Thermodynamics of Aqueous Systems with Industrial Applications 9780841205697, 9780841207080, 0-8412-0569-8

Table of contents :
Title Page......Page 1
Half Title Page......Page 3
Copyright......Page 4
ACS Symposium Series......Page 5
FOREWORD......Page 6
PdftkEmptyString......Page 0
PREFACE......Page 7
1 Conference Overview......Page 9
Sour-water Thermodynamic Data......Page 10
Enthalpies of Steam-containing Mixtures......Page 13
Literature Cited......Page 19
Acid Gas Removal......Page 20
Sulfur Recovery......Page 28
Sulfur Dioxide Removal......Page 35
Wastewater Treatment......Page 42
Literature Cited......Page 50
3 Phase Equilibria in Aqueous Electrolyte Solutions......Page 53
Subscripts......Page 63
Literature cited......Page 64
4 Two New Activity Coefficient Models for the Vapor-Liquid Equilibrium of Electrolyte Systems......Page 65
The Pitzer Equation......Page 66
Previous Applications of the Pitzer Equation to Weak Electrolytes......Page 68
Extension of the Pitzer Equation......Page 69
Application of the Extended Pitzer Equation......Page 70
The Local Composition Model......Page 74
Development of the Local Composition Model......Page 75
Discussion of the Local Composition Model......Page 78
Application of the Local Composition Model......Page 79
Acknowledgement......Page 90
Subscripts......Page 91
Literature Cited......Page 92
5 Chemical Equilibria in Flue Gas Scrubbing Slurries......Page 94
Calculation of Ion and Ion-Pair Activity Coefficients......Page 96
Computational Methods......Page 102
Calculation of Supersaturation Ratios of Flue Gas Scrubbing Slurries......Page 104
Calculation of Dissolved Alkalinity......Page 105
Nomenclature......Page 107
Literature Cited......Page 109
6 Correlation of Vapor-Liquid Equilibria of Aqueous Condensates from Coal Processing......Page 110
Solubility of Gases in Water......Page 111
Salting Out of Gases......Page 116
Notation......Page 134
Acknowledgement......Page 135
Literature Cited......Page 136
Thermodynamics......Page 142
Method by van Krevelen, Hoftijzer and Huntjens (1) (KHH)......Page 146
Procedure of Beutier and Renon (2) (BR)......Page 148
Procedure of Edwards, Maurer, Newman and Prausnitz (3) (EMNP)......Page 151
Comparison with Experimental Results......Page 155
Conclusion......Page 162
Procedure of van Krevelen et al. for calculating VLE......Page 163
On the method of Beutier and Renon used for the calculations of the present work......Page 165
Ionic species i......Page 169
On the method of Edwards et a l.......Page 172
Literature Cited......Page 175
8 Representation of NH3-H2S-H2O, NH3-SO2 -H2O, and NH3-CO2-H2O Vapor-Liquid Equilibria......Page 176
Deviations to Ideality......Page 184
Activity of Water......Page 185
List of Symbols......Page 186
Literature Cited......Page 188
9 Sour Water EquilibriaAmmonia Volatility down to PPM Levels; pH vs. Composition; and Effect of Electrolytes on Ammonia Volatility......Page 190
Measurement Apparatus......Page 191
Measurement Results......Page 195
Summary and Conclusions......Page 228
Literature Cited......Page 229
10 Predicting Vapor-Liquid-Solid Equilibria in Multicomponent Aqueous Solutions of Electrolytes......Page 230
Thermodynamic Framework......Page 232
Overall Structure of the ECES System......Page 237
Using the ECES System to Predict Vapor Liquid Equilibria (NH3-CO2-H2O)......Page 239
Using the ECES System for Vapor-Liquid-Solid Equilibria (FeCl2-HCl-H2O)......Page 245
Conclusions and Significance......Page 247
Literature Cited......Page 248
11 Effects of Aqueous Chemical Equilibria on Wet Scrubbing of Sulfur Dioxide With Magnesia-Enhanced Limestone......Page 250
Formulation and Verification of Chemical Model......Page 251
Correlations for Equilibrium SO2 Partial Pressure and Liquor Composition......Page 255
Equations for Calculating the Degree of Gypsum Saturation......Page 261
Enhancement Effect of Magnesia-Induced Dissolved Sulfite on SO2 Removal......Page 263
Summary and Conclusions......Page 267
Abstract......Page 268
Literature Cited......Page 269
12 Sulfur Dioxide Vapor Pressure and pH of Sodium Citrate Buffer Solutions with Dissolved Sulfur Dioxide......Page 271
Experimental Methods......Page 272
pH Behavior......Page 274
SO2 Vapor Pressure......Page 277
Design Calculations for Absorption/Stripping......Page 286
Nomenclature......Page 291
Acknowledgements......Page 292
Literature Cited......Page 293
Fossil Fuel Characteristics......Page 294
Basic Methods of Coal Conversion......Page 295
Carbon Removal Processes......Page 296
Hydrogen Addition Processes......Page 298
Efficiency Considerations......Page 301
14 Thermodynamic Data for Synthesis Gas and Related Systems Prediction, Development, Evaluation, and Correlation......Page 304
The Magnitude of Work to be Done......Page 305
Methods of Data Development......Page 306
Mixtures with Polar Components......Page 309
Abstract......Page 314
Processes Involved......Page 315
GPA Projects Involving Water......Page 316
Other Work......Page 318
LITERATURE CITED......Page 319
GRI'S HISTORY......Page 320
THE OVERALL GRI R&D PROGRAM......Page 321
THE GAS SUPPLY PROGRAM......Page 322
1.1 UNCONVENTIONAL NATURAL GAS......Page 323
1.2 SNG FROM COAL......Page 324
1.4 SNG FROM BIOMASS......Page 326
1.5 HYDROGEN......Page 328
17 Application of the PFGC-MES Equation of State to Synthetic and Natural Gas Systems......Page 329
Theory......Page 330
Model Validation......Page 335
Sample Problems......Page 340
Summary......Page 352
Nomenclature List......Page 353
REFERENCES......Page 354
18 Considerations Affecting Observation of Interaction Second Virial Coefficients by Chromatography......Page 356
Analysis of Experiment......Page 357
Literature Cited......Page 372
Stoichiometry......Page 374
Critical Points......Page 375
Binary Critical Points......Page 378
Reaction Equilibrium......Page 381
Calculated Critical and Equilibrium Points......Page 383
Literature Cited......Page 386
20 Two- and Three-Phase Equilibrium Calculations for Coal Gasification and Related Processes......Page 388
Non-Hydrocarbon - Water Binaries......Page 390
Hydrocarbon - Water Binaries......Page 393
Literature Cited......Page 408
21 Phase Equilibrium Calculations by Equation of State for Aqueous Systems with Low Mutual Solubility......Page 410
Method of Calculation......Page 412
Determination of the Parameters of Pure Water......Page 414
Mixtures of Water and Inert Components......Page 416
Mixtures with active Compounds......Page 422
Conclusions......Page 426
Acknowledgement......Page 427
Literature Cited......Page 428
22 Excess Enthalpies of Some Binary Steam Mixtures......Page 430
Results for the Mixture Steam + n-Heptane......Page 431
Analysis of the Results at High Pressures......Page 434
The Separated Associated Fluid Interaction Model for Polar + Nonpolar Mixtures......Page 436
Literature Cited......Page 441
23 Thermodynamics of Aqueous Electrolytes at Various Temperatures, Pressures, and Compositions......Page 443
Miscible Electrolytes......Page 445
Virial Coefficient Equations for Electrolytes......Page 448
References......Page 456
24 Current Status of Experimental Knowledge of Thermodynamic Properties of Aqueous Solutions......Page 459
BIBLIOGRAPHY ON THERMODYNAMIC PROPERTIES OF AQUEOUS SOLUTIONS BIBLIOGRAPHIES......Page 474
COMPILATIONS OF DATA......Page 475
TREATISES AND REVIEWS......Page 480
MISCELLANEOUS REPORTS......Page 483
25 Prediction of Activity Coefficients of Strong Electrolytes in Aqueous Systems......Page 486
Subscripts and Superscripts.......Page 501
Literature Cited......Page 502
26 The Solubility of Gases in Water from 350 - 600 Κ......Page 503
The solubility of gases between the temperature of 273 and 350 Κ.......Page 504
The solubility of the gases in water from 350 to 600 K.......Page 505
The effect of pressure on gas solubility......Page 522
Acknowledgment......Page 524
Literature Cited......Page 525
Models and Correlating Equations......Page 527
Experimental Techniques......Page 530
Other Thermodynamic Properties......Page 531
Literature Cited......Page 534
28 Current Trends in the Fundamental Theory of Ionic Solutions......Page 537
1. THERMODYNAMICS AND STRUCTURE......Page 538
2. HAMILTONIAN MODELS AT VARIOUS LEVELS......Page 539
3. MM-LEVEL ū+-(r) FROM BO LEVEL......Page 541
4. REFINED MM-LEVEL MODELS......Page 543
5. NON-THERMODYNAMIC DATA......Page 545
6. CORRESPONDING STATES FOR IONIC SYSTEMS......Page 547
LITERATURE CITED......Page 548
Ionic Media......Page 551
Ion-Pairing......Page 552
Activity Coefficients......Page 553
Equilibrium Constants......Page 556
Literature Cited......Page 557
2) Information Obtained......Page 558
3) Advantages......Page 559
4) Measurements of ΔmΗ......Page 560
5) Heat Capacity Measurements......Page 563
6) Conclusion......Page 567
Literature Cited......Page 569
I. Experimental Methods......Page 570
II . High Pressure Equation of State of Electrolyte Solutions......Page 591
III. Estimation of the PVT Properties of Mixed Electrolyte Solutions......Page 601
Acknowledgement......Page 605
Literature Cited......Page 606
32 Application of Thermodynamics in Hydrometallurgy A State-of-the-Art Review......Page 612
Species in Solution......Page 613
Equilibrium Constants and Free Energy of Formation......Page 614
Activity Coefficients......Page 619
Computer Programs......Page 621
Abstract......Page 624
Literature Cited......Page 625
Phase Rule......Page 629
Solid-Solution Interactions......Page 630
Ion Pair-Complex Competition......Page 636
Literature Cited......Page 638
34 Thermodynamics of High-Temperature Aqueous Systems What the Electricity Generating Industry Needs to Know......Page 639
1.Power Station Water Circuits......Page 640
2.Thermodynamic Considerations......Page 642
3.Applications......Page 654
4.Concluding Remarks......Page 659
5.Literature Cited......Page 660
Principles......Page 666
Methods for a simple case......Page 668
Methods for more complex diagrams......Page 673
Variations of Pourbaix diagrams......Page 676
Program comparisons......Page 682
Literature Cited......Page 684
I. Introduction.......Page 685
II. Extraction Processes.......Page 686
III. Trace Metals and Additives in Electrodeposition.......Page 689
IV. Summary and Conclusions.......Page 695
Literature Cited.......Page 698
37 Activity Coefficients at High Concentrations in Multicomponent Salt Systems......Page 700
Thermodynamics of Dilute Solutions......Page 701
Harned's Rule......Page 703
Thermodynamics of Concentrated Solutions......Page 705
Activity Coefficient of Water in Concentrated Solutions......Page 709
Vapor-Liquid Equilibria......Page 712
Solid-Liquid Equilibria......Page 714
Extension of Technique by Vera and Co-Workers......Page 716
Conclusions......Page 718
Literature Cited......Page 721
38 Modeling the Chemical Equilibria in Solid-Liquid Reactions Application to Leaching of Ores......Page 723
Development of the Partial Equilibrium Model......Page 724
Application of the Partial Equilibrium Model......Page 728
Summary and Conclusion......Page 734
Terms and Solutions......Page 736
Literature Cited......Page 737
A......Page 738
C......Page 739
D......Page 740
E......Page 741
F......Page 742
H......Page 743
I......Page 744
M......Page 745
N......Page 746
P......Page 747
S......Page 748
T......Page 750
W......Page 751
Z......Page 752

Citation preview

Thermodynamics of Aqueous Systems with Industrial Applications

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

Thermodynamics of Aqueous Systems with Industrial Applications Stephen A . Newman, EDITOR Foster Wheeler Energy Corporation ASSOCIATE EDITORS

Herber Max Klein Stanley I. Sandler

Based on a symposium cosponsored by the American Institute of Chemical Engineers, the National Bureau of Standards, and the National Science Foundation at Airlie House Conference Site, Warrenton, Virginia, October 22-25, 1979.

133

ACS SYMPOSIUM SERIES

AMERICAN CHEMICAL SOCIETY WASHINGTON, D. C.

1980

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

Library of Congress Data Thermodynamics of aqueous systems, with industrial applications. (ACS symposium series; 133 ISSN 0097-6156) Includes bibliographies and index. 1. Thermodynamics—Congresses. 2. Chemistry, Tech­ nical—Congresses. I. Newman, Stephen Α., 1938. II. American Institute of Chemical Engineers. III. United States. National Bureau of Standards. IV. United States. Na­ tional Science Foundation. V. Series: American Chemi­ cal Society. ACS symposium series; 133. QD504.T47 ISBN 0-8412-0569-8

660.2'969 ASCMC 8

80-16044 133 1-771 1980

Copyright © 1980 American Chemical Society All Rights Reserved. The appearance of the code at the bottom of the first page of each article in this volume indicates the copyright owner's consent that reprographic copies of the article may be made for personal or internal use or for the personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to copying or transmission by any means—graphic or electronic—for any other purpose, such as for general distribution, for advertising or promotional purposes, for creating new collective works, for resale, or for information storage and retrieval systems. The citation of trade names and/or names of manufacturers in this publication is not to be construed as an endorsement or as approval by ACS of the commercial products or services referenced herein; nor should the mere reference herein to any drawing, specification, chemical process, or other data be regarded as a license or as a conveyance of any right or permission, to the holder, reader, or any other person or corporation, to manufacture, repro­ duce, use, or sell any patented invention or copyrighted work that may in any way be related thereto. PRINTED IN THE UNITED STATES AMERICA

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

ACS Symposium Series M . Joa

Advisory Board David L . Allara

W . Jeffrey Howe

Kenneth B. Bischoff

James D . Idol, Jr.

Donald G . Crosby

James P. Lodge

Donald D . Dollberg

Leon Petrakis

Robert E . Feeney

F. Sherwood Rowland

Jack Halpern

Alan C. Sartorelli

Brian M . Harney

Raymond B. Seymour

Robert A . Hofstader

Gunter Zweig

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

FOREWORD The ACS S Y M P O S I U M SERIES was founded in 1974 to provide a medium for publishin format of the Series parallels that of the continuing A D V A N C E S EST C H E M I S T R Y SERIES except that in order to save time the papers are not typeset but are reproduced as they are submitted by the authors in camera-ready form. Papers are reviewed under the supervision of the Editors with the assistance of the Series Advisory Board and are selected to maintain the integrity of the symposia; however, verbatim reproductions of previously published papers are not accepted. Both reviews and reports of research are acceptable since symposia may embrace both types of presentation.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

PREFACE

T

his volume contains most of the papers presented at a conference on The Thermodynamics of Aqueous Systems with Industrial Applications, held October 22-25, 1979 at Airlie House, Warrenton, Virginia. The conference, cosponsored by the American Institute of Chemical Engineers, the National Bureau of Standards, and the National Science Foundation, was organized by the following members of the AIChE Subcommittee on Thermodynamics (Research Committee) : Stephen A . Newman, Herbert E . Barner, Stanley S. Grossel Sandler. The conference was subdivided into four sessions, and chapters within this text are arranged according to these categories. Papers included in the first section (Thermodynamics of Electrolytes for Pollution Control) provide the reader with insights into the practical aspects of pollution control, as well as an overall appreciation of applied electrolyte phase equilibria. Other chapters include detailed descriptions of thermodynamic models that recently have been developed to describe important industrial pollution control processes with emphasis on acid gas absorption/sour water stripping and flue gas desulfurization. The increasing importance of coal gasification, liquefaction, and shale oil processing has focused attention on a new class of thermodynamic problems. In the second section (Thermodynamics of Synthesis Gas and Related Systems) new data and calculation methods appropriate to watercontaining synthesis gas systems are emphasized. As background to this work, chapters describing industrially important processes and cooperative research organizations dealing with emerging synthesis gas technology have been included. Essentially all of the engineering thermodynamic correlations used in pollution control models and synthesis gas phase equilibria, chemical equilibria, and enthalpy calculation schemes have their foundations in fundamental theory. Experimental data, in addition to being directly useful to designers, allows the correlation developer to assess the validity and suitability of his model. Included within the third section (Properties of Aqueous Solutions—Theory, Experiment, and Prediction) are chapters providing both comprehensive reviews and detailed descriptions of specific areas of concern in the theory and properties of aqueous solutions. The increasing interest in hydrometallurgical processing stems from an increased awareness of the necessity of environmental protection and xi In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

pollution. The final section (Hydrometallurgy, Oceanography, and Geology) includes chapters highlighting theory and applications of electrolyte thermodynamics to hydrometallurgy and related concepts important in oceanography and geology. Each session was initiated by state-of-the-art reviews, summarizing both the theoretical and applied aspects of the subject; these were followed by invited technical papers. A panel discussion among speakers/coauthors, including audience participation, concluded each session. This volume contains only the technical papers of the conference; the questions and answers for the papers will be printed as a separate publication. One of the major goals of our conference was to bring together outstanding investigators in diverse areas to discuss topics of mutual interest. Elaboration on this point is made in the Conference Overview. The constituency of our audience ernment) was indeed varie workers. Our speakers spoke on topics ranging from the most recent concepts of electrolyte phase equilibria theory to the principles and applications of coal processing. Throughout the presentations it was apparent that a common thread linked each theme and that both the practical and theoretical aspects of the subject were important, each providing the other with sustenance. We are confident that in addition to fostering the presentation of many superb technical papers, which we anticipate will be used as reference material for many years to come, the conference provided a means for many investigators to become acquainted with colleagues working in related fields. Hopefully, these contacts will be maintained and flourish. We were fortunate in having several guest speakers and we acknowledge their important contributions to our conference. Specifically, we thank Larry Resen (AIChE), Emanuel Horowitz (NBS), Davis Hubbard (NSF), Donald Ehreth (EPA), and Bernard Lee (IGT). Additionally, we are grateful to J. Charles Forman and Joel Henry of AIChE and Marshall Lih of NSF for their part in allowing the conference to grow from a concept into a reality. A special thanks goes to Marie Kennedy of AIChE who played an important part in cheerfully executing many of the day-to-day chores associated with planning a large meeting, including handling the registration duties at Airlie House. We enjoyed planning the meeting and participating in its evolution and look forward to developing other such rewarding activities. Foster Wheeler Energy Corporation 110 South Orange Avenue Livingston, NJ 07039 February 14, 1980

S T E P H E N A.

NEWMAN

xii In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

1 Conference Overview STEPHEN A . NEWMAN Foster Wheeler Energy Corporation, Livingston, NJ 07039

The theme of the symposium has relevance to workers engaged in a wide variety of activities cepts described in the specifi paper superficially different from each other, yet in a fundamental manner, indeed very similar. The invited conference papers have been organized into reasonably related subject matter, yet run the gamut from the very practical to the very theoretical with the intent of providing the theorist an appreciation of the prac­ tical problems facing the technologist,and the technologist, an awareness of the theoretical tools he can use to solve his pro­ blems. Several applied areas of concern, all involved with water, served as focal points for the meeting. Two of these, pollution control and coal processing, have current social significance and are subjects that everyone can readily appreciate. Practi­ cal insights into the fields were given in the industrially ori­ ented review papers, and the role of thermodynamics in contri­ buting to the solution of the many specific problems encountered in carrying out an engineering design were brought out in other papers. As support to the applied thermodynamic techniques de­ scribed in the application-oriented sessions, one session was devoted to theory. It is this fundamental work that enables the thermodynamic practitioner, be he either academic or industrial, to develop in a rational matter his correlations which are ab­ sorbed into the design techniques applied by process engineers. A very fine example was provided by the extensive use of Profes­ sor Pitzer's electrolyte activity coefficient theory within se­ veral acid gas phase equilibrium models. Another important group o f papers provided i n s i g h t i n t o s e v e r a l very s u c c e s s f u l c o o p e r a t i v e i n d u s t r i a l programs, those sponsored by the Gas Research I n s t i t u t e , the American Petroleum I n s t i t u t e , the Gas Processors A s s o c i a t i o n and the American I n s t i t u t e o f Chemical Engineers. The d e s i g n a t i o n i n f r a t e c h n o l o g y has been a p p l i e d t o those aspects o f t e c h n i c a l i n v e s t i g a t i o n and knowledge t h a t permeate a given i n d u s t r y , yet are n o t s p e c i f i c 0-8412-0569-8/ 80/47-133-001 $05.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

2

THERMODYNAMICS OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

enough t o i n d i v i d u a l c o n s t i t u e n t s t o j u s t i f y e x t e n s i v e i n v e s t i g a t i o n on t h e i r own. F r e q u e n t l y , the problems are so complex and d i f f u s e t h a t i t would be e s s e n t i a l l y u s e l e s s f o r a s i n g l e company t o embark on an i n v e s t i g a t i o n t h a t would take many manyears o f investment w i t h very l i t t l e monetary r a t e - o f - r e t u r n . C e r t a i n segments o f the chemical engineering i n d u s t r y have found a s o l u t i o n t o such problems by c o n s o l i d a t i n g i n t e r e s t s i n c o o p e r a t i v e research o r g a n i z a t i o n s such as those sponsored by A P I , GPA, GRI and AIChE. The growth o f these i n d u s t r i a l c o o p e r a t i v e groups i s encouraging; besides conserving resources and e l i m i n a t i n g d u p l i c a t i o n o f e f f o r t , these groups provide a forum f o r exchange o f ideas and n o n - p r o p r i e t a r y technology. The involvement of academia i n these o r g a n i z a t i o n s , u s u a l l y as research cont r a c t o r s , a l l o w s u n i v e r s i t y researchers an i n t i m a t e i n s i g h t i n t o r e a l - w o r l d problems and h e l p s c l o s e the breach between academia and i n d u s t r y t h a t has becom i o f these f a c t o r s s u b s t a n t i a l l and by i t s very d e f i n i t i o promot productivity One very important element missing from the scene u n t i l r e c e n t l y has been government. Government's involvement has o b v i o u s l y been i n c r e a s i n g and w i l l become a welcome a d d i t i o n by p r o v i d i n g a d d i t i o n a l cohesiveness as w e l l as f i n a n c i a l backing and t e c h n i c a l e x p e r t i s e to f l e d g l i n g groups. As an i n t r o d u c t i o n t o the t e c h n i c a l aspects o f the conference, the r e s u l t s o f some s t u d i e s conducted by the w r i t e r on two r e l e v a n t s u b j e c t s are presented below. The f i r s t commentary i s concerned w i t h the design o f sour-water s t r i p p e r s and the e f f e c t s o f thermodynamic data on these designs; the second commentary i s concerned w i t h the c a l c u l a t i o n o f e n t h a l p i e s o f steam-containing m i x t u r e s , e s s e n t i a l t o the design o f c o a l p r o c e s s i n g and r e l a t e d p l a n t s · Sour-water Thermodynamic Data For the past s e v e r a l years there has been c o n s i d e r a b l e i n t e r e s t i n the phase e q u i l i b r i a o f sour-water systems. T h i s i n t e r e s t l a r g e l y stems from the need t o design sour-water s t r i p pers so t h a t t h e i r l i q u i d e f f l u e n t s a t t a i n the very low l e v e l s mandated by c u r r e n t environmental r e g u l a t i o n s . The EPA l i q u i d emission l e v e l g o a l s , based on e c o l o g i c a l e f f e c t s , are ten PPM (mass) f o r ammonia and two PPM (mass) f o r hydrogen s u l f i d e . The g u i d e l i n e s f o r tower design e s t a b l i s h e d many years ago ( f o r example, Û.06 kgs s t r i p p i n g steam per l i t e r o f hot feed) are outmoded and are not exact enough i n an e r a when s o p h i s t i c a t e d data and c a l c u l a t i o n methods can be a p p l i e d t o the problem once cons i d e r e d so complicated t h a t o n l y e m p i r i c a l r u l e s were accepted p r a c t i c e , f o r l a c k o f anything b e t t e r . A number o f models have been developed t o d e s c r i b e the chemistry o c c u r r i n g i n sour-water s t r i p p i n g and a b s o r p t i o n . The many simultaneous chemical r e a c t i o n s whose s o l u t i o n r e s u l t s i n the establishment o f the phase e q u i l i b r i a o f the com-

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

1.

NEWMAN

Conference Overview

3

ponents are l i s t e d i n Figure 1. This system i s i n s e v e r a l r e spects c o n s i d e r a b l y more complicated than many hydrocarbon and chemical systems i n that i t i s necessary to contend w i t h both chemical and phase e q u i l i b r i a i n e s t a b l i s h i n g the design. Each o f the c i t e d r e a c t i o n s and Henry's law constants, besides being temperature dependent, are a l s o f u n c t i o n s o f the type and concent r a t i o n o f acid-gas components i n s o l u t i o n and, i n some cases, the i o n i c s t r e n g t h o f the s o l u t i o n . In a p r a c t i c a l sense, the most important reason f o r c o n s i d e r i n g these e l e c t r o l y t e r e a c t i o n s i s t h a t o n l y those p o r t i o n s of ammonia, hydrogen s u l f i d e , and carbon d i o x i d e t h a t remain i n molecular, rather than i o n i c form, can be s t r i p p e d from s o l u t i o n . The o b j e c t of the c a l c u l a t i o n s , t h e r e f o r e , i s the determination of the i o n i c and molecular d i s t r i b u t i o n of species as a f u n c t i o n o f temperature,pressure,and composition. The designer can emplo c a l c u l a t i o n s to c a r r y ou as those shown i n Figure 2 as a b a s i s f o r h i s s t r i p p i n g or abs o r p t i o n c a l c u l a t i o n s . The two c h a r t s shown can be used e i t h e r to c a l c u l a t e the ammonia and hydrogen s u l f i d e concentrations i n the l i q u i d - p h a s e from a knowledge o f t h e i r p a r t i a l pressures i n the gas phase; o r , a l t e r n a t e l y , the p a r t i a l pressures can be d i r e c t l y read from the c h a r t s given the s o l u t i o n c o n c e n t r a t i o n of the d i s s o l v e d gases. C a l c u l a t i n g the l i q u i d - p h a s e composition from t h a t o f the gas r e q u i r e s a t r i a l - a n d - e r r o r procedure. A l i q u i d - p h a s e molar r a t i o o f the a c i d gases i s assumed, and from the known p a r t i a l pressures, a l i q u i d - p h a s e composition i s read from the graphs and a c a l c u l a t e d l i q u i d - p h a s e molar r a t i o i s obtained. This c a l c u l a t i o n i s repeated two or three times u n t i l the c a l c u l a t e d l i q u i d - p h a s e molar r a t i o equals the assumed v a l u e , and at t h i s p o i n t the e q u i l i b r i u m l i q u i d - p h a s e composition has been determined. For most sour water s t r i p p e r design work, a computer i s used to perform the c a l c u l a t i o n s . S e v e r a l o f the proposed sourwater modules were incorporated i n t o a tower program and a s e r i e s of designs on a t y p i c a l sour-water s t r i p p e r have been undertaken. Comparisons o f data methods with each other such as those shown i n Figure 3 f o r the Wilson (1) and Mason-Kao (2) methods demonstrate that the Wilson method generates the smaller ammonia and hydrogen s u l f i d e p a r t i a l pressures. In p r a c t i c a l terms, Wilson's p r e d i c t i o n s imply a greater amount o f s t r i p p i n g steam to achieve a d e s i r e d l e v e l of a c i d gas removal when compared to the Mason-Kac p r e d i c t i o n s . U n f o r t u n a t e l y , such comparisons are only s e m i - q u a n t i t a t i v e from a designer's viewpoint and i t i s nenessary to employ the f u l l s t r e n g t h o f a r i g o r o u s tower comput e r s i m u l a t i o n to demonstrate the s i g n i f i c a n c e that the data d i f ferences imply i n terms of equipment s p e c i f i c a t i o n and u t i l i t y comsumption. Some i n s i g h t i s provided i n the comparisons dep i c t e d i n Figures 4 and 5.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4

THERMODYNAMICS O F AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

Qc

SOUR-WATER,—c FEED -

PPM NH , H S, C0 = ? 3

2

2

QR SUMMARY OF CHEMICAL EQUILIBRIA INVOLVED IN CALCULATING NH -H S-C0 -H 0 VLE 3

C0 + H 0 2

2

K

l

2

2

2

HC07+H+

HCOT* COT + H+ κ NH + H+ NH+ -K NH3+HCO3 H NC0 +H 0 2

3

3

4

2

2

2

H S +H+ S=

HS-

H0 H+ + OHI OF ALL ELECTRONIC CHARGES = Ο K ?

2

PNH

3

=

HNH

3

NH

3

Ρco2 = Hco C0 2

; PH S = 2

HH S 2

HS 2

2

IPC Science and Technology

Figure 1.

Figure 2.

Sour-water absorber/stripper VLE (4)

Typical design data charts for NH -H S-H 0 3

2

2

VLE

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

1.

NEWMAN

Conference Overview

The PPM ammonia remaining i n the bottoms product stream o f the s t r i p p e r tower are shown i n Figure 4 as a f u n c t i o n o f the kilograms of steam i n j e c t e d i n t o the tower. The number o f theo r e t i c a l stages used i s shown as a cross-parameter. What i s observed i s t h a t i n a p r a c t i c a l sense, the Wilson and Mason-Kao methods y i e l d e s s e n t i a l l y the same ammonia p u r i t y i n the s t r i p p e d water product, whereas very s u b s t a n t i a l d i f f e r e n c e s are obtained when the c l a s s i c a l van Krevelen c o r r e l a t i o n i s a p p l i e d to design the wastewater s t r i p p e r . Using the amount o f hydrogen s u l f i d e remaining i n the tower bottoms as the c r i t e r i o n , F i g u r e 5 shows s i m i l a r design comparisons. Large d i f f e r e n c e s between the methods are observed; however, the Mason-Kao p r e d i c t i o n s and van Krevelen r e s u l t s are very s i m i l a r . The Wilson method generates a more c o n s e r v a t i v e design i n t h a t to achieve a designated l e v e l o f hydrogen s u l f i d e p u r i t y a designer woul a l t e r n a t e l y , provide f o E n t h a l p i e s o f Steam-containing M i x t u r e s For those engaged i n designing p l a n t s f o r p r o c e s s i n g syngas streams, c o n s i s t i n g o f mixtures o f hydrogen, carbon monoxide, carbon d i o x i d e , n i t r o g e n and methane, there i s a constant need to c a l c u l a t e the e n t h a l p i e s of mixtures o f these gases w i t h steam. These data are r e q u i r e d i n the design o f r e a c t o r s , heat exchangers and s e p a r a t i o n equipment. U n f o r t u n a t e l y , d e s p i t e the prevalence of such systems i n design work, u n t i l very r e c e n t l y , there have been no experimental c a l o r i m e t r i c data w i t h which to assess the v a l i d i t y o f proposed design c o r r e l a t i o n s . With the i n c r e a s e d i n t e r e s t i n s u b s t i t u t e gas processes i n which e n t h a l p i e s f o r mixtures c o n t a i n i n g as much as 50 percent water, at high p r e s s u r e s , are r e q u i r e d , e f f o r t s to o b t a i n experimental enthalpy data f o r these systems have been i n i t i a t e d , and s e v e r a l measurement programs are underway. Some data comparisons were made o f s e v e r a l p r e d i c t i v e methods w i t h steam mixture enthalpy data obtained by P r o f e s s o r Wormald ( 3 ) . To provide a b a s i s o f comparison, Figure 6 i l l u s t r a t e s how three methods c u r r e n t l y i n vogue i n the thermodynamics world perform i n p r e d i c t i n g the enthalpy departures from i d e a l i t y o f methane. The p r e d i c t i o n s o f the Lee-Kesler e q u a t i o n - o f - s t a t e seem t o best r e p l i c a t e the d a t a , w i t h a maximum e r r o r of 1.2 kJ/kg. A p o r t i o n o f the enthalpy-temperature diagram f o r steam i s presented i n F i g u r e 7. F r e q u e n t l y , i n performing heat balance c a l c u l a t i o n s f o r syngas p r o c e s s i n g , i t i s necessary to develop e n t h a l p i e s f o r steam i n mixtures a t c o n d i t i o n s t h a t do not conform t o pure component c o n d i t i o n s . Design engineers f r e q u e n t l y develop t h e i r steam e n t h a l p i e s from the pure component data by e i t h e r using s a t u r a t i o n values or by e x t r a p o l a t i n g i n t o the pure component dome region from the l i n e a r p o r t i o n o f the s u p e r c r i t i c a l i s o b a r s . Some advocates o f t h i s l a t t e r procedure

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

5

THERMODYNAMICS OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

IPC Science and Technology

Figure 4.

Predicted PPM NH Kao; (

3

in tower bottoms (( ) van Krevelen) (4)

) Wilson; (

) Mason-

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

1.

NEWMAN

Conference Overview

7 100.0,

100.0

χ

\

t S s η,

* 10.0

ο t

\ \ \ %

g

\

Έ

\

* 10.0

s

\

\

\ \Ν

\

ν

X

\ s

X \

\

\% 0.15

Figure 5.

0.20 0.25 K6S STEAM/L FEED

0.30

1.0

0.15

0.201 0.25 KGS STEAM/L FEED

Predicted PPM H S in tower bottoms (( Kao; ( ) van Krevelen) 2

5000

10,000

) Wilson; (

0.30

) Mason-

15,000

Figure 6. Comparisons of predicted and experimental enthalpy departures for pure methane at 598 Κ

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

8

THERMODYNAMICS O F AQUEOUS SYSTEMS WITH INDUSTRIAL

500

550

600

Figure 7.

Figure 8.

650

TEMPERATURE/K

700

APPLICATIONS

750

800

Enthalpy diagram for steam

Comparisons of predicted and experimental enthalpy departures for pure steam at 598 Κ

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

1.

NEWMAN

Conference Overview

use enthalpy values at the p a r t i a l pressure of steam, o t h e r s , at the t o t a l system pressure. In the enthalpy diagram, the temperature at which the o n l y p u b l i s h e d steam mixture c a l o r i m e t r i c data were obtained i s i n d i c a t e d . The pressure range o f the data spans from i d e a l gas to s a t u r a t i o n p r e s s u r e , about 12,000 kPa. Figure 8 d e p i c t s how the three popular e q u a t i o n - o f - s t a t e methods c i t e d p r e v i o u s l y perform on pure steam. From a theoret i c a l viewpoint, none of the methods has the foundation to handle mixtures o f polar/non-polar components. Although the agreement w i t h experimental data i s not very s a t i s f a c t o r y f o r any o f the methods, the Lee-Kesler e q u a t i o n - o f - s t a t e does best. I t was a l s o found t h a t by s l i g h t l y a d j u s t i n g the a c e n t r i c f a c t o r o f water, improvement i n the r e p r e s e n t a t i o n o f the enthalpy of steam can be obtained by t h i s method a t 598 K, the c o n d i t i o n s o f the experimental mixtur well. Figure 9 provides a comparison of the p r e d i c t i o n s of emp i r i c a l methods w i t h Wormald's data f o r a 50/50 mole percent mixture o f steam and methane. As can be seen, the f r e q u e n t l y used a r t i f i c e s of c a l c u l a t i n g mixture e n t h a l p i e s by blending the pure component e n t h a l p i e s a t e i t h e r t o t a l or p a r t i a l pressures are very i n a c c u r a t e . L i k e w i s e , the assumption of i d e a l gas ent h a l p y f o r the r e a l gas m i x t u r e , e q u i v a l e n t to a zero enthalpy departure on the diagram, i s an e q u a l l y poor method. In Figure 10 are shown comparisons of the equation of s t a t e methods w i t h the experimental data. The Lee-Kesler methods r e present the data the best. Again, i f the water a c e n t r i c f a c t o r determined to best represent the pure steam enthalpy data i s a p p l i e d to the mixtures, f u r t h e r improvement i s noted f o r the p r e d i c t i o n s by the Lee-Kesler method. Use o f i n t e r a c t i o n cons t a n t s w i t h i n the Lee-Kesler, or other models, would undoubtedly provide even b e t t e r r e p r e s e n t a t i o n o f the data. Although comparisons f o r the steam-methane system have been presented, s i m i l a r trends were noted f o r the other b i n a r y s y s tems p r e v i o u s l y p u b l i s h e d by Wormald, namely mixtures of steam w i t h n i t r o g e n , carbon d i o x i d e , n-hexane, and benzene. P r o f e s s o r Wormald, i n a paper presented a t t h i s conference, has provided a d d i t i o n a l steam mixture enthalpy data and some c o r r e l a t i o n work he has done on the data using an a s s o c i a t i o n model.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9

THERMODYNAMICS O F AQUEOUS SYSTEMS W I T H INDUSTRIAL

200-1

APPLICATIONS

PURE COMPONENT / DATA / (TOTAL PRESSURE) /

EXPERIMENTAL 100-

o >Î3 PURE COMPONENT

PRESSURE/kPa 5000

10,000

15,000

Figure 9. Comparisons of predicted and experimental enthalpy departures for an equimolar steam-methane mixture at 598 Κ (equation-of-state methods)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

1.

NEWMAN

Conference

11

Overview

Literature Cited

1. Wilson, G.M., "A New Correlation of NH , CO and HS Vola­ tility Data from Aqueous Sour Water Systems." Final Report to API Committee on Refinery Environmental Control under EPA Grant No. R804364010, Thermochemical Institute, BYU, Provo, Utah, February 9, 1978. 3

2

2

2. Mason, D., "Vapor-Liquid Equilibria in the NH-CO-HS-HO System", Project 8979, "Preparation of a Coal Conversion Systems Technical Data Book," Quarterly Reports by Institute of Gas Technology for U.S.Department of Energy Contract ΕΧ76-C-01-2286, February and May, 1978. 3

2

2

2

3. Wormald, C.J., "Thermodynamic Properties of Some Mixtures Containing Steam." d National Physical Laboratory Conferenc Fluids and Fluid Mixtures, Teddington, Middlesex, U.K., September 11-12, 1978. Conference Proceedings published by IPC Science and Technology Press. 4. Newman, S.A., "Novel Applications of Phase Equilibria Methods to Process Design Problems." Paper presented at National Physical Laboratory Conference on Chemical Thermo­ dynamic Data on Fluids and Fluid Mixtures, Teddington, Middlesex, U.K., September 11-12, 1978. Conference Pro­ ceedings published by IPC Science and Technology Press. 5. Lee, B.-I. and Kesler, M.G., AIChE Journal, 1975, 12(5), 510. 6. Peng, D.-Y. and Robinson, D.B., Ind. Eng. Chem., Fundam, 1976, 15, 59 7. Soave, G., Chem. Eng. Science, 1972, 27, 1197. 8. van Krevelen, D.W., Hoftijzer, P.J. and Huntjens, F.J., Recueil des Travaux Chimiques des Pays-Bas, 1949, 68, 191. RECEIVED

January 17, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

2 A Survey of Some Industrial Waste Treatment Processes W. T. ATKINS, W. H . SEWARD, and H . J. T A K A C H Mittelhauser Corporation, Downers Grove, IL 60515

This paper was prepared to give a brief overview of some of the technologies used fo the many areas of possibl this paper focuses on sulfur control technologies due to the potentially major cost impact of these technologies on the indus­ trial processes with which they are associated. The process areas covered are acid gas removal, sulfur recovery, sulfur dioxide removal, and wastewater treating. In the first three process areas, alternative process types are described and guide­ lines for process selection are briefly reviewed. Because of the operating difficulties encountered with utility sulfur dioxide removal processes, information on industrial installation of these processes is given. For wastewater treating, a state-of­ -the-art industrial wastewater treatment system is discussed along with some major items to consider in process selection. Acid Gas Removal Acid gas removal is the removal of sulfur compounds and CO2 (acid gas) from process gas streams. The following sections describe available process alternatives, design options, and guidelines for selection among alternatives. Process A l t e r n a t i v e s . A c i d gas removal processes have been e x t e n s i v e l y surveyed i n the p u b l i s h e d l i t e r a t u r e (1,8.,3) . F i g u r e 1 shows how acid-gas-bearing process gases can be genera l l y t r e a t e d i n i n d u s t r i a l processes. The s u l f u r compounds and CO2 may be absorbed i n a l i q u i d medium, such as amines, a l k a l i s a l t s (NaOH, K C 0 ) , p h y s i c a l s o l v e n t s (methanol, propylene carbonate), or water (3). The absorbed a c i d gases are r e l e a s e d by r e d u c t i o n of pressure and/or by a p p l i c a t i o n o f heat. A l t e r n a t i v e l y , the H 2 S and CO2 may chemically combine w i t h the absorbent (as i n NaOH scrubbing) to form s a l t s which are removed i n a l i q u i d treatment u n i t . This r e q u i r e s c o n t i n u a l and expensive makeup of sodium t o the system. 2

3

0-8412-0569-8/80/47-133-015$08.25/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

IN

RICH

ON

LIQUID

LEAN

(IN

PLACE)

REGENERATION

HAS

ACID

SULFUR

SULFUR

TREATMENT

LIQUID

RECOVERY

GAS

PROCESS

Schematic of acid gas removal process alternatives

SOLID

SOLID

LIQUID

ACID-GAS

REGENERATION

ACID-GAS RICH SOLID

LEAN

Figure 1.

SOLID

LIQUID

ACID-GAS

ADSORPTION

LIQUID

ABSORPTION

TREATED

ACID

RECYCLE

SOLID

WASTE

LIQUID

OR

EFFLUENT

SULFUR

SULFURIC

2.

ATKINS E T A L .

17

Industrial Waste Treatment Processes

Released a c i d gases i n the same form as captured, i . e . , H S, COS, C 0 , e t c . a r e converted i n the s u l f u r recovery u n i t t o forms i n which they may be exported from the i n d u s t r i a l f a c i l i t y . S u l f u r recovery i s d i s c u s s e d l a t e r i n the paper. Some l i q u i d a b s o r p t i o n processes produce two separate a c i d gas streams ( s e l e c t i v e AGR). One stream, c o n t a i n i n g the m a j o r i t y of s u l f u r compounds, i s sent to the s u l f u r recovery u n i t , w h i l e the other i s vented t o atmosphere, environmental r e g u l a t i o n s p e r m i t t i n g . Alkanolamines, g e n e r a l l y r e f e r r e d to as amines, a r e organic compounds of the form H -N-(ROH) 3- (3) ' > h y d r o x y l group g e n e r a l l y provides f o r the compounds s o l u b i l i t y i n water, w h i l e the HN group provides the a l k a l i n i t y i n water s o l u t i o n s to cause the a b s o r p t i o n of a c i d gases. Amine processes used commercially are shown i n Table I . These compounds a r e chemical s o l v e n t s ; they combine c h e m i c a l l y w i t h H S, C 0 , and other s u l f u r compounds. They a r e c u s t o m a r i l y regenerate A l k a l i salt solution potassium s a l t s . They, too, a r e chemical s o l v e n t s , r e a c t i n g w i t h H S and C 0 as f o l l o w s (e.g., f o r K C 0 ) : 2

2

t

n

n

e

n

1

2

2

2

2

2

3

K C0

3

+ C 0 + H 0 + 2KHC0

K C0

3

+ H S -> KHS + KHC0

2

2

2

2

2

3

3

This s o l u t i o n i s regenerated by pressure letdown and steam s t r i p ping of the s o l u t i o n (2_) . The p h y s i c a l s o l v e n t s shown i n Table I operate by d i s s o l v i n g the a c i d gases i n the absorbing medium a t e l e v a t e d pressures and low temperatures. Regeneration of the s o l v e n t i s p r i n c i p a l l y by r e d u c t i o n of p r e s s u r e , although h e a t i n g i s o f t e n necessary i n h i g h - e f f i c i e n c y a p p l i c a t i o n s , where H S i s t o be removed to a few ppmv ( 3 ) . Mixed s o l v e n t s a r e combinations of p h y s i c a l and chemical s o l v e n t s which i n c r e a s e the f l e x i b i l i t y of t r e a t i n g ( 1 ) . The chemical s o l v e n t a l l o w s f o r treatment of lower-pressure streams w h i l e the p h y s i c a l s o l v e n t a l l o w s f o r bulk removal of the a c i d gas. A b s o r p t i o n - o x i d a t i o n processes o x i d i z e absorbed H S d i r e c t l y to elemental s u l f u r i n s o l u t i o n ( 1 ) . The p r i n c i p a l example i n c u r r e n t i n d u s t r i a l use i s the S t r e t f o r d process (3)· The chemist r y of the process can be represented by the f o l l o w i n g i d e a l i z e d equations (ADA represents anthraquinone d i s u l f o n i c a c i d ) : 2

2

Na C0 2

3

+ H S + NaHS + NaHC0 2

3

4 NaV0 + 2 NaHS + H 0 + Na Vi,09 + 2S + 4 NaOH 3

Na Vi 0 2

t

9

2

2

+ 2 NaOH + H 0 + 2 ADA + 4 NaV0 + 2 ADA (reduced) 2

3

2 ADA (reduced) + 0 + 2 ADA + H 0 2

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

18

THERMODYNAMICS O F AQUEOUS SYSTEMS W I T H INDUSTRIAL APPLICATIONS

Table I.

Acid Gas Removal Processes

Principal Absorbent^

Process Name

T y p i c a l Absorber Temperature, °F

Absorber Pressure, psi

Components Removed Organic Sulfur

AMINE PROCESSES Monoethanolamine

Atm-1000; not highly sensitive

Yes, down to 1 ppm level

COS , CS 2 , some mercaptan

Diethanolamine

Atm-1000; not highly sensitive

Yes, down to 4 ppm

COS, CS absorbed r e v e r s i b l y (some mercaptans)

Société National des P e t r o l s d'Aquitaine SNPA-DEA

500-1100; high a c i d gas pressure

Yes, down to 4 ppm

Some COS removed

pressure sensitive

removed to 4 ppmv (but not selectively)

normally 25-75% removal

Not highly sensitive

Yes, ppmv

P a r t i a l removal of COS (some mercaptans)

Yes. normally 30-90% removal

Not highly sensitive

Yes, 1 as ^m-> 0. The s u b s c r i p t j r e f e r s to a l l s o l u t e s p e c i e s . 3. Bulk e l e c t r o n e u t r a l i t y o f the l i q u i d phase. 4. F o r t h e m o l e c u l a r s o l u t e , e q u i l i b r i u m between the v a p o r phase and the l i q u i d phase i s g i v e n by: φ y Ρ a-*a Y

=

γ m Η 'a a a

(4)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

52

THERMODYNAMICS

OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

F o r t h e s o l v e n t , water, t h e v a p o r - l i q u i d e q u i l i b r i u m i s g i v e n ^ by: by ( P - P

S

)

(5)

s

φ y Ρ = a P % exp V w www ^ Y

RT

L

Edwards e t a l . (6) made t h e assumption t h a t was e q u a l t o a t t h e same p r e s s u r e and temperatâre. F u r t h e r they used t h e v i r i a l e q u a t i o n , t r u n c a t e d a f t e r the second term t o e s t i m a t e Ρpure a* These assumptions are s a t i s f a c t o r y when t h e t o t a l p r e s s u r e i s low o r when t h e mole f r a c t i o n o f the s o l u t e i n t h e vapor phase i s near u n i t y . F o r t h e water, t h e assumption was made t h a t φ , φ^, and t h e e x p o n e n t i a l term were u n i t y . These assumptions a r e v a l i d when t h e s o l u t i o n c o n s i s t s m o s t l y o f water and t h e t o t a l p r e s s u r e i s low. The a c t i v i t y c o e f f i c i e n c a l c u l a t e d using th pure a

ν

-A, ζ In γ . =

IF

+

2

1

L>

6

ik

^

(6)

kPw

In a p p l y i n g t h i s e q u a t i o n t o m u l t i - s o l u t e systems, t h e i o n i c c o n c e n t r a t i o n s a r e o f s u f f i c i e n t magnitude t h a t m o l e c u l e - i o n and i o n - i o n i n t e r a c t i o n s must be c o n s i d e r e d . Edwards e t a l . (β) used a method p r o p o s e d by Bromley Ç7) f o r t h e e s t i m a t i o n o f t h e β p a r a m e t e r s . The model was found t o be u s e f u l f o r t h e c a l c u l a t i o n o f m u l t i - s o l u t e e q u i l i b r i a i n t h e NH3+H9S+H2O and NH3+CO2+H2O systems. However, because o f t h e assumptions r e g a r d i n g t h e a c t i v i t y o f t h e water and the use o f o n l y two-body i n t e r a c t i o n parameters, t h e model i s s u i t a b l e o n l y up t o m o l e c u l a r c o n c e n t r a t i o n s o f about 2 m o l a l . As w e l l t h e temperature was r e s t r i c t e d t o t h e range 0 ° t o 100 oc because o f t h e e q u a t i o n s used f o r t h e Henry's c o n s t a n t s and t h e d i s s o c i a t i o n c o n s t a n t s . I n a l a t e r s t u d y , Edwards e t a l . (8) extended t h e c o r r e l a t i o n t o h i g h e r concen­ t r a t i o n s (up t o 10 - 20 molal) and h i g h e r tempera­ t u r e s (0° t o 170 ° C ) . I n t h i s work t h e a c t i v i t y c o e f f i c i e n t s o f t h e e l e c t r o l y t e s were c a l c u l a t e d from an e x p r e s s i o n due t o P i t z e r (9):

In γ. 1 1

/Γ Φ 1

[1+1.2 /τ

+ — ln(1+1.2 Γϊ) 1.2 '

(1)

+ 2 1

3) 3

-

J

F

1-Π+2 >/ï)exp(-2/l)j

L

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

3.

MATHER

A N D DESHMUKH

53

Phase Equilibria

" 7 ? ζ S "ϋ * co c o 2

M

RR'NH

C0

" W n C O O

m

" W ' N H

2

M

S= "Ή*

m

+

H

S =

7

Y

m

/

(19) 2

H S ~ "hS"

Y

C0= H+ C 0 = ' HCO" "HiCO-

=

H

co

YuH Sq ? = H J I

2

Y

co

2

m

co

γ

H

2

(21)

(22) 2

(23)

m ν

s

(20)

'2"

b y Ρ = a P Φ, , exp w w w w w w K

C0

-

(P-pS)

8

r

RT

w

(24)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

56

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL

APPLICATIONS

V a l u e s o f t h e d i s s o c i a t i o n c o n s t a n t s and Henry's c o n s t a n t s were d e t e r m i n e d from t h e l i t e r a t u r e . The f u g a c i t y c o e f f i c i e n t s , ^, were c a l c u l a t e d u s i n g t h e Peng-Robinson (J_9) e q u a t i o n o f s t a t e . The a c t i v i t y o f the s o l v e n t , w a t e r , was s e t e q u a l t o i t s mole f r a c t i o n . A l s o t h e f u g a c i t y c o e f f i c i e n t o f water a t i t s v a p o r p r e s s u r e , φ** and t h e P o y n t i n g c o r r e c t i o n were assumed t o be u n i t y . The model i s hence r e s t r i c t e d t o r e l a t i v e ­ l y d i l u t e s o l u t i o n s , b u t t h i s r e s t r i c t i o n c a n be r e ­ moved by d e t e r m i n i n g t h e e x p r e s s i o n f o r a u s i n g t h e Gibbs-Duhem e q u a t i o n , as shown by Edwards e t a l . ( 8 ) . The a c t i v i t y c o e f f i c i e n t s o f t h e s o l u t e s p e c i e s have been d e t e r m i n e d from t h e e x t e n d e d Debye-Huckel ex­ p r e s s i o n g i v e n by Guggenheim ( 2 0 ) , E q u a t i o n ( 6 ) . T h i s e q u a t i o n was used by Edwards e t a l . (6). The major problem i n a p p l y i n g the e s t i m a t i o n o f t h Bromley cannot be used as t h e i n p u t parameters - t h e i o n i c e n t r o p i e s o r s a l t i n g - o u t parameters have n o t been d e t e r m i n e d f o r ethanolammonium o r carbamate i o n s . The f o l l o w i n g b a l a n c e e q u a t i o n s f o r t h e r e a c t i n g s p e c i e s c a n be formed w

Electroneutrality "rr'NHJ

+

'V

=

m

0H~

+

m

HS-

+

^ 0 3

+

"rr'NCOO"

+

2

+

2

m

S=

co=

m

( 2 5 )

Mass b a l a n c e s m

A

m

A

m

=

"rr'NH

°C0

a

= 2

m

+

Itl

C0

RR'NH+ +

2

" W n C O O "

"ΉΟΟ-

2

A H S » "^S

+

+

+

+

m

C0=

+

m

(

RR'NC00-

m

2

(

"HS" S=

(

2

7

)

2

6

8

)

)

Here OLQQ and CXHOS a r e t h e mole r a t i o s i n t h e l i q u i d phase xcarbon t o n i t r o g e n and s u l f u r t o n i t r o g e n ) and a r e t h e e x p e r i m e n t a l l y measured c o n c e n t r a t i o n s . The m a t h e m a t i c a l p r o b l e m i s t o s o l v e E q u a t i o n s (15) t o ( 2 8 ) . Twelve s p e c i e s e x i s t : H S , C 0 , RR'NH, 2

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

3.

MATHER AND DESHMUKH

C 0

57

Phase Equilibria

R R , N H

HS~, S , HCO3, 3' 9 ' RR'NCOO , Η , OH and H 0 . Hence t h e r e a r e t w e n t y - t h r e e unknowns (n^ and Yi f o r a l l s p e c i e s e x c e p t water p l u s x ~ ) . To s o l v e f o r the unknowns t h e r e a r e t w e n t y - t h r e e independent e q u a t i o n s : Seven c h e m i c a l e q u i l i b r i a , t h r e e mass b a l a n ­ c e s , e l e c t r o n e u t r a l i t y , t h e use o f E q u a t i o n (6) f o r t h e e l e v e n a c t i v i t y c o e f f i c i e n t s and t h e phase e q u i l i b r i u m f o r x . The problem i s one o f s o l v i n g a system o f non­ l i n e a r a l g e b r a i c e q u a t i o n s . Brown's method (2J_, 22) was used f o r t h i s purpose. I t i s an e f f i c i e n t p r o c e d u r e , based on a p a r t i a l p i v o t i n g t e c h n i q u e , and i s a n a l o ­ gous t o G a u s s i a n e l i m i n a t i o n i n l i n e a r systems o f equations. The a p p l i c a t i o n o f t h i s model t o a l k a n o l a m i n e s o l u t i o n s i s not p o s s i b l e d i r e c t l y since the s p e c i f i c i n t e r a c t i o n parameter and carbamate i o n s a r c i a t i o n c o n s t a n t f o r t h e s i m p l e s t amines (MEA, DEA, TEA) i s known o n l y o v e r t h e range o f temperatures between 0 ° and 50 °C and t h e e q u i l i b r i u m c o n s t a n t f o r carbamate f o r m a t i o n i s known o n l y a t 18 °C f o r MEA and DEA. In monoethanolamine s o l u t i o n s t h e unknown i n t e r ­ a c t i o n parameters and e q u i l i b r i u m c o n s t a n t s were determined by f i t t i n g t h e model t o d a t a f o r t h e t h r e e component systems C0 +MEA+H 0 and HjS+MEAH^O. The agreement o f t h e f i t t e d model w i t h t h e d a t a was found t o be good. The parameters o b t a i n e d i n t h i s way were then used t o p r e d i c t t h e p a r t i a l p r e s s u r e s o f m i x t u r e s o f H^S and C 0 over aqueous MEA s o l u t i o n s . The p r e ­ d i c t i o n s were i n good agreement w i t h e x p e r i m e n t a l d a t a , except a t the higher p a r t i a l pressures. T h i s p r o c e d u r e c o u l d n o t be employed f o r d i i s o p r o panolamine (DIPA) s o l u t i o n s s i n c e d a t a were a v a i l a b l e o n l y f o r one amine c o n c e n t r a t i o n a t two temperatures. I n t h i s case d a t a f o r m i x t u r e s o f H S+C0 +DIPA+H90 were used t o g e t h e r w i t h t h e d a t a f o r H S+DIPA+H 0 and C0 +DIPA+H 0 t o o b t a i n t h e i n t e r a c t i o n parameters and e q u i l i b r i u m c o n s t a n t s . The r e s u l t s a r e shown i n F i g u r e s 1 and 2 t o be i n good agreement w i t h t h e ex­ p e r i m e n t a l d a t a (23). I n t h i s c a s e , however, i n con­ t r a s t t o t h e case o f MEA, t h e p r e d i c t i o n s use p a r a ­ meters e v a l u a t e d from d a t a f o r t h e f o u r component system. 2

w

2

2

2

2

2

2

2

2

2

Conclusions The c o r r e l a t i o n o f v a p o r - l i q u i d e q u i l i b r i a i n aqueous s o l u t i o n s o f weak e l e c t r o l y t e s i s important f o r the s e p a r a t i o n o f u n d e s i r a b l e components from gases and l i q u i d s . The major problem i n such c o r r e l a t i o n s i s t h e e s t i m a t i o n o f t h e a c t i v i t y

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Figure 2.

Effect of H S on the solubility of C0 (( ) experimental (23); ( 2

2

in 2.5N DIPA solutions at 100°C ) predicted

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

3.

