar. The resultant product may now fit into presently held metabolic pathways; or since it is more water soluble, it may be returned to the environment. The lack of substrate specificity designed into this enzymatic capability concomitantly causes such proteins not to be especially abundant in most organisms. From the organism’s point of view, it would simply be energetically too expensive to maintain a high concentration of these enzymes (like carrying ten Swiss Army knives instead of one). Nonetheless, this principle implies that sometimes organic chemicals, which are unusual to the relevant organisms, may be slowly degradable via the use of such relatively nonspecific enzymes. Whatever the origin of a capability for initial attack, the goal of these reactions is to transform the compound into one or several products structurally more similar to chemicals that microorganisms are used to metabolizing. As a result, after one or just a few transformations, the resulting chemical product(s) can be included in the common metabolic pathways and be fully degraded. A good example of this is the bacterial degradation of substituted benzenes (Fig. 26.3). Initially, these aromatic hydrocarbons are oxidized to catechol (ortho-dihydroxybenzene) or its derivatives by an oxygenase (adding O2 ) and a dehydrogenase (removing hydrogen to NADH): H OH

NADH + H + oxygenase

OH H

O2

benzene

OH

dehydrogenase

OH NADH + H +

catechol

cis-cyclohexa-3,5diene-1,2-diol

(26-5) Catechol and its derivatives are also produced in the metabolism of numerous natural aromatic compounds, like salicylate or vanillate (Suzuki et al., 1991; Brunel and Davison, 1988): O

O

OH OH

O

OH

O2 + H+ + NADH

O

O

(26-6)

O O

O2 + H+ + NADH

+ OH

OCH3 OH

+ HCO 3–

OH

H

H

+ H 2O

(26-7)

855

Some Important Concepts about Microorganisms

substrate

product OH OH

oxygenase

benzene CH3

CH3 OH

toluene OH NH2

OH OH

aniline –NH 4 OH

OH OH

succinate + acetate

phenol COOH

OH OH

benzoic acid

COOH COOH

X

–CO2 Cl

Cl OH

chlorobenzene OH COOH

OH

OH

OH

salicylic acid –CO2 Cl

OH

Cl Cl

Cl

1,2-dichloro-benzene

X

COOH CHO

OH OH NH2

OH OH acetaldehyde + pyruvate

4-chloro-aniline –NH4

Cl

Cl

NO2

OH Cl

HO

Cl

2-chloro-nitrobenzene –NO2 COOH

OH OH

Figure 26.3 Degradation of benzene derivatives so as to fit into existing catechol pathways.

3-chlorobenzoic acid Cl

–CO2

Cl

856

Biotransformations

As a result, pathways are available in many microorganisms for processing catechol derivatives (Fig. 26.3), and thus continued breakdown proceeds via enzymatic pathways, which open the ring between the two hydroxyl substituents (ortho-cleavage) or adjacent to them (meta-cleavage). The resulting compounds are converted to small, useful metabolites. Thus, the initial oxidation of the aromatic ring is the key to delivering the xenobiotic compound into a pre-existing catabolic pathway and thereby allow continued biotransformation since the buildup of initial products would shut down the catalysis of the process. Exceptions exist to this tendency for ready incorporation of the initial transformation products of xenobiotic compounds into a common pathway. First, sometimes a product is formed which is unreactive in subsequent steps in a particular microorganism. Such partially degraded compounds have been referred to as dead-end metabolites (Knackmuss, 1981). An example of this is the 5-chloro-2-hydroxymuconic acid semialdehyde produced by the meta-cleavage of 4-chlorocatechol by a particular pseudomonad species: OH

OH OH

meta-cleavage

COOH

(26-8)

CHO Cl

Cl

Apparently, the presence of the chloro substituent blocks the next reaction which normally operates on 2-hydroxymuconic acid semi-aldehyde to produce 2-oxo-pent-4enoic acid: O

OH

O

COOH

COOH

CHO

CHO

2-hydroxy-muconic acid semialdehyde

COOH

(26-9) 2-oxo-pent4-enoic acid

If a meta-cleavage pathway is the only one available to a particular microorganism, then the 5-chloro-2-hydroxymuconic acid semi-aldehyde (Eq. 26-8) will accumulate unless another “initial” biotransformation is performed on it. Another exception to the tendency for initial biotransformation products to be readily directed into subsequent steps in common metabolic pathways involves the formation of so-called suicide metabolites (Knackmuss, 1981). These problematic products result when the biotransformation yields a compound that subsequently attacks the enzymes involved. If this attack debilitates one of these enzymes, the successful operation of the relevant metabolic pathway is stopped. An example is the

Some Important Concepts about Microorganisms

857

production of acyl halides from 3-halocatechol in certain microorganisms (e.g., Bartels et al., 1984): OH

OH OH

COOH

meta-cleavage

(26-10)

COX

X 3-halo-catechol

an acyl halide

Similar suicide metabolites have been seen for fluorinated compounds (Kiel and Engresser, 2015). Such acyl halides react rapidly with nucleophiles, and consequently these compounds may bind to nucleophilic moieties (e.g., –SH) of the enzyme near the site of their initial production: O

O Enz

Nu

+

Enz R

X

Nu

+ X– R

(26-11)

The resulting change in the enzyme’s structure may limit or even prevent its continued operation, such as is seen for the meta-dioxygenase, which formed an acyl halide from 3-halo-catechol. Thus, if biodegradation of the original compound (e.g., 3-halocatechol) is to proceed, either a rapid hydrolysis of the acyl halide must occur before it can do damage (Mars et al., 1997; Kaschabek et al., 1998) or another metabolic pathway such as ring opening “distal” to the halogen (i.e., between the 1 and 6 carbons, Riegert et al., 1998) must be utilized. By avoiding these potential metabolic pathway problems, many xenobiotic compounds are successfully biotransformed after a suitable initial enzymatic attack is made. Finally, we should recognize that not all of the enzymes which organisms are genetically capable of producing are always present (i.e., they are not constitutive). In response to a new stimulus, such as the introduction of an organic compound, organisms can turn on the production of appropriate enzymes. Those enzymes are referred to as inducible. This process of gearing up for a particular metabolic activity may make the description of the rate of a pollutant’s biotransformation somewhat complicated because a time of no apparent activity, or a lag period, would be seen. Other possible reasons for lag periods include: ! Enzymes that are already available are “repressed ” (i.e., made to be ineffective)

and time must pass or some condition must change before they are altered so as to become active.

! Time may be required for a few bacteria to multiply to significant numbers (see

Section 26.4).

! An interval may be necessary for mutations to enable development of enzymes able

to perform new or more efficient transformations.

858

Biotransformations

! Plasmid/horizontal gene transfers may be required to allow existing microorganisms

to develop or combine suitable enzymatic tools.

! It may simply be that particular species of microorganisms must “immigrate” to

the environmental region of interest or that cysts or spores that are present must germinate.

These phenomena exhibit very different timescales, ranging from minutes for enzyme induction and de-repression to days for sufficient population growth to undetermined lengths of time for “successful” mutations. Therefore, one or more of these factors may make it difficult to predict how fast a chemical in a particular environmental setting will undergo even the initial step of biodegradation.

26.3

Initial Biotransformation Strategies Our next goal is to anticipate how a xenobiotic organic compound may be biologically attacked based on its chemical structure and the conditions in the environment. We do this by looking at particular families of xenobiotic compounds (e.g., organohalides, aromatic hydrocarbons, esters) and noting how microorganisms have been found to initially biotransform them. The chemical workings of relevant enzymes involved in these first biotransformation steps are described in Chapters 22 and 23, in which similar abiotic mechanisms are also discussed. It is notable that there are only a modest number of reaction types that “microbial organic chemists” use to initiate the breakdown of most xenobiotic compounds (Table 26.1). But most importantly, by using these empirical experiences, we may understand whether a xenobiotic compound is likely to be biologically persistent under certain conditions. In the following sections, the individual approaches are briefly discussed and examples of important (a) chemical, (b) microbial, and (c) environmental factors are noted. Hydrolyses

SH O

O

O

H

N

N H NH3

H

glutathione

H

O

O O

First, we note that compounds that have good leaving groups on saturated carbons, such as alkyl halides (Eq. 26-12), or on unsaturated carbons like the esters (Eqs. 2613 and 26-14) can be degraded by enzymatic hydrolysis (see Section 22.3). Importantly, these reactions can occur in both oxic and anoxic conditions since the initial reactions do not need to involve oxidations or reductions. Rather, such hydrolysis can be performed through enzymatically mediated nucleophilic attacks (Table 26.1). The bionucleophiles involved (see margin) may include (a) the thiol group of a cosubstrate called glutathione, (b) the hydroxyl group of the amino acid, serine, or (c) the carboxyl anion of amino acids like glutamate when these latter amino acids are part of an enzyme’s active site (Fersht, 1985). It is also notable that enzymes that catalyze such biotransformations are often constitutive (that is, always present). Perhaps surprisingly, since these appear to involve superficially “simple” nucleophilic reactions, one cannot always understand the relative reactivities of a particular

Initial Biotransformation Strategies

Table 26.1 Important Metabolic Approaches and Tools of Microorganisms for Initiating the Breakdown of Organic Pollutants chemical / environmental factors

metabolic approach and “tools”

uneven electron density due to heteroatoms; oxic or anoxic environment 1. if leaving group on sterically accessible position Enz

δ

SH

+

δ

then nucleophilic attack, e.g., via –CH2–S

–

L

2. if ester-like structure (Z = C, P, or S; X = O, S, or NR)

Enz

R δ+ Z X L

OH Zn+

Enz

(26–12)

then hydrolysis with (a) base catalysis (e.g., serine–O –) or (b) acid catalysis (Zn 2+ and –COO–) R

–

δ

(26–13)

+ L

Z X HO

δ–

X R

+ L

HO

Zδ

+

R

L

C

+ L

Z X

(26–14)

HO

O O

generally even electron density; oxic environment 3. If π, n electrons (N or S), alkyl σ-electrons

Enz

O

Enz

O

then oxidation via electrophilic oxygen (e.g. Fe(IV)O•)

O

S

R1

O S

O

Enz

H 2N

O

R1

H R 2 +

H+

N

δ

O Zn+

(26–17)

then reduction via nucleophilic H – transfers (e.g., from NAD(P)H) and Lewis acid catalysis (e.g., Zn 2+)

H 2N H

(26–16)

HO CH3

H CH3

4. if aliphatic –C(=O)– , –OH have partially oxidized carbon atoms

N

R1 R2

R2

Enz

(26–15)

Enz

O OH +

H C R2 R1

(26–18)

Zn+

(continued )

859

860

Biotransformations

Table 26.1 (Continued) chemical / environmental factors

metabolic approach and “tools”

sterically limited access due to substitution; anoxic (micro)environment 5. if polyhalogenated

then electron transfer from metals (Co(I), Fe(II)) to halogen and addition of H+ to the compound Cl

Cl

Enz(Co (I)) + Cl

H

H+

C C

Cl +

C C Cl

Cl

Cl

(26–19)

Cl

generally even electron density; anoxic environment 6. If benzyl, allyl, alkyl σ-electrons

then H-abstraction via –S• radical and addition to fumarate –OOC

Enz

H

S

CH 2

COO – HOOC HOOC

7. if alkene

CH

CH 2 (26–20)

CH 2

then addition of water

Enz (M)

O

C C

H

OH

H

(26–21)

H

8. if enol (including phenol)

then addition of carboxyl group via –B–COOH

–

δ

Mn

O

H

δ+ OH

C

O

O Enz

X

OH HO

(26–22) C

X

O

hydrolase interacting with a series of structurally related compounds. An example of this has been seen for the haloalkane dehalogenases. While sometimes expected patterns can be seen (e.g., R-Br reacts faster than the corresponding R-Cl), other trends (e.g., larger R groups react faster than smaller ones) do not match reactivity expectations. Such size considerations may result from differences in the sizes of the channels accessing a given haloalkane dehalogenase’s active site and the sizes of the hydrophobic reaction sites (Chovancova et al., 2007; Novak et al., 2014). One key aspect of these enzymatic reactions is that they commonly involve an initial nucleophilic attack that displaces the leaving group, and then a second reaction that releases the enzymatic nucleophile from the remainder of the substrate’s structure.

861

Initial Biotransformation Strategies

Often this second reaction, called a dealkylation for a haloalkane or deacylation for an ester, controls the overall rate of enzyme reaction (e.g., Bosma et al., 2003). It is also important to note that, even if the dealkylation step is overall rate-limiting, one can have significant stable carbon isotope fractionation (see Chapter 27) arising from the preceding, non-overall rate limiting, nucleophilic attack that breaks the carbonhalogen bond. If the products of such biotransformations provide the microorganism with useful energy and/or materials, the hydrolysis reaction may enable growth of the population. As mentioned in Chapter 22, a bacterial species has been found that can grow on methylene chloride as its sole source of carbon (Stucki et al., 1981). But sometimes monohalogenated compounds act as growth inhibitors because the adduct that is formed is difficult to hydrolyze and may even incapacitate the enzyme. Oxidations For compounds such as hydrocarbons without leaving groups, initial microbial attack in aerobic environments may involve oxidation using an electrophilic form of oxygen (Section 23.4). Such reactions involve O2 as a co-substrate, but since O2 in the environment exists primarily as a triplet species (see Chapter 25), it is not very reactive abiotically with most organic compounds. As a result, organisms invest metabolic energy in the form of NAD(P)H to convert this O2 into a more effective oxidant. Also, the oxygenase enzymes use metals to “hold” the reactive oxygen species (Poulos, 2014; Boer et al., 2014; Sirajuddin and Rosenzweig, 2015). The key structural feature of the organic substrate that dictates the microbial point of attack is the site of the most accessible electrons; such as π and nonbonded electrons (Table 26.1, Eqs. 26-15 and 26-16). In the absence of such sites, oxidation can involve the σelectrons of carbon-hydrogen bonds, even for as unreactive a molecule as methane (Dalton and Stirling, 1982; Sirajuddin and Rosenzweig, 2015; Wang et al., 2015). One might expect that electron-withdrawing substituents on aromatic systems make the π-electrons of the ring system less readily attacked by electrophilic oxygen (see Hammett constants, Table 4.8). This is consistent with observations on a series of substituted benzoates where steric factors do not dominate (Knackmuss, 1981): O

O

O

O

O

O

O

O

O

O

O

O O

O

> Cl

Br

Cl Cl

Br

0.22

0.23

CH3 0

–0.06

–0.16

O

O

O

>

CH3

Σσj =

O

0.37

0.40

Cl

Cl Cl 0.74

0.59

(see table 4.8) faster biodegradation

intermediate

slower biodegradation

This trend in relative biodegradability is consistent with a situation in which the ratelimiting step involves an electrophilic attack on the π-electrons of the ring. However,

862

Biotransformations

we must also recognize that the reactive sites of oxidases, like those of the haloalkane dehalogenases previously discussed, are held within a macromolecular protein environment, and steric effects can limit access to the site (Urban et al. 2015; Wang et al., 2015). Also, it may be the case that steps associated with preparing the oxidizing species are overall rate limiting (see Fig. 23.14). As a result, relative rates of reaction cannot always be understood simply in terms of the substrate structure. Reductions

Cl R

C

Cl

Cl C(+III) O R

An example of a xenobiotic compound reduced through such reduction is TNT (trinitrotoluene). This compound is transformed by nitroreductases that deliver a H− (Somerville et al., 1995; Vorbeck et al., 1998; Pak et al., 2000; Bai et al., 2015):

N O N(+III) O

R1

S O S(+II)

For compounds with part, or even all, of their structure carrying strongly electronegative atoms like oxygen or chlorine (see margin), attack by oxidases would not be favored. This is particularly true in anoxic environments. Instead, enzymatic reduction reactions (see Section 23.4) can be used to transform the xenobiotic substrate. As illustrated in Table 26.1, such reactions may involve a nucleophilic form of hydrogen called a hydride, H:− (Eq. 26-18) or highly reduced metals like cobalt in its +I redox state (Eq. 26-19).

ArNO2 R2

nitro-

+ 2e– + 2H+ – H 2O

ArNO nitroso-

+ 2e– + 2H+

ArNHOH

(26-23)

hydroxylamino-

The rates of such reductive biotransformations appear to depend on factors “outside” of the enzyme-mediated reaction such as the availability and type of electron donors in the environment of interest (Fahrenfeld et al., 2015). As a result, understanding the overall rate may require knowing how fast the relevant population of microorganisms is growing. Other reductions of organic substrates occur via electron transfers from reduced metals in enzymes (Fig. 23.15). This is particularly important for highly halogenated compounds. Such reductive transformations have been known for a very long time (e.g., Hill and McCarty, 1967), but the factors controlling the rates of reductive dehalogenation are still somewhat uncertain at sites of interest (Chambon et al. 2013; Schneidewind et al. 2014). Efforts to see whether appropriate microbial species are present in the relevant environments usually, but not always, find “competent” species are present. For example, Hendrickson et al. (2002) detected Dehalococcoides in 21 of 24 sites that they tested using a genetic marker. Further, as H2 is used by microorganisms to drive the overall reduction of compounds like tetrachloroethene (MaymoGatell et al., 1997), perhaps it is not surprising that competition for this valuable H2 among various microbial sub-populations affects rates of tetrachloroethene biotransformations (Yang and McCarty, 1998). Recognizing such competition helps us ) in an environsee why the presence of another electron acceptor like sulfate (SO2− 4 mental setting of interest may impede tetrachloroethene dehalogenation since sulfatereducing bacteria are very good at using H2 too (Berggren et al., 2013). Consequently, while we know that polyhalogenated compounds can be biotransformed by a process

Initial Biotransformation Strategies

863

in which halogen atoms are replaced by hydrogens, it is uncertain whether enzyme chemistry, environmental conditions (e.g., H2 concentration), the presence of metabolically competent microbial species, the growth rate of a particular microbial species, or resource competition between microbial species limits the rates at any particular site of interest. Additions O O

O O fumarate

For xenobiotic compounds that (a) do not have a good leaving group, (b) are already quite “electron rich” so as to not be susceptible to reductions, and (c) are present in anoxic environments, microorganisms may initiate the biotransformations by adding carbon-containing groups or water to the substrate. One such carbon-containing group is fumarate (see margin and Eq. 23-41). The fumarate addition strategy involves a novel enzyme, benzylsuccinate synthase, which uses a free radical mechanism (Eklund and Fontecave, 1999; Krieger et al., 2001; Funk et al. 2015). This enzyme harbors a glycyl radical that can abstract a hydrogen atom from a nearby cysteine residue to begin a catalytic cycle (Spormann and Widdel, 2000). The thiyl radical abstracts a hydrogen from the target substrate, and then the radical substrate product can add to the double bond of fumarate, held in the active site of the enzyme. As noted in Chapter 23 and also addressed in Chapter 27, as an example, toluene is converted to benzoyl-CoA and thereby enters the anaerobic degradation pathway of many hydrocarbon substrates (Harwood and Gibson, 1997; Heider and Fuchs, 1997; Jarling et al., 2015): H O

O O

O

O

(26-42)

SCoA

While Beller et al. (2008) have found benzylsuccinates in groundwater plumes that were toluene and xylene contaminated, little is known about the rates of this type of process in natural environments. However, Kazy et al. (2010) have shown that the rate of toluene degradation in laboratory microcosms made from aquifer solids correlates well with quantitative polymerase chain reaction (qPCR) measures of the presence of the gene coding for benzylsuccinate synthase in the same microcosms. They observed about 4×10−16 mol toluene lost per bssA gene copy per day. Therefore, it may eventually be possible to use molecular genetics to interrogate sites of interest so as to allow estimation of the rate of such a degradation pathway. Two other common addition approaches include adding water to a double bond to make an alcohol and adding a carbonate to aromatic rings (Table 26.1, Eqs. 26-21 and 26-22). Schink (1985a and b) reported that 1-hexadecene and acetylene (HC≡CH) were degraded in the absence of O2 , and it appeared that these unsaturated hydrocarbons were hydrated in the initial anaerobic biotransformation (Eq. 26-21). Since then, others have also found evidence of such addition of water to isolated unsaturated sites (Spormann and Widdel, 2000).

864

Biotransformations

Another approach used by microorganisms to initiate the degradation of some xenobiotic organic compounds in anoxic settings involves converting the substrate to a carboxylated derivative (Kiel et al., 2011) by adding CO2 to the structure (Eq. 26-22). After an initial aromatic ring carboxylation, further degradation can proceed via the benzoyl-CoA pathway (Heider and Fuchs, 1997). In summary, by recognizing the various types of “reagents” microorganisms have, we may anticipate the types of biotransformations that will be used for initial attack given the structure of a xenobiotic compound of interest (Table 26.1; see Wicker et al., 2016). Further, we can begin to see what co-substrates (e.g., O2 , H2 ) may be needed and which environmental conditions encourage a particular biotransformation.

26.4

Rates of Biotransformations Several processes may control the overall rate of a biotransformation (Fig. 26.4). These may include processes outside the microorganisms (e.g., delivery of the substrate to the organisms), enzymatic rates associated with microbial metabolism, and microbial growth. All these aspects are addressed in the following discussion.

unavailable i 5 transport bioavailable 1

4

microbial growth

cts

7

i

uptake

release product(s)

prod u

Figure 26.4 Sequence of events in the overall process of biotransformations: (1) bacterial cell containing enzymes takes up organic chemical, i, (2) i binds to suitable enzyme, (3) enzyme:i complex reacts, producing the transformation product(s) of i, and (4) the product(s) is(are) released from the enzyme. Several additional processes may influence the overall rate such as: (5) transport of i from forms that are unavailable (e.g., sorbed) to the microorganisms, (6) production of new or additional enzyme capacity [e.g., due to turning on genes (induction), due to removing materials which prevent enzyme operation (activation), or due to acquisition of new genetic capabilities via mutation or plasmid transfer], and (7) growth of the total microbial population carrying out the biotransformation of i.

i

enzyme complex

2

3 bioreaction

i other reactants, e.g., O2

6 induced enzyme production

i

Rates of Biotransformations

865

Bioavailability The first process that can limit initial biotransformation rates simply involves delivery of the organic substrates from the environment to the microorganism. This situation is often referred to as a matter of bioavailability. Generally, organic compounds in environmental systems are distributed among co-occurring gaseous, liquid, and/or solid phases. A classic example involves the distribution of an organic pollutant in a sediment bed with some molecules occurring as “dissolved-in-the-pore water” species and others as a “sorbed-to-the-particles” species (see Chapters 12 and 16). As a result, transfer of the chemical from within sediment solids to accessible media like pore water, which contacts the cells is necessary to allow biotransformations (Hatzinger and Alexander, 1995; Kim and Weber, 2005; Ortega-Calvo and Gschwend, 2010). These mass transfers (depicted as step 5 in Fig. 26.4) are most critical whenever we are dealing with situations where most of a chemical of concern is sorbed, such as encountered in sediments, soils, and aquifers for very hydrophobic compounds. So if the rate of desorption is slow compared to the rate of biotransformation, then the overall rate of biotransformation simply becomes the rate of desorption. However, if one can accurately assume that the rate of desorption is fast compared to chemical removal by biotransformation, then the biotransformation kinetics expression reduces to one that reflects the dissolved concentration of the contaminant experienced by the microorganism. In this case, one can use the fraction of i that is dissolved (see Eq. 12-16) in the kinetics expression: (

dCit ∕dt

) bio

′ = −fiw kibio Cit

(26-24)

where (dCit ∕dt)bio is the rate of change of total (subscript “t”) concentration of i, Cit , with time (M s−1 ) due to biotransformation, fiw is the fraction of total i that is dis′ is the (pseudo)first order solved in the aqueous phase (Chapter 12, Eq. 12-18), and kibio −1 rate coefficient for biotransformation of dissolved i (s ). To apply an expression like ′ in the case where chemical access Eq. 26-24, we also need to understand what sets kibio is not limiting. Biouptake Kinetics Another process that may influence the rate of biotransformations of organic compounds involves uptake into the cell (step 1 in Fig. 26.4). Since many chemicals of interest are xenobiotic, in general microorganisms may not have active transport systems designed to accumulate such substances from the surroundings into the cell. However, for nonpolar substances, the lipid-rich cell membranes allow hydrophobic chemicals to dissolve into these cellular boundaries (recall our discussions of biota– water partitioning, Chapter 16), such that nonpolar chemicals can quickly move across the layers of the cell envelope by passive diffusion (Nikaido, 1979; Konings et al., 1981; Sikkema et al., 1995; Bugg et al., 2000). Experimental observations using nonmetabolizable compounds like trichlorobenzene (Ramos et al., 1997; Ramos et al., 1998) and mutants unable to biotransform a test chemical like phenanthrene (Bugg et al., 2000) show that passive transfer of nonpolar compounds occurs relatively quickly, taking only seconds to minutes. Thus, if a compound can diffuse across such

866

Biotransformations

a membrane in about 60 s, and this process limited the biotransformation rate, then ′ kibio would be about (ln 2)/(60 s) or 0.01 s−1 .

OOC OOC

N

COO N

EDTA

COO

We should also note that membranes of microorganisms have “channels” called porins, which permit the entrance of small hydrophilic substances (Koebnik et al., 2000). In studies of enteric bacteria, passive glucose uptake exhibited transmembrane uptake time scales of less than a millisecond (Nikaido, 1979). Thus, the rate of passive uptake of small, hydrophilic molecules (< 500 to 600 molecular mass units) via membrane pores of bacteria is not likely to cause them to avoid biodegradation for prolonged times. But porins are somewhat selective. Larger molecules diffuse in more slowly. And charged chemicals may experience electrostatic repulsions that limit their ability to enter at all. This may explain the situation for highly charged organic compounds like ethylene diamine tetraacetate (EDTA), which are thought to be biologically recalcitrant because of slow or nonexistent passive uptake by most microorganisms. Only cation-complexed (e.g., with Ca2+ ) forms whose charge is neutralized appear suited as uptake (see Egli, 2001). Active uptake mechanisms have been found in some bacteria for various xenobiotic organic anions. These include 4-chlorobenzoate (Groenewegen et al., 1990, Chae and Zylstra 2006), 4-toluene sulfonate (Locher et al., 1993), 2,4-D (Leveau et al., 1998; M¨uller and Hoffman, 2006), mecoprop and dichlorprop (Zipper et al., 1998), and even aminopolycarboxylates (Egli, 2001). Such active uptake appears to be driven by the proton motive force (i.e., depletion of protons in bacterial cytoplasm). These transport mechanisms exhibit saturation kinetics (e.g., Zipper et al., 1998), and so their quantitative treatment is the same as other enzyme-limited metabolic processes (discussed in Michaelis-Menten cases). Michaelis-Menten Enzyme Kinetics Once inside the cell, other processes remain that may govern the overall biotransformation rates. First, the presence of the chemical may cause the organism to produce more key enzymes to help with the degradation of this substance (step 6 in Fig. 26.4). It is possible, though, that the requisite enzymatic apparatus is constitutive (i.e., it is always present), and used to process normal metabolites. But once the enzymes are available, the overall biotransformation rate may depend on the reactions catalyzed by these proteins with other cellular components (steps 2, 3, and 4 in Fig. 26.4). These interactions are best quantified using Michaelis-Menten enzyme kinetics (Michaelis and Menten, 1913 as translated by Johnson and Goody, 2011). To focus on enzyme kinetics, we first assume the biotransformation of the xenobiotic organic compound of interest does not cause growth of the microbial population. If microbial population growth did result, then the quantities of degradative tools available would increase with time too; this situation is addressed in the next section on Monod growth kinetics. Organisms may not grow on particular substrates for various reasons. First, the available concentration of the substrate may be insufficient to support microbial multiplication. For example, Tros et al. (1996) showed that 3-chlorobenzoate was needed at concentrations above 10 μM to allow a Pseudomonas species to grow on it as the sole source of carbon and energy. Lower concentrations were metabolized if another growth substrate like acetate was

Rates of Biotransformations

867

provided. In such cases where the organisms have alternative and abundant primary substrates to use for growth (e.g., acetate), the transformations of the xenobiotic compounds may be incidental processes occurring as secondary metabolism (i.e., involving enzymes that transform minor substances).

N quinoline (Q)

N

Such co-metabolism has also been seen to cause transformations of other xenobiotic compounds (Horvath, 1972; Alexander, 1981; Van Eerd et al., 2003; Nzila, 2013; Frascari et al., 2015). This may apply in many engineered laboratory and field situations (e.g., Kohler et al., 1988; Semprini, 1997; Kim and Hao, 1999; Rittmann and McCarty, 2001). In such cases, the rate of chemical removal may be controlled by the speed with which an enzyme catalyzes the chemical’s structural change (e.g., steps 2, 3 and 4 in Fig. 26.4).

BQ concentration (µmol L—1)

cell numbers (cells L—1)

benzo[f]quinoline (BQ)

Alternatively, a population of organisms may be using a particular substrate for growth, and due to imperfect enzyme specificity, they also transform compounds with similar structures at the same time (see co-metabolism in section 26.2). These unintended substrates may be so recalcitrant that they alone cannot support microbial growth. An example of this involves a culture of bacteria that could grow on quinoline (Q); the microorganisms also degraded benzo[f]quinoline (BQ) if it was present (Smith et al., 1978). However, BQ did not support cell growth (Fig. 26.5).

Figure 26.5 Time courses for bacterial cell numbers (B) and benzo[f]quinoline (BQ) concentrations in a batch culture experiment; data from Smith et al. (1978).

(a)

1011

[B] =1.47 ± 0.04×1010

1010

109

0

6

1

2

3

4

5

(b)

4

2

0 0

1

2 3 time (hours)

4

5

868

Biotransformations

As already introduced in Chapter 21 (Eq. 21-29), such enzyme-mediated kinetics were characterized long ago by Michaelis and Menten (1913), and are, therefore, commonly referred to as Michaelis-Menten cases. For situations in which the products of enzymatically catalyzed reactions are quickly removed, Michaelis and Menten found that the kinetics expression for the removal of i can be written: (

) ViMM Ciw dCiw ∕dt = KiMM + Ciw

(26-25)

where ViMM is the maximum rate for the rate-limiting enzyme-catalyzed reaction step [ML−3 T−1 ] that depends on the abundance of enzyme [Enz]t , Ciw is the dissolved (i.e., bioavailable) substrate concentration [ML−3 ], and KiMM is the half-saturation constant reflecting concentration of i when the enzymatic rate is half maximal [ML−3 ]. KiMM is given the subscript, MM, here to remind us that it reflects Michaelis-Menten enzyme kinetics as distinguished from KiM , which is used to model Monod growth kinetics. With this enzyme kinetics model, we expect: ′ kibio [T−1 ] =

ViMM KiMM + Ciw

(26-26)

Let us briefly look in some depth at a specific type of enzyme, a haloalkane dehalogenase (see Chapter 22, Section 22.3). Initially this enzyme uses a nucleophile to displace an aliphatic halogen, and in so doing it makes an alkylated enzyme. Subsequently, this adduct is hydrolyzed to free the enzyme to carry out further catalysis. As noted in Section 26.3, either the enzyme alkylation step or the dealkylation, or a combination of the two, may be overall rate limiting, but both situations will be faster than the corresponding noncatalyzed rate as indicated by the heights of the maximal energy barriers shown in Fig. 26.6. However, the two cases have significantly different sequences of energy barriers for the enzymatic processes. When the initial nucleophilic attack on the haloalkane is rate limiting, the situation looks like that shown in Fig. 26.6a as the highest barrier in that sequence involves converting the starting haloalkane (S in the figure) into the products (Enz–P + X− ). This contrasts with the other limiting case in which breaking the Enz–P bond, which is dealkylation of the enzyme, limits the rate. Now the highest energy barrier to traverse involves dealkylating the enzyme (or reaction Enz–P to Enz + P; Fig. 26.6b). Of course, if these two maximal energy barriers are similar in height, then both reactions will be involved in setting the overall rate. Now we may ask, what do the Michaelis-Menten expressions look like in these two cases? One can deduce two overall rate expressions shown in Box 26.1, assuming either the alkylation step or the dealkylation step is overall limiting. Consider the following series of steps and associated reaction rate coefficients: Step 1: Enzyme:substrate association to make “EnzS”: k1

−−−− → ← − (Enz–Nu:R–L) Enz–Nu + R–L − k−1

where the colon indicates the noncovalent enzyme-substrate association.

(26-27)

869

Rates of Biotransformations

(b)

(a)

transition state of nonenzymatic reaction Δ‡G0nonenzymatic transition state of enzymatic reaction Δ‡G0enzymatic Enz + S G0

Δr

EnzS

Enz + S

EnzP

EnzS

Δ rG0

EnzP

Enz + P

Enz + P

Enz: enzyme S: substrate EnzS: enzyme-substrate-complex

P: product EnzP: enzyme-product-complex

Figure 26.6 Schematic representation of the change in activation energy barrier for two enzymatically mediated reactions as compared to the analogous non-catalyzed chemical reaction: (a) The initial catalytic step (EnzS to EnzP) is the slowest (rate determining) step. (b) The dissociation (EnzP to Enz+P) is the slowest (rate determining) step. In both cases, Δr G0 is negative; that is, the microorganisms may gain energy from the reaction.

Step 2: Nucleophilic reaction, release of leaving group (alkylation to make Enz–P + X− ): k2

−−−− → (Enz–Nu:R–L) − ← − (Enz–Nu–R+ ) + L− k−2

(26-28)

Step 3: Second nucleophilic reaction, release of remainder of substrate (dealkylation to make Enz + P): k3

−−−− → (Enz–Nu–R+ ) + H2 O − ← − (Enz–Nu) + R–OH + H+ k−3

(26-29)

With this system of reactions, we can derive kinetics expressions assuming either step 2 or step 3 is the overall rate limiting process (Box 26.1). When the initial nucleophilic reaction is the slowest step in the overall process (see Fig. 26.6a), the kinetic expression simplifies to: k [Enz] [R–L] d[R–L] = − 2 −1 t dt K1 + [R–L]

(26-30)

where [Enz]t is the total hydrolase concentration (e.g., mol enzyme L−1 ), k2 is the rate constant for the alkylation or acylation step, and K1−1 is the equilibrium constant quantifying the initial enzyme:substrate association.