MATHER AND DESHMUKH

59

Phase Equilibria

c o e f f i c i e n t s o f the i o n i c s p e c i e s and a l t h o u g h a number o f models have been proposed, the d e t e r m i n a t i o n o f the parameters i n a new case i s not a s i m p l e m a t t e r As w e l l d i s s o c i a t i o n c o n s t a n t s and Henry's c o n s t a n t s f o r a s p e c i e s must be a v a i l a b l e over the temperature range o f i n t e r e s t . Both t h e s e problems o c c u r i n the a p p l i c a t i o n o f the fundamental thermodynamics t o a l k a n o l a m i n e s o l u t i o n s c o n t a i n i n g H S and C 0 . However, by u s i n g l i m i t e d e x p e r i m e n t a l d a t a , the parameters i n the model may be o b t a i n e d and the r e p r e s e n t a t i o n o f the e q u i l i b r i a i s good o v e r the range o f importance i n i n d u s t r i a l processes. 2

a = Αψ = Η = I = Κ = m = Ρ = R = Τ = ν = y = =

2

Nomenclature activity Debye-Huckel paramete Henry's c o n s t a n i o n i c s t r e n g t h = o.5 /Hiti^z^ e q u i l i b r i u m constant m o l a l i t y , mole k g " p r e s s u r e , Pa _^ gas c o n s t a n t , J mol Κ temperature, Κ 3 „1 p a r t i a l molar volume, cm mol vapor phase mole f r a c t i o n i o n i c charge on s p e c i e s i 1

Greek α β, β'°', φ

letters = mole r a t i o i n the l i q u i d phase, mole/mole amine βΠ) = i n t e r a c t i o n parameters, kg mol = vapor phase f u g a c i t y c o e f f i c i e n t

Superscripts saturation

s

=

'

=

a A i,

S u b s c r i p t s= = j, k =

w 1c, 2c 1y, 2y

pseudo-equilibrium

= = =

constant

molecular species carbamate e q u i l i b r i a , amine s p e c i e s o r component, amine equilibria water carbonic acid e q u i l i b r i a hydrogen s u l f i d e e q u i l i b r i a

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

60

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Literature cited

1. Crerar, D.A. Geochim. Cosmochim. Acta, 1975, 39, 1375. 2. Van Krevelen, D.W.; Hoftijzer, P.J.; Huntjens, F.J. Rec. Trav. Chim., 1949, 68, 191. 3. Dankwerts, P.V.; McNeil, K.M. Trans. Inst. Chem. Eng., 1967, 45, T32. 4. Lemkowitz, S.M.; de Cooker, M.G.R.T.; Van den Berg, P.J. J. Appl. Chem. Biotechnol., 1973, 23, 63. 5. Kent, R.L.; Eisenberg, B. Hydrocarbon Processing, 1976, 55, (2), 87. 6. Edwards, T.J.; Newman, J.; Prausnitz, J.M. Α.I.Ch.E.J., 1975, 21, 248. 7. Bromley, L.A. J. Chem. Thermo., 1972, 4, 669. 8. Edwards, T.J.; J.M. Α.I.Ch.E.J. 9. Pitzer, K.S. J. Phys. Chem., 1973, 77, 268. 10. Nakamura, R.; Breedveld, G.J.F.; Prausnitz, J.M. Ind. Eng. Chem. Proc. Des. Dev., 1976, 15, 557. 11. Beutier, D.; Renon, H. Ind. Eng. Chem. Proc. Pes. Dev., 1978, 17, 22o. 12. Edwards, T.J.; Newman, J.; Prausnitz, J.M. Ind. Eng. Chem. Fundam., 1978, 17, 264. 13. Cruz, J.-L.; Renon, Η. Α.I.Ch.E.J., 1978, 24, 817. 14. Cruz, J.-L.; Renon, H. Ind. Eng. Chem. Fundam., 1979, 18, 168. 15. Atwood, K.; Arnold, M.R., Kindrick, R.C. Ind. Eng. Chem., 1957, 49, 1439. 16. Klyamer, S.D.; Kolesnikova, T.L. Zhur. Fiz. Khim., 1972, 46, 1o56. 17. Klyamer, S.D.; Kolesnikova, T.L.; Rodin, Yu.A. Gazov. Prom., 1973, 18(2), 44. 18. Deshmukh, R.D.; Mather, A.E. Chem. Eng. Sci. (in press). 19. Peng, D.-Y.; Robinson, D.B. Ind. Eng. Chem. Fundam., 1976, 15, 59. 20. Guggenheim, E.A. Phil. Mag., 1935, 21, 588. 21. Brown, K.M. SIAM J. Numer. Anal., 1969, 6, 56o. 22. Brown, K.M. in Numerical Solution of Nonlinear Algebraic Equations, ed. by G.D. Byrne and C.A. Hall, Academic Press, 1973, p. 281. 23. Isaacs, E.E.; Otto, F.D.; Mather, A.E. Can. J. Chem. Eng., 1977, 55, 21o. RECEIVED

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4 Two New Activity Coefficient Models for the Vapor-Liquid Equilibrium of Electrolyte Systems CHAU-CHYUN CHEN, HERBERT I. BRITT, JOSEPH F. BOSTON, and LAWRENCE B. EVANS Department of Chemical Engineering and Energy Laboratory, Massachusetts Institute of Technology, Cambridge, M A 02139

The use of modern process simulators for the analysis and design of processes involvin limited by the lack of thermodynamics. For most systems of industrial importance, empirical correlations are applicable only to one particular system, over a limited range of conditions. The empirical correlations do not provide a framework for treating new systems or for extending the range of existing data, because the nonidealities have not been accounted for in a general and consistent manner. As in the nonelectrolyte case, the problem of representing the thermodynamic properties of electrolyte solutions is best regarded as that of finding a suitable expression for the non-ideal part of the chemical potential, or the excess Gibbs energy, as a function of composition, temperature, dielectric constant and any other relevant variables. Recently, there have been a number of significant developments in the modeling of electrolyte systems. Bromley (1), Meissner and Tester (2), Meissner and Kusik (3), Pitzer and co-workers (4,5,6), and Cruz and Renon (7), presented models for calculating the mean ionic activity coefficients of many types of aqueous electrolytes. In addition, Edwards, et al. (8) proposed a thermodynamic framework to calculate equilibrium vapor-liquid compositions for aqueous solutions of one or more volatile weak electrolytes which involved activity coefficients of ionic species. Most recently, Beutier and Renon (9) and Edwards, et al.(10) used simplified forms of the Pitzer equation to represent ionic activity coefficients. In t h i s p a p e r , two new m o d e l s f o r t h e a c t i v i t y c o e f f i c i e n t s o f i o n i c and m o l e c u l a r s p e c i e s i n e l e c t r o l y t e systems a r e p r e s e n t e d . The f i r s t i s an e x t e n s i o n o f t h e P i t z e r e q u a t i o n and i s c o v e r e d i n more d e t a i l i n C h e n , e t a l . ( 1 1 ) . The s e c o n d i s based on t h e l o c a l c o m p o s i t i o n c o n c e p t and r e p r e s e n t s work i n p r o g r e s s .

0-8412-0569-8/80/47-133-061$07.25/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

62

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Nature of E l e c t r o l y t e

Systems

The t h e r m o d y n a m i c p r o p e r t i e s o f a m i x t u r e depend on t h e f o r c e s w h i c h o p e r a t e between t h e s p e c i e s o f t h e m i x t u r e . E l e c t r o l y t e s y s t e m s a r e c h a r a c t e r i z e d by t h e p r e s e n c e o f b o t h m o l e c u l a r s p e c i e s and i o n i c s p e c i e s , r e s u l t i n g i n t h r e e d i f f e r e n t types of i n t e r a c t i o n . They a r e i o n - i o n i n t e r a c t i o n , m o l e c u l e - m o l e c u l e i n t e r a c t i o n , and i o n - m o l e c u l e i n t e r a c t i o n . The f o r c e s i n v o l v e d i n each i n t e r a c t i o n a r e b r i e f l y d i s c u s s e d in the f o l l o w i n g paragraphs. The i o n - i o n i n t e r a c t i o n i s c h a r a c t e r i z e d by e l e c t r o s t a t i c f o r c e s between i o n s . These e l e c t r o s t a t i c f o r c e s a r e i n v e r s e l y p r o p o r t i o n a l t o t h e s q u a r e o f t h e s e p a r a t i o n d i s t a n c e and t h e r e f o r e have a much g r e a t e r r a n g e t h a n i n t e r m o l e c u l a r f o r c e s w h i c h depend on h i g h e r powers o f t h e r e c i p r o c a l d i s t a n c e . E x c e p t at s h o r t - r a n g e , c a n t compared t o t h e i n t e r i o n i Many d i f f e r e n t t y p e s o f f o r c e s a r i s e f r o m m o l e c u l e molecule i n t e r a c t i o n . They may be e l e c t r o s t a t i c f o r c e s between permanent d i p o l e s , i n d u c t i o n f o r c e s between a permanent d i p o l e and i n d u c e d d i p o l e s , o r d i s p e r s i o n f o r c e s between n o n - p o l a r molecules, etc. (Prausnitz, U 2 ) ) . Forces involved in moleculem o l e c u l e i n t e r a c t i o n a r e known t o be s h o r t - r a n g e i n n a t u r e . The f o r c e s i n v o l v e d i n i o n - m o l e c u l e i n t e r a c t i o n a r e a l s o short-range in nature. The d o m i n a n t f o r c e s a r e e l e c t r o s t a t i c f o r c e s between i o n s and permanent d i p o l e s . As d i s c u s s e d by R o b i n s o n and S t o k e s (11) r e g a r d i n g aqueous e l e c t r o l y t e s y s t e m s , i t seems l i k e l y t h a t t h e i o n - m o l e c u l e i n t e r a c t i o n e n e r g i e s o f t h e w a t e r m o l e c u l e s i n t h e f i r s t l a y e r about a monatomic i o n w o u l d be l a r g e compared w i t h t h e t h e r m a l e n e r g y ( R T ) , and t h e s e c o n d l a y e r o f w a t e r m o l e c u l e s w i l l be much l e s s s t r o n g l y bound t o t h e i o n t h a n t h e f i r s t . It is probably only with p o l y v a l e n t monatomic i o n s o f s m a l l s i z e t h a t t h e i n t e r a c t i o n e n e r g i e s o f t h e w a t e r m o l e c u l e s i n t h e s e c o n d l a y e r w o u l d be comparable to the thermal energy. The e x c e s s G i b b s e n e r g y o f e l e c t r o l y t e s y s t e m s can be c o n s i d e r e d as t h e sum o f two t e r m s , one r e l a t e d t o l o n g - r a n g e f o r c e s between i o n s and t h e o t h e r t o s h o r t - r a n g e f o r c e s between a l l the s p e c i e s . As d i s c u s s e d by R o b i n s o n and S t o k e s ( 1 3 ) , long-range f o r c e s dominate i n the r e g i o n of d i l u t e e l e c t r o l y t e c o n c e n t r a t i o n and s h o r t - r a n g e f o r c e s d o m i n a t e i n t h e r e g i o n o f high e l e c t r o l y t e concentration. It i s the long-range nature of t h e e l e c t r o s t a t i c f o r c e s between i o n s t h a t have no c o u n t e r p a r t in n o n e l e c t r o l y t e systems. The P i t z e r

Equation

In a s e r i e s o f p a p e r s . , P i t z e r and h i s c o - w o r k e r s (4,5,6.) proposed a very u s e f u l s e m i e m p i r i c a l equation f o r the

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

CHEN ET AL.

4.

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Activity Coefficient Models

u n s y r c n e t r i c e x c e s s G i b b s f r e e e n e r g y o f aqueous systems. The b a s i c e q u a t i o n i s G

electrolyte

ex*

— ^ ( Π + Σ Σ λ , ^ ΐ ^ ^ + Σ Σ Σ μ ^ ^ ^ n RT ij ijk

(1)

w

The f u n c t i o n f ( I ) e x p r e s s e s t h e e f f e c t o f l o n g - r a n g e e l e c t r o s t a t i c f o r c e s between i o n s . It is a function of ionic s t r e n g t h , t e m p e r a t u r e and s o l v e n t p r o p e r t i e s . The e m p i r i c a l f o r m chosen by P i t z e r f o r f ( I ) i s f(I)

41 =-Α —1η(1+1.2/Γ) 1.2

(2)

φ

The p a r a m e t e r s λ^ t h e e f f e c t o f s h o r t - r a n g e f o r c e s between s o l u t e s i and j ; t h e p a r a m e t e r s y-jjk a r e c o r r e s p o n d i n g t h i r d v i r i a l c o e f f i c i e n t s f o r t h e i n t e r a c t i o n o f t h r e e s o l u t e s i , j , and k. The s e c o n d v i r i a l c o e f f i c i e n t s are a f u n c t i o n o f i o n i c s t r e n g t h . Dependence o f t h e t h i r d v i r i a l c o e f f i c i e n t s on i o n i c s t r e n g t h is neglected. The λ and y m a t r i c e s a r e t a k e n t o be s y m m e t r i c . To make t h e b a s i c P i t z e r e q u a t i o n more u s e f u l f o r d a t a c o r r e l a t i o n o f aqueous s t r o n g e l e c t r o l y t e s y s t e m s , P i t z e r m o d i f i e d i t by d e f i n i n g a new s e t o f more d i r e c t l y o b s e r v a b l e p a r a m e t e r s r e p r e s e n t i n g c e r t a i n c o m b i n a t i o n s o f t h e s e c o n d and third virial coefficients. The m o d i f i e d P i t z e r e q u a t i o n i s G

ex*

=f(I)+^m m ,(0 ,+Zm^ ce' a +2E^ m [B (l)+(Em Z C ca c c

n RT w

c

a

c

c a

c c

c

c

c c

. )+EEm m ,(6 aa )//Z Z ] a

a

a

1

c a

c

a a

,+Em^ c

a a

. ) c

(3)

a

E s s e n t i a l l y , t h e new p a r a m e t e r s Β and θ a r e b i n a r y i o n - i o n p a r a m e t e r s and C and Ψ t e r n a r y i o n - i o n p a r a m e t e r s . The i o n - i o n i n t e r a c t i o n p a r a m e t e r s , Β and C , a r e c h a r a c t e r i s t i c o f each aqueous s i n g l e - e l e c t r o l y t e s y s t e m . The i o n - i o n d i f f e r e n c e p a r a m e t e r s , θ and Ψ , a r e c h a r a c t e r i s t i c o f each aqueous m i x e d - e l e c t r o l y t e system. R e c o g n i z i n g t h e i o n i c s t r e n g t h dependence o f t h e e f f e c t o f s h o r t range f o r c e s i n b i n a r y i n t e r a c t i o n s , P i t z e r was a b l e t o d e v e l o p an e m p i r i c a l r e l a t i o n f o r B ( I ) . The e x p r e s s i o n f o r s y s t e m s c o n t a i n i n g s t r o n g e l e c t r o l y t e s w i t h one o r b o t h i o n s univalent i s ç a

B

c a

(I)

= Bj^+B^tl-d+a/TJexpi-a/T)]^!

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

(4)

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THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

parameters in the m o d i f i e d P i t z e r e q u a t i o n a r e β Ι ) , β ΐ ) , C, θ , and Ψ. The m o d i f i e d P i t z e r e q u a t i o n has been s u c c e s s f u l l y a p p l i e d t o t h e a v a i l a b l e d a t a f o r many p u r e e l e c t r o l y t e s ( P i t z e r and M a y o r g a , (!5)) and m i x e d aqueous e l e c t r o l y t e s ( P i t z e r and K i m , ( 6 J ) . The"~fit t o the experimental data i s w i t h i n the probable experimental e r r o r up t o m o l a l i t i e s o f 6 . H o w e v e r , i n most aqueous e l e c t r o l y t e s y s t e m s o f i n d u s t r i a l i n t e r e s t , not o n l y s t r o n g e l e c t r o l y t e s b u t a l s o weak e l e c t r o ­ l y t e s and m o l e c u l a r n o n e l e c t r o l y t e s a r e p r e s e n t . While the m o d i f i e d P i t z e r e q u a t i o n a p p e a r s t o be a u s e f u l t o o l f o r t h e r e p r e s e n t a t i o n o f aqueous s t r o n g e l e c t r o l y t e s i n c l u d i n g m i x e d e l e c t r o l y t e s , i t c a n n o t be u s e d i n t h e f o r m j u s t p r e s e n t e d t o r e p r e s e n t the i m p o r t a n t case o f systems c o n t a i n i n g m o l e c u l a r solutes. A u n i f i e d t h e r m o d y n a m i c model f o r b o t h i o n i c s o l u t e s and m o l e c u l a r s o l u t e s i systems. ϋ

1

P r e v i o u s A p p l i c a t i o n s of the P i t z e r Equation Electrolytes

t o Weak

R e c e n t l y , t h e P i t z e r e q u a t i o n has been a p p l i e d t o model weak e l e c t r o l y t e s y s t e m s by B e u t i e r and Renon (9.) and E d w a r d s , et a l . (10). B e u t i e r and Renon used a s i m p l i f i e d P i t z e r equation f o r the ion-ion i n t e r a c t i o n c o n t r i b u t i o n , applied D e b y e - M c A u l a y ' s e l e c t r o s t a t i c t h e o r y ( H a r n e d and Owen, ( 1 4 ) ) f o r t h e i o n - m o l e c u l e i n t e r a c t i o n c o n t r i b u t i o n , and adopted" M a r g u l e s t y p e t e r m s f o r m o l e c u l e - m o l e c u l e i n t e r a c t i o n s between t h e same m o l e c u l a r s o l u t e s . Edwards, et a l . a p p l i e d the P i t z e r e q u a t i o n d i r e c t l y , w i t h o u t d e f i n i n g any new t e r m s , f o r a l l i n t e r a c t i o n s ( i o n - i o n , i o n - m o l e c u l e , and m o l e c u l e - m o l e c u l e ) while neglecting a l l ternary parameters. B r o m l e y ' s {I) ideas on a d d i t i v i t y o f i n t e r a c t i o n p a r a m e t e r s o f i n d i v i d u a l i o n s and c o r r e l a t i o n between i n d i v i d u a l i o n and p a r t i a l m o l a r e n t r o p y o f i o n s at i n f i n i t e d i l u t i o n were a d o p t e d i n b o t h s t u d i e s . In a d d i t i o n , they both n e g l e c t e d c o n t r i b u t i o n s from i n t e r a c t i o n s among i o n s o f t h e same s i g n . T h e r e a r e d r a w b a c k s w i t h t h e a p p r o a c h e s t a k e n by b o t h B e u t i e r and R e n o n , and E d w a r d s , e t a l . F i r s t , the P i t z e r e q u a t i o n i s a v i r i a l - e x p a n s i o n t y p e e q u a t i o n and s e m i - e m p i r i c a l in nature. E s t i m a t i n g i n t e r a c t i o n parameters using Bromley's a p p r o a c h i s based on an i n t e r p r e t a t i o n o f t h e p a r a m e t e r s t h a t i s u n c e r t a i n at b e s t and i n any c a s e i s n o t v a l i d a t h i g h i o n i c strength. Second, t e r n a r y parameters i n the P i t z e r equation can be s i g n i f i c a n t f o r s y s t e m s o f h i g h i o n i c s t r e n g t h . These p a r a m e t e r s s h o u l d n o t be n e g l e c t e d i n a model c o v e r i n g h i g h i o n i c strength e l e c t r o l y t e systems. Third, Bronsted's p r i n c i p l e of s p e c i f i c ion i n t e r a c t i o n i s the b a s i s f o r assuming t h a t i n t e r a c t i o n s between i o n s o f t h e same s i g n can be neglected. However, B r o n s t e d ' s p r i n c i p l e of s p e c i f i c i o n

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4.

CHEN ET AL.

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i n t e r a c t i o n i s n o t a l w a y s v a l i d , as d i s c u s s e d i n P i t z e r * s p a p e r (£). Fourth, t h e o r e t i c a l aspects o f the physical chemistry o f s a l t i n g - o u t e f f e c t s on n o n - e l e c t r o l y t e s a r e s t i l l i n a development s t a g e . W h i l e many t h e o r i e s have been p r o p o s e d i n t h e l i t e r a t u r e , none i s q u a n t i t a t i v e l y s a t i s f a c t o r y , i n c l u d i n g Debye-McAulay's e l e c t r o s t a t i c t h e o r y . Extension of t h e P i t z e r

Equation

In t h i s s t u d y t h e P i t z e r e q u a t i o n i s a l s o u s e d , b u t a d i f f e r e n t , more s t r a i g h t f o r w a r d a p p r o a c h i s a d o p t e d i n w h i c h t h e drawbacks j u s t d i s c u s s e d do n o t a r i s e . F i r s t , terms a r e added t o t h e b a s i c v i r i a l f o r m o f t h e P i t z e r e q u a t i o n t o a c c o u n t f o r m o l e c u l e - i o n and m o l e c u l e - m o l e c u l e i n t e r a c t i o n s . Then, f o l l o w i n g P i t z e r , a s e t o f new, more o b s e r v a b l e p a r a m e t e r s a r e defined that are function the P i t z e r equation i s account f o r t h e presence o f m o l e c u l a r s o l u t e s . The i n t e r p r e t a ­ t i o n o f t h e terms and p a r a m e t e r s o f t h e o r i g i n a l P i t z e r e q u a t i o n i s unchanged. The r e s u l t i n g e x t e n d e d P i t z e r e q u a t i o n i s G

ex* =f(I)*Zm m .(e .+Zm^ . )+ZZm m .(e ce' a aa' c

n RT w

c

c c

c c

a

a

a

+2EDn m [B (I)+(zm Z C )//Z^7] c

ca

a

ca

c

c

c

ca

a a

.+Em^ c

a a

. ) c

(5)

%"\η' mm' Σ(E&ca,n¥a- ^cc ' , m ¥ c ') mm ma c'

+ Σ Σ

x

+

1

The p a r a m e t e r s D a r e b i n a r y parameters r e p r e s e n t i n g t h e i n t e r a c t i o n s between s a l t c a and m o l e c u l a r s o l u t e m i n an aqueous s i n g l e s a l t , s i n g l e m o l e c u l a r s o l u t e s y s t e m . Binary parameters ςο',Γη * ^ a ' m represent the differences between t h e i n t e r a c t i o n s o f a s p e c i f i c m o l e c u l a r s o l u t e w i t h two u n l i k e s a l t s s h a r i n g one common a n i o n o r c a t i o n . Ternary molecule-ion v i r i a l c o e f f i c i e n t s are neglected i n t h i s study t o simplify the extension. I t i s i n t e r e s t i n g t o note t h a t t h e molecule-ion i n t e r a c t i o n contribution i n equation (5) i s consistent with t h e w e l l - k n o w n Setschenow e q u a t i o n . The Setschenow e q u a t i o n i s used t o r e p r e s e n t t h e s a l t i n g - o u t e f f e c t o f s a l t s on m o l e c u l a r n o n e l e c t r o l y t e s o l u t e s , when t h e s o l u b i l i t i e s o f t h e l a t t e r a r e small (Gordon, ( 1 5 ) ) . The Setschenow e q u a t i o n i s c a m

ω

l n

Y*m

= k

a n (

s,m s

(6)

m

where k ^ i s t h e Setschenow c o n s t a n t ( a s a l t - m o l e c u l e i n t e r a c t i o n p a r a m e t e r ) and m i s t h e m o l a l i t y o f t h e s a l t . The D ' s a r e e q u i v a l e n t t o t h e Setschenow c o n s t a n t s and t h e ω s a r e e q u i v a l e n t t o d i f f e r e n c e s between Setschenow c o n s t a n t s . s

m

s

1

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

66

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

The t h i r d v i r i a l c o e f f i c i e n t s f o r m o l e c u l e - m o l e c u l e i n t e r a c t i o n s can be t a k e n as z e r o f o r aqueous s y s t e m s c o n t a i n i n g m o l e c u l a r s o l u t e s a t low c o n c e n t r a t i o n . The r e m a i n i n g term f o r the m o l e c u l e - m o l e c u l e i n t e r a c t i o n c o n t r i b u t i o n i s e q u i v a l e n t to the unsymmetric t w o - s u f f i x Margules model. S u m m a r i z i n g t h e r e s u l t s o f t h i s s e c t i o n , an e x c e s s G i b b s f r e e e n e r g y model f o r b o t h i o n i c and m o l e c u l a r s o l u t e s i n aqueous e l e c t r o l y t e s y s t e m s i s o b t a i n e d by e x t e n d i n g t h e P i t z e r equation i n order to account f o r the presence of m o l e c u l a r solutes. Model p a r a m e t e r s i n c l u d e b i n a r y i o n - i o n i n t e r a c t i o n and d i f f e r e n c e p a r a m e t e r s , t e r n a r y i o n - i o n i n t e r a c t i o n and d i f f e r e n c e parameters, s a l t - m o l e c u l e i n t e r a c t i o n parameters or Setschenow c o n s t a n t s , s a l t - s a l t d i f f e r e n c e parameters f o r m o l e c u l a r s o l u t e s a l t i n g , and u n s y m m e t r i c M a r g u l e s p a r a m e t e r s f o r molecule-molecule i n t e r a c t i o n s t h e model i s d e s i g n e d f o t i o n o f aqueous e l e c t r o l y t e s y s t e m s , i n c l u d i n g m i x t u r e s w i t h any number o f m o l e c u l a r and i o n i c s o l u t e s . A p p l i c a t i o n of the Extended P i t z e r

Equation

To t e s t t h e v a l i d i t y o f t h e e x t e n d e d P i t z e r e q u a t i o n , c o r r e l a t i o n s o f v a p o r - l i q u i d e q u i l i b r i u m d a t a were c a r r i e d o u t f o r three systems. Since the extended P i t z e r equation reduces t o t h e P i t z e r e q u a t i o n f o r aqueous s t r o n g e l e c t r o l y t e s y s t e m s , and i s c o n s i s t e n t w i t h t h e S e t s c h e n o w e q u a t i o n f o r m o l e c u l a r n o n - e l e c t r o l y t e s i n aqueous e l e c t r o l y t e s y s t e m s , t h e main i n t e r e s t h e r e i s aqueous s y s t e m s w i t h weak e l e c t r o l y t e s o r partially dissociated electrolytes. The t h r e e s y s t e m s c o n s i d e r e d a r e : t h e h y d r o c h l o r i c a c i d aqueous s o l u t i o n a t 298.15°K and c o n c e n t r a t i o n s up t o 18 m o l a l ; t h e N H 3 - C O 2 aqueous s o l u t i o n a t 2 9 3 . 1 5 ° K ; and t h e K 2 C O 3 - C O 2 aqueous s o l u t i o n o f t h e Hot C a r b o n a t e P r o c e s s . In each c a s e , t h e c h e m i c a l e q u i l i b r i u m between a l l s p e c i e s has been t a k e n i n t o a c c o u n t d i r e c t l y as l i q u i d phase c o n s t r a i n t s . Significant p a r a m e t e r s i n t h e model f o r each s y s t e m were i d e n t i f i e d by a p r e l i m i n a r y o r d e r o f m a g n i t u d e a n a l y s i s and a d j u s t e d i n t h e v a p o r - l i q u i d e q u i l i b r i u m data c o r r e l a t i o n . Detailed discusions and v a l u e s o f p h y s i c a l c o n s t a n t s , s u c h as H e n r y ' s c o n s t a n t s and c h e m i c a l e q u i l i b r i u m c o n s t a n t s , a r e g i v e n i n Chen e t a l . ( 1 1 ) . T-P-x-y d a t a f o r h y d r o c h l o r i c a c i d c o n c e n t r a t i o n up t o 18 m o l a l were o b t a i n e d f r o m Vega and V e r a ( 1 6 J . The f o l l o w i n g r e a c t i o n s occur i n the l i q u i d phase. HC1

H 0 2

% H * H

+ +

+ CT + 0H-

The l e a s t s q u a r e s d a t a c o r r e l a t i o n was c a r r i e d o u t on H C 1 v a p o r m o l e f r a c t i o n and t o t a l

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

CHEN ET AL.

4.

Activity Coefficient Models

D H C l , H C " h Η Π HC1» * H e n r y ' s c o n s t a n t f o r hydrogen c h l o r i d e as a d j u s t a b l e p a r a m e t e r s . F i g u r e 1 shows e x p e r i m e n t a l d a t a and c o r r e l a t i o n r e s u l t s . The a v e r a g e p e r c e n t a g e d e v i a t i o n f o r t o t a l p r e s s u r e i s 0 . 4 4 , and t h a t f o r HC1 v a p o r f r a c t i o n i s 0.35. The same d a t a was p r e v i o u s l y c o r r e l a t e d w i t h t h e same o b j e c t i v e f u n c t i o n by C r u z and Renon ( 7 J . T h e i r r e s u l t s were 0 . 9 9 p e r c e n t d e v i a t i o n f o r t o t a l p r e s s u r e and 0 . 3 4 p e r c e n t d e v i a t i o n f o r HC1 v a p o r f r a c t i o n . The d a t a r e p o r t e d by van K r e v e l e n , e t a l . ( J 7 ) a t 2 9 3 . 1 5 ° K were used f o r d a t a c o r r e l a t i o n o f t h e N H 3 - C O 2 aqueous s o l u t i o n s y s t e m . The f o l l o w i n g r e a c t i o n s o c c u r i n t h e l i q u i d phase. λ

NH C0

a n c

+ H 0 * N H 4 + 0H" + H 0 * H + HCO3

3

2

2

2

HC05 NH3

*

+

=

CO3 + H

+ HCO3

H 0 * H 2

*

+

NH9COO-

+

+ 0H-

+

The l e a s t pressures

s q u a r e s d a t a c o r r e l a t i o n was c a r r i e d o u t on p a r t i a l o f N H 3 and C 0 w i t h e l ) N H H C 0 , 3 ( 0 ) ( N H ) C 0 , 0

2

B(0)NH4NH C00,

DNH HC03,NH3

2

4

a

D

4

3

4

(NH4)2C03,NH , 3

a n d

D

2

3

NHdNH?C00,NH 2

and

adjustable'parameters. The a v e r a g e p e r c e n t d e v i a t i o n o f c a l c u l a t e d v e r s u s measured p a r t i a l p r e s s u r e o f

*K

C0

+

2

?

HC0 ~^C03~ 3

at 3 8 3 . 1 5 0 K

a

s

i s 1 1 . 5 % and f o r H 0 i s 2

10.5%.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

HCI Concentration

(Molality)

Figure 1. Total vapor pressure and vapor phase HCI mole fraction of the HCI aqueous solution at 298.15 Κ (( ) calculated; (O, A) data from Ref. 16)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

CHEN ET AL.

Activity Coefficient Models

Figure 2. Partial pressures of NH and C0 of the NH -C0 aqueous solution at 293.15 K (experimental data ( Ί 7 Λ Ό s (2N NH ); f | J NH (IN NH ); (O) CO, (2N NH ); (Φ) C0 (IN NH ); ( ) calculated) 3

2

N

3

3

3

2

2

H

3

3

3

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

70

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

L i m i t a t i o n s o f the P i t z e r

Equation

The P i t z e r e q u a t i o n j u s t p r e s e n t e d i s s u b j e c t t o a l l o f the l i m i t a t i o n s of a v i r i a l - e x p a n s i o n type e q u a t i o n . The equation parameters, denoting the short-range i n t e r a c t i o n s between and among s o l u t e s p e c i e s , a r e a r b i t r a r y , h i g h l y t e m p e r a t u r e - d e p e n d e n t and a r e c h a r a c t e r i s t i c o f t h e s o l v e n t . B i n a r y p a r a m e t e r s a r e e x p r e s s e d as e m p i r i c a l f u n c t i o n s o f i o n i c strength. D i f f e r e n t e m p i r i c a l f u n c t i o n s are proposed f o r d i f f e r e n t types of e l e c t r o l y t e s . Ternary parameters are r e q u i r e d f o r e l e c t r o l y t e systems at h i g h e r i o n i c s t r e n g t h . F u r t h e r m o r e , f o r the i n d u s t r i a l l y i m p o r t a n t c l a s s o f mixed s o l v e n t e l e c t r o l y t e systems, the P i t z e r equation i s not a p p l i c a b l e b e c a u s e i t s p a r a m e t e r s a r e unknown f u n c t i o n s o f s o l v e n t c o m p o s i t i o n and b e c a u s e t h e e m p i r i c a l e x p r e s s i o n s r e q u i r e d are a v a i l a b l e o n l P i t z e r e q u a t i o n h a s bee r e p r e s e n t a t i o n o f aqueous e l e c t r o l y t e s y s t e m s , a more v e r s a t i l e model i s needed t o c o v e r a w i d e r v a r i e t y o f e l e c t r o l y t e s y s t e m s . The L o c a l

C o m p o s i t i o n Model

N o n e l e c t r o l y t e s y s t e m s , w h i c h a r e c h a r a c t e r i z e d by s h o r t - r a n g e f o r c e s between m o l e c u l e s , h a v e f r e q u e n t l y been s t u d i e d using the l o c a l composition concept. M o d e l s s u c h as W i l s o n ( 1 9 ) , NRTL (Renon and P r a u s n i t z , ( 2 0 ) ) , and UNIQUAC (Abrams and P r a u s n i t z , ( 2 1 ) ) have r e s u l t e d . Such m o d e l s have p r o v e n t o be a g r e a t advancement o v e r o l d e r m o d e l s b a s e d on a l g e b r a i c e x p a n s i o n s o f m o l e f r a c t i o n , s u c h as t h e M a r g u l e s model. In t h i s s t u d y t h e l o c a l c o m p o s i t i o n c o n c e p t i s a p p l i e d to the short range i n t e r a c t i o n f o r c e s o c c u r r i n g i n e l e c t r o l y t e s y s t e m s w i t h t h e hope t h a t a s i m i l a r a d v a n c e o v e r t h e P i t z e r model w i l l r e s u l t . However, i t must be e m p h a s i z e d t h a t t h e l o c a l c o m p o s i t i o n c o n c e p t i s i n no s e n s e r i g o r o u s . I t i s used to develop c o r r e l a t i n g e x p r e s s i o n s , with adjustable parameters, f o r experimental data. The p u r p o s e i n a d o p t i n g a q u a s i t h e o r e t i c a l approach i s t o develop e x p r e s s i o n s w i t h a s m a l l number o f p a r a m e t e r s , t h a t a p p l y o v e r w i d e c o n c e n t r a t i o n r a n g e s , may be e x p r e s s e d as s i m p l e f u n c t i o n s o f t e m p e r a t u r e , and may be u s e d t o p r e d i c t t h e b e h a v i o r o f m u l t i c o m p o n e n t systems. The v a l i d i t y o f t h i s a p p r o a c h may be d e t e r m i n e d o n l y by i t s e m p i r i c a l s u c c e s s o r f a i l u r e . We b e l i e v e t h a t t h e model t o be p r e s e n t e d i n t h i s s t u d y i s q u i t e s u c c e s s f u l by t h e s e c r i t e r i a , as d e m o n s t r a t e d by t h e e x a m p l e s shown i n t h i s p a p e r and a d d i t i o n a l work we have done w i t h m u l t i c o m p o n e n t s y s t e m s i n v o l v i n g weak e l e c t r o l y t e s . A f u n d a m e n t a l d i f f e r e n c e between e l e c t r o l y t e s y s t e m s and n o n e l e c t r o l y t e systems i s the presence o f long range i o n - i o n e l e c t r o s t a t i c f o r c e s in e l e c t r o l y t e systems. No a t t e m p t was made t o d e v e l o p a l o n g - r a n g e c o n t r i b u t i o n model b a s e d on t h e

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4.

CHEN ET AL.

Activity Coefficient Models

71

l o c a l compostion concept. I n s t e a d , t h e Debye-Huckel f o r m u l a as p r o p o s e d by F o w l e r and Guggenheim ( 2 2 ) was used w i t h o u t m o d i f i c a t i o n t o r e p r e s e n t t h e unsymmetric excess Gibbs energy c o n t r i b u t i o n a r i s i n g from t h e long-range ion-ion e l e c t r o s t a t i c forces. N e v e r t h e l e s s , the l o c a l composition concept i s c o n s i s t e n t w i t h t h e Debye-Huckel f o r m u l a i n t h e s e n s e t h a t t h e B o l t z m a n n d i s t r i b u t i o n l a w i s assumed i n b o t h m o d e l s . The Debye-Huckel f o r m u l a i s a f u n c t i o n o f s o l v e n t d e n s i t y , d i e l e c t r i c c o n s t a n t , and i o n i c s t r e n g t h . I t i s known t o c o r r e c t l y account f o r the ion-ion e l e c t r o s t a t i c c o n t r i b u t i o n i n the l i m i t o f i n f i n i t e d i l u t i o n . When e l e c t r o l y t e c o n c e n t r a t i o n i n c r e a s e s , s h o r t - r a n g e f o r c e s s t a r t t o p l a y a r o l e and f i n a l l y dominate i n t h e r e g i o n o f high e l e c t r o l y t e c o n c e n t r a t i o n ( R o b i n s o n and S t o k e s , ( 1 3 ) ) . The g e n e r a l a p p r o a c h t a k e n i n t h e p r e s e n t s t u d y i s as follows. The D e b e y e - H u c k e long-range ion-ion i n t e r a c t i o n concept i s used t o r e p r e s e n t s h o r t range i n t e r a c t i o n s o f a l l kinds. The l o c a l c o m p o s i t i o n model i s b a s e d on two f u n d a m e n t a l a s s u m p t i o n s ; 1) t h a t t h e l o c a l c o m p o s i t i o n o f a n i o n s a r o u n d a n i o n s i s z e r o , and s i m i l a r l y f o r c a t i o n s , w h i c h i s e q u i v a l e n t t o a s s u m i n g t h a t r e p u l s i v e f o r c e s between i o n s o f l i k e c h a r g e are l a r g e , 2) t h a t t h e d i s t r i b u t i o n o f a n i o n s and c a t i o n s around s o l v e n t m o l e c u l e s i s such t h a t t h e n e t i o n i c charge i s zero. The l a t t e r a s s u m p t i o n we r e f e r t o a s l o c a l electroneutrality. The l o c a l c o m p o s t i o n model i s d e v e l o p e d as a s y m m e t r i c m o d e l , b a s e d o n p u r e s o l v e n t and h y p o t h e t i c a l p u r e c o m p l e t e l y dissociated liquid electrolyte. T h i s model i s t h e n n o r m a l i z e d by i n f i n i t e d i l u t i o n a c t i v i t y c o e f f i c i e n t s i n o r d e r t o o b t a i n an u n s y m m e t r i c l o c a l c o m p o s i t i o n m o d e l . F i n a l l y t h e unsymmetric D e b y e - H u c k e l a n d l o c a l c o m p o s i t i o n e x p r e s s i o n s a r e added t o y i e l d t h e excess Gibbs energy e x p r e s s i o n proposed i n t h i s s t u d y . Development o f t h e L o c a l

C o m p o s i t i o n Model

Among t h e v a r i o u s m o d e l s i n c o r p o r a t i n g t h e l o c a l c o m p o s i t i o n c o n c e p t f o r s h o r t - r a n g e i n t e r a c t i o n s , t h e NRTL equation i s adopted i n t h i s s t u d y . E l e c t r o l y t e systems a r e c h a r a c t e r i z e d by e x t r a o r d i n a r i l y l a r g e h e a t s o f m i x i n g . Compared t o t h e h e a t o f m i x i n g , t h e n o n i d e a l e n t r o p y o f m i x i n g i s n e g l i g i b l e , which i s c o n s i s t e n t w i t h t h e b a s i c assumption b e h i n d t h e NRTL e q u a t i o n . In a d d i t i o n , t h e NRTL e q u a t i o n i s a l g e b r a i c a l l y simple w h i l e a p p l i c a b l e t o mixtures which e x h i b i t phase s p l i t t i n g . No s p e c i f i c volume o r a r e a d a t a a r e r e q u i r e d . In t h e NRTL m o d e l , t h e l o c a l m o l e f r a c t i o n s XJ-J and x-ji o f s p e c i e s j and i , r e s p e c t i v e l y , i n t h e i m m e d i a t e neighborhood o f a c e n t r a l molecule o f species i a r e r e l a t e d by

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

72

x

ji/ ii

OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

=( j/ i)Gji

x

x

(7)

x

where Gji ji

=exp(-otTji) (gji-9ii)/RT

T

=

The q u a n t i t i e s gj-j and g-j-j a r e , r e s p e c t i v e l y , e n e r g i e s o f i n t e r a c t i o n between j - i and i - i p a i r s o f s p e c i e s , and a r e i n h e r e n t l y symmetric ( g j i = g i j ) . The nonrandomness f a c t o r , a, was f i x e d a t a v a l u e o f 0 . 2 i n t h i s s t u d y . F o r c o n v e n i e n c e i n r e p r e s e n t i n g o t h e r l o c a l mole f r a c t i o n r a t i o s , we i n t r o d u c e a d d i t i o n a l n o t a t i o n as f o l l o w s : x

ji/*ki

=( j/ k)Gji,ki x

(8)

x

where Gji,ki T

=exp(-cxTji

ji,ki

=(gji-9ki)/

R T

W h i l e t h e d e r i v a t i o n t h a t f o l l o w s may be g e n e r a l i z e d t o handle a l l types o f e l e c t r o l y t e s y s t e m s , f o r the sake o f s i m p l i c i t y , t h e d e r i v a t i o n w i l l be b a s e d on a s i n g l e c o m p l e t e l y - d i s s o c i a t e d e l e c t r o l y t e , s i n g l e solvent system. In a binary mixture of s i n g l e completely-dissociated e l e c t r o l y t e and s i n g l e s o l v e n t , we assume t h a t t h e r e a r e t h r e e t y p e s o f cells. One t y p e c o n s i s t s o f a c e n t r a l s o l v e n t m o l e c u l e w i t h s o l v e n t m o l e c u l e s , a n i o n s and c a t i o n s i n t h e i m m e d i a t e neighborhood. The o t h e r two t y p e s have e i t h e r an a n i o n o r c a t i o n as t h e c e n t r a l s p e c i e s , and an i m m e d i a t e n e i g h b o r h o o d c o n s i s t i n g o f s o l v e n t m o l e c u l e s and o p p o s i t e l y - c h a r g e d i o n s , b u t no i o n s o f l i k e c h a r g e ( i . e . , X c c a a ^ ) l° l mole f r a c t i o n s a r e r e l a t e d by: = x

x x x

cm am mm= 1 mc ac = 1 ma ca + x

+ x

(central (central (central

1

+ x

+ x

=

T h e

c a

solvent cells) cation cells) anion c e l l s )

Among t h e t h r e e t y p e s o f c e l l s t h e r e a r ef o u r d i s t i n c t l o c a l m o l e f r a c t i o n r a t i o s : Xcm/ mm> a m / m m > x / x , and x / caI* notable that the assumption that X c c a a 0 equivalent t o t h e assumption that g and g a r e much g r e a t e r t h a n t h e o t h e r interaction energies. X

x

m c

a c

x

x

i s

m a

= x

c

c

a

=

1 S

a

By combining e q u a t i o n s ( 7 ) , (8) a n d ( 9 ) , t h e f o l l o w i n g expressions f o r t h e local mole f r a c t i o n s i n terms o f o v e r a l l mole f r a c t i o n s may be d e r i v e d :

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

(9)

CHEN ET AL.

4.

xim i^im/( a^am cW m nm) a c = a/ a mGmc,ac ca ~ c'( c m ma,ca' = x

x

x

x

x

x

x

73

Activity Coefficient Models

+ x

x

Π

G

= c

> > ) a

,

m

+ x

x

+ x

1

Λ

λ

00)

G

In o r d e r t o o b t a i n an e x p r e s s i o n f o r t h e e x c e s s G i b b s e n e r g y , we f i r s t d e f i n e g ( ) , g ^ ' , and g ( ) as t h e r e s i d u a l G i b b s e n e r g i e s p e r mole o f c e l l s o f c e n t r a l a n i o n , c e n t r a l c a t i o n and c e n t r a l s o l v e n t m o l e c u l e , r e s p e c t i v e l y . These G i b b s e n e r g i e s a r e r e l a t e d t o t h e l o c a l mole f r a c t i o n s as f o l l o w s : a

9

=

i?i

9 ^ 9

c

m

^ S ma9ma+ ca9ca) a

x

x

m

= Zc( m gmc acgac) x

'

=

x

amgam cmgcm iTmgnfni +x

+x

We t h e n a d o p t t h e p u r e s o l v e n t as t h e r e f e r e n c e s o l v e n t , and a h y p o t h e t i c a e l e c t r o l y t e as t h e r e f e r e n c r e f e r e n c e G i b b s e n e r g i e s p e r mole a r e t h e n : ^ref

"

9ref

= Z

g a

( m

]

,

+ x

C

Z

state

f o r the

c^ac

a9ca

(12)

= 9

ref

^nfîïi

In b o t h e q u a t i o n s ( 1 1 ) and ( 1 2 ) t h e c h a r g e number Z and Z a r e introduced t o account f o r t h e f a c t that t h e r a t i o of t h e c o o r d i n a t i o n number o f c e n t r a l a n i o n c e l l s t o t h a t o f c e n t r a l c a t i o n c e l l s must be e q u a l t o t h e c o r r e s p o n d i n g r a t i o o f c h a r g e n u m b e r s . The m o l a r e x c e s s G i b b s e n e r g y may now be d e r i v e d b y sumning t h e changes i n r e s i d u a l G i b b s e n e r g y r e s u l t i n g when x moles o f s o l v e n t a r e t r a n s f e r e d from t h e s o l v e n t r e f e r e n c e s t a t e t o t h e i r c e l l s i n t h e m i x t u r e , and when x moles o f a n i o n s and x moles of c a t i o n s a r e t r a n s f e r e d from t h e e l e c t r o l y t e r e f e r e n c e s t a t e t o their respective c e l l s in themixture. The e x p r e s s i o n i s : ç

a

m

a

S u b s t i t u t i n g equations g /RT

x

+ x

x

am a z

( 1 3 ) we o b t a i n

=Xm cm^cm m am am

e x

cells

( 1 1 ) and ( 1 2 ) i n t o e q u a t i o n

c

+x

x

c mc c mc,ac x

z

T

i:

+ x

a ma a ma,ca x

z

T

The a s s u m p t i o n o f l o c a l e l e c t r o n e u t r a l i t y a p p l i e d t o t h e o f c e n t r a l s o l v e n t m o l e c u l e s may be s t a t e d as = x

cm c z

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

74

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Substituting equation following equality:

(7)

into t h i s r e l a t i o n s h i p leads to

the (16)

9am ~9cm S i n c e the i n t e r a c t i o n e n e r g i e s are i n f e r r e d from t h i s r e s u l t t h a t : T

am

T

mc,ac " m a , c a

= T

cm

symmetric,

i t may be (17)

~ ca,m T

T

= T

m,ca

(18)

The b i n a r y p a r a m e t e r s T and T t h e n become t h e o n l y two i n d e p e n d e n t a d j u s t a b l e p a r a m e t e r s f o r a s i n g l e c o m p l e t e l y d i s s o c i a t e d e l e c t r o l y t e , s i n g l e solvent system. In o r d e r t o combine e q u a t i o n ( 1 4 ) w i t h t h e D e b y e - H u c k e l f o r m u l a , which account i t i s necessary to normaliz s t a t e f o r the i o n s : C

g */RT e x

A

J

M

M

c

a

= g / R T - x l n Y g > -x 1nY§> ex

c

(19)

a

A f t e r e m p l o y i n g e q u a t i o n (14) t o o b t a i n I n l a n d l n y f a n d s u b s t i t u t i n g back i n t o e q u a t i o n ( 1 9 ) , t h e f i n a l r e s u l t i s : g

e x

/RT

=Xm( cm am) ca,m c mc c m,ca a ma a m,ca ~ c( c m,ca Gcm ca,m) ~ a( a m,ca ^am' ca,m) x

+ x

x

x

x

+x

z

z

T

z

T

T

+ x

+

T

+

x

z

i:

The e q u a t i o n s f o r b i n a r y s y s t e m s j u s t p r e s e n t e d can g e n e r a l i z e d t o m u l t i c o m p o n e n t s y s t e m s c o n s i s t i n g o f any c o m b i n a t i o n o f weak and s t r o n g e l e c t r o l y t e s , m o l e c u l a r s o l v e n t s , and m o l e c u l a r s o l u t e s . D i s c u s s i o n of the Local

(20)

T

T

be

C o m p o s i t i o n Model

The l o c a l c o m p o s i t i o n model makes i t p o s s i b l e t o s t u d y e l e c t r o l y t e thermodynamics over a wide range o f c o m p o s i t i o n s . I t assumes t h a t t h e D e b y e - H u c k e l f o r m u l a i s a d e q u a t e t o r e p r e s e n t t h e l o n g - r a n g e i o n - i o n e l e c t r o s t a t i c c o n t r i b u t i o n and t h e l o c a l c o m p o s i t i o n model can a c c o u n t f o r t h e s h o r t - r a n g e i n t e r a c t i o n s among a l l s p e c i e s . While the v a l i d i t y of the Debye-Huckel f o r m u l a a t h i g h i o n i c s t r e n g t h i s q u e s t i o n a b l e , i t i s hoped t h a t t h e s h o r t - r a n g e c o n t r i b u t i o n w i l l d o m i n a t e a t high i o n i c s t r e n g t h , so t h a t accounting f o r the long-range i o n - i o n e l e c t r o s t a t i c c o n t r i b u t i o n a c c u r a t e l y i s not c r i t i c a l . S y s t e m s w i t h weak e l e c t r o l y t e s , o r p a r t i a l l y d i s s o c i a t e d e l e c t r o l y t e s , c a n be s t u d i e d i f c h e m i c a l e q u i l i b r i u m among i o n i c s p e c i e s and m o l e c u l a r s p e c i e s i s c o n s i d e r e d . Multi-

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4.

CHEN ET AL.

Activity Coefficient Models

75

s o l v e n t s y s t e m s c a n be i n v e s t i g a t e d w i t h t h e k n o w l e d g e o f m i x e d - s o l v e n t d i e l e c t r i c c o n s t a n t and d e n s i t y w h i c h a r e r e q u i r e d f o r t h e Debye-Huckel f o r m u l a . The h y p o t h e t i c a l p u r e c o m p l e t e l y - d i s s o c i a t e d l i q u i d e l e c t r o l y t e model h a s n o t h i n g t o do w i t h s o l i d s a l t c r y s t a l s . However, s a l t p r e c i p i t a t i o n c a n a l s o be s t u d i e d i f s o l u b i l i t y p r o d u c t c o n s t a n t s a r e known. I t s h o u l d be n o t e d t h a t t h e l o c a l c o m p o s i t i o n model i s n o t c o n s i s t e n t w i t h t h e commonly a c c e p t e d s o l v a t i o n t h e o r y . According t o the solvation theory, i o n i c species are completely s o l v a t e d by s o l v e n t m o l e c u l e s . In o t h e r w o r d s , t h e l o c a l mole f r a c t i o n o f s o l v e n t m o l e c u l e s around a c e n t r a l i o n i s u n i t y . T h i s becomes u n r e a l i s t i c when a p p l i e d t o h i g h c o n c e n t r a t i o n e l e c t r o l y t e s y s t e m s s i n c e t h e number o f s o l v e n t m o l e c u l e s w i l l be i n s u f f i c i e n t t o c o m p l e t e l y s o l v a t e i o n s . W i t h t h e l o c a l composition model, a l l ions a r e , e f f e c t i v e l y , completely surrounded by s o l v e n t m o l e c u l e and o n l y p a r t i a l l y s u r r o u n d e concentration e l e c t r o l y t e systems. Therefore, the local c o m p o s i t i o n model i s b e l i e v e d t o be c l o s e r t o t h e p h y s i c a l r e a l i t y than t h e s o l v a t i o n t h e o r y . A p p l i c a t i o n o f the Local

C o m p o s i t i o n Model

A w i d e v a r i e t y o f d a t a f o r mean i o n i c a c t i v i t y c o e f f i c i e n t s , osmotic c o e f f i c i e n t s , vapor pressure d e p r e s s i o n , and v a p o r - l i q u i d e q u i l i b r i u m o f b i n a r y and t e r n a r y e l e c t r o l y t e s y s t e m s have been c o r r e l a t e d s u c c e s s f u l l y by t h e l o c a l composition model. Some r e s u l t s a r e shown i n T a b l e 1 t o T a b l e 10 and F i g u r e 3 t o F i g u r e 7. In each c a s e , t h e c h e m i c a l e q u i l i b r i u m b e t w e e n t h e s p e c i e s h a s been i g n o r e d . That i s , c o m p l e t e d i s s o c i a t i o n o f s t r o n g e l e c t r o l y t e s h a s been a s s u m e d . T h i s a s s u m p t i o n i s n o t r e q u i r e d by t h e l o c a l c o m p o s i t i o n model b u t h a s been made h e r e i n o r d e r t o s i m p l i f y t h e s y s t e m s t r e a t e d . In g e n e r a l , d a t a a r e f i t q u i t e w e l l w i t h t h e m o d e l . F o r e x a m p l e , w i t h o n l y two b i n a r y p a r a m e t e r s , t h e a v e r a g e s t a n d a r d d e v i a t i o n o f c a l c u l a t e d Ι η γ * v e r s u s m e a s u r e d ΙηΎ* o f t h e 50 u n i - u n i v a l e n t aqueous s i n g l e e l e c t r o l y t e s y s t e m s l i s t e d i n Table 1 i s only 0.009. A l t h o u g h t h e f i t i s n o t a s good a s t h e P i t z e r e q u a t i o n , w h i c h a p p l i e s o n l y t o aqueous e l e c t r o l y t e s y s t e m s , w i t h two b i n a r y p a r a m e t e r s and o n e t e r n a r y p a r a m e t e r ( P i t z e r , ( 5 ) ) , i t i s q u i t e s a t i s f a c t o r y and b e t t e r t h a n t h a t o f Bromley's equation ( J J . Data c o r r e l a t i o n r e s u l t s f o r s i n g l e - s a l t , s i n g l e - s o l v e n t b i n a r y s y s t e m s a r e shown i n T a b l e 1 t o T a b l e 6 and F i g u r e 3 t o F i g u r e 6 . T h e r e i s an o b v i o u s t r e n d between ,ca s t a n d a r d d e v i a t i o n o f c a l c u l a t e d Ιηγ* v e r s u s measured Ι η γ * . When t h e a b s o l u t e v a l u e o f x increases, standard deviation also increases. This i s c o n s i s t e n t with t h e physical meaning o f T . The l a r g e r t h e a b s o l u t e v a l u e o f , t h e s t r o n g e r t h e i n t e r a c t i o n between c a t i o n and a n i o n . ' In T

m

Mc

a

c

m

a n c l

a

T

m

c

a

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

76

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Table

1.

Electrolyte

D a t a and R e s u l t s o f F i t f o r Aqueous S o l u t i o n s o f u n i - u n i v a l e n t e l e c t r o l y t e a t 298.15°K - Mean I o n i c A c t i v i t y C o e f f i c i e n t D a t a No. o f d a t a * Points

23 18 21 23 17 12 CSNO3 KAc 18 Κ Br 22 KC1 20 KCNS 21 KF 19 KH m a I o n a t e 21 KH s u c c i n a t e 20 KH2PO4 14 KI 20 KNO3 18 Κ OH 23 LiAc 19 L i Br 23 L i CI 23 19 LiC104 Lil 17 LÏN03 23 LiOH 19 LiTol 20 NaAc 18 NaBr 19 16 NaBr03 Na b u t y r a t e 18 NaCI 23 18 NaC103 23 NaC104 NaCNS 19 NaF 10 Na f o r m a t e 18 NaH2P04 23 Nal 18 Na m a l o n a t e 21 23 NaN03 NaOH 23 Na p r o p i o n a t e 17 Na s u c c i n a t e 21 NH4CI 23 AgNQ3 CsAc CsBr CsCl Csl

molality

T

m,ca

T

ca,m

σ

1ηγ*

0.1· - 6 . 0 0 . Ι ­-3.5 Ο. Ι ­- 5 . 0 Ο. 1·- 6 . 0 0.1-- 3 . 0 0.1· -1.4 0.1· -3.5 0.1· - 5 . 5

7.295 8.462 8.381 8.368 8.280 8.988 8.459 7.901

-3.059 -4.500 -4.034 -4.043 -3.963 -4.057 -4.476 -3.962

0.012 0.009 0.008 0.009 0.007 0.003 0.007 0.002

0.1 - 4 . 0 0.1· - 5 . 0 0.1 -4.5 0.1· - 1 . 8 0.1 -4.5 0.1· - 3 . 5 0.1 - 6 . 0 0.1· - 4 . 0 0.1 - 6 . 0 0.1· - 6 . 0 0.1· - 4 . 0 0.1 - 3 . 0 0.1· - 6 . 0 0.1 - 4 . 0 0.1· - 4 . 5 0.1 - 3 . 5 0.1-- 4 . 0 0.1· - 2 . 5 0.1 - 3 . 5 0.1· - 6 . 0 0.1· - 3 . 5 0.1 - 6 . 0 0.1 - 4 . 0 0.1 - 1 . 0 0.1 - 3 . 5 0.1 - 6 . 0 0.1 - 3 . 5 0.1 - 5 . 0 0.1 - 6 . 0 0.1 - 6 . 0 0.1 - 3 . 0 0.1 - 5 . 0 0.1 - 6 . 0

8.679 7.338 7.982 8.924 7.620 7.642 9.733 8.304 10.331 9.900 9.464 9.157 8.804 8.920 7.396 8.257 8.672 7.587 7.230 8.715 7.128 7.799 7.770 7.517 7.295 8.138 8.752 7.527 7.071 9.225 8.277 8.075 7.614

-4.373 -3.462 -3.861 -4.017 -3.892 -3.327 -4.945 -4.278 -5.251 -5.046 -4.986 -4.889 -4.562 -4.275 -3.710 -4.356 -4.435 -3.589 -4.104 -4.400 -3.527 -3.937 -4.078 -3.677 -3.776 -3.711 -4.535 -3.659 -3.381 -4.647 -4.435 -3.968 -3.800

0.004 0.006 0.002 0.003 0.004 0.008 0.019 0.004 0.046 0.036 0.022 0.024 0.010 0.027 0.012 0.006 0.008 0.001 0.008 0.01,4 0.004 0.007 0.009 0.001 0.003 0.002 0.009 0.003 0.003 0.026 0.006 0.002 0.002

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4.

Activity Coefficient Models

CHEN ET AL.

Table 1.

Continued

RbAc RbBr RbCl Rbl RbNQ3 TIAc

*(Robinson

17 23 23 17 17

HCIO4

HI

HNO3

*(Robinson

Electrolyte

N1SO4 CUSO4

ZnS04 CdS04 UO2SO4

*(Robinson

0.008 0.004 0.003 0.004 0.013 0.014

Highest Molality

m,ca

ca,m

3.0 6.0 6.0 3.0 3.0

9.742 9.957 10.488 9.483 8.327

- 5 . 087 - 5 . 106 - 5 . 328 -5.059 -4.341

σ

1ηγ*

0.014 0.031 0.058 0.017 0.008

and S t o k e s , ( 1 3 ) )

Table 3.

BeS04 MgSC4 MnS04

0.014

D a t a and R e s u l t s o f F i t f o r A c i d s a t 298.15°K Assumin - Mean I o n i

No. o f D a t a * Points

HBr HCI

-3.295 -4.545 -3.891 -3.983 -3.949 -3.287 -3.618

and S t o k e s , ( 1 3 ) )

Table 2.

Acid

7.170 8.602 7.920 8.086 8.052 7.648 7.683

0.1-6.0 0.1-3.5 0.1-5.0 0.1-5.0 0.1-5.0 0.1-4.5 0.1-6.0

23 18 21 21 21 20 23

NH4N03

D a t a and R e s u l t s o f F i t f o r Aqueous S o l u t i o n s o f B i - b i v a l e n t E l e c t r o l y t e s a t 298.15°K - Mean I o n i c A c t i v i t y C o e f f i c i e n t D a t a

No. o f D a t a * Molality Points 18 0.2-4.0 0.2-3.5 16 0.2-4.0 18 0.2-2.5 15 0.2-1.4 11 0.2-3.5 17 0.2-3.5 17 0.2-6.0 22

T

m,ca

11.728 11.623 11.499 11.704 12.128 11.693 11.481 11.316

T

ca,m

-6.905 -6.827 -6.732 -6.826 -7.043 -6.827 -6.704 -6.646

σ

1ηγ*

0.049 0.047 0.046 0.042 0.043 0.046 0.053 0.078

and S t o k e s , ( 1 3 ) )

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

78

Table 4

Electrolyte

D a t a and R e s u l t s o f F i t f o r U n i - u n i v a l e n t E l e c t r o l y t e E f f e c t on t h e Vapor P r e s s u r e o f M e t h a n o l a t 298.05°K No. o f D a t a * Points

LiCl NaBr NaOH Nal KI

9 9 9 16 9

*(Bixon et

al.,

Table 5

T°K

5.3554 1.556 5.9413 4.5200 1.1219

11.783 10.717 10.372 9.716 10.765

28 28 28 28 28

Table 6

Molality

^

0.05-6.0 0.05-6.0 0.05-6.0 0.05-6.0 0.05-6.0

*(Robinson

14 14 14 14 14

m

>

c

Molality

8.831 8.744 8.629 8.510 8.420

0.1-4.0 0.1-4.0 0.1-4.0 0.1-4.0 0.1-4.0

and S t o k e s ,

T

m,ca

7.860 7.831 7.773 7.769 7.760

Fit

σ

a

-4.406 -4.409 -4.380 -4.334 -4.288

1 η γ

(23))

T

ca,m

-3.994 -3.989 -3.970 -3.971 -3.969

*

0.018 0.014 0.011 0.008 0.005

T e m p e r a t u r e E f f e c t on D a t a and R e s u l t s o f f o r Aqueous KBr S o l u t i o n s - Mean I o n i c A c t i v i t y C o e f f i c i e n t D a t a

No. o f D a t a * Points

333.15 343.15 353.15 363.15 373.15

0.034 0.002 0.019 0.011 0.002

T e m p e r a t u r e E f f e c t on D a t a and R e s u l t s o f f o r Aqueous NaCl S o l u t i o n s - Mean I o n i c A c t i v i t y C o e f f i c i e n t D a t a

* s m o o t h e d d a t a ( S i l v e s t e r and P i t z e r ,

T°K

-5.562 -5.176 -5.633 -5.186 -5.138

(25))

No. o f D a t a * Points

273.15 298.15 323.15 348.15 373.15

Highest Molality

σ

Fit

1ηγ* 0.001 0.001 0.001 0.002 0.002

(13))

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4.

CHEN ET AL.

Activity Coefficient Models

T a b l e 7.

Acid HCI HCI HCI HBr HBr HBr

Salt

D a t a and R e s u l t s o f F i t f o r t h e Mean I o n i c A c t i v i t y C o e f f i c i e n t s o f HCL and HBr i n H a l i d e S o l u t i o n s a t 298.15°K A c i d C o n c e n t r a t i o n = 0.01M ( a p p r o x i m a t e d a s 0.01m)

No. o f D a t a * Point 13 9 11 12 11 15

KC1 NaCl L i CI KBr NaBr L i Br

*(Harned

X

T

C09

9 5

HoO =

H 0,C09 2

T

M X , H X ( = • ΗΧ,ΜΧ)

3.0 3.0

Τ

σ

1η *

=

Highest τ Molality 5.732 3.942

5.733 10.414

0.020 0.008

-1.113 -0.307

0.007 0.027

τ

σ

*

] T

-4.115 -6.109

1

m

0.014 0.008

-1.644917+(0.320488D-1)*(T-273.15) T

C0 ,H 0*(2.442172) 2

γ

-1.633 -1.129

D a t a and R e s u l t s o f F i t on S o l u b i l i t y o f C a r b o n D i o x i d e i n Aqueous S o l u t i o n s a t 298.15°K

No. o f Data* Points

NaCl KC1

Highest S a l t Molality 3.5 3.0

and Owen, ( 2 4 ) )

Table 8.

Salt

79

2

b i n a r y d a t a o b t a i n e d f r o m H o u g h t o n , G . , A . M. M c L e a n , and P. D. R i t c h i e , ( 2 6 ) ) (CO2-H26

+ ( Y a s u n i s h i , A . and F. Y o s h i d a , ( 2 4 ) ) + o r i g i n a l d a t a were e x p r e s s e d i n t e r m s o f m o l a r i t y and t h e Ostwald c o e f f i c i e n t

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

80

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Table 9.

x ' 2

0.148 0.148 0.148 0.148 0.292 0.292 0.292 0.292 0.500 0.500 0.500 0.700 0.700 0.700 0.900 0.900

V a p o r - L i q u i d E q u i l i b r i u m Data C o r r e l a t i o n f o r M e t h a n o l - W a t e r - N a B r s y s t e m a t 298.15°K

Salt Molality

Expt. p**

1 2 4 7. 1 1 2 4 5. 7 1 2 4 1 2 2. 8 1 1. 9

49.8 50.1 51.1 50.4 68.0 68.9

0.603 0.627 0.675 0.756 0.742 0.762

50.4 52.7 53.2 47.7 68.7 70.9

85.1 84.35 80.4 99.5 95.7 91.4 114.2 107.3

0.850 0.860 0.884 0.920 0.926 0.932 0.977 0.979

86.9 86.7 79.9 100.4 97.2 92.7 113.6 107.1

0.852 0.852 0.852 0.852 0.708 0.708 0.708 0.708 0.500 0.500 0.500 0.300 0.300 0.300 0.100 0.100

Data* yi

C a l c . Value p** yi

diff Ρ

0.622 0.655 0.686 0.693 0.766 0.783

+0.6 +2.6 +2.1 -2.7 +0.7 +2.0

0.859 0.862 0.853 0.916 0.911 0.906 0.969 0.966 mean dev~

cliffy +0.019 +0.028 +0.011 -0.063 +0.024 +0.021

+ 1.8 +0.009 +2.35 +0.002 - 0 . 5 -0.031 +0.9 -0.-004 +1.5 - 0 . 0 1 5 +1.3 - 0 . 0 2 6 -0.6 -0.008 -0.2 -0.013 1.35 0 . 0 1 9 5

Η ? 0 NaBr =8.672+0.244*(78.48-D)/(78.48-32.66) N a B r H?0 =" .435+0.244*(78.48-D)/(78.48-32.66) CH?0H,NaBr =10.717-3.493*(32.66-D)/(78.48-32.66) NaBr,CHi0H =-5.176-3.493*(32.66-0)/(78.48-32.66) H 0,CH 0H =0.2944 CH 0H,H 0 =0.1936 ( m e t h a n o l - w a t e r b i n a r y d a t a o b t a i n e d f r o m G m e h l i n g , J . and U. Onken, (27)) τ

T

4

T T

T

2

T

3

3

d

2

=0.9971+(-0.163939D-2)*(x ')+(0.1701563D-5)*(xi') -(0.6285073D-7)*(X!') 1

2

3

D

χ x

ΐ' 2

=78.48-(0.4233608)*(xi')-(0.33070470-3)*(xi')2 -(0.3434429D-7)*(x!')3 =

=

x

CH OH/( CH OH H O) H 0/( CH 0H H 07 x

3

X

2

X

+x

3

3

+ X

2

2

* ( C i p a r i s , (28)) * * ( u n i t : mirtigT

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4.

CHEN E T AL.

81

Activity Coefficient Models

T a b l e 10. V a p o r - L i q u i d E q u i l i b r i u m Data C o r r e l a t i o n f o r M e t h a n o l - W a t e r - L i C l s y s t e m a t 298.15°K

X 1

"

Molality

0.152 0.298 0.470 0.700 0.958

0.848 0.702 0.530 0.300 0.042

Η?0 L i C l l i d ' HoO

XH-JOH L i C l

" ρ** P

t

65.3 80.0 96.3 115.3

°

a

t

* yi a

0.765 0.860 0.930 0.993

ρ**

C a l c

ν

65.2 81.0 98.6 117.4

diff P

Ί

* "6 yi

0.751 -0.1 0.840 +1.0 0.917 +2.3 0.988 +2.1 mean d e v . 1.2

diff y

-0.014 -0.020 -0.013 -0.005 0.012

-Π.783-1.853*(32.66-D)/(78.48-32.66)

\iCl,CH30H

=-5.562-1.853*(32.66-D)/(78.48-32.66)

CH 0H,H 0 3

1 1 1 1 1

X

=9.900-0.2239*(78.48-D)/(78.48-32.66) =-5.046-0.2239*(78.48-D)/(78.48-32.66)

τ

T

E

=0.1936

?

H 0,CH 6H =0-2944 ( m e t h a n o l - w a t e r b i n a r y d a t a o b t a i n e d f r o m G m e h l i n g , J . and U. Onken, ( 2 7 ) ) T

2

d

3

=0.9971+(-0.163939D-2)*(x ')+(0.1701563D-5)*(x ') -(0.6285073D-7)*(xi')3 1

1

2

D =78.48-(0.4233608)*(χι')-(0.3307047ϋ-3)*(χ ')2 -(0.3434429D-7)*(xi') Ί

3

χ

ι'

=

χ

2'

= H 0/( CH 0H XH 07

X

X

CH OH/(XCH OH XH O) 3

2

+

3

x

3

+

2

2

* ( C i p a r i s , (28)) * * ( u n i t : mmHgT

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS ι

ι

ι

I

I

I

icient ο

20

-

-

ο ο

^

HCI

>%

:> ο
>

2

Η

§

3

H

κ

g

ο

> Ο G m

*

ο

g

§

£

κ *

6.

MASON AND KAO

113

Aqueous Condensates from Coal Processing

For carbon d i o x i d e , we expressed the Henry's constant i n atm-kg H 0/mole as: 2

log H = 3.822 - 7.8665_x ΙΟ"* exp (T/100) - 0.04145 (T/100) - 17.457 (T/100)

2

2

f o r the temperature range of 20° to 300°C. Values from the equation of EMNP agree w i t h i n 7%. We adopted the equation of C l a r k e and Glew(15), shown i n Figure 5, f o r the Henry's constant of hydrogen s u l f i d e i n atmkg H 0/mole: 2

log H

1

g

= 102.325 - 4423.11 T" - 36.6296 l o g Τ + 0.013870 Τ

I t f i t s the data w e l l from 20° to about 260°C. At temperatures up to 150 C, the equatio We f i t t e d the i n t e r a c t i o represented i n the graphs(8) and given i n Table I I . Values do not d i f f e r s i g n i f i c a n t l y from those of the equations of EMNP(3). Table I I . EFFECT OF TEMPERATURE ON THE ACTIVITY COEFFICIENT OF THE GAS IN BINARY MIXTURE WITH WATER Gas NH3 CO2 C0 HS 2

2

b b b b

Equation l o g γ = bm Temperature Range = 0.0356 - 0.00008 Τ 2 0 - 150 C = -0.767 + 226.7/T 10° - 35°C = -0.143 + 34.56/T 35° - 325°C = -0.143 + 34.56/T 20° - 180°C υ

U

a c

c

s

I o n i z a t i o n Constants Equations f o r the i o n i z a t i o n of water(16) and ammonia(17), each i n c o r p o r a t i n g new data extending to 300 C, have appeared r e c e n t l y (Table I I I ) . A t temperatures up to 150 C e a r l i e r data s e l e c t e d by Barnes e_t al.(18) and represented by the equation of EMNP(3) agree w i t h i n 2.5% f o r water and 6% f o r ammonia. The f i r s t apparent i o n i z a t i o n constant of carbon d i o x i d e (CO2 + H C03) was represented by EMNP i n an equation based on values s e l e c t e d by Barnes et a l . ( 1 8 ) ; l a t e r experimental data by Kryukov agree w i t h the equation w i t h i n 2% (19). Data on the f i r s t i o n i z a t i o n constant of hydrogen s u l f i d e vary more w i d e l y , as shown i n Figure 7. P r o f e s s o r H. L. Barnes(20) has recommended the equation of Naumov(21), a p p l y i n g to the range of 0° to 350°C (Table I I I ) . 2

S a l t i n g Out of Gases S a l t i n g - o u t C o e f f i c i e n t s at 25°C. The e f f e c t of an e l e c ­ t r o l y t e on the s o l u b i l i t y or a c t i v i t y of a gas d i s s o l v e d i n an aqueous s o l u t i o n i s commonly expressed as a s a l t i n g out c o e f f i ­ cient :

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

2

HS

2

3

C0

NH

2

H0

Gas

-3539.1

-5251.53

2.74967X10

81.2824

4

—

-15.97405

94.9734

4

3.12860X10

log Κ =

Table I I I .

Bin Τ

-0.02522

—

-0.0905795

-0.097611

+

CT

—

—

-1.71772X10

6

6

+ Τ

-2.17087X10

+

Ε

12.41

102.2685

-513.761

-606.522

+

0-350

0-225

0-300

Temperature Range, °C 0-300

EFFECT OF TEMPERATURE ON IONIZATION CONSTANTS

(20)

Ç3)

(17)

Reference (16)

MASON AND KAO

Aqueous Condensates from Coal Processing

1

-6.0

20

50

100

150

200

TEMPERATURE, °C

Figure 7. First ionization constant of hydrogen sulfide: (O) Barnes et al; (A) Ellis and Milestone; Ο Ellis and Giggenbach; (V) Ellis; ( 0 ) Helgeson; () Sretenskaya; see Ref. 8

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

116

THERMODYNAMICS

OF

log

AQUEOUS

S -~

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

= l o g γ = kC

Sucii c o e f f i c i e n t s are needed f o r the e f f e c t of ammonium b i c a r ­ bonate, carbamate, and h y d r o s u l f i d e s a l t s on the l i q u i d phase a c t i v i t i e s of ammonia, carbon d i o x i d e , and hydrogen s u l f i d e . They cannot be d i r e c t l y measured because of the chemical r e a c t i o n s of the d i s s o l v e d molecular components, but must be c a l c u l a t e d t h e o r e t i c a l l y or estimated by c o r r e l a t i o n . E l e c t r o s t a t i c theory does not p r e d i c t negative c o e f f i c i e n t s , which are c h a r a c t e r i s t i c of ammonia with some s a l t s . To us, i t appears that scaled par­ t i c l e theory(22) i s probably the best method of c a l c u l a t i o n , but the required parameters ( p o l a r i z a b i l i t y and i o n s i z e ) a r e not a v a i l a b l e f o r the s a l t s of i n t e r e s t . Long and McDevit(23) obtained an expression f o r p r e d i c t i o n of s a l t i n g out of nonpola work required to creat molecules : k

= v°(V -V°)/2.3 RT £ 1 s s ο

—ο where k i s the s a l t i n g - o u t c o e f f i c i e n t on a molar b a s i s , is the p a r t i a l molar volume of the molecular specie at i n f i n i t e d i l u t i o g , V i s the molar volume of the h y p o t h e t i c a l l i q u e f i e d s a l t , V i s the p a r t i a l molar volume of the s a l t i n water at i n f i n i t e d i l u t i o n , and Ê i s the c o m p r e s s i b i l i t y of pure water. This expression i s a l i m i t i n g law f o r i n f i n i t e d i l u t i o n . I t s p h y s i c a l i n t e r p r e t a t i o n i s that the c o n t r a c t i o n i n t o t a l volume that occurs on mixing s a l t and water can be thought of as a compression of the s o l v e n t ; t h i s compression makes i t more d i f f i c u l t to i n s e r t the molecule of n o n e l e c t r o l y t e . This theory has been more s u c c e s s f u l than those based on e l e c t r o s t a t i c e f f e c t s i n e x p l a i n i n g the v a r i a t i o n i n s a l t i n g - o u t c o e f f i c i e n t from s a l t to s a l t , i n c l u d i n g the occurrence of negative values. However, c o e f f i c i e n t s c a l c u l a t e d from t h i s equation or from i t s a l t e r n a t i v e expression using experimental c o m p r e s s i b i l i t y d a t a , do not always agree w e l l w i t h experiment (22). Instead, we use the r e l a t i o n s h i p as the b a s i s of an e m p i r i c a l c o r r e l a t i o n of the e f f e c t of temperature on the s a l t i n g - o u t c o e f f i c i e n t , as described l a t e r . Van Krevelen and H o f t i j z e r developed an e m p i r i c a l c o r r e l a t i o n i n which the c o e f f i c i e n t , on an i o n i c s t r e n g t h b a s i s , i s considered to be the sum of c o n t r i b u t i o n s from the c a t i o n , the anion, and the gas(24): s

s

S log s 6

= (xg + x ca + *an) !

where χ , χ , and χ are s a l t i n g - o u t c o n t r i b u t i o n s from gas, g ca' an

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

6.

MASON AND

KAO

117

Aqueous Condensates from Coal Processing

c a t i o n , and anion, r e s p e c t i v e l y , and I i s i o n i c s t r e n g t h on the molar b a s i s . Once a c o n t r i b u t i o n has been determined from one or more combinations, c o e f f i c i e n t s f o r unmeasured combinations can be c a l c u l a t e d . However, no data were then a v a i l a b l e f o r bicarbonate or h y d r o s u l f i d e s a l t s . More r e c e n t l y , Onda and coworkers (25 26)published a c o r r e l a t i o n u s i n g the same scheme. They measured the s a l t i n g out of ethylene by mixed KHC0 -K C0 and NaHC03-Na2C03 s o l u t i o n s and obtained the c o n t r i b u t i o n o f the bicarbonate i o n by d i f f e r e n c e from t h e i r c o r r e l a t e d values f o r ethylene i n K2CO3 and Na2C03. They give a c o n t r i b u t i o n value f o r the h y d r o s u l f i d e i o n a l s o , but do not reference i t s source. For a s i m i l a r c o r r e l a t i o n , H i k i t a and co-workers measured the s a l t i n g out of n i t r o u s oxide by mixtures of sodium carbonate and sodium bicarbonate.(27) Onda found a standard d e v i a t i o n of 0.0525,/mol f o r h i s comp l e t e set o f data, i n c l u d i n thus provide a c o e f f i c i e n may be i n e r r o r by more than 0.05 £/mol: Onda s c o e f f i c i e n t s f o r gases i n ammonium h y d r o s u l f i d e are of unknown o r i g i n and accuracy, and c o e f f i c i e n t s f o r ammonium carbamate are not provided. I n s h o r t , t h i s type of c o r r e l a t i o n does not provide the needed i n f o r mation. To e s t a b l i s h a data base f o r c o r r e l a t i o n and p r e d i c t i o n of s a l t i n g - o u t c o e f f i c i e n t s , we have gathered a l l the data we could f i n d i n the l i t e r a t u r e on s a l t i n g out of ammonia, carbon d i o x i d e , hydrogen s u l f i d e , and n i t r o u s oxide by ammonium, potassium, and sodium s a l t s of s i n g l e - and double-charged anions. Because m o l a l i t i e s are commonly used f o r expressing c o n c e n t r a t i o n s i n v a p o r - l i q u i d e q u i l i b r i a c o r r e l a t i o n s , we have c a l c u l a t e d the c o e f f i c i e n t s w i t h s a l t c o n c e n t r a t i o n i n gram e q u i v a l e n t s per k i l o g r a m of water and gas s o l u b i l i t y i n amount per kilogram of water. Except f o r s a l t s of low s o l u b i l i t y such as potassium s u l f a t e , bromate, and i o d a t e , measurements were u s u a l l y a v a i l a b l e over a range of c o n c e n t r a t i o n . When c a l c u l a t e d on the molal b a s i s , the s a l t i n g - o u t c o e f f i c i e n t f o r many s a l t s was constant to a few u n i t s i n the t h i r d decimal, but f o r others i t v a r i e d by a maximum of about 0.02 over a 2 m o l a l c o n c e n t r a t i o n range. For t h i s c o m p i l a t i o n , we have chosen mostly c o e f f i c i e n t s obtained a t 1 gram e q u i v a l e n t per k i l o g r a m of water. Values obtained are presented i n Table IV. Table IV shows that potassium and sodium s a l t s have been s t u d i e d much more e x t e n s i v e l y than ammonium s a l t s . However, we found t h a t , f o r any one gas, d i f f e r e n c e s i n the c o e f f i c i e n t between potassium and ammonium s a l t s of the same anion and between sodium and ammonium s a l t s of the same anion are n e a r l y constant. For gases other than carbon d i o x i d e , we have used data on bromides, c h l o r i d e s , n i t r a t e s , and s u l f a t e s from a s i n g l e i n v e s t i g a t o r t o o b t a i n average d i f f e r e n c e s (Table V). For carbon d i o x i d e , such data were not a v a i l a b l e , and we used averages of r e s u l t s on c h l o r i d e s , n i t r a t e s , and s u l f a t e s from d i f f e r e n t i n v e s t i g a t o r s . 9

3

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

3

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4

2

3

3

2

4

2 2°4 K Cr0

C

0.110

0.097,0.079

0.178,0.122

2

K CO

K

0.043,0.032

KNO~

0.049

2

0.136,0.135

0.070

KOH

3

0.004,-0.027

KN0

KIO

2

0.096

KI

KHC0

(2_8,29)

0.149

3

KCIO

KF

(28,29)

c 0.103 ,0.000

(28)

(28,29)

(28,29)

(28,29)

(28)

(28,29)

(28)

(28,29)

(28)

(28)

(28)

0.046,0.027

KC1

(28)

0.049

(28)

KCNS

0.087

0.049

2

(28)

KCN

3

KCH C0

0.083

3

(29)

0.040

KBr0

(29)

-0.039

(28,29)

(29)

(29)

Ref.

0.021

-0.011

0.055

0.008

0.071

-0.016

(30)

(30)

(30)

(30)

(30)

(.30)

(30)

(.10)

-0.061° 0.001

(30)

Ref.

-0.018

Coefficient

Hydrogen Sulfide

0.024,0.025, 0.026

0.035

0,059,0.063, 0.066

0.044

0.040

-0.002

0.022,0.026

Coefficient 0.026

0.071,0.063

0.086

0.009

).128

3.059

(32,33,34; 0.056,0.052

(32)

(32,33,35)0.082,0.083, 0.074

(32)

(34)

(25)

(13,36)

(32)

(32)

(32,33,36)

(32,36)

(36)

(36)

(32,36)

(36)

Ref.

Nitrous Oxide Coefficient

(34,35)0.033,0.035

Ref.

Carbon Dioxide

a b EXPERIMENTAL SALTING-OUT COEFFICIENTS AT 25°

-0.023

0.026,0.002

4

2

-0.052

Coefficient

KBr

4

4 3 (NH ) S0

NH.C1 4

NH, Br 4 NH CH C0

IV.

Ammonia

Table

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

4

4

K S0

0.083

—

(29)

0.097

0.131

—

—

„

0.035

__

0.037

0.063, 0.064

0.018

(30)

"

—

(30)

(31)

AT 25°C

—

0.109

0.148,0.146

—

—

—

0.063,0.061

0.133 0.095

0

—

0.183

0.194

.075

(33,34) 0.175,0.167

'""

—

(33,34)

(33,36:

(36)

(27)

(36)

(33,36)

(36)

(36)

Ref.

Nitrous Oxide Coefficient

(33,36) 0.117,0.106

—

(34)

Ref.

Carbon Dioxide Coefficient

(30,31) 0.097,0.094

(30)

(30)

Ref.

Hydrogen Sulfide Coefficient

3

study.

These values were rejected

c

i n the c o r r e l a t i o n

Except data of Dawson and McCrea(29), obtained at 20°C.

b

k i n the equation l o g (S°/S) » km where S° and S are the respective s o l u b i l i t i e s , i n water and s a l t s o l u t i o n , per unit weight of water, and m i s g equivalents of s a l t per kg of water.

Na^SO, 2 4

2

o

Na2HP0.4 Na S

(28.12.) (29)

(28)

0.108

Na C0

— M»29)

—

-0.002

NaN0

(

(29)

0.099

0.103, 0.116

3

NaOH

2

-0.012,-0.041

3

4

NaC10

Nal

—

-0.001

(28,29)

0.041,0.017

3

NaCl

(28,29)

(28,29)

(28)

(28)

Ref.

EXPERIMENTAL SALTING-OUT C O E F F I C I E N T S

0.020,-0.007

0.099,0.086

0.102

0.113

NaC10

NaBr

2

2

3

2

H P 0

K S0

K

Coefficient

Ammonia

Table IV, Cont.

120

THERMODYNAMICS

These y i e l d e d gases. Table

V.

poorer

OF AQUEOUS

agreement

SYSTEMS

WITH

INDUSTRIAL

t h a n was o b t a i n e d

E F F E C T OF CATION ON SALTING-OUT

APPLICATIONS

on t h e o t h e r

COEFFICIENT

Average D i f f e r e n c e Average Absolute + Deviation Na -NHÎ ΝΗΪ kg H 0/mol

Κ

+

2

Ammonia Carbon Dioxide Hydrogen S u l f i d e N i t r o u s Oxide

0.055 0.045 0.036 0.042

0.006 0.017 0.009 0.004

0.041 0.082 0.052 0.072

We h a v e u s e d t h e s e a v e r a g e d i f f e r e n c e s b e t w e e n p o t a s s i u m and ammonium s a l t s o l u t i o n s a n d b e t w e e n s o d i u m and ammonium s a l t s o l u t i o n s t o c a l c u l a t e averag f o r t h e f o u r g a s e s i n ammoniu w i t h t h e same a n i o n b u t d i f f e r e n t c a t i o n s . A s a m p l e c a l c u l a t i o n f r o m d a t a on ammonia i n b r o m i d e s o l u t i o n s i s shown i n T a b l e V I . Table

Salt NH^Br KBr KBr

VI.

Investigator Dawson a n d M c C r e a Abegg a n d R i e s e n f e l d Dawson and M c C r e a

NaBr Abegg and R i e s e n f e l d NaBr Dawson a n d M c C r e a Average

SAMPLE CALCULATION C o e f f i c i e n t , k g H20/mol Cation NHi+ Difference Observed ( T a b l e I V ) ( T a b l e V) -0.052 0.026 0.002

0.000 0.055 0.055

0.020 -0.007

0.041 0.041

-0 -0 -0 -0 -0 -0

Value

.052 .029 .053 .021 .048 .041

R e s u l t s t h u s o b t a i n e d on s i n g l e - c h a r g e d a n i o n s a n d on s u l f a t e are presented i n Table VII. Other s a l t s with double-charged a n i o n s c o u l d h a v e b e e n a d d e d , b u t we h a v e n o t b e e n a b l e t o u s e the r e s u l t i n g v a l u e s i n c o r r e l a t i o n s f o r p r e d i c t i o n o f s a l t i n g o u t by b i c a r b o n a t e , h y d r o s u l f i d e , a n d c a r b a m a t e s a l t s . Note t h a t t h e r e s u l t f o r h y d r o x y l i o n i s f o r a h y p o t h e t i c a l ammonium h y d r o x i d e t h a t behaves as a s t r o n g e l e c t r o l y t e . Also, results o b t a i n e d f r o m p o t a s s i u m a n d / o r s o d i u m s a l t s may d i f f e r f r o m a c t u a l b e h a v i o r o f ammonium s a l t s b e c a u s e o f p a i r i n g o f ammonium i o n w i t h the a n i o n . F o r l a t e r d i s c u s s i o n we h a v e a l s o c a l c u l a t e d a n a v e r a g e d i f f e r e n c e i n s a l t i n g - o u t c o e f f i c i e n t b e t w e e n ammonia and e a c h other gas. F o r c o r r e l a t i o n o f t h e c o e f f i c i e n t s we h a v e f o u n d two paramet e r s f o r w h i c h v a l u e s a r e known f o r a l l o r most o f t h e s i n g l e charged a n i o n s i n t h e d a t a base and a l s o f o r b i c a r b o n a t e and hydrosulfide. These a r e t h e e n t r o p y o f t h e i o n and t h e thermoc h e m i c a l r a d i u s o f t h e i o n a s c a l c u l a t e d by Y a t s i m i r s k i i ( 3 7 , 3 8 ) .

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

2

—

4 1 4 1

4

—

-0.047 0.015 0.074 -0.006 -0.023 0.039

—

5

1

—

—

1

0.094 0.042

3 3

-0.016 0.071

—

— — —

— — —

—

1

— — —

— — —

-0.047

1

-0.013

— — —

—

0.018

0.028

4

—

0.011

5 2

—

1

-0.010

—

0.000

--

-0.014 0.036

0.007 0.031 0.016

-— —

— — —

-

— — — —

-

~

—

— —

— —

—

1

-0.093*

-

1

-0.061

1

-0.001

—

—

3

—

-0.027

1

0.014

2

5

-0.041 0.028 0.032 -0.006 -0.006 -0.017 -0.048

Not included i n the average.

Avg.

SO4

NO3

NO2

OH-

IO3

I"

HCO3

HCO2

F"

cioi

CIO3

CNCNSCl"

CH3CO2

Br03

Br"

Anion

--

0.028

0.009 0.017

6 3

— —

0.037

— — —

1

—

—

0.054

4 4 0.009 0.094

—

— 0.032 0.055

1

—

—

0.012*

-

0.064

— —

0.086

-

1 1

—

0.142 0.017

— — — ~

-— — —

0.035

7

— — — — —

— —

0.054

7

0.037

— — —

— -— —

— — — —

— — — —

0.066

— — — —

0.025

0.040

4

2

1

2

—

28. 0 31. 4 33. 3 2.8 35. 2 40. 3

26. 0 33. 5 41. 3 18. 5 44. 3 48. 5 3.0 27. 2

24. 6 43. 8

Anion Entropy cal/ k(C0 ) k, kg No. of k(N 0) -k ÇNH3) H20/r.iol De t ' η. -k (NH;}) °K mol 2

N0

— — — —

2

SALTING-OUT COEFFICIENTS AND PARAMETERS FOR AMMONIUM SALTS

co V 3 k, kg No. of k, kg No. of k(H S) k, kg No. of H20/raol Det'n. Η2Ο/Π10Ι De t ' η. -k (NH3) Η2Ο/Π10Ι De l ' η.

NH

Table V I I .

~

1. 59 1.82 1.95 1.81 2.00 2. 36 1.33 1.58 1.63 2.20 1.82 1.40 1.55 1.89

1.96 1.91

Anion Radius,

3

0Q

Ο

3

I

ο

Ο

ο

> α

>

122

THERMODYNAMICS OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

S a l t i n g - o u t c o e f f i c i e n t s f o r ammonia i n ammonium s a l t s a r e ^ p l o t t e d i n Figure 8 against entropy of the anion based on S of hydrogen equal to —5.3 entropy u n i t s (cal/mol K). This b a s i s i s adopted from Friedman and Krishnan(39), but the entropy values are taken from a more recent c o m p i l a t i o n ( 4 0 ) . With some exceptions, values f a l l i n t o two groups: one c o n s i s t i n g of c h l o r i d e , bromide, and i o d i d e , and the other c o n s i s t i n g mostly of oxygenated anions. F l u o r i d e , hydroxide, and cyanide appear to be intermediate. A s i m i l a r e f f e c t , a l s o showing a d i f f e r e n c e between the h a l i d e s and oxygenated anions of about 20 entropy u n i t s , was found by Bromley on a p l o t of a c t i v i t y c o e f f i c i e n t s of anions(4). Y a t s i m i r s k i i ' s thermochemical r a d i i a r e obtained from K a p u s t i n s k i i * s e m p i r i c a l formula f o r the l a t t i c e energy of c r y s t a l l i n e s a l t s . The l a t t i c e energy i s the heat evolved when the gaseous c a t i o n and U

= A H anion (g) + A H c a t i o n (g) - A H s a l t (c)

O

F

F

F

where U i s the l a t t i c e energy i n kcal/mol and A H anion (g), AHf c a t i o n ( g ) , and AHf s a l t (c) are the r e s p e c t i v e heats of formation of gaseous c a t i o n , gaseous anion, and c r y s t a l l i n e s a l t . K a p u s t i n s k i i s formula f o r u n i v a l e n t s a l t s i s — 0

F

1

\ an

ca/ \

an

ca/

where r and r are the r e s p e c t i v e thermochemical r a d i i of anion and c a t i o n i n X. K a p u s t i n s k i i e s t a b l i s h e d h i s formula w i t h the use of Goldschmidt r a d i i of monatomic i o n s . To extend the scheme to multiatomic anions of unknown radius and heat of formation of the gaseous anion, the formula i s a p p l i e d to two s a l t s of the same anion w i t h c a t i o n s of d i f f e r i n g r a d i i . The two simultaneous equations can then be solved f o r the radius and heat of formation of the anion. The c o r r e l a t i o n of s a l t i n g - o u t c o e f f i c i e n t s w i t h thermochemical r a d i i of anions from Y a t s i m i r s k i i i s presented i n Figure 9. The bromate i o n again shows a higher than expected s a l t i n g - o u t c o e f f i c i e n t , which i n d i c a t e s that the c o e f f i c i e n t i s erroneous. The c o e f f i c i e n t f o r n i t r i t e l i e s beneath the curve. We have r e c a l c u l a t e d i t s r a d i u s from K a p u s t i n s k i i s formula w i t h current thermochemical data on barium, calcium, potassium, and sodium n i t r i t e s ( 4 1 , 4 2 ) to o b t a i n values ranging from 1.60 to 1.68 8. An average of these values reduces the disagreement w i t h our c o r r e l a t i o n , but not s u f f i c i e n t l y to b r i n g the d e v i a t i o n i n t o the range, about ±0.02 kg H20/mol, found f o r other s a l t s . In the entropy c o r r e l a t i o n , the bicarbonate i o n should f a l l on the oxygenated anion l i n e , and we assume that the h y d r o s u l f i d e a

n

c

a

f

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

MASON A N D KAO

Aqueous Condensates from Coal Processing

123

Figure 8. Correlation of salting-out coefficients for ammonia in ammonium salts with entropy of the anion

ION THERMOCHEMICAL RADIUS, A

Figure 9. Correlation of salting-out coefficients for ammonia in ammonium salts with radius of the anion

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

124

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

i o n f a l l s on the h a l i d e l i n e . We then o b t a i n the f o l l o w i n g c o e f f i c i e n t s f o r the s a l t i n g out of ammonia by ammonium b i c a r ­ bonate and ammonium h y d r o s u l f i d e a t 25 C:

HC0 HS"

3

Ion Radius Correlation 0.034 -0.022

Entropy C o r r e l a t i o n 0.038 -0.022

The two c o r r e l a t i o n s thus agree very w e l l . The c o r r e l a t i o n parameters are not w e l l e s t a b l i s h e d f o r the carbamate i o n . The determination of entropy of the aqueous s a l t i s u n c e r t a i n because of i t s tendency to decompose to ammonia and bicarbonate i o n s . Entropy of the anion has been estimated by Wagman and Goldberg of NBS a t 22 cal/mol Κ (S° of Η = 0.0). (43) This y i e l d s a salting-ou carbamate of 0.036 kg H £rom thermochemical data of Bernard and Borel(44) we o b t a i n 1.69 A ag the thermochemical radius of the carbamate i o n ( i n s t e a d of 1.93 A as apparently m i s c a l c u l a t e d by Bernard and B o r e l ) . Our value gives a s a l t i n g - o u t c o e f f i c i e n t of 0.024 kg H2O/1ÏÎ0I, i n good agreement w i t h the c o e f f i c i e n t obtained from the entropy of the anion. Thus, averages from the two c o r r e l a t i o n s y i e l d t e n t a t i v e v a l u e s of 0.036, -0.022, and 0.033 kg H 0/mol f o r the s a l t i n g out of ammonia by ammonium bicarbonate, h y d r o s u l f i d e , and carbamate s o l u t i o n s , r e s p e c t i v e l y , a t 25 C. However, f o r ammonia i n ammonium h y d r o s u l f i d e we p r e f e r to use a value from our corr e l a t i o n of the ternary data of M i l e s and Wilson(45^,46) , as discussed l a t e r . The c o e f f i c i e n t s f o r the other gases i n ammonia s a l t s at 25°C (Table V I I ) , show p a t t e r n s s i m i l a r to that of ammonia, but there are i n s u f f i c i e n t data to o b t a i n independent c o r r e l a t i o n s . Instead, we have averaged the d i f f e r e n c e s between each gas and ammonia i n ammonium s a l t s , as shown i n Table V I I , to o b t a i n f o r any given s a l t s o l u t i o n : 2

k

= k + 0.028 a k = k + 0.016 s a E f f e c t of Temperature on Salting-Out C o e f f i c i e n t s . Long and McDevit (23) p o i n t out that on d i f f e r e n t i a t i o n of t h e i r equation w i t h r e s p e c t to temperature, s e v e r a l terms are obtained of which the dV /dT one i s dominant, and the p r e d i c t e d temperature c o e f f i c i e n t i s approximated by the equation: c

s

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

6.

MASON A N D KAO

125

Aqueous Condensates from Coal Processing

The p a r t i a l molar volume of carbon d i o x i d e and the product 3 T are e s s e n t i a l l y constant from 0 to about 60°C; t h i s suggests use of the p a r t i a l molar volume of the s a l t as the only c o r r e l a t i o n parameter. The c o r r e l a t i o n was t e s t e d i n the form: Q

where k t ~ k are s a l t i n g - o u t c o e f f i c i e n t s on the molal b a s i s for a given s a l t at the res_gective_temperatures t and t\; c i s a c o r r e l a t i o n constant; and V^ and are p a r t i a l molar volumes of the s a l t at i n f i n i t e d i l u t i o n at these temperatures. We tested the r e l a t i o n s h i p w i t h data on carbon d i o x i d e i n the temperature range of 0 to 40 C. Markham and Kobe(33) r e p o r t p r e c i s e data at 0.2 , 25 and 40 C f o r s a l t i n g out by a number of s a l t s . Two a d d i t i o n a l data p o i n t s w i t h 15 to 35 C temperature i n t e r v a l s were obtained from data molar volumes of s a l t s o c o m p i l a t i o n by M i l l e r o . ( 4 7 ) R e s u l t s are presented i n Figure 10. (Note that the s a l t s are l i s t e d t h e r e i n the order of i n c r e a s i n g d i f f e r e n c e i n p a r t i a l molar volume.) The c o r r e l a t i o n i s s u r p r i s i n g l y good, w i t h the constant c equal to —0 .0056 kg H 0/cm . E l l i s and Golding(48) and M a l i n i n and coworkers (49,50) have obtained data on the s a l t i n g out of carbon d i o x i d e by aqueous sodium c h l o r i d e s o l u t i o n s at s t i l l higher temperatures, as shown i n Table V I I I . According to these data, the s a l t i n g - o u t coeff i c i e n t has a minimum at about 140 C, whereas the maximum i n the p a r t i a l molar volume of aqueous sodium c h l o r i d e occurs at about 65 C. M a l i n i n * s s a l t i n g - o u t c o e f f i c i e n t s f o r carbon d i o x i d e i n calcium c h l o r i d e s o l u t i o n s , a l s o reported i n Table V I I I , show a minimum at about 60 C, whereas the maximum i n the p a r t i a l molar volume of calcium c h l o r i d e occurs at about 35 C. The s a l t i n g out of methane by sodium c h l o r i d e s o l u t i o n s , on the other hand, does show a minimum at about 70 C(51), c l o s e to the temperature pred i c t e d by the Long-McDevit equation. Probably the behavior of carbon d i o x i d e can be r a t i o n a l i z e d on the b a s i s of the formation of carbonic a c i d or of other i n t e r a c t i o n w i t h water as shown, f o r example, by equations of s t a t e of water-carbon d i o x i d e mixtures (52) . In any case, i t appears that u n c e r t a i n t y i n the v a r i a t i o n of the c o e f f i c i e n t f o r carbon d i o x i d e i n sodium c h l o r i d e s o l u t i o n i s not more than about 0.01 kg H 0/mol i n the temperature range from 25 to 150°C. To apply the c o r r e l a t i o n of Figure 10 f o r p r e d i c t i o n of the s a l t i n g out of carbon d i o x i d e by ammonium h y d r o s u l f i d e and b i carbonate s o l u t i o n s we need to c o r r e c t f o r the d i f f e r e n c e s of t h e i r p a r t i a l molar volumes from that of sodium c h l o r i d e . Partial molar volumes were obtained from E l l i s and McFadden(53) . Volume changes of the h y d r o s u l f i d e and bicarbonate are equal w i t h i n 0.2 cm /mol at temperatures up to 100 C and d i f f e r very l i t t l e at s t i l l higher temperatures: thus, we assume that the changes w i t h temperature of the s a l t i n g - o u t c o e f f i c i e n t s of the two s a l t s are equal up t o 2

t l

2

2

3

2

2

3

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

0. 076 0.,089 0.,128 0.,176

150

200

250

300

Markham and Kobe(33) 2

Malinin (49,50)

—

--

—

0.,084*

0.,087*

0., 088*

0..089*

0..096*

—

—

--

0.102

0.1007

0.0905

0.0931

0.0958

0.0946

—

--

--

—

0.201

0.192

0.180

0.1768

0.1851

Malinin (49,50)

—

—

0.176*

0.174*

0.1685*

0.168*

0.171*

Malinin (49,50)

o 2 Solution 1 molal 0 molal

C a C 1

I n t e r p o l a t e d or extrapolated at IGT. Note that the c o e f f i c i e n t s f o r CaCl^ are on the molal not kg H^O/g equivalent.

0.,087

100

•k

0.,088

75

—

Malinin (49,50)

0 molal

Salting-Out C o e f f i c i e n t s , kg H 0/mol

E l l i s and Golding(48)

0. 095

0.097

Markham and Kobe(32)

1 molal

ΜNaCl π Sco liu t i o n

EFFECT OF TEMPERATURE ON SALTING-OUT OF CARBON DIOXIDE BY SODIUM CHLORIDE AND CALCIUM CHLORIDE SOLUTIONS

50

25

Temp., °C

Salt Concentration

Table V I I I .

is,

S

H

r >

H

c: 03

H

W 2 o

H W

05 en

Crt

οC3

Ο > Ο d w

Q

> §

•


2

Ι

ΪΓ ^ "

00 r^mr^cj>co

CO

Ο

M Cd Ph

CO

— CTv

CcooomP a a J

= m Y H P a a a a

T

y

φ

(3)

Ρ = a π φ (S) w w w

(4)

Ρ

T

WW

w

Dissociation Equilibriu Χ

(I) Β + Η 0 2

Β

+

+ 0Η

type of d i s s o c i a t i o n ( I ) , (II) or ( I I I ) i s reported i n t a b l e 2. a. f o r a c i d s and base.

+

A X A

(II)

(III) A" X (IV)

Β + A

(V)

H0

X

2

7

Ύ

+ Η A

=

+ H

Χ H

ΒΑ

+

Mass Balance +

A = m

A

+

V mA

2

. . . . ι* components on the l e f t side of d i s s o c i a t i o n e q u i l i b r i u m , j , components on the r i g h t side of the same. (5)

m

- «Έ

+ H 0 , f o r example, formation of carbamate

+ OH"

m

ΐ i Κ = —^~γ" j j j

B

+

+

+

(2 equations)

(

"BA"

m = A

+

6

)

(7)

V

E l e c t r o n e u t r a l i ty

V

+

V

-V

+

2

M

+

A=

( 8 )

"OH"

Given (Ρ, Τ, Α, Β ) , the 10 equations (3) to (8) y i e l d the ten unknown ( n y m - , m= , m , m^- , m , m^- , y , γ ) i f the expressions of φ. , Y. , a are known. ι ι w Deviations to I d e a l i t y A

A

B+

H+

A

β

Vapor Phase. The f u g a c i t y c o e f f i c i e n t s are taken for NOTHNAGEL et a l . (5) c o r r e l a t i o n .

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

182

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

L i q u i d Phase. Ύ and a are derived from the f o l l o w i n g s i o n of the excess Gibbs energy. G

E

= G

E

(PITZER) + G

E

(BORN) + G

E

expres­

(EDWARDS)

I n t e r a c t i o n s Between Ions. P I

M

n RT

E R )

°

&

\

m

l\

h L \ k l%

+

l

"k " l ^

i o n s )

( 9 )

L

WW

*"

E l e c t r i c Work of Charge. /

G (BORN), Μ η RT w w

,/V

+ 0,5 V

f

D

V. +0,5 V \ ions) (10)

=

J

J

J

\

f

c

η

ι

c '

I n t e r a c t i o n Betwee G (EDWARDS) M n RT w w

2 2 Σλ m + Σ μ m a aa a a aaa a

(a n e u t r a l

solute)

(11)

A c t i v i t y C o e f f i c i e n t s of Ions (molality s c a l e ) l n γ. =

\ 3ni

l n Ύ. =

RT / η

_J_ 2 3

+

M + 2 Σ λ. _ dl k jk k m

ki

L.

, η, , η

V

+ _J_ Σ _ k l 2 kl dl \ ™ 1

ra

"k i

w

ν. + ν il ι c Vi - V 7** V j

a V £w

1.5 ν V c ( V i - V )a (V, C

c v

c

D, n

(v

vr

-

f

A c t i v i t y C o e f f i c i e n t s of Neutral

(Vi - v ) c

c

Solutes

:

J

(12)

8 l

l n

n

Y

a

\

=

'

a *

8 n

L

- (k k V

V η

T

' vV' n , n"a_ ' "k' ~ 1.5 v , V k

Ό lr V

L

n

a

(Vf - V )

c

c

D

+ 2λ

/ n

aa

n

a

+3y

n

m 2 aaa a

(13)

A c t i v i t y of Water -»

ln a = w

M w

_ Σ m. j J

+

_ L f J _ É_\ M V3n RT/

(?

n

n

]=-M φ m. +Σ m ) w \ j j a a/

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

8.

Vapor-Liquid

RENON

Equilibria

183

In a = M w w

1 1

d

w (

v -v ) f

2

c

w 'n c 1 2 3Ί 1.5 V — I- Σ λ m - 2 Σ μ m (14) __ ^ 2 J a aa a a aaa a J 5

D w

V

Ν

D n

d (V w

L i s t of Symbols a A A

activity i n solution apparent m o l a l i t y of a c i d (mole/kg of water) DEBYE - HUCKEL constan / 2ττ N d J / =

V looo

/

(D~TT) w

( 1 5 )

b = 1.2 Β apparent m o l a l i t y of base (mole/ kg water) Cj to c o e f f i c i e n t s i n equations (20) (22) C

MV MX

p T

-

T Z E R

(29)

ternary i n t e r a c t i o n parameter f o r s a l t MX

3 d^ D

d e n s i t y of water (kg/dm ) d i e l e c t r i c constant of n e u t r a l s o l u t i o n (without ions)

11

D = D i l+ Σ 5Ça_) n w \ a V /

(

1

6

)

n

D w

d i e l e c t r i c constant of water D

e f°

w

= 305.7 exp (-exp (-12.741 + 0.01875 T) - T/219) ( 1 7 )

charge of e l e c t r o n (4,8029 . 1 0 ~ reference f u g a c i t y

f(I)=

df dl E G H

=

4I_ 3 b 2A DH 3 Ll

l

n

( 1

+

1

b

/

I

l /

2

I ±—r-pr + b l 1

/

2

1 0

esu)

)

(

2 1/2 + I l n (1 + b I ) 1 / Z

2

b

1

8

)

(19)

J

excess GIBBS energy i n the d e f i n i t i o n of e l e c t r o c h e m i s t s by r e f e r e n c e to the " i d e a l " s o l u t i o n i n m o l a l i t y s c a l e . _j Henry's constant of u n d i s s o c i a t e d a c i d o r base (atm. kg/mole ) l n H = C, + C / T + C l n Τ + C, Τ (20) a 1 2 3 4 0

I

i o n i c strengh I =

k

\

Σ

m. z?

BOLTZMANN'S constant k = 1.38045 . 1 θ "

(21) 1 6

erg κ"

1

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

184

THERMODYNAMICS

Κ

OF

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

e q u i l i b r i u m constant i n m o l a l i t y s c a l e l n Κ = Cj + C /T + C I n Τ + C Τ 2

L. J

3

(22)

4

dimensionless constant ( r . en A) 2 ο J e ζ· j _ . 10 (23) L j 2 r. kTD J w molecular weight of water 0.018 kg/mole m o l a l i t y mol/kg number of mole oo _ i AV0GADR0 S number Ν = 6.0232 . 10 mol pressure (atm) Combination of PITZER b i n a r y i o n i c i n t e r a c t i o n parameter Q = β(0)/(β(0) ( 1 ) ) POYNTING c o r r e c t i o n ζ

6

Z

8

-

M m η N Ρ Q

1

+

Ρ r, R S Τ ν v^

ionic cavity radiu gas constant ^ sum of PITZER b i n a r y i o n i c i n t e r a c t i o n parameters Q=B +β temperature (Κ) p a r t i a l molar volume, dm^/mol volume of i o n i c c a v i t i e s f o r i o n j per equivalent(dm /mol) r . en A J 3

0

v? = 3

V

c

β

43

π

3

Ν

r . . 10" j

2 7

(24)

3 volume of a l l i o n i c c a v i t i e s (dm /kg of water) V c

= ? v? J J

m. J

(25)

volume of r e a l s o l u t i o n V

= -i- + ? m. v. + Σ f d j j j a w

m

ο (dm /kg water) a

γ

(26)

a

V\ volume of i o n i c s o l u t i o n excluding n e u t r a l s o l u t e s (dnP /kg water) V. = -1 + ? m. v. w volume of n e u t r a l s o l u t i o n excluding J

V η

J

(27)

J

ions (dm3/kg of water)

V = -L + Σ γ n d a a a w y mole f r a c t i o n i n vapor phase z. number of charges of i o n j . 3 - 1 α d i e l e c t r i c c o e f f i c i e n t (dm /mol ) a

(28)

m

a J =

2

ÉS'k^iS'k^ parameters i n PITZER b i n a r y term f o r i n t e r a c t i o n b e t ^ ^ ween ions of opposite s i g n j and k obtained from S and Q. γ a c t i v i t y c o e f f i c i e n t (molality scale) λ EDWARDS extended PITZER b i n a r y c o e f f i c i e n t f o r i n t e r a c t i o n aa _ι of n e u t r a l spec i e s (B i n EDWARDS(IO) ( k g / m o l ) -1

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

8.

Vapor-Liquid

RENON

X

C

aa "

l

+

C

2

/

Equilibria

185

T

PITZER b i n a r y i n t e r a c t i o n c o e f f i c i e n t f o r ions j . k . of d i f ­ f e r e n t signs (kg/mol |)

- ? ? - [ * · ' ( a l l other X j ^ are zero, ^aaa PITZER ternary c o e f f i c i e n t ,

e

x

t

e

n

d

e

β

Λ

,

* "

Λ

+

ί ψ »

d

X

^aaa = " 55TT < aa

+

( 3 2 )

ïëb>

PITZER t e r n a r y i n t e r a c t i o =

^MMX

F

3Γ

=

^MXX

C μ

ΜΜχ

P

MXY

- »mx =

T

f

* ψ -

% X X

R

°

S

"

A

L

T

S

«




/2

+

o

r

]

~

2

s

a

W

l

t

s

*«

( 3 4 )

( 3 5 )

a l l other μ are zero π

vapor pressure of water w log

Φ

3

I 0

π, - 7.96681

fugacity coefficient

-

(36) φ

osmotic c o e f f i c i e n t

Subscripts a neutral solute h i j k l i o n i c species w water Superscript 00

infinite dilution

Literature Cited

1. 2. 3.

VAN AKEN, A.B. ; DREXHAGE, J.J. ; de SWAAN ARONS, J. Ind. Eng. Chem. Fundam., 1975, 14(3), 154. EDWARDS, T.J. ; NEWMAN, J. ; PRAUSNITZ, J.M. ; A.I.Ch.E.J., 1975, 21(2), 248. PITZER, K.S. ; J. Phys. Chem., 1973, 77(19), 268 ; J. Am. Chem. Soc., 1974, 96(18) , 5701.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

186

THERMODYNAMICS

4.

CRUZ, J. ; RENON, H. ; Ind. Eng. Chem. Fundam., 1979, 18(2), 168. NOTHNAGEL, K.H. ; ABRAMS, D.S. ; PRAUSNITZ, J.M., Ind. Eng. Chem. Proc. Des. Devt., 1973, 12(1), 25. BROWN, I. ; EWALD, A.H. ; Austr. J. Sci. Res. Phys. Ser., 1950, 3, 306. CRUZ, J. ; RENON, H. ; A.I.Ch.E. E. Journal, 1978, 24(5),817. BEUTIER, D. ; RENON, H. ; Ind. Eng. Chem. Proc. Des. Devt., 1978, 17(3), 220. BROMLEY, L.A. ; J. Chem. Therm. , 1973, 4, 669. EDWARDS, T.J. ; MAURER, O. ; NEWMAN, J. ; PRAUSNITZ, J.M. ; A.I.Ch.E. Journal, 1978, 24(6), 966.

5. 6. 7. 8. 9. 10.

RECEIVED

OF

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9 Sour Water Equilibria Ammonia Volatility down to PPM Levels; pH vs. Composition; and Effect of Electrolytes on Ammonia Volatility GRANT M . WILSON, RICHARD S. OWENS, and MARSHALL W. ROE Wilco Research Company, 488 South 500 West, Provo, Utah 84601

Undesirable sulfur nitrogen and oxygen compounds are often encountered in commercia ties relating either to syntheti processes Water also occurs as condensate in these gas streams or water is brought in contact with gas streams in various processing steps. As a result aqueous waste streams are produced in which undesir­ able sulfur, nitrogen, and oxygen compounds are present. Their concentrations in the aqueous waste streams depend on their equi­ librium concentrations in gas streams from which the aqueous streams are derived. Present and future environmental control restrictions dictate that the concentrations of these undesirable compounds be maintained at very low levels before the streams can be released to the environment. Thus, methods must be developed for controlling these concentrations. One method used in refin­ eries for controlling the concentrations of undesirable compounds in aqueous waste streams is by means of a steam stripper called a sour water stripper where these trace compounds are steam dis­ t i l l e d and then condensed as a concentrated product in the con­ denser of the stripping column. The principal components in these strippers are hydrogen sulfide, carbon dioxide, and ammonia. This concentrated product stream is then further processed for removal of these undesirable compounds. Similar processes un­ doubtedly will be necessary in existing and new gas production or gas treating f a c i l i t i e s . The design of these processes requires data regarding the equilibrium concentrations of undesirable com­ pounds absorbed into various aqueous waste streams, and then equilibrium data are required relating to the removal of these compounds from aqueous waste streams. T h i s paper r e p o r t s on measurements made i n t h r e e a r e a s p e r t a i n i n g t o t h e p r o c e s s i n g o f aqueous w a s t e s t r e a m s as f o l l o w s . A. B. C.

V a p o r - l i q u i d e q u i l i b r i u m measurements on N H 3 - H 2 O m i x t u r e s a t 80 and 120°C pH o f NH3-H S-C0 -HoO m i x t u r e s a t 25 and 80°C E f f e c t - o f sodium h y d r o x i d e and sodium a c e t a t e on N H 3 v o l a t i l i t y a t 80°C 2

2

0-8412-0569-8/80/47-133-187$10.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

188

THERMODYNAMICS

Measurement

OF

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Apparatus

A f l o w - t y p e v a p o r - l i q u i d e q u i l i b r i u m a p p a r a t u s shown s c h e m a t i c a l l y i n F i g u r e 1 was used f o r t h e v a p o r - l i q u i d e q u i l i b r i u m measurements on N H 3 - H 2 O . The method i n v o l v e s t h e a n a l y s i s o f an e q u i l i b r i u m n i t r o g e n s t r e a m f o r NHU a f t e r e q u i l i b r a t i o n w i t h a N H 3 - H 2 O m i x t u r e c o n t a i n e d i n c y l i n d e r s 1 and 2 o f F i g u r e 1 . The p a r t i a l p r e s s u r e o f N H 3 i s t h e n c a l c u l a t e d f r o m t h e v a p o r mole f r a c t i o n of N H 3 times the t o t a l pressure o f the system. Two c y l i n d e r s were used t o s a t u r a t e t h e n i t r o g e n s t r e a m i n o r d e r t o m i n i m i z e l i q u i d d e p l e t i o n e f f e c t s and t o i n s u r e e q u i l i b r i u m b e tween t h e gas and l i q u i d p h a s e s . Vapor phase a n a l y s e s were made by a b s o r b i n g t h e N H 3 i n t o an aqueous HCI s o l u t i o n w h i c h was s u b s e q u e n t l y t i t r a t e d and by m e a s u r i n g t h e amount o f n i t r o g e n i n t h e sample by use o f a c a l i b r a t e d wet t e s t m e t e r a c c u r a t e t o + 1 % . P r e s s u r e s were measured b f calibrated a c c u r a t e t o + 0 . 1 % , an c a l i b r a t e d thermocouples a c c u r a t e to + 0.05°C. The c o m p o s i t i o n o f b o t h t h e v a p o r and t h e l i q u i d s a m p l e s were d e t e r m i n e d by p o t e n t i o m e t r i c t i t r a t i o n by a d d i t i o n o f s t a n d a r d i z e d NaOH s o l u t i o n t o samples which i n i t i a l l y c o n t a i n e d a s l i g h t excess o f HCI. T h i s method worked v e r y w e l l even a t t h e ppm l e v e l s s t u d i e d i n some o f t h e r u n s . The same t i t r a t i n g s o l u t i o n was used f o r a n a l y z i n g b o t h t h e v a p o r and t h e l i q u i d s a m p l e s o f each r u n t h u s m i n i m i z i n g e r r o r s p r o d u c e d i n s t a n d a r d i z i n g t h e NaOH s o l u t i o n . F i g u r e 2 g i v e s a s c h e m a t i c o f t h e a p p a r a t u s used f o r pH measurements a t 25 and 8 0 ° C . It consisted o f a stoppered Erlenmeyer f l a s k submerged i n a t e m p e r a t u r e b a t h r e g u l a t e d a t e i t h e r 25 o r 8 0 ° C . The c o n t e n t s o f t h e f l a s k were s t i r r e d by means o f a m a g n e t i c s t i r r e r c o u p l e d t o a m o t o r b e n e a t h t h e b a t h . A pH p r o b e and t h e r m o m e t e r were i n s e r t e d t h r o u g h t h e s t o p p e r a t t h e t o p o f t h e f l a s k and a n o t h e r h o l e was s t o p p e r e d f o r use i n p i p e t i n g s o l u t i o n i n t o or out o f the f l a s k . Measurements were made by f i r s t c a l i b r a t i n g t h e pH p r o b e u s i n g two b u f f e r s o l u t i o n s a t p H ' s o f 7 and 10 s u p p l i e d by Van Labs o f Van W a t e r s and Rogers Equipment Company . These s o l u t i o n s have been c e r t i f i e d by t h e N a t i o n a l B u r e a u o f S t a n d a r d s t o be a c c u r a t e t o + 0.01 pH u n i t a t 2 5 ° C . T h i s pH c a l i b r a t i o n was made w i t h t h e p r o b e i n s e r t e d i n b u f f e r s o l u t i o n a t t h e same t e m p e r a t u r e as t h e pH measurements were made. A f t e r c a l i b r a t i o n t h e p r o b e was i n s e r t e d i n t o t h e f l a s k shown i n F i g u r e 2 . A concentrated s o l u t i o n of NH3-H2S-CO0-H2O o f measured d e n s i t y was t h e n p i p e t e d i n t o t h e f l a s k and a f t e r t e m p e r a t u r e and pH e q u i l i b r a t i o n t h e pH was r e a d . This normally took a period of f i v e minutes f o r the e q u i l i b r a t i o n process. A f t e r r e a d i n g t h e p H , t h e s o l u t i o n was d i l u t e d w i t h w a t e r by f i r s t r e m o v i n g by p i p e t a p o r t i o n o f t h e s o l u t i o n i n t h e f l a s k and by s u b s e q u e n t a d d i t i o n o f w a t e r t o r e p l a c e t h e s o l u t i o n

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

oo VO (and electrolyte) vapor-liquid equilib3

2

Schematicflowapparatus used for NH -H 0 rium measurements Figure L In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

probe) measurements 3

Figure 2. Schematic of apparatus used for pH (or NH In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

ET

Sour Water Equilibria

AL.

191

removed. B o i l e d d i s t i l l e d w a t e r was used f o r b o t h t h e s o l u t i o n p r e p a r a t i o n and d i l u t i o n s t a g e s o f t h e e x p e r i m e n t . A f t e r each d i l u t i o n , t h e pH was a g a i n r e a d . The c o n c e n t r a t e d s o l u t i o n s were p r e p a r e d by b u b b l i n g a c i d gas i n t o a s o l u t i o n o f ammonia and w a t e r . No gas was a l l o w e d t o e s c a p e so t h a t t h e i n c r e a s e i n t h e w e i g h t o f t h e s o l u t i o n r e p r e s e n t e d t h e amount o f HoS o r C 0 a d d e d . No p r o b l e m s were e n c o u n t e r e d when a d d i n g H^S by t h i s m e t h o d , but C 0 i s a b s o r b e d v e r y s l o w l y and l o n g p e r i o d s o f a g i t a t i o n o f t h e s o l u t i o n i n c o n t a c t w i t h gaseous C 0 were n e c e s s a r y t o a c h i e v e t h e d e s i r e d l e v e l s . A t t h e h i g h e r l o a d i n g s o f a c i d gas t o ammonia, p r o b l e m s were e n c o u n t e r e d when t h e s e s o l u t i o n s were h e a t e d t o 80°C b e c a u s e t h e a b s o r b e d gases t e n d e d t o be d r i v e n o f f . T h i s p r o b l e m was s o l v e d by c o n n e c t i n g t h e a b s o r p t i o n t r a i n composed o f d i g l y c o l a m i n e (DGA) on sand shown i n F i g u r e 2 . By t h i s m e t h o d , any components d i s c h a r g e d from t h e c e l The t u b e s were t h e n weighe p o s i t i o n o f the s o l u t i o n i n the Erlenmeyer f l a s k . Some p r o b l e m s were e n c o u n t e r e d w i t h t h e pH p r o b e s used i n t h e pH measurements because t h e r e f e r e n c e e l e c t r o d e i s s a t u r a t e d with AgCl. Hydrogen s u l f i d e can r e a c t w i t h t h e AgCl i n s o l u t i o n , t h u s p r e c i p i t a t i n g AgS a t t h e KCl j u n c t i o n between t h e r e f e r e n c e e l e c t r o d e and t h e s o l u t i o n . In t h i s r e g a r d i t was f o u n d t h a t c e r t a i n p r o b e s work b e t t e r t h a n o t h e r s . Our o b s e r v a t i o n s a r e as follows. 2

2

2

1.

Some r e f e r e n c e e l e c t r o d e s have an e x p o s e d f i l l i n g h o l e f o r a d d i n g A g C l - s a t u r a t e d K C l . The h o l e i s l o c a t e d on t h e s i d e o f t h e probe where H S can r e a d i l y e n t e r and contaminate the s o l u t i o n . These e l e c t r o d e s p r o v e d entirely unsatisfactory. Some e l e c t r o d e s have t h e KCl s o l u t i o n i n a g e l f o r m . These e l e c t r o d e s work f a i r l y w e l l but e v e n t u a l l y t h e g e l becomes c o n t a m i n a t e d w i t h s i l v e r s u l f i d e and t h e p r o b e must be r e p l a c e d . T h i s t y p e o f p r o b e was used f o r t h e measurements g i v e n i n t h i s r e p o r t . Two p r o b e s were a c t u a l l y used f o r t h e e n t i r e s e t o f m e a s u r e m e n t s . T h e r e a r e a l s o e l e c t r o d e s a v a i l a b l e w h i c h have a g r o u n d g l a s s j u n c t i o n between t h e r e f e r e n c e e l e c t r o d e and t h e s o l u t i o n b e i n g m e a s u r e d . These p r o b e s w o u l d p r o b a b l y be most s u i t a b l e b e c a u s e t h e y can be d i s m a n t l e d and cleaned. A probe a r r i v e d as o u r measurements were b e i n g c o m p l e t e d so t h i s t y p e o f p r o b e has not y e t been t e s t e d i n our l a b o r a t o r y . 2

2.

3.