870

Biotransformations

Box 26.1

Kinetic Expressions for Enzymatic Hydrolysis of R–L Under Simplifying Assumptions

Assume initial nucleophilic reaction (alkylation or acylation) is slowest step d[R–L] = −k2 [Enz–Nu:R–L] dt Assume the complexation step is describable by an equilibrium constant:

(1)

[Enz–Nu:R–L] [Enz–Nu][R–L] (3) [Enz]t = [Enz–Nu] + [Enz–Nu:R–L] (2) K1 =

Assume second nucleophilic reaction (dealkylation or deacylation) is slowest step d[R–L] − k3 [H2 O][Enz–Nu–R] dt Assume the complexation step and the first nucleophilic reaction are describable by equilibrium constants:

(6)

[Enz–Nu:R–L] [Enz–Nu][R–L] [Enz–Nu–R][L− ] (8) K2 = [Enz–Nu:R–L]

(7) K1 =

(9) [Enz]t = [Enz–Nu] + [Enz–Nu:R–L] + [Enz–Nu–R] Use Eqs. (2) and (3) to find: (4) [Enz–Nu:R–L] =

Use Eqs. (7), (8), and (9) to find:

[Enz]t [R–L] K1−1 + [R–L]

(10) [Enz–Nu+ –R] =

[Enz]t [R–L] [L− ]K1−1 K2−1 + [L− ][R–L]K2−1 + [R–L]

Substitute (4) into (1) k [Enz] [R–L] d[R–L] = − 2 −1 t (5) dt K1 + [R–L]

Substitute (10) into (6)

giving

giving

Vmax = k2 [Enz]t KiMM = K1−1

(11)

k [H O][Enz]t [R–L] d[R–L] = − − −1 3−1 2 − dt [L ]K1 K2 + [L ][R–L]K2−1 + [R–L]

Vmax = k3 [H2 O] [Enz]t KiMM = [L− ]K1−1 K2−1 + [L− ][RL]K2−1

Alternatively, if the second reaction (dealkylation or deacylation of the enzyme) is rate limiting (see Fig. 26.6), we may deduce that: k [H O][Enz] [R–L] d[R–L] = − −1 −1 3− 2 −1 − t dt K1 K2 [L ]+K2 [L ][R–L] + [R–L]

(26-31)

where K2 is the equilibrium constant quantifying the ratio of chemical species established in step 2 whenever step 3 proves to be the slowest in the sequence, and k3 is the rate constant associated with the dealkylation or deacylation step in the enzymecatalyzed hydrolysis. Both of these rate expressions (Eq. 26-30 and 26-31) are hyperbolic as a function of substrate concentration, [R–L]. That is, at low concentrations of [R–L], the rate linearly increases with [R–L]; but at high concentrations, the rate becomes independent of [R–L]. These kinetic expressions also enable us to understand what chemical and

Rates of Biotransformations

871

biological information is imbedded within the Michaelis-Menten type formulation typically used to describe such enzyme kinetics (Eq. 26-25). First, we see that KiMM is given by: KiMM = K1−1

(26-32)

when enzyme alkylation/acylation is rate limiting or: KiMM = K1−1 K2−1 [L− ] + K2−1 [L− ][R–L]

(26-33)

when enzyme dealkylation/deacylation is rate limiting. Next, we see that Vimax (the rate when [R–L] is large relative to KiMM ) is different for our two cases of hydrolysis limitation. This parameter always reflects the product of the rate constant of the slowest step and the concentration of total hydrolyzing enzyme present: Vimax (1st nucleophilic attack slowest) = −k2 [Enz]t

(26-34)

Vimax (2nd nucleophilic attack slowest) = −k3 [H2 O][Enz]t

(26-35)

or:

Despite the somewhat complex terms, one still finds the model of Michaelis and Menten would fit this system. But one also sees that the meaning of the parameters, ViMM and KiMM , may not be simply estimated based on the substrate’s structure (Koudelakova et al., 2011). If the xenobiotic compound of interest is rather dilute (Ciw ≪ KiMM ), then this expression suggests the rate of biotransformation may have the general form: (dCiw ∕dt) =

Vimax C KiMM iw

(26-36)

′ , is equal to and so the pseudo-first order biotransformation rate constant, kibio (Vimax /KiMM ) for such low-substrate concentration cases. This ratio is sometimes called kcat and has units of T−1 . Often, one is interested in relating such rate information found in one system to another case. Since such overall rates depend on the enzyme abundance (recall Vimax is proportional to [Enz]t no matter which case in Box 26.1), one may normalize the Vimax term so as to “tune it” for the enzyme’s concentration in each case:

(dCiw ∕dt) =

′ Vimax B

KiMM

Ciw

(26-37)

where B is a “biological parameter” that is equal to the total abundance of the relevant enzyme, [Enz]t , normalized by the parameter, B. If B is cell numbers, the constant is enzyme per cell number, while if B reflects total protein, then the constant is enzyme per total protein. Such metrics may enable translation of rates seen in one circumstance (e.g., in the lab) to another (e.g., in the field), but they require assuming that the [Enz]t /B ratio is the same in both cases. Table 26.2 shows some KiMM and Vi′max values

872

Biotransformations

(normalized to total protein) for a variety of substrates metabolized in settings ranging from grab samples from an environment to cultures in the lab to enzyme isolates. We are now in a position to estimate biodegradation rates when the overall process is limited by enzyme kinetics. For cases of interest to us, we need information on: the enzymatic parameters, Vi′max and KiMM , for the compound, organisms, and conditions of interest. Often previous investigators have examined situations that are similar to new ones we are trying to model, and values of enzymatic parameters have been determined (Table 26.2). Half-saturation constants (KiMM ) for a wide variety of xenobiotic compounds are often in the micromolar range, although nanomolar and millimolar cases have also been measured. Perhaps not surprisingly, values of Vi′max (here Vimax normalized by total protein) vary widely since (a) active microbial species abundances also vary widely between natural and engineered systems, and (b) the enzyme contributes a greater and greater fraction of the total protein in going from natural populations to cultures of microorganisms selected for their ability to carry out the reaction of interest to enzymes that have been purified. Nonetheless, for instances in which the environmental setting of interest is tested for the short-term degradation of the substrate as a function of that substrate’s concentration, values of Vi′max and KiMM that allow reasonably accurate predictions can be found. For example, using laboratory information on an enzymatic process of interest, one may be able to predict the impact of biodegradation in a field setting (see Problem 26.11). To conclude, by recognizing cases of enzyme-limited biotransformation, these approaches allow us to estimate rates for a wide range of xenobiotic and trace natural organic compounds. We also need to emphasize several points of caution. First, we must be sure that transport limitations are not controlling the overall rate; that is, desorption from nearby solids or transport into the cell must not be the slowest step in the process (steps 1 or 5 in Fig. 26.4). Second, we must know that the enzymes acting on the substrates of interest are essentially unchanging in their abundance (i.e., [Enz]t is not increasing as indicated by steps 6 or 7 of Fig. 26.4). Finally, we must know KiMM and Vi′max values. Since KiMM values are frequently found to be in the micromolar or even nanomolar range (Table 26.2), we may expect millimolar and higher substrate concentrations will exhibit saturation enzyme kinetics (i.e., d[i]/dt = – Vimax . Conversely, in Michaelis-Menten cases, biodegradation rates for nanomolar and lower ′ , given by: concentrations may be characterized with rate constants, kibio ′ kibio

=

′ Vimax B

KiMM

(26-38)

where B reflects a measure of the biomass present in the environment of interest in the units to which Vi′max has been normalized. While KiMM data may be somewhat applicable from case to case as long as the same key enzyme is involved, one should not expect the same to hold for Vi′max information since this parameter depends on the concentration of active enzyme, which in turn is certainly dependent on the abundance of the relevant microbial species. Therefore, efforts using tools like qPCR may help quantify enzyme presence at sites of interest and thereby facilitate tuning Eq. 26-37 (Beller et al., 2008; Kazy et al., 2010; Paszczynski et al., 2011; Schneidewind et al., 2014).

Table 26.2 Apparent Michaelis-Menten Parameters Reported for Microbial Degradation of Various Substrates Substrate

KiMM

′ Vimax (mol kg−1 protein s−1 )

A. Natural populations a Toluene in seawater c Biphenyl in seawater c Toluene in stream d Benzene in lake water with methanotrophs e m–Cresol in estuarine seawater f Chlorobenzene in estuarine seawater f Trichlorobenzene in estuarine seawater f Nitrilotriacetic acid in estuarine seawater f

18 nM 1.5 nM 2 μM 2 μM 6–17 nM 9–46 nM 25–38 nM 290–580 nM

6×10−10 4×10−8 – ca. 2×10−3 5 - 4000×10−9 2 - 4×10−8 1 - 2×10−8 4 - 400×10−7

B. Intact Microorganisms b Benzene by Methylosinus trichosporium g Toluene by Cycloclasticus oligotrophus h Toluene by Pseudomonas sp. h CH2 Cl2 by Methylomicrobium album with pMMO i Trichloroethene by Methylomicrobium album with pMMO i 3-Chlorobenzoate by methanogenic consortium j 3,5-Dichlorobenzoate by methanogenic consortium j Trichloroethene by methanotrophs (geom mean of N = 15) k

– 100 nM 500 nM 70 μM 60 μM 67 μM 47 μM 30 (1 to 200) μM

Trichloroethene by toluene or phenol degraders (N = 8) k

10 (1 to 80) μM

Trichloroethene by methanotroph mixed culture l cis-Dichloroethene by methanotroph mixed culture m Vinyl chloride by methanotroph mixed culture m

15 μM 30 μM 60 μM

2×10−3 7×10−3 8×10−4 6×10−4 7×10−5 1.1×10−4 3.6×10−5 3×10−4 (8×10−6 to 1×10−2 ) 8×10−5 (3×10−5 to 3×10−4 ) 3×10−5 2×10−3 2×10−3

C. Cell-free extracts or isolated enzymes Naphthalene by sMMO from Methylosinus sp. n 4-Chlorobenzoic acid → 4-hydroxybenzoic acid o Fluoroacetate → hydroxyacetate (glycolate) p Chloroacetate → hydroxyacetate p 1-Chlorohexane →1-hexanol q 1-Chloropropane →1-propanol r 1-Bromopropane →1-propanol r 1-Iodopropane →1-propanol r haloalkane dehalogenases s CH2 Cl2 t CH2 BrClt 2-Hydroxybiphenyl → 2,3-dihydroxybiphenyl u 2-sec-Butylphenol → 2,3-dihydroxy-sec-butylphenol u Linuron → (3,4-Dichlorophenyl)-1-methoxy-1-methylurea v o-Nitrophenol → catechol w Nitrobenzene → hydroxylaminobenzene x 2,4,6-Trinitrotoluene → 4-hydroxylamino-2,6-dinitrotoluenzene y 4-Amino-2,6-dinitrotoluene → 2-hydroxylamino-4-amino-6-nitrotoluenzene y

40 μM 30 μM 2.4 mM 20 mM 40 μM 120 μM 20 μM 80 μM 5 μM to 50 mM 30 μM 15 μM 3 μM 6 μM 2 μM 8 μM 5 μM 29 μM, 17 μM 640 μM, 520 μM

9×10−5 2×10−3 – – 4.7×10−4 1.7×10−4 1.1×10−3 1.3×10−3 10−3 to 1 1.7×10−2 1.5×10−2 6×10−2 4×10−2 2.5×10−3 8× 10−2 2×100 2×100 , 1.4×100 4×10−2 , 1×10−1

Cell counts were converted to protein assuming 1×10−16 kg of protein per cell. Assuming 0.3 pg dry mass per cell, and dry mass is 50% protein. Data from c Reichardt et al. (1981); d Kim et al. (1995); e McNeill et al. (unpub., 2006); f Bartholomew and Pfaender (1983); g Burrows et al. (1984); h Button (1998); i Han et al. (1999); j Suflita et al. (1983); k Alvarez-Cohen and Speitel (2001); l Chang and Criddle (1997); m Chang and Alvarez-Cohen (1996); n Koh et al. (1993); o Marks et al. (1989); p Goldman (1965); q Scholtz et al. (1987a); r Scholtz et al. (1987b); s Koudelakova et al. (2013); t Kohler-Staub and Leisinger (1985); u Suske et al. (1997); v Engelhar et al. (1973); w Zeyer and Kocher (1988); x Somerville et al. (1995); and y Bai et al. (2015). a b

874

Biotransformations

Despite such complications, understanding the nature and dependencies of enzymelimited biotransformations has proven very helpful in problems like designing field remediations (e.g., Semprini, 1997; McCarty et al., 1998; Pandey et al., 2014), permitting clean-up designs using enzymes directly (e.g., Glod et al., 1997; Dvorak et al., 2014), or both (Lal et al., 2010). Monod Population Growth Kinetics Finally, if the metabolism of the chemical of interest results in substantial energy yield and/or biomass-building materials, then the overall rate of biotransformation may be dictated by the rate of microbial population increase. In these cases, Monod microbial population dynamics (Monod, 1949) must be included in our analysis (step 7 in Fig. 26.4). The key assumption is the concentration of the chemical of interest limits the rate of growth of the degrading microorganisms. Such situations may occur when there is a large new input of substrate into the environment. To illustrate, let us examine the removal of p-cresol by a laboratory culture (Fig. 26.7; Smith et al., 1978). In this case, microorganisms that could grow on p-cresol were enriched from pond water by the investigators. When a suspension of these microorganisms at 107 cells L−1 (corresponding to about 1 to 10 μg biomass per liter) was exposed to a ∼47 μM solution of p-cresol (∼ 5000 μg L−1 ), it appeared that the chemical was not metabolized because no change in p-cresol concentration could be detected for the first 8 hours (see lower panel in Fig. 26.6). However, because the microorganisms were selected based on their ability to metabolize p-cresol, it can be assumed that the apparent absence of degradation was not due to their enzymatic capabilities. Rather, initially the microbial population was too small to have any discernible impact on the total p-cresol mass. The cells multiplied quickly in the period from 2 to 16 hours (Fig. 26.6, upper panel). When the microorganisms finally reached abundances greater than 109 cells L−1 (i.e., approaching 1000 μg biomass L−1 , a biomass comparable to the initial p-cresol concentration), enough bacteria were present to cause significant substrate depletion. Thus, to describe the time course of chemical removal in such cases, the microbial population dynamics have to be quantified in the system. This can be done using the microbial population modeling approach developed by Monod (1949). We begin by considering the relationship between microbial cell numbers and time for a growing population limited by a substrate like p-cresol. In response to a new growth opportunity, the cell numbers increase exponentially. This period of exponential growth can be described using: dB = μB dt

or

B(t) = B(t = 0)eμt

(26-39)

where B is the cell abundance (cells L−1 ), and μ is the specific growth rate (e.g., with units of h−1 ). Therefore, the ln B will change in direct proportion to time: ln B(t2 ) = ln B(t1 ) + μ(t2 − t1 )

(26-40)

875

Rates of Biotransformations

(a)

cell numbers (cells L–1)

1010

109

108

Figure 26.7 Time courses for cell numbers (a) and p-cresol concentrations (b) in a laboratory experiment (Smith et al., 1978) immediately after this substrate and bacteria capable of degrading p-cresol were mixed together.

p-cresol concentration (µmol L–1 )

107

0

4

8

12

16

20

16

20

(b)

50

OH

40 30 20 10 0

0

4

8

12

time (hours)

Put another way, during so-called exponential growth, the microbial population will double in number for every time interval, Δt = (ln 2)/μ. Monod (1949) recognized that the growth rate of a microbial population was related to the concentration of a critical substance (or substances) sustaining its growth. More “food” means faster growth, up to a certain point when the maximum growth rate, μmax , is achieved. At this point, another factor becomes limiting. Monod mathematically related this population growth response to the concentration of the substance limiting growth with the so-called Monod equation: μ=

μmax Ciw KiM + Ciw

(26-41)

where μmax is the fastest possible growth rate (e.g., h−1 ) corresponding to the situation when the limiting chemical is present in excess, Ciw is the concentration (e.g., mol L−1 ) of the growth-limiting chemical, and KiM is the Monod constant (e.g., mol

876

Biotransformations

(a)

μ (h–1)

μ max

1/2 μ max

0

μ=

KiM

0

μ max Ciw

KiM+Ciw

Ciw (mol L–1)

(b) – dCiw / dt

μ max [B]

Figure 26.8 Relationships of: (a) microbial population specific growth rate, 𝜇, versus substrate concentration after Monod (1949), and (b) consequent substrate disappearance rate, −dCiw /dt, versus substrate concentration.

1/2

Yi

μ max [B] Yi

μ max [B] KiMYi

0 0

KiM

Ciw (mol L–1)

L−1 ) equivalent to the chemical concentration of i at which population growth is half maximal. KiM is often denoted with Kis in the microbiology literature, but here we use the subscript, iM, to emphasize Monod growth on i is rate-limiting. This formulation yields a hyperbolic dependency of μ on Ciw (Fig. 26.8). That is, when i is present at low levels (Ciw ≪ KiM ), its concentration limits the rate of increase in cell numbers. However, when there is a surplus level of the “food” chemical, other factors limit the rate of population increase and μ = μmax . The model expressed by Eq. 26-41 implies that no other substance is simultaneously limiting microbial population growth. This assumption may be invalid; for example, an electron acceptor like O2 may be simultaneously needed for the biotransformation of the organic chemical of interest. Such dual-limiting substrate cases require modifying Eq. 26-41 to reflect the impacts of both chemicals (see Box 26.2, case 2). An interesting remediation situation where such co-substrates are important involves the combination of the electron donor, H2 , and unusual electron acceptors like tetrachloroethene (Yang and McCarty, 1998; Haston and McCarty, 1999). Half saturation

Rates of Biotransformations

877

Box 26.2 Monod Limiting-Substrate Models of Microbial Population Growth Case 1: Single limiting substrate, i (Monod, 1949): μ= where μ

μmax Ciw KiM + Ciw

(1)

is the specific growth rate of the microbial population [T−1 ]

μmax is the maximum growth rate [T−1 ] of the microbial population in the presence of excess i, Ciw is the concentration of substrate i [ML−3 ], and KiM is the concentration of i when growth is half-maximal [ML−3 ] Case 2: Limitation by two substrates, i and j, whose simultaneous bioreaction limits population growth (Bae and Rittmann, 1996): μ = μmax

Cjw Ciw × KiM + Ciw KjM + Cjw

(2)

Examples: i may be an organic compound like toluene and j would be an inorganic species like O2 , or i may be an inorganic species like H2 and j could be an organic compound like tetrachloroethene. When either Ciw ≫ KiM or Cjw ≫ KjM , Eq. 2 simplifies to Eq. 1. Case 3: Limitation by n growth substrates processed by the same single bottleneck metabolic step (Guha et al., 1999): μtot =

n ∑

μi

(3)

i=1

and: μi =

μimax Ciw n K ∑ iM KiM + Cjw j=1 KjM

(4)

where μimax is the maximum specific growth rate when i is limiting, KiM is the half-saturation coefficient for substrate i, and KjM is the half-saturation coefficient for each of the competing substrates, j, including i. Example: Substrates are a mixture of structurally similar hydrocarbons all oxidized for growth by a common ratelimiting enzymatic process.

878

Biotransformations

constants for H2 used to dechlorinate compounds like tetrachloroethene are near 10 to 100 nM (Smatlak et al., 1996; Ballapragada et al., 1997). Since this key electron donor is commonly at low nanomolar concentrations in subsurface environments of interest, the dual-substrate limiting model may be most appropriate (Haston and McCarty, 1999). Whenever environmental settings exhibit concentrations of the limiting cosubstrates that are near or below the applicable half saturation constants, additional terms will be needed to accurately quantify microbial growth kinetics. However, we may often be justified to use the one-limiting-substrate model if one of the two potential limiting substrates is present in excess. It is also possible that more than one organic substrate contributes carbon and energy to a single microbial species. If such substrates are all processed by the same enzymatic system, and therefore compete with one another at a single metabolic transformation step, then overall population growth will reflect the contributions of numerous substrates (see Case 3 in Box 26.2). This may occur when structurally related mixtures of compounds (e.g., a mix of polycyclic aromatic hydrocarbons) co-occur in the environment and are being simultaneously degraded (Guha et al., 1999). In this case, the overall growth of the microbial population reflects the use of all the substrates. Since all the substrates are competing for the same enzyme, the chemical concentration ∑ in the denominator of each compound’s Monod expression is modified by a factor ( (KiM ∕KjM )×Cjw from j = 1 to n in Eq. 4 of Box 26.2). This factor quantifies the relative usage of the competing chemicals, j, at the bottleneck step. As a result, the biotransformation for any one organic chemical may be enhanced or diminished relative to the case where it serves as the only growth-limiting substrate. It is possible that the overall microbial growth rate will be enhanced by the use of multiple compounds and thereby increase the rate of removal of a single substrate of interest. It is also possible that competitive effects involving access to a key enzyme cause particular substrates to be “ignored” and their degradation decreased (Guha et al., 1999). Each case will reflect a balance of these effects. For now, we focus on cases in which microbial growth is limited by the single substrate of interest (i.e., Case 1 in Box 26.2). In order to evaluate changes in the limiting chemical’s concentration, we need to relate microbial growth to changes in compound concentration. This can be done by recognizing that biodegrading a certain amount of limiting-chemical mass enables a proportional enhancement in microbial biomass: dB∕dt (cell L−1 h−1 ) −dCiw ∕dt (mol L−1 h−1 )

( = Yi

cells grown moles substrate i used

) (26-42)

This proportionality is called the yield of the biological processing, Y. For carbonlimiting substrates oxidized by aerobes, biomass yields are usually near 0.5 g biomass g−1 carbon (Neidhardt et al., 1990). Using yield information relevant to a particular compound/microbial species/ environmental conditions combination, we can now relate the production rate of new cells to the disappearance rate of the chemical of concern: ( ) dCiw μB = Yi − (26-43) dt

Rates of Biotransformations

879

And, upon rearranging: (

dCiw dt

) =−

μB Yi

(26-44)

Substituting Monod’s expression for microbial population growth, μ, as a function of substrate concentration, Ciw , we have: (

dCiw dt

) =−

μmax B C Yi (KiM + Ciw ) iw

(26-45)

This chemical removal rate, dCiw /dt, has a hyperbolic dependency on concentration, Ciw (Fig. 26.7). This relationship of microbial growth to chemical removal implies that when the chemical is present at low levels (Ciw ≪ KiM ), its instantaneous rate of degradation (i.e., at a particular time, t, and microbial abundance, B(t)) is linearly proportional to its concentration and the “concentration” of the microorganisms “reacting” with it: (

dCiw dt

) ≈−

μmax B(t)Ciw Yi KiM

(26-46)

In such cases, we have a “Monod-case second-order rate constant”: kbio = μi max ∕(KiM Yi )

(26-47)

with kbio having units like (L cell−1 h−1 ). Note that a further pseudo-first order simplification would have the rate constant changing with time as B(t) is changing. In contrast, when the chemical is present in large amounts relative to the microbial community needs (Ciw ≫ KiM ), then its rate of removal becomes independent of its concentration: ( ) dCiw μ ≈ − max B(t) (26-48) dt Yi (

dCiw dt

) ≈ −kibio B(t)

(26-49)

Consequently, kibio is now equal to μmax Yi−1 and has units like (mol cell−1 h−1 ) for Ciw ≫ KiM . In both of these limiting cases, and obviously for the transitional conditions between, we need information on the factors quantifying microbial growth, 𝜇 max , KiM , and Yi , and on the abundance of cells, B(t), to be able to predict transformation rates of the compound when it limits population growth. Returning to the example of p-cresol degradation (Fig. 26.7), we can see how some of these biological parameters are deduced. First, we recognize that in the early part of the experiment, when p-cresol concentrations do not observably change (< 8 h), we have the condition [p-cresol]w ≫ Kp-cresolM , so the changing cell numbers reflect

880

Biotransformations

μmax . From the upper portion of the figure, we see that cell numbers increase from about 107 cells L−1 at 2 hours to a little more than 109 cells L−1 at 10 hours. Using Eq. 26-40, we estimate: μmax =

ln (B(t2 )∕B(t1 )) ln (100) ≈ ≅ 0.6 h−1 (t2 − t1 ) 8h

(26-50)

Examining the results between about 10 and 14 hours, we can estimate the yield factor: Yi = =

B(14h) − B(10h) [p-cresol](14h) − [p-cresol](10h) (9.4 − 1.3)×109 cells L−1 (44 − 1.3)×10−6 mol L−1

(26-51) 14

≃ 2×10 cells mol

−1

Since bacterial cells weigh about 0.3 pg dry weight per cell (Loferer-Krossbacher et al. 1998; Czechowska et al., 2013) and their dry mass is about 50% carbon, this yield appears reasonable (i.e., about 60 g of cells from 100 g of p-cresol). Finally, to deduce Kp-cresolM we need to examine growth rates over a range of levels of the substrate. Inversion of Eq. 26-41 yields: 1 Kp-cresolM 1 1 × + = μ μmax Cp-cresol μmax

(26-52)

Hence a fit of (Cp-cresol )−1 versus μ−1 yields an intercept = μ−1 max and a slope of Kp-cresolM 𝜇 −1 . Using the data shown in Fig. 26.7, we find μ = 0.69 h−1 and Kp-cresolM = max max 6.1 μM using the whole time course. With such microbial population growth information, we are now in a position to estimate biodegradation rates for compounds supporting growth as was the case for p-cresol. In the situation depicted in Fig. 26.7, we have for the early part of the experiment: kp-cresolbio =

𝜇 max (since Cp-cresol ≫ Kp-cresolM ) Yp-cresol

0.69 h−1 ≈ 3×10−15 mol cell−1 h−1 ≈ 14 −1 2×10 cells mol

(26-53)

Thus, early in the time course when Cp-cresol ≫ Kp-cresolM , the rate of p-cresol removal was independent of p-cresol concentration and was continuously changing as the microorganism population increased, ranging from about 3×10–8 mol L−1 h−1 at 2 h when B(2h) ∼ 107 cells L−1 to about 3×10–6 mol L−1 h−1 at 10 h when B(10h) ∼ 109 cells L−1 . Subsequently, the rate of p-cresol removal became a function of the

881

Rates of Biotransformations

Table 26.3 Some Monod Biodegradation Parameters Obtained from Pure or Enrichment Cultures Grown on the Substrate Indicated (Yields Estimated Assuming Cell Mass of 0.3 pg per Cell) Substrate i

Source of Microorganisms

μmax (h−1 )

KiM (μM)

Yi (cells mol−1 )

Glucose a

pure cultures: Vibrio, Aerobacter, E. coli, Achromobacter pure cultures: Achromobacter, Aerobacter Pseudomonas sp. enrichments from pond water enrichments from pond water enrichments from creek enrichments from river water Pseudomonas sp. enrichment from landfill enrichment from aquifer solids enrichment from landfill enrichments from aquifer solids enrichments from aquifer solids enrichments from aquifer enrichment from soil enrichment from soil enrichment from soil enrichments of Pseudomonas sp. mutants mycobacterium aurum L1

0.40 - 0.65

17 - 46

–

0.55, 1.2

11, 120

–

0.28 0.69 0.74 0.61 0.37 0.13 0.02 0.07 0.02 0.02 0.03 0.05 0.23 0.037 0.0008 0.11

1600 6.4 1.2 10 2.2 50 70 400 20 10 10 – 200 4 0.5 –

7×1013 2×1014 2×1014 2×1014 4×1010 2×1014 2×1013 2×1013 1×1014 9×1013 2×1014 1×1014 2×1014 3×1014 3×1014 1013 to 1014

0.04

3

5×1013

0.04 - 0.3

0.1 - 200

ca. 1014

Glycerol b Acetate c p-Cresol d Quinoline d Methyl parathion d Malathion e 3-Chlorobenzoate c Methane f Methane g Propane f Toluene f Toluene h Phenol h Naphthalene i Phenanthrene i Pyrene i Dichloromethane j Chloroethene (vinyl chloride) k Tetrachloroethene l

various, reduction with H2

Data from a Jannasch (1968); b Jannasch (1967); c Tros et al. (1996); d Smith et al. (1978); e Paris et al. (1975); f Chang and Alvarez-Cohen (1995); g Chang and Criddle (1997); h Jenal-Wanner and McCarty (1997); i Guha et al. (1999); j Brunner et al. (1980); k Hartmans and de Bont (1992); and l Rittmann and McCarty (2001).

concentration of this substrate; so near the end of the incubation (say 14 hours with [p-cresol] at 3 μM) we have: dCp-cresolw dt

=− =−

μmax B(14 h) C Yp-cresol (Kp-cresolM + Cp-cresol ) p-cresol (0.69 h−1 )(1010 cells L−1 )(3×10−6 mol L−1 )

(26-54)

(9×10−6 mol L−1 )(2×1014 cells mol−1 )

≃ −1×10−5 mol L−1 h−1 at 14 h Now, we can see how to estimate the biodegradation of chemicals that prove to be growth-limiting substrates of particular microbial species. Various natural and xenobiotic compounds have been studied for their ability to be the sole support of growth for microorganisms. From the data shown in Table 26.3,

882

Biotransformations

a few cautious generalizations can be made. First, maximum cell growth rates for acclimated cultures appear to correspond to doubling times of hours (recall t1/2 = ln 2/μmax ). This is not too different from cells grown on standard substrates like glucose. An exception may be for organisms growing on highly water-insoluble compounds like pyrene (Guha et al., 1999). Next, KiM values are commonly between μM and mM levels. Since such values are fairly high (ca. 0.1 to 100 mg L−1 ), it may be usual to find Ciw ≪ KiM values. Finally, the cell yields usually fall in the range such that 10 to 50% of xenobiotic compound carbon mass is translated into biomass carbon. An obvious exception to this is seen for malathion (Ymalathion = 4×1010 cells mol−1 ≈10−4 g cells g−1 substrate). Further study of this anomalous result found that the malathion was initially hydrolyzed to the monoacid and ethanol, and then only the ethanol was used as a growth substrate. The acid product was accumulated without being used further. The gross yield in such cases would not be as large. With such data, we can now begin to understand the dynamics of a bioreactor. Such engineered systems are used to remove compounds capable of serving as a growth substrates for a chosen microorganism from wastewaters. Also, we may now use the typical values of μmax , KiM , and Yi , to analyze situations where a xenobiotic chemical is added to an environment in excess (e.g., from a chemical spill). If the environmental system contains a microorganism capable of living on the spilled substance as a growth substrate, but due to the spill [i] ≫ KiM , then we might expect kibio to be (Eq. 26-48): kibio ≈ ≈

0.1 to 1 h−1 1014 cell mol−1 10−15

−14

to 10

(26-55) −1

mol cell

h−1

As a result, the key environmental factor controlling the time it would take for significant compound degradation would be the total abundance of the relevant microbial subpopulation, B(t), capable of growth on the compound. This brings us to the major weakness in trying to quantify degradation limited by microbial growth: how does one know what subset(s) of microorganisms are involved and what their abundance is for any particular occurrence of interest? This may not be too much of a problem as long as other critical species such as electron acceptors like O2 or nutrients such as nitrogen or phosphorus are present in sufficient quantities to permit unchecked microbial growth. In some systems, especially ones we engineer, we may anticipate that the microbial population grows up to some steady-state condition reflecting a balance of growth versus microbial losses due to die off, wash out, or predation. In natural environments where microorganisms have to respond to dynamic conditions (e.g., inputs due to spills), some uncertainty will derive from our ignorance of the presence of suitable microbial species and their predation by other organisms.

26.5

Questions and Problems Special note: Problem solutions are available on the book’s website. Solutions to problems marked with an asterisk are available for everyone. Unmarked problems have solutions only available to teachers, practitioners, and others with special permission.

Questions and Problems

883

Questions Q 26.1 Why can the rate of biotransformation be greater than the rate of mineralization (i.e., conversion to CO2 , HNO3 , H2 SO4 , H3 PO4 , etc.)? Q 26.2 List three processes that can limit the macroscopically observed rate of a chemical’s biodegradation. Q 26.3* Indicate the type of initial biotransformation and product you would expect for the following compounds if they occurred in an oxic stream; you might expect no significant biological transformation in some cases. (a) propane

(b) isopropanol (2-propanol)

OH

Cl

(c) n-propylchloride (chloropropane)

Cl

(d) chlorobenzene

O (e) n-propylacetate

O O

(f) di-n-propylphosphate

O Cl

P O

Cl

(g) 1,1,2-trichloropropene Cl Cl

Cl

(h) 1,1,2,3-tetrachloropropene Cl (i) acetone (2-propanone)

Cl O

O (j) propanoic acid

OH

O

884

Biotransformations

Q 26.4 Indicate the type of initial biotransformation and product you would expect for the compounds listed in Q 26.3 if they occurred in an anoxic groundwater. Note that you might expect no significant biological transformation in some cases. Q 26.5 Give two reasons why an organic compound present in a system at “high” concentrations can be found to be biodegraded at a rate that is independent of that compound’s concentration. That is, the loss can be modeled: dCiw ∕dt = −kibio [ML−3 T−1 ] Q 26.6 When a labile compound is catastrophically released to an environmental system, why does its removal typically show a lag period? Q 26.7 What mathematical expression could be used to represent the growth rate of a microbial population limited by three substrates all simultaneously used in the same enzymatic step? How many parameters do you need to know to apply such an expression to a new system of interest? Q 26.8 Why are some compounds able to be biodegraded even though microorganisms cannot use them as a sole source of carbon and energy? Q 26.9 What factor must be used to convert a Vi′max value determined using a pure culture of a particular microbial species and given in mol substrate kg−1 protein s−1 to a Vi′max value in units of mol substrate L−1 s−1 ? What does that factor represent? Problems P 26.1∗ Is It Thermodynamically Feasible for Benzene to Be Degraded in an Anaerobic Groundwater? benzene

Δf G0C

6 H6

(l ) = +123.0 kJ mol−1

Δf G0H O (1) = −237.2 kJ mol−1 2

Δf G0HCO− (aq) = −586.9 kJ mol−1 3

Δf G0CH (g) = −50.8 kJ mol−1 4

Δf G0H (aq) = 0 kJ mol−1 2

A colleague suggests that benzene (C6 H6 ) can be “naturally attenuated” by microorganisms in groundwater under conditions of methanogenesis, producing bicarbonate and methane. Check the thermodynamic feasibility of this transformation at 25◦ C assuming: the solution pH is 7, the bicarbonate concentration is 1 mM, the methane concentration is 100 μM, and the benzene concentration is 1 μM. In the literature (Hanselmann, 1991), you find the free energies of formation at 25◦ C (see margin). P 26.2 How Much Biomass Do You Expect? You want to grow a bacterial culture capable of using dichloromethane (CH2 Cl2 ) as its sole source of carbon.

Questions and Problems

(a) Write a stoichiometrically balanced reaction in which 50% of the carbon in CH2 Cl2 is oxidized to CO2 and the other 50% is used to make new biomass (assume the stoichiometry of biomass to be CH2 O).

H Cl

H

Cl

885

dichloromethane CH3

(b) If 50% of the carbon in this CH2 Cl2 is converted to CO2 (energy use) and the other 50% is used to synthesize new biomass (assume composition CH2 O), what yield in units of g cells g−1 substrate do you expect? (c) If a single cell weighs 0.3 pg (0.3×10−12 g), what yield do you expect in units of cells mol−1 substrate?

toluene

(d) What values do you get if the substrate is toluene? Why are the results so different? P 26.3∗ Evaluating the Biodegradation of Glycerol by Microorganisms in a WellMixed Tank Reactor You need to purify a wastewater stream containing a readily biodegradable compound, glycerol, present in fairly high concentrations, 100 μM (9 ppm). If one can deliver this wastewater into a well-mixed tank (often called a continuously stirred tank reactor or CSTR), which is simultaneously receiving all other necessary supplies needed for microbial growth (e.g., O2 , nutrients), then one can build up a microbial population capable of degrading the glycerol to innocuous substances like CO2 and H2 O before the water is discharged.

OH HO

OH glycerol

Calculate the output glycerol concentration (μM) after the microorganisms have increased their biomass to a steady-state level. Also calculate what the steady-state biomass level would be (cells m−3 ). Assume you have a tank with V = 10 m3 , a wastewater flow Q = 50 m3 d−1 , and a microbial inoculum with growth properties like those shown in Table 26.3 for Aerobacter sp., a glycerol-to-biomass yield of 1014 cells mol−1 , and a die off coefficient, b, of 0.1 d−1 (that is, cells die at a rate of 0.1×B(t) per day). P 26.4 Optimizing a Bioreactor Suppose you are interested in improving the degradation of glycerol by the 10 m3 bioreactor discussed in P 26.3. (a) One option is to vary the volume of the well-mixed reactor. What percent of incoming glycerol do you expect will be degraded if you double the tank volume to 20 m3 ? (b) Another suggestion is to feed the effluent from the first 10 m3 tank into a second similar 10 m3 tank (with additional O2 and nutrients as necessary). What percentage of the original glycerol will be degraded in this second tank? P 26.5 How Effective Will This Low-O2 Bioreactor Be at Removing Toluene? You have a 10 m3 bioreactor containing a diverse mixture of bacteria. It is fed at 2 m3 d−1 with a wastewater containing 100 μM toluene. The wastewater also contains a complex mixture of nontoxic organic chemicals. Due to the biodegradation of all the substances in the waste, the steady-state O2 concentration in the reactor is only 3 μM.

886

Biotransformations

Bacteria characteristics μmax = 0.5 d−1 Y toluene = 2×1014 cells mol−1 Die off at 0.1 d−1 KtolueneM = 10 μM KoxygenM = 1 μM

If the toluene oxidizers in the tank exhibit the properties shown in the margin, what will the steady-state toluene concentration (μM) be exiting the tank? How would this result change if O2 could be added to maintain a 30 μM steady-state concentration of O2 in the reactor? P 26.6 A Case of Oxygen-Limited Biodegradation Isopropanol (rubbing alcohol) is continuously discharged into a shallow (2 meters) pond. As a result, a bacterial species with μmax of 0.3 hr−1 , KisopropanolM of 100 μM, and Yisopropanol of 2×1014 cells mol−1 has increased in numbers throughout the pond. After a time, the isopropanol concentration becomes constant at 30 μM (i.e., inputs are exactly balanced by biodegradation).

OH

(a) If air-to-water exchange limits the input of oxygen to the pond to only 1×10−2 mol O2 m−2 hr−1 , and this oxygen flux limits the degradation of isopropanol, what is the maximum rate of isopropanol degradation in the pond (mol m−3 hr−1 ) assuming it is completely mineralized to CO2 and H2 O? Assume the pond is well-mixed vertically.

isopropanol (2-propanol)

(b) For this isopropanol biodegradation rate, what bacterial cell density (cells m−3 ) is necessary? P 26.7∗ Estimating the Time to Degrade a Spilled Chemical Imagine a case in which p-cresol (PC, structure see Fig. 26.7) is spilled into a pond and dispersed to a initial concentration, [PC]0 , of 1 mM (ca. 100 ppm). How long (days) would it be before this contaminant was mostly (>50%) degraded by the indigenous microorganisms living in the pond water? P 26.8 Can Phenanthrene Degradation Limit Bacterial Growth in an Oxic Sediment Bed? Phenanthrene is present in an oxic sediment bed at 10 μmol kg−1 . You know that some bacteria have been shown to use this polycyclic aromatic hydrocarbon as a growth substrate in the laboratory. Those bacteria exhibited a μmax of 0.9 d−1 , a KiM of 4 μmol L−1 , and a yield of 3×1014 cells mol−1 when their growth was limited by phenanthrene. phenanthrene

Assuming such bacteria in the oxic sediment bed are removed by predation at 0.2 d−1 , could they establish a steady-state population growing on phenanthrene dissolved in the pore water? Assume the sediment bed has a porosity of 0.6, Kid is 200 L kg−1 , and desorption is fast compared to biodegradation. P 26.9 Biodegradation of Nitrilotriacetic Acid (NTA) in a Lake

COO OOC

N

COO

nitrilotriacetate (NTA)

Ulrich et al. (1994) reported that the kNTAbio values necessary to explain the mass balance of nitrilotriacetic acid (NTA) present in a Swiss lake at 1 to 10 nM ranged from 0.02 to 0.05 d−1 . In another study, Bartholomew et al. (1983) tested an estuarine water for NTA biodegradation as a function NTA concentration, and they found Vmax between 0.3 and 3 nmol L−1 h−1 and KiMM between 300 and 600 nM. Are the results of these two investigations consistent? Identify any assumptions you must make.

Questions and Problems

887

P 26.10∗ Estimating the Biotransformation Rate of an Organic Pollutant in a Natural System You are concerned about the fate of 2-nitrophenol (NP) found at a concentration of about 10 ppb (0.07 μM) in some groundwater. According to the literature (Zeyer and Kocher, 1988), this compound can be degraded aerobically by soil bacteria. The biodegradation pathway begins with an oxygenase that converts NP to catechol: OH

OH NO2

OH

oxygenase

2-nitrophenol

catechol

In order to anticipate the biodegradation of NP, a soil pseudomonad is grown up and the protein fraction containing the oxygenase is isolated and purified by a factor of 40. With this protein isolate, you observed the rate of NP degradation as a function of that substrate’s concentration:

[NP] (μM) 2 3 4 5 10 20

Rate of degradation (μmol g−1 enzyme min−1 ) 1040 1420 1920 2150 2480 2530

′ (a) Using these data, calculate the protein-normalized VNPmax and KNPMM for this enzymatic reaction.

(b) Assuming the NP biotransformation is limited by reactions with such an oxygenase in groundwater microorganisms, what kNPbio would you estimate for NP if there are 107 NP-degrading cells L−1 of the groundwater ? (c) Assuming the NP exhibits a KNPd for the aquifer solids of 5 L kg−1 , what overall half-life do you expect for NP in this groundwater assuming biodegradation is the chief removal mechanism? P 26.11 Assessing the Rate of Toluene Biodegradation in a Shallow Stream Groundwater leachate from a waste site causes a stream to have 4 μM toluene at the point of exfiltration (after Kim et al. 1995). This concentration decreases to about 0.01 μM some 400 meters downstream. Could this concentration change be due to biodegradation? Assume the following apply: (a) the stream bottom is covered with a “film” of organisms at 1200 g biomass m−2 of stream bottom; (b) using film scrapings in a laboratory

888

Biotransformations

suspension at 2 g biomass L−1 , you find that toluene added at 0.2 μM disappears at a rate of 1.2 hr−1 ; and (c) using film scrapings in a laboratory suspension you find the rate of toluene degradation is half maximal at 2 μM. Also assume the stream is 0.1 m deep, flows at 200 m hr−1 , and does not incorporate significant additional exfiltrating groundwater in the 400-meter-long reach in question. Finally, assume that toluene and O2 mass transfers from the shallow water column into the biomass film are not rate limiting. P 26.12 Estimating the Biodegradability of Linuron in a River Cl

O O

N

N H linuron

Cl

You are concerned about the longevity of the herbicide, linuron (LIN), leaching into a river from some neighboring farmland. Given the structure of this urea derivative, you expect it will be biodegraded via a hydrolysis mechanism. You recall a report of a hydrolase enzyme from a common bacterium that exhibits a half-saturation constant, ′ , for linuron of KLINMM , for linuron of 2 μM and a maximum degradation rate, VLINmax −1 −1 2500 μmol kg protein s . (a) Experimenting with some river water, you find that linuron added at 0.1 μM degrades with a half-life of 60 days. What would the hydrolase enzyme concentration (kg protein L−1 ) in the river water have to be if biodegradation via such an enzyme accounted for all the linuron removal? Assuming a bacterial abundance in the river water of 109 cells L−1 , that they are 70% water and average 1 μm in diameter, and that their dry mass is half protein of specific density 1.5 g mL−1 , is the hydrolase concentration feasible? (b) Would you expect linuron biodegradation in the river water to exhibit a lag phase? Explain your reasoning. (c) If linuron leached into the river at 0.01 μM, what biodegradation half life (days) would you expect it to have assuming the hydrolase concentration in the river water proved to be 3×10−10 kg protein L−1 ? P 26.13 Biodegradation to Remove Trichloroethene from a Subsurface Site In order to degrade trichloroethene (TCE) contaminating some groundwater at 5 μM (660 ppb), you want to inject toluene (“tol”, for structure see P 26.2) and O2 below ground and grow a bacterial community capable of growing on the toluene and simultaneously co-metabolizing the TCE (after McCarty et al., 1998.) Using one liter of subsurface site material (containing 0.33 L of water and 0.67 L of solids and having a sorption coefficient for toluene of Ktold = 0.1 L kg−1 ) in an enclosed column in the laboratory, you flush it with water containing 100 μM toluene and O2 in stoichiometric excess. You find the steady-state dry biomass is 10 mg biomass L−1 (i.e., 30 mg biomass L−1 of water). By varying the influent toluene concentration, you find the μmax on this substrate is 1 d−1 , the die off coefficient is 0.15 d−1 , the halfsaturation constant with respect to dissolved toluene is 10 μM, and the dry biomass yield from toluene is 8×104 mg biomass mol−1 toluene. (a) Assuming the laboratory parameters apply at the contaminated site, if toluene is injected at 100 μM, what half-life (time for toluene concentration to decrease to half its

Bibliography

889

initial concentration in days) would you expect for this growth substrate? Also assume the total toluene losses in the field should be modeled with: (d[toluene]t /dt)in situ = – ftolw kbio [toluene]t where ftolw is the fraction of toluene dissolved in the groundwater and you assume sorptive exchange is fast relative to biodegradation. (b) Does the half-life change if you inject toluene at 10 μM? Explain why it does or does not. (c) You are interested in how closely treatment wells should be placed in the field. You reason that you want injected toluene to be present at significant concentrations everywhere in the treatment area. Using three times the toluene degradation half-life (100 μM case) as a metric for the time in which toluene would be consumed below ground, how far (meters) into the aquifer would you expect the toluene-oxidizing bacteria to occur assuming the toluene/O2 solution was injected at 40 L min−1 through a well with a 5-meter-long screen? Assume flow into the subsurface is cylindrical and recall that the porosity is 0.33. (d) If the bacteria grown on toluene in the laboratory also co-metabolize TCE with ′ of 11 mol kg−1 protein d−1 , estimate the below-ground KTCEMM of 10 μM and VTCE max kTCEbio (d−1 ) for trichloroethene assuming the bacteria establish a steady-state dry biomass equivalent to 10 mg dry biomass L−1 of intact aquifer and the bacteria are 50% protein. Also, assume KTCEd = 0.1 L kg−1 . Cl

Cl

Cl

H

(e) Assuming the TCE biodegradation rate is proportional to the fraction of TCE that is dissolved in situ (i.e., d[TCE]t /dt)in situ = – fTCEw ×kTCEbio [TCE]t ), what half-life (days) do you expect for this chlorinated solvent if the total TCE present at the site is 0.05 mol L−1 porous medium due to sorption (KTCEd = 0.1 L kg−1 )? Note any assumptions.

trichloroethene (TCE)

26.6

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study combining mathematical-modeling and field-measurements. Environ. Sci. Technol. 1994, 28(9), 1674–1685. Urban, P.; Truan, G.; Pompon, D., Access channels to the buried active site control substrate specificity in CYP1A P450 enzymes. Bba-Gen Subjects 2015, 1850(4), 696–707. Van Eerd, L. L.; Hoagland, R. E.; Zablotowicz, R. M.; Hall, J. C., Pesticide metabolism in plants and microorganisms. Weed Sci. 2003, 51(4), 472–495. Vorbeck, C.; Lenke, H.; Fischer, P.; Spain, J. C.; Knackmuss, H. J., Initial reductive reactions in aerobic microbial metabolism of 2,4,6-trinitrotoluene. Appl. Environ. Microbiol. 1998, 64(1), 246–252. Wang, W. X.; Liang, A. D.; Lippard, S. J., Coupling oxygen consumption with hydrocarbon oxidation in bacterial multicomponent monooxygenases. Acc. Chem. Res. 2015, 48(9), 2632–2639. Wicker, J.; Lorsbach, T.; Gutlein, M.; Schmid, E.; Latino, D.; Kramer, S.; and Fenner, K. enviPath The environmental contaminant biotransformation pathway resource. Nucleic Acids Res. 2016, 44(D1), D502–D508. Wilson, J. T.; Wilson, B. H., Biotransformation of trichloroethylene in soil. Appl. Environ. Microbiol. 1985, 49(1), 242–243. Yang, Y. R.; McCarty, P. L., Competition for hydrogen within a chlorinated solvent dehalogenating anaerobic mixed culture. Environ. Sci. Technol. 1998, 32(22), 3591–3597. Zeyer, J.; Kocher, H. P., Purification and characterization of a bacterial nitrophenol oxygenase which converts ortho-nitrophenol to catechol and nitrite. J. Bacteriol. 1988, 170(4), 1789–1794. Zipper, C.; Bunk, M.; Zehnder, A. J. B.; Kohler, H. P. E., Enantioselective uptake and degradation of the chiral herbicide dichlorprop (RS)-2-(2,4-dichlorophenoxy)propanoic acid by Sphingomonas herbicidovorans MH. J. Bacteriol. 1998, 180(13), 3368–3374.

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Chapter 27

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA) 27.1 Introduction, Methodology, and Theoretical Background Isotopologues and Isotopomers Methodological Aspects: The (Bulk) Isotopic Signature of a Compound (δh E) Rayleigh Equation and Bulk Enrichment Factors (εE ) The Kinetic Isotope Effect Dual Isotope Plots and Derivation of Apparent Kinetic Isotope Effects (AKIEE s) from Bulk Enrichment Factors Additional Factors Influencing Experimental Bulk Enrichment Factors 27.2 Using CSIA for Assessing Organic Compound Transformations in Laboratory and Field Systems Microbial Transformation of BTEX Under Aerobic and Anaerobic Conditions Abiotic and Biological Transformation of Nitroaromatic Compounds (NACs) Under Aerobic and Anaerobic Conditions Abiotic and Biological Transformation of Atrazine under Aerobic Conditions Abiotic and Biological Transformation of Polychlorinated C1 – and C2 –Compounds under Aerobic and Anaerobic Conditions Overview of (Apparent) Kinetic Isotope Effects 27.3 Questions and Problems 27.4 Bibliography Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

898

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

27.1

Introduction, Methodology, and Theoretical Background We conclude our treatment of transformation processes (Chapters 21 to 26) by acquainting ourselves with compound-specific isotope analysis (CSIA), a method that is extremely useful for (1) assessing whether a compound has undergone any transformation in a given system, and, in case of transformation, (2) estimating the extent of transformation, and (3) for obtaining important hints on the mechanism(s) of the underlying types of abiotic and biological reactions. The method is based on the ability to measure the bulk isotopic composition at natural abundance of an organic compound with respect to one or several elements. In Chapter 2 (Section 2.1), we showed that most of the elements commonly present in organic chemicals (i.e., H, C, N, O, S, Si, Cl, Br, see Table 2.1) exhibit heavier stable isotopes with quite different natural abundances relative to the main (lighter) isotope, ranging from as low as 0.015% (2 H) to as high as almost 50% (81 Br). This means that a subset of the molecules of a given compound will exhibit higher molecular masses, a different symmetry, and one or several sites in the molecule where bonds are somewhat different (i.e., different bond strength, different bond length) as compared to the same sites in the molecules not containing the heavier isotopes involved in those bonds. These differences translate into small but important differences in physicochemical properties and intrinsic reactivities among these fractions of molecules. From evaluating measured changes in the bulk isotopic composition of one or several different elements (commonly referred to as isotopic or isotope fractionation) present in the organic compound as a function of time and space in a given laboratory, engineered, or field system, one can then often draw important conclusions about the types of processes to which the compound has been subjected. In this chapter, we focus primarily on evaluating isotopic fractionation that are caused by transformation reactions, and this will also allow us to re-examine some the most important types of reactions treated in Chapters 22 to 26. We also note that, in general, isotopic fractionations caused by transformation reactions, during which bonds are broken and new bonds are formed, are commonly much more pronounced than isotopic fractionations associated with physical processes including molecular diffusion or partitioning processes. For a discussion of these processes, we refer to the literature (molecular diffusion: Jeannottat and Hunkeler, 2013; Jin et al., 2014; Wanner and Hunkeler, 2015; volatilization: Kuder et al. 2009; Jeannottat and Hunkeler, 2013; sorption: Kopinke et al., 2005; H¨ohener and Yu, 2012; Eckert et al., 2013). Finally, we should point out we discuss this subject at a rather introductory level. For a more advanced treatment of various aspects of this topic, we suggest other textbooks (e.g., Aelion et al., 2010; Jochmann and Schmidt, 2012) and reviews (e.g., Elsner, 2010; Elsner et al., 2012; Thullner et al., 2012; Hofstetter et al., 2014). Isotopologues and Isotopomers Compounds Containing Only Carbon, Hydrogen, Nitrogen, and Oxygen. Before we get into methodological aspects of compound specific-isotope analysis (CSIA) and into the interpretation of experimental data, it is useful to have a closer look at the various isotopically different types of molecules and their relative natural abundances a given compound is composed of. We start by considering organic compounds that are only made with elements exhibiting heavier stable isotopes that occur at low natural abundances, that is, around or below 1%. These elements include C, H, N, and

Introduction, Methodology, and Theoretical Background

Table 27.1 Stable Isotope Ratios of the Most Common Elements (Except Fluorine, Phosphorus, and Iodine that do not Exhibit Stable Isotopes) Present in Organic Compounds a H:1 H = 0.00015:1 C:12 C = 0.011:1 15 N:14 N = 0.0037:1 17 O:16 O = 0.0004:1 18 O:16 O = 0.0020:1 29 Si:28 Si = 0.051:1 30 Si:28 Si = 0.034:1 34 32 S: S = 0.044:1 37 Cl:35 Cl = 0.32:1 81 Br:79 Br = 0.98:1 2

13

a

Data from Pretsch (2009).

899

O (Table 27.1). Since to date, in contrast to studies of hydrological and biogeochemical processes, stable oxygen isotopes have rarely been used to assess processes involving organic compounds, we confine our discussion here to the other three elements. For these elements, we can assume that only those molecules that exhibit one and not several heavier isotopes (one 13 C or one 2 H or one 15 N but no combinations of them) are sufficiently abundant to be important for our analyses. We note, however, that the first papers on the measurements of “clumped isotopes” (two heavy isotopes of low natural abundance present in the same molecule) have recently appeared. An example is the determination of the relative abundance of 13 C2 H1 H2 for evaluating microbial methane formation (Wang et al., 2015). We also note that 13 C is commonly more abundant than 2 H and 15 N in organic compounds, which is one of the main reasons why in the early days of CSIA primarily carbon isotope measurements have been performed. To illustrate the various isotopically different types of molecules that have to be considered when evaluating the isotopic fractionation of C, H, and N, respectively, occurring during a given process, we consider para-nitrotoluene (p-NT) as an example. As shown in Fig. 27.1, neglecting O isotopes, four different p-NT isotopologues are of interest, that is, molecules that differ in their isotopic composition. These isotopologues include the species composed of only the light elements [i.e., 12 C7 1 H7 14 NO2 (≈ 92%); compound I], and the three isotopologues each containing one different heavy isotope [i.e., 13 C12 C6 1 H7 14 NO2 (≈ 7.7%), compounds II-VI; 12 C7 2 H1 H6 14 NO2 (≈ 0.11%), compounds VII-XI; 12 C7 1 H7 15 NO2 (≈ 0.37%), compound X]. As can be seen from Fig. 27.1, among the molecules exhibiting a 13 C- or a 2 H-atom, several isotopic isomers exist [five (II-VI) and three (VII-IX) respectively]. They are commonly referred to as isotopomers (the heavy isotope may be in different locations in the molecule). In the case of 15 N, there are no isotopomers because only one nitrogen is present and because there is no steric isomerism present. Thus, when we investigate changes in the bulk 15 N/14 N composition of p-NT in a given system, we only have to evaluate how the different processes discriminate between two species (i.e., I versus X in Fig. 27.1). In contrast, in the case of 13 C and 2 H fractionation there are six (I versus II, III, IV, V, and VI) and three (I versus VII, VIII, and IX) isotopically different species, respectively, that have to be considered. For processes such as diffusion or partitioning, which depend primarily on the properties of the whole molecule (e.g. size, cross sectional area), and which do not change significantly when substituting the light by the heavy element, one commonly assumes that the different isotopomers behave quite similarly. However, this is very different in transformation reactions, in which isotopic fractionation is primarily taking place in the isotopomer exhibiting the heavy isotope(s) at the location or close to the location at which the reaction takes place. As a consequence, those isotopomers that do not contribute to fractionation will “dilute” the measured bulk value. This effect can lead to severe restrictions for the application of CSIA to investigate transformation reactions of larger compounds. For example, assuming a uniform distribution of the heavy isotopes, in the case of the oxidation of p-NT at the methyl group (e.g., by H-abstraction), the experimental bulk 13 C– and 2 H–fractionations are “diluted” by all other 13 C and 2 H atoms respectively, not involved in the reaction. Hence, only 1/7 and 3/7, respectively, of the fractionation is observed compared to the fractionation that would be measured if only the relevant isotopologues (VI and IX, respectively) would be considered. We come back to this issue later in this chapter.

900

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

14NO 12

1H

12 1H

13

1H

1H

1H 12 12 12 1H C 1H

12 1H

1H 12 12 12 1H C 1H

12

1H

1H

1H

12 1H

C

III (2/7)

14NO

12 1H

12

1H

2

12 1H

12

12

1H 12 13 12 1H C 1H

1H

12

12 1H

1H

12 1H

C

V (1/7)

1H VI (1/7)

14NO

14NO

14NO

12

1H

13

1H IV (2/7)

2

12 2H

12

1H

2

12 1H

12 1H

2H 12 12 12 1H C 1H

1H

1H

VII (2/7)

VIII (2/7)

12 1H

12 1H

12

12 12 12

1H

C

1H 2H

IX (3/7)

2

12 1H

12 1H

2

1H

15NO 12

12

1H

12

12

1H 12 12 12 1H C 1H

1H

Figure 27.1 The different carbon (IVI), hydrogen (I, VII-IX), and nitrogen (I,X) isotopologues/isotopomers of para-nitrotoluene (p-NT) that are relevant for isotope fractionation.

12

1H

2

12

13

12 1H

12

12

1H

14NO

2

12

1H

1H

II (1/7)

14NO

2

13 1H

12

1H

I

12

12

1H

12

1H

1H

12 1H

12

1H 12 12 12 1H C 1H

1H

14NO

2

12

12 1H

14NO

2

12

1H 12 12 12 1H C 1H 1H

X

Compounds Containing Sulfur, Chlorine, and Bromine Atoms. A different, somewhat more complicated situation with respect to the number and nature of isotopologues and isotopomers is encountered when studying compounds containing elements that exhibit more abundant isotopes as compared to C, H, and N. As shown in Table 27.1, such elements include sulfur (about 4% 34 S), silicon (about 5% 29 Si and 3.5% 30 Si, respectively), chlorine (about 24% 37 Cl), and bromine (about 49% 81 Br). Since, similarly to oxygen, to date, sulfur isotopes have been very rarely used to assess organic compound behaviors in the environment, and since very little data is available for bromine, in this chapter, in addition to carbon, hydrogen, and nitrogen

Introduction, Methodology, and Theoretical Background

35Cl

35Cl

C

35Cl

C

35Cl

37Cl

C 35Cl

35Cl

42.2%

35Cl

C

37Cl

C

35Cl

C

35Cl

33%

37Cl

37Cl

C

35Cl

901

37Cl

35Cl

C

37Cl

C

35Cl

35Cl

C 37Cl

all three isotopomers together: 20.2%

Figure 27.2 The various tetrachloroethene (PCE) chlorine isotopologues/isotopomers and their relative abundances (isotopic abundances of various combinations of chlorine, bromine, sulfur, and silicon can be found in Pretsch et al., 2009, Table 2.5.5).

35Cl

37Cl

C 37Cl

37Cl

C 37Cl

4.3%

37Cl

C 37Cl

C 37Cl

0.3%

we primarily address chlorine isotope fractionation. To illustrate how many chlorine isotopologues and isotopomers have to be considered when evaluating chlorine isotope fractionation for a given compound, we take our companion tetrachloroethene (PCE) as an example. Figure 27.2 shows that PCE has five chlorine isotopologues of different abundances (given as approximate values in parentheses), with one isotopologue (C2 35 Cl2 37 Cl2 ) being divided into three isotopomers (cis, trans, and vicinal positions of the two 37 Cl atoms). We should point out that about 2.2% of the carbon atoms present in PCE are 13 C isotopes. These isotopologues/isotopomers containing one 13 C as well as any composition of chlorine isotopes are, however, negligible when we are solely interested in chlorine isotope fractionation. They are, of course, the relevant molecules determining the extent of carbon isotope fractionation. In conclusion, we note that when we apply CSIA to study isotope fractionation for a given compound in a given system, for each element (e.g., C, H, N, Cl) another subset of the compound molecules including their various isotopologues and isotopomers are responsible for contributing to the overall (bulk) fractionation that we can measure. Methodological Aspects: The (Bulk) Isotopic Signature of a Compound (𝛅h E) Methodological Aspects. The use of CSIA for assessing organic pollutant behavior in a given system hinges on the ability to measure minute differences in the bulk isotopic composition of the compound with respect to a given element, that is, differences in the ratio of the abundances of the heavy (h E) and the light (l E) isotope, given by RE = h E / l E as a function of time or space. To this end, special instrumentation is required, commonly involving a chromatographic separation system [either a gas chromatograph (GC), or more recently a high performance liquid chromatograph (HPLC)] coupled to a chemical conversion unit and a sophisticated isotope ratio

902

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

(a) compound A

compound mixture A + B

A AA

magnet

M

h l

B B B

A

M

B

M

M

chemical conversion (M = CO2, N2, H2, CO, ...)

chromatographic separation (gas or liquid chromatography)

(b)

M

compound B

M

M

ion source

isotope ratio mass spectrometry (IRMS)

injector compound A compound B

magnet

CO2 CO2

13CO 12CO

ion source

gas chromatograph (GC)

combustion oven

isotope ratio mass spectrometry (IRMS)

2 2

monitoring gas: CO2

Figure 27.3 Upper panel: the principle of compound-specific isotope analysis by chromatography-IRMS. Compound mixtures are separated by chromatography. The continuous carrier flow with the baseline-separated analyte peaks is directed into a chemical conversion interface. Individual analytes are converted into a measurement gas M that is suitable for isotope analysis. Peaks of M are transferred in a He carrier stream into the isotope-ratio mass spectrometer. Lower panel: instrumentation for carbon-isotope analysis by GC-IRMS. Figure from Elsner et al. (2012).

mass spectrometer (IRMS) optimized to measure isotope ratios of a given element with very high sensitivity and precision (see schematic in Fig. 27.3 and data in Table 27.2; for more details see Sessions, 2006; Elsner et al., 2012; Jochmann and Schmidt, 2012). For the analysis of chlorine isotopes, some direct analysis using a GC-quadrupole MS (GC-qMS) system has also been used with reasonable success (see comparison with GC-IRMS given in Bernstein et al., 2011). Finally, for the few bromine isotope measurements, a method using gas chromatograph coupled to a multicollector inductively coupled plasma mass spectrometer (GC-MCICPMS) has been applied (Sylva et al., 2007; Bernstein et al., 2013). Besides using the chromatographic system to separate the compound completely from other compounds so as to avoid isotopic background signals, other challenges need to be solved when determining isotope ratios. They include enrichment procedures from the (environmental) matrix (e.g., from air, water, or soil), and possibly, derivatization of the compound to make it amenable to transport through the chromatographic system. In order not to create methodological artifacts, all these analytical steps should, of course, not lead to significant changes in the isotopic composition of the compound or such changes should be taken into account (see Elsner et al., 2012; Jochmann and Schmidt, 2012). The Bulk Isotopic Signature of an Organic Compound (δh E). For a given element, the bulk isotopic signature, that is, the measured ratio of the abundances of the

Introduction, Methodology, and Theoretical Background

903

Table 27.2 Natural Abundances of the Heavier (Minor) Isotopes of the Most Important Elements Used in CSIA, Amount Required for Analysis and Precision of CSIA Measurements

Element E

Minor Heavy Isotope h E

Hydrogen Carbon Nitrogen Chlorine

H C 15 N 37 Cl

2

13

Common Reference Standard a (“std”)

Natural Abundance of Standard b hE std (%)

Isotope Ratio of Standard RE,std = h E /l E std std

Relative Precision c (± 2σ,‰)

VSMOW VPDB AIR-N2 SMOC

0.01557 1.1056 0.3663 24.221

0.00015575 0.0111802 0.003678 0.31963

6 0.5 1 0.2 - 1

a

Values for international reference standard material, given to the last significant digit. VSMOW = Vienna Standard Mean Ocean Water; VPDB = Vienna Pee Dee Belemnite; AIR-N2 = Nitrogen from air; SMOC = Standard mean ocean chloride; for more details and other commonly used reference standard materials see Brand et al. (2014). c From Elsner et al. (2012). b

heavy and the light isotope, RE (= h E / l E), is commonly not expressed as an absolute number but relative to an internationally accepted reference standard (subscript “std”, see Table 27.2). This relative parameter is commonly denoted as δh E and defined as: δh E =

RE − RE,Std RE,Std

=

RE −1 RE,Std

(27-1)

To illustrate, using VPDB as reference standard (see footnote in Table 27.2), a compound with a 13 C/12 C ratio, RC , of 0.0111914 has a positive δh E of about 0.001 or 1‰, a small difference that can be reliably determined for carbon (see precision given in Table 27.2). We note that a positive δh E means that the compound is enriched in the heavy isotope relative to the reference standard, while a negative value means it is depleted. Before we turn to the discussion on how changes in the bulk isotope signature(s) of a compound due to a given isotope fractionating process are commonly expressed, we briefly address the use of δh E values as “fingerprints” for identification of its source or origin. Particularly when isotope signatures are available for more than one element, such source identifications are often quite successful, and have been widely applied as a forensic tool not only in environmental and biogeochemical applications, but also in food and beverage control (oil, coffee, wine), in athlete doping tests, archeology, and many other fields (see Jochmann and Schmidt, 2012; Gentile et al., 2015). The reason for such successful applications is the fact that, depending on the way it is naturally produced or industrially manufactured, the same chemical may have a quite different isotopic signature. A classical example is the use of the carbon and hydrogen isotope signature for source identification of methane (CH4 ). As shown in Fig. 27.4, biogenic methane is generally significantly lighter in both carbon and hydrogen isotopes as compared to thermogenic methane as found in fossil fuels. This can be used, for example, for assessing whether or not water quality is impacted by seepages of methane and other gases from shale-gas extractions or whether it has a natural biogenic origin (e.g., Molofski et al., 2013; Heilweil et al., 2015).

904

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

–60 –80

atmosphere

–100 –120 –140

coal mining

–160

4

δ2HCH (‰)

–180

natural gas

–200

hydrates

–220

biomass burning

–240 –260 –280

ruminants

–300 Figure 27.4 The isotopic carbon and hydrogen signatures (relative to VPDB and VSMOW, respectively; see Table 27.2) of methane from different sources. Data from Quay et al. (1999) and Whiticar (1999), and figure adapted from Centre for Ice and Climate (2015).

landfills

–320 –340 –360 –70

wetlands rice paddies

–60

–50 13

δ

–40

–30

–20

CCH (‰) 4

The ranges of bulk isotopic signatures determined for some ubiquitous organic pollutants stemming from different manufacturers/sources are summarized in Table 27.3. For these chemicals, source identification is important, particularly with respect to water pollution. By far the most abundant isotope data available for organic pollutants are δ13 C data. In many cases, however, the availability of only δ13 C is not sufficient to unequivocally identify a certain product, since the δ13 C range is relatively narrow and reflects the typical range encountered in fossil fuel components (for more details see refs given in Table 27.3). This is not too surprising as many industrially manufactured chemicals are based on starting materials derived from petroleum products, and since during synthesis, carbon isotope fractionation seems not to be very large, primarily because the carbon skeleton is not significantly affected. In this context, we should also note that, for source identification, in addition to 13 C there is an increasing number of studies using radioactive 14 C measurements (e.g., Griffith et al., 2012 for distinguishing natural from synthetic estrogens). For the other three elements, but particularly for hydrogen, the variability in the bulk isotopic is much larger, and therefore, in combination with δ13 C often allows us to distinguish source materials. As we see in Section 27.2, the same holds for the identification of transformation mechanisms in well-defined systems as well as for the interpretation of field data.

Introduction, Methodology, and Theoretical Background

905

Table 27.3 Ranges in Isotopic Composition of Some Organic Chemicals Stemming from Different Manufacturers/Sources a Compound

Nb

δ13 C Range (‰)

δ2 H Range (‰)

MTBE TCE PCE TNT Diclofenac Benzotriazole BTEX (gas, gasoline) n–Alkanes (crude oil) e

7 18 4 5 9 6 8 21

−31 to –27 −32 to –26 −35 to –23 −27 to –22 −31 to –26 −28 to –25 −28 to –25 −31 to –26

−101 to –54 −50 to +700

−150 to –30 d −95 to –85

δ15 N Range (‰)

−6 to +9 −3.2 to 0 −28 to –8

δ37 Cl Range (‰) −4 to +4 −2.5 to +0.3

Ref c 1 2 3 4 5 6 7, 8 9, 10

The δh E values are expressed relative to the reference standards given in Table 27.2. N = number of different products/sources. c Data from 1: Shin et al. (2013); 2: Shouakar-Stash et al. (2003); 3: Beneteau et al. (1999); 4: Coffin et al. (2001); 5: Maier et al. (2014); 6: Spahr et al. (2013); 7: In gasoline and standard gas mixture, Kichuchi and Kawashima (2013); Kawashima and Murakami (2014); 8: standard gas mixtures, Vitzthum von Eckstaedt et al. (2011 and 2012); 9: Li et al. (2009); 10: Muhammad et al. (2015). d Large differences are found between different compounds, i.e., benzene: –120 to –100‰ ; toluene –60 to –30‰; ethylbenzene: –40 to –35‰, o-xylene: –150‰ ; m-xylene: –85 to –65‰; p-xylene: –65 to –55‰. e C12 to C33 . a b

Rayleigh Equation and Bulk Enrichment Factors (𝛆E ) Let us now see how we can quantitatively describe changes in δh E of a given compound resulting from an isotope fractionating transformation reaction. As an example, we consider the changes in the bulk δ13 C, δ2 H, and δ15 N values determined during the microbial oxidation of nitrobenzene, which is initiated by a dioxygenase, a reaction that we already encountered in Chapter 23 (Section 23.4). As shown in Figure 27.5a, in the course of the reaction expressed by the fraction, f (=C/C0 ), of the nitrobenzene remaining (i.e., not transformed), all three elements were enriched in an exponential way, though to different degrees. As the simplest approach, we can quantify this change in isotope composition (much like we have treated a first-order reaction) by linearly relating the natural logarithm of δh E = δh E0 + Δδh E, expressed relative to the δh E0 value of the starting material, to ln f : ln

δh E0 + Δδh E + 1 C = εE ln f = εE ln C0 δh E0 +1

(27-2)

where εE is the so-called bulk enrichment factor for the element E. εE can be determined by a linear regression, and it reflects the change in δh E with a change in concentration of the compound of interest. When applying Eq. 27-2, which is commonly referred to as Rayleigh Equation (originally developed for simple distillation), we assume that the enrichment factor is a constant, like a first-order rate constant. This means we assume that, at any time, isotope fractionation is the same. For the derivation of the Rayleigh Equation as well as for a discussion of cases in which its application is inappropriate, we refer to the literature (e.g., Elsner et al., 2005; Hunkeler and Elsner, 2010; Wijker et al., 2013b; Dorer et al., 2014a).

906

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

Dioxygenation of nitrobenzene by Comamonas sp. strain JS765 NO2

O2N

OH

OH OH

O2

rate-limiting

δ

15

N (‰)

C

H

CO2

1 N

AKIEN = 1.0008 ± 0.0001

H

AKIEH = 1.045 ± 0.002

(b)

(a)

4

AKIEC = 1.024 ± 0.001

OH

–NO–2

O

+

N

bulk compound

– O

isotope enrichment factor 1.25×10–2

2

εH = –6.3 ± 0.5‰ εC = –3.9 ± 0.1‰

0

–25

H

–35

2

εE 1

5.00×10–3

NO2

δ H (‰)

7.50×10–3

ln

–30 H

H

H

2.50×10–3

H

–40

–45

δE0 + 1

NO2

δ

13

C (‰)

–20

δE0 + ΔδE + 1

1.00×10–2

εN = –0.8 ± 0.1‰ 0 1

0.8

0.6

0.4 C/C0 (–)

0.2

0

–3

–2.5

–2

–1.5

–1

–0.5

0

ln (C/C0)

Figure 27.5 Carbon, hydrogen, and nitrogen fractionation during oxidative transformation of nitrobenzene by Comamonas sp Strain JS765 (adapted from Hofstetter et al., 2008a). (a) Change in the isotopic signature as a function of the remaining nitrobenzene fraction. (b) Raleigh plots (Eq. 27.2) of the data shown in Fig. 27.5a. AKIEE stands for the apparent kinetic isotope effect.