The e f f e c t s o f sodium a c e t a t e and sodium h y d r o x i d e on NH3 v o l a t i l i t y a t 80°C were s t u d i e d by two m e t h o d s . Data on t h e e f f e c t o f sodium a c e t a t e were measured i n t h e same a p p a r a t u s used t o measure t h e NH3-H0O d a t a shown i n F i g u r e 1. In t h i s c a s e , sodium a c e t a t e was a l s o added t o t h e l i q u i d phase w i t h s u b s e q u e n t

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

192

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

N H 3 p a r t i a l p r e s s u r e measurements made i n t h e same manner used f o r the N H 3 - H 2 O measurements. Data on t h e e f f e c t o f sodium h y d r o x i d e were measured by means o f an N H 3 probe s u p p l i e d by O r i o n R e s e a r c h Company w h i c h o p e r a t e s i n a manner a n a l o g o u s t o a pH p r o b e e x c e p t t h a t a mem­ b r a n e i s used t h r o u g h w h i c h o n l y t h e N H 3 p e r m e a t e s . Thus t h e response o f the probe i s p r o p o r t i o n a l t o t h e a c t i v i t y (or p a r t i a l p r e s s u r e ) o f ammonia. E . m . f . d a t a on t h e e f f e c t o f sodium h y d r o x i d e were c o n v e r t e d t o ammonia p a r t i a l p r e s s u r e d a t a u s i n g t h e f o l l o w i n g e q u a t i o n . mv - m v % 3

=

where f

f

NH 3

f

ref

m v

r

5

=

f

u

9

a

c

i

t

y

·

1

(

= f u g a c i t y o f NH

N H 3

N H 3 *

F

1 0

r e f

1

)

3

°

e . m . f . o u t p u t o f NFL e l e c t r o d e i n m i l l i v o l t s mv ^ u . .4-t p » .u.4-t o ~ -Γ ef.= o f NM Hi 3l e_ 1l e c tX.r .o—d eI « i *_ n tΛ-h Ue ~ r e f e-C~w.~ r e n c e ~ s o l"Iu. t i o n βΤ = m i l l i v o l t s p e r d e c a d e , a t 80°C Τ = 70.1 mv/decade

A t l o w p r e s s u r e s t h e f u g a c i t y o f a component can be r e p l a c e d by i t s p a r t i a l p r e s s u r e so t h a t E q u a t i o n 1 can be a p p r o x i m a t e d as follows. mv - mv

ref.

N H - NH3f* (2) One p r o b l e m e n c o u n t e r e d w i t h t h e N H p r o b e was t h a t i t s c a l i ­ b r a t i o n d r i f t e d w i t h t i m e , thus r e q u i r i n g frequent r e c a l i b r a t i o n of the probe. For t h i s r e a s o n t h e p r o b e was abandoned when t h e measurements w i t h sodium a c e t a t e were made. P

3

P

1 0

T

3

Measurement

Results

Vapor-Liquid E q u i l i b r i u m Data. Vapor-liquid equilibrium measurements on N H - H 0 m i x t u r e s a t 80 and 120°C a r e summarized i n T a b l e s 1 and 2 , r e s p e c t i v e l y . A t each c o n d i t i o n , s e v e r a l v a p o r and l i q u i d s a m p l e s were removed f o r a n a l y s i s b e f o r e p r o ­ ceeding to the next c o n d i t i o n . These t a b l e s summarize t h e a n a l y ­ s e s o f t h e s e s a m p l e s a t each c o n d i t i o n and t h e n g i v e an a v e r a g e v a l u e f o r each r u n c o n d i t i o n . The c h a r g e a n a l y s e s a r e based on a n a l y s e s o f t h e s o l u t i o n c h a r g e d t o t h e measurement a p p a r a t u s a t t h e b e g i n n i n g o f each run and l i q u i d a n a l y s e s a r e based on sam­ p l e s removed from t h e a p p a r a t u s d u r i n g t h e r u n . A c o m p a r i s o n o f t h e s e a n a l y s e s shows t h a t t h e l i q u i d a n a l y s e s a r e a l l s l i g h t l y l o w e r t h a n t h e c h a r g e a n a l y s i s and t h a t t h e l i q u i d a n a l y s e s d e ­ c r e a s e s l i g h t l y w i t h each s a m p l e . T h i s e f f e c t i s due t o l o s s o f ammonia t o t h e v a p o r phase i n s a m p l i n g t h e v a p o r and t h u s 3

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

WILSON

ET

193

Sour Water Equilibria

AL.

TABLE 1.

Ammonia-Water Vapor-Liquid E q u i l i b r i u m Measurements a t 80°C by Flow C e l l Method

wt % NH, in in liquid charge

13.39 13.37

1.39 1.40

1.24 1.25 1.22

1.240 1.250 1.247 1.246

6.80 6.80 6.80 6.80

8.04 8.05 8.05 8.05

1.25 1.28 1.31 1.28

1.23 1.26 1.29 1.26

.122 .119 .119 .120

6.86 6.86 6.86 6.86

6.98 6.98 6.98 6.98

1.23 1.21 1.23 1.23

1.25 1.23 1.25 1.25

99.2 ppm 97.7 96.0 94.3 96.8

.0111 .0113 .0112 .0110 .0112

6.87 6.87 6.87 6.87 6.87

6.88 6.88 6.88 6.88 6.88

1.12 1.16 1.17 1.17 1.16

1.18 1.22 1.23 1.23 1.22

10.08 ppm 10.04 9.93 10.02

.00108 .00108 .00107 .00108

6.87 6.87 6.87 6.87

6.87 6.87 6.87 6.87

1.07 1.08 1.08 1.08

1.26 1.27 1.27 1.27

.994 .974 .950 .973

average

.0991 .0983 .0965 .0980

.0993

average

average 10.09 ppm

average

3

b

—3 6.51 6.51

1.000

100.0 ppm

Total V o l a t i l i t y Ratio Pressure, PNH /wt % . Uncorr. Corr. > psi a

6.88 6.86

4.94 4.90 4.8 4.9

4.97

Partial Pressure, psia

^Actual measurements were made under nitrogen pressure according to conditions summarized i n Table 4. The p a r t i a l pressure o f water as given here i s based on Raoult's Law which applies a t the low NHo concentrations given here. By t h i s method the p a r t i a l pressure of water i s given as f o l l o w s . P

P

X

H 0 " H 0 H 0' 2

2

P° Q = vapor pressure of pure water

2

x

u

n

= water mole f r a c t i o n

in liquid

The vapor pressure o f water was taken from the CRC Handbook, 52nd Ed., page D-147. b)See t e x t f o r c o r r e c t i o n s applied.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

194

THERMODYNAMICS

TABLE 2.

OF

AQUEOUS

3

average

average 9.83 ppm

Partial Pressure p s i a %

18.5 18.2 18.6

Total Pressure

V o l a t i l i t y Ratio ^NHo/wt %

4..02 4..09 4,.04

3.83 3.89 3.85

28.52 28.53 28.54 28.53

32.1 32.1 32.1 32.1

3,.99 4,.03 4,.09 4..04

3.97 4.01 4.07 4.02

.342 .341 .329 .315 .332

28.77 28.77 28.77 28.77 28.77

29.1 29.1 29.1 29.1 29.1

3,.64 3..73 3,.75 3..75 3..72

3.69 3.78 3.80 3.80 3.77

92.2 ppm 90.0 87.8 84.8 88.7

.0332 .0332 .0326 .0317 .0327

28.79 28.79 28.79 28.79 28.79

28.8 28.8 28.8 28.8 28.8

3.,60 3..69 3.,71 3..74 3..69

3.77 3.86 3.88 3.91 3.86

9.72 ppm 9.44 9.12 . 9.43

.00358 .00368 .00367 .00364

28.80 28.80 28.80 28.80

28.8 28.8 28.8 28.8

3.,68 3. 90 4.,02 3.,86

4.24) 4.49(appear 4.63( high 4.45)

.0940 .0914 .0878 .0840 .0893

93.4 ppm

APPLICATIONS

45.9 45.6 46.0

.0955

average

INDUSTRIAL

27.39 27.44 27.39

.900 .880 .850 .877

.0898 .0856

average .

4.75 4.60 4.45 4.60

.905 .889 .867 average ,

WITH

Ammonia-Water Vapor-Liquid E q u i l i b r i u m Measurements a t 120°C by Flow Cell Method

wt % NH in in charge liqui 4.83 4.68

SYSTEMS

3.59 3.55 3.48 3.54

See footnote'a" at the bottom of Table 2. See t e x t f o r c o r r e c t i o n s applied.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

ET

Sour Water Equilibria

AL.

195

r e p r e s e n t s s l i g h t d e p l e t i o n o f t h e l i q u i d w i t h each v a p o r s a m p l e . The l i q u i d a n a l y s e s i n t h e s e t a b l e s a r e a v e r a g e s o f a n a l y s e s made b e f o r e and a f t e r s a m p l i n g t h e v a p o r so t h e c o n c e n t r a t i o n s g i v e n r e p r e s e n t t h e a v e r a g e l i q u i d c o m p o s i t i o n d u r i n g t h e v a p o r sam­ pling process. The ammonia p a r t i a l p r e s s u r e s g i v e n i n T a b l e s 1 and 2 a r e based on t h e c o n c e n t r a t i o n o f ammonia f o u n d i n t h e v a p o r s t r e a m times the t o t a l pressure. The a c t u a l p r e s s u r e s a p p l i e d a t each run c o n d i t i o n a r e summarized i n T a b l e 3 where t h e p r e s s u r e s v a r i e d f r o m 15 p s i a a t 80°C t o 90 p s i a a t 120°C. B e c a u s e n i t r o ­ gen was used as a p r e s s u r i z i n g f l u i d , t h e p a r t i a l p r e s s u r e o f w a t e r and t h e t o t a l p r e s s u r e e x c l u d i n g n i t r o g e n have been compu­ t e d i n T a b l e s 1 and 2 based on R a o u l f s l a w f o r w a t e r as n o t e d a t t h e b o t t o m o f T a b l e 1. R a o u l t ' s law a p p l i e s f o r the p a r t i a l p r e s ­ s u r e o f w a t e r because t h e a c t i v i t y c o e f f i c i e n t o f w a t e r i s v i r ­ t u a l l y u n i t y at the low phase. M i n o r e f f e c t s du applied. The l a s t two columns o f T a b l e s 1 and 2 g i v e e q u i l i b r i u m v o l a t i l i t y r a t i o s o f ammonia p a r t i a l p r e s s u r e d i v i d e d by t h e w e i g h t p e r c e n t o f ammonia i n t h e l i q u i d p h a s e . The column l a ­ beled " U n c o r r . " gives the v o l a t i l i t y r a t i o computed s i m p l y as t h e p a r t i a l p r e s s u r e o f ammonia d i v i d e d by t h e t o t a l w e i g h t p e r ­ c e n t o f ammonia i n s o l u t i o n . The s e c o n d column g i v e s a c o r r e c t e d v o l a t i l i t y r a t i o based on t h e d i s s o c i a t i o n o f ammonia a t l o w c o n ­ c e n t r a t i o n s and e x t r a p o l a t i o n t o z e r o c o n c e n t r a t i o n o f ammonia. The d i s s o c i a t i o n c o r r e c t i o n was a p p l i e d by d i v i d i n g t h e u n c o r r e c ­ t e d v o l a t i l i t y r a t i o by t h e computed r a t i o o f f r e e ammonia o v e r t o t a l ammonia i n s o l u t i o n . The r a t i o o f f r e e ammonia o v e r t o t a l ammonia was computed from t h e d i s s o c i a t i o n c o n s t a n t o f ammonia g i v e n by Edwards and P r a u s n i t z (]_) as f o l l o w s . NH 0H-^NH 4

Temperature

4

+

+ OFT

°C

Dissociation

25 80 120

Constant

1.78 χ 1 0 ~ 1 .66 χ Ι Ο " 1 .19 χ 1 0 " 5

5

5

W i t h no o t h e r i o n s p r e s e n t t h e c o n c e n t r a t i o n o f f r e e ammonia o v e r t o t a l ammonia p r e s e n t i s g i v e n by t h e f o l l o w i n g e q u a t i o n : (NH*)-

0 1

( 3)total where k = d i s s o c i a t i o n c o n s t a n t o f NFL C = t o t a l c o n c e n t r a t i o n o f NHg m o l e s / K g w a t e r N H

4 C

In a d d i t i o n t o t h i s c o r r e c t i o n t h e v o l a t i l i t y r a t i o o f ammonia

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

196

THERMODYNAMICS

TABLE 3.

OF

AQUEOUS

WITH

INDUSTRIAL

APPLICATIONS

Measurement Pressures f o r Ammonia-Water Vapor-Liquid E q u i l i b r i u m Runs

Temp. °C

NH w

80

5

0

1

30

0

20

.1

0

15

100 ppm

0

15

10 ppm

0

15

25

20

1

15

20

1

5

20

5

0

90

1

0

60

.1

0

60

100 ppm

0

60

10 ppm

0

60

1 wt

120

SYSTEMS

%

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

197

Sour Water Equilibria

WILSON E T A L .

v a r i e s due t o t h e s o l v e n t e f f e c t o f f r e e ammonia a c c o r d i n g t o t h e f o l l o w i n g equation given in Table 1 of reference 2. 1n(H

N H 3

)

- ln(H^

H 3

)

+

fiC

N

H

(4)

3

where H ° = v o l a t i l i t y r a t i o a t z e r o c o n c e n t r a t i o n o f f r e e ammonia CJS^HO e f f e c t o f f r e e ammonia on t h e v o l a t i l i t y 3 = t e m p e r a t u r e d e p e n d e n t c o n s t a n t ; β = 131.4/T°R - .1682 =

CNH3

=

c

o

n

c

e

n

t

r

a

t

Solving for ln(HNH ) 3

1Π(ΗΝΗ )

R

NH

H

=

3

H

o

NH

3

E

X

P

°^

n

f

r

e

e

a m m o n l

" »

moles/Kg water

a

gives the f o l l o w i n g equation.

= ln(H

3

O

l

N H 3

)

- 3 C

N

H

(5)

3

(^ NH ) C

(

6

)

E q u a t i o n s 2 and 5 can b follows. /

P u \° (P /wt % N F L ) exp(-BC ) 3 j = H Uncorr. 3 (7) Iwt % N H I . p^jr JTlNfT Π ' free total Thus t h e l a s t column i n T a b l e s 1 and 2 c o r r e s p o n d s t o t h e v o l a ­ t i l i t y r a t i o o f ammonia based on f r e e ammonia and e x t r a p o l a t e d t o z e r o c o n c e n t r a t i o n o f f r e e ammonia. T h i s number s h o u l d be i n d e ­ pendent o f t h e c o n c e n t r a t i o n s s t u d i e d a t a g i v e n t e m p e r a t u r e , and any v a r i a t i o n r e p r e s e n t s e r r o r s i n e i t h e r t h e measured d a t a o r i n t h e a p p l i e d c o r r e c t i o n s . The f o l l o w i n g i s a c o m p a r i s o n o f t h e a v e r a g e s f r o m each r u n . M U

N

N H

N

3

C

o

r

M U

3

3

N H

r

J

NH Concentration 3

5 wt % 1 wt % .1 wt % 100 ppm 10 ppm A v e r a g e ( E x c l u d i n g 10 ppm p o i n t a t 120°C)

(P u N

m

3 80°C

3

/wt % ) ° Corr. 120°C

1.24 1 .26 1.25 1 .22 1.27

3.85 4.02 3.77 3.86 4.45

1 .25 + 2%

3 . 8 8 + 4%

(appears

high)

T h i s agreement i s c o n s i d e r e d t o be q u i t e good when a l l o w a n c e i s made f o r t h e f a c t t h a t t h e s e a r e i n d e p e n d e n t l y measured r u n s a t c o n c e n t r a t i o n s v a r y i n g by a r a t i o o f 5000 t o 1! The 10 ppm r u n a t 120°C i s p r o b a b l y i n e r r o r due t o a t r a c e c o n t a m i n a n t i n t h e vapor samples observed i n t h e p o t e n t i o m e t r i c t i t r a t i o n c u r v e . T h i s p r o b l e m was n o t o b s e r v e d a t 8 0 ° C . The f a v o r a b l e c o m p a r i s o n g i v e n above shows t h a t t h e ammonia

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

198

THERMODYNAMICS

O F AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

v o l a t i l i t y r a t i o can be r e l i a b l y e x t r a p o l a t e d t o l o w c o n c e n t r a ­ tions without loss o f accuracy. T h i s i s i m p o r t a n t because t h e b u l k o f p u b l i s h e d l i t e r a t u r e d a t a on t h e v o l a t i l i t y o f ammonia a r e a t c o n c e n t r a t i o n s o f λ% NhL o r h i g h e r . A c o m p a r i s o n o f t h i s new v o l a t i l i t y r a t i o w i t h measured l i ­ t e r a t u r e d a t a i s g i v e n i n F i g u r e 3 where d e v i a t i o n r a t i o s o f N H 3 ( m e a s ) / 3 ( c a l c ) a r e p l o t t e d v e r s u s t e m p e r a t u r e where com­ p a r i s o n i s made w i t h t h e SWEQ c a l c u l a t i o n model o f r e f e r e n c e 2 . T h i s p l o t shows t h a t t h e s e new d a t a a r e i n f a i r agreement w i t h t h e c a l c u l a t e d v a l u e s w i t h r a t i o s o f a b o u t 1.05 a t b o t h 80 and 120°C. F o r t u n a t e l y f o r the authors these data a l s o agree q u i t e w e l l w i t h p r e v i o u s l y measured d a t a r e p o r t e d by M i l e s and W i l s o n P

PNH

(3). In summary t h e f o l l o w i n g can be c o n c l u d e d from t h e g i v e n i n T a b l e s 1 and 2 . 1.

2.

data

The v o l a t i l i t t e d from t h e i o n i z a t i o n c o n s t a n t o f ammonia combined w i t h v o l a t i l i t y d a t a measured a t h i g h e r c o n c e n t r a t i o n s o f ammonia. The v o l a t i l i t y o f ammonia a t 80 and 1 2 0 ° C i s a b o u t 5% h i g h e r t h a n i s now p r e d i c t e d by t h e SWEQ m o d e l . This means t h a t t h e SWEQ model w i l l p r e d i c t s l i g h t l y more steam f o r a g i v e n s e p a r a t i o n , a l l o t h e r e f f e c t s b e i n g e q u a l , t h a n w i l l a c t u a l l y be r e q u i r e d .

pH o f NH3-H2S-CO2-H2O M i x t u r e s . pH measurements on NHo- H SCO2-H0O m i x t u r e s have been made a t 2 5 ° C and 8 0 ° C a s o u t l i n e d i n P a r t Β o f t h e Measurement P r o g r a m . The r e s u l t s o f t h e s e m e a s u r e ­ ments a r e g i v e n i n T a b l e s 4 t o 2 2 . Each t a b l e g i v e s t h e c o m p o s i ­ t i o n o f each s o l u t i o n a t v a r i o u s d i l u t i o n s and measured and c o r ­ r e l a t e d pH d a t a a t each c o m p o s i t i o n . The SWEQ c o m p u t e r program ( 2 j does n o t a c c u r a t e l y p r e d i c t t h e s e pH d a t a , so an e m p i r i c a l c o r r e l a t i o n o f t h e d a t a was made i n o r d e r t o g i v e c o m p a r i s o n s between t h e d a t a and a s m o o t h i n g f u n c t i o n . T h i s s m o o t h i n g f u n c ­ t i o n i s based on t h e f o l l o w i n g e q u i l i b r i u m w h i c h i s assumed t o be a f u n c t i o n o f t h e c o n c e n t r a t i o n o f t h e components i n s o l u t i o n . 2

NH3 + H ~ > N H +

4

(8)

+

(9) In E q u a t i o n 9, t h e hydrogen i o n c o n c e n t r a t i o n i s g i v e n by t h e pH m e a s u r e m e n t s ; and t h e r a t i o o f N r ^ / N H ^ can be a p p r o x i m a t e d from t h e m o l e s o f a c i d gas per mole o f NH3 a s s u m i n g a l l o f t h e a c i d gas r e a c t s a s f o l l o w s . NH

3

+ HA — > N H

4

+

+A"

,

A ' = HCO3

o

r H S

~

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

(10)

9.

WILSON

ET AL.

20

30

199

Sour Water Equilibria

40

50

70

80

Ί00 110 120 130 140 150

Temperature, °C Figure 3. Ammonia mean ratio of measured over calculated partial pressures based on SWEQ correlation (®) new data; see Figure 2 of Réf. 1 for the following: (O) Miles & Wilson; Ο Clifford; (A) Van Krevelen NH -C0 ; (V) Cardon & Wilson; Badger & Silver; ( 0 ) Breitenback & Perman) 3

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

200

THERMODYNAMICS

OF

TABLE 4.

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Measured and Correlated pH of Water-Ammonia Mixtures with no Acid Gas Present, 25°C

Rati 3

Ammonia ^ wt %

NH3/NH

(SWEQ)

Meas.

Correl.

Diff.

2.82

9.491

9.606

-.115

.00308

5.19

9.807

9.875

-.068

.00925

9.34

10.123

10.137

-.014

.00103

.0277

16.5

10.369

10.397

-.028

.111

33.4

10.726

10.733

-.007

.335

58.6

11.014

11.021

-.007

1.01

102

11.283

11.337

-.054

3.05

177

11.597

11.709

-.112

6.17

254

11.883

11.997

-.114

8.30

293

12.066

12.130

-.064

11.21

339

12.272

12.276

-.004

15.20

391

12.588

12.436

.152

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

ET AL.

201

Sour Water Equilibria

TABLE 5. Measured and Correlated pH o f Water-Ammonia Mixtures with 0.253 Mole of H S/Mole o f NhU 25°C 9

ù

3

0

Ammonia ^ wt %

HS> wt %

(SWEQ)

Meas.

Correl.

Diff.

.00135

.00068

1.69

9.303

9.385

-.082

.00404

.00205

2.26

9.414

9.517

-.103

.0121

.00612

2.66

9.495

9.604

-.109

.0364

.0184

2.85

9.567

9.643

-.076

.109

.0552

2.91

9.669

9.680

-.011

.328

.166

2.94

9.772

9.732

.040

.985

.499

2.95

9.896

9.818

.078

a

2

2.96

1.50

2.95

9.996

9.963

.033

5.97

3.02

2.96

10.083

10.108

-.025

8.90

4.50

2.96

10.155

10.216

-.061

10.50

5.31

2.96

10.196

10.267

-.071

14.11

7.14

2.96

10.230

10.370

-.140

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

202

THERMODYNAMICS

OF

TABLE 6.

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Measured and Correlated pH of Water-Ammonia Mixtures with 0.491 Mole of H-S/Mole of NH 25°C

?

3

Ammonia ^ wt %

H S wt %

a )

2

Meas.

PH Correl.

Diff.

9.040

9.143

-.103

NH3/NH4

(SWEQ)

.00407

.00400

.0122

.0120

1.01

9.080

9.178

-.098

.0366

.0359

1.03

9.174

9.204

-.030

.110

.108

1.04

9.290

9.239

.051

.330

.324

1.04

9.405

9.292

.113

.952

1.04

9.497

9.383

.114

2.97

2.91

1.05

9.599

9.546

.053

5.94

5.83

1.04

9.649

9.697

-.048

9.92

9.73

1.04

9.758

9.852

-.094

13.23

12.98

1.04

9.734

9.958

-.224

.990

.971

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Sour Water Equilibria

TABLE 7.

Measured and Correlated pH of WaterAmmonia Mixtures with 0.251 Mole of C0 / Mole o f NH , 25°C ?

3

aï Ammonia wt %

a) C0 wt %

NH3/NH

.00180

.00117

1.66

9.343

9.379

-.036

.00457

.00296

1.93

9.438

9.461

-.023

.0116

.00750

2.18

9.463

9.512

-.049

.0295

.0191

2.27

9.509

9.543

-.034

.0748

.0485

2.29

9.573

9.569

.004

.190

.123

2.29

9.606

9.605

.001

.481

.312

2.25

9.644

9.653

-.009

.791

a;

1.22

Ratio

a ;

2

(SWEQ

2.19

9.735

9.731

.004

1.75

1.13

2.17

9.768

9.775

-.007

5.72

3.71

2.07

10.005

9.988

.017

7.60

4.92

2.06

10.095

10.065

.030

10.1

6.53

2.04

10.210

10.153

.057

13.4

8.65

2.03

10.379

10.256

.123

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

204

THERMODYNAMICS

OF

TABLE 8.

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Measured and Correlated pH of WaterAmmonia Mixtures with 0.520 Mole of C0 / Mole o f NH , 25°C ?

3

3

Ammonia ^ wt %

a )

C0 wt % 2

.000297

.00040

.000754

.0010

.00191

Ratio NH /NH (SWEQ) 3

+

Meas.

PH Correl.

Diff.

8.951

9.003

-.052

4

.00257

.695

.00486

.00654

.746

9.028

9.040

-.012

.0123

.0166

.761

9.074

9.060

.014

.0313

.0421

.768

9.096

9.080

.016

.0794

.107

.748

9.105

9.096

.009

.201

.271

.704

9.127

9.112

.015

.661

.890

.597

9.138

9.133

.005

.507

9.162

9.146

.016

1.31

1.77

1.74

2.35

.466

9.163

9.154

.009

2.31

3.11

.428

9.176

9.168

.008

3.06

4.12

.388

9.189

9.184

.005

4.04

5.44

.349

9.210

9.204

.006

5.32

7.16

.314

9.240

9.233

.007

6.97

9.38

.280

9.277

9.268

.009

9.10

12.25

.248

9.329

9.311

.018

11.81

15.89

.220

9.430

9.366

.064

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Sour Water Equilibria

TABLE 9.

Measured and Correlated pH of WaterAmmonia Mixtures with .755 Mole of C0«/ Mole o f NH , 25°C 3

a) Ammonia* wt %

*) C0 wt %

ΝΗο/ΝΗλ (SWEQ)

Meas.

PH Correl.

Diff.

.00238

.00463

.278

8.629

8.608

.021

.00579

.0113

.283

8.679

8.623

.056

.0141

.0274

.289

8.709

8.644

.065

.0342

.0664

.285

8.716

8.657

.059

.0828

.161

.271

8.725

8.664

.061

.201

.391

.244

8.718

8.664

.054

.486

;

;

2

.201

8.698

8.650

.048

1..17

2..27

.145

8.641

8.616

.025

2..31

4..49

.0990

8.577

8.574

.003

4..50

8..74

.0632

8.500

8.549

-.049

5..90

11..46

.0513

8.472

8.545

-.073

.944

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

206

THERMODYNAMICS

OF AQUEOUS

TABLE 10.

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Measured and Correlated pH of WaterAmmonia Mixtures with 0.886 Mole of C0 / Mole o f NH , 25°C ?

3

3

Ammonia ^ wt %

a

C0 wt % 2

NH /NH (SWEQ)

Meas.

PH Correl.

Diff.

3

4

.000902

.00207

.110

8.265

8.200

.065

.00219

.00501

.119

8.345

8.239

.106

.00532

.0122

.119

8.393

8.247

.146

.0129

.0295

.122

8.400

8.270

.130

.0314

.0719

.118

8.391

8.274

.117

.0761

.174

.113

8.400

8.285

.115

.185

.423

.0996

8.382

8.276

.106

1.02

.0789

8.335

8.245

.090

1.07

2.46

.0521

8.233

8.174

.059

2.11

4.83

.0346

8.131

8.120

.011

2.78

6.37

.0281

8.084

8.093

-.009

.446

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

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207

Sour Water Equilibria

AL.

TABLE 11. Measured and Correlated pH of WaterAmmonia Mixtures with .124 Mole of C0 and .124 Mole o f H S per Mole of NhL, 25°C

2

?

ά

Rati Ammonia ^ wt %

co wt %

0.00298

0..000954

0.000737

2.003

9,.248

9.463

-0.215

0.00724

0,.00232

0.00179

2.311

9,.435

9.531

-0.096

0.0176

0.,00563

0.0435

2.494

9,.489

9.574

-0.085

0.0427

0.,0137

0.0106

2.568

9..476

9.601

-0.125

0.104

0.,0332

0.0256

2.623

9.,546

9.634

-0.088

0.252

0.,0806

0.0623

2.622

9.,631

9.670

-0.039

0.612

0.,196

0.151

2.613

9.,733

9.724

0.009

1.49

0.476

0.367

2.603

9.,845

9.811

0.034

3.61

1. 16

0.893

2.562

9. 975

9.941

0.034

7.24

2.32

1.79

2.556

10. 116

10.100

0.016

9.67

3.09

2.39

2.560

10. 194

10.185

0.009

4. 13

3.19

2.554

10. 298

10.281

0.017

3

12.91

2

a )

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

208

THERMODYNAMICS

OF

TABLE 12.

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Measured and Correlated pH o f WaterAmmonia Mixtures with .277 Mole of CO. and .277 Mole o f H S per Mole of NH ' 25°C ?

V

Ammonia ^ wt %

co wt %

wt %

(SWEQ)

Meas.

Correl.

0.00136

0.000964

0.000753

0..635

8..576

8. 961

-0. 385

8.,745

9.,011

-0.,266

3

2

a ) 2

Diff.

0.00363

0.00257

0.00201

0..704

0.00967

0.00686

0.00535

0..732

8.,877

9.,036

-0.,159

0.0258

0.0183

0.0143

0.,740

8.,934

9.,055

-0.,121

0.0687

0.0488

0.0382

0.,730

9.,002

9.,072

-0. 070

0.183

0.130

0.102

0. 706

9.,085

9.,095

-0.,010

0.408

0.346

0.271

0.,682

9.,150

9. 127

-0. 023

1.296

0.919

0.720

0.,587

9.,209

9. 177

0.,032

3.422

2.428

1.900

0.,499

9.,293

9. 273

0. 020

6.443

4.571

3.577

0.,447

9. 376

9.388

-0. 012

8.380

6.013

4.653

0.,417

9.,416

9. 443

-0.,027

7.800

6.035

0.,399

9. 479

9. 519

-0. 040

10.87

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

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209

Sour Water Equilibria

AL.

TABLE 13 .

Measured and Correlated pH of WaterAmmonia Mixtures with 0.375 Mole of H S and 0.372 Mole o f CO? per Mole of NhL, 25°C ?

0

3

Ammonia ^ wt %

C0o wt %

a)

wt %

(SWEQ)

Meas.

Correl.

Diff.

0.00280

0.,00269

0.00210

0.3074

8.542

8.650

-0.108

0.00680

0..00653

0.00509

0.3176

8.598

8.671

-0.073

0.0165

0.,0159

0.0124

0.3155

8.643

8.679

-0.036

0.0401

0.,0385

0.0300

0.3183

8.686

8.700

-0.014

0.0973

0..0934

0.0729

0.3091

8.732

8.714

0.018

0.0236

0..227

0.177

0.2886

8.768

8.647

0.121

0.0572

0..549

0.428

0.2573

8.774

8.617

0.157

1.38

1..33

1.034

0.2055

8.764

8.746

0.018

3.30

3..17

2.47

0.1514

8.740

8.772

-0.032

5.92

5,.69

4.44

0.1145

8.719

8.805

-0.086

7.56

7,.27

5.67

0.1003

8.715

8.827

-0.112

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

210

THERMODYNAMICS

OF

TABLE 14.

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Measured and Correlated pH of WaterAmmonia Mixtures with No Acid-Gas Present, 80°C

Ratio 3

Ammonia ^ wt % 0.00202

Meas.

PH Correl.

Diff.

8.077

8.138

-.061

NH3/NH4

(SWE0)

4.4484

0.0121

11.565

8.432

8.636

-.204

0.0273

17.572

8.636

8.881

-.245

0.0614

26.638

8.826

9.143

-.317

0.221

51.020

9.156

9.597

-.441

10.127

-.601

0.887

102.43

9.526

1.79

145.48

9.717

10.396

-.679

3.61

208.46

9.865

10.662

-.797

b)

Balance i s water These differences i n d i c a t e that the NH /NH r a t i o from the SWEQ computer program are too high. 3

+ 4

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

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Sour Water Equilibria

211

TABLE 15. Measured and Correlated pH o f WaterAmmonia Mixtures with 0.258 Mole o f H?S/

Ratio 3

Ammonia ^ wt %

H S wt %

a )

2

(SWEQ)

Meas.

PH Correl.

Diff.

NH3/NH4

0.00292

0.00151

2.150

7.805

7.840

-.035

0.00709

0.00366

2.504

7.966

7.950

.016

0.0172

0.00889

2.709

8.057

8.045

.012

0.0418

0.0216

2.818

8.208

8.147

.061

0.102

0.0524

2.869

8.323

8.265

.058

0.246

0.127

2.891

8.470

8.400

.070

0.600

0.309

2.898

8.575

8.550

.025

1.46

0.756

2.894

8.675

8.699

-.024

3.58

1.85

2.891

8.777

8.836

-.059

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

212

THERMODYNAMICS

OF

TABLE 16 .

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Measured and Correlated pH of WaterAmmonia Mixtures with 0.480 Mole of H S/ Mole o f N H , 80°C ?

3

Ratio 3

Ammonia ^ wt %

H S wt %

a )

(SWEQ)

Meas.

PH Correl.

Diff.

0.00178

.948

7.511

7.472

.039

0.00468

0.00451

1.041

7.618

7.553

.065

0.0119

0.0114

1.085

7.724

7.631

.093

0.0302

0.0291

1.105

7.863

7.722

.141

0.0767

0.0738

1.113

7.952

7.836

.116

0.195

0.187

1.115

8.062

7.975

.087

0.494

0.477

1.111

8.152

8.128

.024

1.26

1.22

1.107

8.235

8.283

-.048

3.21

3.12

1.096

8.324

8.422

-.098

0.00185

N H

2

3

/ N H /

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

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213

Sour Water Equilibria

TABLE 17. Mole of NH , 80°C 3

a) Ammonia wt %

d;

a) H S wt %

Ratio

Eb

a ;

2

NH0/NH4

(SWEQ)

Meas.

Correl.

Diff.

.0935

.104

0.8439

7.809

7.750

.059

.187

.208

0.8453

7.853

7.855

-.002

.375

.416

0.8453

7.874

7.970

-.096

0.8453

7.916

8.088

-.172

.752

.834

1.55

1.70

0.8628

7.985

8.215

-.230

3.07

3.89

0.6293

8.094

8.187

-.093

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

214

THERMODYNAMICS

OF

TABLE 18.

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Measured and Correlated pH of WaterAmmonia Mixtures with .315 Mole of CO?/ Mole o f NH , 80°C 3

Ratio 3

Ammonia ^ wt %

C0 wt %

3 )

2

(SWEQ)

Meas.

PH Correl.

Diff.

NH3/NH4

0.00175

0.,00142

1,.572

7.,830

7.687

.143

0.00425

0.,00346

1,.845

7.,927

7.792

.135

0.0103

0..00840

2..011

8..048

7.880

.168

0.0878

0,,0714

2..108

8.,272

8.118

.154

0.213

0..173

2,.075

8.,405

8.242

.163

0.515

0..420

1,.989

8..496

8.371

.125

1.25

1..02

1,.853

8.,591

8.491

.100

3.01

2..46

1..665

8..692

8.584

.108

5.98

4..95

1,.487

8..830

8.630

.200

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

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Sour Water Equilibria

215

TABLE 19. Measured and Correlated pH of WaterAmmonia Mixture with .429 Mole of CO?/ Mole of N H 80°C V

Ratio 3

Ammonia ^ wt %

co wt % 2

a )

(SWEQ?

Meas.

PH Correl.

Diff.

NH0/NH4

0.00244

0.00269

1.164

7.557

7.571

-.013

0.00548

0.00605

1.260

7.601

7.643

-.042 -.058

0.0123

0.0136

1.309

7.654

7.712

0.0278

0.0306

1.327

7.742

7.789

-.047

0.166

0.183

1.297

7.950

8.011

-.061

0.373

0.412

1.243

8.039

8.125

-.086

1.33

1.46

1.079

8.141

8.282

-.141

2.63

2.96

.908

8.210

8.316

-.106

5.13

6.08

.690

8.308

8.293

.015

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

216

THERMODYNAMICS

OF AQUEOUS

TABLE 20.

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

Measured and Correlated pH of WaterAmmonia Mixtures with .121 Mole of H S and .126 Mole of C0 per Mole of NFU, 80°C ?

?

ù

0

Ratio NH3/NH4 (SWEQ)

Meas.

E±L Correl.

Diff.

0.000430

1.962

7.737

7.783

-.046

0.,00131

0.000968

2.051

7.794

7.834

-.041

0.00902

0.,00294

0.00218

2.675

7.816

7.992

-.176

0.0542

0. 0176

0.0131

2.954

8.124

8.196

-.072

0.122

0. 0397

0.0295

2.977

8.264

8.306

-.042

0.275

0.,0895

0.0664

2.967

8.416

8.429

-.013

0.765

0.,252

0.185

2.889

8.609

8.589

.020

2.78

0. 925

0.670

2.740

8.787

8.777

.010

5.70

1.,90

1.39

2.622

8.901

8.858

.043

3

Ammonia ^ wt %

a )

C0 wt %

H S wt %

0.00178

0.000581

0.00401

2

a )

2

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

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111

Sour Water Equilibria

AL.

TABLE 21 . Measured and Correlated pH of WaterAmmonia Mixtures with .188 Mole of H S and .225 Mole o f CO? per Mole of NH,7 ?

Ratio.

co wt %

HS> wt %

0.00439

0.00236

0.00988

3

Ammonia ^ wt %

a

(SWEQ)

Meas.

PH Correl.

Diff.

0.00165

1.481

7.579

7.700

-.120

0.00530

0.00372

1.573

7.607

7.773

-.166

0.0593

0.0318

0.0223

1.635

7.833

7.962

-.129

0.133

0.0716

0.0502

1.643

8.020

8.074

-.054

0.300

0.161

0.113

1.608

8.158

8.193

-.035

1.08

0.581

0.406

1.522

8.336

8.387

-.051

2.16

1.26

0.813

1.214

8.408

8.406

.002

4.33

2.56

1.65

1.097

8.465

8.463

.002

8.68

5.28

3.50

0.933

8.596

8.480

.116

2

a )

2

NH3/NH4

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

218

THERMODYNAMICS

OF AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

TABLE 22 Ammonia Mixtures with .363 Mole o f H S and .328 Mole of C 0 per Mole of N H L , 80°C ?

o

Ratio co wt %

wt %

(SWEQ)

Meas.

0.988

0.838

0.717

.4244

7.903

7.851

.052

1.97

1.71

1.45

.3584

7.926

7.889

.037

3.92

3.45

2.93

.2903

7.970

7.897

.073

3

Ammonia ^ wt %

2

a )

H

2

S

A

)

N H O / N H /

PH Correl.

Diff

Balance i s water

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

ET

free N H 3

"

n

NHt = 4 free

NH

NH NH

4

=

NH

n

NH

3

N

R

(11 )

±™1

α

«

+

- α

3

α

+

= τ .

3

NH

4

3

219

Sour Water Equilibria

AL.

= m o l e s a c i d gas p e r m o l e N H 3

' P

R

N

NH

NH3 (12)

3

T h i s e s t i m a t e d r a t i o can be i m p r o v e d by u s i n g t h e SWEQ c o m p u t e r program w h i c h t a k e s t h e i o n i z a t i o n o f N H i n t o a c c o u n t a t l o w c o n ­ centrations. For example i n T a b l e 5 , E q u a t i o n 12 g i v e s a N H 3 / N H J ratio of 2.95. This agree t r a t i o n s , but a t low c o n c e n t r a t i o n t h e i o n i z a t i o n o f ammonia. In o r d e r t o t a k e t h i s i o n i z a t i o n e f f e c t i n t o a c c o u n t , t h e SWEQ c o m p u t e r program has been used t o c a l c u l a t e t h e N h L / N H ^ r a t i o s i n each t a b l e f o r use i n t h e s m o o t h i n g f u n c t i o n . These c a l c u l a t e d r a t i o s a r e t h e r e f o r e g i v e n i n e a c h t a b l e , and t h e s m o o t h i n g f u n c t i o n now i n v o l v e s a c o r r e l a ­ t i o n o f t h e e q u i l i b r i u m c o n s t a n t g i v e n by E q u a t i o n 9 as a f u n c ­ t i o n o f t h e c o n c e n t r a t i o n s o f t h e c o m p o n e n t s . The r e s u l t i n g equations are the f o l l o w i n g . 3

B\/(1 log

1 0

(k)

where A , B,

= A +

C

+

D>

/(1

+ R)(

wt % N H ) 3

+ R)(wt

% NH )

U

3

3

C, and D = c o n s t a n t s

ΝΤΓ+ + NH P °9 4 3 R = moles a c i d gas/mole NH wt % N H = t o t a l w e i g h t p e r c e n t o f ammonia i n V a l u e s o f t h e p a r a m e t e r s were f o u n d t o be as f o l l o w s . R

=

Η

F

R

O

M

S

W

E

Q

R

R A M

3

3

Temp.

soin.

Parameter

°C

A

25 80

Β

9.15 7.42

C

.178 1.36

1

D 0 1

.9

The f i r s t p a r a m e t e r , A , i s t h e p K o f N H w h i c h c a n be compared w i t h l i t e r a t u r e d a t a ; t h e c o m p a r i s o n i s as f o l l o w s . a

Temp.

3

pJC

°C

Meas.

LU.(2,4)

25 80

9.15 7.42

9.25 7.84

Difference -.10 -.42

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

)

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THERMODYNAMICS

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From t h i s c o m p a r i s o n t h e agreement i s q u i t e good a t 2 5 ° C . A t 80°C t h e agreement i s n o t a s g o o d , but t h e l a r g e r d i f f e r e n c e i s n o t s u r p r i s i n g because b o t h t h e measurements r e p o r t e d h e r e and measurements i n t h e l i t e r a t u r e s u f f e r from measurement p r o b l e m s at higher temperatures. However, i t would be s u r p r i s i n g i f t h e d a t a r e p o r t e d h e r e a r e o f f by 0 . 4 u n i t because NBS recommended b u f f e r s o l u t i o n s a c c u r a t e t o + 0.01 pH u n i t o v e r t h e t e m p e r a t u r e r a n g e t o 80°C were u s e d . I f the data given here are r i g h t , i t p r o b a b l y means t h a t t h e d i s s o c i a t i o n c o n s t a n t o f ammonia a t 80°C i s a b o u t 0 . 6 5 χ 1 0 ~ r a t h e r t h a n 1.66 χ 1 0 " computed from t h e e q u a t i o n o f Edwards and P r a u s n i t z (1_). D i f f e r e n c e s between measured and c o r r e l a t e d pH d a t a a r e g i v e n i n each o f T a b l e s 4 t o 2 2 . No a t t e m p t was made t o do a l e a s t - s q u a r e f i t o f t h e d a t a so i n some c a s e s d e v i a t i o n s between t h e c o r r e l a t i o n and t h e d a t a can be r a t h e r l a r g e w i t h o u t any s i g n i f i c a n t error i n th d data Nevertheless f the d e v i a t i o n s a r e l e s d a t a i n T a b l e 14 on t h e pH o f NH3-H0O a t 80°C w i t h no a c i d gas p r e s e n t ; i n t h i s c a s e t h e c a l c u l a t e d pH d a t a depend h e a v i l y on t h e NH3/NH4" r a t i o g i v e n by t h e SWEQ m o d e l . D i f f e r e n c e s up t o 0 . 7 9 7 pH u n i t i n d i c a t e t h e m a g n i t u d e o f e r r o r i n t h e SWEQ model a t 8 0 ° C . S i m i l a r d a t a a t 25°C i n T a b l e 3 a r e b e t t e r p r e d i c t e d . The d a t a i n T a b l e s 4 t o 13 a t 25°C p l o t n e a r l y as v e r t i c a l l i n e s i n d e p e n d e n t o f t h e wt % NH3 i n s o l u t i o n e x c e p t f o r pure ammonia. A t low c o n c e n t r a t i o n s t h e curves tend t o d e v i a t e b e ­ c a u s e o f t h e i o n i z a t i o n o f NH3 and w a t e r . I f t h e amount o f am­ monia i n s o l u t i o n i s a p p r o x i m a t e l y known, t h e s e c u r v e s can be used t o e s t i m a t e t h e m o l e s o f a c i d gas p e r mole o f NH3 w i t h f a i r l y good a c c u r a c y . A t 80°C t h e c u r v e s t e n d t o s l a n t more so t h e amount o f ammonia i n s o l u t i o n w o u l d have t o be known more a c c u r a t e l y b e f o r e an e s t i m a t e o f t h e r a t i o o f a c i d gas t o ammonia c o u l d be made. A l s o we do n o t recommend t h e use o f a pH probe a t 80°C a s a c o n t r o l i n d i c a t o r because t h e r e s p o n s e o f t h e p r o b e i s more e r r a t i c , and p r e c i s e d a t a a r e d i f f i c u l t t o o b t a i n . The use o f an i n d i c a t o r p r o b e a t 25°C seems more l o g i c a l because t h e o u t ­ put i s more s t a b l e . One o b s e r v a t i o n t h a t can be made from t h e pH d a t a i n T a b l e s 4 t o 22 i s t h a t t h e pH a p p e a r s t o be a f f e c t e d a b o u t e q u a l l y by e i t h e r H2S o r CO2. T h i s r e s u l t c a n be seen f r o m an e x a m i n a t i o n o f t h e p l o t s g i v e n i n F i g u r e s 4 and 5. I n t h e s e f i g u r e s t h e pH i s p l o t t e d v e r s u s t h e m o l e s o f a c i d gas per mole o f NH3 a t a f i x e d c o n c e n t r a t i o n o f 1.0 wt % NH3. The c u r v e s i n F i g u r e 4 c o r r e s p o n d t o r e s u l t s a t 2 5 ° C , and t h e p l o t i n F i g u r e 5 c o r r e s ­ ponds t o r e s u l t s a t 8 0 ° C . The p o i n t s p l o t t e d i n t h e s e two f i g ­ u r e s r e p r e s e n t smoothed v a l u e s o b t a i n e d from T a b l e s 4 t o 2 2 . Data a t 25°C i n F i g u r e 4 c l e a r l y s e p a r a t e i n t o t h r e e d i s t i n c t curves although the curves a r e c l o s e t o g e t h e r . T h i s shows t h a t t h e r e i s some d i f f e r e n c e between t h e a c i d g a s e s , b u t n o t a l a r g e difference. The p o i n t s i n F i g u r e 5 a t 80°C do n o t r e s o l v e i n t o s e p a r a t e c u r v e s because t h e r e i s some s c a t t e r i n t h e p o i n t s . 5

5

4

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

ET AL.

221

Sour Water Equilibria

101

7

1

I

.

1

1

ι

ι

1

j

ι

1

1

1

.

.

.5

0

1

ι

r

ι

I

1.0

moles a c i d gas/mole Ν Η ,

Figure 5.

The pH of LO wt % H S-C0 -NH^-H 0 mixtures vs. acid gas loading at 80°C ((A) 100% CO,; Ο 100% H S; (0)50:50 H S/C0 ) 2

2

2

2

2

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

222

THERMODYNAMICS

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SYSTEMS

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APPLICATIONS

W i t h i n t h i s s c a t t e r , t h e t h r e e t y p e s o f d a t a a p p e a r t o be c o r r e ­ l a t e d by a s i n g l e c u r v e ; t h u s s h o w i n g t h a t t h e r e i s n o t a g r e a t d i f f e r e n c e i n t h e e f f e c t o f the a c i d gases a t 80°C. In summary t h e f o l l o w i n g c a n be c o n c l u d e d r e g a r d i n g t h e pH data i n Tables 4 to 2 2 . 1. 2. 3.

4.

5.

The d a t a can be c o r r e l a t e d u s i n g an e q u i l i b r i u m c o n s t a n t a p p r o a c h w i t h most d e v i a t i o n s b e i n g l e s s t h a n + 0.1 pH unit. The p K o f ammonia d e r i v e d f r o m t h e s e d a t a a g r e e s w i t h l i t e r a t u r e d a t a w i t h i n 0.1 pH u n i t a t 25°C and 0 . 4 2 pH u n i t at 80°C. The m o l a r r a t i o s o f H S / N r L o r C 0 / N H have a b o u t e q u a l e f f e c t s on t h e p H . A t 2 5 ° C , CO^ a p p e a r s t o have a s l i g h t l y greater e f f e c t . A s i m i l a r c o n c l u s i o n a t 80°C can be made e x c e p gases i s v i s i b l The pH p r o b e i s more s t a b l e a t 25°C t h a n a t 8 0 ° C . For t h i s r e a s o n i t i s recommended t h a t i f a pH p r o b e i s used as a c o n t r o l s e n s o r i n a p r o c e s s t h a t i t be used a t 25°C so t h a t t h e r e s p o n s e w i l l t e n d t o be more a c c u r a t e . pH d a t a a t 25°C i n T a b l e s 4 t o 13 can be used t o e s t i ­ mate t h e m o l e s o f a c i d gas p e r m o l e s o f N H i n s o l u t i o n w i t h o n l y an a p p r o x i m a t e knowledge o f t h e t o t a l amount o f NH i n s o l u t i o n . a

2

2

3

3

3

Sodium H y d r o x i d e and Sodium A c e t a t e E f f e c t on NHg V o l a t i l i t y . Ammonia v o l a t i l i t y measurements a t v a r i o u s c o n c e n t r a t i o n s o f s o ­ dium h y d r o x i d e and s o d i u m a c e t a t e a t 80°C a r e g i v e n i n T a b l e s 23 and 24 r e s p e c t i v e l y . Data on t h e e f f e c t o f sodium h y d r o x i d e were measured u s i n g an ammonia p r o b e f r o m O r i o n R e s e a r c h Company. These measurements were r e d u c e d t o NHo p a r t i a l p r e s s u r e m e a s u r e ­ ments u s i n g E q u a t i o n 2 g i v e n a b o v e . In t h i s c a s e , t h e r e f e r e n c e s o l u t i o n i s the composition reached at zero s a l t c o n c e n t r a t i o n at t h e bottom o f T a b l e 2 3 . The ammonia p a r t i a l p r e s s u r e above t h i s s o l u t i o n can be i n f e r r e d f r o m T a b l e 1 where P N H 3 / w t % N H 3 a t 0.1 wt % N H 3 has a v a l u e o f 1 . 2 3 . This i n f o r m a t i o n gives the f o l ­ l o w i n g v a l u e s f o r PjJ[jf- and m v r e f

Pj^fmv

ref.

= 0 . 1 0 0 5 χ 1.23 = 0 . 1 2 4

psia

_ = - 5 7 . 3 mv

These v a l u e s and t h e p r o b e o u t p u t d a t a i n T a b l e 23 were s u b s t i t u ­ ted i n t o Equation 1 to give the p a r t i a l pressure data given i n Table 23. The d a t a i n T a b l e 24 on t h e e f f e c t o f sodium a c e t a t e were measured i n t h e same manner as d a t a i n T a b l e s 1 and 2 , so no a s ­ s u m p t i o n s a b o u t t h e ammonia probe b e h a v i o r were n e c e s s a r y . This was done b e c a u s e r e a d i n g s f r o m t h e N H p r o b e became e r r a t i c a f t e r 3

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9.

WILSON

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223

TABLE 23. E f f e c t o f Sodium Hydroxide E l e c t r o l y t e on Ammonia V o l a t i l i t y a t 80°C from Ammonia Probe Data ) 3

3

wt % i n L i q u i d NH NaOH 3

p

Output mv

NH psia

NH /wt psia

P

3

3

0800

22.5

-57.1

.123

1.54

0891

12.7

-57.5

.125

1.40

0944

6.82

-57.3

.124

1.31

0974

3.60

-57.2

.124

1.27

.124

1.25

0995

1.27

1005

0

a

-57.3 ref

b

mv =-57.3 )

1.23

^ 0 r i o n Research Company ^This value of -57.3 mv was not d i r e c t l y measured, but i s a value obtained by e x t r a p o l a t i n g mv vs wt % NaOH to zero wt NaOH.

r) 'This p a r t i a l pressure f o r NFU was obtained from the NH p a r t i a l pressure data i n Table 2 a t 0.1 wt % ίΙΗ . The same r a t i o o f P N H 3 / ^ % NH , uncorr. was used at .1005 wt % NH to give P j ^ as follows. 3

3

w

3

3

P

N H

= 1.23 χ .1005 = .124 psia

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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TABLE 24. E f f e c t of Sodium Acetate E l e c t r o l y t e on Ammonia V o l a t i l i t y a t 80°C from Flow C e l l Data

NH

3

.802

charge, wt % NaAc

25

average

.931

15

average .931

5

averaqe

1.00

0

3 Liquid wt %

η *\ NH psia

.781 .734 .684 .644 .711

1.838 1.778 1.712 1.620 1.737

2.35 2.42 2.50 2.51 2.45

.992 .975 .959 .942 .967

1.812 1.817 1.796 1.756 1.795

1.83 1.86 1.87 1.86 1.86

.995 .985 .974 .964 .980

1.381 1.411 1.405 1.380 1.394

1.39 1.43 1.44 1.43 1.42

.973

1.246

1.28 average from Table 2

p

a ;

3

F

NH?M %

^Sampled a t 20 psia

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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t h e measurements a t 80°C on t h e e f f e c t o f sodium h y d r o x i d e . These d a t a were measured a t a b o u t 1 wt % N H i n t h e l i q u i d phase i n s t e a d o f 0.1 wt % N H used f o r t h e NaOH m e a s u r e m e n t s . For t h i s r e a s o n t h e y do n o t e x t r a p o l a t e t o t h e same v o l a t i l i t y r a t i o a t zero concentration of e l e c t r o l y t e . When c o r r e c t i o n i s made f o r i o n i z a t i o n and s o l v e n t e f f e c t s o f ammonia, t h e n t h e two i n t e r cepts agree. From t h e d a t a i n T a b l e s 23 and 2 4 , t h e f o l l o w i n g can be c o n cluded. 3

3

1.

2.

The v o l a t i l i t y o f ammonia can be s i g n i f i c a n t e l y a f f e c t e d by h i g h c o n c e n t r a t i o n s o f d i s s o l v e d i o n s i n t h e l i q u i d phase. In sodium a c e t a t e t h e v o l a t i l i t y i n c r e a s e s by a f a c t o r o f 1.9 a t 25 wt % o f s a l t . In sodium h y d r o x i d e t h e v o l a t i l i t y i s enhanced t o a l e s s e r d e g r e e w i t h an i n c r e a s e o f 1.2 produce ions w i t e f f e c t s on t h e v o l a t i l i t y o f ammonia a r e s i g n i f i c a n t l y different. Thus t h e e f f e c t s o f v a r i o u s i o n i c components must be s t u d i e d i n d i v i d u a l l y i n o r d e r t o d e t e r m i n e t h e i r e f f e c t on t h e v o l a t i l i t y o f N H 3 . At the low i o n i c c o n c e n t r a t i o n s encountered i n sour wat e r s t r i p p e r s , the e f f e c t of d i s s o l v e d ions i s probably small. Thus a t a 1% c o n c e n t r a t i o n o f sodium a c e t a t e t h e v o l a t i l i t y o f ammonia o n l y i n c r e a s e s a b o u t 2 . 5 % due t o the s a l t . This i s w i t h i n the p r e d i c t i o n accuracy o f the ammonia v o l a t i l i t y d a t a and no c o r r e c t i o n i s t h e r e f o r e required. However s i g n i f i c a n t i o n i c e f f e c t s c o u l d e x i s t i n t h e c o n d e n s e r where h i g h c o n c e n t r a t i o n s o f t h e i o n i c components c o u l d e x i s t .

Summary and

Conclusions

Ammonia p a r t i a l p r e s s u r e d a t a have been d e t e r m i n e d a t c o n c e n t r a t i o n s from 10 ppm up t o 5 wt % i n w a t e r a t t e m p e r a t u r e s o f 80 and 120°C. The pH o f N H o - H S - C 0 - H 0 m i x t u r e s have a l s o been measured a t 25 and 8 0 ° C . A l s o t h e e f f e c t s o f sodium h y d r o x i d e and sodium a c e t a t e on ammonia v o l a t i l i t y d a t a have been measured a t 80°C. V a r i o u s c o n c l u s i o n s made from t h e d a t a a r e as f o l l o w s . 2

1.

2. 3.

2

2

The v o l a t i l i t y o f N H 3 a t ppm l e v e l s can be c a l c u l a t e d from t h e i o n i z a t i o n c o n s t a n t o f ammonia combined w i t h v o l a t i l i t y d a t a measured a t h i g h e r c o n c e n t r a t i o n s o f ammonia. The v o l a t i l i t y o f ammonia a t 80 and 120°C i s a b o u t 5% h i g h e r t h a n i s now p r e d i c t e d by t h e SWEQ m o d e l . The v o l a t i l i t y o f ammonia can be s i g n i f i c a n t l y a f f e c t e d by h i g h c o n c e n t r a t i o n s o f d i s s o l v e d i o n s i n t h e l i q u i d phase. U n f o r t u n a t e l y t h e e f f e c t v a r i e s d e p e n d i n g on t h e t y p e s o f i o n s i n s o l u t i o n . Sodium a c e t a t e p r o d u c e s a

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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THERMODYNAMICS

4.

5. 6.

7. 8.

9.

10.

OF AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

much l a r g e r enhancement i n t h e v o l a t i l i t y t h a n i s p r o ­ duced by sodium h y d r o x i d e . A t t h e low i o n i c c o n c e n t r a t i o n s encountered i n sour w a ­ t e r s t r i p p e r s , the e f f e c t o f d i s s o l v e d ions i s probably small. A 1% c o n c e n t r a t i o n o f sodium a c e t a t e o n l y e n ­ hances t h e v o l a t i l i t y o f ammonia by a b o u t 2 . 5 % . High i o n i c c o n c e n t r a t i o n s i n t h e c o n d e n s e r may p r o d u c e b i g g e r effects. M e a s u r e d pH d a t a on NH3-H2S-CO2- H 0 m i x t u r e s can be c o r ­ r e l a t e d u s i n g an e q u i l i b r i u m c o n s t a n t a p p r o a c h w i t h most d e v i a t i o n s b e i n g l e s s t h a n + 0.1 ρ H u n i t . The p K o f ammonia d e r i v e d f r o m t h e pH d a t a a g r e e s w i t h l i t e r a t u r e d a t a w i t h i n 0.1 pH u n i t a t 2 5 ° C . A t 80°C t h e agreement i s n o t as good w i t h a d i f f e r e n c e o f 0 . 4 2 pH unit. HoS and CO? hav COo-NHo-H^O m i x t u r e e f f e c t a t 25°C. pH measurements a t 25°C t e n d t o be more r e l i a b l e t h a n d a t a a t h i g h e r t e m p e r a t u r e s b e c a u s e t h e o u t p u t from t h e p r o b e i s more s t a b l e a t 2 5 ° C . For t h i s reason i t i s recommended t h a t i f a pH p r o b e i s used as a c o n t r o l s e n ­ s o r i n a p r o c e s s t h a t i t be used a t 2 5 ° C . Measured pH d a t a on H0S-CO0-NH3- H 0 m i x t u r e s a t 25°C c a n be used t o e s t i m a t e t h e m o l e s o f a c i d gas per mole o f ammonia i n s o l u t i o n w i t h o n l y an a p p r o x i m a t e knowledge o f t h e t o t a l amount o f ammonia i n s o l u t i o n . C e r t a i n t y p e s o f r e f e r e n c e e l e c t r o d e s a r e f o u n d t o be more s u i t a b l e t h a n o t h e r s when d e t e r m i n i n g t h e pH o f s o l u t i o n s c o n t a i n i n g H2S. Recommendations r e g a r d i n g various electrodes a r e given i n t h e t e x t o f the paper. 2

a

2

Acknowledgment T h i s work was s u p p o r t e d by t h e Gas P r o c e s s o r s A s s o c i a t i o n a n d the American Petroleum I n s t i t u t e . The c o n s c i e n t i o u s work o f K e n t C . W i l s o n i n d o i n g many o f t h e p o t e n t i o m e t r i c t i t r a t i o n s and K a t i e Toepke f o r t y p i n g t h i s r e p o r t is appreciated. Literature Cited

1. Edwards, T. J. and Prausnitz, J. M. A.I.Ch.E. Journal, 1975, 21, (2), 248-259. 2. Wilson, G. M. "A New Correlation of NH , CO , and HS Volatil­ ity Data from Aqueous Sour Water Systems", American Petroleum Institute, February 1978. 3. Miles, D. H. and Wilson, G. M. "Vapor-Liquid Equilibrium Data for Design of Sour Water Strippers", Annual Report to the American Petroleum Institute for 1974, October 1975 (Data in this report are also summarized in reference 2). 4. CRC Handbook, 51st Edition, page D-122 (1970-1971). 3

2

2

RECEIVED February 27, 1980. In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

10 Predicting Vapor-Liquid-Solid Equilibria in Multicomponent Aqueous Solutions of Electrolytes JOSEPH F. ZEMAITIS, JR. OLI Systems, Inc., 15 James Street, Morristown, NJ 07960

It is evident from result of recent requirement process wastewater streams, improved techniques for predicting the vapor-liquid-solid equilibria of multicomponent aqueous solutions of strong and/or weak electrolytes are needed. In addition to the thermodynamic models necessary for such predictions, tools have to be developed so that the engineer or scientist can use these thermodynamic models correctly and with relative ease. Within the past few years the advances made in hydrocarbon thermodynamics combined wtih increased sophistication in computer software and hardware have made it quite simple for engineers to predict phase equilibria or simulate complex fractionation towers to a high degree of accuracy through software systems such as SSI's PROCESS, Monsanto's FLOWTRAN, and Chemshare's DISTILL among others. This has not beem the case for electrolyte systems. For processes involving electrolytes either directly or indirectly, the techniques used have relied heavily on correlations of limited data which are often embedded into design techniques where inexact extrapolations are the rule rather than the exception. Hampering the improvement of design tools to a level comparable to that for hydrocarbons have been several restrictions such as: ο

The lack of good simple data f o r strong and/or weak electrolytes.