Figure 27.5b shows that in our example, Eq. 27-2 fits the experimental data reasonably well, and that negative bulk enrichment factors are found for all three elements. We note that a negative enrichment factor indicates that, with respect to the element considered, the compound is enriched in the heavy isotope. This is referred to as a normal isotope effect. For example, a bulk enrichment factor of –3.9‰, as found for carbon during the oxidation of nitrobenzene (Fig. 27.5b) means that a decrease in concentration by a factor “e” (factor 2.72) leads to an increase in δ13 C of 3.9‰ in the remaining nitrobenzene. In cases in which the light isotope is enriched (i.e., positive εE ), we speak of an inverse isotope effect. We encounter some of these less common cases in Section 27.2. We should also note that the Rayleigh approach also works for elements exhibiting higher isotope abundances such as chlorine (Elsner and Hunkeler,

Introduction, Methodology, and Theoretical Background

907

2008). In this chapter, we confine ourselves to cases in which the Rayleigh Equation can be applied. In these cases, and when assuming that no other processes influence the decrease in concentration of a pollutant as a function of time or space in a given system, we may assess the degree or extent of transformation, B (the notation B stems from the application in biotransformation processes), i.e., the fraction transformed, 1f, by rearranging Eq. 27-2: ( B=1−f =1−

δh E + 1 δh E0 +1

)1∕εE (27-3)

where δh E = δh E0 + Δδh E (Eq. 27-2). In this context, it is also useful to inspect the isotopic signature of (stable) transformation products. We address this issue in Section 27.2. Before we learn how to gain mechanistic information from bulk enrichment factors, we first need to address some basic aspects of isotope fractionation happening during transformation reactions. We do this in a rather descriptive way following the treatment given by Elsner et al. (2005). For a much more in-depth discussion of this topic, we refer to Elsner (2010) or Hunkeler and Elsner (2010). The Kinetic Isotope Effect Let us consider an elementary reaction in which a particular bond is broken in the ratelimiting step. Substitution of the light isotope by the heavy isotope of a given element that is directly located at or close to the bond that is broken, generally leads to a slightly different (often slower) reaction rate. If we describe the rates of reaction of the lighter and heavier isotopologue, respectively, by (pseudo-) first-order rate constants, l kE and h k , we can define an intrinsic kinetic isotope effect, KIE , as : E E KIEE =

1k

E

hk

E

(27-4)

or, when using the transition state theory to express rate constants (Chapter 21, Section 21.3): KIEE = e−Δ1h Δ G ∕RT ‡

0

(27-5)

where Δ1h Δ‡ G0 is the difference in the standard free energies of activation between the isotopologues exhibiting a light and those with a heavy atom at the site of reaction. KIEE values are largest if the heavy isotope is directly involved in the bond that is broken (primary isotope effect) and commonly significantly smaller, but often not negligible, when present only adjacent to the reaction center (secondary isotope effect). If KIEE > 1, that is, if the lighter isotopologue reacts faster, one speaks of a normal isotope effect, if the heavier isotopologue reacts faster (KIEE < 1), of an inverse isotope effect. When considering reactions of a compound in its ground state, the differences in Δ‡ G0 between the respective light and heavy isotopologue arise primarily from differences that are mass sensitive, reflected primarily in differences in the vibrational energies (caused by vibrations of atoms inside the molecule) between the ground state and the transition state. These differences are commonly dominated by the different vibrational energies of the isotopologues in the ground state, since bonds

908

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

may already be partly cleaved in the transition state. Furthermore, we should note that the contributions of vibrational energies to the overall Δ‡ G0 are small as compared to electronic energies. As a consequence, in general kinetic isotope effects are not correlated to reaction rates. For example, the carbon bulk enrichment factors measured for the reductive dehalogenation of tetrachloromethane (CCl4 ) by a variety of reduced iron phases were very similar, although the reaction rates varied by several orders of magnitude (Zwank et al., 2005). Let us now have a look at the factors that determine the magnitude of primary and secondary isotope effects. As we might recall from basic physics or chemistry courses, vibrational energies depend primarily on atomic masses and bond strengths as expressed by the force constant of the vibrating bond (see Isaacs, 1995). Therefore, these parameters have the main influence on KIEE . From transition state theory using the so-called “zero-point energy approximation,” some general comments and qualitative “rules of thumb” can be made that are helpful to identify reaction mechanisms from isotope fractionation data (for a more detailed treatment see Elsner et al., 2005 and Elsner, 2010). 1. Influence of Isotope Masses. The highest isotope effects may be expected for elements that have the greatest relative mass difference between their heavy and light isotope. For the elements of interest to us, this is hydrogen. KIEH expected and found for primary isotope effects are usually orders of magnitude higher for H than for C, N, and Cl. 2. Influence of Bonding Partners. For a given element that is present in covalent bonds with comparable force constants, isotope effects tend to be greater if the element is bound to a heavier atom. For example, carbon isotope effects are generally larger in cleavage of C–N or C–Cl bonds as compared to the cleavage of C–H bonds. 3. Influence of Changes in Bond Strength. Isotope effects are generally larger the more the strength of bonds is changed between the ground state and the transition state during a given reaction. In the case of primary isotope effects associated with bond cleavage, this change is greatest if the bond is already completely broken in the transition state, meaning if the transition state has more product-like characteristics. On the other hand, small effects are expected if the transition state has more substrate-like characteristics. Exceptions are reactions where breakage of a bond is accompanied by the simultaneous formation of a new bond as, for example, encountered in SN 2reactions (see Chapter 22, Fig. 22.1). 4. Secondary Isotope Effects. As previously mentioned, compared to primary isotope effects, secondary isotope effects are significantly smaller (up to one order of magnitude or even more), since changes in bonding involving the heavy isotope are much smaller if these bonds are not cleaved but only slightly impacted by being located close (e.g., adjacent) to the reaction center. Such impacts include, for example, changing of the coordination geometry at the reaction center as is occurring during nucleophilic substitution reactions reactions (Fig. 22.1). 5. Stabilization at the Reactive Center by Adjacent Bonds. As covered in Chapter 22 when discussing nucleophilic substitution reactions at primary, secondary, and tertiary carbon atoms, adjacent bonds (e.g., –H versus –CH3 ) may have a significant influence on the stabilization of the transition state (e.g., stabilization of a positive

Introduction, Methodology, and Theoretical Background

909

charge by hyperconjugation). The net isotopic effect at the reaction position is then caused by all participating bonds. For example, if a C–Cl bond is broken in the hydrolysis of chlorinated alkanes, large carbon isotope effects at the reacting C-atom may be expected (see Section 27.2) for a concerted substitution mechanism (i.e., SN 2). Such effects are much smaller in a dissociation-association mechanism (i.e., SN 1) where loss in bonding is compensated by increased stabilization of all adjacent bonds to the reacting C-bond. 6. Concerted Reactions: Effects in Several Positions. Although bond changes are often confined to only one reactive bond, there are cases where a reaction may be “concerted,” leading to primary isotope effects at several locations simultaneously. For example, as we see in Section 27.2, the reductive transformation of chlorinated ethanes and ethenes (Chapter 23) may involve only one C–Cl bond or engage both carbon atoms at the same time. Also, in the enzymatic oxidation of double bonds of aromatic compounds (Chapter 23, Eqs. 23-34 and 23-35), the initial reaction may either be localized at only one carbon or involve both atoms as in the case of epoxidation of a double bond by a monooxygenase. Dual Isotope Plots and Derivation of Apparent Kinetic Isotope Effects (AKIEE s) from Bulk Enrichment Factors Let us now see how to derive apparent kinetic isotope effects (AKIEE s) from bulk isotope fractionation data. We should note that we use the term “apparent” to distinguish a kinetic isotope effect derived from experimental data from the intrinsic isotope effect, KIEE (Eq. 27-3), for a specific elementary reaction. Commonly, the AKIEE is smaller than the KIEE because other less fractionating reaction steps may determine the measured bulk enrichment factors. In fact, quite often, AKIEE values do not simply reflect an elementary reaction step but may be the result of two consecutive reaction steps with different KIEE s, of which either one or both may be rate determining. One example is the base- catalyzed hydrolysis of carboxylic esters (see Chapter 22, Eq. 22-26 and Fig. 22.6) where either the addition of HO– , the dissociation of the leaving group, or both may determine the overall rate and thus the magnitude of the AKIEE . Another example is the aromatic electrophilic substitution where an electrophile (e.g., enzymatic oxidation by an oxygenase or enzymatic carboxylation see Chapter 23, Section 23.4) is added to the aromatic ring followed by abstraction of H+ , where, again, either or both steps may be rate-determining. In addition, particularly in enzymatic reactions, other non- or only weakly fractionating processes (e.g., transport to the organism, binding to an enzyme’s active site) may “mask” the intrinsic KIEE (see the following discussion), and thus render interpretations more difficult. Nevertheless, comparison of AKIEE values derived for different assumed reaction mechanisms with KIEE values estimated from theory for these reactions is often very helpful to get important hints on the actual reactions occurring, or at least on which reactions can be excluded. This is particularly the case if isotope fractionation data is available for more than one element. As an illustrative example, we now inspect the isotope fractionation observed during three different transformation reactions (and postulated reaction mechanisms) of our companion MTBE: (i) aerobic microbial oxidation (H-abstraction at the methyl group bound to the oxygen), (ii) abiotic acid catalyzed hydrolysis (SN 1 mechanism), and

910

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

δ2H in per mill

40 aerobic biodegradation 20 H

H 0

–20

C H

H3 C O

acid hydrolysis

CH3

C

H H3C

H

CH3

C

O

H

oxidation

CH3

C

C

–CH3OH

CH3

CH3

H3 C

H+

CH3 SN1 reaction

–40

–60 anaerobic biodegradation

–80

H Nucleophile C H

–100

H H3 C O

CH3

C

H H+

Nucleophile

CH3

C H

OC(CH3 )3 H SN2 reaction

–120 –32

H

–30

–28

–26

–24

–22

–20

–18

–16

–14

δ13C in per mill

Figure 27.6 Changes in carbon and hydrogen isotope ratios of methyl- tert-butyl ether (MTBE) during different transformation reactions. Error bars indicate the total uncertainty of ±0.5‰ for carbon and ±5‰ for hydrogen. Figure from Elsner (2010).

(iii) anaerobic microbial hydrolysis (SN 2 mechanism), see Fig. 22.1. From the “dual isotope plots” given for hydrogen and carbon in Fig. 27.6, we can see that the relative changes in isotopic composition occurring during the course of the three reactions show a distinctly different picture. We can also see that the experimental data can be fitted reasonably well by a linear regression line. Furthermore, the slopes of the regression lines correspond approximately to the ratios of the individual bulk enrichment factors determined by the Rayleigh Equation (the corresponding εE values and regression equations are given in Table 27.4; for more details see Elsner et al., 2007a): slope = ΛH∕C =

ε Δδ2 H ≈ H 13 Δδ C εC

(27-6)

Therefore, using the simple Rayleigh approach to evaluate the isotope fractionation seems to be appropriate for all three reactions. We should note that, particularly for large hydrogen fractionation, in some cases, the Raleigh approach may not be directly applicable over the whole concentration range considered (Dorer et al., 2014a), but there are ways of correcting for such situations (Wijker et al., 2013b). As already previously pointed out, in order to derive AKIEE values from the εE values given in Table 27.4, we first need to postulate at which locations in the molecule a given reaction actually takes place. For our MTBE example, the postulated mechanisms are indicated in Fig. 27.6. Before we go on deriving the AKIEE s for these three

911

Introduction, Methodology, and Theoretical Background

Table 27.4 Bulk Enrichment Factors for Carbon and Hydrogen Fractionation and Slopes of Linear Regression Analysis of the δ2 H Versus δ13 C Plots for the Three Different Transformation Reactions of MBTE Shown in Fig. 27.6 Type of reaction

a

H-abstraction at methyl group c SN 1-reaction at t-butyl group b SN 2-reaction at methyl group d

εC (‰)

εH (‰)

ΛH/C = εH /εC (-)

−2.0 −4.9 −13

−34 −55 −16

17 11 1.2

ΛH/C = slope (-) b 18 11 1.2

a

See also Fig. 27.6. Data from Elsner et al. (2007a). c Data from Gray et al. (2002). d Data from Kuder et al. (2005). b

reactions, let us briefly check whether the postulated reaction mechanisms do not contradict the qualitative rules given above for isotope fractionation. First, for the aerobic oxidation occurring by H-abstraction at the methyl group, the (primary) isotope effect is found to be large for hydrogen as compared to carbon, which concurs with rules 1 and 2. The opposite is true for the SN 2 reaction, and an intermediate situation is encountered for the SN 1 reaction (in accordance with rules 3 to 5). Furthermore, we note that in the case of the SN 1 and SN 2 reactions, the hydrogen isotope effects are secondary effects, but that they are quite substantial because the hydrogens are involved in stabilizing the transition state, particularly in the SN 1 case (conforms with rule 5). Finally, at first glance, the primary hydrogen effect observed for the oxidation of MTBE at the methyl group bound to the oxygen seems to be smaller than the secondary effect determined for the acid hydrolysis (SN 1), which seems to violate rule 4. This violation is, however, only seemingly a violation because in the oxidation reaction only 3 out of 12 hydrogens are involved, whereas in the SN 1 case, nine hydrogens contribute to the bulk enrichment factor. Hence, the actual kinetic isotope effect at the reactive sites, and the resulting site-specific enrichment factors and AKIE values are, as expected (rule 4), significantly larger for the oxidation than for the acid hydrolysis (see Table 27.5 and Eqs. 27-9 and 27-10). At this point we should emphasize that bulk enrichment factors and derived AKIEE values can usually not be used as a solid proof of a postulated reaction mechanism, but rather as supporting evidence. However, in many cases, they can help to exclude certain mechanisms. For calculating the reactive site-specific enrichment factor (εE, reactive site ), we need to account for all those isotopomers that are not contributing to the bulk enrichment factor and thus the number of heavy atoms that “dilute” the measured value. This can be achieved by multiplying the bulk enrichment factor by the fraction of all these species, which is given by: εE, reactive site ≈ (n∕x)εE

(27-7)

where n is the total number of the atoms of a given element and x is the number of atoms involved in the reaction. Table 27.5 summarizes the resulting εE, reactive site values for the three reactions. We note that when using Eq. 27-7, we assume an even distribution of the heavy isotopes in the molecule, which, particularly for hydrogen, is

912

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

Table 27.5 Reactive Site-Specific Enrichment Factors (Eq. 27-7) and Corresponding AKIEE Values (Eq. 27-10) for Carbon and Hydrogen for the Three Different Transformation Reactions Shown in Fig. 27.6 Type of reactiona

nC

xC

εC,reactive site (‰)

zC

AKIEC

nH

xH

εH,reactive site (‰)

zH

AKIEH

H-abstraction SN 1-reaction SN 2-reaction

5 5 5

1 1 1

−10 −25 −65

1 1 1

1.01 1.03 1.07

12 12 12

3 9 3

−136 −73 −64

3 1 1

1.69 1.08 1.07

a

See Figure 27.6.

not always the case (McKelvie et al., 2010). We also note that Eq. 27-7 (like Eq. 27-6) is an approximation, which may yield too high εE, reactive site values, again primarily for hydrogen (Elsner et al., 2005 and 2007a; Dorer et al., 2014a). In these cases, a linear regression analysis of the original “raw data” using Eq. 27-8 yields more accurate εE, reactive site values: ln

δh E0 + (n∕x)Δδh E + 1 C = εE,reactive site ln = εE,reactive site ln f h C δ E0 +1 0

(27-8)

Nevertheless, for our following discussions we mostly use Eq. 27-7 to derive εE,reactive site . Except for hydrogen isotope fractionation occurring by H-abstraction at the methyl group (oxidation, see the following), we can now calculate the apparent kinetic isotope effects, AKIEE s, for carbon and hydrogen, respectively, using Eq. 27-9 (Table 27.4; for the derivation of Eq. 27-9 see Elsner et al., 2005 or, in more depth, Elsner, 2010): AKIEE =

1 1 = 1 + εE,reactive site 1 + (n∕x) εE

(27-9)

For the oxidation reaction, we need to introduce an additional parameter z to denote the number of atoms of an element E that are in intramolecular competition for a given reaction: AKIEE =

1 1 + z εE,reactive site

=

1 1 + (n∕x) z εE

(27-10)

In the case of aerobic MTBE oxidation, the three hydrogens of the methyl group compete with each other. Since only one heavy hydrogen is present in the methyl group of the isotopologues responsible for hydrogen fractionation caused by H-abstraction, the εE,reactive site value derived from Eq. 27-7 underestimates the actual site-specific enrichment factor by a factor of three (z = 3). The reason is that Eq. 27-9 assumes that every abstraction of a hydrogen leads to an isotope fractionation, which, of course, is not true in 2/3 of the cases. In contrast, in the case of the secondary hydrogen isotope effect observed in the acid catalyzed MTBE hydrolysis (SN 1 mechanism), no competition of the nine hydrogen atoms present in the tert-butyl group can be expected. Here, the main effect leading to hydrogen fractionation is stabilization of the transition state by “hyperconjugation,” which is a “concerted action” of all nine positions, and hence, no

Introduction, Methodology, and Theoretical Background

913

competition (z = 1). Sometimes it is also useful to predict an expected bulk enrichment factor from an assumed kinetic isotope effect. Rearrangement of Eq. 27-10 yields: 1 − AKIEE εE = ( ) n z AKIEE x

(27-11)

Finally, for a more mechanistic interpretation of dual element isotope fractionation data, particularly when comparing reactions of different compounds, it may be useful to compare ratios of reactive site specific enrichment factors, e.g., for hydrogen and carbon: ( ) εH,reactive site nH ∕xH reactive site = = (27-12) ΛH∕C ΛH∕C εC,reactive site nC ∕xC site For the three reactions of MTBE (Table 27.5), the thus calculated Λreactive are 13.6 H∕C for H-abstraction, 2.9 for the SN 1 and about 1 for the SN 2 reaction, which particularly for the SN 1 reaction, is quite different from the ΛH/C value derived from the bulk enrichment factors (Table 27.4). Nevertheless, our qualitative assessment using the previously given rules of thumb are still valid.

Additional Factors Influencing Experimental Bulk Enrichment Factors Effect of Preceding Non- or Weakly Fractionating Rate-Determining Steps. When deriving AKIEE values from experimental data, particularly from measurements in more complex laboratory or field systems, it is important to realize that intrinsic isotope effects can only be properly determined if the bond changes involving the element E represent the rate-determining step in the overall process. Occasionally, the bond conversion is preceded by a non- or only weakly fractionating step, for example, mass transfer processes like the dissolution from an organic phase (e.g., an organic liquid phase such as a NAPL or DNAPL), desorption, transport to reactive sites or formation of enzyme-substrate complexes in biotransformation reactions. If so, every molecule that reaches the site of reaction is transformed irrespective of its isotopic composition, and only minor isotope fractionation will be observed despite the fact that there would be a significant intrinsic kinetic isotope effect (see e.g., Aeppli et al., 2009; Thullner et al., 2013; Renpenning et al., 2015). Another case is the dioxygenation of an aromatic ring in which the production of activated O2 may be rate determining (Wijker et al., 2015; Pati et al., 2016). One then commonly speaks of a masking of KIEE . In biologically catalyzed transformations, the term “commitment to catalysis” is used if all the molecules binding to the enzyme are transformed, that is, if the reverse step is very slow. In cases in which non- or only weakly fractionating steps only partly mask the actual (A)KIEE , that is, in cases in which fractionation can still be measured, it is particularly advantageous to have data on isotope fractionation for more than one element. Since one can usually assume that all isotopologues exhibit the same degree of masking or commitment to catalysis, this effect cancels out if the ratio of the respective bulk enrichment factors are evaluated. This is illustrated in Fig. 27.7, which shows dual hydrogen-carbon isotope plots for the anaerobic degradation of toluene by a dissimilatory iron-reducing bacteria using either dissolved or particulate iron (III). As is evident, although very different

914

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

CH3

CH3

150

Figure 27.7 Changes in carbon and hydrogen isotope ratios of toluene during anaerobic oxidation (Habstraction at the methyl group, see fumarate addition reaction; Chapter 23, Eqs. 23.41 and 23.42) by a dissimilatory iron-reducing microorganism (G. metallireducens) with dissolved Fe(III) (black symbols/ lines) versus a solid Fe(III)-mineral (red symbols/lines) as terminal electron acceptor. The experiments were carried out in batch systems. From Hofstetter et al. (2008a) based on data published by Tobler et al. (2008).

δ2H (‰)

100 50

CO2 εH = –98±3‰ εC = –3.6±0.7‰ Terminal electron acceptor for G. metallireducens: dissolved Fe(III) citrate

CH3

0

CH3 CO2

–50

εH = –35±1‰ εC = –1.3±0.1‰

–100 –150 –25

Terminal electron acceptor for G. metallireducens: solid Fe(III) mineral

–22

–19 –16 δ13C (‰)

–13

–10

absolute εH and εC values were measured in the two batch systems with the same pure culture of toluene-degrading bacteria, virtually identical dual isotope plots are obtained. These results indicate identical rate-limiting reaction mechanisms but significant “masking” in the case of the solid electron acceptor, which could reflect both transfer limitation and/or commitment to catalysis. As we see in Section 27.2, such factors masking isotope fractionation may render the interpretation of field data more difficult. Before we discuss some field data, we need to learn more about typical kinetic isotope effects observed for well-defined transformation reactions.

27.2

Using CSIA for Assessing Organic Compound Transformations in Laboratory and Field Systems With the examples discussed in this section we pursue three goals: (1) to further demonstrate how CSIA can help us to gain insights into the mechanisms and rate limiting steps of abiotic and biological transformation reactions, and, at the same time, to repeat some of the material that we have acquainted ourselves within Chapters 21 to 26, (2) to review typical fractionation factors and related (apparent) kinetic isotope effects reported for some important types of reactions, and (3) to show how CSIA may help to identify transformation processes in the field. However, we do not do this by addressing specific types of reactions as done in Chapters 21 to 26, but by picking individual or structurally related model compounds for which we will discuss possible abiotic and biological transformations that they may undergo in the environment. This allows us to get some “feelings” about the unique possibilities as well as the limitations of using CSIA for distinguishing different reaction pathways. The main groups or classes of compounds for which sufficient experimental data are available include BTEX components (gasoline components, solvents), dialkyl ethers (fuel oxygenates, solvents), nitroaromatic compounds (NACs, solvents, pesticides,

Using CSIA for Assessing Organic Compound Transformations

915

explosives), polychlorinated C1 – and C2 –compounds (solvents, pesticides), and some additional pesticides. As we noticed in Chapter 3, these compounds are used in large amounts, and, as a consequence of their use, they are among the most ubiquitous and notorious groundwater and soil pollutants. Therefore, their fate in contaminated soils and aquifers is of great interest. One key question is whether in a given situation, these chemicals are transformed under natural conditions (“natural attenuation”). In cases in which natural attenuation is not sufficient and remediation actions have to be taken (see Noubactep et al., 2012; Salter-Blanc et al., 2012; O’Carrol et al., 2013; Fu et al., 2014; Obiri-Nyarko et al., 2014), the question to be answered is whether these actions have been successful. For both cases, CSIA has been shown to be quite a useful method to help answer these questions. Of course, in field systems, spatial differences in compound concentrations are usually not only the result of transformation reactions but also of other processes including dilution, dispersion, volatilization, and sorption. In addition, the presence of multiple sources may complicate the situation. Particularly for a quantitative assessment of transformation processes, other information such as historical, hydrodynamic, geochemical, and/or microbiological data have to be used to appropriately interpret CSIA data measured in the field. In addition, the availability of concentrations and isotopic signatures of transformation products may also be very useful to establish whether and to what extent a given pollutant has been transformed (e.g., Aeppli et al., 2010; Hunkeler et al., 2011; H¨ohener and Atteia, 2014; H¨ohener et al., 2015). In the following, we focus primarily on isotope fractionation observed in well-defined laboratory systems, and only discuss some simple illustrative examples of field applications. For a more comprehensive treatment of CSIA field applications, which often involve more sophisticated modeling approaches, we refer to the literature (e.g., Pommer et al., 2009; Hunkeler et al., 2011; Thullner et al., 2012; Hatzinger et al., 2013; Lutz and Van Breukelen, 2014a and 2014b; H¨oying et al., 2015). Microbial Transformation of BTEX Under Aerobic and Anaerobic Conditions

CH3

ring monooxygenation

methyl oxidation

ring dioxygenation

Results from Laboratory Studies in Well-Defined Systems. Let us start by considering microbial transformations of benzene, toluene, ethyl benzene, and 1,3dimethylbenzene (1,3-xylene), which are the sole transformation processes for these compounds in the subsurface under both oxic and anoxic conditions (Chapter 23, Section 23.4). Table 27.6 summarizes some carbon and hydrogen isotope fractionation data reported in the literature for these compounds from measurements in pure cultures, mixed cultures, and in microcosms. As we already pointed out in Section 27.1, when dealing with microbial transformations, bulk enrichment factors may be masked by non-fractionating, rate limiting steps such as transport (see example given in Fig. 27.7) and/or binding to the enzyme’s reactive site. In addition, in the case of ring oxidation by mono- or dioxygenases, enzymatic oxygen activation may be at least partly rate determining, thus also diminishing measured bulk enrichment factors (Wijker et al., 2015; Pati et al., 2016). Finally, as already pointed out earlier, electrophilic ring oxidation occurs in two steps, that is, addition of the oxygen followed by H+ abstraction, where either or both steps may determine the extent of C- and H-fractionation. Nevertheless, from the data summarized in Table 27.6, some important general conclusions can be drawn: 1. Under aerobic conditions there are two distinctly different strategies that microorganisms pursue. (i) First, one or two oxygen atoms are added to the benzene ring

916

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

Table 27.6 Carbon and Hydrogen Isotope Fractionation Data Reported for the Microbial Transformation of BTEX Compounds by Pure Cultures, Mixed Cultures, and in Microcosms Under Aerobic and Anaerobic Conditions Redox Conditions Benzene Aerobic Nitrate reducing Iron reducing Sulfate reducing Methanogenic Toluene Aerobic Aerobic Nitrate reducing Iron reducing Sulfate reducing Ethylbenzene Aerobic Aerobic Nitrate reducing 1,3-Xylene Nitrate reducing Sulfate reducing

Postulated Reaction a

Nb

εC Range (‰)

εH Range (‰)

ΛH/C c

Site ΛReactive H∕C Average d

ring ox (add.) substitution substitution substitution substitution

2 4 1 3 3

−1.7 to –4.3 −1.9 to –2.8 −3 −1.9 to –3.6 − 0.8 to –2.1

−11 to –17 −31 to –47 −55 −56 to –79 −34 to –59

7±4 17 ± 1 18 26 ± 5 33 ± 6

7 17 18 26 33

1 2 3 1, 3 2

ring ox (add.) methyl ox fumarate add. fumarate add. fumarate add.

1 5 9

−1.8 −1.8 to –2.8 −2.7 to –6.2

−2 −97 to –159 −35 to –79

1.1 58 ± 5 14 ± 2

1 22 5

4 4, 5 4, 6

3

−1.3 to –3.6

−35 to –98

30 ± 3

10

6, 7

5

−2.0 to –2.9

−59 to –80

30 ± 4

10

4, 6

ring ox (add.) ethyl ox H-abstraction

2 1 3

−0.4 to –0.6 −0.5 −3.7 to –4.1

−2 to –6 −28 −111 ± 1

7±2 56 29 ± 1

7 28 18

8 8 8

fumarate add. fumarate add.

1

−2.3

−50

22

9

9

1

−2.7

−48

18

8

9

Ref. e

Ring ox = mono- or dioxygenation Eqs. 23-34 and 23-35 (Chapter 23); Substitution = electrophilic aromatic substitution of a H-atom leading to the insertion of a carboxyl (Eq. 23-43, Chapter 23), hydroxyl, or methyl group (see, e.g., Heider (2007); Vogt et al. (2011); methyl ox = H-abstraction at methyl group by a methyl monooxygenase (e.g. Fig. 23.14, Chapter 23); fumarate add. = addition of fumarate at the methyl group (Eq. 23-42, Chapter 23) which involves H-abstraction at the methyl group; ethyl ox = H-abstraction at the ethyl group at both the CH2 – and CH3 – groups, hence, nH /xH = 10/5 and nC /xC = 8/2; H-abstraction = hydride abstraction at CH2 – group by ethyl benzene dehydrogenase (Heider, 2007; Philipp and Schink, 2012), hence nH /xH = 10/2 and nC /xC = 8/1. b N = number of different pure or mixed cultures or microcosms. c Eq. 27-6. d Eq. 27-12. e References: 1: Fischer et al. (2008); 2: Mancini et al. (2008); 3: Bergmann et al. (2011); 4: Vogt et al. (2008); 5: Mancini et al. (2006); 6: K¨ummel et al. (2013); 7: Tobler et al. (2008); 8: Dorer et al. (2014b); Hermann et al. (2009). a

by a mono- or dioxygenase respectively. (ii) Second, abstraction of a hydrogen at the methyl- or ethyl group, occurs by a methyloxygenase or ethylbenzene dehydrogenase, respectively. As is evident from Table 27.6, based solely on carbon isotope enrichment factors, which in all cases represent primary isotope effects, no distinction can be made between the different reactions. However, when combined with hydrogen

Using CSIA for Assessing Organic Compound Transformations

917

enrichment factors, ring oxidation (secondary H-isotope effect) can be clearly distinguished from oxidation at the alkyl group (primary H-isotope effect, compare ΛH/C values). No significant difference exists between mono- and dioxygenation of the aromatic ring (data not explicitly shown), where in both cases the electrophilic addition of the oxygen seems to be the rate-limiting step, thus leading only to a smaller (secondary) H-isotope effect. 2. In order to transform benzene under anaerobic conditions, microorganisms first invest energy to activate the benzene ring by electrophilic substitution/addition of a carboxyl, hydroxyl or methyl group, so they can further break it down (see Section 23.4; and Heider, 2007; Kunapuli et al., 2008; Fuchs et al., 2011; Vogt et al., 2011). As is indicated by the bulk enrichment factors given in Table 27.6, these reactions seem to exhibit primary isotope effects for both carbon and hydrogen, indicating that H-abstraction is (at least partly) rate determining (compare ΛH/C values with those for anoxic H-abstraction by fumarate addition at methyl groups). Thus, the availability of both carbon and hydrogen fractionation data allows us to clearly distinguish aerobic versus anaerobic benzene degradation. 3. Compared to methyl oxidation with molecular oxygen, the anaerobic methyl oxidation, which is postulated to proceed primarily by the fumarate addition mechasite values (5 to 10 as nism (Eq. 23-42, Chapter 23), exhibits distinctly smaller Λreactive H∕C compared to 22 ± 2) and can thus be distinguished from the oxic reaction. An excepsite tion is the anaerobic oxidation of the CH2 group of ethylbenzene (Λreactive = 18), H∕C which can be rationalized by the fact that this oxidation does not proceed by a radical mechanism (fumarate addition) but through hydride (H– ) abstraction by an enzyme called ethylbenzene dehydrogenase (Heider, 2007; Philipp and Schink, 2012). In conclusion, carbon or hydrogen CSIA can be used to qualitatively assess whether or not microbial transformation of BTEX compounds has taken place or not. However, the AKIEC and AKIEH values derived from the data given in Table 27.6 cover a quite wide range of 1.005 to 1.03 and 1.01 to 1.10, respectively, for ring oxidation, and 1.01 to 1.04 and 2 to 5, respectively, for oxic and anoxic H– abstraction at the methyl group. Therefore, for a more quantitative treatment and for the distinction between different reaction pathways both carbon and hydrogen isotope data are required. Example of a Field Application. Since pollution of the subsurface with BTEX compounds is quite common, numerous field studies have been conducted to evaluate whether these compounds are degraded under aerobic and anaerobic conditions (for an overview see Thullner et al., 2012). In our following illustrative example, we consider a case in which the fate of benzene has been investigated in an aquifer located in the area of a former hydrogenation and benzene production plant (Fischer et al., 2007 and 2009). At this site, sulfate reducing conditions prevailed with other inorganic species (i.e., oxygen, nitrate, manganese, iron, and carbon dioxide) being of minor importance as electron acceptors. The question was, whether and to what extent was benzene transformed under these conditions? To answer this question, groundwater samples were taken at five wells at

918

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

Table 27.7 Concentrations and Isotope Signatures of Benzene in a Contaminated Aquifer at Different Depths Along a Transect of about 400 m from the Source of Contamination Following the Main Groundwater Flow a Location Benzene Distance from Concentration δ13 C ± SD δ2 H ± SD (‰) (‰) δ2 H/δ13 C Δδ2 H/Δδ13 C b Source/Depth (m) (mg L–1 ) 0/12 109/11.4 109/16.7

1309 122 310

−28.8 ± 0.5 −147 ± 1 −28.6 ± 0.1 −143 ± 2 −28.5 ± 0.1 −138 ± 1

5.1 5.0 4.5

20 27

186/11.5 186/16.5 186/20.5

1 55 1

−23.0 ± 0.4 −39 ± 5 −27.1 ± 0.1 −134 ± 1 −22.7 ± 0.1 −28 ± 5

1.7 5.0 1.2

19 8 20

420/11.5 420/16.5 420/18.5

3 44 2

−24.6 ± 0.2 −65 ± 4 −25.0 ± 0.1 −65 ± 5 −24.1 ± 0.2 −27 ± 5

2.6 2.6 1.1

20 22 26

a

Data from Fischer et al. (2007 and 2009). Δδ13 C and Δδ2 H represent the difference of the carbon and hydrogen isotopic signatures between the source signatures and the signatures measured at the respective wells.

b

different depths along a transect of about 400 meters from the source of contamination following the main groundwater flow path. Table 27.7 summarizes some selected concentrations and measured carbon and hydrogen isotopic signatures of benzene along this transect. As is evident from these data, within the first 100 meters and for the 16.5 m deep well at 186 meters distance, benzene concentrations dropped significantly, but rather little isotope fractionation was observed. This indicates that non- or weakly fractionating processes including dilution, dispersion, and possibly volatilization may have been primarily responsible for the concentration decrease. However, microbial transformation cannot be ruled out since, with exception of the 186/16.5 well, the Δδ2 H/Δδ13 C values (which represent ΛH/C values) were very similar to the samples where significant fractionation was observed. In fact, an average Δδ2 H/Δδ13 C value of 24 ± 2 was obtained for all samples for which significant fractionation was observed, which is consistent with the ΛH/C values obtained from benzene degradation by sulfate reducing bacteria in the laboratory (ΛH/C = 26 ± 5, see Table 27.5). Hence, the availability of dual carbon and hydrogen isotope data, Fisher et al. (2007 and 2009) could, at least qualitatively, support the prospect of benzene degradation by sulfate reducing bacteria at this field site. Using average εC = –2.7‰ and εH = –65‰ values determined in the laboratory (Table 27.6), we can now estimate how much of the concentration depletion in the different wells along the transect can at minimum be attributed to microbial transformation. At minimum means that we assume that no non-fractionating steps mask the fractionation in the field as well as in the laboratory studies. As an example, we consider well 186/20.5. Insertion of the respective signatures (well and source) into Eq. 27.3 using either the carbon or hydrogen signatures yields the

Using CSIA for Assessing Organic Compound Transformations

919

fraction transformed (B): (

) 1 − 0.0227 1∕−0.0027 = 0.90 1 − 0.0288 ( ) 1 − 0.028 1∕−0.065 B(based on hydrogen) = 1 − = 0.87 1 − 0.147 B(based on carbon) = 1 −

This means that we would predict that in this location about 90% of the concentration depletion can be attributed to biotransformation. The lower than predicted benzene concentration detected in well 186/20.5 could be due to either dilution and/or masking of isotope fractionation by mass transfer limitations, or other non-fractionating processes. As discussed in the review by Braeckevelt et al. (2012) who address the same case study as this illustrative example, additional information (e.g., hydraulic data, chemical composition of the groundwater, probability of volatilization as a removal process) needs to be considered to obtain a more complete quantitative picture of the fate of benzene under such complex field conditions. Abiotic and Biological Transformation of Nitroaromatic Compounds (NACs) Under Aerobic and Anaerobic Conditions Results From Laboratory Studies in Well Defined Systems. We first consider the nitrogen isotope fractionation occurring during the abiotic reduction of monosubstituted nitrobenzenes by various homogeneous and heterogeneous reductants (see also Chapter 23 (Section 23.3). With a few exceptions, independent of substitution and therefore, on reaction rate, large bulk enrichment factors, εN , of between 30 and 45‰ have been reported (Hartenbach et al., 2006 and 2008; Tobler et al., 2007; Hofstetter et al., 2008c). This translates into AKIEN values of between 1.03 and 1.04 (n = 1, x = 1, z = 1 in Eq. 27.10) which is on the order of what is predicted from density functional theory (DFO) for N–O cleavage in the rate determining step (Hofstetter et al., 2008c). In some cases, however, significant lower AKIEN values of between 1.01 and 1.02 have been found which can be attributed to a shift from N–O cleavage to other less fractionating rate-determining steps in the transition state (for details see Hofstetter et al., 2008cc; Gorski et al., 2010). Nevertheless, as is also illustrated by the following examples, significant nitrogen isotope fractionation (i.e., AKIEN = 1.02 to 1.045) during transformation of NACs always indicates at least partial reduction of the nitro group (i.e., formation of the nitroso compound, see Chapter 23, Eq. 23-22) in the initial rate-determining step. Table 27.8 summarizes some carbon, hydrogen, and nitrogen fractionation data reported for the microbial transformation of nitrobenzene, 4-nitrotoluene, and 4-nitrophenol under aerobic conditions. The indicated reactions cover the most important strategies of aerobic bacteria to initiate NAC transformation: ring monoand dioxygenation (see Fig. 27.3), methyl oxidation (H-abstraction), and partial reduction to the corresponding nitroso compound. We note that monooxygenation is very common for initiating transformation of phenolic compounds. In the case of 4-nitrophenol, there are two different monooxygenase pathways Path a (Eq. 27-13)

920

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

Table 27.8 Carbon, Hydrogen, and Nitrogen Isotope Fractionation Data Reported for the Microbial and Enzymatic Transformation of Some Nitroaromatic Compounds Under Aerobic Conditions Type of (Enzymatic) Reaction

Na

εC Range (‰)

εH Range (‰)

εN Range (‰)

Ref. b

Nitrobenzene Dioxygenation (whole cells) Dioxygenation (enzyme) Partial reduction (whole cells)

5 2 1

−3.5 to –3.9 −0.8 / –3.7 −0.6

−5.6 to –6.3 −3.4 / –5.6 n.d.