ο

U n t i l r e c e n t l y , there was no need to reduce l e v e l s to the ppm range.

ο

A l a c k of understanding of e l e c t r o l y t e thermodynamics w i t h regards to the need to s a t i s f y the i o n i c e q u i l i ­ b r i a and e l e c t r o n e u t r a l i t y expressions f o r the p a r t i c u ­ l a r set of species of i n t e r e s t . This one point has negated many design approaches proposed i n the past.

pollutant

0-8412-0569-8/80/47-133-227$05.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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o

The lack of a s u i t a b l e thermodynamic framework f o r e l e c t r o l y t e s over a wide range of concentrations and temperatures.

ο

Mistaken approaches to data gathering, l e a d i n g to the c o l l e c t i o n of considerable data i n doped s o l u t i o n s to h o l d i o n i c strength constant.

Recognizing these problems w h i l e f o r s e e i n g the need f o r a new t o o l u s e f u l f o r aqueous systems by users i n a wide v a r i e t y of a p p l i c a t i o n s we began i n 1974 to forge the proper t o o l s . We were f o r t u n a t e to s t a r t at that time and not f i v e years sooner since i t was during the e a r l y 1970's when a resurgence i n work i n the area of e l e c t r o l y t e thermodynamics s t a r t e d being published by s e v e r a l of our symposium's d i s t i n g u i s h e d p a r t i c i p a n t s . In t h i s paper I w i l are c o n t i n u i n g to develo d e s c r i b e the basic thermodynamic framework which we have synthesized *nd how t h i s framework i s implemented into a computer software system that: ο

P r e d i c t s the v a p o r - l i q u i d - s o l i d e q u i l i b r i u m of m u l t i component aqueous systems.

ο

Allows the user to expand the system's data bank through a s e r i e s of programs to reduce raw data and regress to f i t the thermodynamic framework of the system.

ο

Allows the user to f u r t h e r exnand the da*-a a v a i l a b l e through a s e r i e s of e s t i m a t i n g and/or e x t r a p o l a t i n g programs when l i t t l e or no data are a v a i l a b l e .

ο

Solves complex systems and p r e d i c t s r e s u l t s as a f u n c t i o n of temperature or concentrations i n order to develop phase diagrams or study the e f f e c t s of various l e v e l s of certain constituents.

ο

Incorporates the thermodynamic framework and associated data e s t i m a t i o n techniques i n t o m u l t i s t a g e multicomponent f r a c t i o n a t i o n tower software f o r the design and/or s i m u l a t i o n of sour water s t r i p p e r s , n i t r i c acid towers, amine scrubbers or any other tower where i o n i c e q u i l i b r i a and/or r e a c t i o n s occur.

To i l l u s t r a t e the power of the general purpose t o o l s we have developed, I w i l l describe the a p p l i c a t i o n of our software to two systems. F i r s t , since most of the p a r t i c i p a n t s i n t h i s session are using i t as an example, and because i t i s important, I w i l l give some of our r e s u l t s f o r the N H 3 - C O 2 - H 2 O system. Secondly, to i l l u s t r a t e the p r e d i c t i o n of combined v a p o r - l i q u i d - s o l i d

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

10.

ZEMAiTis

Multicomponent Aqueous Electrolyte Solutions

229

e q u i l i b r i a and the e f f e c t of high i o n i c s t r e n g t h s , I w i l l present some of our r e s u l t s f o r an i n t e r e s t i n g system, that o f FeCl -HCl-H 0. In r e f e r r i n g to the computer software system which I developed, the acronym ECES w i l l be used. ECES s i g n i f i e s the E q u i l i b r i u m Composition of E l e c t r o l y t e Systems. 2

2

Thermodynamic Framework In developing the thermodynamic framework f o r ECES, we attempted to synthesize computer software that would c o r r e c t l y p r e d i c t the v a p o r - l i q u i d - s o l i d e q u i l i b r i a over a wide range of c o n d i t i o n s f o r multicomponent systems. To do t h i s we needed a good b a s i s which would make evident to the user the chemical and i o n i c e q u i l i b r i a present i n aqueous systems. We chose as our cornerstone the law of product of the a c t i v i t i e to the power i n d i c a t e d by i t s numerical c o e f f i c i e n t , d i v i d e d by the product of the a c t i v i t i e s of the r e a c t a n t s , each r a i s e d to a corresponding power, i s a constant at a given temperature." I f the user w r i t e s a simple mass balance f o r the s o l u b i l i t y e q u i l i b r i u m or i o n i c e q u i l i b r i u m such as - the r e a c t i o n of b moles of Β w i t h c moles of C has come to e q u i l i b r i u m w i t h the product of d moles of D and e moles of E, then the mass balance i s given by bB + cC = dD + eE (1) and the law of mass a c t i o n s t a t e s at e q u i l i b r i u m d e , b c

T

r

/

0

x

where Κ i s the thermodynamic e q u i l i b r i u m constant f o r the temperature of i n t e r e s t . The thermodynamic e q u i l i b r i u m constant can be r e a d i l y c a l c u l a t e d at any temperature i f we can evaluate the standard free energy of formation f o r the r e a c t i o n expressed by equation (1) at the temperature d e s i r e d . Such computations can be done r a t h e r e a s i l y i f we have a v a i l a b l e information on the standard free energy of formation, the heat of formation, and standard heat c a p a c i t i e s f o r each of the c o n s t i t u e n t s of our e q u i l i b r i u m equation. A c o n s i d e r a b l e amount of t h i s type of data i s a v a i l a b l e i n compilations published by the N a t i o n a l Bureau of Standards (I) and others. Such information has been stored w i t h i n a database i n the ECES system. Then, using user input i n the form of equation ( 1 ) , ECES w r i t e s the expression f o r computing the thermodynamic e q u i l i b r i u m constant as a f u n c t i o n of temperature to a f i l e where i t w i l l e v e n t u a l l y become part of a program to solve the many e q u i l i b r i a that might describe a complex system. In order to describe f u l l y the system, methods f o r e v a l u a t i n g the a c t i v i t i e s o f the v a r i o u s species i n equation (2)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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must be used. For an e l e c t r o l y t e s o l u t i o n the a c t i v i t y of an i n d i v i d u a l i o n i c species i s given by a. = γ . m. i i i

/ 0

T

n

(3)

where the a c t i v i t y of the species i s based on the h y p o t h e t i c a l i d e a l s o l u t i o n of u n i t m o l a l i t y . The m o l a l i t y of the i o n i i s d e f i n e d by m£ equal to the number of gram-moles of ion i n 1000 grams of water. For a pure s a l t d i s s o l v e d i n water i t i s not f e a s i b l e to determine the a c t i v i t y c o e f f i c i e n t , , f o r the c a t i o n and anion s e p a r a t e l y so that the mean a c t i v i t y c o e f f i c i e n t concept has been defined f o r a s a l t s c a t i o n - a n i o n p a i r as 1

+

γ !

/

=(γ + γ_ ") +

7^Γ7-

(4)

The mean a c t i v i t y expressing e l e c t r o l y t e dat compilation experimental data such as Hamer and Wu (2^) or i n p r e d i c t i o n s based on extensions to the Debye-Huckel model of e l e c t r o l y t e behavior. Receni-ly several advances i n the p r e d i c t i o n and c o r r e l a t i o n of mean a c t i v i t y c o e f f i c i e n t s have been presented i n a s e r i e s of papers s t a r t i n g i n 1972 by P i t z e r C 3 ) , Meissner ( 4 ) , and Bromley (_5 ) among others. As the basis f o r p r e d i c t i n g i o n i c a c t i v i t y c o e f f i c i e n t s we chose to adoptait e m p i r i c a l m o d i f i c a t i o n of Bromley's (_5) e x t e n s i o n of the Debye-Huckel model. The mean a c t i v i t y c o e f f i c i e n t of a pure s a l t i n water i s given by logV + = -

A

1

^ +

V

I

Ι 1

/

2

χ 1 / 2 +

(0-06+0-6B) | z V |

(l Al2L)

+

B I

+

C I

2

+

M

3

( 5 )

2

+

kV ι where A i s the Debye-Huckel parameter, a f u n c t i o n of temperature, and B, C, D are e m p i r i c a l c o e f f i c i e n t s which are functions of temperature and of the s a l t i n question. We chose the Bromley form due to the fact that Bromley's v e r s i o n of equation (5) which neglected the polynomial terms e s t a b l i s h e d a b a s i s f o r p r e d i c t i n g the c o e f f i c i e n t Β f o r s a l t s where no data was a v a i l a b l e that would give reasonable r e s u l t s to i o n i c s t r e n g t h s , I , of about 6 mo 1*1. The t y p i c a l system f o r which the e q u i l i b r i u m composition i s desired however does not contain a s i n g l e s a l t i n s o l u t i o n but more u s u a l l y the equivalent of s e v e r a l s a l t s i n s o l u t i o n . In a d d i t i o n , the a c t i v i t i e s required i n e q u i l i b r i u m expressions a r i s i n g from the law of mass a c t i o n are s i n g l e i o n a c t i v i t i e s or in g e n e r a l , s i n g l e i o n a c t i v i t y c o e f f i c i e n t s . And, we are i n t e r e s t e d i n the i o n i c a c t i v i t y c o e f f i c e i n t of each species i n a multicomponent system.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

10.

231

Multicomponent Aqueous Electrolyte Solutions

ZEMAiTis

As our b a s i s we chose the Bronsted-Guggenheim (6) equation f o r the mean a c t i v i t y c o e f f i c i e n t χ of the e l e c t r o l y t e in a s o l u t i o n of s e v e r a l e l e c t r o l y t e s having c a t i o n R and anion X. The mean a c t i v i t y c o e f f i c i e n t Y ^ i s given by

^R,X=

^ P

+

!

+

I

R

j

x

l

V

l/2

(6) Σ 3 m R R ,x R

+

1

• ++•-

1

1

1

I f we take the logarithm of equation (4) and apply the r u l e s of logs we o b t a i n +

(/

+/-) l o g y

Which i f we combine with equation (6) we can develop a d e f i n i t i o n of the a c t i v i t y c o e f f i c i e n t of a s i n g l e ion i n a m u l t i - i o n s o l u t i o n as , . 1 0 8

„

=

+ Σ ι β„ ι

mι

(8)

Κ

. χ Κ,χ χ ι+ι A common f a i l i n g of e a r l i e r work on multicomponent s o l u t i o n s was to consider the 3 R,x to be a constant f o r each s a l t . As Bromley (_5) pointed out, the equations developed from the Bronsted-Guggenheim approach to multicomponent equations are only exact i f PR,χ i s constant, the b a s i c equations are reasonable exact i f 3R,x i s a s l o w l y v a r y i n g f u n c t i o n of c o n c e n t r a t i o n and Harned's Rule (1) f o r mixed e l e c t r o l y t e s through an e m p i r i c a l c o r r e l a t i o n does show such of an e f f e c t . For ECES as our b a s i s of developing a c o n c e n t r a t i o n dependence f o r the i n t e r a c t i o n c o e f f i c i e n t we equated equation (5) to the a l t e r n a t e expression ^2 Α / ζ

1 + I and developed the f o l l o w i n g expression f o r the i n t e r a c t i o n c o e f f i c i e n t of a c a t i o n - a n i o n p a i r :

G

R

X

.(0.06

* 0.6B)| « V |

+

B

p

Rx (

Kx

2 Kx

(10)

1 + 1.5 I j 2

I

+

z z

I

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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which i s used i n Bromley's form of the Bronsted-Guggenheim equation 1/2 1 / Z

-"A j z" V'|*l

= logv = Rx D

6

1

^ +

_ J/R L^

1

1 + I

/

r

V

Σ, x

. ,„

R \ X

R

2 x 1

mi x

1

(11)

"V

2

\ X

„ R.x

1

/x

/R

V

x

6 ! Tt.x

z

R + x where Z R 2 This i s our basic expression f o r the a c t i v i t y c o e f f i c i e n t of an i o n i n a multicomponent s o l u t i o n , the r e s u l t f o r the a c t i v i t y c o e f f i c i e n t of a c a t i o n i s Z

=

X

g i v e n by

>z ι

1/2

- IV A

L

0

G

Y

R

+

1

Σ

1/2

R

χ

1

^R.x

1

' R . X

1

V

(12)

where t h e ? R , x ^ are given by equation (10) and are functions of c o n c e n t r a t i o n and temperature. The a c t i v i t y of the solvent (water) i n a s o l u t i o n of pure e l e c t r o l y t e d i s s o l v e d i n water can be computed by a p p l i c a t i o n of the Gibbs-Duhem equation: -55.51

d ( l n a ) = (/+ + /_)m d ( l n (γη))

(13)

w

which can be i n t e g r a t e d upon s u b s t i t u t i o n of equation (5) t o give:

2 I ζ z

-2 l n (1 + I

1 / 2

+

+

-A| Z Z | [ ( 1 + I

4.606

+

I

Iz

) - 1/(1 + I

1 / 2

+

z

1/2

)

I +

) ] + (0.06 + .6B) l| z z |

0775 1 + 3 I/(| z V j) (1 + 1.5I/

p

Experimental Methods S o l u t i o n P r e p a r a t i o n . S o l u t i o n s were prepared from reagent grade c i t r i c a c i d monohydrate, sodium c i t r a t e d i h y d r a t e , N a H S 0 3 , Na2S04, NaCl, and s t a n d a r d i z e d NaOH s o l u t i o n . Hydroquinone (0.1 wt %) was added to i n h i b i t o x i d a t i o n of s o l u t i o n s w i t h NaHS03. The NaHSÛ3 was analyzed by i o d i n e t i t r a t i o n and was t y p i c a l l y 97-98% of the expected S O 2 content. S e v e r a l of the s o l u t i o n s used f o r v a p o r / l i q u i d e q u i l i b r i u m experiments were analyzed f o r t o t a l S O 2 and found to c o n t a i n 5 to 10% l e s s than the nominal concent r a t i o n . Nominal c o n c e n t r a t i o n s were used i n p r e s e n t i n g and a n a l y z i n g the d a t a , unless noted otherwise. Therefore, c o r r e l a t e d v a l u e s of P S O 2 be 5 to 10% low f o r a given s o l u t i o n composition. m a v

pH Measurements. A Ag/AgCl combination e l e c t r o d e was used f o r a l l measurements at 25°C. A thalamid combination e l e c t r o d e was used at 55° and 95°C. I t was c o n d i t i o n e d i n pH 4.00 b u f f e r at 55° or 95°C f o r at l e a s t 24 hours before use. The e l e c t r o d e s were s t a n d a r d i z e d at the measurement temperature by p h t h a l a t e b u f f e r at pH 4.00 and phosphate b u f f e r at pH 7.00. Response of the e l e c t r o d e s to c i t r a t e b u f f e r s r e q u i r e d 15 t o 30 minutes f o r

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

12.

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271

Sulfur Dioxide Vapor Pressure

a s t a b l e r e a d i n g . I n l a t e r experiments secondary c i t r a t e b u f f e r s were used t o s t a n d a r d i z e the e l e c t r o d e s and thereby reduce e q u i l i ­ brium time. Dynamic S a t u r a t i o n . Dynamic s a t u r a t i o n was the primary method used f o r v a p o r - l i q u i d e q u i l i b r i u m (VLE) determinations. T y p i c a l apparatus i s shown i n f i g u r e 1. N 2 gas was sparged through a s o l u t i o n o f known, r e l a t i v e l y constant composition, then analyzed f o r S O 2 . T y p i c a l l y 1 t o 5 l i t e r s o f N 2 o r N 2 / S O 2 was sparged through a coarse, f r i t t e d - g l a s s d i s p e r s i o n tube sub­ merged 7 t o 15 cm i n 125 t o 300 ml o f s o l u t i o n i n a s i n g l e - s t a g e g l a s s o r s t a i n l e s s s t e e l s a t u r a t o r . Gas l e a v i n g the s a t u r a t o r was assumed to be i n e q u i l i b r i u m w i t h the s o l u t i o n . Comparable r e s u l t s were obtained i n experiments u s i n g three s a t u r a t o r s i n s e r i e s and i n experiments u s i n g S O 2 a b s o r p t i o n r a t h e r than des o r p t i o n . The s a t u r a t o maintained ± 1°C Most dat t 25° to 55°C were taken a t atmospheri were taken at 4.4 t o 1 S O 2 content of the gas was determined by sparging i n t o a 125 ml gas washing b o t t l e c o n t a i n i n g a known amount of I 2 i n acetate b u f f e r a t pH 4-5.5 w i t h a s t a r c h i n d i c a t o r . N 2 f l o w was measured by a wet t e s t meter. Water content of the gas l e a v i n g the s a t u r a t o r was estimated using a m o d i f i e d Raoult's law. Constants f o r vapor pressure lowering were obtained from Weast ( 8 ) . Constants f o r NaH2Citrate, Na2HCitrate, N a 3 C i t r a t e , and NaHS03 were assumed to be equal t o those f o r NaH2P04, N a 2 H P 0 4 , Na3P04, and NaCl, r e s p e c t i v e l y . The a c t i v i t y o f water was assumed t o be independent of temperature and i s given by: ^ (1 - a ) 7 6 0 = 30.0 [ N a C i t ] + 23.5 [Na HCit] + 21.0 [NaH Cit] un

0

0

0

+25.2 ([NaHS0 ] + [NaCl]) 3

+ 25.0 ( [ N a S 0 ] + [ 2

4

N a

S 2

2°3

] )

The lowest water a c t i v i t y encountered i n these experiments was about 0.88 (2 M C i t r a t e ) . The vapor pressure of water over the s o l u t i o n i s g i v e n by: P

H 0

=

Ρ

*Η 0 Η 0

2

st

2

n

2

e

where Pj^O * vapor pressure of pure water a t the s a t u r a t o r temperature. Assuming that the vapor l e a v i n g the s a t u r a t o r i s an i d e a l gas the S O 2 vapor pressure i s g i v e n by:

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

272

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

ri SO ρ

= S 0

a n d

(ρ

± n

2 n

S0

+

a r e

t h e

_ ρ

T

\

2

m

e s

H

o f

s

)

2° o

a n d

N

a n d

P

i s

where n g o N2 °l 2 2 T the totalpressure. Under most c o n d i t i o n s Pr^O l e s s than 1 0 % of P-p. Therefore, P S O 2 r e l a t i v e l y i n s e n s i t i v e to e r r o r s i n Ρ Η 0 · 2

w

a

s

i s

2

SO? E l e c t r o d e . A gas-sensing S O 2 e l e c t r o d e marketed by I o n i c s , Inc. was used to provide a d d i t i o n a l VLE data a t 25°C as a f u n c t i o n of composition. Aqueous S 0 e q u i l i b r a t e s across a p o l y ­ meric membrane w i t h a f i l l i n g s o l u t i o n c o n t a i n i n g about 0 . 1 M NaHSO^. I o n i c species do not d i f f u s e across the membrane. A small combination g l a s s e l e c t r o d e measures the pH of the f i l l i n g s o l u t i o n . The S O 2 a c t i v i t y (PsOo) p r o p o r t i o n a l to the a c t i v i t y of Η"*" ( 1 0 ~ P ^ ) , because 2

i s

HS0 " + "Ws0 (g) + H 0 3

H

P

2

S0

=

K

a

2

2

a

H+ HS0~ a s

o w

a s

The S O 2 e l e c t r o d e has a l i n e a r response to P g 0 2 ^ ^ ^ atm. Water a l s o d i f f u s e s across the polymer membrane to a l i m i t e d extent. Therefore the e l e c t r o d e response i s unstable and u n r e l i ­ able i f there i s a s i g n i f i c a n t d i f f e r e n c e between the osmotic pressure of the f i l l i n g s o l u t i o n and the unknown s o l u t i o n . To p a r t i a l l y a l l e v i a t e t h i s problem, data were taken w i t h f i l l i n g s o l u t i o n s c o n t a i n i n g 0 , 1 . 0 , and 2 . 0 M a d d i t i o n a l K C l . The response of the S O 2 e l e c t r o d e i s a c t u a l l y read as v o l ­ tage, (mV). Two constants are needed t o convert t h i s t o Ρ : so l o g

p

so

= 2

C

+

2

d

We have used the t h e o r e t i c a l value of d at 25°C which i s 59.16 mV. The constant c must be determined by measurement o f a known s o l u t i o n each day the e l e c t r o d e i s used. A l t e r n a t i v e l y , the e l e c t r o d e can be used t o provide r e l a t i v e P^Q f o r a s e r i e s o f measurements. 2 pH Behavior A s e m i e m p i r i c a l c o r r e l a t i o n of pH measurements w i t h 156 s o l u t i o n s gave the f o l l o w i n g r e l a t i o n s h i p :

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

12.

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Sulfur Dioxide Vapor Pressure

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a

+

l

a

2

f+

a 3

[

A n i

°n] °*

5

(1)

T

2.77 ± 0.05 3.60 ± 0.05 -0.53 The

± 0.03

t o t a l c o n c e n t r a t i o n of anions i s given by: [ A n i o n ] = [ C i t r a t e ] + [ N a S 0 ] + [NaCl] + [NaHSO^ T

2

+

N e g l e c t i n g H and assumin fraction neutralizatio +

[Na ] f

=

4

that S 0 i

t

bisulfite

th

=

- [S0 ] - [Cl~] - 2 [ S 0 ] 2

4

3[Citrate]

This c o r r e l a t i o n i n c l u d e s s o l u t i o n s over the f o l l o w i n g range of conditions : f = 0.20 - 0.833 [ C i t r a t e ] = 0.05 - 2.0 M [ N a S 0 ] = 0 - 1.5 M 2

4

[NaHS0 ] = 0 - 1.0 M 3

[NaCl] = 0 - 1.9 M The

standard d e v i a t i o n of pH p r e d i c t i o n i s 0.12 pH u n i t s . In these s o l u t i o n s pH i s more s t r o n g l y c o r r e l a t e d w i t h t o t a l anion c o n c e n t r a t i o n than w i t h i o n i c s t r e n g t h . Thus 1 M Na2S04 and 1 M NaCl have about the same e f f e c t on the pH of a s o l u t i o n at a given f r a c t i o n n e u t r a l i z a t i o n . F i g u r e 2 shows pH a t 50% n e u t r a l i z a t i o n as a f u n c t i o n of anion c o n c e n t r a t i o n i n the s o l u t i o n s which are p r i m a r i l y c i t r a t e , N a 2 S 0 4 , or NaCl, as w e l l as i n mixed s o l u t i o n s . The e f f e c t of s o l u t i o n a n i o n i c c o n c e n t r a t i o n i s probably r e l a t e d to e f f e c t s on a c t i v i t y c o e f f i c i e n t s and i o n p a i r forma t i o n o f more h i g h l y charged b u f f e r species. In more concentrated s o l u t i o n s , the a c t i v i t y of the h i g h l y charged species i s reduced by both i o n i c s t r e n g t h and i o n p a i r formation. The e f f e c t on l e s s charged, a c i d i c species i s l e s s . Therefore, as s o l u t i o n s become more concentrated, the a c t i v i t y of b a s i c species i s r e duced r e l a t i v e to that of a c i d i c species, and at a given f r a c t i o n

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

274

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Regulator

Thermometer ^Pressure Gauge

Μ Λΐ Needle ΛΛ

Λ

\

Valve

Shutoff Valve N

Saturator

2

Graduated Cylinder

I

I I Ο ο ο _0

Absorber

Gas Trap

Carrier Gas

Figure 1.

Figure 2.

A pparatus for dynamic saturation

Dependence of pH on total anion concentration ((%) infinite dilution; (O) NaCl; ( Q ) Na S0 ; (A) sodium citrate; (V) mixed solution) 2

4

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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275

Sulfur Dioxide Vapor Pressure

n e u t r a l i z a t i o n the pH decreases. I n concentrated s o l u t i o n s p o l y ­ v a l e n t anions such as S O 4 " and c i t r a t e " probably form i o n p a i r s such as NaS04~ and N a 2 c i t r a t e . Therefore the e f f e c t i v e i o n i c s t r e n g t h and N a c o n c e n t r a t i o n a v a i l a b l e f o r i o n p a i r formation v a r i e s w i t h t o t a l anion c o n c e n t r a t i o n r a t h e r than i o n i c s t r e n g t h . The e f f e c t of f r a c t i o n n e u t r a l i z a t i o n on pH i s i l l u s t r a t e d i n f i g u r e 3 f o r a s o l u t i o n of constant a n i o n i c c o n c e n t r a t i o n . This corresponds to t i t r a t i n g c i t r i c a c i d w i t h NaOH. The t i t r a ­ t i o n curve i s very n e a r l y l i n e a r from pH 2.2 to about pH 5.5 w i t h a slope of 3.60. The e f f e c t s of the three f u n c t i o n a l b u f f e r groups of c i t r i c a c i d are smeared so t h a t no S-shape or i n f l e c ­ t i o n p o i n t s are apparent. As shown i n f i g u r e 4, t i t r a t i o n w i t h HCI or a b s o r p t i o n of S O 2 as b i s u l f i t e r e s u l t s i n a d i f f e r e n t dependence of pH on f r a c t i o n n e u t r a l i z a t i o n because the t o t a l anion c o n c e n t r a t i o n i s increased. The slope o 4.0 and i s modeled by equatio As shown i n Table I , the ΔΗ values of the b u f f e r r e a c t i o n s corresponding roughly to K i , K 2 , and K 3 (16.7, 50.0, and 83.3% n e u t r a l i z a t i o n , r e s p e c t i v e l y ) a l l have absolute values l e s s than 2.0 kcal/g-mole. The r e a c t i o n s corresponding to K 2 and K 3 , which are most r e l e v a n t f o r S O 2 a b s o r p t i o n / s t r i p p i n g , had ΔΗ values of -0.7 and +0.1 kcal/g-mole, r e s p e c t i v e l y . The c a r e f u l data of Bates and P i n c h i n g ( 9 ) i n d i l u t e c i t r a t e s o l u t i o n s g i v e ΔΗ values between 25° and 50°C of -0.01, -0.002, and +0.03 k c a l / g mole, r e s p e c t i v e l y f o r K i , K 2 , and K 3» Because o v e r a l l tem­ perature e f f e c t s i n S O 2 a b s o r p t i o n / s t r i p p i n g are on the order o f 10 kcal/g-mole, we can n e g l e c t the enthalpy change of the b u f f e r reaction. +

+

a

a

a

a

a

S0

?

a

a

a

Vapor Pressure

S O 2 vapor pressure was determined i n e i g h t s e r i e s of e x p e r i ­ ments (Tables I I and I I I ) w i t h a t o t a l o f about 80 s o l u t i o n s over the f o l l o w i n g range of c o n d i t i o n s : f = 0.40 - 0.80 [ C i t r a t e ] = 0.2 - 2.0 M [NaHS0 ] = 0.025 - 1.0 M 3

[Na S0 ] = 0 - 1 M 2

4

[ N a S 0 ] = 0 - 0.6 M 2

2

3

Τ = 25 - 168°C A s e m i e m p i r i c a l c o r r e l a t i o n of the data g i v e s :

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Figure 4.

Dependence of pH on fraction neutralization—titration with HCI orS0 (0) 2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

(A)

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277

Sulfur Dioxide Vapor Pressure

+

Table I : Heat of Reaction of H w i t h Concentrated Sodium C i t r a t e B u f f e r s Solution composition ^—)

a Fraction neutralization 0.167

0.500

0.833

, . Q ΔΗ (kcal/g-mole)

0.30 NaCl 1.50 0.60 C i t r a t e 3.00

+ -

Mean

- 2.0 ± 1.7

C

0.30 NaCl

0.9

0.15 C i t r a t e 0.50 0.75 1.00 2.00

-

Mean

- 0.7 ± 0.5

0.30 NaCl 1.50 0.50 Na2S0 0.0667 C i t r a t e 0.333 0.50 1.00 2.00

+ + + + -

Mean

+ 0.1 ± 0.6

4

+

0.7 1.5 0.1 1.0 0.9 C

C

C

0.7 0.3 0.4 0.7 0.1 0.2 0.4 0.9C C

C

=

[Na ] - [ C l ~ ] - 2 [ S 0 ]

a

4

fraction neutralization = b

ς

1.6 0.2 2.8 3.8

3[Citratel

C h l o r i d e and s u l f a t e s o l u t i o n s c o n t a i n 0.00667 M C i t r a t e . A l l s o l u t i o n s c o n t a i n NaOH as i n d i c a t e d by f r a c t i o n n e u t r a l i z a ­ tion

ΔΗ c a l c u l a t e d from pH values a t 25° and 95°C

^ΔΗ c a l c u l a t e d from pH values at 25° and 55°C unless noted

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Table I I : SO2 Vapor Pressure Obtained by Dynamic S a t u r a t i o n a t 25° t o 158°C, S e r i e s 1 S o l u t i o n Composition (M)

so

Citrate 0.5

r

0.533

0.25

0.583

1

0.80

0.700

14.8 12.1 14.7 14.2 14.0 12.4 14.3

mean

13.7

24 55 75 95 115 135

14.6 18.8 16.3 16.5 17.1 15.7

55 75 95 115 135 mean

0.5

a

0.533

0.20

25 168 mean

1.0

0.164

b

0.612

χ 10

the h u m i d i f i e d i n l e t s t a c k gas (1). This steam requirement i s i n dependent of the s t r i p p e r temperature, but assumes that the s t r i p per feed i s preheated to i t s b o i l i n g p o i n t , that there are an i n f i n i t e number of stages i n the absorber and s t r i p p e r , and that the e q u i l i b r i u m curve i s l i n e a r . 2

2

2

2

2

p

2

o f

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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285

Sulfur Dioxide Vapor Pressure

The second c h a r a c t e r i s t i c of e q u i l i b r i u m data a f f e c t i n g steam requirements i s the n o n l i n e a r i t y of PsOo/ HoO versus [SO2]. That n o n l i n e a r i t y i s q u a n t i f i e d p r i m a r i l y by the dependence of K on f. F i g u r e 6 shows p r e d i c t e d and measured values of P s 0 ^ HoO [δ0 ] f o r 1 M c i t r a t e s o l u t i o n s w i t h 1.5,2.0,and 2.5 M Na . Performance of a simple a b s o r p t i o n / s t r i p p i n g system can be determined by use of a McCabe-Thiele diagram. E q u i l i b r i u m f o r both s t r i p p e r and absorber can be represented as a s i n g l e l i n e when p l o t t i n g Ps02/ H?0 versus [SO2]. M a t e r i a l balance gives o p e r a t i n g l i n e s f o r the absorber and s t r i p p e r . The slope of the absorber o p e r a t i n g l i n e i s the r a t i o of l i t e r s of c i r c u l a t i n g s o l u t i o n to moles of H2O i n the s a t u r a t e d s t a c k gas. The slope of the s t r i p p e r o p e r a t i n g l i n e i s the r a t i o of l i t e r s of c i r c u ­ l a t i n g s o l u t i o n to moles of steam. The steam requirement i n moles per mole of SO2 absorbe r a t i o , Ps02/ H20> F i g u r e 7 i l l u s t r a t e s how minimum steam requirements can be estimated f o r 1 M c i t r a t e w i t h 2.0 molar N a i n a simple absorp­ t i o n / s t r i p p i n g system to remove 90% of the S 0 from stack gas at 55°C c o n t a i n i n g 3000 ppm SO2. The o p e r a t i n g l i n e s f o r the absorber and s t r i p p e r are s t r a i g h t , assuming that the H 0 vapor r a t e i s constant throughout the absorber and throughout the s t r i p p e r . With an i n f i n i t e number of stages the absorber i s pinched at the top and bottom. Using l i v e steam, the s t r i p p e r pinches i n the middle because of the n o n l i n e a r i t y of the e q u i l i b ­ rium curve. The gas l e a v i n g the s t r i p p e r would have Pso /* H20 equal to 0.0173, g i v i n g a minimum steam requirement of 57.8 moles H20/mole SO2 (16.3 kg/kg). I f the e q u i l i b r i u m were l i n e a r the minimum steam requirement would be 50 moles H20/mole SO2. Thus, n o n l i n e a r i t y i n c r e a s e s the steam requirement by a f a c t o r of 1.16. F i g u r e 8 i l l u s t r a t e s the performance of a system w i t h three e q u i l i b r i u m stages i n the absorber and s i x i n the s t r i p p e r . The a c t u a l steam requirement i s 147 moles/mole SO2 (41.3 kg/kg). The use of a f i n i t e number of stages i n c r e a s e s the steam requirement a f a c t o r of 2.5 from the case of i n f i n i t e stages w i t h a non­ linear equilibrium. Table IV g i v e s minimum steam requirement ( i n f i n i t e stages) at s e v e r a l d i f f e r e n t s o l u t i o n c a p a c i t i e s . The f a c t o r a t t r i b u able to e q u i l i b r i u m n o n l i n e a r i t y i n c r e a s e s as more SO2 i s absorbed, because the b u f f e r c a p a c i t y i s consumed to a g r e a t e r extent. Any c a p a c i t y f o r S 0 a b s o r p t i o n can be achieved by v a r y i n g Na c o n c e n t r a t i o n (pH) i n the s o l u t i o n . At low pH ([Na] = 1.5 M) the s o l u t i o n c a p a c i t y f o r SO2 a b s o r p t i o n i s s m a l l , but the n o n l i n e a r i t y f a c t o r i s a l s o s m a l l (1.05). S o l u t i o n c a p a c i t y can be i n c r e a s e d by o p e r a t i n g at higher pH ([Na] = 2.5 Μ ) , but n o n l i n e a r i t y i s more severe (1.32). As shown by case 3 i n Table IV, the minimum steam r e q u i r e ­ ment i n an optimized system i s not s e n s i t i v e to the magnitude o f PS0 over the s o l u t i o n , but only to i t s dependence on temperature p

c

2

p

v

e

r

s

u

s

2

+

p

p

a

t t

n

+

2

2

>

2

2

9

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

286

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

\S02J Figure 6.

(g-moles/liter)

Dependence of P on solution composition—1.0M citrate, 25°C ((O) SO electrode; f Q ) dynamic saturation) 802

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

Figure 7. Minimum steam requirement, simple absorption/stripping with live steam, 3000 ppm SO in at 55°C, 90% removal, l.OM citrate, 2.0M Na g

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL

APPLICATIONS

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Sulfur Dioxide Vapor Pressure

and S O 2 s o l u t i o n c o n c e n t r a t i o n . I f the constant a i n the equation f o r K i s 0.30 r a t h e r than 0.46, the minimum steam re­ quirement i n c r e a s e s by only 3%. 4

c

Minimum steam requirement, i n l e t Table IV / P ο = 0.02, 90% S 0 removal, Ρ i n f i n i t e stages, 1.0 M C i t r a t e s o

H

2

[Na] (M)

Steam Requirement Moles H 0/Mole S 0

1.5 2.0 2.0 2.5

52.4 57.8 59.5 65.8

2

a

Value of a

4

2

taken to be 0.30

Nonlinearity Factor

Capacity Moles S 0 / l i t e r

1.05 1.16 1.19 1.32

0.103 0.173 0.262 0.368

r a t h e r than

2

0.46.

Conclusions 1.

Temperature dependence of pH and P s o / ^ H 0 over sodium citrate buffer solutions i s insignificant. Composition dependence of pH and P s o / H 0 rep­ resented as a f u n c t i o n of f r a c t i o n n e u t r a l i z a t i o n and t o t a l anion c o n c e n t r a t i o n . A c t u a l steam requirement w i t h t y p i c a l s t a c k gas should be about 41 kg/kg S 0 . Optimized steam requirement i s r e l a t i v e l y i n s e n s i t i v e to s o l u t i o n pH. S o l u t i o n c a p a c i t y f o r S O 2 a b s o r p t i o n can reasonably vary from 0.1 to 0.4 g-moles S 0 / l i t e r . The S 0 gas sensing e l e c t r o d e i s an e f f e c t i v e t o o l f o r v a p o r / l i q u i d e q u i l i b r i u m a t room temperature. 2

2

p

2

c

a

n D

e

2

2

4.

2

5.

2

Nomenclature a l, 3> a

a

a , a , a 6 2

4

a

Activity Constants i n c o r r e l a t i o n of pH and S 0 Constants w i t h a n i o n i c concent j t r a t i o n i n corr e l a t i o n of pH and Pgo^ MO-5 I n t e r c e p t f o r c a l i b r a t i o n of S 0 e l e c t r o d e . T o t a l c o n c e n t r a t i o n of c i t r i c a c i d and i t s anions, M Slope f o r c a l i b r a t i o n of S 0 e l e c t r o d e , mV Fraction neutralization E q u i l i b r i u m constant f o r S 0 a b s o r p t i o n as b i s u l f i t e , atm M" E q u i l i b r i u m constants f o r d i s s o c i a t i o n of c i t r i c acid, M Dependent v a r i a b l e i n c o r r e l a t i o n of S 0 vapor pressure, M~^ p

5

2

2

[Citrate] d f Κ

2

2

2

K

K

K

a l > a2> a 3

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

290

THERMODYNAMICS

M η Ρ

OF AQUEOUS SYSTEMS W I T H INDUSTRIAL APPLICATIONS

Molarity, gmol/liter Number o f g-moles Pressure o r p a r t i a l pressure, atm Vapor o r p a r t i a l pressure o f SO2, atm Vapor pressure of pure water, atm Vapor o r p a r t i a l pressure o f H2O, atm Total concentration of species (mostly bisulfite), M Concentration, M

Pfi 0 PHoO 2

[s6 ] 2

[]

Abstract

SO vapor pressure(PSO )wasmeasuredby dynamic saturation and by a gas-sensing SO electrode over solutions containing 0.5 to 2.0 M sodium citrate at pH 3.5 to 5 with up to 1 M NaHSO, Na SO , and NaCl, PSO was measured at 25° to 168°C; pH at 25° to 95°C. Both pH and th independent of temperature compositio temperatur pendence of the data are correlated by the semiempirical expres­ sions: 2

2

2

3

2

4

where f is the fraction neutralization of the citrate buffer. The steam requirement for simple absorption/stripping with 90% removal of SO from stack gas containing 3000 ppm SO at 55°C was estimated to be about 40 kg/kg SO . 2

2

2

Acknowledgements This work was p r i m a r i l y supported by c o n t r a c t s TPS 77-747 and RP 1402-2 w i t h the E l e c t r i c Power Research I n s t i t u t e . C u r t i s Cavanaugh, Richard U l r i c h , P u i L i n , and Michael Ragsdale have c o n t r i b u t e d experimental data as research a s s i s t a n t s . Legal Notice This work was prepared by the U n i v e r s i t y o f Texas a t A u s t i n as an account o f work sponsored by the E l e c t r i c Power Research I n s t i t u t e , Inc. ("EPRI"). N e i t h e r EPRI, members o f the EPRI, nor the U n i v e r s i t y of Texas a t A u s t i n , nor any person a c t i n g on behalf o f e i t h e r : a. Makes any warranty o r r e p r e s e n t a t i o n , expressed o r im­ p l i e d , w i t h respect to the accuracy, completeness, o r usefulness of the i n f o r m a t i o n contained i n t h i s r e p o r t , o r that the use o f

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

12.

ROCHELLE

Sulfur Dioxide Vapor Pressure

291

any i n f o r m a t i o n , apparatus, method, or process d i s c l o s e d i n t h i s report may not i n f r i n g e p r i v a t e l y owned r i g h t s ; o r , b. Assumes any l i a b i l i t i e s w i t h respect to the use o f , o r for damages r e s u l t i n g from the use o f , any i n f o r m a t i o n , apparatus, method o r process d i s c l o s e d i n t h i s r e p o r t . Literature Cited

1. Rochelle, G. T., "Proceedings: Symposium on Flue Gas Desul­ furization - Hollywood, FL", EPA-600/7-78-058b, p. 902 (1977). 2. Johnstone, H. F., H. F. Read, and H. C. Blankmeyer, Ind. Eng. Chem., 30, 101 (1938). 3. Boswell, M. C., U. S. Patent 1,972,074, Sept. 4, 1934. 4. Applebey, M. P., J. Soc. Chem. Ind. Trans., 56, 139 (1937). 5. Nissen, W. I., D. A. Elkins, and W. A. McKinney, "Proceedings: Symposium on Flue Ga Desulfurizatio Ne Orleans" EPA 600/2-76-136b, p. 6. Farrington, J. F. and S. Bengtsson, "The Flakt-Boliden Pro cess forSO Recovery", presented at AIME annual Meeting, February 19, 1979. 7. Johnstone, H. F., Ind. Eng. Chem., 39, 3896 (1935). 8. Weast, R. C., "Handbook of Chemistry and Physics", 54th ed., CRC Press, pp. D-70, E-l (1973). 9. Bates, R. G. and G. D. Pinching, J . Am. Chem. Soc.,71, 1274 (1949). 2

RECEIVED

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

13 Principles of Coal Conversion JOSEPH F. McMAHON Foster Wheeler Energy Corporation, Livingston, NJ 07039

Direct use of coal a primar fuel i ofte th t effi cient and economic metho source. In many cases, however, certain undesirable properties of coal make direct utilization difficult. Coal is a solid and requires more effort to handle, measure and control than gases or liquids. Coal is usually contaminated with ash and other unde­ sirable components and has widely variable chemical and physical properties. As a result, there is often a need to convert coal into more convenient and cleaner forms of energy and products. Before considering the basic principles of coal conversion, some important characteristics of fossil fuels will be reviewed. Fossil Fuel Characteristics Carbon and hydrogen are the two elements in fossil fuels of primary importance with respect to energy and chemical products. The hydrogen to carbon ratios (H/C) of light hydrocarbon gases, petroleum liquids and coal are compared in Figure 1. Methane, the principal component of natural gas, has the highest H/C ratio of the hydrocarbon series. Petroleum fractions have H/C ratios ranging from about 2.3 for naphtha through 1.5 for distillate oils. Coal has the lowest H/C ratio, ranging from about 0.8 for bituminous coal to about 0.4 or lower for anthracite coal and cokes. The chemical energy content o f f o s s i l f u e l s g e n e r a l l y p a r a l l e l s the H/C r a t i o as shown i n Table 1. Methane has the h i g h e s t heating value o f the hydrocarbon s e r i e s , corresponding t o i t s high H/C r a t i o w h i l e c o a l has t h e lowest h e a t i n g v a l u e . The normal p h y s i c a l s t a t e o f f o s s i l f u e l s a l s o p a r a l l e l s the H/C ratio. Methane i s a gas a t ambient temperature and pressure conditions. Petroleum f r a c t i o n s are mobile l i q u i d s except f o r the h e a v i e s t f r a c t i o n which can be s o l i d a t ambient temperature. Coal i s a s o l i d m a t e r i a l .

0-8412-0569-8/80/47-133-295$05.00/0 © 1980 American Chemical Society In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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APPLICATIONS

Table 1 Heating Values Of Selected F o s s i l F u e l s Fuel

kJ/kg

Methane

53,800

Naphtha

46,500-48,800

Crude O i l

44,200-46,500

Resid

39,500-41,900

Coal*

27,900-32,600

*maf Methane ( n a t u r a l gas) and petroleum are c l e a r l y more convenient to handle and use than c o a l . This s i t u a t i o n l e d to widespread i n d u s t r i a l use o f these f u e l s f o r e l e c t r i c power production, i n d u s t r i a l and r e s i d e n t i a l f u e l requirements and chemicals production. Recently, however, i t has become apparent that more use must be made o f c o a l t o conserve s u p p l i e s o f n a t u r a l gas and petroleum despite the d i f f i c u l t i e s i n handling and use. There are large reserves o f c o a l i n many p a r t s o f the world, many near centers o f p o p u l a t i o n and i n d u s t r i a l a c t i v i t y . Basic Methods o f Coal Conversion Conversion o f c o a l to more d e s i r a b l e forms o f energy such as: p i p e l i n e gas s y n t h e s i s gas f u e l gas l i q u i d hydrocarbons chemicals g e n e r a l l y r e q u i r e s c o n s i d e r a b l e t e c h n i c a l e f f o r t . There are many v a r i a t i o n s i n t e c h n i c a l processes that have been developed f o r c o n v e r t i n g c o a l to secondary f u e l s . These processes, however, a l l have the common o b j e c t i v e o f e i t h e r removing carbon from or adding hydrogen to c o a l to improve i t s o r i g i n a l H/C r a t i o . The choice o f method and the extent o f improvement i n H/C r a t i o depends on the type o f product required and c o n s i d e r a t i o n s o f c o s t . Removal o f carbon can be accomplished by pyrolysis gasification

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Principles of Coal Conversion

while processes f o r hydrogen a d d i t i o n

include

liquefaction hydrogasification Carbon Removal Processes Pyrolysis. Conversion o f c o a l by p y r o l y s i s i n v o l v e s heating c o a l t o a temperature o f 500 t o 700°C. Gases and l i q u i d s a r e evolved from the c o a l a t these temperatures, l e a v i n g char which has a lower H/C r a t i o than the o r i g i n a l c o a l : coal

heat

gas

+

liquid

+

char

P y r o l y s i s processes d i f f e r p r i m a r i l y i n the means used to supply the required heat to th by burning a p o r t i o n o In some cases, a c i r c u l a t i n g stream o f char i s used t o c a r r y the heat to the f r e s h c o a l . A l t e r n a t e l y , an i n e r t s o l i d i s used as heat c a r r i e r although, i n t h i s case, means must be provided t o separate heat c a r r i e r from product char. G a s i f i c a t i o n . The extent o f carbon removal from c o a l by pyr o l y s i s i s r e l a t i v e l y l i m i t e d . As a r e s u l t , the y i e l d s of secondary f u e l s having increased H/C r a t i o are not l a r g e . E s s e n t i a l l y complete c o n t r o l of the amount of carbon removed can be achieved, however, by complete g a s i f i c a t i o n of c o a l with an oxygen-containing gas and steam: coal

+ 0

o

+

Major components o f the gaseous product are hydrogen, carbon monoxide and v a r i a b l e amounts of methane and l i g h t hydrocarbons, as w e l l as carbon d i o x i d e . Carbon i s removed from the system by separating carbon dioxide from the gas by w e l l known gas scrubbing processes. Some a d d i t i o n a l hydrogen over that contained i n the o r i g i n a l c o a l i s introduced by r e a c t i o n o f steam with the c o a l . The r e s u l t i s a hydrogen-carbon monoxide gas mixture having an e f f e c t i v e H/C r a t i o o f two or higher. This gas mixture, o f t e n r e f e r r e d to as s n y t h e s i s gas, can be f u r t h e r processed t o p i p e l i n e gas, l i q u i d hydrocarbons, or chemicals such as methanol and ammonia. The common feature of c o a l g a s i f i c a t i o n processes i s that c o a l i s contacted i n a g a s i f i e r with an oxygen-containing gas and steam a t a temperature o f a t l e a s t 700 C. The main types o f g a s i f i e r s are: moving bed f l u i d i z e d bed entrained flow

(Figure 2) (Figure 3) (Figure 4)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Figure 1.

H/C

ratios for various fossil fuels

M o v i n g B e d

C o a l

G a s

O

2

—

1

S T M

A s h

Figure 2.

Schematic of moving-bed coal gasifier with typical reaction temperature profiles

F l u i d B e d

ι—-

À * C o a l Ο

2

S T M

H -

Gl ai as s

2ζ 0 0 0

T ° C

1 0 0 0

r

G a s

v

.

.

.

Κ

C o a l

τ

A s h

Figure 3.

Schematic offiuidized-bedcoal gasifier with typical reactor temperature profiles

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

13.

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Principles of Coal Conversion

299

In the moving bed g a s i f i e r , lump s i z e c o a l flows downward through the g a s i f i e r , countercurrent t o ascending hot gases. Coal flows s u c c e s s i v e l y through d r y i n g , d e v o l a t i l i z a t i o n , g a s i f i c a t i o n and combustion zones, each zone o p e r a t i n g a t i n c r e a s i n g l y higher temperatures up t o and beyond the m e l t i n g p o i n t o f the a s h . Ash i s withdrawn from the bottom o f the g a s i f i e r . Oxygen or a i r , together w i t h steam, are i n t r o d u c e d i n t o the g a s i f i c a t i o n zone and flow upward through the g a s i f i e r . In the f l u i d i z e d bed g a s i f i e r , crushed c o a l i s introduced i n t o a f l u i d i z e d bed o f char together w i t h oxygen or a i r and steam. Coal undergoes d r y i n g , d e v o l a t i l i z a t i o n , g a s i f i c a t i o n and combust i o n a t e s s e n t i a l l y constant temperature o f about 1000 C because o f the r a p i d mixing c h a r a c t e r i s t i c s o f f l u i d i z e d beds. In the entrained flow g a s i f i e r , p u l v e r i z e d c o a l flows cocurr e n t l y w i t h oxygen and steam through a r e a c t i o n zone a t temperat u r e s up t o 1800°C. Th i n the f l o w i n g gases. Coa t i o n and combustion occur very r a p i d l y i n the high temperature r e a c t i o n zone. E n t r a i n e d flow g a s i f i e r s may be s i n g l e stage o r two stage, the l a t t e r i n v o l v i n g i n t r o d u c t i o n o f c o a l i n t o a f i r s t stage where i t i s r a p i d l y d e v o l a t i l i z e d by hot gases from a second stage. Char i s recovered from the f i r s t stage and g a s i f i e d w i t h steam and oxygen or a i r i n the second stage. The o v e r a l l process o f c o a l g a s i f i c a t i o n i s endothermic and heat must be s u p p l i e d t o the system. Up t o H0% o f the h e a t i n g value o f the c o a l may be used f o r t h i s purpose, depending on the s p e c i f i c g a s i f i c a t i o n process and c o a l used. Countercurrent processes u s u a l l y produce the highest r a t i o o f chemical t o s e n s i ble heat i n the product gas because o f r e l a t i v e l y low gas o u t l e t temperature. Cocurrent s i n g l e stage entrained flow processes produce t h e lowest r a t i o o f chemical t o s e n s i b l e heat i n t h e product gas; f l u i d i z e d bed processes are intermediate i n t h i s r e s p e c t . Heat i s u s u a l l y s u p p l i e d by p a r t i a l combustion o f char i n the g a s i f i e r w i t h oxygen or a i r . The p r o p e r t i e s o f c o a l ash, p a r t i c u l a r l y s o f t e n i n g temperat u r e , have an important e f f e c t on g a s i f i c a t i o n processes. Ash can be discharged i n "dry" form, i n which case the maximum temperature i n the g a s i f i e r cannot exceed the ash s o f t e n i n g p o i n t . I n moving bed processes, the maximum temperature occurs i n the comb u s t i o n zone and steam i s added f o r temperature c o n t r o l . Higher temperatures can be allowed i f the ash i s removed as s i n t e r e d agglomerates or as a l i q u i d . I n these cases, increased gas production and a g r e a t e r extent o f g a s i f i c a t i o n can be achieved compared to dry ash o p e r a t i o n . Hydrogen A d d i t i o n Processes Liquefaction.

(Figure 5) Coal l i q u e f a c t i o n i n v o l v e s a d d i t i o n

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Entrained Flow

O STM 2

Gas

Ash Figure 4.

Schematic of entrained flow coal gasifier with typical reactor temperature profiles

Coal Liquefaction

Coal

H,

Liquefaction Separation Solvent Recovery

Solids Solvent

Solvent Hydrogénation

Coal L i q u i d Upgrading Products Figure 5.

Generalized flowchart for coal liquefaction processes

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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of hydrogen to c o a l t o produce secondary f u e l s o f increased H/C r a t i o . I t has been known f o r many years that heating a mixture o f c o a l and hydrogen donor solvent t o temperatures o f 400 t o 500 C r e s u l t s i n the production of l i q u i d s of increased H/C r a t i o compared to the o r i g i n a l c o a l . Hydrogen donor solvents are compounds such as t e t r a l i n or mixtures of s i m i l a r compounds c o n t a i n i n g l a b i l e hydrogen atoms. At elevated temperatures, these hydrogen atoms o f the solvent react w i t h c o a l , breaking down the three dimensional c o a l s t r u c t u r e i n t o fragments which d i s s o l v e i n the s o l v e n t . The molecular weight o f these fragments decreases as the amount of hydrogen reacted i n c r e a s e s . Contaminants such as s u l f u r , n i t r o g e n and oxygen are e l i m i n a t e d as hydrogen s u l f i d e , ammonia and water. The p r i n c i p l e o f donor hydrogen r e a c t i o n with c o a l has been a p p l i e d i n various ways i n processes f o r c o a l l i q u e f a c t i o n . I n one a p p l i c a t i o n , hydroge c o a l i t s e l f . The s o l v e n t c o a l l i q u i d product, i s hydrogenated and r e c y c l e d t o the c o a l liquefaction reaction. In a v a r i a t i o n of t h i s technique, molecular hydrogen i s added to the l i q u e f a c t i o n r e a c t o r together w i t h the s o l v e n t . Hydrogen uptake i s u s u a l l y l i m i t e d to about two weight percent of the c o a l and the l i q u e f i e d c o a l product has a melting point of about 150 t o 200°C. I n a f u r t h e r v a r i a t i o n , a p o r t i o n o f the high b o i l i n g l i q u i d product i s r e c y c l e d to the r e a c t o r . The ash contained i n t h i s stream exerts a c a t a l y t i c e f f e c t on the hydrogen donor reaction. Hydrogen uptake i s increased and a f u l l b o i l i n g range l i q u i d product i s produced c o n t a i n i n g naphtha, gas o i l and heavy fuel o i l fractions. C a t a l y t i c c o a l l i q u e f a c t i o n processes do not s p e c i f i c a l l y use hydrogen donor solvents although c o a l i s introduced i n t o t h e l i q u e f a c t i o n r e a c t o r as a s l u r r y i n a r e c y c l e l i q u i d stream. C a t a l y s t i s used as a powder o r as granules such as p e l l e t s o r extrudates. I f powdered c a t a l y s t i s used, i t i s mixed with the c o a l / l i q u i d stream e n t e r i n g the r e a c t o r . P e l l e t e d c a t a l y s t can be used i n f i x e d bed r e a c t o r s i f precautions are taken to avoid plugging with s o l i d s or i n f l u i d i z e d bed r e a c t o r s . In the l a t t e r case, the r e a c t i n g system i s a c t u a l l y a three phase f l u i d i z e d bed, t h a t i s , c a t a l y s t p a r t i c l e s and c o a l s o l i d s , as w e l l as l i q u i d , are f l u i d i z e d by gas. Hydrogénation of c o a l i s a h i g h l y exothermic r e a c t i o n c o r r e s ponding to a heat e v o l u t i o n of about 15 k i l o j o u l e s per cubic metre of hydrogen reacted. Means must be provided to remove t h i s heat from the r e a c t i o n zone so t h a t the r e a c t i o n temperature can be maintained i n the optimum range. This i s u s u a l l y accomplished by i n j e c t i n g c o a l l i q u i d as quench i n t o various s e c t i o n s o f t h e reactor.

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H y d r o g a s i f i c a t i o n . H y d r o g a s i f i c a t i o n o f c o a l i n v o l v e s react i o n o f hydrogen w i t h c o a l c a r r i e d out a t elevated temperatures under high p a r t i a l pressure o f hydrogen. The o b j e c t i v e i s t o add s u f f i c i e n t hydrogen t o c o a l t o produce methane as the major product. I t has been found that many types o f c o a l can be h y d r o g a s i f i e d i f the c o a l i s heated r a p i d l y t o r e a c t i o n temperatures. Even under f a v o r a b l e c o n d i t i o n s , however, conversion t o methane i s not complete and aromatics such as benzene are made as by-products. H y d r o g a s i f i c a t i o n o f c o a l i s a l s o a very exothermic r e a c t i o n . One means o f absorbing the heat o f r e a c t i o n i s t o use a f l u i d i z e d bed r e a c t o r and i n j e c t hydrogen and c o a l r e a c t a n t s a t s u f f i c i e n t l y low temperature so t h a t the s e n s i b l e heat r e q u i r e d t o heat c o a l and hydrogen to r e a c t i o n temperature i s e q u i v a l e n t to the heat o f reaction. E f f i c i e n c y Consideration Heat recovery e f f i c i e n c y i s a c o n s i d e r a t i o n o f major importance i n the conversion o f c o a l t o secondary f u e l s . T h i s parame t e r i s defined as the percent o f the heating value o f the c o a l used which i s recovered as heating value i n the d e s i r e d secondary f u e l . Heat recovery e f f i c i e n c y which can be a t t a i n e d i n a c o a l conversion process depends f i r s t l y on the t h e o r e t i c a l chemical and thermodynamic requirements o f the process, and secondly on the p r a c t i c a l r e a l i z a t i o n o f the process. The f i r s t f a c t o r determines the t h e o r e t i c a l maximum heat recovery e f f i c i e n c y that can be obtained under i d e a l circumstances. The second f a c t o r determines the extent to which the p r a c t i c a l process approaches the t h e o r e t i c a l i d e a l . S e v e r a l aspects o f the concept o f t h e o r e t i c a l heat recovery e f f i c i e n c y can be understood by c o n s i d e r i n g an i d e a l i z e d convers i o n o f c o a l to a secondary f u e l having a high H/C r a t i o , such as methane. I n the f o l l o w i n g d i s c u s s i o n , i t i s assumed t h a t the conversion r e a c t i o n s proceed to completion a t a temperature o f 15 C and a pressure o f 1 atmosphere although, o f course, t h i s cannot be r e a l i z e d i n p r a c t i c e . Coal i s assumed to have the i d e a l i z e d chemical formula o f C Hg. S e v e r a l important chemical r e a c t i o n s f o r the conversion o f c o a l t o methane are shown i n Table 2. Steam conversion i n v o l v e s the r e a c t i o n o f c o a l w i t h steam to produce hydrogen and carbon monoxide. Hydrogen conversion i s a r e a c t i o n i n which c o a l and hydrogen r e a c t to form methane. Oxygen conversion produces hydrogen and carbon monoxide by p a r t i a l o x i d a t i o n o f c o a l . Methana t i o n i n v o l v e s a r e a c t i o n i n which methane and water are produced from carbon monoxide and hydrogen. The water gas s h i f t r e a c t i o n between carbon monoxide and steam produces carbon d i o x i d e and hydrogen. S e v e r a l o f these r e a c t i o n s can occur simultaneously or can be used c o n s e c u t i v e l y t o produce methane from c o a l . Methanation and 1 Q

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303

Principles of Coal Conversion

water gas s h i f t r e a c t i o n s occur simultaneously i n v a r y i n g degrees w i t h steam and oxygen conversion r e a c t i o n s . Hydrogen r e q u i r e d f o r hydrogen conversion can be produced by steam or oxygen g a s i fication.