−0.8 to –1.0 (N = 3) n.d. −26.6

1,2 3 1

4-Nitrotoluene Dioxygenation (enzyme) Methyl oxidation (whole cell) Partial reduction (whole cell)

2 1 1

−0.1 / –1.4 −2.2 −0.6

−2.6 / –5.5 −111 −9.9

n.d. −2.3 −25.3

3 4 4

4-Nitrophenol c Monooxygenation (Pa; whole cell) Monooxygenation (Pb; whole cell)

1 1

−1.8 −0.3

n.d. n.d.

−0.9 −0.5

5 5

a

Number of different cultures or enzyme systems. References: 1: Hofstetter et al. (2008b); 2: Pati et al. (2014); 3: Pati et al. (2016); 4: Wijker at al. (2013a); 5: Wijker et al. (2013c). c Pa refers to the hydroxyl-1,4-benzoquinone pathway (Eq. 27-13); Pb to the 1,4-benzoquinone pathway (Eq. 27-14). n.d. = not determined. b

and Path b (Eq. 27-14) leading to the desired di- or trihydroxy compounds that are then further transformed by ring cleavage (Wijker et al., 2013c): path a: hydroxy-1,4-benzoquinone pathway NO2

NO2

NO2 OH

OH

O

OH

H

OH

O

–NO2–

OH

OH

OH

OH

O

(27-13) path b: 1,4-benzoquinone pathway

NO2

O2N

O

OH

OH

(27-14) –NO2–

OH

O

O

OH

Inspection of Table 27.8 shows that in the case of ring oxygenases, as well as for methyl oxidation (4-nitrotoluene), not too surprisingly, quite similar isotope fractionation patterns are obtained for carbon and hydrogen as for the aerobic transformation of the BTEX compounds (Table 27.6). As for the BTEX compounds, ring and methyl oxidation can be clearly distinguished based on carbon and hydrogen enrichment factors. Finally, the availability of nitrogen isotope data allows to unequivocally identify

921

Using CSIA for Assessing Organic Compound Transformations

Table 27.9 Concentrations and Carbon, Hydrogen, and Nitrogen Isotopic Signatures of 2,4- and 2,6-Dinitrotoluene (2,4-DNT, 2,6-DNT) in Contaminated Soil at the Site of a Former Explosives Factory a Sample (depth)

Conc. mg kg–1

δ13 C; Δδ13 C (‰)

δ2 H; Δδ2 H (‰)

δ15 N; Δδ15 N (‰)

Δδ2 H / Δδ13 C

2,4-DNT Source 2m 5m 6m

30 14 12

−31; 0 −30; +1 −27.5; +3.5 −28; +3

−10; 0 +18; +28 +40; +50 +30; +40

−8; 0 −4; +4 +6; +14 +2; +10

28 14 13.3

2,6-DNT Source 2m 5m 6m

30 15 10

−31; 0 −30.5; +0.5 −29.5; +1.5 −28.3; +2.7

−19; 0 0; +19 +42; +61 +70; +89

−7.5; 0 −5; +2.5 +3; +10.5 −8; –0.5

a

38 40 33

Δδ15 N / Δδ13 C

4 4 3.3

5 7 −1.8

Data from Wijkers et al. (2013a).

nitro group reduction as initial transformation step, since for all other reactions εN is rather small (secondary isotope effect). Example of a Field Application. In contrast to BTEX and chlorinated solvents, to date, field studies using CSIA to assess nitroaromatic compounds (NACs) in the environment are rather scarce, although there are numerous sites that are contaminated with such compounds. Prominent examples are explosives and related compounds including trinitrotoluene (TNT) and dinitrotoluene (DNT) isomers (Kalder et al., 2011). Using carbon, hydrogen and nitrogen CSIA, Wijker et al. (2013a) addressed the question whether and, if yes, by which type of (microbial) processes TNT, as well as 2,4- and 2,6-DNT were transformed under aerobic conditions in the soil at a contaminated site of a former explosives factory. They determined depth profiles of the concentrations and isotopic signatures of the three compounds, which they compared with the signatures of the likely source materials collected in the former storage room. One complicating aspect in the analysis of the data was, however, that over the years, the isotopic signatures of the original NACs could have varied, and thus could have contributed to the variability of signatures found along the soil profile, particularly with respect to the hydrogen and nitrogen isotopic signatures. Therefore, only qualitative or at most semiquantitative, but nevertheless valuable, statements could be made. In general, differences in isotope signatures between the soil samples and the storage samples were not very large pointing either to significant mass transfer limitations and/or commitment to catalysis or to a rather slow transformation of the compounds, or both. The latter seems to be primarily the case, the half-lives estimated by Wijkers et al. (2013a) were between 10 and 30 years at this site. From our previous discussion we recall that, under aerobic conditions, nitro toluenes may react by three different biotransformation pathways, i.e., ring oxydation, methyl oxidation, and reduction of the nitro group KIEE (Table 27.8). Whereas TNT was found to be primarily transformed by reduction of one of the nitro group (small change in carbon, large change in the nitrogen isotope signature), the two DNT isomers showed quite a different pattern. Table 27.9 summarizes the isotopic signatures of the two

922

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

compounds determined in samples from the storage room and from three different depths in the soil profile. Also included are the Δδ2 H/Δδ13 C and Δδ15 N/Δδ13 C values, which as we previously discussed in our benzene example (Table 27.7), can be viewed as ΛH/C and ΛN/C values. Comparison of Table 27.9 with the enrichment factors determined for 4-nitrotoluene in Table 27.8 shows that, for both compounds, nitro reduction was most likely not the dominating initial transformation step (ΛN/C = εN /εC = 42 versus Δδ15 N/Δδ13 C < 10). A quantitative distinction between the two other pathways is rather difficult. Qualitatively one can, however, conclude that methyl oxidation (larger Δδ2 H/Δδ13 C) was more important for 2,6-DNT, whereas dioxygenation was probably more dominant for 2,4-DNT. The same conclusion was made by Wijkers et al. (2013a) who performed a much more sophisticated analysis of the data. Abiotic and Biological Transformation of Atrazine under Aerobic Conditions The major metabolites of atrazine that are frequently detected in the environment are hydroxyatrazine, desethyl- atrazine, and desisopropyl-atrazine (structures in margin, Fenner et al., 2013). While the former is the product of a hydrolysis reaction, the transformation to the desalkyl metabolites is initiated by H-abstraction at the two alkyl goups (Meyer et al., 2014). Table 27.10 summarizes some carbon and nitrogen fractionation data reported for the abiotic and microbial transformation of atrazine. We should note that for carbon, the bulk enrichment factors represent primary, whereas for nitrogen they seem to represent secondary isotope effects (see examples in Table 27.8 for primary nitrogen isotope effects). Whereas the dealkylation reactions that are initiated by H-abstraction at the ethyl- and/or isopropyl group, respectively, shows a fractionation behavior similar to the methyl oxidation discussed earlier for Table 27.10 Carbon and Nitrogen Isotope Fractionation Data Reported for the Abiotic and Microbial Transformation of Atrazine Under Aerobic Conditions Na

εC Range (‰)

εN Range (‰)

ΛN/C b

Abiotic Hydrolysis pH 3 / 60◦ C pH 12 / 60 and 20◦ C

1 2

−4.8 −3.7 / –5.6

+2.5 −0.9 / –1.2

−0.52 +0.26 / +0.22

1 1

Biological Hydrolysis Whole cells Enzymatic (hydrolases)

3 2

−1.8 to –5.4 −4.2 / –2.1

+0.6 to +3.3 +2.1 / +2.5

−0.32 to –0.65 −0.50 / –0.54

1 2

Abiotic Dealkylation Ind. photolysis (HO∙ )d Ind. photolysis (3 4-CBP∗ )d Iron porphyrin (Fe(IV)=O)d

1 1 1

−0.52 −1.7 − 2.4

−0.26 −0.69 −1.9

+0.24 +0.41 +0.88

3 3 4

Biological Dealkylation Whole cells

2

−3.8 / –4.0

−1.5 / –1.4

+0.39 / +0.35

Type of Reaction

a

Ref.c

4, 5

Number of different experiments. b Eq. 27.6. References: 1: Meyer at al. (2009); 2: Sch¨urner et al. (2015); 3: Hartenbach et al. (2008); 4: Meyer et al. (2014); 5: Meyer and Elsner (2013). d Large hydrogen fractionation supports H-abstraction as initial step. c

Using CSIA for Assessing Organic Compound Transformations

BTEX compounds and NACs, the hydrolysis reaction provides us with some new insights. A comparison of the abiotic acid and base catalyzed hydrolyses (negative versus positive ΛN/C ) with the microbially or enzymatically catalyzed reactions clearly indicates that the biological reaction is acid catalyzed (by protons or another Lewis acid, Sch¨urner et al., 2015). In analogy to the acid catalyzed hydrolysis of, for example, carboxylic acid esters (Chapter 22, Fig. 22.6), protonation or complexation of one of the nitrogen atoms facilitates the attack of the nucleophile (e.g., H2 O) at the carbon bound to the chlorine. The key evidence for this kind of reaction mechanism is the inverse isotope effect found for the acid catalyzed as compared to the base catalyzed reaction. This finding can be rationalized at least in part by the fact that 15 N exhibits a somewhat stronger basicity as compared to 14 N (Skarpeli-Liati, 2011b). This (inverse) nitrogen equilibrium isotope effect may depend on the solution pH and/or degree of complexation within the enzyme lead to a situation in which a larger fraction of the more reactive protonated “heavy” isotopologues are present as compared to the “light” isotopomers. Other more complex examples in which inverse nitrogen isotope effects have been observed include the abiotic and biological oxidation of substituted anilines (Skarpeli-Liati et al., 2011a,b and 2012; Pati et al, 2012).

Cl N

N

N

N

N

H

H atrazine OH N

N

N N

N

H

H

hydroxy-atrazine OH N N

N N

N

H

H

H

desethyl-atrazine OH N H

N H

923

N N

N H

desisopropyl-atrazine

Abiotic and Biological Transformation of Polychlorinated C1 – and C2 –Compounds under Aerobic and Anaerobic Conditions We conclude our discussion of isotope fractionation of selected organic compounds by addressing a group of chemicals that, historically, have been by far the most intensively investigated, at least with respect to carbon isotope fractionation. Recently, these compounds have also been examined for chlorine isotope fractionation. Because of analytical difficulties in measuring hydrogen isotope fractionation of chlorinated compounds, only very little data on hydrogen enrichment factors are available for polychlorinated alkanes and alkenes (Kuder et al., 2013; Nadalig et al., 2013; Gehre et al. 2015). In the following, we first discuss reactions of some (poly)chlorinated methanes and ethanes which can undergo a variety of abiotic and biological transformation reactions including hydrolysis and β-elimination (Chapter 22), as well as reductive dechlorination (Chapter 23). The latter type of reaction is also of pivotal importance for the transformation of chlorinated ethenes, including tri- and tetrachloroethene (Chapter 23), which we address afterwards. (Poly)chlorinated Methanes and Ethanes. Table 27.11 summarizes some carbon and chlorine isotope fractionation data reported in the literature for abiotic and biological transformations of polychlorinated methanes and ethanes. Let us first look at the carbon enrichment factors and derived AKIEC values and then make a few comments on the rather scarce chlorine isotope fractionation data available. First, we note that as we would have expected from our discussion in Section 27.1, in all cases in which a carbon-chlorine bond is broken during the rate-determining step, except for the SN 1/E1 reaction (CH3 –CCl3 ), we observe significant carbon isotope fractionation with AKIEc values of between about 1.02 and 1.06 (SN 2, E2 , red), and much smaller ones for the oxidative H-abstraction (AKIEc < 1.01). Under aerobic conditions, we can clearly distinguish between hydrolysis or β-elimination (SN 2, E2 ) and oxidation by H-abstraction. Under anerobic/anoxic conditions we may,

924

Assessing Transformation Processes Using Compound-Specific Isotope Analysis (CSIA)

Table 27.11 Carbon and Chlorine Isotope Fractionation Data Reported for the Abiotic and Microbial Transformation of Chlorinated Methanes and Ethanes under Aerobic and Anaerobic Conditions Abiotic/Microbial, Redox Conditions, Reaction Type a

Nb

εC (‰)

AKIEC

εCl (‰)

CH3 Cl Microbial, aerobic, SN 2 Abiotic, Br– , SN 2

5 1

−42.6 ± 3.7 −65

1.044 ± 0.004 1.069

n.d. n.d.

1, 2 3

CCl4 Abiotic, Fe(II) oxides, red Abiotic, Fe(II) sulfides, red

8 2

−29.0 ± 3.0 −15.9 ± 0.3

1.030 ± 0.003 1.016 ± 0.0003

n.d. n.d.

4 4

CH2 Cl – CH2 Cl Microbial, aerobic, SN 2 Microbial, aerobic, ox Microbial, anaerobic, SN 2 Microbial, anaerobic, red

4 2 1 3

−29.8 ± 2.3 −3.7 ± 0.2 −25.8 −30.6 ± 1.6

−4.3 ± 0.1 (N=2) −3.8 (N=1) n.d. n.d.

Abiotic, Zn(0),red

3

−29.7 ± 1.5

1.063 ± 0.007 1.0075 ± 0.0001 1.054 1.032 ± 0.002 d 1.065 ± 0.004 d 1.031 ± 0.002 d 1.063 ± 0.004 d

n.d.

9

CH3 – CCl3 Abiotic, persulfate, ox Abiotic, SN 1/E1 Abiotic, Fe(0), red Abiotic, Cr(II),Fe/Cu(0) red

1 1 1 3

−4.0 −1.6 −7.8 −14.4 ± 1.2

1.008 1.0032 1.016 1.030 ± 0.003

h (if As < Ao ). For process 7 (mixing with adjacent boxes), the area is Anb (‘nb’ stands for ‘neighbor box’). The following discussion points to the chapters in which the specific rate constants of processes 4 to 7 are discussed. Air–Water Exchange (process 4) is described as a linear two-way (exchange) flux across an interface boundary (Eq. 18-9) with exchange velocity viaw (Box 19.3). The equilibrium between the concentrations at the interface is described by the air– water partition constant (nondimensional Henry’s law constant) Kiaw = (Cia /Ciw )eq (Eq. 9-15). In Table 28.1, we have approximated Ciw (e.g., mol m−3 water ) by Cid (e.g., −3 mol mtot ) = fiw Cit , a valid simplification as long as in the box the relative volume

One-Box Model: The Universal Tool for Process Integration

951

occupied by suspended solids is very small (see Table 12.1). Recipes for how to estimate the size of viaw from wind speed and other environmental factors are given in Chapter 19. Particle Settling (process 5), an output process like the loss to the sediment bed, is described by an average sinking velocity, vs , times the particulate concentration Cip = (1 – fiw ) Cit . The process of particle settling was discussed in Section 5.3, and typical settling velocities are given in Table 5.8. Sediment–Water Exchange (process 6) is a two-way exchange process. Since the sediment cannot be considered as a well-mixed compartment (like the atmosphere), the sediment–water surface commonly acts as a wall boundary with phase change, and the exchange flux decreases with time as t−1/2 (Eq. 18-20). The exchange takes place via the dissolved phase (assuming sediment solids are not resuspended); that is, Ciw is continuous across the boundary, while the total concentration undergoes a discontinuous change. The corresponding equilibrium distribution ratio between the sediments and the aqueous box under consideration, Rised/box , is derived in Box 20.1 and the result given in Eq. 20-2. For the special situation of a distinct interface between a sediment column and the open water column with a negligible volume of suspended solids (Eq. 20-3), the equilibrium distribution ratio can be approximated by: sc Rised∕box ≈ ϕsc ∕fiw

(28-4)

where the superscript ‘sc’ refers to the sediment column. With the relations summarized in Box 12.1, this expression can be written as: Rised∕box = ϕsc + ρs Kid (1 − ϕsc )

(28-5)

where ϕsc is sediment porosity, ρs density of sediment particles, and Kid the solid– water distribution coefficient of substance i (Chapter 12). As discussed in Chapter 20, the sediment–water exchange velocity, visedex , depends on the structure and mixing regime of the boundary. Here, we describe the sediment as a one-sided interface wall boundary (Fig. 18.4) between compartment 1 (overlying water) and compartment 2 (sediment bed). Since in Table 28.1, we describe the flux in terms of the concentrations expressed in terms of compartment 1 (water), Eq. 18-20b is the appropriate expression to be used in Eq. 28-1: ( visedex (t) = Ri sed∕box

Di eff πt

)1∕2 (28-6)

Dieff is the effective diffusivity in the sediment (Eqs. 20-4 and 20-5). Due to the finite and tortuous pore space and possible sorption of chemical i on the sediment particles, effective diffusivity in a porous media like sediment is smaller than molecular diffusivity in the open water. Since visedex is time-dependent, the rate constant ksedex is time-dependent as well: kisedex (t) =

vi sedex (t) Ri sed∕box = Vbox ∕As Vbox ∕As

(

Di eff πt

)1∕2 (28-7)

952

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

We can either solve Eq. 28-2 for a time-dependent overall rate constant, kit , (see Box 6.2) or replace kisedex (t) by its mean for the time period between t = 0 and −1∕2 t = to . Since the mean of the function (t−1/2 ) over time to is (2 to ), we get:

kisedex = 2

Ri sed∕box Vbox ∕As

(

Di eff πto

)1∕2 (average rate constant for time period to )

(28-8)

Mixing with Adjacent Boxes (process 7) was introduced in Section 6.3. It is an , the volexchange process without phase change that can be quantified by Qex box∕nb ume of water per unit time that is exchanged across the interface area, Anb , to the = Qex ∕Anb and the correspondneighboring box. The exchange velocity is vex box∕nb box∕nb ex ex ing exchange rate is kbox∕nb = Qbox∕nb ∕Vbox . We point out that in Fig. 6.8 and Eq. 6-26, the normalized flux between layer n and (n + 1), Fn,n+1 , is used instead of vex . box∕nb In the following case studies, the relevant box may not always be an aquatic compartment, and not all transport and transformation processes are always relevant. We also run into situations where two or more boxes are needed to depict the important feature of the problem, thus the description of the concentration in the “neighbor box” may also require a mass balance equation like Eq. 28-1. Boxes and processes are building blocks that can easily be adapted to the needs of a particular situation.

28.2

Assessing Equilibrium Partitioning in Simple Multimedia Systems Equilibrium Distribution of a Chemical i in a Multimedia System: Some General Considerations Before we turn to some case studies, let us first see how we can generally describe the equilibrium partitioning of an organic compound in a system made up of several different media (or phases). We start out by considering the partitioning of a compound i between two bulk phases 1 and 2 exhibiting the volumes V1 and V2 . At equilibrium, the molar concentrations Ci1 and Ci2 of i in the two phases are related by the corresponding equilibrium partition constant/coefficients (Chapters 4 and 7):

Ki12 =

Ci1 Ci2

(28-9)

It is now easy to see that you may calculate the fraction of the total mass of i present at equilibrium in phase 1, f i1 , simply by: fi1 =

Ci1 V1 mass of i in phase 1 = total mass of i Ci1 V1 + Ci2 V2

(28-10)

Assessing Equilibrium Partitioning in Simple Multimedia Systems

953

Dividing the numerator and denominator of the right-hand side of Eq. 28-10 by (Ci1 V1 ) yields: fi1 =

1 C V 1 + i2 2 Ci1 V1

(28-11)

By substituting Eq. 28-9 into Eq. 28-11 and by defining the (volume) ratio of the two phases r12 = V1 /V2 , one obtains: fi1 =

1 1 1+ Ki12 r12

=

Ki12 r12 1 + Ki12 r12

(28-12)

and analogously for the fraction of i in phase 2: fi2 =

1 1 + Ki12 r12

(28-13)

Of course, in a two-phase system, fi1 + fi2 must be equal to 1 (which can be easily checked). Equations 28-12 and 28-13 are also valid if one of the phases is a solid (e.g., solid–water partitioning in a lake or in an aquifer) or a gas (e.g., solid–air partitioning in the atmosphere) (see Chapters 12 and 15). In such cases, Ki12 is often expressed by the ratio of mole of i per mass of solid concentration and mole of i per volume concentration. Therefore, r12 is then given by the ratio of the mass of solid and the volume of the bulk liquid or gas phase present in the system considered. The equations derived for calculating the fractions of total i present in each phase at equilibrium in a two-phase system can now be easily extended to a multiphase system containing n phases (e.g., to a “unit world”). If we pick one phase (denoted as phase 1) as the reference phase and if we use the partition constants of i between this phase and all other phases present in the system: Ki1m =

Ci1 Cim

where m = 2, 3 … n

(28-14)

Then, the fraction of i in phase 1 is given by: fi1 =

1 n ∑ 1 1 1+ K r m=2 i1m 1m

(28-15)

or, when using the reciprocal K and V values: fi1 =

1 n ∑ 1+ Kim1 rm1 m=2

(28-16)

954

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

Since any of the phases can be chosen as phase 1, Eqs. 28-15 or 28-16 can be used to calculate the fraction of total i at equilibrium in each of the phases present in the system. Also, note that the sum of all fractions has to be equal to 1. Case Study 28.1. Some Questions about Partitioning and the “Aquarium Problem” As we pointed out in Chapter 1, the first step for assessing existing and new chemicals with respect to their potential to accumulate in the environment is to evaluate their “intrinsic” partitioning behavior between different well-defined phases or compartments mimicking environmental systems.

Br Br Br

O

Br Br

2,2',4,4'‚5-Pentabromodiphenyl ether (PBDE 99) I OH

(a) By just looking at their structures, rank the three organic chemicals (I to III) given in the margin in the order of their increasing tendency to partition: (i) from water into air (Chapter 9) (ii) from water into the storage lipids of an organism (Chapter 16) (iii) from air into aerosols (Chapter 15) (iv) from air onto a quartz surface at low (e.g., 45%) relative humidity (Chapter 11).

phenol II

n-hexane III

Rationalize your choices. Comment on your assumptions. In some cases, if you cannot make a clear decision, give the reasons why. Hint The discussion on the molecular characteristics affecting partitioning in Chapter 7 (bulk phase partitioning) and Chapter 11 (adsorption to mineral surfaces) might help you in making your choices. (b) Estimate (using pp-LFERs) the respective equilibrium partition constants/coefficients at 25◦ C (and 15◦ C for quartz–air partitioning) for the three chemicals for the two-phase systems (i) to (iv). Are the relative sizes of these partition constants/coefficients in accordance with your ranking made in (a)? (c) Consider now a small closed aquarium [1 m (length) × 0.5 m (width) × 0.5 m (height)] containing 200 L of water, 50 L of air, a thin, well mixed “sediment” layer of 0.2 cm thickness (porosity ϕ = 0.8; density of solids ρs = 2.5 g cm−3 ; fraction organic carbon foc = 0.2), and 10 small fish (wet weight 5 g fish−1 ; lipid content, mostly storage lipids, fslip = 0.1 g lipid g−1 fish w.w., protein content fprot = 0.6 g protein g−1 fish w.w.). The temperature is 25◦ C. All three compounds are present in the aquarium with the same total mass, it . For each of the three compounds, calculate the fraction of the total mass accumulated in the 10 fish (fifish ) by assuming that equilibrium is established between all compartments and by neglecting any sorption to dissolved organic matter. Does partitioning into the protein of the fish play any role?

Assessing Equilibrium Partitioning in Simple Multimedia Systems

955

How much total PBDE 99 (compound I; PBDE99t ) would have to be present in the aquarium to kill 50% of the fish (LCiw50 in mol L−1 ) by assuming only non-specific toxicity. In the literature (Escher and Schwarzenbach, 2002, Box 1), you find a relationship for guppies (see also Chapter 16, Section 16.4): log (1∕LCiw50 ) = 0.83 log Kimlipw + 1.52 Would the other two compounds significantly contribute to the overall non-specific toxicity to the fish when assuming concentration addition for the toxic effect? If yes, which of the two compounds would contribute more? Abraham Parameters for the three compounds (Appendix C): (I) PBDE 99: (II) phenol: (III) n-hexane

Case Study 28.2. The “Soup Bowl Problem”

i

Cl

Consider a closed soup bowl containing 1 L of soup (very diluted bouillon; containing 1 g of salt (NaCl)), 1 L of air, and a floating blob of fat (e.g., olive oil, subscript “oo”) of a volume of 1 mL (density about 1 g mL−1 ). The cross-sectional area of the bowl is A = 100 cm2 , the contact areas between the oil and the bouillon and between the oil and the air are Aoo = 5 cm2 . Initially, the olive oil blob is contaminated with a total amount it of an organic pollutant i. Assume that no significant amount of olive oil has dissolved in the water or evaporated into the air.

Cl

Cl

Cl Cl

Cl

PCB 153

O Si O O

O Si

O

(a) Calculate the fraction of the total amount of i in each phase, that is, in the soup (water, fiw ), in the air (fia ), and in the olive oil (fioo ) at equilibrium for the following compounds in the closed soup bowl. Neglect the effects of the organic constituents and of the salt present in the bouillon. Also assume that any charged species are only present in the aqueous phase. Are all these assumptions reasonable? (i) For our companions PCB 153 (Vi = 2.06, Li = 9.59, Si = 1.74, Ai = 0, Bi = 0.11) and D5 (Vi = 2.93, Li = 5.24, Si = –0.10, Ai = 0, Bi = 0.50) at pH 7 for 25◦ and 65◦ C, comment on any differences between these two hydrophobic compounds.

Si

Si

Vi = 2.26, Li = 11.71, Si = 1.51, Ai = 0, Bi = 0.44 Vi = 0.78, Li = 3.77, Si = 0.89, Ai = 0.60, Bi = 0.30 Vi = 0.95, Li = 2.67, Si = 0, Ai = 0, Bi = 0

Si

decamethylcyclopentasiloxane (D5) OH NO2

NO2 2-sec-butyl-4,6-dinitrophenol (dinoseb)

(ii) For the acidic herbicide, dinoseb (pKia = 4.62; Vi = 1.69, Li = 7.76, Si = 1.75, Ai = 0.17, Bi = 0.46) at 25◦ C at pH 7 and pH 5. (b) Derive a general expression for the half-life of i in the closed soup bowl if a neutral compound is transformed in the aqueous phase (the bouillon) by a (pseudo)-first-order rate constant, kobs , under the assumption that equilibrium between the three different phases is always established. Is this a reasonable assumption (see also question (d))? (c) Using the expression derived in (b), estimate the half-live of the “reacting” solvent pentachloroethane (PCA, CHCl2 –CCl3 ; Vi = 1.00, Ei = 0.65, Li = 4.27, Si = 0.66,

956

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

Ai = 0.17, Bi = 0.06) in the closed soup bowl at 25◦ C and at pH 7 and pH 9. In water, PCA hydrolyzes with the following rate constants at 25◦ C (see Table 22.2): Neutral reaction: kN = 8×10−10 s−1 Base catalyzed reaction: kB = 27 M−1 s−1 What kind of reaction does PCA undergo and what are the major products. Does the salt present in the soup have any effect on the transformation of PCA? (d) In question (b), it was assumed that the equilibrium between the three phases is always established. Check whether this assumption is indeed valid for the case of PCA, question (c), by developing a one-box model for the aqueous phase that includes the transfer of PCA from the oil to the bouillon and the first-order reaction of PCA in the bouillon. Determine the steady-state solution for PCA in the bouillon and compare it with the concentration in equilibrium with the oil. Hint Use a one-box model for the water compartment, and assume as a first approximation that the concentration of chemical i in the olive oil is constant. The answer to question (a) may help to justify this assumption. We do not really know the size of the waterside exchange velocity in a soup bowl, but we can estimate its approximate size from the “standard value” for CO2 (Eq. 19-5), 10−3 cm s−1 and transform it to PCA with the diffusivity ratio (Eq. 19-12). The diffusion coefficient of PCA in water can be calculated from Eq. 17-24a and the molar volume of PCA, VPCA = 100 cm3 mol−1 .

28.3 Cl

Simple Dynamic Systems Case Study 28.3. Which Processes Determine the Residence Time of Triclosan (TC) in the Epilimnion of a Lake (Greifensee) in Switzerland?

OH O

Between August and October 1999, Singer et al. (2002) determined the input and the total mass (calculated from vertical concentration profiles) of our companion triclosan (TC) and of various pharmaceuticals (Tixier et al., 2003) in Greifensee, a small lake triclosan that we have already encountered in earlier chapters, for example, in Chapters 24 and 25. TC is a widely used biocide present in numerous consumer products (see Dhillon TC Concentration in Greifensee et al., 2015). It reaches surface waters primarily by effluents of wastewater treatment Date Epilimnoin Hypolimnion plants (WWTPs). In the summer and fall, Greifensee is stratified and the input of Aug 16 8.0 μg m−3 11.5 μg m−3 organic pollutants by WWTP effluents occurs primarily into the epilimnion of the lake. Between August 16 and October 22, the average TC concentration in both the epilOct 22 6.0 10.0 imnion and the hypolimnion decreased (see table in the margin), although an input of 720 g was estimated from an intensive sampling campaign covering all relevant input sources. Obviously some processes led to the elimination of TC during this 67-day period. Cl

Cl

(a) Consider the epilimnion as a well-mixed box. Using the compound properties, lake characteristics, and environmental parameters given in Table 28.2 and in other chapters of the book (see hints), assess the relative importance of possible internal transformation processes (Fig. 28.1, process 3). Since it has been shown that direct

Simple Dynamic Systems

957

Table 28.2 Characteristics of Greifensee and Environmental Parameters During the Study Period Surface area (Ao ) Area at the thermocline (Ath ) Volume of epilimnion (VE ) Mean depth of epilimnion (hE = VE /Ao ) Volume of hypolimnion (VH ) Thermocline thickness (dth ) Turbulent vertical diffusivity in thermocline (Eth ) a Mean water throughflow (Q) Suspended particle concentration Fraction organic carbon of suspended solids (foc , Eq. 13-2) Average sedimentation velocity (vs ) Dissolved organic carbon concentration ([DOC], Eq. 13-1) Average pH during study period Average temperature during study period 24-hour average intensity of solar radiation during study period at surface (W(24 h, λ); take 1/4 of clear summer day values (1/2 for seasonal difference (fall/summer see Fig. 24.11) and 1/2 for cloudy skies. Average beam attenuation coefficient α(λ) Average wind velocity 10 m above water surface (ū 10 ) a

8.2×106 m2 7.5×106 m2 50×106 m3 6m 100×106 m3 4m 0.2 m2 d−1 3.4×105 m3 d−1 5 g m−3 0.4 kgoc kg−1 solid 1 m d−1 4×10−3 kg m−3 epi: 8.6; hypo: 7.5 epi: 15◦ C; hypo: 5◦ C see Chapter 24, Table 24.5 Table 24.5 1 m s−1

Estimated from vertical density gradient in the thermocline (see Imboden and W¨uest, 1995).

photolysis of TC leads to transformation products that are of environmental concern (e.g., dioxins, Kliegman et al., 2013; see also Chapter 24, Fig. 24.1a), you are particularly interested in the contribution of this process to overall TC elimination (see data given below). Assume that indirect photolysis can be neglected. (b) Make a simple mass balance model of the epilimnion of Greifensee for the study period (August to October, 1999) by including the following processes: external input (720 g), loss through the outlet, internal transformation processes (see question (a)). Since the first three processes are known or can be deduced from the information given in the tables, the contribution of the internal transformation processes can be quantified. Assuming that the transformation process is first-order, determine the resulting reaction rate constant, kitrE , and compare it with the rate calculated for photolysis (question (a)). (c) Refine your calculation by taking into account (i) the flux of TC between the epilimnion and hypolimnion due to turbulent mixing (what is the direction of the net flux?) and (ii) other possible boundary fluxes like air–water exchange and removal by particle settling. Recalculate kitrE . Does the result change significantly and if yes, due to which process? (d) Make a mass balance of TC in the hypolimnion by taking into account those processes that are relevant for the hypolimnion. Assume that input of TC from outside Greifensee occurs in the epilimnion only. Does the mass balance suggest the existence of an internal transformation process? If yes, describe it as a first-order process and determine the rate constant in the hypolimnion, kitrH .

958

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

(e) Singer et al. (2002) measured a TC concentration of about 50 ng g−1 solids in the surface sediments of Greifensee. Does this match your calculations of particle–water partitioning if you assume that the surface sediments reflect primarily sedimentation out of the hypolimnion (pH 7.5, T = 5◦ C)? λ (nm) 290 295 300 305 310 315 320

ε (λ) (L

mol−1 cm−1 ) 6600 6800 6000 4600 2700 900 300

Triclosan (Compound Properties) Abraham parameters (Appendix C): Vi = 1.87, Li = 8.96, Si = 1.81, Ai = 0.92, Bi = 0.30. Acidity constant (pKTCa ) = 8.1. Reaction quantum yield, ϕTCr (λ), at λ = 313 nm: 0.30 (Tixier et al., 2002). Decadic molar absorption coefficients for the deprotonated (anionic) form of TC; note that the neutral phenol does not absorb UV-radiation above 290 nm (see table in margin; Tixier et al., 2002). Hint Use Eqs. 4 and 5 in Table 28.1 to quantify air–water exchange and sedimentation respectively. For air–water exchange, you find the relevant equations in Box 19.3, and the diffusivities in air and water can be estimated from Figs. 17.5 and 17.6. Use Eqs. 12-18 and 12-19 to calculate the fractions of TC in dissolved and particulate forms respectively. Use Eqs. 13-14 and 13-17 (Table 13.3) to estimate the KTCocw values for sorption to particulate and dissolved organic matter, respectively. Use Eqs. 9-18 and 9-27 to estimate the air–water partition constant, KTCaw . Assume that all light is absorbed in the epilimnion; consult Table 24.5 for determining the light absorption rate of TC in the epilimnion of Greifensee. Describe the thermocline as a bottleneck boundary (Section 18.2) and use the information given in the table to calculate the vertical exchange velocity between epilimnion and hypolimnion. Case Study 28.4. The Passive Sampler Problem Note: In order to not further complicate the notation, the compound subscript i is omitted in this example. You are planning an investigation in a fresh water lake that is known to be highly polluted with various organic compounds. A selection of chemicals that you want to measure in the lake water is given in Table 28.3. You decide to use passive samplers made of polyethylene (PE) sheets to assess concentrations in the lake. Based on a problem that you have solved while studying Chapter 20 (P 20.5), you want to address the question of, what kind of chemicals you can suitably determine for concentrations with a PE passive sampler, given the fact that you cannot leave the samplers for longer than 10 days in the lake. You remember that Tcaciuc et al. (2015), based on a mathematical model considering an aqueous boundary layer of thickness δw and a PE sheet of thickness 2δs (s = sheet), concluded that some of the models that have been used to calculate equilibration times of the PE sampler are too simple to give a reliable picture of the uptake dynamics of the chemical by the sampler. (a) As a first task, you decide to use a suitably refined, but still simple analytical model with the aim of reproducing the mass transfer modeling results generated by

Simple Dynamic Systems

959

Table 28.3 Characteristics of Three Test Substances in Water and in the PE Sheet

molar mass Mi (g mol−1 ) molar volume V̄ i a (cm3 mol−1 ) Dw b (cm2 s−1 ) DPE c (cm2 s−1 ) KPEw c (–) Koc at T = 5◦ C (L/kg−1 ) a

water

aqueous boundary layer

b

sampler

●

Csb = KswCwb

●



●

Cm

●

Cwb

●

δw

δs

δs

Cw0

δw

Phenanthrene C14 H10

PCB 18 2,2′ ,5trichlorobiphenyl C12 H7 Cl3

PCB 153 2,2′ ,4,4′ ,5,5′ hexachlorobiphenyl C12 H4 Cl6

178.2

257.5

360.9

145

169

206

6.3×10−6 2.0×10−9 1.4×104 1.05×104

5.7×10−6 3.2×10−9 7.2×104 2.3×104

5.0×10−6 5.0×10−10 5.7×106 8×105

Calculated by the method of Abraham and McGowan (1987), see Box 7.2; From molar volume and Fig. 17.6; c From Lohmann (2012).

Tcaciuc et al. (2015). The idea of the model is sketched in the figure in the margin. Use 2δs = 50 μm (thickness of the PE sheet) and δw = 100 μm (thickness of the aqueous boundary layer). As a first approximation, you visualize the concentration gradients inside the PE to always be linear. Hint Remember that the flux across the aqueous boundary layer must always be equal to the flux into the sampler. This yields a relationship between the gradient in the aqueous boundary layer, (Cw0 − Cwb )∕δw , and the gradient in the sampler, (Csb − Cm )∕δs . Furthermore, at the interface, the water-side and sampler-side concentrations are always taken to be at equilibrium. Finally, having assumed linear gradients, the total mass in the sampler per unit area of the PE sheet, ∗ , can be expressed in terms of Cm and Csb , and thus the change of total mass can be expressed in terms of the changes of Cm and Csb . This yields a linear differential equation for Cm for which one can calculate a first-order rate constant and the time to achieve a particular fraction of equilibration, such as 95% (see Chapter 6). (b) Based on the model you perform a sensitivity analysis to make the sampler suitable for a wider class of chemicals. Parameters that you may want to optimize are area and thickness of the PE sheet. The minimum thickness that you may get is 30 μm. You remember from Tcacuic et al. (2015)’s work that by stirring the surrounding water the performance of the sampler could be improved, so you think to enclose the sampler in an open cylinder through which water is pumped. By doing so, you hope to reduce the thickness of the aqueous boundary layer to about 50 μm. (c) Based on the optimized design, give a range of chemicals (characterized by their KPEw and DPE ) for which an exposure time of 10 days would lead to at least 95% equilibration of the sampler with the surrounding water.

960

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

(d) Passive samplers are also used to measure chemicals in the sediment beds (see Lydy et al., 2014). You are interested in how the time to equilibration would change in this case. (i) Use the sampler design of question a (thickness of PE sheet 2δs = 50 μm) and assume the following sediment properties: Porosity ϕ = 0.8, density of solid particles ρs = 2.5 kg L−1 , organic matter content of sediment material foc = 0.05, no tortuosity (τ = 1). You find the Kocw -values for the three chemicals in the following table. (ii) As a second thought you realize that much of the chemical in the pore water may be sorbed on colloids. When you redo your calculation, assume a DOC concentration in the pore water [DOC] = 20 mgoc L−1 (as in Problem P13.7). As a first estimate, it is sufficient to assume that the Kocw -values of highly hydrophobic compounds for colloids are by a factor 5 to 10 smaller than the values for the soil or sediment material (see Chapter 13, Fig. 13.5) and that the movement of the colloids in the pore water can be neglected compared to the diffusion of the dissolved fraction.

phenanthrene

Cl

Cl

Cl

2,2',5-trichlorobiphenyl PCB 18

Cl

Cl

Cl

Cl Cl

Cl

PCB 153

28.4

Hint The mass exchange between the sediments and the PE sheet can be described as a two-sided boundary layer with different diffusivities on both sides of the interface (see Eq. 18-21 and Box 18.1). As an approximation, disregard the finite thickness of the PE sheet, calculate the total exchanged mass per unit area as a function of diffusion time t, ∗ (t), (see Eq. 18-18) and determine the time, teq , at which ∗ (teq ) would correspond to a fully equilibrated PE sheet. To get a relationship between the different concentrations in the sheet (CPE ) and the fractions in the sediment (total, dissolved, on colloids, in solids), consult Chapter 20, especially Eq. 20-3 and Box 20.1. You may want to use the sediment as compartment 1 and the PE sheet as compartment 2. You then can calculate the corresponding equilibrium concentration ratio at the interface, Rs/sed , with the same procedure as in Box 20.1. Finally, you have to calculate the effective diffusivity of the chemical in the sediments (Eq. 20-4, 20-5). As stated before, neglect tortuosity (τ = 1) and the mobility of the colloids in the pore water.

Systems Driven by Advection Case Study 28.5. The Schweizerhalle Accident: Chemical Pollution of the River Rhine Due to a Fire in a Storehouse After a fire in a chemical storehouse at Schweizerhalle, Switzerland, in November 1986, several tons of various pesticides, solvents, dyes, and other raw and intermediate chemicals were flushed into the Rhine River during a period of 12 hours by the fire fighting water, leading to a massive kill of fish and other aquatic organisms (Capel et al., 1988). Since numerous waterworks along the Rhine River use bank filtration from the river to nearby groundwater as a source for drinking water, there was considerable concern that the toxic chemicals present in the river water would also contaminate the drinking water wells. Therefore, each of the waterworks wanted to know immediately what concentration-time courses of the various chemicals, particularly their maximum concentrations, would be predicted in the river water for their location. Unfortunately, at that time, no simple models were available to answer this question. Particularly, the pertinent compound-specific properties and intrinsic reactivities of most of the chemicals introduced into the

Systems Driven by Advection

961

The Netherlands

Lobith 865 km

Germany

Bad Honnef 640 km

N

Mainz 498 km

Maxau 362 km

France Figure 28.2 Map of River Rhine showing the site of the accident (Schweizerhalle) and the sampling stations at Maxau, Mainz, Bad Honnef, and Lobith. Adapted from Wanner et al. (1989).

Lake Constance Schweizerhalle 159 km

Switzerland

river water were not known at the time, and, of course, the 1st edition of our textbook “Environmental Organic Chemistry” had not yet appeared. With the present knowledge and modeling tools that you have acquired in this 3rd edition of our textbook, you should, however, now be in the position to deal much better with the question asked by the waterworks. Using a simple modeling approach, you can test that yourself with the following example.

S (H3CH2CO)2P

SCH2CH2SCH2CH3

disulfoton

One of the major constituents in the firewater was the insecticide disulfoton (Vi = 2.05, Li = 7.84, Si = 1.29, Ai = 0, Bi = 0.84), of which an estimated 3.3 metric tons were introduced into the river during the 12 hours (Wanner et al., 1989). From monitoring measurements conducted after the accident at several locations along Rhine River (see Fig. 28.2), it was estimated later that during the 8 days “travel time” from Schweizerhalle to Lobith at the Dutch border, about 2.5 metric tons of this compound were “eliminated” from the river water. Table 28.4 summarizes the relevant information for the system (River Rhine) as well as on disulfoton. In order to build a simple model for describing the concentration-time course of disulfoton, particularly to predict its maximum concentration as a function of distance (or travel time), and for assessing its fate in the Rhine River, you first want to know

962

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

Table 28.4 Information Required to Model the Behavior of Disulfoton in the Rhine River Accident Approximate duration of spill Total input of disulfoton into the river at Schweizerhalle Total removal during 8 days travel time to Lobith

Δto = 12 h i = 3.3×103 kg iremoved = 2.5×103 kg

River Rhine Distance from Schweizerhalle to Lobith Mean flow velocity Mean depth Discharge of Rhine at Schweizerhalle Discharge of Rhine at Lobith Concentration of suspended solids in Rhine Organic carbon content of suspended solids Settling velocity of particles Coefficient of dispersion Air–water transfer velocity in air for H2 O in water for O2 Water temperature (approximate) pH

xo = 700 km ū = 1 m s−1 h=5m Qo = 750 m3 s−1 Q1 = 2,300 m3 s−1 rsw = 0.4 kgs m−3 sus = 0.005 kg kg −1 foc oc s vs = 2 m d−1 Edis = 2.8×103 m2 s−1 via (H2 O) = 5×10−3 m s−1 viw (O2 ) = 2×10−5 m s−1 Tw = 10◦ C 7.5

Disulfoton Molar mass Nondimensional Henry’s law constant at 10◦ C Air–water transfer velocity in air (va ) and in water (vw ) Molecular diffusion coefficient in water at 10◦ C

Mi = 274.4 g mol−1 Kiaw = 5×10−5 reduced by a factor of 5 relative to H2 O and O2 , respectively Diw = 3.8×10−10 m2 s−1

which processes (i.e., gas exchange, sedimentation, as well as chemical, photochemical, and microbial transformation) were primarily responsible for the removal of this compound from the river water. The box model presented in Section 28.1 provides a possible framework for answering the questions asked by the water works. Yet there remains a basic question: How could the modeling tools developed in Chapter 6 and in Section 28.1 be applied to a system that is dominated by advection, that is, by a distinct direction of flow? Hint: How to use Box Models in Rivers? A one-box model of the River Rhine with a single box reaching from Basel to the Netherlands would hardly be the right approach. In such a box, the elongation of the box would be far too big to attain a homogeneous concentration distribution. Furthermore, by assuming homogeneity we would loose exactly that mechanism in which we are interested, that is, the description of the pollutant front moving downstream from Switzerland to the Netherlands. Alternatively, we could subdivide the river into a couple of adjacent boxes as we have done for the two lakes connected by a channel (Fig. 6.7) or for the m-box model shown in Fig. 6.8. By doing so, we would be faced with a dilemma: Either we choose boxes that are small enough (e.g., 1 km long) so that one could think of them as completely mixed boxes, but then between Schweizerhalle

Systems Driven by Advection

963

and Lobith we would have to deal with 700 of them. Or we take just a few boxes, but then the boxes would again be very long. There is an elegant trick to overcome this difficulty. Instead of a box fixed in space, we consider a (virtual) box moving along the river with the mean flow velocity of the river, ū = 1 m s−1 in the case of River Rhine (Table 28.4). This is like using a moving coordinate system (a Lagrangian system, as physicists call it) instead of a fixed coordinate system (Eulerian system). To make life simple, we can define the size of the box such that all the disulfoton that entered the river is initially confined in it. Since the spill lasted for 12 hours, the box would have a length of 12 × 3600 s × 1 m s−1 = 43.2×103 m ≈ 43 km. This is still a fairly long box (rather a moving tube instead of a box), so we could come up with the same argument against such a box as used before. Indeed, just downstream of the spill, the disulfoton is not at all evenly distributed in the river, but turbulent diffusion induced by the flow will sooner or later mix the pollutant across the whole river, vertically faster than across the river (for more details see Schwarzenbach et al., 2003, Chapter 24). Along the river, some homogeneity is already attained by the continuous addition of the chemical while the virtual ‘tube-box’ is passing the polluted outlet. At some distance from the spill we can, as a rough approximation, assume that the total mass of spilled disulfoton, i , is homogeneously mixed into the total volume of water that flowed by the location of the spill. (a) Initial Mean Concentration Calculate the initial mean concentration of disulfoton downstream of Schweizerhalle. Assume that the chemical is homogeneously mixed into the whole cross section of Figure 28.3 Deformation of the pol- the river bed and that the concentration profile along the river looks like Fig. 28.3a. Hint Calculate the volume of water using the river discharge at Schweizerhalle, Qo , and the duration of the spill, Δto (Table 28.4). (b) Removal Processes Assume that you can describe all removal processes by first-order rate laws. Table 28.4 gives you the pertinent information that you need for quantifying removal by gas (a)

(b) u

concentration

lutant cloud by dispersion while it moves downstream on the River Rhine with mean velocity ū . The coordinate ξ measures the distance along the river relative to the actual location of the cloud center. (a) The initial concentration distribution is assumed to be rectangular with concentration Co . While the upstream and downstream interfaces of the cloud move with mean velocity ū , the velocity on individual streamlines may be above average (u+ ) or below average (u− ) leading to exchange velocities relative to the moving interface (black arrows). The resulting mixing process, called dispersion, is described by a diffusionlike dispersion coefficient, Edis . (b) Due to dispersion, the edges begin to erode. (c) Once the erosion fronts meet in the middle of the cloud, the cloud starts to look like a normal distribution along the river with increasing standard deviation, σ(t), and decreasing maximal concentration, Cmax (t).

(c) u

C0

C0 Cmax(t)

u u– u

+

u

u+

ξ=0

u–

2σ(t)

ξ=0 distance relative to cloud center

ξ=0

964

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

exchange and sedimentation. In addition, Wanner et al. (1989) estimated the rate constant for indirect photolysis to be 7×10−4 d−1 , and they reported the following pHdependent hydrolysis rate data (kobs -values) measured at temperatures higher than the river water (10◦ C): kobs (s−1 ) T (◦ C) 20 30 40 45 50 a

pH 6.0 4.0×10−7 a

pH 11.98 1.3×10−5

9.6×10−7 1.5×10−6 2.9×10−6

pH 11.72 3.6×10−5

A similar kobs -value was obtained at pH 4.0 and 30◦ C.

Estimate the total (pseudo-)first-order rate constant for removal of disulfoton from the river between Schweizerhalle and Lobith based on the removed mass, iremoved (see Table 28.4). Calculate the first-order removal rates for the individual processes: (i) sedimentation (ii) gas exchange (iii) abiotic hydrolysis. Also, answer the following questions: (iv) What is the relative importance of these processes as well as of indirect photolysis for removal of disulfoton from the river water? (v) Could direct photolysis be important? (vi) How important is microbial transformation (which is difficult to predict; assume that microbial transformation is responsible for the removal that cannot be accounted for by the other processes)? Assume that exchange with the sediments can be neglected during the passing of the “sulfoton plume” in the river, but note that this process might have become important at a later stage after the accident (see question (d)). (vii) What (initial) products would you expect from chemical or microbial transformation? Formulate the respective reaction mechanisms.Which photoxidants could play the most important role in transforming disulfoton in the river, and what could be possible products? Hint Remember from Chapter 6 that linear (or first-order) processes behave like they were independent of each other. This is also true for the process of dispersion and dilution

Systems Driven by Advection

965

(question d). Thus, we can analyze all processes independently and then simply add their effects. For estimating the Kiocw value of disulfoton use Eq. 13.14 (Chapter 13) and for quantifying sedimentation use the information given in Tables 28.1 and 28.4. For quantifying gas exchange, use Chapter 19 and the information given in Tables 28.1 and 28.4. An overview of chemical and enzymatically catalyzed hydrolysis and redox reactions of phosphoric and thiophosphoric acids can be found in Chapters 22 and 23 respectively. Finally, pertinent information about direct and indirect photolysis can be found in Chapters 24 (particularly Section 24.2) and 25. (d) Dispersion and Dilution In river flow, there are two additional mechanisms that reduce the maximum concentration of a pollutant cloud without reducing total load. Since they do not have a direct analogue among the processes listed in Table 28.1, some additional hints are needed. In fact, the effect of dilution by merging rivers occurs step-wise every time a tributary is joining the Rhine. In order to compare its effect with other processes, we can calculate a pseudo first-order rate constant, kdil , by assuming that discharge Q grows continuously (instead of step-wise) from Qo at Schweizerhalle to Qt at Lobith. Use an exponential curve, Qt = Qo exp(kdil t), and calculate kdil by assuming that the flow time from Schweizerhalle to Lobith is t = 8 days. Flow in rivers or groundwater is always accompanied by a process called dispersion (Chapters 5 and 17). Dispersion is caused by the fact that not all water parcels move with the same velocity. There are streamlines on which the flow velocity is below average (e.g., close to the bottom of the river bed where friction slows the water down), and there are other streamlines (typically at the water surface in the middle of the river) that move faster than average. Relative to a surface perpendicular to the flow that moves at mean speed ū , (the upstream and downstream boundaries of the moving hose-like box are such surfaces), these streamlines act like an exchange flux between the box and the water flowing behind or ahead of it, that is, like process 7 in Table 28.1. Assume that the flow is to the right and consider the upstream boundary of the box (Fig. 28.3a). Streamlines with above-average velocity pass the boundary from left to right (flux from outside into the box) while streamlines with below-average velocity pass the boundary from right to left (or rather the boundary is passing them from behind). Since dispersion acts like an exchange flux across the moving box boundary, it can be looked at like a two-sided wall boundary (Section 6.3) with a ‘diffusion coefficient’, Edis , (dimension [L2 T−1 ]) called the dispersion coefficient. Assume that initially the concentration of disulfoton is Cio inside the moving box and zero outside (Fig. 28.3a). Dispersion causes ‘erosion’ of the ‘concentration edges’ at the upper and lower boundary of the moving box (Fig. 28.3b). After some time, tini , the erosion fronts of the two boundaries meet in the middle of the box, the maximum concentration, Cio , starts to decrease and the concentration cloud of the pollutant moving along the river looks more and more like a normal distribution (Fig. 28.3c). tini is about 1 day. It can be estimated from the Einstein-Smoluchowski relation (Eq. 6-36) by taking as distance, Ldiff , half of the initial cloud length along the river. The further change of the concentration distribution follows from Eq. 17-8, where diffusivity D is replaced by the dispersion coefficient, Edisp , and x, the space coordinate along

966

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

the river, is replaced by ξ, the distance relative to the moving concentration maxima, Cmax (ξ = 0) of the cloud (see Eq. 17-39): ( ) ∗i ξ2 Ci (ξ, t) = exp − (28-17) [ML−3 ] 4Edis t 2(πEdis t)1∕2

∗i has the unit of mass per area. (Its size is not relevant for the following considerations, but the curious reader may want to find out how it is related to the total input of disulfoton, i .) Here, we are only interested in the ratio of the maximum concentration at time t = tini = 1 day and t = to = 8 d, respectively. As for the case of dilution, we assume that the maximum concentration drops exponentially like exp(−kdis Δt) with Δt = to – tini = 7 d. This allows us to estimate the (pseudo first-order) rate constant for the decrease of the maximum concentration due to dispersion, kdis . (d) Sediment–Water Exchange We do not really have enough information on the sediments of the River Rhine to quantify the flux from the water into the sediments based on Eqs. 28-5 to 28-8. To estimate at least its order of magnitude, use sediment porosity ϕ = 0.8, particle density ρs = 2500 kg m−3 , and the same organic carbon content as for the suspended particles. As it turns out, the contribution of sediment–water exchange to the total removal is of similar order as the other processes (except biological transformation). Nonetheless, its effect on the river may be important. In which sense? Hint You need the exposure time of the sediments to the polluted water. At Schweizerhalle it is 12 hours. The calculation of dispersion helps to estimate how the exposure time changes from Schweizerhalle to Lobith. (e) Putting everything together With all this information, you are ready to fill in the relevant numbers into Table 28.5. Case Study 28.6. How Likely is it that Spilled Tetrachloroethene (PCE) will Significantly Contaminate a Nearby River? A dry cleaning establishment has spilled tetrachloroethene (PCE, CCl2 =CCl2 ) and contaminated the shallow groundwater below. The spill occurred about 60 meters from a nearby river (at the location of “well 1” in the table). You have been asked to evaluate the likelihood that the PCE will contaminant a nearby river. Many properties of PCE are given in Appendix C.

well 1 2 3

distance from river (m) 60 40 30

pH

EH (mV)

Cl− (mM)

PCE (μM)

δ13 CPCE (o /oo )

6.8 6.6 6.8

–70 –20 –480

2.8 2.6 1.4

360 40 80

–24.4 –17.8 –16.2

Systems Driven by Advection

967

Table 28.5 Relative Contributions of Different Physical and Chemical Processes to the Reduction of (a) Load and (b) Maximum Concentration of Disulfoton between Schweizerhalle and Lobith Provided that all Processes are Described by a First-Order Approximation Rate

(d−1 )

% of load reduction

% of reduction of max. concentration

Load Reduction (Mixing and Transformation) Total load reduction Hydrolysis Photochemical transformation Air–water exchange Sedimentation Sediment–water exchange Biological transformation (calculated) Dispersion and Dilution Dispersion Dilution Total of all processes Remaining total load at Lobith Remaining maximal concentration at Lobith

(a) What maximum concentration of PCE (μM) do you expect in the groundwater adjacent to the DNAPL at “well 1” assuming that the PCE exists as a dense nonaqueous phase liquid (DNAPL, PCE’s density is 1.6 g mL−1 ) sitting on an aquitard about 10 m below the ground. An aquitard is a water-saturated sediment or rock with very low permeability. Assume that the groundwater temperature is 10◦ C, it has a dissolved NaCl concentration of 3 mM and a dissolved organic carbon (DOC) concentration of 2 mg DOC L−1 ? Hint See Section 9.4, Chapter 13, and Appendix C to find information about PCE in water and its partitioning to DOC. (b) Your hydrogeology colleagues tell you that the groundwater at the site is flowing towards the river at a velocity between 1 and 8 m yr−1 . In order to estimate the shortest possible time of arrival of the PCE at the river (60 m from the spill), you assume the groundwater is moving at 8 m yr−1 . If the subsurface solids have a porosity of 0.5, and contain 0.3% organic carbon, and the groundwater is carrying 2 mg DOC L−1 , at what velocity (m yr−1 ) do you expect PCE to advect toward the river carried by the groundwater? Neglect dispersive spreading of the plume toward the river. Hint See Section 12.2 to assess the effect of sorption on PCE transport in the groundwater. Assume that the density of the aquifer material, ρs , is 2.5 kg L−1 .

968

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

(c) Since only trace O2 concentrations (perhaps analytical artifacts) and detectable ferrous iron (Fe+2 ) and hydrogen sulfide (H2 S) concentrations are measured in groundwater samples near the spill, you suspect the PCE may be biotransformed via reductive dehalogenation (see Sections 23.4 and 26.3): Cl

Cl

+H2

Cl

Cl

Cl

Cl

–HCl

Cl

H

PCE

TCE

You wonder if the H2 concentrations are suitable for such microbial biotransformations; concentrations in the nanomolar range have been found to be needed (Smatlak et al., 1996; Ballapragada et al., 1997). Given the pH of the water is 6.8, what H2 (aq) concentration (nM) would you expect at equilibrium if the EH is –100 mV? (d) Next, you wonder if this PCE transformation might be thermodynamically feasible. Estimate the Δr G (kJ mol−1 ) of this reaction assuming: the pH is 6.8, [Cl− ] is 3 mM, H2 (aq) is 10 nM, and the PCE concentration is equal to the TCE concentration. What would be the [TCE]/[PCE] ratio at equilibrium under these conditions? Hint See Section 21.2. (e) Investigators measure PCE and its prospective dehalogenation products, trichloroethene (TCE; CCl2 =CHCl), dichloroethene (DCE; CHCl=CHCl, CCl2 =CH2 ), and vinyl chloride (VC; CH2 =CHCl), in groundwater about 30 m downgradient from the edge of the DNAPL towards the river and find the following concentrations: tetrachloroethene (PCE) = 80 μM trichloroethene (TCE) = 110 μM cis-dichloroethene (DCE) = 73 μM chloroethene (VC) = 17 μM Assuming this mixture took 10 years to move from the DNAPL spill to this location 30 m away, neglecting differential retardation of the transport of these compounds, and also assuming all the TCE, DCE, and VC derived from the spilled PCE, estimate the PCE degradation rate (yr−1 ) that would explain these results. Since these compounds all have different retardation factors, they do not stay together during transport, so this calculation is only a rough estimate! Hint Assume all the measured TCE, DCE, and VC started as PCE 10 years ago. Also, neglect the possibility that other products such as ethene have also been produced from the PCE.

Systems Driven by Advection

969

(f) You also hear that colleagues have measured the δ13 C of the PCE in the spilled DNAPL to be –24.4‰ and in the groundwater 20 m downgradient to be –17.8‰ and 30 m downgradient to be –16.2‰. Looking at the literature, you decide a bulk enrichment factor of –3‰ might be suitable for your site. Based on these compound-specific isotope analyses data, what transformation rate (yr−1 ) do you estimate for the PCE assuming the water 20 m and 30 m downgradient took 7 and 10 years, respectively, to get to those locations? Hint See Section 27.2, Eq. 27-3. (g) Finally, assuming (a) PCE dissolved in the groundwater near the spill is 300 μM, the groundwater velocity is 8 m yr−1 , PCE’s retardation factor (RfPCE =1/fPCEw ) in the groundwater is 3, and its biotransformation rate is spatially constant at 0.3 yr−1 , what concentration of PCE (μM) do you expect will arrive at the rive’s edge that is 60 m from the spill? (Note that the drinking water maximum for PCE is 5 ppb or 0.03 μM.) Hint Assume a parcel of water leaves the spill with its initial concentration, it advects toward the river with a retarded velocity, and is degraded along the way at a constant rate. Case Study 28.7. The Long-Range Transport Potential (LRTP) of Organic Chemicals An alternative method to the “unit world approach” for assessing the potential environmental impact of an organic pollutant (see Chapter 1 and Section 28.2) is to evaluate its “Long-Range Transport Potential” (LRTP; Fenner et al., 2005). As the name indicates, the goal is to assess the distance a given chemical is able to travel in an environmental compartment, particularly in the atmosphere, where transport is fastest. Similar to the unit world approach, this method allows us to quickly assess a great number of chemicals using just a few characteristic compound and system parameters. The characteristic travel distance (CTD) is used as a measure of LRTP. For the environmental compartment, s (s stands for atmosphere, river, ocean etc.), CTDs is defined as: CTDis = us τis

(28-18)

where us is the mean transport velocity in compartment, s (e.g., wind speed, flow velocity of river etc.), and τis is mean residence time of chemical i in compartment s. In the following, we extend this traditional concept to a situation where transport occurs simultaneously in two environmental compartments, the atmosphere (atm) and the ocean (sea), which are coupled by air–water exchange and by transport from the atmosphere into the ocean by dry and wet deposition. Our aim is to extend the system-specific CTDis (Eq. 28-18) to a combined or total CTDitot . Two different

970

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

Table 28.6 Set of Model Compounds Used to Evaluate the CTD of Organic Chemicals. The Table also Contains Some Pertinent Data Required for Estimating the Partitioning of the Compounds in the Atmosphere/Ocean System Considered as well as Their Reactivities in the Atmosphere with Respect to Reactions Involving OH-Radicals Compound (structures in margin, next page)

Kiaw a (25◦ C)

Δaw Hi b (kJ mol−1 )

Kiocw c (15◦ C) (m3 goc −1 )

CHF–CF3 (HFC-134a) CH2 =CFCF3 (HFC-1234xf) HCB γ-HCH PCB 153 D5 PBDE 180

4.0×100

30

3×10−6

3×10−15

4.0×100

30

3×10−6

1×10−12

3.2×10−2 1.2×10−4 1.7×10−2 1.3×10+3 3.2×10−6

46 50 70 80 100

8×10−2 2×10−3 0.6 0.065 15

3×10−14 4×10−13 2×10−13 2×10−12 3×10−13 h

′ d kiHO ∙

fig

e

fiw

f

kiatm g (d−1 )

a

Kiaw values from Appendix C, except HFC-134a (Sander, 2015). The air–water partition constant of HFC-1234xf was not found in the literature; assume a similar value as for HFC-134a. b Δaw Hi from Table 9.2, for PBDE 180 estimated using Eq. 9-27; for HFC-1234xf assume a similar value as for HFC-134a. c Estimated using Eqs.13-14 and Eq. 10-18 for temperature correction. d Second-order rate constant for the gas phase reaction with OH-radicals (molecule cm−3 )−1 s−1 ; temperature dependence can be neglected (see Section 25.3); data from Atkinson (1989); Franklin (1993); Anderson and Hites (1996); Brubaker and Hites (1998); Safron et al. (2015); Vera et al. (2015); and Vollmer et al. (2015). e Fraction in the gas phase (Eq. 15-13); assume an aerosol concentration [PMx ] = 100 μg m−3 , also assume that sorption of HFC-1234xf is similar to HFC-134a. f Fraction in dissolved form (Eq. 12-18), assume that Kid = foc Kiocw . g Assume an average OH-radical concentration of 106 molecule cm−3 ; also assume that only molecules in the gas phase react. h Assuming a similar reactivity as PBDE 99; note that highly brominated PBDE congeners may also undergo direct photolysis in the gas, but not in the particulate phase (see Raff and Hites, 2007).

modeling approaches are introduced, and their validity is examined using a set of model compounds that cover a wide range of physicochemical properties (Table 28.6). Before we do this, however, let us make some brief comments on our model compounds. In the early 1990s, HFC-134a was introduced as a replacement of CFC12 (CCl2 F2 ) which had an estimate half-life in the atmosphere of 100 years (Hodnebrog et al., 2013; contains data of how these chemicals have accumulated in the atmosphere). HFC-134a used in large quantities as refrigerant in car air-conditioners was to be phased out by 2017 (Vollmer et al., 2015). One of the replacements is HFC-1234xf (CH2 =CFCF3 ), which can already be detected in the atmosphere (Vollmer et al., 2015). The question is, to what extent will this compound also accumulate in the atmosphere? Hexachlorobenzene (HCB), γ-hexachlorocyclohexane (γ-HCH), and PCB 153 represent three members of the so-called “Legacy POPs” (Fig. 3.1) that are of great environmental concern. As discussed in Chapter 3, decamethylcyclopentasiloxane (D5) is a widely used solvent (e.g., in personal care products). It exhibits rather unusual

Systems Driven by Advection

properties due to its weak van der Waals interactions (Chapter 7). Finally, 2,2′ ,3,4,4′ ,5′ ,6-heptabromodiphenyl ether (PBDE 180) represents one of the more heavily brominated diphenylether flame retardants (Chapter 3) that are of considerable environmental concern. Except for HFC-1234xf, each of these compounds have been detected all over the world. Hence, your following LRTP assessment of these compounds should indicate whether one could have anticipated their global occurrence.

Cl Cl

Cl

Cl

Cl Cl

hexachlorobenzene (HCB)

(a) Getting All Compound-Specific Parameters Ready In order to be able to perform the CTD calculations, calculate first all the required compound-specific parameters (Table 28.6, empty columns) assuming an average temperature in the atmosphere/ocean system considered of 15◦ C as well as a relative humidity of about 50%. In order to evaluate the effect of temperature on CTD, also get all parameters and perform the calculations for PCB 153 at a temperature of 5◦ C

Cl Cl

Cl

Cl

Cl Cl HCH

Cl

Cl

Cl

Cl Cl

Cl

PCB 153 Br Br

Br

Br O

Br

Br Br

2,2',3,4,4'‚Äö5',6-heptabromodiphenyl ether (PBDE 180) O Si O Si

Si

O

O Si

O

971

Si

decamethylcyclopentasiloxane (D5)

Hint Table 28.6 summarizes the estimated air–water and SOM–water partition constants/coefficients (Kiaw , Kiocw ), as well as their second-order reaction rate constants with OH-radicals in the atmosphere collected from the literature. Read carefully the footnotes because they contain important hints for estimating/calculating all required parameters. For estimating aerosol–air partition coefficients, use Eq. 15-17 (Chapter 15), which provides you directly with the values valid for the assumed conditions (15◦ C and 50% RH). Also, assume that sorption of HFC-1234xf is similar to HFC-134a. For calculating the fraction in dissolved form (fiw ) in the ocean, take a POC concentration of 0.5 goc m−3 . Furthermore, since we consider seawater, you may need to take into account the effect of salt on Kiaw and Kiocw (assume 0.5M NaCl; see Chapter 9, Eqs. 9-29 and 9-33). For which compounds do you choose to do so? Abraham parameters: HFC-134a: Vi = 0.46, Li = 0.40, Si = 0.16, Ai = 0.16, Bi = 0.05; log KiPMa (m3 air g−1 dry aerosol, Eq. 15-17) = ? HCB: Vi = 1.45, Li = 7.39, Si = 0.99, Ai = 0, Bi = 0; log KiPMa (m3 air g−1 dry aerosol, Eq. 15-17) = ? γ-HCH: Vi = 1.58, Li = 7.57, Si = 1.28, Ai = 0, Bi = 0.50; log KiPMa (m3 air g−1 dry aerosol, Eq. 15-17) = ? PCB 153: Vi = 2.06, Li = 9.59, Si = 1.74, Ai = 0, Bi = 0.11 log KiPMa (m3 air g−1 dry aerosol, Eq. 15-17) = ? D5: Vi = 2.93, Li = 5.24, Si = –0.1, Ai = 0, Bi = 0.50 log KiPMa (m3 air g−1 dry aerosol, Eq. 15-17) = ? PBDE 180: Vi = 2.61, Li = 13.62, Si = 1.65, Ai = 0, Bi = 0.57 log KiPMa (m3 air g−1 dry aerosol, Eq. 15-17) = ?