Table 2 Coal Conversion Chemical

C

Steam Conversion Hg + 10 H 0 > 10 CO + 14 H

1Q

C

Reaction

2

1Q

2

Hg Oxygen Conversion

C

H

+

10 8

5

°2

CO + 3 H

2

C

0 +

4 H

2

Methanation > CH^ + H 0

Water Gas S h i f t CO + H 0 > C0 2

2

2

+H

2

The p o t e n t i a l of these r e a c t i o n s f o r methane production can be compared i n terms of t h e o r e t i c a l y i e l d s and heat recovery e f f i c i e n c i e s . T h e o r e t i c a l methane y i e l d i s defined by the chemical equations. T h e o r e t i c a l heat recovery e f f i c i e n c y i s defined as the percent o f the higher h e a t i n g value o f the c o a l which i s recovered i n the form of methane product. These i d e a l i z e d parame t e r s provide a measure of the u l t i m a t e c a p a b i l i t y of conversion systems and are u s e f u l f o r e v a l u a t i n g a c t u a l conversion processes. Table 3 shows the t h e o r e t i c a l methane y i e l d s and heat recovery efficiencies for steam conversion-methanation hydrogen conversion oxygen conversion-methanation

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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304

Table 3 T h e o r e t i c a l Methane Y i e l d and Heat Recovery

Feedstock

C

i n

H

ft

(coal)

Heat Recovery Efficiency %

Steam Conversion - Methanation 0.067 1.11

100

Hydrogen Conversion 0.067

92

Hydrogen Conversion - H

a

Yield nT/kg

H:C Wt. Ratio

Efficiency

0.067

1.84

Supply by Oxygen Conversion

0.86

Oxygen Conversion - Methanation 0.067 0.65

81 61

Steam conversion/methanation has a t h e o r e t i c a l heat recovery e f f i c i e n c y o f 100?. Hydrogen conversion has a t h e o r e t i c a l e f f i ciency o f about 90%; i f the production o f hydrogen by steam conv e r s i o n i s taken i n t o account, however, the t h e o r e t i c a l e f f i c i e n c y drops to 81%· Oxygen conversion/methanation has a theor e t i c a l e f f i c i e n c y of only 61% which i s the lowest of the convers i o n systems. P r a c t i c a l conversion processes can only approach the t h e o r e t i c a l e f f i c i e n c i e s shown i n Table 3· The c o a l conversion r e a c t i o n s do not proceed to completion at ambient temperatures w i t h i n pract i c a l time l i m i t a t i o n s . As a r e s u l t , a p o r t i o n o f the c o a l feedstock must be burned to supply heat so that the r e a c t i o n s can be c a r r i e d out a t elevated temperatures and pressure where the r a t e s o f conversion are r a p i d . In p r a c t i c a l systems, t h i s a d d i t i o n a l heat can only be p a r t i a l l y recovered. Consequently, pract i c a l conversion processes have a c t u a l heat recovery e f f i c i e n c i e s of about 60-70% f o r production o f high H/C r a t i o products. Production o f secondary f u e l s having somewhat lower H/C r a t i o , i . e . about 2.0, permits attainment o f heat recovery e f f i c i e n c i e s o f 70 to 80%. Although conversion processes r e s u l t i n the l o s s of a s i g n i f i cant part o f the chemical heat energy o f the o r i g i n a l c o a l , secondary f u e l s are produced which are clean and are more convenient to handle. The favorable c h a r a c t e r i s t i c s o f these clean secondary f u e l s j u s t i f y i n many cases the cost o f plant and energy required f o r conversion. RECEIVED February 14, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

14 Thermodynamic Data for Synthesis Gas and Related Systems Prediction, Development, Evaluation, and Correlation GRANT M . WILSON Wilco Research Company, 488 South 500 West, Provo, UT 84601

The problems associated with new synthesis gas processes are far greater than problem or refineries because o , , sludge, , sols present in the process streams. These problems need to be resolved rapidly if we are to meet our energy needs of the next decade. For this reason we cannot wait for data on one plant to be used in designing another one as has been done in refinery development. Therefore we must use available basic data, pilot plant data, and our capabilities involving mathematical tools and computers to develop reliable processes without having to learn from the failures of prior processes. When basic mathematical models predict pilot plant results, then one has considerable faith in using the model to predict full-scale plant operation. The advantages of the mathematical models are that the effects of varying stream rates, temperatures, and pressures can be predicted with considerable reliability by simply establishing that existing pilot plant data agree with the models. This means that when dif­ ferences between pilot plant data and the models exist that they have to be reconciled. In general, the cost of developing the necessary basic data and models is considerably less than the cost of operation of pilot plants or the cost associated with ineffi­ ciency of operation of full-scale plants. Unfortunately the de­ velopment of basic data and mathematical models takes time, so full scale plants have to be built in situations where the neces­ sary basic data are not adequate. When this occurs, enough inef­ ficient over-design has to be built into the process to compensate for uncertainties in the basic data. In these situations, the process of development of new basic data should continue because the results will be useful when operating problems occur in the new plant or when designing additional plants. Thus our immediate and long range needs are for basic data which can be used in mathematical model developments. If this information is developed rapidly, the overall cost to our economy will be considerably less than i f the data are developed slowly. Subsequent sections of this paper discuss the magnitude of work that needs to be done, 0-8412-0569-8/80/ 47-133-305$05.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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THERMODYNAMICS

OF

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

how t h i s i s t o be a c c o m p l i s h e d , and i d e n t i f i e s some o f t h e r e q u i r i n g development.

areas

The M a g n i t u d e o f Work t o be Done E x i s t i n g p r o c e s s e s f o r p r o d u c i n g o i l and gas p r o d u c t s have r e q u i r e d t h e d e v e l o p m e n t o f phase b e h a v i o r and o t h e r thermodynamic d a t a on l i g h t h y d r o c a r b o n s , heavy h y d r o c a r b o n s , and t h e a c i d g a s e s C O 2 and HoS. For t h i s r e a s o n a l o t o f b a s i c d a t a a r e a v a i l a b l e on t h e s e s y s t e m s ; but t h e r e i s s t i l l a l o t we d o n ' t know s u c h as how to c h a r a c t e r i z e the behavior o f hydrocarbon f r a c t i o n s c o n t a i n i n g numerous p a r a f f i n , n a p h t h e n e , and a r o m a t i c c o m p o n e n t s . A d d i t i o n a l b a s i c d a t a on t h e s e s y s t e m s w o u l d h e l p t o i m p r o v e t h e e f f i c i e n c y o f these e x i s t i n g processes. The p i c t u r e becomes c o n s i d e r a b l y more c o m p l i c a t e d when t h e a d d i t i o n a l components o v a r i o u s t y p e s o f component where each t y p e o f component i s i n d i c a t e d by a c i r c l e . The c o m p o n e n t s o f e x i s t i n g o i l and gas p r o c e s s e s , shown on t h e r i g h t - h a n d p o r t i o n o f the f i g u r e , p r i m a r i l y i n v o l v e the l i g h t hydrocarbons C-j, C , C 3 , C , and C ; t h e o i l f r a c t i o n s : C + ; and t h e a c i d gas components: composed p r i m a r i l y o f H S and C O 2 . The d e v e l o p m e n t o f b a s i c m o d e l i n g d a t a i n v o l v e s t h e d e v e l o p ment o f i n t e r a c t i o n d a t a between components i n each t y p e and i n t e r a c t i o n d a t a between t y p e s . In t h e c a s e o f o i l and gas compon e n t s t h e s e i n v o l v e i n t e r a c t i o n s between t h r e e d i f f e r e n t t y p e s o f compounds o r t h r e e i n t e r a c t i o n s between t y p e s o f g r o u p s . The work r e q u i r e d t o d e v e l o p d a t a on t h e s e s y s t e m s has been v e r y l a r g e and has i n v o l v e d a t i m e span o f many y e a r s . But t h e work has been n e c e s s a r y , and much c o u l d have been s a v e d i n p l a n t c o s t s and o p e r a t i n g e f f i c i e n c y i f t h e d a t a had been d e v e l o p e d f a s t e r . T h r e e a d d i t i o n a l c i r c l e s have been added a t t h e l e f t o f F i g u r e 1 t o r e p r e s e n t t h e a d d i t i o n a l components i n v o l v e d i n t h e p r o d u c t i o n of synthesis gas. These i n v o l v e t h e l i g h t g a s e s : H and CO, w i t h N , 0 , and A r as m i n o r c o m p o n e n t s ; w a t e r and ammonia w i t h amines a s m i n o r c o m p o n e n t s ; and c r e s o l s and o t h e r o r g a n i c components. These t h r e e a d d i t i o n a l t y p e s o f components p r o d u c e a t o t a l o f 15 c o m b i n a t i o n s o f i n t e r a c t i o n s between t h e v a r i o u s t y p e s o f components o r 12 a d d i t i o n a l i n t e r a c t i o n s . Thus t h e a d d i t i o n a l work t o be done c o u l d be as much as f o u r t o f i v e t i m e s t h e amount a l r e a d y done on o i l and gas c o m p o n e n t s . 2

4

5

g

2

2

2

2

Some examples o f new p r o b l e m s e n c o u n t e r e d i n s y n t h e s i s production are the f o l l o w i n g . 1.

gas

Ammonia. Ammonia i n t e r f e r e s w i t h e x i s t i n g a c i d gas r e m o v a l p r o c e s s e s b e c a u s e i t can pass on t h r o u g h t h e s c r u b b e r s and t h e n s o l i d i f y on c y r o g e n i c s u r f a c e s o r i t can go w i t h t h e a c i d g a s e s and p o i s o n t h e s u l f u r conversion c a t a l y s t s . I f ammonia i s a b s o r b e d i n t o an aqueous s t r e a m , t h e n t h i s aqueous s t r e a m must be

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

14.

WILSON

2.

3.

Synthesis Gas and Related Systems

307

f u r t h e r p r o c e s s e d t o remove t h e ammonia i n o r d e r t o a v o i d i t s r e l e a s e a s an aqueous w a s t e - s t r e a m p o l l u t a n t . C r e s o l - T y p e Components. L a r g e amounts o f c r e s o l - t y p e components a r e p r o d u c e d i n s y n t h e s i s gas p r o c e s s e s . These components c o n c e n t r a t e i n aqueous s t r e a m s a n d r e p r e s e n t a s e r i o u s p o l l u t i o n t h r e a t because o f t h e i r toxicity. F o r t h i s r e a s o n t h e y must be r e c o v e r e d f r o m any aqueous w a s t e s t r e a m b e f o r e l e a v i n g a p l a n t . W a t e r . Water i s a m a j o r component i n s y n t h e s i s g a s p r o c e s s e s a s i t i s t h e main s o u r c e o f h y d r o g e n . Thus t h e phase b e h a v i o r o f w a t e r w i t h π ^ , Ο Ο , l i g h t h y d r o ­ c a r b o n s , heavy h y d r o c a r b o n s , e t c . needs t o be known i n o r d e r t o design processes which w i l l handle streams c o n t a i n i n g s i g n i f i c a n t amounts o f w a t e r . S i n c e water i s an e x t r e m e l y p o l a r component t h i s p r e s e n t s new problems i n p r e d i c t i n of mixtures. Existin a d e q u a t e so new methods t o h a n d l e t h e s e m i x t u r e s must be d e v e l o p e d .

The s o l u t i o n o f t h e s e p r o b l e m s w i l l i n v o l v e a d d i t i o n a l p r o ­ c e s s i n g w h i c h w o u l d n o t be e n c o u n t e r e d i n e x i s t i n g o i l and g a s p r o c e s s e s ; t h u s d a t a f o r a l l t h r e e c l a s s e s o f components m e n ­ t i o n e d above a r e e s s e n t i a l t o t h e s u c c e s s f u l d e v e l o p m e n t o f s y n ­ t h e s i s g a s and o t h e r c o a l c o n v e r s i o n p r o c e s s e s . A d d i t i o n a l p r o b ­ lems w h i c h a r e e q u a l l y a s s e r i o u s may a p p e a r a s t h e s e p r o c e s s e s a r e f u r t h e r d e v e l o p e d , t h u s c o n s i d e r a b l e t h o u g h t must be g i v e n t o t h e o r d e r l y development o f data r e l a t i n g t o these new p r o c e s s e s . Methods o f Data

Development

The o r d e r l y d e v e l o p m e n t o f b a s i c d a t a i n v o l v e s a r e s e a r c h c y c l e shown s c h e m a t i c a l l y i n F i g u r e 2 . T h i s c y c l e i n v o l v e s f o u r stages as f o l l o w s . 1. 2. 3. 4.

P l a n new m e a s u r e m e n t s ; p r e d i c t o r guess o r d e r o f magnitude o f experimental r e s u l t . Make measurements Evaluate data C o r r e l a t e data

T h i s c y c l e w i l l be most s u c c e s s f u l when each o f t h e s t a g e s a r e carefully carried out. F a i l u r e i n any one s t a g e c a n n e g a t e t h e r e s u l t s o f s u b s e q u e n t s t a g e s , t h u s c a u s i n g e r r o r s and i n e f f i ­ ciency. The f i n a l p r o d u c t , u s e f u l f o r p r o c e s s d e s i g n , a r e t h e c o r r e l a t i o n s p r o d u c e d a s a r e u l t o f t h e r e s e a r c h c y c l e . The r a p i d development o f t h e s e c o r r e l a t i o n s thus r e q u i r e s t h a t a t t e n ­ t i o n be g i v e n t o each o f t h e s t a g e s o f t h e r e s e a r c h c y c l e . In some s i t u a t i o n s i t has a p p e a r e d t h a t much work has been s p e n t on o n l y one o r two s t a g e s w i t h o u t much a t t e n t i o n t o t h e o t h e r s t a g e s .

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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New Components

Natural Gas Components 3 Combinations 21 Total Combinations

Figure 1.

Figure 2.

Synthesis gas components

Re-search cycle

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

14.

WILSON

Synthesis Gas and Related Systems

309

F o r e x a m p l e , much e f f o r t can be s p e n t c o r r e l a t i n g e x i s t i n g d a t a when i n r e a l i t y more b a s i c d a t a measurements a r e n e e d e d . This l a c k o f e m p h a s i s on c e r t a i n s t a g e s p r o d u c e s i n e f f i c i e n c y i n t h e r e s e a r c h p r o c e s s w h i c h impedes t h e d e v e l o p m e n t o f i m p r o v e d c o r r e l a t i o n s ; t h u s a t t e n t i o n must be g i v e n t o each s t a g e . The f i r s t s t a g e o f t h e r e s e a r c h c y c l e i s t h e p l a n n i n g a n d predicting stage. P l a n n e d measurements must be c o o r d i n a t e d w i t h i n d u s t r y needs s o t h a t c o r r e l a t i o n s c a n be p r o d u c e d i n a r e a s o f need. A f t e r t h e measurements a r e p l a n n e d , and t h e b e t t e r one c a n p r e d i c t r e s u l t s ? t h e more s u c c e s s f u l t h e measurements w i l l b e . T h i s o c c u r s because p r e d i c t e d data h e l p t o i d e n t i f y p o s s i b l e a r e a s o f measurement p r o b l e m s . For example, a d i f f e r e n t a n a l y t i c a l p r o c e d u r e m i g h t be used t o d e t e r m i n e t h e c o n c e n t r a t i o n o f a t r a c e component t h a n f o r a m a j o r c o m p o n e n t . Predicated d a t a h e l p t o i d e n t i f y when t h i s w i l l o c c u r . G e n e r a l l y s p e a k i n g , t h e more t h a t i s known--the mor mation useful i n p r e d i c t i n p r o p e r t y c o m p i l a t i o n s , data b o o k s , e q u a t i o n s o f s t a t e , group c o n t r i b u t i o n methods, c o r r e l a t i o n s , e t c . I n many c a s e s , i n t e r a c t i o n s between t h e components have t o be " g u e s s e d ' i n o r d e r t o make a p r e d i c t i o n ; b u t t h i s i s b e t t e r t h a n no e s t i m a t e a t a l l . The s e c o n d s t a g e o f t h e r e s e a r c h c y c l e i s t h e measurement stage. T h i s i s p r o b a b l y t h e most d i f f i c u l t s t a g e b e c a u s e a s u c c e s s f u l e x p e r i m e n t i n v o l v e s t h e s i m u l t a n e o u s o p e r a t i o n o f many d i f f e r e n t t y p e s o f measurement and c o n t r o l e q u i p m e n t . The f a i l u r e o f j u s t one p a r t n e g a t e s t h e r e s u l t s o f t h e e n t i r e e x p e r i m e n t . The p r o b a b i l i t y o f t h i s h a p p e n i n g i s q u i t e h i g h b e c a u s e a m a l f u n c t i o n i n t h e a p p a r a t u s c a n r e - o c c u r o r new m a l f u n c t i o n s c a n appear. I n some c a s e s , t h e s e m a l f u n c t i o n s c a n go u n d e t e c t e d u n t i l an e x a m i n a t i o n o f t h e r e s u l t s shows t h a t t h e y a r e e n t i r e l y inconsistent with predicted data. The t h i r d s t a g e o f t h e r e s e a r c h c y c l e i s t h e e v a l u a t i o n stage. I t i s i m p o r t a n t t h a t t h i s s t a g e be done by t h e same g r o u p d o i n g t h e measurements so t h a t a n y d i f f e r e n c e s between m e a s u r e d and p r e d i c t e d d a t a c a n be r e c o n c i l e d . Too o f t e n d a t a a r e measured and r e p o r t e d w i t h o u t b e i n g e v a l u a t e d . When t h i s o c c u r s , t h e e f f o r t o f an e n t i r e r e s e a r c h c y c l e can be l o s t . B u t when i m m e d i a t e e v a l u a t i o n i s made, i t i s e a s y t o go back and m o d i f y t h e e x p e r i m e n t i n o r d e r t o c o n f i r m o r remedy t h e d a t a ; t h u s s i g n i f i cantly improving the e f f i c i e n c y o f the research c y c l e . The f o u r t h and most u s e f u l s t a g e o f t h e r e s e a r c h c y c l e i s t h e c o r r e l a t i o n s t a g e b e c a u s e t h i s i s where r e s u l t s a p p e a r t h a t can be used i n p r o c e s s d e s i g n c a l c u l a t i o n s . B e c a u s e o f t h e i r i m m e d i a t e u t i l i t y , t h e r e i s a t e n d e n c y on t h e p a r t o f i n d i v i d u a l c o m p a n i e s t o o v e r - e m p h a s i z e t h e c o r r e l a t i o n s t a g e w i t h o u t enough e m p h a s i s on t h e o t h e r s t a g e s o f t h e r e s e a r c h c y c l e . Thus d a t a t e n d t o be o v e r c o r r e l a t e d w i t h t h e same b a s i c p r o b l e m s i n a l l o f t h e c o r r e l a t i o n s due t o l a c k o f i n p u t d a t a . Nevertheless, correl a t i o n s a r e a n e c e s s a r y and i m p o r t a n t s t a g e o f t h e r e s e a r c h cycle. 1

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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When p o s s i b l e , new d a t a s h o u l d be i n t e g r a t e d i n t o e x i s t i n g c o r r e l a t i o n s ; t h u s m a k i n g i t p o s s i b l e t o i m m e d i a t e l y use t h e r e s u l t s in process c a l c u l a t i o n s . New c o r r e l a t i o n methods p r e s e n t p r o b l e m s even t h o u g h t h e y may be more a c c u r a t e because t h e new c o r r e l a t i o n must be added t o t h e d e s i g n c a l c u l a t i o n p r o c e d u r e b e f o r e i t can be u s e d . This u s u a l l y causes a time l a g which o f t e n p r e v e n t s t h e new c o r r e l a t i o n from b e i n g used f o r l o n g t i m e periods. Thus new methods s h o u l d o n l y be used when o l d methods s i m p l y are not s u i t a b l e . When t h i s o c c u r s , i t i s h e l p f u l t o t r y t o a n t i c i p a t e t h e needs o f i n d u s t r y so t h a t u s e f u l c o r r e l a t i o n methods c a p a b l e o f a w i d e r a n g e o f p r o b l e m s can be a d o p t e d . Mixtures with Polar

Components

R a t h e r t h a n a t t e m p t t o d i s c u s s a l l a r e a s where d a t a a r e needed, o n l y the proble t i e s of mixtures containin here. E x i s t i n g methods based on e q u a t i o n s o f s t a t e a p p e a r t o be a d e q u a t e f o r e n g i n e e r i n g p u r p o s e s when o n l y n o n - p o l a r and s l i g h t l y p o l a r components a r e p r e s e n t . Various v e r s i o n s of the R e d l i c h - K w o n g e q u a t i o n , BWR e q u a t i o n , and v a r i a t i o n s o f t h e s e e q u a t i o n s s u c h as t h e P e n g - R o b i n s o n e q u a t i o n o f s t a t e a r e now i n use. These e q u a t i o n s o f s t a t e have p r o v e d t o be v e r y u s e f u l f o r p r e d i c t i n g phase b e h a v i o r and t h e r m o d y n a m i c d a t a on h y d r o c a r b o n systems. U n f o r t u n a t e l y these equations o f s t a t e appear i n c a p a b l e o f c o r r e l a t i n g the behavior of water-hydrocarbon systems w i t h o u t u s i n g s e p a r a t e i n t e r a c t i o n c o e f f i c i e n t s f o r t h e aqueous and h y d r o carbon phases. The use o f s e p a r a t e i n t e r a c t i o n c o e f f i c i e n t s r e p r e s e n t s an i m m e d i a t e s o l u t i o n t o t h e p r o b l e m f o r c u r r e n t p r o c e s s c a l c u l a t i o n s when o n l y w a t e r i s p r e s e n t , b u t i t does n o t r e p r e s e n t a l o n g - r a n g e s o l u t i o n t o h a n d l e s i t u a t i o n s where s i g n i f i c a n t c o n c e n t r a t i o n s o f w a t e r - s o l u b l e components a r e a l s o p r e s e n t i n c l u d i n g r e g i o n s near the upper c o n s o l u t e temperature o f waterhydrocarbon systems. When t h i s o c c u r s , t h e same i n t e r a c t i o n c o e f f i c i e n t s must a p p l y o v e r t h e e n t i r e c o m p o s i t i o n r a n g e . The b a s i c f e a t u r e s o f e q u a t i o n s o f s t a t e a r e n o t c o m p l i c a t e d when t h e y a r e e x p r e s s e d as PV/RT v e r s u s d e n s i t y . Figure 3 is a sample p l o t f o r m e t h a n o l . These c u r v e s a r e c h a r a c t e r i s t i c o f a l l f l u i d s , and e q u a t i o n s o f s t a t e o n l y d i f f e r i n t h e i r a b i l i t y t o a c c u r a t e l y p r e d i c t these curves. The a c t u a l c u r v e s a r e r e l a t i v e l y s i m p l e and t h e y change o n l y s l i g h t l y f r o m one m a t e r i a l t o a n o t h e r ; f o r t h i s r e a s o n , s i m p l e e q u a t i o n s o f s t a t e s u c h as t h e R e d l i c h Kwong e q u a t i o n have been a b o u t as s u c c e s s f u l as t h e BWR e q u a t i o n . The s i m p l i c i t y o f t h e a c t u a l c u r v e s i s o f t e n h i d d e n b e c a u s e t h e d a t a a r e n o t u s u a l l y p l o t t e d as PV/RT v e r s u s d e n s i t y . More o f t e n t h e d a t a a r e p l o t t e d as PV/RT v e r s u s p r e s s u r e shown i n F i g u r e 4 , o r p r e s s u r e v e r s u s volume shown i n F i g u r e 5. Both o f these p l o t s o b s c u r e t h e r e a l s i m p l i c i t y shown i n F i g u r e 3. The r e a l p r o b l e m w i t h e q u a t i o n s o f s t a t e i s i n t h e a c c u r a t e prediction of mixture behavior. T h i s i s somewhat a n a l o g o u s t o

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

14.

WILSON

Synthesis Gas and Related Systems

311

Density, g/cc Figure

3.

Compressibility

factor of methanol

l.o ^^^^e^i^or

Region

_

" ^ • ^ ^ T r a n s i t i o n from Vapor to Liquid ^ ^ > * ^ a t 202.5 psia (Vapor Pressure)

\

-

\

_

\

/

J /

*~ ο

0

100

200

^ 1 300

Liquid Region

1 400

1 500

! 600

700

Pressure, psia

Figure 4.

Compressibility

factor of methanol

at 302 °F

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Liquid Region Vapor Pressure Equals 202.5 psia

_

ι α

Vapor Regional

r Areas Are Equal

-Region of Negative Pressure

10

15

Volume. ft71b-»ole

Figure 5.

P-V isotherm of methanol at 302°F

Figure 6. Redlich-Kwong correlation of nonpolar-nonpolar benzene-η heptane at 60°C (data of I. Brown and A. H. Ewald, Austral. J. Sci. Res., (A), 4,198 (1951))

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

14.

WILSON

Synthesis Gas and Related Systems

313

the problem o f p r e d i c t i n g a c t i v i t y c o e f f i c i e n t s o f non-ideal mixtures. I f t h i s p r o b l e m were s o l v e d , t h e r e s t w o u l d be r e l a t i v e l y easy. To i l l u s t r a t e t h e p r o b l e m w i t h m i x t u r e s , t h e R e d l i c h - K w o n g e q u a t i o n has been used t o c o r r e l a t e l i t e r a t u r e d a t a on t h r e e types o f mixtures as f o l l o w s . Type o f M i x t u r e s Nonpolar-Nonpolar Polar-Polar Nonpolar-Polar

Components benzene/n-heptane ethanol/water n-hexane/methanol

In each c a s e pure component p a r a m e t e r s were c h o s e n t o f i t t h e p u r e component v a p o r p r e s s u r e and l i q u i d d e n s i t y , and a b i n a r y i n t e r a c t i o n p a r a m e t e r wa a t t h e 5 0 : 5 0 mole p e r c e n the e q u a t i o n o f s t a t e i s adequate f o r r e p r e s e n t i n g these m i x t u r e s , t h e n t h i s s h o u l d be s u f f i c i e n t i n f o r m a t i o n f o r p r e d i c t i n g d a t a a t o t h e r c o m p o s i t i o n s . The r e s u l t s a r e g i v e n i n F i g u r e s 6 t o 8 . F i g u r e 6 shows t h a t d a t a on n o n p o l a r - n o n p o l a r b e n z e n e / n h e p t a n e a r e f a i r l y w e l l r e p r e s e n t e d by t h e R e d l i c h - K w o n g e q u a tion. T h i s i s n ' t s u r p r i s i n g because t h e Redlich-Kwong e q u a t i o n i s w i d e l y used f o r m i x t u r e s o f t h i s t y p e . F i g u r e 7 shows t h a t d a t a on p o l a r - p o l a r e t h a n o l - w a t e r a r e p r e d i c t e d w i t h some d e g r e e of accuracy. T h i s r e s u l t i s a b i t s u r p r i s i n g and s u g g e s t s t h a t t h e e q u a t i o n may be s u i t a b l e f o r c o r r e l a t i n g m i x t u r e d a t a when t h e components o n l y d i f f e r s l i g h t l y i n p o l a r i t y ; r e g a r d l e s s o f w h e t h e r t h e components a r e p o l a r o r n o n p o l a r . F i g u r e 8 shows t h a t d a t a o n n o n p o l a r - p o l a r n-hexane/methanol a r e n o t p r e d i c t e d v e r y w e l l a t a l l . Thus t h e most s e r i o u s p r o b l e m s o c c u r w i t h m i x t u r e s o f n o n p o l a r and p o l a r c o m p o n e n t s . One g e n e r a l i t y c a n be drawn f r o m e x a m i n i n g F i g u r e s 7 and 8 ; namely t h a t t h e a c t i v i t y c o e f f i c i e n t o f t h e p o l a r component a t l o w c o n c e n t r a t i o n s i s h i g h e r t h a n p r e d i c t e d and t h e a c t i v i t y c o e f f i c i e n t o f t h e n o n p o l a r component i s l o w e r t h a n p r e d i c t e d . One can show by e x a m i n ing other mixtures that t h i s trend c o n s i s t e n t l y o c c u r s ; thus t h i s g i v e s a c l u e t h a t a d e q u a t e e q u a t i o n s can be d e v e l o p e d w h i c h w i l l compensate f o r t h e s y s t e m a t i c p r e d i c t i o n e r r o r o f t h e R e d l i c h Kwong e q u a t i o n . T h i s s y s t e m a t i c n a t u r e o f t h e main e r r o r t e n d s t o i n d i c a t e t h a t o n l y m i n o r changes i n t h e R e d l i c h - K w o n g e q u a t i o n m i g h t be n e c e s s a r y t o y i e l d a c c u r a t e p r e d i c t i o n s f o r t h e s e s y s tems. I n a d d i t i o n , i t may be p o s s i b l e t o d e v e l o p o t h e r r e l a t i v e l y simple equations o f s t a t e which w i l l p r e d i c t t h i s behavior. T h i s d i s c u s s i o n shows t h a t t h e r e a r e t e s t s w h i c h can be a p p l i e d i n o r d e r t o determine t h e adequacy o r inadequacy o f e q u a t i o n s o f s t a t e when components o f d i f f e r i n g p o l a r i t y a r e p r e s e n t i n a m i x t u r e . However no a t t e m p t i s made h e r e t o s u g g e s t what changes may be n e c e s s a r y i n o r d e r t o a d e q u a t e l y m o d i f y t h e e q u a t i o n s o f s t a t e o r t o d e v e l o p new e q u a t i o n s o f s t a t e .

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

314

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS 5 4

—ι

\ \ \ \

1

-i

1

ι

Polar-Polar

\\ 3

Py_ P°x

Λ

\

2

1.5

-

Ethanol

>

-

cy

t^gZ-—

\ \ \ Θ \ \

-

1.0 appears to be nearly linear with temperature for most systems. A typical set of SRK based k|j s of the methanewater system are shown in Figure 1. This kind of temperature dependence was observed for a l l binary pairs when using the SRK equation of state. The PFGC-MES equation of state required tem­ perature dependent k i j s for only a few groups (molecules). The PFGC-MES kjj s were also linear in temperature. For ternary and higher order mixtures, we have usually as­ sumed that the interaction parameters for the non-water binary pairs in the water rich phase are identical to the vapor (hydro­ carbon rich liquid phase) interaction parameters. Some work has been done on changing a l l water phase interaction parameters; we concluded that predicted results were not improved enough to warrant the expenditure of time required to develop the addi­ tional parameters. A third interaction parameter for the hydro­ carbon rich liquid could also be determined. Again, our work indicated that l i t t l e improvement resulted from using this third parameter. Additional work is being done on both points. The experimental data for water hydrocarbon systems are relatively limited. Consequently, a generalized correlation was developed to estimate the equation for the temperature dependent kij term for those compounds for which no data are available. This generalized correlation was developed only for the SRK equation of state. The variation in the slopes of the kij 2

T

!

?

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

Figure 1. Effect of temperature on methane

2

k jj

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

17.

MOSHFEGHiAN ET AL.

PFGC-MES

Equation of State

339

equation for the various homologous hydrocarbon series and selected specific properties are considered. The quality of this correlation is unknown--no data are available to evaluate i t . Note that a similar correlation did not have to be developed for the PFGC-MES equation of state. Adequate data were available to develop (or estimate) group parameters for a l l the molecules considered in this work. The predicted water solubilities of the higher molecular weight components appear to be reasonable, but no data are available to check the quality of the predictions. A similar strategy was used to develop the PFGC-MES equation of state parameters for describing the behavior of methanol hydrocarbon acid gas water systems. Multiple phase binary interaction parameters were used as required. Again, these second phase binary interaction parameters were usually not temperature dependent. Model Validation The parameters for both equations of state were developed using the available binary water data. The quality of agreement between predicted and experimental results should be good to excellent for these systems. Results for the methane-water system are shown in Figure 2; these results are typical of the results for the hydrocarbon systems. For pressures up to 350 bars both the SRK and PFGC-MES give excellent predictions of the concentrations of the various phases including the water rich and hydrocarbon rich liquid phase. In fact, the predictions from both equations of state are coincident for a l l temperatures except 38 and 71°C. At pressures above 350 bars, the SRK continues to perform well, while the quality of PFGC-MES predictions are not very good. Similar results were noted for a l l systems except the C0 -water and H S-water systems. At temperatures below about 100°C and pressures greater than 70 bars significant errors in the predicted values were observed for these systems. At other conditions, excluding this region, agreement commensurate with the hydrocarbon results was found. After the available binary data had been used to determine the various parameters, the available multicomponent (ternary and higher order systems) were used to validate both equations of state. Some of the results of the validation are given in Tables III through V and Figure 3. The hydrocarbon compositions are summarized in Table IV. Again, the available data are skimpy and some are of doubtful quality. As a general rule, both equations of state give excellent agreement with the experimental values up to 350 bars. Above this pressure limit, the SRK is superior to the PFGC-MES equation. Validation of the PFGC-MES on methanol-water-hydrocarbonacid gas systems was practically impossible. Many investigators have reported data for the C - C paraffin aromatic naphthenic 2

2

5

8

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

340

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS i.o.

I

I

I I I


-K > Ή CD U CD 4-> Ph 0 U C P-i O U O -H μ

03 :

if) U

CO CD

in

CD

bJC

g

P

CO

Κ)

ο

to

(NI CNI

(NI Ln LO

Ln

vO

o

(NI Ln

rH CNI

Ln Ln

O

σι

00

o

rH

^-

to

00 tO

00 00 r-1

o

LO

vO

O 00

L

O σ> vO

CN] (NI

CT> cr>

to

00

LO

o

CNl

sa (Λ

ι

ι

E-« τ! s'CO;

c/)

CD O

ÎE

rH

rH

oo to

oo to

rH LO

SO

g en S

LO

O

Ln

o

rH

LO o m

CNJ O

(NJ

Ο σ> LO

to

to to ο vO

rH

LO CNI

8

CO (Ν

Ο

C0 CO

U

r—I U

CNJ

f—I LO

U

Ο Ο

U

δ δ S

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

342

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

TABLE IV EXPERIMENTAL MULT I COMPONENT MIXTURE COMPOSITIONS (From Reference 2)

1

N

2

Ci

-

.0100

.148

-

.8851

.9436

.7379

.8690

C0

2

-

.0060

.003

.0210

C

2

.0602

.0264

.066

.0740

.0318

.0096

.039

.0220

.0046

-

.0035

.0051

nC^

-

.0044

.0048

.0043

iC

5

.0098

-

-

-

nC

5

.0085

-

-

.0025

nC

6

-

-

-

.0018

nC

7

-

-

-

.0013

c

3

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

17.

MOSHFEGHiAN

ET A L .

PFGC-MES

343

Equation of State

TABLE V COMPARISON OF PREDICTED AND EXPERIMENTA MULTICOMPONEN (From Reference 2) Absolute Avg Error in Predicted Water Content of Vapor Phase SRK PFGC-MES*

System No.

Temperature Range, °C

Pressure Range Bars

1

37.8/65,6

68.95/137.90

4.25

4.03

2

37.8

68.95/137.90

7.32

4.18

3

104.6

71.71/680.17

2.01

5.70

4

104.6

70.88/689.13

1.18

2.22

* pressure limited to 350 bars

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

344

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL

APPLICATIONS

range hydrocarbon-methanol systems; the data available for lighter hydrocarbons is sparse. The binary data for MeOH-other component systems is generally well represented; some of these results have been reported earlier (161. The results for two binary systems are reported here-- 3 " 2 CH OH-H s(Figures 4 and 5) . The predicted bubble pressures agree with the experimental values within about 5%. Unfortunately, only one set of experimental vapor phase compositions was available (Katayama). The absolute average error in the predicted vapor phase composition for carbon dioxide was less than 1%. Predicted and experimental bubble point pressures for a four component system-nitrogen, carbon dioxide, hydrogen sulfide and methanol--are reported in Table VI. The average error in the predicted bubble point pressures is about 5%. Though not shown, the absolute average error in the nitrogen vapor phase concentration is about 8%. Similar evaluation when possible. Most o tary data--results very similar to the values shown here have been obtained. Predictions of the vapor volume and enthalpy departure for a water containing natural gases were compared with data being generated by Hall and coworkers at Texas A§M under GPA sponsorship (10). Both equations of state performed well; the average error in the predicted volume was less than one percent (abs) and the absolute average error in the predicted enthalpy departure was about four KJ/kg. Based on our evaluations, we believe that the SRK equation of state gives reasonable predictions of water hydrocarbon behavior at any pressure up to about 700 bars and over the temperature range 0°C to 300°C. The upper pressure limit of the PFGC-MES appears to be about 350 bars while the valid temperature range is about the same as the SRK. CH

OH

co

a

n

d

3

2

Sample Problems A sample calculation has been made to illustrate the practical application of the PFGC-MES equation of state. The problem is a typical pipeline transporting a water saturated natural gas. The pipeline conditions are such that hydrates could form in the pipeline. Methanol will be used to depress the hydrate foimation temperature to an acceptable level (a 15°C hydrate depression was used). Three different approaches to this problem can be developed These are: 1. Conventional pipeline calculations in which "dry" hydrocarbon flashes are performed to determine the hydrocarbon liquid formation; the liquid water condensed is estimated using one of the available natural gas water content charts (1, _15), and the Hammerschmidt equation (11) and a graphical correlation are used to

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

MOSHFEGHIAN ET AL.

PFGC-MES

0.2

0.4

MOL FRACTION IN

0.6

Equation of State

0.8

HYDROGEN

LIQUID

345

1.0 SULFIDE

PHASE

Figure 5. Comparison of predicted and experimental bubble point pressures for methanol-hydrogen sulfide system ((Ο, A, V) (24); ( ) predicted)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

346

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL

APPLICATIONS

TABLE VI COMPARISO BUBBLE POINT PRESSURE FOR THE NITROGEN-CARBON DIOXIDE, HYDROGEN SULFIDE, METHANOL SYSTEM AT -15°C (From Reference 9) Experimental Bubble Point Pressure, bars

Experimental Values Liquid Phase Mol Fraction N C0 HS MeOH 2

2

2

Predicted Bubble Point Pressure bars

9.49

.003

.069

.001

.927

10.28

9.88

.003

.067

.001

.929

10.17

20.16

.007

.083

.001

.909

20.31

28.27

.010

.070

.001

.919

26.71

35.06

.013

.065

.002

.920

33.95

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

17.

MOSHFEGHIAN E T A L .

PFGC-MES

347

Equation of State

estimate the methanol requirements (4). Perform wet hydrocarbon flashes to estimate the hydrocarbon and water liquid formation and estimate the methanol requirements using the above approach. 3. Perform wet -methanol-hydrocarbon flashes to estimate the liquid water plus methanol and hydrocarbon phases; the methanol concentration is adjusted to satisfy the Hammerschmidt equation prediction for the desired hydrate formation temperature depression. Calculations for a l l three cases have been performed for the system described in Tables VII and VIII and Figure 6. In this case the raw feed gas was flashed at 66°C and 138 bars with sufficient water to assure that the gas leaving the separator was water saturated. Each of the calculational philosophies described above was used to predict the phase behavior of the systems at each pressur results of these calculation XI and Figures 7 through 10. Several factors become immediately apparent after analysis of these results: 1. The type of flash calculation-- dry , wet or "wet" plus methanol--has no practical effect on the predicted hydrocarbon liquid formation. 2. The conventional technology of pipeline calculations does not normally predict the carbon dioxide or hydrocarbon content of the water rich phase. These can be estimated by other graphical correlations. 3. Both 'Vet flash calculations predict a higher concentration of water in the vapor phase than the graphical correlations. The presence of methanol reduces the predicted water content of the vapor phase. 4. The presence of methanol in the liquid water phase substantially increases the predicted carbon dioxide solubility in that phase. 5. Methanol has l i t t l e effect on the predicted solubility of hydrocarbons in the liquid water phase. 6. A l l three approaches predict about the same methanol requirements to give the specific hydrate formation temperature depression. Most of these effects were expected; three deserve further comment. Most of the available water content charts are applicable only to sweet lean natural gases, Moore, et a l , (15) have developed a set of charts which are based on the Heidemann (8, 12) version of the SRK water prediction. The system used in tfïis study contains nearly 6.0% carbon dioxide. The acid gases cause increased water solubility in the vapor phase. Our calculations simply verify these observations. The wet -methanol-hydrocarbon flash predicts the complete phase distribution of methanol at each point in the system. 2.

ff

M

M

M

M

M

M

M

11

M

M

American Chemical Society Library 1155 16th St. N. W. In Thermodynamics of Aqueous Systems withD. Industrial Applications; Newman, S., et al.; Washington, C. 20036 ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

348

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

TABLE VII FEED COMPOSITION

Component

Mol Percent

N

2.76

2

0%

76.95

C0

2

5.30

CH

6

4.06

C3H8

1.94

iCi+Hio

0.43

nCi+Hi 0

0.76

iC H

12

0.39

nC H

12

0.33

2

5

5

Lt. Aromatics (C H ) 6

C

7 +

(nC H ) 10

H0 2

22

6

0.42 3.75 2.91

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

17.

MOSHFEGHIAN E T A L .

PFGC-MES

Equation of State

TABLE VIII PROCESS/PIPELINE CONDITIONS Primary Separato Pipeline Pressure Temperature Profile

P, Bars Inlet from separator

Discharge from pipeline

T, C

138.00

66

124.00

38

110.00

27

96.50

21

82.70

16

68.95

16

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

349

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980. 3

-

24.75

256 190 205

1 780 1 846 1 831

29.14

32.28

31.38

96.50/21

82.70/16

68.95/16

6

* 10 normal cubic meters

740

-

331

1 901

25.66

110.00/27

-

18.86

124.00/38

-

-

-

138.00/66 560

3

Methanol Water Rich Vapor Phase Liquid wt% kg/Mm (N)

1 476

Water kg/Mn (N)* Liquid Vapor

1 354

3

-

3

Hydrocarbon Liq m /Mm (N)* 2 036

P/T Bars/C

RESULTS BASED ON DRY HYDROCARBON FLASH

TABLE IX

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

-

24.75

673 410 325 256 281

1 469 1 732 1 817 1 886 1 861

18.86

25.60

29.08

32.11

31.33

124.00/38

110.00/27

96.50/21

82.70/16

68.95/16

6

* 10 normal cubic meters

740

1 354

-

2 142

-

3

Methanol Water Rich Vapor Phase Liquid wt% kg/Mm (N)*

-

Water kg/Mm (N)*

138.00/66

3

Vapor

Bars/C

3

Liquid

Hydrocarbon Liq

m /Mm (Ν)*

P/T

RESULTS BASED ON WET HYDROCARBON FLASH

TABLE Χ

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

2 143

1 536

-

18.88

25.53

138.00/66

124.00/38

110.00/27

96.50/21

Water kg/Μη (N)* Vapor

3

711 601 606

22.68 24.78 24.77

275 213 233

1 868 1 930 1 910

29.04

32.14

31.28

82.70/16

68.95/16

normal cubic meters

819 20.40

356

1 787

6

1 013

16.22

607

*.10

1 339

Methanol Water Rich Vapor Phase Liquid wt% kg/Mn (N)* -

3

Liquid

3

m /Nfai (N)*

Hydrocarbon Liq

Bars/C

P/T

RESULTS BASED ON WET-METHANOL-HYDROCARBON FLASH

TABLE XI

MOSHFEGHiAN

ET AL.

PFGC-MES

Equation of State

353

METHANOL INJECTION -TO PIPELINE-

FEED • LIQUID HYDROCARBON •LIQUID WATER

Figure 6.

Diagram of process

Figure 7. Vapor phase water concentration profile ((O) conventional technology; (A) wet hydrocarbonflash;(S7) wet methanol hydrocarbon flash)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

354

THERMODYNAMICS

I6OO1

OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

1

1

APPLICATIONS

Γ

Ο

PIPELINE

PRESSURE,

BARS

Figure 8. Vapor phase methanol concentration profile ((O) dry hydrocarbon flash; (A) wet hydrocarbonflash;(V) wet methanol hydrocarbon flash)

PIPELINE

PRESSURE,

BARS

Figure 9. Effect of methanol on predicted hydrocarbon solubility in water phase ((A) wet hydrocarbonflash;(V) wet methanol hydrocarbon flash)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

MOSHFEGHIAN E T

Figure 10.

AL.

PFGC-MES

Equation of State

355

Effect of methanol on predicted C0 solubility in water phase ((A) wet hydrocarbonflash;(V) wet methanol hydrocarbon flash) 2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

356

THERMODYNAMICS

O F AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

Anomolous pressure-temperature profiles in a pipeline can cause unusual behavior of the water condensation profile in the line. If this happens, the methanol requirements predicted on the basis of terminal pipeline conditions could be low. Probably the most important feature of the "wet" methanol hydrocarbon flash results in the enhanced carbon dioxide solubility in the liquid water phase. This would probably mean potentially more severe corrosion problems in the pipeline and associated equipment. The design and operation of the corrosion prevention system and program can be substantially improved. Current and Future Work We believe that the SRK equation of state has been pushed to its limits. Some improvements in its ability to describe the behavior of hydrocarbo ably be made. Some of liquid behavior of selected organic water systems could be reasonably well described Ç7, 2 3 ) . Unfortunately, the results of this work could not be extended beyond the range of data used in the fitting process. Our major efforts are being devoted to extension of the capabilities of the PFGC-MES equation of state. We are or soon will be developing parameters for: 1. The glycols used in natural/synthetic gas dehydration processes. 2. The physical absorbents for acid gas removal from natural and synthetic gases. 3. The aromatic molecules which contain nitrogen, sulfur and oxygen that commonly occur in coal liquefaction processes. 4. The sulfur containing components which occur in coal gasification/liquefaction systems such as, carbonyl sulfide, methyl and ethyl mercaptans, etc. 5. The halogenated refrigerants. 6. Other organic chemicals. In addition, we are evaluating the ability of the equation of state to predict the vapor liquid equilibria for systems appropriate to each group of compounds. We recognize that these objectives represent a very ambitious project; we hesitate to speculate about the completion date or quality of the final results. Summary The ability of the SRK equation of state to reliably predict the vapor phase water content of natural and synthetic gas systems has been demonstrated. In addition, the ability of the PFGC-MES equation to describe the phase behavior of hydrocarbon, acid gas, methanol, water systems has been described. Both

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

MOSHFEGHIAN ET A L .

17.

PFGC-MES

Equation of State

357

equations o f s t a t e appear to g i v e p r e d i c t i o n s o f the phase be­ h a v i o r o f the subject systems that are completely adequate f o r r o u t i n e engineering d e s i g n / e v a l u a t i o n work p r o v i d e d the l i m i t s o f the c o r r e l a t i o n are not exceeded. We b e l i e v e that the PFGC equation o f s t a t e approach w i l l be the most f r u i t f u l new route to p r e d i c t i n g phase behavior o f the d i v e r s e systems encountered i n the n a t u r a l gas/petroleum/coal l i q u e f a c t i o n g a s i f i c a t i o n process i n d u s t r y . We commend i t to your a t t e n t i o n . ACKNOWLEDGEMENT The authors g r e a t l y a p p r e c i a t e the f i n a n c i a l support o f the Oklahoma State U n i v e r s i t y C o l l e g e o f Engineering and the M o b i l Research Foundation which made t h i s work p o s s i b l e . We a l s o appreciate the generou

Nomenclature L i s t A

- parameter i n SRK equation o f s t a t e - parameter i n SRK equation o f s t a t e - mixture parameter i n SRK equation o f s t a t e parameter i n SRK equation o f s t a t e - parameter i n SRK equation o f s t a t e - term i n SRK equation o f s t a t e based enthalpy departure equation b - parameter i n SRK o r PFGC-MES equation o f s t a t e c / b - a r b i t r a r y constant i n PFGC equation o f s t a t e ΔΗ - isothermal e f f e c t o f pressure on enthalpy AS - isothermal e f f e c t o f pressure on entropy Ε - parameter i n PFGC-MES equation o f s t a t e k - b i n a r y i n t e r a c t i o n parameter f o r SRK o r PFGC-MES equation of s t a t e Κ - vapor l i q u i d Κ value = y / x m component c h a r a c t e r i s t i c parameter f o r SRK equation o f s t a t e o r number o f groups i n molecule i Ρ - p r e s s u r e , absolute u n i t s P° - reference pressure f o r entropy c a l c u l a t i o n s , absolute u n i t s Pc - c r i t i c a l p r e s s u r e , absolute u n i t s Φ - volume f r a c t i o n o f group R - gas law constant Τ - temperature, absolute u n i t s τ parameter i n PFGC-MES equation o f s t a t e Te - c r i t i c a l temperature, absolute u n i t s ν molar volume χ l i q u i d phase (or phase) mol f r a c t i o n y - vapor mol f r a c t i o n ζ compressibility factor a aca a Β 3 c

H

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

358

OF AQUEOUS SYSTEMS WITH

INDUSTRIAL APPLICATIONS

subscripts i - any component k - any group η - any group superscripts 2 (0) (1) (2)

-

second pha^e binary interation parameter coefficient of T° coefficient of T coefficient of T 1

2

Summation counters k - number of groups i c - number of component η - number of components in SRK equation of state

REFERENCES

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

_____, Engineering Data Book, 9th edition, GPSA, 1972. _____ , IGT Research Bulletin No. 8, Reproduced by Socony Mobil Oil Co., Inc., FRL. with Institute of Gas Technology permission, 1955. Bartlett, E. P., JACS, January 11, 1927. Campbell, J. Μ., Gas Conditioning and Processing, Vol. 2, Campbell Petroleum Series, Norman, OK (1978). Campbell, J. Μ., Private Communication (1979). Cunningham, J. and G. M. Wilson, Proceedings of the 54th GPA National Meeting, Denver, Colorado (1974). Erbar, J. Η., Invited paper presented at Polish Academy of Sciences Symposium, Jablonna, Poland, November (1975). Evelein, Κ. Α., R. G. Moore and R. A. Heidemann, Ind. Eng. Chem. Process Des. Dev., Vol. 15, p. 423, 1976. Ferrell, J. K., R.W. Rousseau and D. B. Bass, "The Solubil­ ity of Acid Gases in Methanol," EPA Report - 600/7-79097 (April, 1979). Hall, K. R., Private Communication (1979). Hamerschmidt, E. G., Western Gas 9, 9-11, 29, December (1933). Heidemann, R. Α., AIChE J, Vol. 20, p. 847, 1974. Hopke, S. W. and G. J. Lin, Paper presented at 76th National Meeting Tulsa, OK (1974). Katayama, T., O. Kazunari, G. Mackawa, M. Goto and T. Nagano Journal of Chem. Eng. of Japan, Vol. 8, p. 89 (1975). Moore, R. G., R. A. Heidemann and E. Wichert, Energy Processing/Canada, p. 40, January, 1979. M

11

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

17. MOSHFEGHIAN ET AL.

PFGC-MES Equation of State359

16. Moshfeghian, M., A. Shariat and J. H. Erbar, "Application of the PFGC Equation of State to Gas Processing Systems," presented at the National AIChE meeting, Houston, Texas, April 5, 1979. 17. Olds, R. H., B. H. Sage and W. N. Lacey, Ind. Eng. Chem., Vol. 34 p. 1223, 1942. 18. Peng, D. Y. and D. B. Robinson, Canadian Journal of Chemical Engineering, Vol. 54, p. 595, December, 1976. 19. Soave, G., Chem. Eng. Sci., Vol. 27, p. 1197, 1972. 20. Starling, K. E. and M. S. Han, Hydrocarbon Processing, Vol. 51, No. 5, p. 129 (1972). 21. Sultanov, R. G., Skripka, V. G. and A. Y. Namiot, Gazovaia Promyshlennost, Vol. 16, No. 4, p. 6, 1971. 22. Sultanov, R. G., Skripka, V. G. and A. Y. Namiot, Gazovaia Promyshlennost, Vol. 17, No. 5, p. 6, 1972. 23. Vellendorf, G., Master' (1976). 24. Yorizane, M., Sada Moto, H. Masuoka, and Y. Eto, Kogyo Kagoku. Zashins, Vol. 72, p. 2174 (1969). RECEIVED

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

18 Considerations Affecting Observation of Interaction Second Virial Coefficients by Chromatography 1

Κ. N. ROGERS, S. H. TEDDER , J. C. HOLSTE, P. T. EUBANK, and K. R. H A L L Chemical Engineering Department, Texas A&M University, College Station, T X 77843

Its precise basis in statistical mechanics makes the virial equation of state a powerfu of thermodynamic propertie Within the study of mixtures, the interaction second virial coef­ ficient occupies an important position because of its relation­ ship to the interaction potential between unlike molecules. On a more practical basis, this coefficient is useful in developing predictive correlations for mixture properties. Several techniques are available for measuring values of interaction second virial coefficients. The primary methods are: reduction of mixture virial coefficients determined from PoT data; reduction of vapor-liquid equilibrium data; the differen­ tial pressure technique of Knobler et al.(1959); the Burnettisochoric method of Hall and Eubank (1973); and reduction of gas chromatography data as originally proposed by Desty et al.(1962). The latter procedure is by far the most rapid, although it is probably the least accurate. Besides speed, the chromatography experiment has the advan­ tage that relatively "nasty" systems present minimal problems. Coal chemicals i n l i g h t c a r r i e r gases o r H^S systems are good examples. Such c o n s i d e r a t i o n s l e d us t o develop a chromatography apparatus w i t h the s p e c i f i c goal of o b t a i n i n g i n t e r a c t i o n second v i r i a l c o e f f i c i e n t s . A v a s t l i t e r a t u r e was a v a i l a b l e t o guide us i n t h i s e f f o r t . The more noteable references i n c l u d e the book by L i t t l e w o o d (1970) and review a r t i c l e s by Conder (1968), Locke (1976) and Kobayashi elt a l . (1967) . Papers which s p e c i f i ­ c a l l y address determination of the i n t e r a c t i o n v i r i a l c o e f f i ­ c i e n t , among other p r o p e r t i e s , i n c l u d e those by E v e r e t t (1965), Laub and Pecsok (1974), Young and coworkers (1966, 1967, 1968, 1968, 1969). Conder and P u r n e l l (1968, 1968, 1969, 1969) provide an e x c e l l e n t overview o f the t o t a l experiment. We have chosen the water - carbon d i o x i d e system f o r t h i s study f o r s e v e r a l reasons. R e l a t i v e l y l i t t l e l i t e r a t u r e e x i s t s f o r t h i s important system. This mixture i s important i n combus1

Current address: AMOCO Production Company, Tulsa, OK 0-8412-0569-8/80/47-133-361$05.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

362

OF

AQUEOUS

SYSTEMS

WITH

INDUSTRIAL

APPLICATIONS

t i o n s t u d i e s , ordinance d e s i g n , and t e r t i a r y o i l recovery. F i ­ n a l l y , i t i s a d i f f i c u l t system to study and we reasoned that i t would demonstrate equipment c a p a b i l i t y and inadequacy. A n a l y s i s of Experiment The a n a l y s i s p r o v i d i n g i n t e r a c t i o n second v i r i a l c o e f f i ­ c i e n t s from chromatography r e s t s upon three p r i n c i p a l assump­ t i o n s : 1) v a p o r - l i q u i d e q u i l i b r i u m e x i s t s i n the column; 2) the s o l u t e (component 1) i s s o l u b l e i n both the c a r r i e r gas (compo­ nent 2) and the s t a t i o n a r y l i q u i d phase (component 3 ) ; 3) the c a r r i e r gas and s t a t i o n a r y l i q u i d are i n s o l u b l e . Under assump­ t i o n #1, we can w r i t e fi = f i

(1)

where f ^ i s the f u g a c i t s u p e r s c r i p t s i n d i c a t e vapor and . l i q u i d . Taking the vapor side of the e q u a t i o n , we w r i t e Λ

.ν

Λ

ν f l = Υ ΡΦ 1

(2)

1

where y. i s the vapor-phase composition, Ρ i s the p r e s s u r e , and $ i i s tne vapor-phase f u g a c i t y c o e f f i c i e n t of component i . This equation a l s o serves to define $Y. Standard thermodynamic d e r i ­ v a t i o n s , such as those of Smith and Van Ness (1975), provide the r e l a t i o n s h i f t 1|ϋΰ£2|

λη ;=| Φ

- i ^ ^ l - A n Z '

(3)

where nV i s the t o t a l volume, n^ i s number of moles of component i and Ζ i s the c o m p r e s s i b i l i t y f a c t o r . Note that assumption #3 forces the vapor (and the l i q u i d ) to be b i n a r y m i x t u r e s . From the v i r i a l e q u a t i o n , we o b t a i n Z = 1 + (yjB 3y2y C 2

1 1 2

where B. . and C_,

2

n

+ y B 2

+ 3y

i y

2

+ (yjc

+ ly^B^/V

2 2

+ y^C^^/V

C l 2 2

2

m

+

+ ...

Ξ

1 2

2

+ 1.5 C ^ / V

2

APPLICATIONS

+

(11) which, i n combination w i t h Equation 10, becomes rP 1

K

&n !

P

,vap

ρ r

2*1

(V*)°° 1 dP RT

- 1.5C,

Now, r e c a l l i n g that P^ = P ^

ap

- 0, we can approximate the

p a r t i a l molar volume by

U,

and

SYSTEMS

1

1 3

γ..

=

2b.. - β. - β.

(13)

Bi

1

=

2a3.3. - b ( a . 3 . + a.3. + ay..) ι J ^ι J J ι 'IR

(14)

B

2

=

-Βχ - 2a .b

2

(15)

ij

The f i r s t o f the two c r i t i c a l c r i t e r i a i s that Q

Ξ det(Q)

=

0

(16)

When t h i s equation i s s a t i s f i e d , there i s a v e c t o r Δη Δη

Ξ

(Δη , Δ η , . . . ) τ

Τ

(17)

2

which s a t i s f i e s Q-Δη

=

0

(18)

Heidemann and K h a l i l (14) use as the second c r i t i c a l c r i t e ­ r i o n that the cubic form C i s zero where, C

=

2

2

2

£(v-b)/2bj ΣΣΣη (3 £ηί /8η 3η^)Δη Δη^.Δη τ

ί

κ

ί

κ

(19)

(In (14) the second d e r i v a t i v e s o f £nfi are given i n d e t a i l f o r the SRK equation.) The Δη i n t h i s equation i s the normalized vec­ t o r which s a t i s f i e s (18). Michelsen (15, 16) has pointed out that the e v a l u a t i o n o f the cubic form i n (19) can be performed very economically. T y p i c a l terms i n (19) can be reduced as f o l l o w s : ΣΣΣΔη.Δη.Δη. = ι j k ΣΣΣβ.Δη.Δη.Δη = ι ι 3 k ΣΣΣa..Δη.Δη.Δη. IJ ι 3 k

=

(ΣΔη.) ι

3

(Σβ.Δη.) (ΣΔη.) ι ι ι

(20) 2

(21)

ν

(ZZa..Δη.Δη.)(ΣΔη.) 13 ι 3 ι

(22)

Because o f these and s i m i l a r i d e n t i t i e s the t r i p l e sum i n (19) can

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

19.

HEIDEMANN

Critical Points in Reacting Mixtures

383

be replaced by terms i n v o l v i n g , at most, double sums. The two equations, (16) and C

= 0,

(23)

together d e f i n e the c r i t i c a l p o i n t . E v a l u a t i n g C r i t i c a l Points I t was found most convenient, as the f i r s t stage i n f i n d i n g a c r i t i c a l p o i n t f o r a given mixture, to solve f o r the temperature which makes Q equal to zero at a given volume. The temperature volume p a i r gives one p o i n t on the s t a b i l i t y l i m i t . Corresponding to t h i s p o i n t , there i s a v e c t o r Δη which s a t ­ i s f i e s equation (18). The second stage i n the c r i t i c a l p o i n t c a l ­ c u l a t i o n i s to s o l v e f o Δη i s then employed to The cubic form evaluated i n t h i s way i s a f u n c t i o n of volume alone (since the temperature and Δη are f i x e d by the volume). To f i n d the c r i t i c a l p o i n t r e q u i r e s to f i n d a volume at which the cubic form i s zero. In Heidemann and K h a l i l (14) a d d i t i o n a l d e t a i l i s given about numerical procedures which were found e f f e c t i v e i n s o l v i n g these equations. The o v e r a l l s o l u t i o n s t r a t e g y , as described above, r e q u i r e s nested one-dimensional searches; the c r i t i c a l volume i s found by s o l v i n g (23), but at each volume (16) must be solved f o r the temperature. The m u l t i p l i e r (T/100) i n each term of the matrix Q and the m u l t i p l i e r [(v-b)/2b] i n the cubic form were introduced to improve the behavior of the numerical methods. 2

Water-Gas S h i f t Mixtures The s p e c i f i c r e a c t i o n examined i n t h i s paper i s the water-gas shift reaction H0 2

+ CO -> H + C 0 2

2

(24)

As t h i s r e a c t i o n proceeds, beginning w i t h some i n i t i a l mixture, each o f the four mole f r a c t i o n s can be represented as a f u n c t i o n of a s i n g l e r e a c t i o n extent, ε. At every ε the mixture c r i t i c a l p o i n t ( i f indeed, the mixture has a c r i t i c a l p o i n t ) can be found using the procedure described above. Binary C r i t i c a l P o i n t s Before d e s c r i b i n g v a r i a t i o n s i n the c r i t i c a l p o i n t s i n the four-component water-gas s h i f t mixture i t i s i n s t r u c t i v e to exam­ ine the c r i t i c a l p o i n t s i n the various b i n a r y mixtures. There are s i x b i n a r y p a i r s to consider.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

384

APPLICATIONS

The c a l c u l a t e d c r i t i c a l p o i n t s o f the b i n a r y p a i r s , p a r t i c u l a r l y the c r i t i c a l p r e s s u r e s , are q u i t e s e n s i t i v e t o the values used f o r the i n t e r a c t i o n parameters i n the mixing r u l e s f o r a and b i n the equation o f s t a t e . One problem i n undertaking t h i s study i s t h a t no data are a v a i l a b l e on the c r i t i c a l l i n e s o f any of the b i n a r y p a i r s except f o r C O 2 - H 0. Even f o r C 0 - H 0, two sets o f c r i t i c a l data a v a i l a b l e (18, 19) are i n poor q u a n t i t a t i v e agreement, though they present the same q u a l i t a t i v e p i c t u r e o f the c r i t i c a l phenomena. Because o f the u n c e r t a i n t y as t o the data and because o f the s e n s i t i v i t y t o the parameters i t should be understood t h a t c a l c u l a t e d c r i t i c a l p o i n t s reported i n t h i s paper need not represent a c t u a l behavior, even o f the b i n a r y p a i r s . Most o f the i n t e r a c t i o n parameters employed were taken from other s t u d i e s (20, 21), and are r e p o r t e d l y obtained by minimizing e r r o r s i n the match o f phas e q u i l i b r i u data i (21) the SRK equation employe here. The parameters f o r C 0 - H 0 were chosen because they had been shown t o give a c r i t i c a l l i n e which i s q u a l i t a t i v e l y c o r r e c t . The H 0 - CO i n t e r a c t i o n parameter i s the value given i n (20) f o r H S - CO. For H 0 - H , k j j was taken t o be -0.25 i n the absence of any l i t e r a t u r e s t u d i e s . 2

2

2

2

2

2

2

2

2

Table I. System H0 2

-C0

H0

- CO

H0

- H

C0

2

C0

INTERACTION PARAMETERS

k

2

ij

0.0

Cij

Reference

-0.03 0

-

-0.25

0

-

- CO

-0.064

0

21_

2

- H

2

-0.3570

0

20

CO

- H

2

0.1000

0

20

2

2

2

0.0603

The c a l c u l a t e d c r i t i c a l l i n e s f o r the b i n a r y p a i r s are shown i n Figure 1. A l l these l i n e s are d i s c o n t i n u o u s , i n d i c a t i n g high d e n s i t y phase s e p a r a t i o n s . For each b i n a r y p a i r the p r i n c i p a l p a r t o f the c r i t i c a l l i n e begins a t the c r i t i c a l p o i n t f o r the component w i t h the higher c r i t i c a l temperature. There i s a second branch o f each o f the c r i t i c a l l i n e s , beginning a t t h e c r i t i c a l p o i n t o f the component w i t h the lower c r i t i c a l temperat u r e , which terminates on i n t e r s e c t i n g a l i q u i d - l i q u i d - v a p o r three-phase l i n e .

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

HEIDEMANN

19.

0

385

Critical Points in Reacting Mixtures

100

200

300 TEMPERATURE , KELVINS

6ÔÔ

700

Figure 1. Critical lines in water-gas shift binary pairs

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

386

THERMODYNAMICS

OF

AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

In Figure 1 the low temperature branches o f the c r i t i c a l l i n e s have been omitted, except f o r the CO2 - H2O b i n a r y . The reason f o r the omission i s t h a t these l i n e s are extremely short and are not o f much i n t e r e s t . The mole f r a c t i o n o f the component whose c r i t i c a l p o i n t i s the o r i g i n o f the c r i t i c a l l i n e has been i n d i c a t e d as a parameter along each o f the l i n e s . I t should be noted from these numbers that there are compositions i n each o f the b i n a r y p a i r s f o r which there i s no c r i t i c a l p o i n t . I t should a l s o be noted t h a t some CO2 - CO mixtures have two c r i t i c a l p o i n t s . I t i s most s i g n i f i c a n t that c e r t a i n b i n a r y mixtures have no c r i t i c a l p o i n t . With t h i s i n mind i t i s not s u r p r i s i n g t h a t c e r t a i n four-component mixtures have no c r i t i c a l p o i n t . The general shape o f the b i n a r y c r i t i c a l l i n e s d i c t a t e s the shape o f c r i t i c a l l i n e s i n the r e a c t i n g mixtures. Water-Gas S h i f t C r i t i c a Mixtures r i c h i n the three l i g h t e r components have no c r i t i ­ c a l p o i n t u n l e s s the water content i s l e s s than a few percent. The more i n t e r e s t i n g behavior i s i n mixtures r i c h i n water. The mixture mole f r a c t i o n s reached during the r e a c t i o n depends on the i n i t i a l composition. The s o r t s o f mixtures s t u d i e d here are generated by beginning w i t h water and carbon monoxide, the water i n excess. C r i t i c a l p o i n t s have been c a l c u l a t e d f o r such mixtures w i t h v a r i o u s i n i t i a l H2O/CO r a t i o s . The r e s u l t s are shown i n Figure 2. In t h i s f i g u r e , the l i n e o f zero conversion i s the c r i t i c a l l i n e f o r H 0 - CO b i n a r y . For mixtures w i t h i n i t i a l H 0/C0 r a t i o s g r e a t e r than about 4, i t i s p o s s i b l e t o f i n d c r i t i c a l p o i n t s f o r a l l conversions. When the i n i t i a l r a t i o i s l e s s , t h i s i s no longer p o s s i b l e . Lines o f 25%, 50% and 75% conversion are a l s o shown i n Figure 2. The c r i t i c a l p o i n t s i n these mixtures are a l l at pressures h i g h e r than the c r i t i c a l pressure o f water; many are at tempera­ t u r e s higher than the water c r i t i c a l temperature. The mixture c r i t i c a l p o i n t s i n d i c a t e t h a t high d e n s i t y phase separations per­ s i s t t o extreme c o n d i t i o n s o f temperature and pressure. 2

2

Reaction E q u i l i b r i u m The necessary c o n d i t i o n f o r e q u i l i b r i u m i n the chemical r e a c t i o n s o f equation (1) i s t h a t In

Κ. 3

=

Σ ^

v..Inf.; iJ 1

j = 1, R.

(25)

The e q u i l i b r i u m c o n s t a n t s , K j , may be evaluated as f u n c t i o n s o f temperature u s i n g r e a d i l y a v a i l a b l e thermochemical data. A procedure was developed that permitted l o c a t i o n o f p o i n t s

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

19.

HEIDEMANN

387

Critical Points in Reacting Mixtures

TEMPERATURE, KELVINS Figure 2. Critical lines in reacting mixtures of CO with excess H O z

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

388

T H E R M O D Y N A M I C S OF

AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

which are c r i t i c a l p o i n t s and which obey equation (25) f o r the water gas s h i f t r e a c t i o n . The necessary thermochemical data were taken from Reid, P r a u s n i t z and Sherwood (22). The f u g a c i t i e s of the four r e a c t i n g species were evaluated u s i n g the SRK equation of s t a t e . For every i n i t i a l H 0/C0 r a t i o , the mixture mole f r a c t i o n s , hence the c r i t i c a l temperature and volume, are determined by the r e a c t i o n extent ε. The e q u i l i b r i u m constant i s c a l c u l a t e d at the c r i t i c a l temperature. The f u g a c i t i e s are c a l c u l a t e d a l s o at the c r i t i c a l c o n d i t i o n f o r the given ε. The f u n c t i o n F, d e f i n e d as 2

Ρ(ε)

=

-lnK+

£n(f

C 0 2

f )/(f f H 2

C 0

H 2 0

(26)

)

hence v a r i e s w i t h ε alone. Although i t has been shown that thermodynamic models which imply phase separation i n s o l v i n g the r e a c t i o proved to be only one s o l u t i o n to equation (26) under the condi­ t i o n s s t u d i e d . I t i s conceivable that more than one c r i t i c a l p o i n t could be found f o r some r e a c t i n g mixtures at c e r t a i n reac­ t i o n extents (two c r i t i c a l p o i n t s are indeed i n d i c a t e d i n Figure 1 f o r some C0 - CO m i x t u r e s ) , i n which case F(e) w i l l not be a s i n g l e - v a l u e d f u n c t i o n . This p o s s i b i l i t y was not explored. In the mixtures w i t h i n i t i a l H 0/C0 r a t i o s g r e a t e r than 4, unique c r i t i c a l p o i n t s were found f o r a l l ε covering the range from zero to 100% conversion of CO. In t h i s range F(ε) v a r i e s from -°° to +°°, hence must cross zero at some ε. There was o n l y one such zero c r o s s i n g , however, i n d i c a t i n g that non-uniqueness, i f i t occurs, w i l l a r i s e o n l y because o f the branching of F ( e ) . 2

2

C a l c u l a t e d C r i t i c a l and E q u i l i b r i u m P o i n t s The Newton-Raphson procedure was used to f i n d ε s a t i s f y i n g F(ε) = 0. I t e r a t i o n s began at high conversion and the d e r i v a t i v e d F > ^ was found by numerical d i f f e r e n t i a t i o n . Convergence was obtained i n 5 i t e r a t i o n s , w i t h 10 c r i t i c a l p o i n t e v a l u a t i o n s , i n about 10 seconds. The computer used was the U n i v e r s i t y of Calgary Honeywell HIS-Multics system. R e s u l t s of these c a l c u l a t i o n s are given i n Table 2 and i n Figure 3. A l s o shown are r e s u l t s of c a l c u l a t i o n s made assuming the mixture to be a p e r f e c t gas at the c a l c u l a t e d c r i t i c a l temp­ e r a t u r e . (The pressure has no e f f e c t on the c a l c u l a t e d i d e a l gas conversion i n t h i s r e a c t i o n . ) A l s o c a l c u l a t e d and presented i n Table 2 i s the q u a n t i t y Κ , d e f i n e d by =

( P

/

P

^ CO PH P O H O 2

2

C

(27)

)

2

which provides an i n d i c a t i o n o f the e f f e c t due t o non-ideal

gas

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

19.

HEIDEMANN

Critical Points in Reacting Mixtures

389

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In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

390

T H E R M O D Y N A M I C S O F AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

4 6 8 10 MOL Η,Ο/MOL CO Figure 3.

Critical

and reaction equilibrium points: (a) critical pressure; (b) temperature; (c) conversion of CO

critical

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

19.

HEIDEMANN

Critical Points in Reacting Mixtures

391

behavior. In the case o f the water-gas s h i f t r e a c t i o n a t the c r i t i c a l p o i n t , Κφ i s greater than 1.0 i n d i c a t i n g t h a t e q u i l i b r i ­ um conversions w i l l be l e s s than would be c a l c u l a t e d assuming p e r f e c t gases. I t i s the n o n - i d e a l i t y o f water which most a f f e c t s Κψ but none o f the other species could be regarded as i d e a l gases at the temperatures and pressures o f the c r i t i c a l p o i n t s . The e q u i l i b r i u m conversions o f CO achieved at the c r i t i c a l p o i n t are shown i n Figure 3.c. The conversions a t t a i n a b l e are w e l l below the values corresponding t o i d e a l gas behavior at the c r i t i c a l temperature. Conclusions The study d e s c r i b e d above f o r the water-gas s h i f t r e a c t i o n employed computational methods t h a t could be used f o r other syn­ t h e s i s gas o p e r a t i o n s of Heidemann and K h a l i t u r e s i n v o l v e d . In the case o f one r e a c t i o n , i t was p o s s i b l e t o f i n d c o n d i t i o n s under which a c r i t i c a l mixture was at chemical r e a c t i o n e q u i l i b r i u m by u s i n g a one dimensional Newton-Raphson procedures along the c r i t i c a l l i n e d e f i n e d by v a r y i n g r e a c t i o n extents. In t h e case o f more than one independent chemical r e a c t i o n , a Newton-Raphson procedure i n t h e s e v e r a l r e a c t i o n extents would be a candidate as an approach t o s a t i s f y i n g the s e v e r a l e q u i l i b r i u m constant equations, (25). Since s y n t h e s i s gas mixtures are capable o f showing more than one c r i t i c a l p o i n t , there i s a p o s s i b i l i t y o f f i n d i n g more than one s o l u t i o n t o the simultaneous equations d e f i n i n g r e a c t i o n e q u i l i b r i a and the c r i t i c a l p o i n t . This p o s s i b i l i t y was not encountered i n the present study. Acknowledgment This work was supported by a grant from the N a t i o n a l Science and Engineering Research C o u n c i l o f Canada. Literature Cited

1. Soave, G. Chem. Eng. Sci., 1972, 27, 1197. 2. Wilson, G.M., 1969, paper presented at the 65th National AIChE Mtg., Cleveland. 3. Peng, D.-Y.; Robinson, D.B. Ind. Eng. Chem. Fundamentals, 1976, 15, 59. 4. Heidemann, R.A. AIChE J, 1974, 20, 847. 5. Evelein, K.A.; Moore, R.G.; Heidemann, R.A. Ind. Eng. Chem. Process Des. Dev., 1976, 15, 423. 6. Peng, D.-Y.; Robinson, D.B. Canadian J. of Chem. Engng, 1976, 54, 595. 7. van Zeggeren, F.; Storey, H.S. "The Computation of Chemical Equilibria", Cambridge University Press, Cambridge, 1970.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

392 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

8. Danes, F.E.; Geana, D. Revista de Chimie, 1979, 30, Nr. 3, 244. 9. Dluzniewski, J.H.; Adler, S.B.; Ozkardesh, H.; Barner, H.E., 1973, paper presented at the 75th National AIChE Mtg., Detroit. 10. Heidemann, R.A. Chem. Eng. Sci., 1978, 33, 1517. 11. Reid, R.C.; Beegle, B.L. AIChE J., 1977, 23, 726. 12. Peng, D.-Y.; Robinson, D.B. AIChE J., 1977, 23, 137. 13. Baker, L.E.; Luks, K.D., 1978, paper SPE 7478 presented at the 53rd Annual Conference, Soc. Pet. Eng. of the AIME, Houston. 14. Heidemann, R.A.; Khalil, A.M., 1979, paper presented at the 86th National AIChE Mtg., Houston. 15. Michelsen, M.L., personal communication, 1979. 16. Michelsen, M.L. Fluid Phase Equilibria (in press). 17. Soave, G. Chem. Eng Sci 1979 34 225 18. Takenouchi, S.; Kennedy 19. Todheide, K.; Franck, E.U. Z. Phys. Chem. (Frankfort am Main), 1963, 37, 387. 20. Oellrich, L.; Plocker, U.; Prausnitz, J.M.; Knapp, H. Chem. Ing. Tech., 1977, 12, 955. 21. Graboski, M.S.: Daubert, T.E. Ind. Eng. Chem. Process Des. Dev., 1978, 17, 448. 22. Reid, R.C.; Prausnitz, J.M.; Sherwood, T.K. "Properties of Gases and Liquids", 3rd Edition, McGraw-Hill, New York, 1977. 23. Caram, H.S.; Scriven, L.E. Chem. Eng. Sci., 1976, 31, 163. 24. Othmer, H.G. Chem. Eng. Sci, 1976, 31, 993. RECEIVED

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

20 Two- and Three-Phase Equilibrium Calculations for Coal Gasification and Related Processes D.-Y.

PENG and D. B. ROBINSON

Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G6

The gasificiation o hydrocarbon base stocks inevitably leads to the production of process streams which contain a very wide range of paraffinie, naphthenic, aromatic and olefinic hydrocarbons in the presence of associated non-hydrocarbons such as hydrogen, nitrogen, carbon dioxide, hydrogen sulfide and ammonia. These streams are often contacted with water at process conditions which normally lead to either gas - water - rich liquid equilibrium or gas water - rich liquid - hydrocarbon rich liquid equilibrium. The processing conditions and stream compositions which may lead to the formation of these different phases and the distribution of the components between phases are of great importance to the design engineer. For this reason the establishment of reliable procedures for predicting the behavior of these mixtures in the one-, two-, and three-phase regions is a matter of considerable importance. In an earlier paper (1), the authors presented an efficient procedure for predicting the phase behavior of systems exhibiting a water - rich liquid phase, a hydrocarbon - rich liquid phase, and a v a p o r p h a s e . The P e n g - R o b i n s o n e q u a t i o n o f s t a t e (2) was used t o r e p r e s e n t t h e b e h a v i o r o f a l l t h r e e phases. I t has t h e following form: . a(T) v-b " v ( v + b j + b ( v - b )

= KL v

(1)

where a ( T ) = a α a

c

= 0.45724

- j ±

= 1 + K(1-T ^ ) R

2

(2)

0-8412-0569-8/80/47-133-393$05.50/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

394

THERMODYNAMICS

OF AQUEOUS SYSTEMS

W I T H INDUSTRIAL

κ = 0 . 3 7 4 6 4 + 1.54226ω - 0.26992ω R T

b = 0.07780 For m i x t u r e s

b =

I

x.

APPLICATIONS

2

(3)

c

ψ-± c

b.

(5)

A l t h o u g h t h e c a l c u l a t e d phase c o m p o s i t i o n s f o r t h e h y d r o ­ c a r b o n - r i c h l i q u i d phase and t h e v a p o r phase showed e x c e l l e n t agreement w i t h the e x p e r i m e n t a l d a t a , the c a l c u l a t e d hydrocarbon c o n t e n t s o f t h e aqueous l i q u i d phase was c o n s i s t e n t l y s e v e r a l o r d e r s o f magnitude lowe I t was s p e c u l a t e d t h a a c t i o n p a r a m e t e r s w o u l d be r e q u i r e d t o b r i n g t h e p r e d i c t e d v a l u e s and t h e e x p e r i m e n t a l r e s u l t s i n t o q u a n t i t a t i v e a g r e e m e n t ; n e v e r ­ t h e l e s s , no a t t e m p t was made a t t h a t t i m e t o t r y t o a c c o m p l i s h this. In t h i s s t u d y , i t has been p o s s i b l e t o d e v i s e a p r o c e d u r e w h i c h c a n be used t o g e n e r a t e r e l i a b l e phase c o m p o s i t i o n s f o r b o t h t h e h y d r o c a r b o n - r i c h phase and t h e aqueous phase o v e r a w i d e r a n g e o f t e m p e r a t u r e and p r e s s u r e . Moreover, the c a l c u l a t i o n p r o c e d u r e has been s u c c e s s f u l l y a p p l i e d t o n o n - h y d r o c a r b o n water systems w i t h q u a n t i t a t i v e r e s u l t s . C a l c u l a t i o n Procedure. W i t h t h e e x c e p t i o n o f two s i g n i f i c a n t m o d i f i c a t i o n s , t h e c a l c u l a t i o n p r o c e d u r e used i n t h i s s t u d y was b a s i c a l l y t h e same as t h a t used p r e v i o u s l y . The f i r s t m o d i f i c a t i o n c o n c e r n s t h e use o f E q n . ( 2 ) f o r water. When d e v e l o p i n g t h e o r i g i n a l c o r r e l a t i o n f o r oh and κ as e x p r e s s e d by E q n . ( 2 ) and ( 3 ) , w a t e r was n o t i n c l u d e d as one o f t h e c o m p o n e n t s , and c o n s e q u e n t l y t h e p r e d i c t e d v a p o r p r e s s u r e s f o r w a t e r w e r e n o t as good as e x p e c t e d . Thus i n o r d e r t o c o r r e l a t e t h e v a p o r p r e s s u r e o f w a t e r more a c c u r a t e l y o v e r t h e e n t i r e t e m p e r a t u r e range^ E q n . ( 2 ) was m o d i f i e d f o r t h i s compound a t t e m p e r a t u r e s where T R ^ < 0 . 8 5 as f o l l o w s : h

a

= 1.0085677

+ 0.82154

(I-TJ*)

ν

(6)

K

A t t e m p e r a t u r e s where T >_ 0 . 8 5 , E q n . ( 2 ) s t i l l a p p l i e s . The s e c o n d m o d i f i c a t i o n c o n c e r n s t h e c o r r e l a t i o n o f t h e c o m p o s i t i o n o f t h e aqueous l i q u i d p h a s e . In o r d e r t o a c c o m p l i s h t h i s , a t e m p e r a t u r e - d e p e n d e n t i n t e r a c t i o n p a r a m e t e r was used f o r t h e aqueous l i q u i d phase and t h e p r e v i o u s t e m p e r a t u r e i n d e p e n d e n t p a r a m e t e r was u s e d f o r t h e non-aqueous l i q u i d phase and t h e v a p o r p h a s e . Thus f o r t h e aqueous - l i q u i d phase E q n . ( 4 ) becomes R

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

20.

PENG AND ROBINSON

Coal Gasification and Related Processes

395

where τ-jj i s a t e m p e r a t u r e - d e p e n d e n t i n t e r a c t i o n p a r a m e t e r . The i n t r o d u c t i o n o f t h i s p a r a m e t e r f o r each aqueous b i n a r y p a i r means t h a t t h e i n t e r a c t i o n between t h e w a t e r m o l e c u l e and t h e g a s m o l e c u l e i n t h e aqueous l i q u i d phase i s much d i f f e r e n t f r o m t h a t i n t h e nonaqueous p h a s e s . F o r a l l t h e aqueous b i n a r i e s w h i c h have been e x a m i n e d i n t h i s s t u d y , t h e t e m p e r a t u r e d e p e n d e n t i n t e r a c t i o n p a r a m e t e r s t a k e on n e g a t i v e v a l u e s a t a m b i e n t t e m p e r a t u r e and m o n o t o n i c a l l y i n c r e a s e a s t e m p e r a t u r e increases. T h i s i n d i c a t e s t h a t t h e a t t r a c t i o n e n e r g y between t h e w a t e r m o l e c u l a r and t h e o t h e r m o l e c u l e s d e c r e a s e s as t h e temperature i n c r e a s e s . Non-Hydrocarbon - Wate Of t h e many p o s s i b l w h i c h a r e r e l a t e d t o s u b s t i t u t e gas p r o c e s s e s , t h e d a t a on o n l y t h e w a t e r b i n a r i e s c o n t a i n i n g H S , C 0 , N , and N H were u s e d i n this study. The t r e a t m e n t o f h y d r o g e n , a quantum g a s , i s d i f f e r e n t from t h a t o f t h e o t h e r g a s e s . A separate paper w i l l deal w i t h t h e c o r r e l a t i o n o f t h e d a t a on hydrogen m i x t u r e s . 2

2

2

3

Hydrogen S u l f i d e - Water S y s t e m . The d a t a o f S e l l e c k e t a l . (J3) were used t o e v a l u a t e t h e i n t e r a c t i o n p a r a m e t e r s f o r t h e hydrogen s u l f i d e - water s y s t e m . The d a t a i n c l u d e t h e c o m p o s i t i o n o f b o t h p h a s e s a t t e m p e r a t u r e s f r o m 100°F t o 340°F a n d p r e s s u r e s f r o m 100 t o 5000 p s i a i n t h e c o e x i s t i n g v a p o r and aqueous l i q u i d hydrogen s u l f i d e - r i c h l i q u i d - vapor e q u i l i b r i u m l o c u s . A s i n g l e , c o n s t a n t i n t e r a c t i o n p a r a m e t e r has been d e t e r m i n e d f o r the hydrogen s u l f i d e - r i c h p h a s e s . T h i s d e t e r m i n a t i o n was b a s e d on t h e t h r e e - p h a s e p r e s s u r e - t e m p e r a t u r e l o c u s . While i n v e s t i g a t i n g t h e t h r e e - p h a s e r e g i o n , i t was n o t e d t h a t t h e t h r e e phase l o c u s a n d t h e c o m p o s i t i o n o f t h e h y d r o g e n s u l f i d e - r i c h phase w e r e r a t h e r i n s e n s i t i v e t o t h e t e m p e r a t u r e - d e p e n d e n t aqueous phase i n t e r a c t i o n p a r a m e t e r . Furthermore, the composition o f t h e aqueous phase was r e l a t i v e l y i n d e p e n d e n t o f t h e c o n s t a n t i n t e r a c t i o n parameter. For these reasons, the s o l u b i l i t y o f h y d r o g e n s u l f i d e i n t h e aqueous l i q u i d was c o r r e l a t e d a t t h e same t i m e as t h e p a r a m e t e r was b e i n g d e t e r m i n e d f o r t h e h y d r o g e n s u l f i d e - r i c h phases. The c a l c u l a t e d and e x p e r i m e n t a l g a s e o u s and l i q u i d phase c o m p o s i t i o n s a r e shown i n F i g u r e s 1 a n d 2 r e s p e c t i v e l y . C a r b o n D i o x i d e - Water S y s t e m . The d a t a o f Wiebe and Gaddy (1? §) e x c l u s i v e l y i n t h i s study to determine the i n t e r a c t i o n parameters f o r the carbon d i o x i d e - water b i n a r y system. These d a t a c o v e r t h e t e m p e r a t u r e a n d p r e s s u r e r a n g e f r o m 12°C t o 100°C a n d f r o m 25 atm t o 700 atm r e s p e c t i v e l y . As w i t h t h e H2S - H2O s y s t e m , a c o n s t a n t i n t e r a c t i o n p a r a m e t e r has been o b t a i n e d f o r t h e g a s e o u s phase and t h e c a r b o n d i o x i d e - r i c h w

e

r

e

u

s

e

d

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

396

THERMODYNAMICS

OF AQUEOUS SYSTEMS

W I T H INDUSTRIAL

APPLICATIONS

4000

0

I 0.80

1 0.85

L 0.90

0.95

1.00

M O L E FRACTION H Y D R O G E N S U L F I D E

Figure 1. Experimental and predicted vapor phase compositions for the hydrogen sulfide-water system (( ) P-R prediction; data from Ref. 3: (Φ) 340°F; (O) 280°F;(0) 220° F; (A) 160°F)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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M O L E FRACTION H Y D R O G E N S U L F I D E Figure 2. Experimental and predicted aqueous liquid phase compositions for the hydrogen sulfide-water system (( ) P-R prediction; data from Ref. 3: (Φ) 160°F; (A) 220°F; (U> 280 T; Cf) 340°F)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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l i q u i d phase. A t each t e m p e r a t u r e , t h e s o l u b i l i t y o f carbon d i o x i d e i n w a t e r c a n be c o r r e l a t e d a c c u r a t e l y t h r o u g h t h e w h o l e p r e s s u r e r a n g e u s i n g one i n t e r a c t i o n p a r a m e t e r f o r t h e aqueous phase. The e q u i l i b r i u m aqueous l i q u i d and v a p o r c o m p o s i t i o n s f o r t h i s b i n a r y a t two t e m p e r a t u r e s a r e shown i n F i g . 3 . M a l i n i n ( 7 ) , T o d h e i d e and F r a n c k ( 8 ) a n d T a k e n o u c h i and Kennedy ( 9 ) r e p o r t e d e q u i l i b r i u m d a t a f o r t h i s s y s t e m a t t e m p e r a t u r e s up t o 350°C a n d p r e s s u r e s t o 3500 b a r s . However, t h e v a p o r phase d a t a o f t h e s e a u t h o r s do n o t a l w a y s a g r e e w i t h each o t h e r . The aqueous phase d a t a have been used t o e x t e n d t h e t e m p e r a t u r e - d e p e n d e n t i n t e r a c t i o n p a r a m e t e r t o 300°C. N i t r o g e n - Water System. The i n t e r a c t i o n p a r a m e t e r s f o r t h e n i t r o g e n - w a t e r s y s t e m have been e v a l u a t e d u s i n g t h e d a t a o f Wiebe and Gaddy ( 1 0 ) , P a r a t e l l a a n d S a g r a m o r a (21), Rigby and P r a u s n i t z ( 1 2 ) a n d 0 ' S u l l i v a n and S m i t h ( 1 3 ) As w i t h t h e two previous systems, only necessary to c o r r e l a t e i n t e r a c t i o n p a r a m e t e r f o r t h e aqueous l i q u i d phase i n c r e a s e d monotonically with temperature. A comparison o f the c a l c u l a t e d and e x p e r i m e n t a l v a p o r phase and aqueous l i q u i d phase c o m p o s i t i o n s i s g i v e n i n T a b l e I. Ammonia - W a t e r S y s t e m . I n t e r a c t i o n parameter f o r the ammonia - w a t e r s y s t e m was o b t a i n e d u s i n g t h e d a t a o f C l i f f o r d and H u n t e r ( 1 4 ) and o f M a c r i s s e t a l . ( 1 5 ) . A s i n g l e - v a l u e d p a r a m e t e r was c a p a b l e o f r e p r e s e n t i n g t h e c o m p o s i t i o n o f t h e l i q u i d phase r e a s o n a b l y w e l l a t a l l t e m p e r a t u r e s , h o w e v e r , t h e c a l c u l a t e d amount o f w a t e r i n t h e v a p o r phase i n t h e v e r y h i g h ammonia c o n c e n t r a t i o n r e g i o n was somewhat l o w e r t h a n t h e d a t a o f C l i f f o r d and H u n t e r and M a c r i s s e t a l . Edwards e t a l . ( 1 6 ) have a p p l i e d a new t h e r m o d y n a m i c c o n s i s t e n c y t e s t t o t h e d a t a o f M a c r i s s e t a l and have c o n c l u d e d t h a t t h e d a t a a p p e a r t o be i n c o n s i s t e n t and t h a t t h e r e p o r t e d w a t e r c o n t e n t o f t h e v a p o r phase i s t o o h i g h . The e x p e r i m e n t a l d a t a and t h e c a l c u l a t e d r e s u l t s a r e g i v e n i n Fig. 4. Hydrocarbon - Water B i n a r i e s The i n t e r a c t i o n p a r a m e t e r s f o r b i n a r y s y s t e m s c o n t a i n i n g w a t e r w i t h m e t h a n e , e t h a n e , p r o p a n e , η-butane, n - p e n t a n e , n - h e x a n e , η - o c t a n e , and benzene have been d e t e r m i n e d u s i n g d a t a from t h e l i t e r a t u r e . The phase b e h a v i o r o f t h e p a r a f f i n - w a t e r s y s t e m s c a n be r e p r e s e n t e d v e r y w e l l u s i n g t h e m o d i f i e d p r o c e d u r e . H o w e v e r , t h e a r o m a t i c - w a t e r s y s t e m c a n n o t be c o r r e l a t e d satisfactorily. P o s s i b l y a d i f f e r e t n type o f m i x i n g r u l e w i l l be r e q u i r e d f o r t h e a r o m a t i c - w a t e r s y s t e m s , a l t h o u g h t h i s has n o t as y e t been e x p l o r e d . Methane - W a t e r S y s t e m . I n t e r a c t i o n p a r a m e t e r s were g e n e r a t e d f o r t h e v a p o r phase and t h e aqueous l i q u i d phase f o r t h e methane -

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

PENG AND ROBINSON

Coal Gasification and Related Processes

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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400

TABLE I.

Experimental

APPLICATIONS

and C a l c u l a t e d Aqueous L i q u i d and V a p o r

Phase C o m p o s i t i o n s f o r t h e N i t r o g e n - W a t e r S y s t e m . Pressure, atm.

* 3 x χ 10

y

N

Expt.

Calc.

*

Expt.

Χ 10

3

Calc.

Τ = 25°C 22.20

1.529

1.502

30.50

1.149

1.123

38.19

0.941

0.919

6.260

6.190

3.680

3.640

59.04

2.420

2.410

75.99

1.956

1.952

25

50

0.280

0.278

0.54

100

1.01

200

1.812

300

2.455

2.458

500

3.558

3.555

800

4.909

4.869

1000

5.720

5.604

1.795

Τ = 50°C 20.81 25

0.219

0.220

36.93 50

0.436

0.428

100

0.812

0.810

200

1.470

1.470

300

2.034

2.032

500

2.982

2.968

800

4.181

4.084

1000

4.900

4.701

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

20.

PENG AND ROBINSON

Table

401

Coal Gasification and Related Processes

I - continued.

Pressure,

atm.

* χ

N

Expt.

3 χ 10 Calc.

y

*

Expt.

Χ 10

3

Calc.

Τ = 75°C 25

0.204

0.203

41.66

10.09

50

0.397

10.12

0.398

60.35

7.21

7.25

88.55

5.23

5.23

100

0.76

200

1.390

1.395

300

1.936

1.942

500

2.872

2.859

800

4.052

3.948

1000

4.747

4.544 Τ = 100°C

25

0.214

0.206

50

0.415

0.410

56.42

19.94

19.94

78.44

15.03

14.89

12.19

12.09

100

0.792

0.792

100.o9 200

1.462

1.470

300

2.042

500

3.044

3.052

800

4.294

4.223

1000

5.003

4.857

2.060

* Mole

Fraction

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

402

THERMODYNAMICS

0

OF

0.2

AQUEOUS

0.4

SYSTEMS W I T H INDUSTRIAL

0.6

0.8

APPLICATIONS

10

M O L E FRACTION AMMONIA

Figure 4. Experimental and predicted vapor and liquid phase compositions for the ammonia-water system (( ) P-R prediction; data from Ref. 15: liquid— (A) 300°F; (f) 200°F; (*) 100°F; vapor—(A) 300°F; (V) 200°F; (O) 100°F)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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403

w a t e r b i n a r y s y s t e m u s i n g e x p e r i m e n t a l d a t a r e p o r t e d by S u l t a n o v e t a l . (17_, 1 8 ) , O l d s e t a l . ( 1 9 ) , a n d C u l b e r s o n and McKetta ( 2 0 ) . The v a p o r - p h a s e mole f r a c t i o n s o f w a t e r o f O l d s e t a l . ( 1 9 ) can be r e p r e s e n t e d v e r y w e l l u s i n g t h e P e n g - R o b i n s o n e q u a t i o n o f s t a t e i n c o n j u n c t i o n w i t h a constant i n t e r a c t i o n parameter over t h e t e m p e r a t u r e r a n g e f r o m 100°F t o 4 6 0 ° F . The same i n t e r a c t i o n p a r a m e t e r c a n be u s e d t o r e p r o d u c e t h e d a t a o f S u l t a n o v e t a l . (18) up t o 300°C w i t h good r e s u l t s . However, a t h i g h e r t e m p e r a t u r e s t h e c a l c u l a t e d w a t e r c o n t e n t i n t h e v a p o r phase d e v i a t e d somewhat f r o m t h e i r d a t a . The t e m p e r a t u r e - d e p e n d e n t i n t e r a c t i o n p a r a m e t e r s were d e t e r m i n e d f r o m 7 7 ° F t o 680°F u s i n g t h e d a t a o f C u l b e r s o n a n d McKetta ( 2 0 ) a n d o f S u l t a n o v e t a l . (1_8). This parameter i n c r e a s e s w i t h temperature and appears t o converge t o t h e v a l u e o f the constant paramete c r i t i c a l temperature o The e x p e r i m e n t a l a n d c a l c u l a t e d r e s u l t s f o r t h i s b i n a r y s y s t e m a t 250°C a r e p r e s e n t e d i n F i g u r e 5 . Ethane - Water System. The d a t a u s e d f o r t h e d e t e r m i n a t i o n o f the i n t e r a c t i o n parameters f o r the ethane - water b i n a r y a r e t h o s e o f C u l b e r s o n and M c K e t t a ( 2 1 ) , C u l b e r s o n e t a l . ( 2 2 ) and Reamer e t a l . (230 · A c o n s t a n t i n t e r a c t i o n p a r a m e t e r was c a p a b l e o f r e p r e s e n t i n g t h e mole f r a c t i o n o f w a t e r i n t h e v a p o r phase w i t h i n e x p e r i m e n t a l u n c e r t a i n t y o v e r t h e t e m p e r a t u r e r a n g e f r o m 100°F t o 4 6 0 ° F . As w i t h t h e methane - w a t e r s y s t e m , t h e t e m p e r a t u r e - d e p e n d e n t i n t e r a c t i o n parameter i s a l s o a m o n o t o n i c a l l y i n c r e a s i n g f u n c t i o n of temperature. However, a t each s p e c i f i e d t e m p e r a t u r e , t h e i n t e r a c t i o n parameter f o r t h i s system i s n u m e r i c a l l y g r e a t e r than t h a t f o r t h e methane - w a t e r s y s t e m . Although i t i s p o s s i b l e f o r t h i s b i n a r y t o f o r m a t h r e e - p h a s e e q u i l i b r i u m l o c u s , no e x p e r i m e n t a l d a t a on t h i s e f f e c t have been r e p o r t e d . F i g u r e 6 i l l u s t r a t e s t h e c a l c u l a t e d and e x p e r i m e n t a l e q u i l i b r i u m phase c o m p o s i t i o n s a t 220°F f o r t h i s b i n a r y s y s t e m . Propane - Water System. The i n t e r a c t i o n p a r a m e t e r s f o r t h e p r o p a n e - w a t e r s y s t e m were o b t a i n e d o v e r a t e m p e r a t u r e r a n g e f r o m 4 2 ° F t o 310°F u s i n g e x c l u s i v e l y t h e d a t a o f K o b a y a s h i a n d Katz (2^). T h i s i s b e c a u s e among t h e a v a i l a b l e l i t e r a t u r e on t h e phase b e h a v i o r o f t h i s b i n a r y s y s t e m , t h e i r d a t a a p p e a r t o g i v e t h e most e x t e n s i v e i n f o r m a t i o n . A c o n s t a n t i n t e r a c t i o n p a r a m e t e r was o b t a i n e d f o r t h e p r o p a n e - r i c h p h a s e s a t a l l temperatures. The m a g n i t u d e o f t h e t e m p e r a t u r e - d e p e n d e n t i n t e r a c t i o n p a r a m e t e r f o r t h i s b i n a r y was l e s s t h a n t h a t f o r t h e e t h a n e - w a t e r b i n a r y a t t h e same t e m p e r a t u r e . Azarnoosh and McKetta (25) a l s o presented experimental data f o r the s o l u b i l i t y o f p r o p a n e i n w a t e r o v e r a b o u t t h e same t e m p e r a t u r e r a n g e a s t h a t o f K o b a y a s h i and K a t z b u t a t p r e s s u r e s up t o 500 p s i a o n l y . However, a d i f f e r e n t s e t o f t e m p e r a t u r e - dependent parameters

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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APPLICATIONS

Figure 5. Experimental and predicted vapor and liquid phase compositions for methane-water system at 250°C (( ) P-R prediction; (A) (17); (A) (IS))

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Related Processes

405

M O L E FRACTION Figure 6. Experimental and predicted vapor and liquid phase compositions for the ethane-water system at 220°F (( ; P-R prediction; (A) (21); (O) (23))

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

406

THERMODYNAMICS

OF

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w o u l d be r e q u i r e d t o a c c u r a t e l y c o r r e l a t e t h e i r r e s u l t s . The w a t e r c o n t e n t o f t h e p r o p a n e - r i c h p h a s e s i n t h e aqueous l i q u i d - p r o p a n e l i q u i d - v a p o r r e g i o n a r e i l l u s t r a t e d i n F i g u r e 7. η-Butane - W a t e r S y s t e m . Reamer e t a l . (26) have d e t e r m i n e d t h e c o n c e n t r a t i o n o f w a t e r i n t h e n-butane - w a t e r s y s t e m i n t h e v a p o r and t h e η-butane l i q u i d phases i n t h e t h r e e - p h a s e r e g i o n . Reamer e t a l . (27) have p u b l i s h e d e x p e r i m e n t a l d a t a f o r t h e s o l u b i l i t y o f η-butane i n w a t e r and o f w a t e r i n η-butane i n t h e two-phase r e g i o n c o v e r i n g a t e m p e r a t u r e r a n g e f r o m 100°F t o 460°F and a t p r e s s u r e s up t o 1 0 , 0 0 0 p s i a . L e B r e t o n and M c K e t t a (28) have p r e s e n t e d t h e r e s u l t s o f an e x p e r i m e n t a l s t u d y on t h e s o l u b i l i t y o f η-butane i n w a t e r a t f o u r t e m p e r a t u r e s b u t a t p r e s s u r e s up t o o n l y 1000 p s i a . W h i l e the r e p o r t e d three-phase p r e s s u r e s f r o m t h e s e two s o u r c e s a g r e e v e r y w e l l , t h e d a t a on t h e s o l u b i l i t y o f η-butane s o l u b i l i t y values presente e n t l y l o w e r t h a n t h o s e r e p o r t e d by Reamer e t a l . In v i e w o f t h e f a c t t h a t t h e d a t a o f Reamer e t a l . c o v e r e d a much b r o a d e r r a n g e o f b o t h t e m p e r a t u r e and p r e s s u r e , t h e i r d a t a w e r e used f o r d e t e r m i n i n g the i n t e r a c t i o n parameters f o r t h i s system. As w i t h t h e f i r s t t h r e e p a r a f f i n - w a t e r s y s t e m s , o n l y a c o n s t a n t p a r a m e t e r was r e q u i r e d t o c o r r e l a t e t h e h y d r o c a r b o n r i c h phases a l t h o u g h a t e m p e r a t u r e - d e p e n d e n t p a r a m e t e r was n e c e s s a r y t o f i t t h e aqueous - l i q u i d phase d a t a . The e q u i l i b r i u m c o m p o s i t i o n o f t h e n-butane - w a t e r b i n a r y i n the three-phase r e g i o n a r e i l l u s t r a t e d i n F i g u r e 8. n-Pentane - W a t e r S y s t e m . S c h e f f e r (29) has p r e s e n t e d t h e t h r e e - p h a s e l o c u s f o r a m i x t u r e o f i - p e n t a n e and n-pentane o v e r a t e m p e r a t u r e r a n g e f r o m 150°C t o 1 8 7 . 1 ° C . H o w e v e r , no c o m p o s i t i o n a l measurements were r e p o r t e d . N a m i o t and B e i d e r (30) r e p o r t e d t h e s o l u b i l i t y o f n-pentane i n w a t e r a t t h r e e temperatures a l o n g the three-phase l o c u s . I n t e r a c t i o n parameters f o r t h e n-pentane - w a t e r s y s t e m w e r e d e t e r m i n e d u s i n g t h e s e d a t a . n-Hexane - W a t e r S y s t e m . The n-hexane - w a t e r s y s t e m i s t h e l i g h t e s t p a r a f f i n - w a t e r b i n a r y where t h e v a p o r p r e s s u r e l o c u s o f the hydrocarbon i n t e r s e c t s t h a t f o r pure w a t e r . The e x p e r i ­ m e n t a l phase b e h a v i o r d a t a a v a i l a b l e i n t h e l i t e r a t u r e f o r t h i s s y s t e m c o v e r a w i d e r a n g e o f t e m p e r a t u r e and p r e s s u r e . Unfort­ u n a t e l y t h e s e d a t a do n o t c o r r o b o r a t e each o t h e r and n o t i c e a b l e discrepancies e x i s t . The d a t a o f S c h e f f e r ( 3 1 ) , R e b e r t and Hayworth ( 3 2 ) , and S u l t a n o v and S k r i p k a ( 3 3 j were employed i n d e t e r m i n i n g the i n t e r a c t i o n parameter f o r the hydrocarbon - r i c h phases. A unique value f o r t h i s i n t e r a c t i o n parameter c o u l d not be o b t a i n e d b e c a u s e o f t h e d i s c r e p a n c i e s among t h e d a t a . However, a t e n t a t i v e v a l u e , b a s e d on t h e e x t r a p o l a t i o n o f t h e v a l u e s f o r o t h e r p a r a f f i n - w a t e r i n t e r a c t i o n p a r a m e t e r s , has been a s s i g n e d to the c o n s t a n t i n t e r a c t i o n parameter. The i n t e r a c t i o n p a r a m e t e r s f o r t h e aqueous l i q u i d phase were d e t e r m i n e d u s i n g t h e d a t a o f

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M O L E FRACTION WATER χ 103 Figure 7. Experimental and predicted water content of propane liquid and vapor phases for the propane-water system along the three-phase locus (( ) P-R prediction; data from Ref. 24: (O) vapor; (Φ) liquid)

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Figure 8. Experimental and predicted water content of n-butane and vapor phases for the n-butane-water system along the three-phase locus (( ) P-R prediction; (·) (2D)

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K u d c h a d k e r and M c K e t t a (34). Their s o l u b i l i t y data i n the v a p o r - l i q u i d r e g i o n a r e b e l i e v e d t o be i n e r r o r p r o b a b l y due t o t h e i r i n c o r r e c t p r o c e d u r e o f s m o o t h i n g t h e raw d a t a . However, t h e i r d a t a i n t h e l i q u i d - l i q u i d r e g i o n seem t o be a c c e p t a b l e . The d a t a o f R e b e r t and H a y w o r t h ( 3 2 ) were used t o e x t e n d t h e temperature - dependent i n t e r a c t i o n parameters t o temperatures above t h e c r i t i c a l p o i n t o f n - h e x a n e . Other Hydrocarbon - Water Systems. I n t e r a c t i o n parameters w e r e g e n e r a t e d f o r t h e benzene - w a t e r s y s t e m . The d a t a u s e d were t h o s e o f S c h e f f e r (3]_), R e b e r t a n d Kay (35)> and C o n n o l l y (36). As w i t h t h e a l k a n e - w a t e r s y s t e m s , t h e i n t e r a c t i o n p a r a m e t e r s f o r t h e aqueous l i q u i d phase were f o u n d t o be temperature - dependent. However, t h e c o m p o s i t i o n s f o r t h e b e n z e n e - r i c h p h a s e s c o u l d n o t be a c c u r a t e l y r e p r e s e n t e d u s i n g any s i n g l e v a l u e f o r t h c o n s t a n t i n t e r a c t i o parameter Th c a l c u l a t e d w a t e r mole f r a c t i o n were a l w a y s g r e a t e r t h a experimenta reporte y R e b e r t and Kay ( 3 5 ) . The f i n a l v a l u e f o r t h e c o n s t a n t i n t e r a c t i o n p a r a m e t e r was c h o s e n t o f i t t h e t h r e e phase l o c u s o f t h i s system. N e v e r t h e l e s s , the c a l c u l a t e d three-phase c r i t i c a l p o i n t was a b o u t 9°C l o w e r t h a n t h e e x p e r i m e n t a l v a l u e . I n t e r a c t i o n p a r a m e t e r was a l s o g e n e r a t e d f o r t h e h y d r o c a r b o n r i c h phases o f t h e n-octane - water s y s t e m . The d a t a o f K a l a f a t i and P i i r ( 3 7 ) were u s e d . T h e r e were no d a t a a v a i l a b l e f o r t h e w a t e r - r i c h l i q u i d phase f o r t h i s b i n a r y . E x p e r i m e n t a l s o l u b i l i t y d a t a a r e a v a i l a b l e f o r some h i g h e r alkane - water systems ( s e e , f o r example, S k r i p k a e t a l . , (38)). However, these d a t a e i t h e r c o v e r o n l y a v e r y l i m i t e d temperature r a n g e o r c o n t a i n r e s u l t s f o r one phase o n l y . No a t t e m p t h a s been made t o d e t e r m i n e t h e i n t e r a c t i o n p a r a m e t e r s f o r w a t e r - h y d r o c a r b o n s y s t e m s where t h e h y d r o c a r b o n i s l a r g e r t h a n n - o c t a n e . The t e m p e r a t u r e - d e p e n d e n t i n t e r a c t i o n p a r a m e t e r s d e t e r m i n e d f o r s e v e r a l a l k a n e - w a t e r s y s t e m s a r e p l o t t e d i n F i g u r e 9 . The v a l u e s f o r t h e hydrogen s u l f i d e - carbon d i o x i d e - , and n i t r o g e n w a t e r b i n a r i e s a r e g i v e n i n F i g u r e 1 0 . I t c a n be s e e n t h a t a systematic trend e x i s t s f o r these parameters. The i n t e r a c t i o n p a r a m e t e r i n c r e a s e s w i t h t h e s i z e o f t h e m o l e c u l e and f u r t h e r m o r e i t a p p e a r s t o c o n v e r g e r a p i d l y a s t h e c a r b o n number i n c r e a s e s . A t a g i v e n temperature and p r e s s u r e , t h e s o l u b i l i t y o f a l k a n e s i n w a t e r g e n e r a l l y d e c r e a s e s as t h e m o l e c u l a r w e i g h t o f t h e h y d r o carbon i n c r e a s e s . The amount o f n - o c t a n e a n d h e a v i e r h y d r o c a r b o n s d i s s o l v e d i n water streams r e s u l t i n g from s y n t h e t i c gas p r o c e s s e s i s b e l i e v e d t o be i n s i g n i f i c a n t . The c a l c u l a t i o n o f t h e s o l u b i l i t y o f t h e s e compounds i n w a t e r u n d e r t h e s e c o n d i t i o n s by u s i n g e x t r a p o l a t e d values from i n t e r a c t i o n parameters o f l i g h t e r p a r a f f i n - water b i n a r i e s p r o b a b l y w i l l n o t cause l a r g e e r r o r s . Three-Phase L o c i . F i g u r e 11 shows t h e t h r e e - p h a s e l o c i f o r the a l k a n e - water systems. No e x p e r i m e n t a l t h r e e - p h a s e d a t a w e r e a v a i l a b l e i n t h e l i t e r a t u r e f o r the ethane - water b i n a r y .

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-0.4 \-

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Temperature-dependent interaction parameters for selected paraffinwater binary systems

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Reduced Temperature Figure 10.

Temperature-dependent interaction parameters for nitrogen, carbon dioxide, and hydrogen sulfide with water

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Figure 11. Experimental and predicted three-phase loci for selected paraffin-water binary systems (( ) P-R prediction; (V) (24); (·) (21); ( 0 ) (39); (O) (29); (k) (3l);(A)PV;W(3V)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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N e v e r t h e l e s s , a c a l c u l a t e d locus i s i n c l u d e d f o r completeness and t o i n d i c a t e t h e p o s s i b l e r e g i o n o f t h r e e - p h a s e e q u i l i b r i u m . As was m e n t i o n e d e a r l i e r , t h e t h r e e - p h a s e d a t a r e p o r t e d by S c h e f f e r (29) f o r p e n t a n e - w a t e r were f o r a " b i n a r y " composed o f w a t e r ancf a m i x t u r e o f i - p e n t a n e a n d n - p e n t a n e . As shown i n t h e f i g u r e , t h e s e d a t a a r e bounded b y t h e c a l c u l a t e d l o c i o f t h e i - p e n t a n e - w a t e r and n-pentane - w a t e r s y s t e m s . Conclusion. The m i x i n g r u l e f o r u s e w i t h t h e P e n g - R o b i n s o n e q u a t i o n o f s t a t e has been m o d i f i e d t o i n c l u d e t e m p e r a t u r e dependent i n t e r a c t i o n parameters. Both t h e c o n s t a n t and t h e temperature - dependent i n t e r a c t i o n parameters c o v e r i n g a wide r a n g e o f t e m p e r a t u r e s have been d e t e r m i n e d f o r h y d r o c a r b o n w a t e r s y s t e m s i n c l u d i n g methane - w a t e r , e t h a n e - w a t e r , p r o p a n e w a t e r , n-butane - w a t e r , a n d n-hexane - w a t e r a n d n o n - h y d r o c a r b o n water systems i n c l u d i n g hydrogen s u l f i d e water carbon d i o x i d e water, nitrogen - water these temperature - dependen t h e a c c u r a c y o f p r e d i c t i o n s o f t h r e e - p h a s e a n d two-phase e q u i l i ­ brium f o r systems i n v o l v i n g w a t e r . Acknowledgement. The f i n a n c i a l s u p p o r t r e c e i v e d f r o m t h e N a t i o n a l S c i e n c e a n d E n g i n e e r i n g R e s e a r c h C o u n c i l o f Canada i s sincerely appreciated. Abstract

Two-constant equation of state phase behavior calculations for aqueous mixtures often require the use of temperature dependent binary interaction parameters. The methods used for evaluating these parameters for some of the typical aqueous binary pairs found in coal gasification and related process streams are described. Experimental and predicted phase compositions based on these methods are illustrated for aqueous pairs containing CO , H S, NH , and other gases. 2

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Literature Cited

1. Peng, D.-Y., Robinson, D.B., Can. J. Chem. Eng., 1976, 54, 595. 2. Peng, D.-Y., Robinson, D.B., Ind. Eng. Chem. Fundam., 1976, 15, 59. 3. Selleck, F.T., Carmichael, L.T., Sage, B.H., Ind. Eng. Chem., 1952, 44, 2219. 4. Wiebe, R., Gaddy, V.L., J. Am. Chem. Soc., 1939, 61, 315. 5. Wiebe, R., Gaddy, V.L., J. Am. Chem. Soc., 1940, 62, 815. 6. Wiebe, R., Gaddy, V.L., J. Am. Chem. Soc., 1941, 63, 475. 7. Malinin, S.D., Geokhimiya, 1959,3,235. 8. Todheide, K., Franck, E.U., Ζ. Physik. Chem. (Frankfurt), 1963, 37, 387. 9. Takenouchi, S., Kennedy, G.C., Am. J. Sci., 1964, 262, 1055. 10. Wiebe, R., Gaddy, V.L., Heins, C., J. Am. Chem. Soc., 1933, 55, 947.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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11. 12. 13. 14. 15.

Paratella, Α., Sagramora, G., Ricerca Sci., 1959, 29, 2605. Rigby, Μ., Prausnitz, J.M., J. Phys. Chem. 1968, 72, 330. O'Sullivan, T.D., Smith, N.O., J. Phys. Chem. 1970, 74, 1460. Clifford, I.L., Hunter, E., J. Phys. Chem. 1933, 37, 101. Macriss, R.A., Eakin, B.E., Ellington, R.T., Huebler, J., Research Bulletin, No. 34, American Gas Association, 1964. 16. Edwards, T.J., Newman, J., Prausnitz, J.M., Ind. Eng. Chem. Fundam., 1978, 17, 264. 17. Sultanov, R.G., Skripka, V.G., Namiot, A. Yu., Gazovaya Promyshlennost, 1971, 16 (4), 6. 18. Sultanov, R.G., Skripka, V.G., Namiot, A. Yu., Gazovaya Promyshlennost, 1972, 17 (5), 6. 19. Olds, R.H., Sage, B.H., Lacey, W.N., Ind. Eng. Chem., 1942, 34, 1226. 20. Culberson, O.L., McKetta, J.J., Petrol. Trans. AIME, 1951, 192, 223. 21. Culberson, O.L., McKetta 189, 319. 22. Culberson, O.L., Horn, A.B., McKetta, J.J., Petrol. Trans. AIME, 1950, 189, 1. 23. Reamer, H.H., Olds, R.H., Sage, B.H., Lacey, W.N., Ind. Eng. Chem. 1943, 35, 790. 24. Kobayashi, R., Katz, D.L., Ind. Eng. Chem., 1953, 45, 440. 25. Azarnoosh, Α., McKetta, J.J., Petroleum Refiner. 1958, 37, (11), 275. 26. Reamer, H.H., Olds, R.H., Sage, B.H., Lacey, W.N., Ind. Eng. Chem., 1944, 36, 381. 27. Reamer, H.H., Sage, B.H., Lacey, W.N., Ind. Eng. Chem., 1952, 44, 609. 28. LeBreton, J.G., McKetta, J.J., Hydrocarbon Processing & Petrol. Refiner. 1964, 43, (6), 136. 29. Scheffer, F.E.C., Proc. Kon. Akad. Wet. Amsterdam, 1914, 17, 834. 30. Namiot, A. Yu., Beider, S. Ya., Khim. Tekhnol. Topliv. Masel 1960, 5, (7), 52. 31. Scheffer, F.E.C., Proc. Kon. Akad. Wet. Amsterdam, 1913, 16, 404. 32. Rebert, C.J., Hayworth, K.E., Α.I.Ch.E.J., 1967, 13, 118. 33. Sultanov, R.G., Skripka, V.G., Zh. Fiz. Khim., 1972, 46, (8), 2170. 34. Kudchadker, A.P., McKetta, J.J., Hydrocarbon Processing & Petrol. Refiner. 1961, 40, (9), 231. 35. Rebert, C.J., Kay, W.B., A.I.Ch.E.J., 1959, 5, 285. 36. Connolly, J.F., J. Chem. Eng. Data, 1966, 11, 13. 37. Kalafati, D.D., Piir, A.E., Zh. Fiz. Khim., 1972, 46, (2), 325. 38. Skripka, V.G., Hubkina, G.F., Boksha, O.A., Zh. Fiz. Khim., 1974, 48, (3), 781. 39. Roof, J.G., J. Chem. Eng. Data, 1970, 15, 301. RECEIVED January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

21 Phase Equilibrium Calculations by Equation of State for Aqueous Systems with Low Mutual Solubility M. BAUMGAERTNER, R. A. S. MOORWOOD, and H. WENZEL Lehrstuhl fuer Technische Chemie, Universitaet Erlangen-Nuernberg, Egerlandstrasse 3, D-8520 Erlangen, Fed. Rep. of Germany

At present there ar y approache available for calculating phase equilibria, one utilising activity coefficients and the other an equation of state. In the case of vapour-liquid equilibrium (VLE), the first method is an extension of Raoult's Law. For binary systems it requires typically three Antoine parameters for each component and two parameters for the activity coefficients to describe the pure-component vapour pressure and the phase equilibrium. Further parameters are needed to represent the temperature dependence of the activity coeffi­ cients, therebly allowing the heat of mixing to be calculated. The equation-of-state method, on the other hand, uses typically three parameters p , Τ andωfor each pure component and one binary interaction parameter k , which can often be taken as constant over a relatively wide temperature range. It represents the pure-component vapour pressure curve over a wider temperature range, includes the critical data p and Τ , and besides predic­ ting the phase equilibrium also describes volume, enthalpy and entropy, thus enabling the heat of mixing, Joule-Thompson effect, adiabatic compressibility in the two-phase region etc. to be calculated. c

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In v i e w o f t h e o b v i o u s a d v a n t a g e s o f u s i n g an e q u a t i o n o f s t a t e , i t i s perhaps s u r p r i s i n g t h a t t h e a c t i v i t y - c o e f f i c i e n t a p p r o a c h i s s t i l l i n w i d e s p r e a d u s e and t h e o b j e c t o f c u r r e n t r e s e a r c h . T h i s i s b e c a u s e e q u a t i o n s o f s t a t e c o n n o t be g e n e r a l l y a p p l i e d t o s y s t e m s i n w h i c h h y d r o g e n b o n d i n g o c c u r s . Such s y s t e m s r e p r e s e n t a l a r g e p r o p o r t i o n o f t h o s e o f i n d u s t r i a l i n t e r e s t and a l s o i n c l u d e most s y s t e m s e x h i b i t i n g l i q u i d - l i q u i d e q u i l i b r i u m (LLE). T h e r e a r e , h o w e v e r , some p u b l i s h e d e x a m p l e s o f e q u a t i o n s o f s t a t e b e i n g a p p l i e d t o a s s o c i a t i n g s u b s t a n c e s . Heidemann (1) used t h e R e d l i c h - K w o n g e q u a t i o n as m o d i f i e d by W i l s o n ( 2 ) t o c a l c u l a t e aqueous h y d r o c a r b o n s y s t e m s . S i m i l a r c a l c u l a t i o n s were done by Peng and R o b i n s o n (3) u s i n g t h e i r own e q u a t i o n o f s t a t e . In b o t h

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c a s e s t h e r e p r e s e n t a t i o n o f t h e o r g a n i c phase was good b u t t h e aqueous phase was i n c o r r e c t by some o r d e r s o f m a g n i t u d e . E v e l e i n , Moore and Heidemann (4) i n 1976 used S o a v e * s m o d i f i c a t i o n o f t h e RK e q u a t i o n t o c a l c u l a t e t h e s y s t e m s H^O-H^S and H^O-CCL o v e r a w i d e t e m p e r a t u r e and p r e s s u r e r a n g e ; t n e y were a b l e t o r e p r e s e n t V L E , L L E and g a s - g a s e q u i l i b r i u m b u t had t o u s e two a d j u s t a b l e binary parameters. In 1977 De S a n t i s e t a l . (5J as w e l l a s Heidemann e t a l . (6) c a l c u l a t e d t h e g a s - p h a s e f u g a c i t i e s i n t h e s y s t e m s H^O-air and HpO-^-COp by e q u a t i o n o f s t a t e ; i n t h e s e c a l c u l a t i o n s t h e l i q u i d pnase was n o t i n c l u d e d . One o f t h e a u t h o r s (7) showed i n 1978 t h a t aqueous s y s t e m s w i t h some i n e r t g a s e s and a l k a n e s a s w e l l a s H S and COp c o u l d be r e p r e s e n t e d by an e q u a t i o n o f s t a t e i f t h e m o l e c u l a r w e i g h t o f w a t e r was a r t i f i c i a l l y i n c r e a s e d . An e x t e n s i o n o f t h i s method a p p l i e d t o a l c o h o l s was f o u n d t o be o n l y p a r t i a l l y s u c c e s s f u l . G m e h l i n g e a l (8) d pola f l u i d h a l c o h o l s , k e t o n e s and w a t e Donohue's e q u a t i o n o f s t a t (9); system g m e t h a n o l and w a t e r - e t h a n o l were s u c c u s s f u l l y r e p r e s e n t e d . The p r e s e n c e o f h y d r o g e n b o n d i n g i n w a t e r i s shown by i t s anomalous t h e r m o p h y s i c a l p r o p e r t i e s and has been c o n f i r m e d by more r e c e n t methods o f i n v e s t i g a t i n g i t s s t r u c t u r e s u c h a s NMR, neutron s c a t t e r i n g , d i e l e c t r i c r e l a x a t i o n , u l t r a s o n i c a b s o r p t i o n , IR and Raman s p e c t r o s c o p y e t c . Many m o d e l s f o r t h e s t r u c t u r e o f w a t e r have been p r o p o s e d b u t l i t t l e concensus e x i s t s as t o t h e i r v a l i d i t y . F o r example, V i n o g r a d o v (14) r e p o r t s t h a t i n a c o m p a r i s o n o f t w e n t y p u b l i s h e d m o d e l s i t was f o u n d t h a t t h e p r e d i c t e d c o n c e n t r a t i o n s o f b r o k e n h y d r o g e n bonds a t 0 C v a r i e d between 2.5 % and 70 %. The m o d e l s m a i n l y f a l l i n t o two c a t e g o r i e s : a s s o c i a t i o n m o d e l s w h i c h assume t h a t water i s a m i x t u r e o f s p e c i f i e d polymer types ( e . g . Eucken's m o n o m e r - d i v e r - t e t r a m e r - o c t a m e r model (11)) and c o n t i n u u m m o d e l s w h i c h assume t h a t w a t e r i s a c o n t i n u o u s b u t m o b i l e n e t w o r k o f m o l e c u l e s l i n k e d by h y d r o g e n b o n d s , i n w h i c h i t i s m e a n i n g l e s s t o c o n s i d e r i n d i v i d u a l water polymers ( e . g . t h e models o f Bernai (12) and P o p l e (13)). The v a r i o u s e x p e r i m e n t a l methods o f i n v e s t i g a t i n g water g i v e c o n t r a d i c t o r y r e s u l t s : Vinogradov concluded that I.R. s p e c t r o s c o p y t e n d s t o s u p p o r t t h e c o n t i n u u m model w h i l e Raman s p e c t r o s c o p y i n d i c a t e s t h e p r e s e n c e o f i n d i v i d u a l p o l y m e r s ; NMR measurements s u g g e s t t h a t w a t e r p o l y m e r s o f h i g h m o l e c u l a r w e i g h t do n o t o c c u r . Thus t h e s t r u c t u r e o f w a t e r r e m a i n s u n c e r t a i n . F o r a s s o c i a t i o n m o d e l s , h o w e v e r , most a u t h o r s assume l o w c o n c e n t r a t i o n s o f monomers i n l i q u i d w a t e r a t 0 C . T h e r e a r e no f i r m i n d i c a t i o n s a s t o t h e n a t u r e and c o n c e n t r a t i o n s o f t h e h i g h e r polymers present i n the l i q u i d phase; v i r i a l - c o e f f i c i e n t measurements s u g g e s t , h o w e v e r , t h a t t h e v a p o u r phase i s p r e d o m i n a n t l y monomeric. 2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

21.