972

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

Physical and physicochemical characteristics of coupled atmosphere–ocean system: Atmosphere (atm) height hatm wind speed uatm aerosol conc. [PMx ] dry deposition velocity vd (Eq. 15-31) volumetric precipitation vr scavenging ratio Sr (Eq. 15-35)

104 m 5 m s−1 = 4.3×105 m d−1 100 μg m−3 0.6 cm s−1 ≈ 500 m d−1 0.003 m d−1 3.5×105

Ocean (sea) depth mixed layer hsea current velocity usea particular organic carbon Sfoc settling velocity of particles vs thickness of thermocline hth vertical turbulent diffusivity in thermocline Ez

100 m 0.1 m s−1 = 8.6×103 m d−1 0.5 goc m−3 10 m d−1 50 m 3 cm2 s−1 ≈ 25 m2 d−1

Air–Water Exchange air-side exchange velocity via (Eq. 19-5) water-side exchange vel. viw

1 cm s−1 10−3 cm s−1

(b) A First Modeling Attempt: Steady State due to Air–Water Exchange We consider a situation over the ocean where the direction of water currents and wind is alike. We want to calculate the steady-state concentrations profile of the chemical i along the x-axis in the atmosphere and in the ocean, Ciatm (x) and Cisea (x), respectively by assuming an instantaneous equilibrium between air and water due to air–water exchange. The input of chemical i into the ocean or the atmosphere shall be confined to the region x < 0; no further input occurs for x > 0. (x = 0 could be the coastline). As typical transport velocities, use usea = 0.1 m s−1 for the ocean and uatm = 5 m s−1 for the atmosphere. Mixing depths of the ocean (hsea = 100 m) and the atmosphere (hatm = 10 km) are assumed to be constant everywhere along the path of the chemical. Use the results from question (a) to calculate the first-order removal rates in the ocean and atmosphere, kisea and kiatm , respectively. The relevant characteristics of the coupled atmosphere–ocean system are summarized in the above table. Since we assume that all processes can be described linearly, we expect that the resulting concentration profiles are exponential functions of the form Ci (x) = Ci0 exp(–ηis x). ηis is a “spatial rate constant” (the spatial analog to the temporal rate constant, k) for chemical i in system s; it has the dimension L−1 . We use its inverse, (ηis )−1 , (dimension L) as a measure for the Critical Transport Distance (CTD): CTDis = (ηis )−1

(28-19)

Systems Driven by Advection

973

(i) Derive a general expression for CTDis = (ηis )−1 . (ii) Discuss the conditions for which (1) transport is mainly in the ocean, (2) transport is mainly in the atmosphere, (3) transport is of similar magnitude in both compartments. (iii) Calculate CTDis for the chemicals listed in Table 28.6 and discuss the result based on the very different physico–chemical properties of these compounds using the answer for (ii). (iv) Check whether it is reasonable to assume that air–water exchange keeps the atmosphere and the ocean at equilibrium, that is, Ciatm = Kiaw Cisea . For the air–water exchange velocities use the standard values of Eq. 19-5, via = 1 cm s−1 and viw = 1×10−3 cm s−1 , and neglect the influence of molecular diffusivities of the chemicals on these velocities (but not of the nondimensional Henry’s law coefficient). Hint Start out with the one-dimensional linear transport-reaction equation (Eq. 6-38) with J, D = 0 and a yet unknown exchange flux between atmosphere and water per unit area and time, ϕ. You get two linear differential equation for the concentrations Ciatm (x) and Cisea (x) as a function of the space coordinate x: ∂C ∂Ciatm ϕ = −uatm iatm − kiatm Ciatm + ∂t ∂x hatm ∂Cisea ∂Cisea ϕ = −usea − kisea Cisea − ∂t ∂x hsea

(28-20a) (28-20b)

Since the two concentrations are coupled by the equilibrium condition, Ciatm = Kiaw Cisea , the system 28-20 is only pseudo-two-dimensional. For instance, Ciatm can be replaced by Kiaw Cisea . Furthermore, if the first equation is multiplied with hatm , the second with hsea , and both equations added, the unknown exchange term ϕ drops out. By assuming steady state (temporal derivatives are zero), one gets an ordinary first-order linear differential equation for Cisea (x) that can be solved with the help of Box 6.2. (It does not matter that in this case the variable is x instead of t.) The result has the form Cisea (x) = const. exp(–ηitot x), where ηitot is the inverse CTD-value of the combined atmosphere–ocean system. The corresponding value for transport in the atmosphere alone is η∗iatmo = kiatm /uatm . By comparing ηitot and η∗iatm , you can find out whether the interaction of the atmosphere with the ocean plays a significant role for the CTD value for the particular chemical. Note that in Eq. 28-20 the linear removal rates, kiatm and kisea , refer only to those processes that remove the chemical from the combined atmosphere–ocean system. In the atmosphere, it is a chemical reaction (which one?), in the ocean where chemical reactions are disregarded relative to other processes, removal is by particle settling and by turbulent mixing through the thermocline (no back-transport since the concentration of chemical i below the mixed layer is assumed to be zero). Yet the rates do not include internal transport between the two compartments (such as air–water exchange or dry or wet deposition from the atmosphere onto the ocean), since these processes are indirectly taken care of by the equilibrium condition, Ciatm = Kiaw Cisea . To answer question (iv), compare the size of the air–water exchange rates (see via and viw listed in table) to the rates kiatm and kisea . If the latter are much larger than the former, the basic assumption of the model is not valid and another approach is needed.

974

Exposure Assessment of Organic Pollutants Using Simple Modeling Approaches

(c) A Second Modeling Attempt: Dynamic model without Feedback from the Ocean into the Atmosphere The obvious next step to model transport in the coupled atmosphere–ocean system would be to introduce a two-layer model with exchange fluxes in both directions and then solve the model by assuming steady-state with respect to time. This results in a coupled two-dimensional linear system of two coupled differential equations for the concentrations along the x-axis, Ciatm (x) and Cisea (x). In Chapter 6 (Box 6.5), methods have been developed to solve such systems. However, for our purposes, it may be good enough to look at a simplified version of the system. By neglecting the transport from the ocean into the atmosphere, the system becomes hierarchical (see Fig. 6.7). Develop such a model for the characteristic travel distances (CTD) in the combined atmosphere–ocean system and apply it to the chemicals introduced before. Hint Start with Eqs. 28-20. In the first equation, replace the term containing ϕ by the transfer of the chemical from the atmosphere to the ocean and by the different processes that describe dry and wet deposition from the atmosphere to the ocean (Eqs. 15-28 to 15-35). Neglect the back-flux by air–water exchange from the ocean to the atmosphere. In the second equation (describing Cisea ), replace the term containing ϕ by the corresponding input from the atmosphere by air–water exchange and by dry and wet deposition. Neglect the back-flux from the ocean to the atmosphere. Evaluate the resulting equations for steady state (temporal derivatives equal zero). Since the equation for Ciatm does not contain Cisea , it can be solved according to the method described in Box 6.2. Since the equation is linear, its solution must be of the form Ciatm (x) = C0 iatm exp(–ηiatm x). It can be inserted as time-dependent inhomogeneous term into the second equation. The solution follows from Box 6.2, Eq. 5. It consists of the sum of two exponential terms, one having the η-value of the first one (ηiatm ). The second term has the form const. exp(-ηisea x). The relative size of the inverse values, (ηiatm )−1 and (ηisea )−1 , tells you whether the CTD-value for the chemical i is primarily determined by transport in the atmosphere, in the ocean, or by both.

28.5

Bibliography Anderson, P. N.; Hites, R. A., OH radical reactions: The major removal pathway for polychlorinated biphenyls from the atmosphere. Environ. Sci. Technol. 1996, 30(5), 1756–1763. Atkinson, R., Kinetics of the gas-phase reactions of a series of organosilicon compounds with OH and NO3 radicals and O-3 at 297 +/- 2-K. Environ. Sci. Technol. 1991, 25(5), 863–866. Atkinson, R.; Aschmann, S. M., Rate constants for the gas-phase reactions of the OH radical with a series of aromatic hydrocarbons at 296 +/- 2-K. Int. J. Chem. Kinet. 1989, 21(5), 355–365. Ballapragada, B. S.; Stensel, H. D.; Puhakka, J. A.; Ferguson, J. F., Effect of hydrogen on reductive dechlorination of chlorinated ethenes. Environ. Sci. Technol. 1997, 31(6), 1728–1734. Brubaker, W. W., Jr.; Hites, R. A., OH reaction kinetics of gas-phase alpha- and gammahexachlorocyclohexane and hexachlorobenzene. Environ. Sci. Technol. 1998, 32(6), 766–769.

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975

Capel, P. D.; Giger, W.; Reichert, P.; Wanner, O., Accidental input of pesticides into the Rhine River. Environ. Sci. Technol. 1988, 22(9), 992–997. Dhillon, G. S.; Kaur, S.; Pulicharla, R.; Brar, S. K.; Cledon, M.; Verma, M.; Surampalli, R. Y., Triclosan: Current status, occurrence, environmental risks and bioaccumulation potential. Int. J. Environ. Res. Public Health 2015, 12(5), 5657–5684. Escher, B. I.; Schwarzenbach, R. P., Mechanistic studies on baseline toxicity and uncoupling of organic compounds as a basis for modeling effective membrane concentrations in aquatic organisms. Aquat. Sci. 2002, 64(1), 20–35. Fenner, K.; Scheringer, M.; MacLeod, M.; Matthies, M.; McKone, T.; Stroebe, M.; Beyer, A.; Bonnell, M.; Le Gall, A. C.; Klasmeier, J.; Mackay, D.; Van De Meent, D.; Pennington, D.; Scharenberg, B.; Suzuki, N.; Wania, F., Comparing estimates of persistence and long-range transport potential among multimedia models. Environ. Sci. Technol. 2005, 39(7), 1932–1942. Franklin, J., The atmospheric degradation and impact of 1,1,1,2-tetrafluoroethane (hydrofluorocarbon 134a) Chemosphere 1993, 27(8), 1565–1601. Hodnebrog, O.; Etminan, M.; Fuglestvedt, J. S.; Marston, G.; Myhre, G.; Nielsen, C. J.; Shine, K. P.; Wallington, T. J., Global warming potentials and radiative efficiencies of halocarbons and related compounds: A comprehensive review. Rev. Geophys. 2013, 51(2), 300–378. Imboden, D. M.; W¨uest, A., Mixing mechanisms in lakes. In Physics and Chemistry of Lakes, Lerman, A.; Imboden, D. M.; Gat, J., Eds. Springer: Heidelberg, 1995; pp 83–138. Kliegman, S.; Eustis, S. N.; Arnold, W. A.; McNeill, K., Experimental and theoretical insights into the involvement of radicals in triclosan phototransformation. Environ. Sci. Technol. 2013, 47(13), 6756–6763. Lohmann, R., Critical review of low-density polyethylene’s partitioning and diffusion coefficients for trace organic contaminants and implications for its use as a passive sampler. Environ. Sci. Technol. 2012, 46(2), 606–618. Lydy, M. J.; Landrum, P. F.; Oen, A. M. P.; Allinson, M.; Smedes, F.; Harwood, A. D.; Li, H. Z.; Maruya, K. A.; Liu, J. F., Passive sampling methods for contaminated sediments: State of the science for organic contaminants. Integr. Environ. Assess. Manag. 2014, 10(2), 167–178. Raff, J. D.; Hites, R. A., Gas-phase reactions of brominated diphenyl ethers with OH radicals. J. Phys. Chem. A 2006, 110(37), 10783–10792. Raff, J. D.; Hites, R. A., Deposition versus photochemical removal of PBDEs from lake superior air. Environ. Sci. Technol. 2007, 41(19), 6725–6731. Safron, A.; Strandell, M.; Kierkegaard, A.; Macleod, M., Rate constants and activation energies for gas-phase reactions of three cyclic volatile methyl siloxanes with the hydroxyl radical. Int. J. Chem. Kinet. 2015, 47(7), 420–428. Sander, R., Compilation of Henry’s law constants (version 4.0) for water as solvent. Atmos. Chem. Phys. 2015, 15(8), 4399–4981. Schwarzenbach, R. P.; Gschwend, P. M.; Imboden, D. M., Environmental Organic Chemistry. John Wiley&Sons, Inc.: Hoboken, New Yersey, 2003. Singer, H.; Muller, S.; Tixier, C.; Pillonel, L., Triclosan: Occurrence and fate of a widely used biocide in the aquatic environment: Field measurements in wastewater treatment plants, surface waters, and lake sediments. Environ. Sci. Technol. 2002, 36(23), 4998–5004. Smatlak, C. R.; Gossett, J. M.; Zinder, S. H., Comparative kinetics of hydrogen utilization for reductive dechlorination of tetrachloroethene and methanogenesis in an anaerobic enrichment culture. Environ. Sci. Technol. 1996, 30(9), 2850–2858. Tcaciuc, A. P.; Apell, J. N.; Gschwend, P. M., Modeling the transport of organic chemicals between polyethylene passive samplers and water in finite and infinite bath conditions. Environ. Toxicol. Chem. 2015, 34(12), 2739–2749. Tixier, C.; Singer, H. P.; Canonica, S.; Muller, S. R., Phototransformation of triclosan in surface waters: A relevant elimination process for this widely used biocide - Laboratory studies, field measurements, and modeling. Environ. Sci. Technol. 2002, 36(16), 3482–3489.

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Tixier, C.; Singer, H. P.; Oellers, S.; Muller, S. R., Occurrence and fate of carbamazepine, clofibric acid, diclofenac, ibuprofen, ketoprofen, and naproxen in surface waters. Environ. Sci. Technol. 2003, 37(6), 1061–1068. Vera, T.; Borras, E.; Chen, J.; Coscolla, C.; Daele, V.; Mellouki, A.; Rodenas, M.; Sidebottom, H.; Sun, X.; Yusa, V.; Zhang, X.; Munoz, A., Atmospheric degradation of lindane and 1,3dichloroacetone in the gas phase. Studies at the EUPHORE simulation chamber. Chemosphere 2015, 138, 112–119. Vollmer, M. K.; Reimann, S.; Hill, M.; Brunner, D., First observations of the fourth generation synthetic halocarbons HFC-1234yf, HFC-1234ze(E), and HCFC-1233zd(E) in the atmosphere. Environ. Sci. Technol. 2015, 49(5), 2703–2708. Wanner, O.; Egli, T.; Fleischmann, T.; Lanz, K.; Reichert, P.; Schwarzenbach, R. P., Behavior of the insecticides disulfoton and thiometon in the Rhine River-A chemodynamic study. Environ. Sci. Technol. 1989, 23(10), 1232–1242.

977

Appendix

Appendix A:

Mathematics

Appendix B:

Physical Constants and Units

Appendix C:

Physical Properties of Organic Compounds

Appendix D:

Temperature Dependence of Equilibrium Constants and Rate Constants

Appendix E:

Estimation of Gas-Phase Hydroxyl Radical Reaction Rate Constants of Organic Chemicals

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

979

Appendix A

Mathematics

A.1

The Normal Distribution

A.2

The Error Function

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

980

Appendix

A.1

The Normal Distribution The one-dimensional normal (or Gaussian) distribution along the x-axis is defined by: ( ) x2 1 exp − 2 pσ (x) = 2σ (2π)1∕2 σ

(17-3)

where σ is the standard deviation and σ2 is the variance of the distribution. pσ (x) has the following properties: ∞

∫

Normalization

pσ (x)dx = 1

(1)

x pσ (x)dx = 0

(2)

x2 pσ (x)dx = σ2

(3)

−∞ ∞

Mean value x̄ =

∫

−∞ ∞

x2 =

Variance

∫

−∞

Integrals within finite boundaries have the following values: ∫

σ

pσ (x)dx = 0.683

(4)

pσ (x)dx = 0.954

(5)

−σ 2σ

∫

−2σ

A.2

The Error Function The Error Function erf(y) along the y-axis is defined by: y

2 2 erf(y) = √ e−x dx ∫ π

(1)

0

The Complementary Error Function is: ∞

2 2 erfc(y) = 1 − erf(y) = √ e−x dx ∫ π

y

(2)

Appendix A

981

Symmetry properties and integral: erf(−y) = −erf(y) ;

erfc(−y) = 2 − erfc(y) = 1 + erf(y)

∞

∫

(3)

∞

erf(y) dy =

0

1 erfc(y) dy = √ ∫ π

(4)

0

0.5

0.4

pσ (x)

0.3

34.1% 34.1%

0.2

0.1 0.1%

0.0

Figure A.1 The normal distribution where each band on the x-axis has a width of one standard deviation (σ).

1.0

2.1%

–3σ

13.6%

–2σ

13.6%

–1σ

0 x

(a)

erfc(y)

erf(y)

3σ

0.8

0.0

–0.5

0.6 0.4 0.2 0.0

–1.0 –3

2σ

0.1%

(b)

1.0

0.5

Figure A.2 (a) The Error Function erf(y) for y = – 3 to y = + 3. (b) Onesided diffusion from a boundary at y = 0 (Eq. 17-9) is given by the Complementary Error Function erfc(y) for y > 0.

1σ

2.1%

–2

–1

0 y

1

2

3

0

1

2 y

3

982

Appendix

Special values: y 0 0.48 0.5 1 2 ∞

erf(y) 0 ≈ 0.5 0.521 0.842 0.995 1

erfc(y) 1 ≈ 0.5 0.479 0.158 0.005 0

Table A.2 The Error Function and its Complement Only available online at the book’s companion website.

983

Appendix B

Physical Constants and Units

B.1

Some Useful Constants (IUPAC)

B.2

Dimension and Units of Physical Quantities

B.3

Specific Properties of Water at 20◦ C

B.4

Specific Properties of Dry Air

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

984

Appendix

B.1

B.2

Some Useful Constants (IUPAC)

Atomic mass Avogadro’s number Boltzmann’s constant Elementary charge Faraday’s constant Gas (molar) constant

mu NA k e F R

Gravitational acceleration Molar volume of an ideal gas at 1 bar and 25◦ C Permittivity of vacuum Planck’s constant Zero of Celsius scale

g V̄ ideal gas

≅ 1.6605402×10−27 kg ≅ 6.0221367×1023 mol−1 ≅ 1.380658×10−23 J K−1 ≅ 1.60217733×10−19 C ≅ 9.6485309×104 C mol−1 = k × N = 8.314510 J mol−1 K−1 ≈ 0.083145 L bar mol−1 K−1 = 9.80665 m s−2 = 24.465 L mol−1

εo h 0◦ C

≅ 8.854187×10−12 C V−1 m−1 ≅ 6.6260755×10−34 J s = 273.15 K

Dimension and Units of Physical Quantities Dimensions are: M = mass; L = length; T = time; I = current

Physical Quantity

Name of Unit

Symbol

Amount of photons Concentration Dipole moment Electric charge Electric potential Energy

einstein molar debye coulomb volt joule volt-coulomb watt-second erg liter-atmopshere calorie electron-volt newton dyne hertz

einstein M D C V J VC Ws erg L atm cal eV N dyn Hz

Force Frequency

Dimensions ML−3 LTI TI ML2 T−3 I−1

ML2 T−2

MLT−2 T−1

SI Units mol photons 103 mol m−3 ∼ 3.34×1030 C m As J C−1 = kg m2 s−3 A−1 N m = kg m2 s−2 J J 10−7 J 101.325 J 4.184 J ∼ 1.60×10−19 J kg m s−2 10−5 N s−1

Appendix B

Physical Quantity

Name of Unit

Symbol

Length

angstrom nanometer micrometer millimeter centimeter kilometer ton (metric) pascal bar atmosphere torr millimeter mercury pounds per square inch minute hour day year (365.25 d) centipoise liter milliliter microliter

˚ A nm μm mm cm km t Pa bar atm torr mm Hg psi min h d yr cp L mL μL

Mass Pressure

Time

Dynamic viscosity Volume

B.3

Table B.3a Specific Properties of Water as a Function of Temperature Only available online at the book’s companion website.

Table B.3b Water Phase Schmidt Numbers of Solutes Only available online at the book’s companion website.

Dimensions

985

SI Units 10−10 m 10−9 m 10−6 m 10−3 m 10−2 m 103 m 103 kg N m−2 = kg m−1 s−2 105 Pa 101,325 Pa 133.32 Pa ∼ 133.32 Pa ∼ 6.89×103 Pa 60 s 3,600 s 86,400 s 31,557,600 s 10−3 kg m−1 s−1 10−3 m3 10−6 m3 10−9 m3

L M

ML−1 T−2

T ML−1 T−1 L3

Specific Properties of Water at 20◦ C

Density

ρw

Thermal expansivity

α=−

1 ρw

(

Dynamic viscosity Kinematic viscosity Specific heat (at constant pressure) Specific thermal conductivity

ηw νw = ηw /ρw cpw

Thermal diffusivity

Dthw =

Equilibrium concentration of water vapor in air in contact with liquid water

CH Oa

λw eq

2

∂ρw ∂T

λw cpw ρw

) p

998.205

kg m−3

206.78×10−6 K−1 1.002×10−3 1.004×10−6 4.18×103

kg m−1 s−1 m2 s−1 J kg−1 K−1

0.592

W m−1 K−1

0.142×10−6

m2 s−1

17.3

g m−3

986

Appendix

B.4

Specific Properties of Dry Air Mean pressure at sea level

po

Density

ρa

Kinematic viscosity

νa

Specific heat (at constant pressure) Specific thermal conductivity Thermal diffusivity

cpa λa Dtha

1.0133×105 Pa 1.293 kg m−3 1.270 1.247 1.226 1.205 1.184 0.13 cm2 s−1 0.15 1.005×103 J kg−1 K−1 2.56×102 W m−1 K−1 2.11×10−5 m2 s−1

T = 0◦ C 5◦ C 10◦ C 15◦ C 20◦ C 25◦ C T = 0◦ C 20 ◦ C T = 20◦ C T = 20◦ C T = 20◦ C

987

Appendix C

Physical Properties of Organic Compounds

Appendix C contains the names, molecular formula, molar mass (Mi ), density (ρi ), sat ), melting point (Tm ), boiling point (Tb ), vapor pressure (p∗i ), aqueous solubility (Ciw air–water partition constant (Kiaw ), octanol–water partition constant (Kiow ), acidity constant (Kia , where appropriate), and Abraham parameters of some environmentally relevant organic chemicals. Except for density (20◦ C), all data are given for 25◦ C. The data have been collected from various data compilations as cited in the bibliography accompanying the data. Table C.1 Physicochemical Properties of Organic Compounds Only available online at the book’s companion website. Table C.2 Abraham Parameters of Selected Cationic Organic Ammonium Compounds and Inorganic Ions Only available online at the book’s companion website.

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

989

Appendix D

Temperature Dependence of Equilibrium Constants and Rate Constants

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

990

Appendix

Table D.1 Temperature Dependence of Equilibrium Constants (Ki12 , Kr ) or Rate Constants (k) as a Function of the Corresponding Enthalpy Changes [Δ12 Hi (Eq. 4-34), Δr H0 (Eq. 4-58)] or Activation Energy [Ea (Eq. 21-32)]. Values Given as Percent of the Value at 25◦ C (T = 298 K). Δ12 Hi , Δr or Ea (kJ mol–1 )

0◦ C

5◦ C

10◦ C

15◦ C

20◦ C

25◦ C

30◦ C

35◦ C

40◦ C

Average factor for a change in T of 10◦ C

10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150

69.1 57.4 47.7 39.7 33.0 27.4 22.8 19.0 15.8 13.1 10.9 9.1 7.5 6.3 5.2 4.3 3.6 3.0 2.5 2.1 1.7 1.4 1.2 1.0 0.8 0.7 0.6 0.5 0.4

74.8 64.7 55.9 48.4 41.8 36.2 31.3 27.1 23.4 20.3 17.5 15.1 13.1 11.3 9.8 8.5 7.3 6.3 5.5 4.7 4.1 3.5 3.1 2.7 2.3 2.0 1.7 1.5 1.3

80.7 72.6 65.2 58.6 52.6 47.3 42.5 38.2 34.3 30.8 27.7 24.9 22.4 20.1 18.1 16.2 14.6 13.1 11.8 10.6 9.5 8.5 7.7 6.9 6.2 5.6 5.0 4.5 4.0

86.9 81.0 75.6 70.4 65.7 61.2 57.1 53.2 49.6 46.3 43.1 40.2 37.5 35.0 32.6 30.4 28.3 26.4 24.6 23.0 21.4 20.0 18.6 17.3 16.2 15.1 14.1 13.1 12.2

93.3 90.2 87.1 84.2 81.3 78.6 75.9 73.3 70.9 68.5 66.2 63.9 61.7 59.7 57.6 55.7 53.8 52.0 50.2 48.5 46.9 45.3 43.8 42.3 40.8 39.5 38.1 36.8 35.6

100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

106.9 110.5 114.2 118.1 122.1 126.3 130.5 134.9 139.5 144.2 149.1 154.2 159.4 164.8 170.4 176.1 182.1 188.3 194.6 201.2 208.1 215.1 222.4 229.9 237.7 245.7 254.1 262.7 271.6

114.0 121.7 130.0 138.8 148.2 158.2 168.9 180.3 192.6 205.6 219.5 234.4 250.2 267.2 285.3 304.6 325.2 347.2 370.8 395.9 422.7 451.3 481.9 514.5 549.3 586.5 626.2 668.6 713.9

121.3 133.7 147.2 162.2 178.6 196.8 216.8 238.8 263.0 289.7 319.2 351.6 387.3 426.6 469.9 517.6 570.2 628.1 691.8 762.1 839.5 924.7 1018.6 1122.0 1236.0 1361.5 1499.7 1652.0 1819.8

1.2 1.2 1.3 1.4 1.5 1.6 1.8 1.9 2.0 2.2 2.3 2.5 2.7 2.9 3.1 3.3 3.6 3.8 4.1 4.4 4.7 5.1 5.4 5.8 6.3 6.7 7.2 7.8 8.3

H0 ,

Table D.2 Temperature Dependence of the Ion Product of Water a, b T (◦ C) 0 5 10 15 a b

KW

pKW

T (◦ C)

KW

pKW

0.12×10–14 0.18×10–14 0.29×10–14 0.45×10–14

14.93 14.73 14.53 14.35

20 25 30 35

0.68×10–14 1.01×10–14 1.47×10–14 5.48×10–14

14.17 14.00 13.83 13.26

Data from Stumm and Morgen (1996). log KW = –4471 / T + 6.0875 – 0.01706 T (T in K).

Appendix D

991

Bibliography for Appendix D Stumm, W.; Morgen, J. J., Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters. 3rd ed.; Wiley: 1996.

993

Appendix E

Estimation of Gas-Phase Hydroxyl Radical Reaction Rate Constants of Organic Chemicals

Various methods for the estimation of gas-phase hydroxyl radical (HO∙ ) reaction rate constants for organic compounds have been proposed, ranging from estimation methods for single classes to generalized estimation methods for the complete range of organic compounds. However, gas-phase second-order rate constants for reactions of HO∙ with organic pollutants can be estimated with reasonable accuracy from simple structure-reactivity relationships using fragment methods (Kwok and Atkinson, 1995). A short description and some applications can be found in Appendix E, only available online at the book’s companion website. Bibliography for Appendix E Kwok, E. S. C.; Atkinson, R., Estimation of hydroxyl radical reaction rate constants for gas-phase organic compounds using a structure-reactivity relationship: An update. Atmos. Environ. 1995, 29(14), 1685–1695.

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

995

Index

A Abraham parameters, see poly-parameter linear free energy relationships (pp-LFERs) acid definition, 98 effect of pH on air–water partitioning, 281 effect of pH on aqueous solubility, 280 effect of pH on natural organic matter–water partitioning, 389 examples of organic acids, 102 membrane lipid–water distribution ratio and toxicity, 504–505 molar extinction coefficient as a function of pH, 783 natural organic matter–water partitioning, 388 reaction with singlet oxygen, effect of pH, 824–825 speciation in natural waters, 106 thermodynamics of acid/base equilibrium, 100 acid-catalyzed hydrolysis, see hydrolysis (chemical) acid dissociation constant, see acidity constant acidity constant definition, 100 effect of temperature, 105 estimation, Hammett relationship, 111 inductive effect of substituent, 107 mineral surfaces in water, 409 proximity effect of substituent, 109 resonance effect of substituent, 108 activation energy comparison with standard enthalpy of activation, 655 definition, 653 activity definition, 90 activity coefficient definition, 90 in water, see aqueous activity coefficient additions, microbial. See also redox reactions (enzymatic) benzylsuccinate synthase, 863 fumarate addition, 863

advection mathematical description, 198 transport distance, 199 adsorption from air to surfaces, see surface–air partitioning adsorption from water to surfaces, see surface–water partitioning and ion exchange adsorption and surface complexation aerobic conditions, see redox conditions aerosol–air partition coefficient apparent from experimental data, 446 pp-LFERs for prediction, 451 temperature dependence, 449 aerosol–air partitioning simple modeling approach for quantification, 447 aerosol organic matter definition, composition, 445, 447 aerosols composition, 130, 444 concentrations, 129, 443 primary, definition, 442 residence times, 444 secondary, definition, 442 size distribution, 443 aggregate state definition, 239 phase diagram, 240 air composition, 129–130 specific properties, 986 air–water exchange linear rate constant, 598–599 air–water exchange in flowing waters influence of wind versus flow velocity, 603 large roughness model, 600, 602 small roughness model, 600–601 air–water exchange velocity air-phase controlled, 587, 592 estimated from evaporation rates of pure organic liquids, 594 estimated from evaporation rates of water, 586 influence of Schmidt number, 589 influence of water temperature, 608

influence of wind speed, 592, 595 overall rate constant, 597 water-phase controlled, 587, 596 air–water interface as bottleneck boundary, 583 boundary layer model (Deacon), 588 exposure time, 584 smooth and rough water surface, 585 surface renewal model, 599 thickness of boundary layer, 584 as wall boundary, 583 air–water partition constant approximation from vapor pressure and aqueous solubility, 266 definition, 265 effect of dissolved salt, 277 effect of organic cosolvent, see organic cosolvent effect of temperature, 275 enthalpic and entropic contributions to the free energy of air–water partitioning, 267–268 pp-LFER for estimation the enthalpy of air–water partitioning, 275 prediction using a bond contribution method, 271 prediction using a pp-LFER, 270 alcohol dehydrogenases, 753–754 Amagat’s law, 95 anaerobic conditions, see redox conditions anilines chemical oxidation, 745–746 anoxic conditions, see redox conditions antioxidants, 743 Antoine equation, 244 apolar compounds definition, 40, 218 aqueous activity coefficient and aqueous solubility, see aqueous solubility concentration dependence, 265 definition, 262 effect of dissolved salt, 276 effect of organic cosolvent, see organic cosolvent effect of temperature, 274 at saturation versus infinite dilution, examples, 266

Environmental Organic Chemistry, Third Edition. Ren´e P. Schwarzenbach, Philip M. Gschwend, and Dieter M. Imboden. Copyright © 2017 John Wiley & Sons, Inc. Published 2017 by John Wiley & Sons, Inc. Companion website: www.wiley.com/go/Schwarzenbach/EnvironmentalOrganChem3e

996

Index

aqueous solubility and aqueous activity coefficient of gases, 264 and aqueous activity coefficient of liquids, 263 and aqueous activity coefficient of solids, 263 definition, 261 effect of dissolved salt, 276 effect of organic cosolvent, see organic cosolvent effect of temperature, 274 enthalpic and entropic contributions to the free energy, 267–270 thermodynamic considerations, 262 thermodynamic cycle, 261 aromaticity definition, 35 examples, 36 Arrhenius equation definition, 653 use for describing the temperature dependence of reaction rate constants, 653 atmosphere air pressure and density, 126 chemical composition, 129–130 freons, 127 global circulation, 128 ozone, 127 transport and mixing, 127 vertical structure, 125 atmospheric aerosols, see aerosols atomic mass of elements present in organic compounds, 21

B base definition, 98 effect of pH on air–water partitioning, 281 effect of pH on aqueous solubility, 281 effect of pH on natural organic matter–water partitioning, 390 examples of organic bases, 104 molar extinction coefficient as a function of pH, 783 natural organic matter–water partitioning, 390 speciation in natural waters, 106 thermodynamics of acid/base equilibrium, 100 base-catalyzed hydrolysis, see hydrolysis (chemical) baseline toxicity definition, 503 sp-LFERs for prediction, 504 basicity constant, see acidity constant binominal distribution approximation by de Moivre and Laplace, 528 definition, 526 bioaccumulation in aquatic systems, 485 as a dynamic process, 488 in terrestrial systems, 498

bioaccumulation factor (BAF) definition, 486 examples, 492, 500 bioavailability, 865 bioconcentration factor (BCF) definition, 487 biological phase–air partition coefficient definition, 476 pp-LFERs for prediction, overview, 477 temperature dependence, 484 biological phase–water partition coefficient definition, 476 pp-LFERs for prediction, overview, 477 temperature dependence, 484 biological phases definition, overview, 473–474 globular proteins, 481 lignin, 483 membrane lipids, 477 plant lipids, 480 polysaccharides, 483 storage lipids, 477 structural proteins, 481 biomagnification aquatic food webs, 495 definition, 487 terrestrial food webs, 501 biomagnification factor (BMF) aquatic systems, 492, 494 definition, 487 terrestrial systems, 500 biota global mass and production, 155 biota-sediment/soil accumulation factor (BSAF) definition, 487 examples, 492, 500 biotransformation rates effect of bioavailability, 865 effect of uptake kinetics, 865 Michaelis–Menten enzyme kinetics, 652, 866, 873 Michaelis–Menten rate coefficient, 866, 871 Monod-case second order rate coefficient, 879 Monod growth kinetics, 874 overview, 864 biotransformations co-metabolism, 853, 867 competitive inhibitors, 853 dependence on environmental conditions, 848 fortuitous biotransformation, 852 hydrolysis, 858 initial biotransformation, 858 natural attenuation, 847 syntropy, 848 bioturbation at sediment–water interface, 625 bipolar compounds definition, 40, 218

black carbon in aerosols, 444, 447 definition, 375 quantification of black carbon–water partitioning, 386 sp-LFER for predicting black carbon–water partition coefficient, 396 visualization of black carbon–water partitioning, 386–387 boiling point definition of normal and standard boiling point, 241 dependency on pressure, 241 bond, see chemical bond bottleneck boundary around a sphere, 580 at an interface, 564 definition, 561 exchange velocity, 563 simple bottleneck, 562 three-layer bottleneck boundary, 579 two-layer at interface, 565 boundary bottleneck boundary, 560 hybrid boundaries, 572 interface boundary, 560 non-interface boundary, 560 wall boundary, 560 boundary condition for diffusion/advection/reaction equation, 201 for solution of second Fick’s law, 529 box models, 175 breakthrough time in unsaturated soil, 628 Brønsted relationship definition, 693–694 relating chemical hydrolysis rate constants of carbamates, 694 Brownian motion, 526 BTEX compounds (benzene–toluene–xylenes) definition, 51, 53 isotope fractionation during microbial transformation, 915 bulk diffusivity definition, 542 in sediments, 621 in unsaturated soil, 627 bulk enrichment factor, see compound-specific isotope analysis (CSIA)

C carbonate radical formation, 819 reaction with organic compound, 836 carboxylic acid esters abiotic hydrolysis, see hydrolysis (chemical) chemical bond bond angles, 31

Index

bond enthalpies, 26 bond lengths, 26 covalent bond, 23 double bond, 24 π-bond, 34 single bond, 23 triple bond, 24 chemical potential definition, 84 chemisorption adsorption via surface bonding, 408, 426 chromophore definition, 779–780 in organic compounds, examples, 780–784 chromophoric dissolved organic matter (CDOM) in indirect photolysis excitation in natural water body, 817 reaction of 3 CDOM∗ with organic compounds, 826–827 as source for reactive oxygen species, 817–818 commitment to catalysis, 913 compartment definition used in modeling, 123–124 global, 124 complementary Error function definition, 980 relation to diffusion at a wall, 530–531, 568 compound-specific isotope analysis (CSIA). See also stable isotopes in organic compounds additional factors influencing experimental bulk enrichment factors, 913 apparent kinetic isotope effect (AKIE), definition, 912 assessing the extent of transformation, 907, 918–919 deriving AKIE values from bulk enrichment factors, 912 dual isotope plots, 909–910 experimental AKIE values (ranges) for important transformation reactions, 929 isotopic signature of compound, definition, and determination for a given element, 902–903 isotopic signature of compound, use as forensic tool, 904–905 kinetic isotope effect, definition, 907 kinetic isotope effect, interpretation, 908–909 Rayleigh equation and bulk enrichment factor, 905–906 conjugate acid definition, 98 conjugate base definition, 98 continuous models definition, 194 diffusion-advection-reaction equation, 200, 202

cosolvent effect, see organic cosolvents coupled FOLIDE, see first-order linear inhomogeneous differential equation critical time at wall boundary with boundary layer, 576

D Damk¨ohler number, 201 Debye energies definition, 38 decadic beam attenuation coefficient, 778, 790, 798 dehydrogenase definition, 854 Michaelis–Menten kinetics, 868 delocalization of electrons definition, 34 examples, 36 delta function definition, 530 detergents definition, 60 examples, 61 diffusion. See also molecular diffusion length scale, 547 mathematical description, 198 one-sided wall boundary, 530 symmetric at wall boundary, 530 transport distance, 199 two-sided wall boundary, 532 two-sided with different diffusivities, 533 diffusion coefficient. See also molecular diffusion in air, 535–538 in porous media, 541–543 in water, 538–541 relation to mean free path and mean velocity, 529 relation to random walk, 529 turbulent in atmosphere, 200 turbulent in water, 200 dilution rate definition, 176 direct photolysis definition, 775 effect of ice surfaces, 804 effect of particles, 803 effect of soil surfaces, 803 physical and chemical processes of excited species, 785 quantification in natural water body, 801 reaction quantum yield, definition, 787 direct photolysis rate constant, 801 dispersion due to flow, 549 rivers, 143, 557, 963

997

dissolved organic carbon (DOC) concentration in river water, 144 concentration in seawater, 136 definition, 137 distribution ratio of organic acids and bases between air and water, 281 between natural organic matter and water, 388, 391 between octanol and water, 504 definition, 216 dry deposition of particle-bound compound definition, 454 dry versus wet deposition of particle-bound compounds, 459 simple model for quantification, 455

E Eddy diffusion, see turbulent diffusion coefficient effective diffusivity in sediments, 621 sorbing chemical in porous media, 544 in unsaturated soil, 626, 628 Einstein–Smoluchowski law, 199, 526 electrode potential in soil, 152 electron donor-acceptor interactions definition, 39 electronegativity definition, 27 electronic configuration of elements electron shells of some elements, 21 elemental carbon. See also black carbon in aerosols, 447 elemental composition of a compound, definition, 20 elimination β-elimination, 641, 668–669 β-elimination versus nucleophilic substitution, 669–670 reductive dihaloelimination, see polyhalogenated alkanes and alkenes enthalpy definition, 84 enthalpy of activation, see standard enthalpy of activation enthalpy of phase transfer, see standard enthalpy of phase transfer entropy definition, 84 entropy of activation, see standard entropy of activation entropy of phase transfer, see standard entropy of phase transfer enzyme-catalyzed hydrolysis reactions examples, see hydrolysis (enzymatic) general comments, 695

998

Index

enzyme-catalyzed redox reactions, see redox reactions (enzymatic) enzymes as catalysts, 851 at the sediment–water interface, 620 constitutive enzyme, definition, 857 co-substrates, 864 dead-end metabolites, 856 inducible enzyme, definition, 857 lag period, definition, 857 ortho- and meta- aromatic ring cleavage, 856 substrate specificity, 852, 854 suicide metabolites, 856 equilibrium partition coefficient, see partition coefficient equilibrium partition constant, see partition constant equilibrium partitioning in an aquarium, 954 in a soup bowl, 955 multiple-phase, 953 two-phase, 952 equilibrium reaction constant and standard free energy of reaction, 645 temperature dependence, 645, 990 (Appendix Table D.1) error function, Appendix Table A.2 evaporation global volumes, 131 evaporation of organic liquid, 308, 607 excess enthalpy in aqueous solution, 267–268 definition, 91 excess entropy in aqueous solution, 267–268 definition, 91 excess free energy in aqueous solution, 267–268 definition, 91 exchange flux at simple bottleneck boundary, 563 at simple wall boundary, 569 at two-sided wall boundary, 570–571 by fluid motion, 184 definition, 183 exchange velocity, 195–196, 584, 950 linear, 185 mathematical description, 185 overall at two-layer bottleneck boundary, 566 time-to-steady state, 185 excited chemical species physical deactivation, 785 chemical reactions, 776, 785–786 exposure assessment definition, 6 estimation of bioaccumulation: 490, 501 external force definition in modeling, 169

F Ferrel cells, 128 Fick’s laws first Fick’s law, 196, 198 second Fick’s law, 198 time-dependent solution of second Fick’s law, 529 first-order kinetics definition, 651 first-order linear inhomogeneous differential equation (FOLIDE) coupled (coupled FOLIDE), 186, 188 definition, 177–178 solution, 177–178 steady state, 180 time-to-steady state, 179 first-order rate constant definition, 177 temperature dependence, 653 first-order rate constant for describing air–water exchange, 599, 949 biotransformations, 865, 871, 879 direct photolysis in water, 801 dry deposition, 455 flushing (dilution), 176, 364, 949 hydrolysis reactions, 680, 682 indirect photolysis in water, 828 reactions with nucleophiles, 680 sediment–water exchange, 949 sedimentation, 365, 949 wet deposition, 457 first-order reaction constant definition, 651 temperature dependence, 653 flame retardants definition, 56 examples, 57

free energy definition, 84 free energy of activation, see standard free energy of activation free energy of phase transfer, see standard free energy of phase transfer free energy of reaction. See also standard free energy of reaction definition, 644 and reduction potential difference, 648–649. See also Nernst equation Froude number influence on air–water exchange in rivers, 603 fugacity definition, 84 of liquids and solids, 89 use for evaluation of bioaccumulation in aquatic systems, 493–494 use for evaluation of bioaccumulation in terrestrial systems, 500–501 functional groups definition, 36 examples, 37

G Galton box, 526 gas exchange, see air–water exchange gas–liquid partitioning general considerations, 218 Gauss’ theorem, 197 Gaussian distribution, see normal distribution Gibbs free energy, see free energy

FOLIDE, see first-order linear inhomogeneous differential equation fraction black carbon, 137, 386

glutathione, 858 groundwater chemical composition, 153 flow, 153 hydraulic conductivity, 153 saturated zone, 152 transport and transformation of chemicals, 722, 966

fraction as dissolved species in water, definition, 361

H

flushing rate definition, 176

fraction organic carbon definition, 137, 372 fraction in particulate phase in air, definition, 449 in water, definition, 361 fraction as vapor species in atmosphere, definition, 449 fragment contribution method for estimating Henry constants, 271 for estimating octanol–water partition constants, 298 for estimating reaction rates with hydroxyl radical in air, 833, Appendix E general comments, 226

Hadley cells, 128 half reaction definition, 647 Hammett substituent constants, see Hammett relationship Hammett relationship estimation of acidity constants, 113 estimation of chemical hydrolysis rate constants, 692–693 substituent constants, 112, 115, 828 hard and soft Lewis acids and bases (HSAB), 673 hemimicelles formation on surfaces in water, 424

Index

Henry’s law constant, see air–water partition constant hexadecane–air partition constant correlation with molar volume, 220 correlation with octanol–air partition constant, 227 use in pp-LFERs, 230 values for specific compounds, Appendix Table C.1 humic substances as surrogates for natural organic matter in sorption processes, 371, 378 definition, 137 hydrogen bonding definition, 28 hydrogen donor–acceptor interactions definition, 39 hydrolases, see hydrolysis (enzymatic) hydrolysis (chemical). See also nucleophilic substitution reaction amides, 687 carbamates, base-catalyzed, 688–689 carbamates, Brønsted relationship, 694 carbamates, overview, 687 carboxylic acid derivatives, overview, 680 carboxylic acid esters, acid-catalyzed, 682–683 carboxylic acid esters, base-catalyzed, 685 carboxylic acid esters, effect of pH, 681 carboxylic acid esters, Hammett relationship, 692–693 carboxylic acid esters, neutral, 686 carboxylic acid esters, overview of mechanisms, 684 phosphoric and thiophosphoric acid esters, 677–678 polyhalogenated hydrocarbons, 669–671 sorbates bonded to natural solids, 427 hydrolysis (enzymatic) carboxylic acid esters, mechanisms, 698, 700 general remarks, 695 hydrolase kinetics, 860 microbial, 858 phosphoric acid esters, 697 polyhalogenated alkanes, 696 SN 2 mechanism, 696–697 hydroxyl radical in the atmosphere formation, 830–831 rate constants for reaction with organic compounds, 832, Appendix E steady-state concentrations, 817, 831 hydroxyl radical in water. See also reaction with hydroxyl radical in water formation, 818 rate constants for reaction with organic compounds, 822 sources, 818 steady-state concentrations in natural water body, 817

I indirect photolysis in water definition, overview, 816–819 formation of reactive oxygen species, 818 kinetic approach, 819–820 quantification in natural water body, 820–821 reaction with excited chromophoric dissolved organic matter (3 CDOM∗ ), 826–827 reaction with hydroxyl radical, 821–822 reaction with singlet oxygen, 823–825 initial condition for diffusion-advection-reaction equation, 201 for solution of second Fick’s law, 529 integrated flux ratio at wall boundary with boundary layer, 575 interface boundary, 560 sediment-water interface, 618 simple bottleneck, 564 soil–air interface, 629 intermolecular interactions, see molecular interactions internal process definition in modeling, 169 ion exchange adsorption, 414 Abraham solute parameters for charged molecules, 418, Appendix Table C.2 anion exchange capacity (AEC), 408 cation exchange capacity (CEC), 408 co-ion, 409, 422 competing ion, 409, 414 electrostatic free energy, 410, 414, 424 hydrophobic free energy of ion exchange adsorption, 414, 417, 422 natural organic matter as an ion exchange sorbent, 413, 419 outer sphere complex, 428 pp-LFER to estimate the ion exchange sorption coefficient, 418 properties of mineral surfaces in water, 409 sorption coefficient due to ion exchange, 407, 414, 430 ion product of water definition, 103 temperature dependence, Appendix Table D.2 iron-reducing conditions, see redox conditions isomers cis/trans isomers, 33 definition, 22 geometric isomers, 33 optical isomers, 32 stereoisomers, 31 structural isomers, 23 isotope fractionation during transformation of atrazine under oxic conditions, 922–923 BTEX under oxic and anoxic conditions, 915–919 MTBE under oxic conditions, 909–910 nitroaromatic compounds under oxic and anoxic conditions, 906, 919–921

999

polychlorinated C1 –, and C2 –alkanes under oxic and anoxic conditions, 923–924 TCE and PCE under anoxic conditions, 925–928 isotopes in organic compounds. See also compound-specific isotope analysis (CSIA) definition, 20 determination of isotopic signature for a given element, 902–903 isotopologues and isotopomers, 898–901 ratios in organic compounds, 21, 899 isotopic signature, see compound-specific isotope analysis (CSIA)

K Keesom energies definition, 38 kinetic isotope effect. See also compound-specific isotope analysis definition, 907 interpretation, 908–909 Knudsen effect, 541

L lakes areas, 139 chemical composition, 141 deep water mixing, 140 depths, 139 mixing and stratification, 139 models of different complexity, 171, 173–174 one-box model, 181 residence time of chemical, 956 seasonal stratification, 140 thermal bar, 141 two-box model, 189, 948, 956 volumes, 138 leaving group. See also hydrolysis, nucleophilic substitution, and elimination overview, 640 relative “goodness”, of halides as, 672–673 ligand adsorption of organic ligands to solid surfaces in water, 427 light absorption by organic compound Beer-Lambert law, 778 bond energies versus light energies, 777 molar extinction coefficient, 778–779 UV-vis spectra, 779 light absorption of organic compound in natural water body as a function of season and geographical latitude, example, 797 near-surface specific rate of light absorption, 791–792, 795–796 specific rate of light absorption in well-mixed water body, 791, 797–798 use of screening factor for prediction, 800

1000

Index

light and light attenuation in a natural water body decadic beam attenuation coefficient, 778, 790, 798 diffuse light attenuation coefficient, 789–790 light absorption in water body per unit surface area, 790 light absorption in water body per unit volume, 790 spectral photon fluence rate of sunlight, definition and data, 788–789, 792–793, 795 light screening factor definition, 799 use for prediction of light absorption by compound in water body, 800 lignin, see biological phases linear free-energy relationships. See also single parameter-linear free energy relationships and polyparameter-linear free energy relationships general comments, 225, 656 lipid–air partition coefficient pp-LFERs for prediction, 478 temperature dependence, 484 lipid–water partition coefficient comparison with protein–water partition coefficient, 482 comparison of storage lipid–water and membrane lipid–water partition coefficient, 479 pp-LFERs for prediction, 478 temperature dependence, 484 lipids, see biological phases liquid mixtures, see organic liquid mixtures long-range transport potential (LRTP) coupled atmosphere-ocean model, 970 definition, 969 London dispersive forces definition, 38 in gas-liquid partitioning, 219, 248, 270

M mass balance box models, 176 in a lake, 949 in a river, 962 mathematical model, see model matrix definition in environmental systems, 124 mean free path relation to diffusion coefficient, 529, 535 medium definition in environmental systems, 124 melting point. See also aggregate state definition, 239 membrane lipid–water partition coefficient and baseline toxicity, 504 pp-LFER for prediction, 478

membrane lipid–water partition ratio of acids and baseline toxicity, 505 definition, 504 methanogenic conditions, see redox conditions Michaelis–Menten enzyme kinetics, see biotransformation rates microorganisms active uptake systems, 865 dual limiting growth substrates, 876 exponential growth, 874 growth-limiting chemical, 875 growth yield, 878, 881 horizontal gene transfers, 850 maximum cell growth rates, 881 microbial cell dry mass, 880 passive diffusive uptake, 865 plasmids, 850 porins, 866 mineral surface–air partition constant, see surface–air partition constant mineral surface–air partitioning, see surface–air partitioning mineral surface–water partition constant, see surface–water partition constant mineral surface–water partitioning, see surface–water partitioning mineral surfaces characteristics, 323, 409 model applications, 947 box, 174 continuous, 194 definition, 167, 170 dynamic, 170 molar extinction coefficient, see light absorption by organic compound molar mass, see molecular weight molar volume estimation, 221 use in estimation of molecular diffusivities, 535–541 use in pp-LFERs, 228 values of McGowan molar volumes, Appendix Table C.1 mole fraction definition, 87 molecular diffusion and self-diffusion, 534 definition, 534 in polyethylene membranes, 554 molecular diffusion in air approximation by Fuller et al., 537 approximation by molar mass and volume, 536 effect of temperature and pressure, 553 estimation by different methods, 538 molecular theory of gases, 535 molecular diffusion in porous media effect of porosity and tortuosity, 541

sorbing chemical, 544–545 molecular diffusion in water approximation by molar mass and volume, 538–539 effect of viscosity, 560 estimation by different methods, 560 relation by Othmer and Thakar, 539 relation by Wilke and Chang, 540 molecular formula of compound definition, 20 molecular interactions classification of organic compounds, 218 definitions, 38, 40 governing bulk phase partitioning, 217 governing vapor pressure, 246 molecular structure, see structure of compound molecular weight definition, 20 Monod kinetics, see biotransformation rates monopolar compounds definition, 40, 218 multi-box model, 182, 195

N NAPL (non-aqueous-phase liquid) dissolution into aqueous phase, 611 narcosis, see baseline toxicity natural organic matter (NOM). See also organic matter (OM) composition and structural diversity, 371 natural organic matter–water partition coefficient definition, 376 effect of dissolved salts and pH, 384 effect of temperature, 383 effect of the presence of black carbon, 385 pp-LFERs for prediction, 379–380 sp-LFERs for prediction, 378 variability, 377 natural organic matter–water partitioning effect of black carbon, 385 introduction, 371 ion exchange sorbent, 413, 419 of acids, 388 of bases, 390 surface complexation sorbent, 426 Nernst equation, 648 nitrate-reducing conditions, see redox conditions nitroaromatic compounds (NACs) correlation between reduction rate and one-electron standard reduction potential, 735–736 isotope fractionation during abiotic and microbial transformation, 919 one-electron reduction potential, 733

Index

reaction quantum yields in direct photolysis, 802 reduction, general considerations, 731–732 reduction mediated by NOM constituents, 732, 736–737 reduction mediated by reduced iron species, 737–738 specific adsorption to clay mineral surfaces, 338 non-interface boundary, 560 nonlinear reaction nonlinear degradation in reactor, 208 normal distribution definition, 528, 980 relation to random walk, 528 solution of diffusion equation, 530 nucleophile classification as hard and soft Lewis acids and bases, 673 definition, 639 relative effectiveness (“goodness”), 671–672, 675 nucleophilic substitution reaction in enzymatic hydrolyses, 858–861, 869–871 mechanistic considerations, 665 of alkyl halides, 667, 669 of phosphoric and thiophosphoric acid esters, 677–678 overall rate law, 679 overview, 639–640 SN 1- and SN 2-mechanisms, 665–666 SN i-mechanism, 676 Swain–Scott relationship, 672 versus β-elimination, 669–670

O ocean currents, 133 formation of deep water, 135 global circulation, 133, 135 global volumes, 131 long-range transport potential (LRTP), 969 mean residence times of water, 133 vertical mixing, 133 vertical stability of water column, 135 octanol–air partition constant correlation with hexadecane–air partition constant, 227 correlation with molar volume, 220 dry versus wet octanol, 295 effect of temperature, 296 estimation of enthalpy of octanol–air partitioning from pp-LFER, 297 pp-LFER for estimation, 294 octanol–water partition constant atom/fragment method for estimation, 298 baseline toxicity, 504 correlation with hexadecane–water partition constant, 227

correlation with molar volume, 220 effect of temperature, 296 estimation of enthalpy of octanol–water partitioning from pp-LFER, 298 estimation of lethal concentrations, 504 estimatation of polysaccharide-water coefficients, 483 pp-LFER for estimation, 230, 294 use to estimate organic carbon-water coefficients, 378 olive oil–air partition constant correlation with octanol–air partition constant, 296 pp-LFER for estimation, 294 olive oil–water partition constant correlation with octanol–water partition constant, 295–296 pp-LFER for estimation, 294 one-box model aquatic systems, 949 definition, 175 lakes, 181 linear one-box model with one state variable, 175 mass balance, 176 organic acid, see acid organic base, see base organic cosolvent definition, 302 effect on activity coefficient and solubility, 303–304 effect on bulk phase–water including air–water partitioning, 307 ethanol as cosolvent, pp-LFER quantifying the effect on aqueous activity coefficient, 306 examples, 304 quantification of cosolvent effect on activity coefficient, 305 organic liquid–air partition constant definition, 291 pp-LFER for estimation, examples, 294 organic liquid–air partitioning general considerations, 218 thermodynamics, 291 organic liquid mixtures dissolution into water, 309 evaporation, 308 organic liquid–water partition constant definition, 292 pp-LFER for estimation, examples, 294 role of aqueous activity coefficient, 292 organic liquid–water partitioning general considerations, 224 thermodynamicsx, 292 organic matter (OM) definition, 137 organic matter–water partition coefficient, see natural organic matter–water partition coefficient

1001

organic solvent–water mixtures, see organic cosolvents organic solvents BTEX compounds, 53 as groundwater pollutants, 53 mole fraction when saturated with water, examples, 293 polychlorinated C1 –, and C2 –hydrocarbons, 54, 966 tertiary alkyl ethers, 54 volatile methylsiloxanes (VMS), 55 organism–air partition coefficient definition, 475 modeling approach, 477 organism–water partition coefficient definition, 475 modeling approach, 477 organisms chemical composition, 471, 474 output definition in modeling, 169 oxic conditions, see redox conditions oxidation states of elements in organic compounds definition, 29 determination, 30, 716 oxidations, microbial, 861. See also redox reactions (enzymatic) oxygenase definition, 854 electrophilic oxygen, 861 use of metals, 861

P P450 monooxygenase, 750 PAHs, see polycyclic aromatic hydrocarbons PCBs, see polychlorinated biphenyls particulate organic matter (POM), see natural organic matter partition coefficient. See also aerosol–air partition coefficient, biological phase–air partition coefficient, biological phase–water partition coefficient, lipid–air partition coefficient, lipid–water partition coefficient, natural organic matter–water partition coefficient, organism–air partition coefficient, organism–water partition coefficient, polysaccharide–water partition coefficient, protein–air partition coefficient, protein–water partition coefficient versus partition constant, definition, 216 partition constant definition, 93, 216 effect of temperature, 96, Appendix Table D.1 molar concentration basis, 95

1002

Index

partition constant (Continued) mole fraction basis, 94. See also air–water partition constant, hexadecane–air partition constant, octanol–air partition constant, octanol–water partition constant, olive oil–air partition constant, olive oil–water partition constant standard free energy of transfer, 94 passive polyethylene sampler equilibration time, 633, 958 Peclet number, 202 penetration depth diffusion into a wall boundary, 531 sediment–water interface, 622 persistent organic pollutants (POPs) definition, 47 examples, 48 personal care products definition, 63 examples, 66 pesticides definition, 66 examples, 67 hydrolysis, 680 petroleum hydrocarbons aliphatic and olefinic, 50 BTEX (benzene–toluene–xylenes), 51, 53. See also BTEX compounds definition, 49 polycyclic aromatic hydrocarbons (PAHs), 51 weathering, 52 pharmaceuticals definition, 63 examples, 64 phase definition in environmental systems, 124 phenols chemical oxidation, 743–744, 765 photolysis, see direct photolysis, indirect photolysis photooxidants in natural waters introduction, overview, 816–819 photooxidants in the atmosphere introduction, overview, 816–817, 830 plant lipids, see biological phases polar cells, 128 polar interactions definition, 39 polychlorinated methanes and ethanes, see polyhalogenated alkanes and alkenes polycyclic aromatic hydrocarbons (PAHs) aerosol-air partition coefficients, 445 black carbon-water partition coefficients, 386 definition, 51 mineral surface-water partitioning, 335 organic carbon-water partition coefficients, 378 reaction quantum yields in direct photolysis, 802

UV-vis spectra, 781 polychlorinated biphenyls (PCBs) bioaccumulation in sediment dwelling organisms, 492 biomagnification in aquatic food chains, 497 definition, 48 historical record in sediment, 2 solubility of mixture in water, 310 sp-LFER for estimating SOM-water partition coefficients, 378 polyfluorinated compounds definition, examples, 59 polyhalogenated alkanes and alkenes β-elimination, 668, 670 enzymatic reduction of chlorinated ethenes by cobalt-containing enzymes, 755–756 hydrolysis, 669–671 isotope fractionation during abiotic and microbial transformation, 923, 966 one-electron reduction potential, 740 reductive (chemical) dehalogenation, 738 poly-parameter linear free-energy relationships (pp-LFERs) for assessing partitioning between bulk phases, general approach, 228 for assessing partitioning between surfaces and air, general approach, 328 H-acceptor (e− -donor) and H-donor (e− -acceptor) properties of various surfaces, 329–330 solute descriptors (Abraham parameters) for charged molecules, 418 solute descriptors (Abraham parameters) for neutral molecules, 230 van der Waals surface descriptors for various surfaces, 329 poly-parameter linear free energy relationships for prediction of aerosol–air partition coefficients, 451 air–water partition constants, 270 enthalpy of air–water partitioning, 275 enthalpy of octanol–air partitioning, 297 enthalpy of octanol–water partitioning, 298 ion exchange coefficient, 417–419 lipid–air partition coefficients, 478 lipid–water partition coefficients, 478 natural organic carbon–water partition coefficients, 379–380 octanol–air partition constants, 294 octanol–water partition constants, 294 olive oil–air partition constants, 294 olive oil–water partition constants, 294 protein–air partition coefficients, 478 protein–water partition coefficients, 478 Setschenow (salting out) constants, 279 vapor pressure of (subcooled) liquid, 249 water surface–air partition constants, 332 polysaccharides, see biological phases polysaccharide–water partition coefficient sp-LFER for prediction, 483

POPs, see persistent organic pollutants pore water chemical composition in soils, 151 transport in sediment: 623 porosity definition, 146 effect on diffusion in porous media, 541 soils, 150 pp-LFERs, see poly-parameter linear free energy relationships precipitation global, 131 primary kinetic isotope effect, see kinetic isotope effect protein, see biological phases protein–air partition coefficient pp-LFERs for prediction, 478 temperature dependence, 484 protein–water partition coefficient comparison with storage lipid–water partition constant, 482 pp-LFERs for prediction, 478 pseudo-first-order reaction constant, see first-order reaction constant

Q quantitative polymerase chain reactions (qPCR), 863, 872 quantitative structure–activity relationships (QSARs) definition, 504 for prediction of toxicity, 504–505 quantum yield, 787. See also reaction quantum yield

R random motion, 526 Raoult’s law applications, 308, 310 definition, 90 Rayleigh equation, see compound-specific isotope analysis (CSIA) reaction kinetics introduction, general rate law, 650 reaction quantum yield definition, 787 of organic compounds, examples, 802 reaction quotient definition, 645 reaction rate definition, 650 impact of solution composition, 657 reaction rate constant definition, 650 temperature dependence, 653, Appendix Table D.1

Index

reaction with hydroxyl radical in the atmosphere, see hydroxyl radical in the atmosphere reaction with hydroxyl radical in water, see indirect photolysis in water reactions with nucleophiles. See also nucleophilic substitution reactions, hydrolysis definition, overview, 639–640 reaction with singlet oxygen in water, see indirect photolysis in water reactive oxygen species (ROS), see indirect photolysis reactive sites identification of within a molecule, 638, 859 reactor half-life of chemical, 206 nonlinear reaction, 208 one-box model, 206–207 Redfield ratio, 136 redox conditions determining processes in the environment, 721–722 range in soils, 152 sequence in soils and sediments, 721–722 redox potential, see reduction potential redox reactions (chemical) definition, overview, 641–642, 718 introductory comments, 716 kinetic considerations, 730 oxidation of anilines, see anilines oxidation of phenols, see phenols reduction of nitroaromatic compounds, see nitroaromatic compounds (NACs) reductive dehalogenation of polyhalogenated alkanes and alkenes, see polyhalogenated alkanes and alkenes thermodynamic considerations, 723, 725, 728 redox reactions (enzymatic) by carboxylation, 752–753 by fumarate addition, 751–752 oxidation using O2 as co-substrate, general comments, 747–748 oxidation with cytochrome P450 monooxygenase, 749–750 reduction by alcohol dehydrogenase, 754 reduction of polyhalogenated compound by cobalamines, 755–756 reduction potential definition, 648 of a hydrogen sulfide solution as a function of pH, 727 reduction potential difference and free energy of reaction, 647–648 reduction reactions, microbial nitroreductases, 862 reductive dehalogenases, 862 reduction reactions, see redox reactions

reference state definition, 88 relative humidity (RH) effect on H-acceptor (e− -donor) and H-donor (e− -acceptor) properties of various surfaces, 329–330 effect on van der Waals properties of various surfaces, 329–330 effect on water surface coverage of a mineral surface, 325 Renkin effect, 541 retardation of organic compound transport in porous media impact on PCE transport in groundwater, 969 quantification of, 363–364 risk assessment definition, 4 rivers chemical composition, 143–144 chemical pollution, 960 discharge and length, 142 dispersion, 143, 963 effect of dilution, 965 mass balance model, 962 mixing, 143 sediment–water exchange, 966 runoff global flow, 131

S salinity lakes, 134 ocean, 134 salting-out definition, 276 quantification, see Setschenow constant Schmidt Number as a function of water temperature, 590 definition, 589 influence on air–water exchange velocity, 589 seawater chemical composition, 135–136 organic carbon, 137 salinity, 136, 277 secondary kinetic isotope effect, see kinetic isotope effect sedimentation of organic compounds quantification, 365 sediment organic matter (SOM), see natural organic matter sediment–water exchange modeling, 618, 951 sediment–water interface as one-sided interface boundary, 618 bioturbation, 625 boundary layer, 624 penetration depth, 622

1003

sediments accumulation rates, 144 composition, 147 equivalent grain diameter of sediment material, 601 exchange with overlying water, 146, 618 porosity, 145 self-diffusion, 534 Setschenow constant definition, 276 examples, 279 prediction using a pp-LFER, 279 single-parameter linear free energy relationships (sp-LFERs) correlation between surface–air partition constant and (subcooled) liquid vapor pressure, 327 for prediction of black carbon–water partition coefficient, 396 for prediction of natural organic carbon–water partition coefficients, 378 for prediction of polysaccharide–water partition coefficients, 483 general considerations, 226 singlet oxygen in water. See also reaction with singlet oxygen in water formation, 818 steady-state concentrations, 817 SN 1-, SN 2-, SN i-mechanisms, see nucleophilic substitution reactions soil electrode potential, 152 fulvic acids, 150 horizons, 149 humic acids, 150 input from the atmosphere, 632 mineral composition, 150 mineral properties, 409 organic matter, 150 pore water chemical composition, 151 porosity, 150 redox conditions and pH, 152 saturated, 148 structure and composition, 148 transport at surface, 629–630 unsaturated, 148 soil organic matter (SOM), see natural organic matter solid–water distribution coefficient complex nature, 358, 407 definition, 357 solubility in water, see aqueous solubility sorption and retardation in porous media, 363 and sedimentation, 364 fraction in dissolved form, 360–361 fraction in particulate form, 360–361 from air to aerosols, 445

1004

Index

sorption (Continued) from water to mineral surfaces, see ion exchange adsorption, surface complexation, surface–water partitioning from water to natural organic matter, see natural organic matter–water partitioning general introduction, 352 various sorbent–sorbate interactions, 353 sorption isotherms complex, 423, 426 Freundlich, 355 Langmuir, 356, 416, 430 linear, 355, 416 various types, 354 sp-LFERs, see single-parameter linear free energy relationship specific rate of light absorption of compound, see light absorption of organic compound in a water body stable isotopes in organic compounds, see isotopes in organic compounds standard deviation relation to diffusion coefficient, 529 standard enthalpy of activation definition, 655 hydrolysis of alkyl halides, 667 standard enthalpy of phase transfer general definition, 97 of air–water partitioning, 267–268 of aqueous solubility, 267–268 of fusion, 244 of octanol–air partitioning, estimation from pp-LFER, 297 of octanol–water partitioning, estimation from pp-LFER, 298 of sublimation, 244 of vaporization, 243, 268 standard enthalpy of reaction temperature dependence of equilibrium reaction constant, 105, 645 standard entropy of activation definition, 655 hydrolysis of alkyl halides, 667 standard entropy of phase transfer air–water partitioning, 267–268 aqueous solubility, 267–268 fusion, definition 245 fusion, prediction from melting point, 250 vaporization, 243, 268 vaporization, constancy at boiling point, 248 standard free energy of activation definition, 655 standard free energy of phase transfer definition, 94 fusion, 244 fusion, prediction from melting point, 253 sublimation, 243 vaporization, 243 standard free energy of reaction definition, 100, 644

equilibrium reaction constant, 100, 645 standard reduction potential difference, 648–649 standard hydrogen electrode (SHE), 646–647 standard one-electron oxidation potential correlation with chemical oxidation rates of phenols and anilines, 745–746, 765 substituted phenols, 764 standard redox potential, see standard reduction potential standard reduction potential definition, 648 environmentally relevant redox couples, 720 organic compound redox couples, 724 one-electron of organic compound redox couples, 726 standard reduction potential difference and standard free energy of reaction, 648, 720 standard state definition, 88 state variable continuous, 169 definition, 169 stereoisomers, see isomers stratopause, 125 stratosphere, 125 structure of compound conventions symbolizing structures of organic compounds, 24 definition, 22 structural isomers, definition, 22 sulfate-reducing bacteria competition for H2 , 862 sulfate-reducing conditions, see redox conditions surface–air partition constant correlation with (subcooled) liquid vapor pressure, 327 definition, 326 effect of relative humidity, 331 estimation of enthalpy of surface–air partitioning, 326 H-acceptor (e-donor) and H-donor (e-acceptor) properties of various surfaces, 329–330 pp-LFER for prediction, general approach, 328 pp-LFER for prediction of water surface–air partition constant, 331 sp-LFER for prediction from vapor pressure, general approach, 327 temperature dependence, 326 van der Waals surface descriptors for various surfaces, 329 surface–air partitioning general considerations, 322 quantification, 328

surface complexation bidentate sorption, 427 binuclear sorption, 427 carbonyls as reactive NOM sites for sorbate bonding, 427 carboxylic acids bonding to mineral surfaces, 428 free energy of surface reaction, 429 inner sphere complex adsorption, 408, 427 monodentate sorption, 427 mononuclear sorption, 427 sorption via surface bonding, 426 surface–water partitioning of nonionic compounds definition, 335 examples, 336, 342 nonspecific adsorption to mineral surfaces, 335 specific adsorption of nitroaromatic compounds to mineral surfaces, 338 surfactant adsorption, 417, 421, 425 suspended solids concentrations in oceans and lakes, 145 settling velocities, 145 system boundary, 170 definition in modeling, 124, 168 Swain–Scott relationship, 672

T temperature dependence aqueous solubility, 272 base-catalyzed hydrolysis of carbamates, 691 equilibrium partition constant, 97, Appendix Table D.1 equilibrium reaction constant, 645, Appendix Table D.1 Henry constant, 272 ion product of water, Appendix Table D.2 neutral hydrolysis of alkyl halides, 667 reaction rate: 653, Appendix Table D.1 vapor pressure, 244 thermal bar lakes, 141 as non-interface boundary, 560 thermocline lakes, 139 thermodynamic cycle relating aqueous solubility, vapor pressure, and air–water partition constant, 261 relating bulk-phase partition constants, 217, 261 tortuosity effect on diffusion, 541 toxicity ratio, 506 transfer velocity, see exchange velocity transformation kinetics, see reaction kinetics transformation reaction introduction, 638

Index

transition state theory, 654–655

V

W

transport process deterministic (directed), 191 mathematical description, 193 random, 191 tropopause, 125, 127, 560 troposphere, 125

van der Waals Interactions definition, 38 van’t Hoff equation derivation, 96 vapor pressure definition, 238 enthalpic and entropic contributions to the free energy of vaporization, 268 phase diagram, 240 prediction of solid vapor pressure from subcooled liquid vapor pressure, 250 prediction of (subcooled) liquid vapor pressure from boiling point, 248 prediction of (subcooled) liquid vapor pressure using a pp-LFER, 249 thermodynamic description of vapor pressure-temperature relationship, 243 vicinal water, 409, 425

wall boundary with boundary layer, 572 definition, 561 integrated flux ratio, 575 one-sided, 567 water density of fresh water, 139 specific properties, 985 water cycle global volume flow, 131–132 residence times of water, 132

Trouton’s rule, 248 turbulent diffusion coefficient definition, 546 measurement using natural radon, 550, 555 measurement of vertical turbulent diffusivity, 548–549 in natural waters, 547 two-box model definition, 183 exchange fluxes, 183 lake, 189 linear, 186–187

U unsaturated soil breakthrough time, 628 bulk diffusivity, 627 effective diffusivity, 626, 628

vitamin B12 as co-factor in reductive dehalogenation of polychlorinated ethenes, 755–756

1005

wet deposition of gaseous and particle-bound compounds definition, 456 dry versus wet deposition of particle-bound compound, 459 gaseous versus particle-bound compound, 458 simple model for quantification, 457 wind global system, 128

X xenobiotic compounds definition, 851