BAUMGAERTNER

ET

AL.

411

Systems with Low Mutual Solubility

Scope The o b j e c t o f t h i s work was t o e x t e n d t h e f i e l d o f a p p l i c a t i o n o f t h e e q u a t i o n - o f - s t a t e m e t h o d . The method was a p p l i e d t o aqueous s y s t e m s i n c o n j u n c t i o n w i t h a model t h a t t r e a t s w a t e r as a m i x t u r e o f a l i m i t e d number o f p o l y m e r s , an a p p r o a c h s i m i l a r t o t h a t p r e v i o u s l y adopted f o r t h e c a r b o x y l i c a c i d s ( 2 ) . A s s o c i a t i o n i s c a l c u l a t e d by t h e l a w o f mass a c t i o n ; c o r r e c t i o n s f o r n o n - i d e a l b e h a v i o u r a r e made by means t h e e q u a t i o n o f s t a t e . A m a j o r p r o b l e m o f t h e method i s t h e l a r g e number o f p a r a m e t e r s needed t o d e s c r i b e t h e p r o p e r t i e s and c o n c e n t r a t i o n s o f t h e p o l y m e r s t o g e t h e r w i t h t h e i r i n t e r a c t i o n w i t h m o l e c u l e s o f o t h e r s u b s t a n c e s . The Mecke-Kemptner model (1_5) ( a l s o known a s t h e K r e t s c h m e r - W i e b e model ( 1 6 ) and e x p e r i m e n t a l v a l u e s f o r hydrogen-bond e n e r g i e s were usëcT f o r g u i d a n c e i n f i x i n g t h e s e p a r a m e t e r s . Method o f C a l c u l a t i o n state

The e q u a t i o n o f s t a t e . ( 1 7 ) was u s e d :

P

=

!I

V - b

V

2

A recently

+ (1 +3ω)

published equation of

bV - 3 * > b

m 2

where W i s P i t z e r ' s a c e n t r i c f a c t o r and a and b a t t h e c r i t i c a l p o i n t a r e f u n c t i o n s o f t h e c r i t i c a l p r o p e r t i e s Ρ and Τ . The t e m p e r a t u r e dependence o f t h e p a r a m e t e r a i s s i m i l a r t o t h a t g i v e n by S o a v e ' s e x p r e s s i o n ( 1 8 ) , and b i s c o n s t a n t . Thus a p u r e component i s c h a r a c t e r i s e d by t h e t h r e e q u a n t i t i e s Ρ , Τ and uO. The f o l l o w i n g m i x i n g r u l e s were u s e d : a

=

f

f

V j

b =éy.b.

a

i j

w

i

t

h

a

i j = (

X

· ij) k

V^i^J

1

j

(2)

6 V = £ y . ^ ^ ~ ^1 1

where y . a r e t h e v a p o u r - p h a s e mole f r a c t i o n s . A n a l o g o u s e x p r e s r s i o n s f o r t h e l i q u i d phase were used w i t h x . s u b s t i t u t e d f o r y . . k . . i s a n i n t e r a c t i o n p a r a m e t e r t o be f i t t e d t o t h e e q u i l i b rium Compositions o f a b i n a r y system. E q n . ( 1 ) has t h e a d v a n t a g e o v e r o t h e r commonly used e q u a t i o n s o f t h e v a n d e r W a a l ' s t y p e o f g i v i n g an i m p r o v e d r e p r e s e n t a t i o n o f t h e v a p o u r p r e s s u r e and m o l a r l i q u i d v o l u m e . A l s o , l i k e a l l c u b i c e q u a t i o n s o f s t a t e , E q n . (1) r e q u i r e s r e l a t i v e l y l i t t l e computing time f o r c a l c u l a t i n g thermophysical properties.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

418

APPLICATIONS

Physical equilibrium. When two phases a r e i n e q u i l i b r i u m , t h e c h e m i c a l p o t e n t i a l s A . f o r each component i must be e q u a l i n e a c h p h a s e . The K - f a c t o r s Κ. = yj/x.- c a n be o b t a i n e d f r o m t h i s c o n d i t i o n , using the r e l a t i o n s h i p : Vi

(3)

where V . i s t h e p a r t i a l m o l a r volume o f component i , w h i c h c a n be c a l c u l a t e d by t h e e q u a t i o n o f s t a t e . S e v e r a l p a p e r s ( e . g . 1 9 , 2 0 ) show f o r s i m i l a r e q u a t i o n s o f s t a t e how t h e e x p r e s s i o n f o r K. can be d e r i v e d . Chemical e q u i l i b r i u m . The p o l y m e r c o n c e n t r a t i o n s i n t h e i d e a l g a s phase o f w a t e r a r e r e l a t e d t o t h e a s s o c i a t i o n e q u i l i b ­ rium constants according t o t h e e x p r e s s i o n :

k

k

o

=

! i

pi

(4)

r

-^-Tyr Y

P

l

where ρ i s t h e p r e s s u r e and y . t h e m o l e f r a c t i o n o f component i , w i t h y , r e f e r r i n g t o t h e monomer. Component i i s d e f i n e d a s b e i n g f o r m e d by t h e a s s o c i a t i o n o f n . monomers. The t e m p e r a t u r e d e p e n ­ d e n c e o f t h e e q u i l i b r i u m constant k . i s g i v e n by

pi "

R

T

where t h e a s s o c i a t i o n e n t h a l p y 4 H and e n t r o p y 4 S are r e ­ g a r d e d a s i n d e p e n d e n t o f t e m p é r a t u r e . C r o s s - d i m e r s may a l s o o c c u r between t h e w a t e r m o l e c u l e s and t h o s e o f t h e non-aqueous component f o r w h i c h t h e e x p r e s s i o n c o r r e s p o n d i n g t o E q n . ( 4 ) i s

yO p

=

cross

y

cross y ! y

i

n

(6) e

r

t

Ρ

The c o m p o s i t i o n s i n t h e g a s phase f o l l o w f r o m t h e c o n t r a i n t f

^1

+

^inert

+

^cross

=

1

7

where o n l y one i n e r t component and one c r o s s - d i m e r a r e c o n s i d e r e d . I f t h e e q u i l i b r i u m c o n s t a n t s and y , are s p e c i f i e d , a l l the c o n c e n t r a t i o n s i n E q n . ( 7 ) may be e x p r e s s e d i n t e r m s o f y , u s i n g E q n s . ( 4 ) and ( 6 ) . E q n . ( 7 ) i s t h e n s o l v e d f o r y u s i n g N e w t o n ' s n e r t

1

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

21.

BAUMGAERTNER

ET

AL.

Systems with Low Mutual Solubility

419

m e t h o d . Once y^ i s f o u n d , a l l o t h e r c o m p o s i t i o n s f o l l o w f r o m E q n . (4) and E q n . ( 6 ) . C o n c e n t r a t i o n s u n d e r n o n - i d e a l c o n d i t i o n s s u c h a s i n t h e l i q u i d phase o r i n a c o m p r e s s e d g a s phase a r e c a l c u l a t e d u s i n g e x p r e s s i o n s o f t h e t y p e / V . d p w h i c h , as i s d e s c r i b e d e l s e w h e r e ( 2 0 ) , c a n be e v a l u a t e d by means o f t h e e q u a ­ tion of state. Combined p h y s i c a l and c h e m i c a l e q u i l i b r i u m . V a p o u r - l i q u i d equilibria were d e t e r m i n e d i n t h i s work by p e r f o r m i n g d e w - p o i n t c a l c u l a t i o n s . The p r o c e d u r e i s : (1) Choose an a r b i t r a r y v a l u e o f t e m p e r a t u r e Τ and i n e r t concentration (2) Estimate a dew-point pressure Ρ (3) C a l c u l a t e the a s s o c i a t i o n e q u i l i b r i u m i n t h e vapour phase a t Τ and P, as p r e v i o u s l y o u t l i n e d . (4) From t h e c o n d i t i o n s o f p h y s i c a l e q u i l i b r i u m , c a l c u l a t e the K-factors (5) C a l c u l a t e t h e y ι κ. sum S = r χ . . M o d i f y Ρ u s i n g a Newton r o u t i n e and r e p e a t s t e p s ( 3 ) t o (5) u n t i l S = 1. Because o f t h e p h y s i c a l e q u i l i b r i u m , t h e a s s o c i a t i o n i n t h e l i q u i d phase i s d e t e r m i n d e d by t h a t i n t h e v a p o u r p h a s e . T h e r e f o r e no a d d i t i o n a l a s s o c i a t i o n c o n s t a n t s a r e r e q u i r e d f o r t h e l i q u i d p h a s e . In t h e c a s e o f l i q u i d - l i q u i d e q u i l i b r i u m c a l c u l a t i o n s , an a n a l o g o u s p r o c e d u r e was a d o p t e d u s i n g c o n v e r g e n c e t e s t ( 5 ) , w i t h y . r e f e r r i n g t o t h e second l i q u i d phase. 1

D e t e r m i n a t i o n o f the Parameters

o f P u r e Water

The m o d e l s t e s t e d i n more d e t a i l i n t h i s work were t h e 1-2-3, 1-2-3-4, 1-2-4-8 and 1-2-4-8-12 m o d e l s , where t h e numbers r e f e r t o t h e t y p e s o f p o l y m e r s p r o p o s e d . The 1-2-4-8-12 model gave t h e b e s t r e s u l t s , t h e p a r a m e t e r s o f w h i c h a r e shown i n T a b l e 1. The i n t e r a c t i o n p a r a m e t e r s k . . o f E q n . ( 2 ) between t h e d i f f e r e n t w a t e r p o l y m e r s were a l l s e t ^ o z e r o . The p a r a m e t e r s were o p t i m i s e d t o r e p r e s e n t t h e c r i t i c a l d a t a ρ and Τ , t h e v a p o u r p r e s s u r e f r o m room t e m p e r a t u r e up t o t h e c r i t i c a l p o i n t and t h e s a t u r a t e d v a p o u r and l i q u i d m o l a r v o l u m e s . A c c o u n t was a l s o t a k e n o f t h e r e p r e s e n t a t i o n o f t h e b i n a r y s y s t e m s r L O - C H . t o C . H . Q . I n i t i a l l y t h e method o f P o w e l l (22) was used b u t l a t e r t h e ' S i m p l e x M e t h o d ' o f N e l d e r and Mead (Z5) was f o u n d t o be more r e l i a b l e f o r t h i s p r o b l e m . A c o m p a r i s o n o f c a l c u l a t e d and e x p e r i m e n t a l v a l u e s o f v a p o u r p r e s s u r e and s a t u r a t e d l i q u i d and v a p o u r v o l u m e s a t v a r i o u s t e m ­ p e r a t u r e s i s shown i n T a b l e 2 . The w a t e r c o m p o s i t i o n i n t h e l i q u i d phase and t h e c o r r e s p o n d i n g d e g r e e o f a s s o c i a t i o n , DA = x , + 2 x + 4 x ^ + 8 x . + 1 2 χ , a r e g i v e n a t v a r i o u s t e m p e r a ­ t u r e s Tn T a b f e 3 . E x c e p t i n t h e c r i t i c a l r e g i o n , t h e v a p o u r c o m p o ­ s i t i o n i s v i r t u a l l y c o m p l e t e l y monomer. F o r e x a m p l e , a t room t e m ­ p e r a t u r e , t h e monomer and d i m e r c o n c e n t r a t i o n s a r e y , = 0 . 9 9 8 8 and y = 0 . 0 0 1 2 r e s p e c t i v e l y . A t 200 C t h e v a l u e s a r e y = 0.9814 2

2

ς

1

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

420

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

Table

APPLICATIONS

1

P a r a m e t e r s f o r t h e Assumed S p e c i e s i n Water Species of u/atpv w

a

t

e

r

Monomer Dimer Tetramer Octamer Dodecamer

Τ

P

Ί
6

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

BAUMGAERTNER ET AL.

Figure 3.

Systems with Low

Mutual Solubility

425

VLE in the system H 0-propane at 427.6°K, k, = 0.55; experimental data: (%) (25); (O) (21); (O) fitting point; ( '-) calculated 2

6

Figure 4. VLE and LLE in the system H 0-n-butane at 344.3°K, k = 0.50; experimental data from Ref. 26; (Ο) fitting point; ( ) calculated 2

1>6

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

426

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

Figure 5. VLE and LLE in the system H 0-n-butane at 377.6°K, k = 0.50; experimental data from Ref. 26; (O) fitting point; ( ) calculated; (---) calculated with water taken as monomer 2

Figure 6.

1>6

VLE in the system H 0-n-butane at 477.6°K, k = 0.37; experimental data from Ref. 26; (O)fittingpoint; ( ) calculated 2

1

a l s o the q u a n t i t y Ζ i s d e f i n e d t o be Ζ = Y m. |z. Ι = 2 Y m ζ . h ι ι c c 1 c 1

1

(12)

L

The mixed e l e c t r o l y t e terms i n Θ and ψ account f o r d i f f e r ­ ences among i n t e r a c t i o n s between ions of l i k e s i g n . The d e f i n i n g equations f o r the second v i r i a l c o e f f i c i e n t s , Θ.., a r e given by Equations (13), 1 J

°ij

0

i 3

=

e

=

ij

e

+

+

+

i J

E

0

i 3

(

I

l

E

e

i j

(

I

)

( 1 3 a )

)

( 1 3 b )

θ!. = % ( ! )

(13c)

θ.., a s i n g l e parameter f o r each p a i r o f anions or each p a i r o f c a i i o n s , i s the o n l y a d j u s t a b l e parameter i n Equations (13). The terms 6 i j ( I ) and θ ^ ( I ) account f o r the e l e c t r o s t a t i c e f f e c t s o f unsymmetrical mixing. Equations f o r c a l c u l a t i n g these terms were d e r i v e d by P i t z e r (39); t h i s e f f e c t was d i s c o v e r e d by Friedman (6) . The important f e a t u r e s of Θ _ ( Ι ) and θ ^ (I) a r e that they depend only on the charges of the *'ions i and j and the t o t a l i o n i c s t r e n g t h . They do not c o n s t i t u t e a d d i t i o n a l para­ m e t e r i z a t i o n . 0£j(I) and θ ^ ( I ) a r e zero when the ions i and j are of the same charge. Although these terms a r e important f o r 1-3 m i x t u r e s , such as H C l - A l C l g , they d i d not appear t o be r e a l l y needed f o r simple 1-2 mixtures. However, Harvie and Weare (37) have found these s p e c i a l e l e c t r o s t a t i c terms t o be important f o r the CaSO^-NaCl system and some more complex mixtures i n v o l v i n g s i n g l y and doubly charged i o n s . E

Ε

Ε

Ε

1

E

Ε

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

23.

PITZER

463

Thermodynamics of Aqueous Electrolytes

Table I Parameters

M

f o r v i r i a l c o e f f i c i e n t equations a t 25°C ( 0 )

R MX

X

( 2 )

3

β MX

C* MX L

3

MX

Na

Cl

.07650

.2264

—

.00127

Na

SO. 4

.01958

1.1130

—

.00497

K

Cl

.04835

.2122

—

-.00084

K

SO, 4

.04995

.7793

—

Mg

Cl

.3523

Mg

SO, 4

.22100

3.3430

-37.25

.025

Ca

Cl

.31590

1.6140

—

-.00034

Ca

S 0

.20000

2.650

4

0

—

-57.70

Table I I Parameters f o r mixed e l e c t r o l y t e s w i t h the v i r i a l c o e f f i c i e n t equations (at 25°C) θ. .

Na

K

Na

Mg

Na

Ca

Κ

Mg

Κ

Cl SO, 4 CI SO, 4 CI SO, 4

φ...

-.012

-.0018 -.010

.07

-.012 -.015

.07

-.014 -.023

CI SO, 4

.0

-.022 -.048

Ca

CI SO, 4

.032

-.025 0

Mg

Ca

CI SO, 4

.007

-.012 .05

CI

SO

Na Κ Mg Ca

.02

.0014 0 -.004 0

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I t would burden t h i s paper e x c e s s i v e l y t o l i s t the parameters for a l l known e l e c t r o l y t e s , even a t room temperature. As examples g i v i n g the p a t t e r n of magnitudes as w e l l as values f o r w i d e l y appearing s a l t s , the values f o r the Na-K-Mg-Ca-Cl-SO^-^O system are l i s t e d i n Tables I and I I . Most o f these a r e taken from P i t z e r and Mayorga (23) o r P i t z e r and Kim (11) but a few were r e v i s e d i n l a t e r work i n c l u d i n g that o f Harvie and Weare (37). I t i s apparent that the p u r e - e l e c t r o l y t e parameters i n Table I a r e much l a r g e r than those f o r mixing o f ions o f the same s i g n i n Table I I . A l s o the second v i r i a l c o e f f i c i e n t s are much l a r g e r than the t h i r d v i r i a l c o e f f i c i e n t s i n Table I . Conclusions I t i s shown that the p r o p e r t i e s of f u l l y i o n i z e d aqueous e l e c t r o l y t e systems ca t i o n s over wide ranges tems f o r which data are a v a i l a b l e over the f u l l range to fused s a l t . A simple equation commonly used f o r n o n e l e c t r o l y t e s f i t s the measured vapor pressure of water reasonably w e l l and f u r t h e r refinements are c l e a r l y p o s s i b l e . Over the somewhat more l i m i t e d composition range up to s a t u r a t i o n of t y p i c a l s a l t s such as NaCl, the equations r e p r e s e n t i n g thermodynamic p r o p e r t i e s w i t h a DebyeHiickel term p l u s second and t h i r d v i r i a l c o e f f i c i e n t s are very s u c c e s s f u l and these c o e f f i c i e n t s are known f o r n e a r l y 300 e l e c t r o l y t e s a t room temperature. These same equations e f f e c t i v e l y p r e d i c t the p r o p e r t i e s of mixed e l e c t r o l y t e s . A s t r i n g e n t t e s t i s o f f e r e d by the c a l c u l a t i o n of the s o l u b i l i t y r e l a t i o n s h i p s of the system Na-K-Mg-Ca-Cl-SO^-^O and the c a l c u l a t e d r e s u l t s of Harvie and Weare show e x c e l l e n t agreement w i t h experiment. Acknowled gemen t s This research was supported by the O f f i c e of B a s i c Energy Sciences, U. S. Department of Energy, under Contract No. W-7405Eng-48. I thank Dr. John H. Weare f o r sending me h i s r e s u l t s i n advance of p u b l i c a t i o n . References

1. Debye, P. and Hückel, Ε., Physik. Z. (1923) 24, 185, 334; (1924) 25, 97. 2. Harned, H. S. and Owen, Β. Β., "The Physical Chemistry of Electrolyte Solutions," 3rd Ed. Reinhold Publishing Co., New York (1958). 3. Robinson, R. A. and Stokes, R. Η., "Electrolyte Solutions," Butterworths, London, 1955, revised 1959.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

23. PITZER Thermodynamics of Aqueous Electrolytes 465

4. Card, D. N. and Valleau, J. P., J. Chem. Phys. (1970) 52, 6232. 5. Pitzer, K. S., Accounts of Chemical Research, (1977) 10, 371. 6. Friedman, H. L. "Ionic Solution Theory," Interscience (1962). 7. Anderson, H. C., "Improvements upon the Debye-Hückel Theory of Ionic Solutions," in "Modern Aspects of Electrochemistry," No. 11, Β. E. Conway and J. O'M. Bockris, Eds., Plenum Press, New York, 1975. 8. Ramanathan, P. S. and Friedman, H. L., J. Chem. Phys. (1971) 54, 1086. 9. Bronsted, J. N., Kgl Dan Vidensk Selsk. Mat Fys Medd. (1929) 4, (4); J 2898. 10. Guggenheim, Ε. Α., Phil. Mag. [7] (1935) 19, 588; also Guggenheim, E. A. and Turgeon, J. C., Trans. Faraday Soc., (1955) 51, 747. 11. Pitzer, K. S. and Kim, J. J., J. Am. Chem. Soc. (1974) 96, 5701. 12. Trudelle, M-C, Abraham, M. and Sangster, J., Can. J. Chem. (1977) 55, 1713. 13. Tripp, T. B. and Braunstein, J., J. Am. Chem. Soc. (1954) 73, 1984. 14. Braunstein, H. and Braunstein, J., J. Chem. Thermodynamics (1971) 3, 419. 15. van Laar, J. J., Z. physik. Chem. (1906) 72; (1910) 723. 16. Prausnitz, J. Μ., "Molecular Thermodynamics of Fluid-Phase Equilibria," Prentice-Hall, Inc., Englewood Cliffs, NJ (1969). 17. Pitzer, K. S., in preparation for publication. 18. McMillan, W. G. and Mayer, J. E., J. Chem. Phys., (1945) 22, 276. 19. Mayer, J. E., J. Chem. Phys. (1950) 18, 1426; see also Reference 6. 20. Pitzer, K. S., J. Phys. Chem. (1973) 77, 268. 21. Scatchard, G., J. Am. Chem. Soc. (1968) 90, 3124.

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22. Scatchard, G., Rush, R. M. and Johnson, J. S., J. Phys. Chem. (1970) 74, 3786. 23. Pitzer, K. S. and Mayorga, G., J. Phys. Chem. (1973) 77, 2300; J. Solution Chem. (1974) 3, 539. 24. Pitzer, K. S. and Silvester, L. F., J. Solution Chem., (1976) 5, 269. 25. Pitzer, K. S., Roy, R. Ν., and Silvester, L. F., J. Am. Chem. Soc. (1977) 99, 4930. 26. Pitzer, K. S., Peterson, J. R., and Silvester, L. F., J. Solution Chem. (1978) 7, 45. 27. Pitzer, K. S. and Silvester L F. J Phys Chem (1978) 82 1239. 28. Downes, C. J. and Pitzer, K. S., J. Solution Chem. (1976) 5, 389. 29. Silvester, L. F. and Pitzer, K. S., J. Solution Chem. (1978) 7, 327. 30. Liu, C. and Lindsay, W. T., J. Solution Chem. (1972) 1, 45; J. Phys. Chem. (1970) 74, 341. 31. Puchkow, L. V., Styazhkin, P. S., and Federov, Μ. Κ., J. Appl. Chem. (USSR) (1977) 50, 1004; Atonov, Ν. Α., Gilyarov, V. Ν., Zarembo, V. I., and Federov, Μ. Κ., ibid, (1976) 49, 120; and other papers there cited. 32. Silvester, L. F. and Pitzer, K. S., J. Phys. Chem. (1977) 81, 1822. 33. Pitzer, K. S., Bradley, D. J., Rogers, P. S. Ζ., and Peiper, J. C , paper at Honolulu meeting of the A.C.S. (1979), to be published. 34. Bradley, D. J. and Pitzer, K. S., J. Phys. Chem., (1979) 83, 1599. 35. Holmes, H. F., Baes, C. F., Jr., and Mesmer, R. Ε., J. Chem. Thermo. (1978) 10, 983. 36. For example, Marshall, W. L., J. Phys. Chem. (1967) 71, 3584. 38. Braitsch, O., "Salt deposits: their origin and composition," Springer Verlag (1971). 39. Pitzer, K. S., J. Solution Chem. (1975) 4, 249. RECEIVED

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

24 Current Status of Experimental Knowledge of Thermodynamic Properties of Aqueous Solutions RANDOLPH C. WILHOIT Thermodynamics Research Center, Texas A&M University, College Station, T X 77843

The current state f knowledg f solution i th result of all that has have formed a major part of modern science since its beginning. Theories of aqueous electrolytes have played a major role in the history of chemistry. We can recognize four main periods in the history of the study of aqueous solutions. Each period starts with one or more basic discoveries or advances in theoretical understanding. The first period, from about 1800 to 1890, was triggered by the discovery of the electrolysis of water followed by the investi­ gation of other electrolysis reactions and electrochemical cells. Developments during this period are associated with names such as Davy, Faraday, Gay-Lussac, Hittorf, Ostwald, and Kohlrausch. The distinction between electrolytes and nonelectrolytes was made, the laws of electrolysis were quantitatively formulated, the electrical conductivity of electrolyte solutions was studied, and the concept of independent ions in solutions was proposed. The second p e r i o d , from 1890 t o around 1920, was charact e r i z e d by the idea o f i o n i c d i s s o c i a t i o n and the e q u i l i b r i u m between n e u t r a l and i o n i c s p e c i e s . This model was used by Arrhenius t o account f o r the concentration dependence o f e l e c t r i c a l c o n d u c t i v i t y and c e r t a i n other p r o p e r t i e s o f aqueous e l e c t r o l y t e s . I t was r e i n f o r c e d by the research o f V a n t Hoff on the c o l l i g a t i v e p r o p e r t i e s o f s o l u t i o n s . However, the i n a b i l i t y o f i o n i c d i s s o c i a t i o n t o e x p l a i n q u a n t i t a t i v e l y the p r o p e r t i e s o f e l e c t r o l y t e s o l u t i o n s was soon recognized. The theory proposed by Debye and Huckel dominated the study of aqueous e l e c t r o l y t e s from around 1920 t o near the end o f the 1950's. The Debye-Huckel theory was based on a model o f e l e c t r o l y t e s o l u t i o n s i n which the ions were t r e a t e d as p o i n t charges ( l a t e r as charged spheres), and the solvent was considered t o be a homogeneous d i e l e c t r i c . Deviations from i d e a l behaviors were assumed t o be due only t o the long range e l e c t r o s t a t i c forces between i o n s . Refinements t o i n c l u d e i o n - i o n p a i r i n g and i o n f

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h y d r a t i o n were e v e n t u a l l y added. Most o f the experimental work by p h y s i c a l chemists d u r i n g t h i s p e r i o d was done to d i s c o v e r the l i m i t i n g c o n c e n t r a t i o n dependence o f v a r i o u s thermodynamic and t r a n s p o r t p r o p e r t i e s at i n f i n i t e d i l u t i o n s and to compare such r e s u l t s to the p r e d i c t i o n s o f the Debye-Huckel theory. I t was found t h a t the Debye-Huckel theory does p r e d i c t the c o r r e c t l i m i t i n g laws f o r a l l p r o p e r t i e s which have been s u f f i c i e n t l y s t u d i e d . However, f o r some p r o p e r t i e s ; i . e . , p a r t i a l molal enthalpy, the c o n c e n t r a t i o n must be very low. The f a i l u r e o f the Debye-Huckel theory and i t s v a r i o u s m o d i f i c a t i o n s to account f o r p r o p e r t i e s o f s o l u t i o n s more concentrated than a few tenths molal l e d to a stalemate i n f u r t h e r understanding o f such s o l u t i o n s during the 1940 s and the 1950 s. The prevalence o f water i n many i n d u s t r i a l processes has l e d to the accumulation o f a l a r g e body o f experimental data on aqueous s o l u t i o n s o f bot I t i s commonly recognize h i g h l y n o n - i d e a l , but u n t i l recent years, no t h e o r e t i c a l ex p l a n a t i o n was a v a i l a b l e f o r aqueous s o l u t i o n s o f n o n e l e c t r o l y t e s . The past f i f t e e n years or so have seen a decided resurgence i n t h e o r i e s o f aqueous s o l u t i o n s . Although these t h e o r i e s are not the r e s u l t o f any s i n g l e event, the main components o f t h i s f i n a l and f o u r t h p e r i o d can be recognized. The newer ideas i n c o r p o r a t e s p e c i f i c i n t e r a c t i o n s between water molecules and between water and s o l u t e molecules. They a l s o make extensive use o f the accumulated knowledge on the i n t e r m o l e c u l a r s t r u c t u r e and order o f l i q u i d water and o f the geometrical c o n s t r a i n t s which they imply. The new developments have been p a r t l y i n s p i r e d by the i n v e s t i g a t i o n o f biochemists and b i o p h y s i c i s t s on the e f f e c t o f water and aqueous s o l u t e s on the t e r t i a r y s t r u c t u r e o f b i o l o g i c a l macromolecules. Terms such as "hydrophobic bonding" and " s t r u c t u r e making" and " s t r u c t u r e b r e a k i n g " s o l u t e s o r i g i n a t e from these s t u d i e s . The s p e c t a c u l a r r i s e i n the study o f molten s a l t s d u r i n g the past twenty years has a l s o had an e f f e c t . F i n a l l y , the prevalence of computers i n recent years has made the use o f more r e a l i s t i c , and thus more complicated, models p o s s i b l e . Computer simul a t i o n s o f a l l kinds o f f l u i d s have given important c l u e s f o r the behavior o f s o l u t e s i n water. I t i s now apparent t h a t the new t h e o r i e s not o n l y are beginning to provide an understanding of moderately concentrated aqueous s o l u t i o n s o f e l e c t r o l y t e s but a l s o o f n o n e l e c t r o l y t e s and e l e c t r o l y t e - n o n e l e c t r o l y t e s o l u t i o n s as w e l l . Figure 1 l i s t s the major i n d u s t r i a l processes t h a t use thermodynamic data and the k i n d o f data t h a t are r e l e v a n t . The design and use o f d i s t i l l a t i o n columns are the l a r g e s t consumers o f thermodynamic data. The feed stream to most i n d u s t r i a l c o l umns contains a t l e a s t s e v e r a l components. The p r e d i c a t i o n o f the o p e r a t i n g c h a r a c t e r i s t i c s o f such columns r e q u i r e s complicated c a l c u l a t i o n s , and much computer software has been w r i t t e n f

f

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WILHOIT

Thermodynamic Properties of Aqueous Solutions

I. Separation Processes A. Distillation Vapor-liquid equilibrium compositions, Κ-values, activity coeff., etc., azeotrope temperature and composition, enthalpy and heat capacity, heats of vaporization B. Solvent extraction Activity coefficients, distribution coefficients, equilibrium constants for reactions C. Ion-exchange Activity ceofficients, surface and absorption effects, equilibrium constants of reactions D. Crystallization from Phase diagrams, solubilit E. Osmosis Activity of solvent, volumetric data, properties at high pressure II. Heat and Mass Transport Enthalpy and heat capacity, volumetric properties, surface tension, transport properties III. Water Treatment Equilibrium constants for many reactions among electrolytes and non-electro­ lytes, and solubility data under a wide range of conditions A. Boiler feed B. Waste water C. Sea water IV. Electrochemical Processes Thermochemical data, oxidation-reduction potentials, activity coefficients, surface properties A. Electrolysis B. Electroplating C. Storage cells and fuel cells D. Corrosion V. Chemical Manufacturing Thermochemical data VI. Metallurgy A. Hydrometallurgy Solubility, vapor pressure, distribution coefficient, reaction equilibria B. Electrometallurgy Electrode potentials, equilibrium constants Figure 1.

Industrial processes that use thermodynamic data

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f o r t h i s purpose. To separate components which have s i m i l a r b o i l i n g p o i n t s o r which form azeotropes, i t i s becoming i n c r e a s i n g l y common t o feed a d d i t i o n a l components t o the column. I f the a d d i t i o n a l substance i s v o l a t i l e and migrates p r i m a r i l y t o the vapor stream, the process i s c a l l e d a z e o t r o p i c d i s t i l l a t i o n . I f the a d d i t i o n a l substance stays i n the r e s i d u e , the process i s c a l l e d e x t r a c t i v e d i s t i l l a t i o n o f aqueous s o l u t i o n s . The sepa r a t i o n s o f v a r i o u s a l c o h o l s , ethylene g l y c o l , a c e t i c a c i d , acetone, and n i t r i c a c i d from water i s an example i n which ext r a c t i v e d i s t i l l a t i o n has been used o r proposed. References (108) and (126) d e s c r i b e processes. Solvent e x t r a c t i o n i s a major i n d u s t r i a l technique. The usual o b j e c t i v e i s to s e l e c t i v e l y remove one o r more s o l u t e s from a complex mixture. S e l e c t i v i t y u s u a l l y depends on s t r o n g s p e c i f i c s o l v e n t - s o l u t e i n t e r a c t i o n s o r on the formation o f complexes between ions ligands extractio systems are l i k e l y to to e x h i b i t l a r g e d e v i a t i o n s from i d e a l i t y . The design o f l i q u i d e x t r a c t i o n processes may r e q u i r e many kinds o f data. References (31, 32, 55, 61, 81, and 118) are concerned s p e c i f i c a l l y w i t h solvent extraction. The treatment o f b o i l e r feed water i s a s p e c i a l i z e d t o p i c which depends s t r o n g l y on e m p i r i c a l and p r o p r i e t a r y methods. The problem o f removing o b j e c t i o n a b l e m a t e r i a l from waste water streams has become acute i n recent years. Petroleum r e f i n e r i e s , coal p r o c e s s i n g p l a n t s , and many chemical manufacturing operat i o n s produce l a r g e volumes o f waste water. Because o f government r e g u l a t i o n s and the i n c r e a s e d need f o r energy e f f i c i e n c y , p r a c t i c e s used i n the past may no longer be acceptable. Several aspects o f t h i s problem have a l r e a d y been discussed i n t h i s symposium. The Thermodynamic p r o p e r t i e s o f sea water have been e x t e n s i v e l y s t u d i e d during the past decade. This has occurred because o f t h e i r a p p l i c a t i o n s to oceanography and because sea water i s used i n some i n d u s t r i a l o p e r a t i o n s . References (21, 37, 42, 48, 49, and 100) describe sea water. References (37, 45, 48, 64, 108, 117, 118, 126, and 133) emphasize v a r i o u s i n d u s t r i a l a p p l i c a t i o n s f o r the thermodynamics o f aqueous s o l u t i o n s . References (19^, 45_, 48, 64, 58, 99^, 119, 120, 121, 12^, 141, and 142) r e p o r t data a t temperatures above the normal b o i l i n g p o i n t . T h e o r e t i c a l aspects o f aqueous s o l u t i o n s are being d i s cussed by o t h e r speakers a t t h i s s e s s i o n . Kruss (112) has w r i t ten a u s e f u l i n t r o d u c t i o n t o both t h e o r e t i c a l and experimental s t u d i e s o f s o l u t i o n s . A d d i t i o n a l reviews o f modern theory may be found i n references (76, 813, S2_, 87_, 90-101, 111, 114, 116, 119, 120, and 121) . By an extension o f the Debye-Huckel equat i o n , P i t z e r and h i s co-workers (129, 130, 131, 134, 135, 141, 143, and 144) have developed a popular mathematical model o f the thermodynamic p r o p e r t i e s o f aqueous e l e c t r o l y t e s o l u t i o n s . However, i t i s my i n t e n t i o n t o provide a guide f o r the r a p i d l o c a t i o n o f numerical values o f thermodynamic p r o p e r t i e s o f aqueous

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WILHOIT

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s o l u t i o n s o f importance to i n d u s t r y . For data on aqueous s o l u t i o n s , the engineer must s t i l l r e l y p r i m a r i l y , e i t h e r d i r e c t l y o r i n d i r e c t l y , on experimental measurements. Figure 2 summarizes the p r i n c i p a l techniques f o r measuring thermodynamic p r o p e r t i e s . I t i s important to note t h a t none o f these are new. As most o f these techniques have been used r e g u l a r l y f o r n e a r l y e i g h t y years and some f o r n e a r l y one hundred years, each one i d e n t i f i e d i n Figure 2 has a long h i s t o r y o f development and refinement. A l l have p a r t i c i p a t e d i n the general improvement i n accuracy and s o p h i s t i c a t i o n i n l a b o r a t o r y instruments over the years. S h i f t s i n the r e l a t i v e amounts o f usage o f d i f f e r e n t techniques have occurred d u r i n g t h i s p e r i o d . Many o f these procedures are d e s c r i b e d i n reference (136). The measurement o f the composition o f phases i n mutual e q u i l i b r i u m has many d i r e c t a p p l i c a t i o n s . However, i t i s common to reduce such data t i n c l u d e excess Gibbs energ r e l a t i v e to some standard s t a t e , a c t i v i t i e s , a c t i v i t y c o e f f i c i e n t s , o r Gibbs energy o f t r a n s f e r from one s o l v e n t t o another. These c a l c u l a t i o n s depend on the f a c t t h a t the chemical p o t e n t i a l o f any component i s the same i n a l l phases i n mutual e q u i l i b r i u m . Phase e q u i l i b r i u m measurements a t d i f f e r e n t temperatures a l l o w the c a l c u l a t i o n o f the corresponding enthalpy, entropy, and heat capacity. Most data on v a p o r - l i q u i d e q u i l i b r i a i n which a t l e a s t two components are v o l a t i l e , have been obtained by the use o f some k i n d o f r e c i r c u l a t i n g e b u l l i o m e t e r . The l i q u i d mixture i s b o i l e d i n a c l o s e d system u n t i l a steady s t a t e i s reached. Then the temperature i s noted and samples o f the l i q u i d and vapor phases are withdrawn f o r a n a l y s i s . The c o n s t r a i n t s o f mass balance and of the Gibbs-Duhem equation impose f u n c t i o n a l dependence among the chemical p o t e n t i a l s o f the components o f the system. Thus much e f f o r t has been devoted to d e v i s i n g methods o f t e s t i n g data obtained by e b u l l i o m e t e r s f o r thermodynamic c o n s i s t e n c y . I t i s p o s s i b l e t o c a l c u l a t e the chemical p o t e n t i a l s o f the components i n a system c o n s i s t i n g o f l i q u i d and vapor phases a t e q u i l i b r i u m from o b s e r v a t i o n s on o n l y the t o t a l vapor pressure as a f u n c t i o n o f composition. This technique avoids the thermodynamic c o n s i s tency problem, as w e l l as many other d i f f i c u l t i e s , w i t h the use o f e b u l l i o m e t e r s . Vapor pressures o f mixtures are u s u a l l y measured by a s t a t i c technique i n a sealed system. The c a l c u l a t i o n o f chemical p o t e n t i a l s from t o t a l vapor pressure data i s much more d i f f i c u l t than i t i s from e b u l l i o m e t r i c data, but the ready a v a i l a b i l i t y o f computer algorithms f o r t h i s c a l c u l a t i o n has e l i m i n a t e d t h i s disadvantage f o r b i n a r y s o l u t i o n s . The i s o p i e s t i c method has been used f r e q u e n t l y to measure the vapor pressure o f aqueous s o l u t i o n s o f n o n v o l a t i l e s o l u t e s . In t h i s technique, two o r more s o l u t i o n s are p l a c e d i n separate cups and s t o r e d i n a sealed c o n t a i n e r . A l l the cups are open to a common vapor space. A i r i s removed from the c o n t a i n e r and

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Phase Equilibria - Gibbs Energy and Related Properties as Functions of Composition A. Vapor-liquid 1. Ebulliometry 2. Total vapor pressure (direct and isopiestic) B.

Freezing point

C.

Solubility

D. Osmotic pressure II.

Calorimetry — Enthalpy and Heat Capacity A. Thermochemistry (heats of reaction) B.

Solution, mixing, dilution

C. Heat capacity III.

Volumetric Measurements A . Density and volume B.

IV.

Sound velocity (adiabatic compressibility)

Electrochemical Measurements - Gibbs Energy and Related Quantities for Chemical Reactions A. Reversible cell potentials

V.

B.

Polarography

C.

Electrical conductivity

Equilibrium Constants of Chemical Reactions - Gibbs Energy, Enthalpy, Entropy for Reactions A.

Potentiometric

B.

Spectrophotometric

C. Thermometric

Figure 2.

Techniques for measuring thermodynamic properties

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i t i s shaken g e n t l y f o r a p e r i o d of time i n a c a r e f u l l y thermos t a t t e d environment. Water d i s t i l l s back and f o r t h between the d i f f e r e n t s o l u t i o n s u n t i l they a l l a t t a i n the same vapor p r e s sure. G e n e r a l l y s e v e r a l days are r e q u i r e d to reach e q u i l i b r i u m . The s o l u t i o n s are then removed and t h e i r c o n c e n t r a t i o n s are measured. One o f the s o l u t i o n s i s a standard whose vapor pressure as a f u n c t i o n o f temperature has been e s t a b l i s h e d by other methods. Thus the vapor pressures of a l l the other s o l u t i o n s are a l s o determined at the e q u i l i b r i u m c o n c e n t r a t i o n . Roughly h a l f o f the data on the a c t i v i t i e s o f e l e c t r o l y t e s i n aqueous s o l u t i o n s and most o f the data f o r n o n e l e c t r o l y t e s , have been obtained by i s o p i e s t i c technique. I t has two main disadvantages. A great deal o f s k i l l and time i s needed to obt a i n r e l i a b l e data i n t h i s way. I t i s i m p r a c t i c a l to measure vapor pressures o f s o l u t i o n s much below one molal by the i s o p i e s t i c technique becaus reach e q u i l i b r i u m . Thi c a l c u l a t i o n o f a c t i v i t y c o e f f i c i e n t s o f n o n e l e c t r o l y t e s , but the c a l c u l a t i o n f o r e l e c t r o l y t e s r e q u i r e s data at lower concentrat i o n s , which must be obtained by other means. From a thermodynamic standpoint, f r e e z i n g p o i n t measurements and i s o p i e s t i c measurements are s i m i l a r s i n c e both y i e l d d i r e c t l y the a c t i v i t y of the s o l v e n t . When done c a r e f u l l y , f r e e z i n g p o i n t data can generate a c t i v i t y c o e f f i c i e n t values a t concentrations down to 0.001 m o l a l . During the f i r s t h a l f o f t h i s century, much a c t i v i t y c o e f f i c i e n t data was obtained from f r e e z i n g p o i n t measurements. However, the p o p u l a r i t y of t h i s technique has decreased and i s seldom used f o r aqueous s o l u t i o n s at the present time. The design and o p e r a t i o n o f s o l u t i o n c a l o r i m e t e r s i s an extensive t o p i c . Reference (125) reviews modem c a l o r i m e t r y and i d e n t i f i e s e a r l i e r d i s c u s s i o n s . The thermometric t i t r a t i o n type of c a l o r i m e t e r has been p e r f e c t e d during the past f i f t e e n o r twenty years. I t i s e s p e c i a l l y u s e f u l f o r measuring heats o f r e a c t i o n t h a t take place i n s e v e r a l steps. The a v a i l a b i l i t y o f advances i n thermometry has had a major e f f e c t on c a l o r i m e t r y . New types o f thermometers i n c l u d e s e n s i t i v e and r e l i a b l e t h e r m i s t o r s and quartz c r y s t a l thermometers. R e v e r s i b l e c e l l p o t e n t i a l s have been the source of much thermodynamic data on aqueous e l e c t r o l y t e s . In recent years, t h i s technique has been extended to nonaqueous s o l u t i o n s and t o molten s a l t systems. I t s use f o r aqueous s o l u t i o n s , r e l a t i v e t o other techniques, has decreased. Various i o n s p e c i f i c e l e c trodes have been developed i n recent years. These are used p r i m a r i l y i n a n a l y t i c a l chemistry and have not produced much thermodynamic data. Figures 3 and 4 i l l u s t r a t e some trends i n the p u b l i c a t i o n of experimental data from 1931 to 1976. They graph the number of a r t i c l e s appearing during c e r t a i n s e l e c t e d years f o r the f o r t y four year p e r i o d . A r t i c l e s p u b l i s h e d before 1967 were i d e n t i f i e d

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by a scan o f appropriate s e c t i o n s o f Chemical A b s t r a c t s . From 1967 to 1976, they were i d e n t i f i e d by searching the b i b l i o g r a p h i c s e c t i o n o f the B u l l e t i n o f Chemical Thermodynamics (1). At t h i s time, o n l y two volumes o f the B u l l e t i n have been i s s u e d s i n c e 1976. Since at l e a s t three volumes are needed to c o l l e c t a l l references f o r a p a r t i c u l a r year, the count f o r 1976 i s probably about 20% low. Only those papers which r e p o r t e d q u a n t i t a t i v e measurements o f e q u i l i b r i u m thermodynamic p r o p e r t i e s of w e l l defined systems were counted. Aqueous systems were d e f i n e d as those i n which water i s a major component. Studies on c o l l o i d s o r polymers were not i n c l u d e d . The o v e r a l l i n c r e a s e i n r a t e o f p u b l i c a t i o n r e f l e c t s the general trend i n s c i e n t i f i c l i t e r a t u r e . However the slump during the 1940-1960 p e r i o d i s obvious, and a peak during the e a r l y p a r t o f the 1970's i s suggested. Figure 3 graphs the measurements d e r i v e d from phase e q u i l i b r i u properties of a single components. They are c l a s s i f i e d according to the type of com ponents other than water. The f i g u r e shows the r a p i d increase i n s t u d i e s o f n o n e l e c t r o l y t e s and i n e l e c t r o l y t e - n o n e l e c t r o l y t e systems during the past f i f t e e n years. Figure 4 shows the number o f a r t i c l e s which r e p o r t data on e l e c t r o d e and c e l l potent i a l s , on thermodynamic p r o p e r t i e s o f i o n i c r e a c t i o n s , and on t r a n s p o r t p r o p e r t i e s . I t p o i n t s out the great p o p u l a r i t y o f i o n i c e q u i l i b r i u m s t u d i e s during the p e r i o d o f 1967-1970. The l a r g e s t increase i n experimental measurements on aqueous s o l u t i o n s has been i n those designed to f u r n i s h i n f o r m a t i o n on molecular i n t e r a c t i o n s and order. These techniques, along w i t h the kinds o f i n f o r m a t i o n which can be d e r i v e d from them, are outl i n e d i n Figure 5. Although the p r i n c i p l e s behind a l l these techniques have been known f o r many years, advances i n i n s t r u mentation and i n data c o l l e c t i o n have encouraged t h e i r widespread a p p l i c a t i o n to s o l u t i o n s o f a l l k i n d s . The use o f mass spectrometry to study i n t e r a c t i o n s between i s o l a t e d s o l v e n t and s o l u t e molecules has been p e r f e c t e d l a r g e l y w i t h i n the past ten years. This t o p i c i s reviewed i n reference (113). The l i s t o f 145 references at the end o f t h i s chapter has been c o l l e c t e d to help those l o o k i n g f o r numerical values o f thermodynamic p r o p e r t i e s o f aqueous s o l u t i o n s f o r i n d u s t r i a l a p p l i c a t i o n s . The emphasis has been p r i m a r i l y on items p u b l i s h e d s i n c e 1964, although a few o l d e r ones o f s p e c i a l u t i l i t y have been i n c l u d e d . The f i r s t group c o n s i s t s of eleven b i b l i o g r a p h i e s on v a r i o u s aspects of the thermodynamics o f aqueous s o l u t i o n s . Extensive b i b l i o g r a p h i e s may a l s o be found i n many other references i n the l i s t . The B u l l e t i n o f Chemical Thermodynamics (formerly the B u l l e t i n o f Thermodynamics and Thermochemistry), reference (1_), deserves s p e c i a l mention. This document i s i s s u e d a n n u a l l y under the sponsorship o f the I n t e r n a t i o n a l Union o f Pure and A p p l i e d Chemistry (IUPAC). I t began p u b l i c a t i o n under the

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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I. Spectroscopic Techniques

A. Infrared and Raman — vibrational energy levels

Vibration-translation energy transfer, solute-solvent interaction, H-bonds, ion pairs

B. Nuclear Magnetic

Molecular conformations, solute-solvent interactions, chemical reactions

II. Ultrasonic Absorption — Relaxation Phenomena Involving Τ and Ρ Changes Molecular conformations, solute-solvent interactions, chemical reactions

III.

Dielectric Relaxation — Relaxation Phenomena Involving Electric Moment

Changes

IV. Scattering Phenomena

A. X-Ray — electron density Structure and order at molecular level, radial distribution function

B. Light — density and concentration fluctuations Orientation relaxations, long range order

C. Neutron — nuclear position Molecular rotation, diffusion, chemical equilibria V. Ion-Molecule Reactions in the Gas Phase — Mass Spectra VI.

Thermochemistry of ion-solvent reactions, proton affinity Computer Simulations — Testing of Models

A. Monte-Carlo

B. Molecular dynamics Figure 5.

Techniques for studying intermolecular forces and structure

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e d i t o r s h i p o f H. A. Skinner i n 1955. P r o f e s s o r Edgar Westrum served as e d i t o r from 1965 t o 1976, and Dr. Robert D. Freeman has served s i n c e t h a t time. I t was not comprehensive o r widelyc i r c u l a t e d u n t i l 1963. I t i s an i n t e r n a t i o n a l cooperative p r o j e c t . For the past f i f t e e n y e a r s , the O f f i c e o f Standard Reference Data o f the N a t i o n a l Bureau o f Standards has s u p p l i e d a major f i n a n c i a l subsidy f o r the work. Each i s s u e o f the B u l l e t i n c o n s i s t s o f two major p a r t s . One p a r t presents b r i e f d e s c r i p t i o n s o f work on thermodynamics and thermochemistry i n progress a t the time, which are submitted by research i n v e s t i g a t o r s from around the world. The other p a r t c o n s i s t s o f a substance-property index and a b i b l i o g r a p h y o f p u b l i s h e d l i t e r a t u r e . This l a t t e r p a r t i s separated i n t o f o u r main s e c t i o n s : Organic substances, organic m i x t u r e s , i n o r g a n i c compounds and mixtures, and b i o l o g i c a l systems. Since 1970, the substance-property Bureau o f Standards by by tapes prepared by cooperating i n s t i t u t i o n s . The B u l l e t i n a l s o contains news items and other i n f o r m a t i o n about developments i n chemical thermodynamics. D e t a i l s about the contents and i n s t r u c t i o n s f o r o r d e r i n g copies can be obtained from P r o f e s s o r Freeman (see reference ( 1 ) ) . The second group o f c i t a t i o n s i d e n t i f i e s c o m p i l a t i o n s o f numerical data. A d d i t i o n a l s p e c i a l i z e d t a b l e s can a l s o be found i n some o f the references l i s t e d i n the t h i r d and f o u r t h groups. References (13) and (14) are the l a s t two volumes o f a four volume c o m p i l a t i o n o f p r o p e r t i e s o f mixtures prepared by J . Timmermans. They c o n t a i n a l a r g e c o m p i l a t i o n o f v a r i o u s p r o p e r t i e s o f aqueous s o l u t i o n s c o l l e c t e d from a l l the previous l i t e r a t u r e . They are n e i t h e r complete nor s e l e c t i v e , however. References (20, 22, 23, 24, 29, and 74) comprise the s e r i e s o f T e c h n i c a l Notes 270 from the Chemical Thermodynamics Data Center a t the N a t i o n a l Bureau o f Standards. These g i v e s e l e c t e d values o f e n t h a l p i e s and Gibbs energies o f formation and o f e n t r o p i e s and heat c a p a c i t i e s o f pure compounds and o f aqueous species i n t h e i r standard s t a t e s a t 25 °C. They i n c l u d e a l l i n o r g a n i c compounds o f one and two carbon atoms per molecule. They a l s o l i s t e n t h a l p i e s o f formation a t a s e r i e s o f concentrat i o n s f o r many s o l u t e s i n water. There are f o u r other major p r o j e c t s which are conducting c o n t i n u i n g and systematic compilations o f evaluated thermodynamic data on aqueous s o l u t i o n s . One o f these i s the E l e c t r o l y t e Data Center o f the N a t i o n a l Bureau o f Standards. Publications of t h i s and r e l a t e d groups a t NBS are c i t e d i n r e f e r e n c e s (10, 11, 17, 2J5, 52_, 59, 63^, 71_, 72_, 73^, 122, and 139). This work w i l l be d e s c r i b e d more f u l l y by Dr. S t a p l e s i n the f i f t h l e c t u r e o f t h i s session. The Deutsche G e s e l l s c h a f t f u r Chemisches p u b l i s h e s a s e r i e s o f data c o m p i l a t i o n s under the DECHEMA s e r i e s . I t i s intended p r i m a r i l y f o r engineering a p p l i c a t i o n s . Reference (50) c i t e s

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t a b l e s f o r aqueous n o n e l e c t r o l y t e s o l u t i o n s from t h i s s e r i e s . Another c o n t i n u i n g p r o j e c t on aqueous n o n e l e c t r o l y t e s i s the I n t e r n a t i o n a l Data S e r i e s B. The e d i t o r i s Dr. J . A. L a r k i n o f the N a t i o n a l P h y s i c a l Laboratory i n England. I t i s p u b l i s h e d i n the form of supplements of l o o s e - l e a f sheets and issued a t i r r e g u l a r i n t e r v a l s of a few months. Each sheet i s prepared and submitted by an author or authors. The data are presented i n a standard format and must f o l l o w c e r t a i n r u l e s with regard t o k i n d o f p r o p e r t i e s , s t y l e , u n i t s , and k i n d o f a u x i l i a r y i n f o r ­ mation to be i n c l u d e d . Standard t a b l e formats have been designed f o r each k i n d o f p r o p e r t y i n c l u d e d . Each t a b l e i s reviewed by an e d i t o r s p e c i a l l y s e l e c t e d from an i n t e r n a t i o n a l panel. The data may be the r e s u l t of o r i g i n a l measurements not p r e v i o u s l y p u b l i s h e d , data which have been p u b l i s h e d elsewhere but have been modified to conform to the requirements o f IDS B, or compilations gathere n a t i o n a l Data S e r i e s combine search j o u r n a l w i t h those of a data c o m p i l a t i o n . The f i r s t i s s u e of IDS S e r i e s Β appeared i n 1978 and con­ t a i n e d 66 data sheets. Two i s s u e s c o n t a i n i n g about the same number of data sheets are planned f o r 1979. IDS S e r i e s Β i s a companion p r o j e c t to the I n t e r n a t i o n a l Data S e r i e s A. S e r i e s A r e p o r t s data on nonaqueous organic mixtures. I t i s published by the Thermodynamics Research Center at Texas A CM U n i v e r s i t y i n College S t a t i o n , Texas. The Executive O f f i c e r i s P r o f e s s o r Bruno J . Z w o l i n s k i . The general o b j e c t i v e s and manner o f processing data are q u i t e s i m i l a r f o r the two s e r i e s o f IDS. S e r i e s A s t a r t e d p u b l i c a t i o n i n 1973 and about 750 data sheets have been issued. Other s e c t i o n s , o r s e r i e s , o f IDS are planned, i n c l u d i n g a s e r i e s on e l e c t r o l y t e s , one on metal a l l o y s , and one on mixtures of s p e c i a l importance to i n d u s t r y . The e d i t o r - i n - c h i e f of IDS S e r i e s A i s Henry V. Kehiaian of M a r s e i l l e , France. The f i n a l major c o n t i n u i n g p r o j e c t i s the S o l u b i l i t y Data P r o j e c t , which i s sponsored by the I n t e r n a t i o n a l Union o f Pure and A p p l i e d Chemistry (IUPAC). The p r o j e c t has been underway f o r s e v e r a l years, and the r e s u l t s are appearing as a s e r i e s o f volumes of the " S o l u b i l i t y Data S e r i e s " . The c o l l e c t i o n , com­ p i l a t i o n , and e v a l u a t i o n o f data are being c a r r i e d out by a l a r g e s t a f f o f experts i n each area on a world-wide b a s i s . The f i r s t e i g h t volumes have been announced f o r 1979. References (67, 68, 69, and 70) are scheduled f o r p u b l i c a t i o n i n 1979 and 1980. Dr. A. S. Kertes o f I s r a e l i s e d i t o r - i n - c h i e f o f the series. S p e c i a l mention should be made o f r e c e n t l y p u b l i s h e d v o l ­ umes o f the Landolt-Bornstein Tables, references (35) and (51). These c o n t a i n a l a r g e amount of data on aqueous s o l u t i o n s pre­ sented i n a compact form. Reference (58) c i t e s a new handbook on the thermodynamic p r o p e r t i e s o f i n o r g a n i c compounds. I t gives t a b l e s of enthalpy, Gibbs energy, entropy, and heat

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Electrolytes Phase Equilibria Gas Solubility

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Electrolyte Non-electrolyte

Non-electrolyte

37,64,123,124, 127

44,54,88,102, 111,138

Vapor-Liquid

13.14.18.19, 21,57,64,99

108,126

14,18,27,34,35, 50,56,57

Condensed Phases

13,14,28,36, 41,43,67,70

37

14,15,37,43,44, 56,68,99,104, 111,137

12,64,95,108,

14,15,56,57,

Gibbs Energy & Derived 13,14,25,26, Properties 40,42,52,53 57,58,59,65 66,71,72,73, 87,119,122, 128,130,131, 134,140 Enthalpy & Heat Capacity

13.14.17.20, 22,23,24,29, 33,42,48,51, 74,94,120, 141,144

14,17,20,22,23, 24,29,51,56,74

Volumetric Properties

13,14,21,41, 49,51,57,75, 91

14,51,56,57

Transport Properties

13,14,21,38, 48,57,76

Thermochemical and Chemical Equilibria

16,20,22,23, 24,29,33,34, 43,45,47,55, 58,61,62,63, 64,69,74,80, 85,115,117

Electrode & Cell Potentials

30,43,60

Distribution Coefficients

31,32,55,61

Note:

Numbers

refer to references

Figure 6.

cited in

108

14,38,57 20,22,23,24,29, 43,74

31,32,55,61 Bibliography.

Index to sources of compiled or correlated properties

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c a p a c i t y over a range o f temperatures f o r both pure compounds and ions i n s o l u t i o n . The t h i r d s e c t i o n o f the reference l i s t i d e n t i f i e s t r e a t i s e s and reviews which deal p r i m a r i l y w i t h the t h e o r e t i c a l aspects o f aqueous s o l u t i o n s . Many o f them c o n t a i n some numerical data as w e l l . The s e c t i o n e n t i t l e d Miscellaneous Reports c i t e s r e f e r ences which give u s e f u l methods o f c o r r e l a t i n g and p r e d i c t i n g data and a l s o d i s c u s s i o n s o f s p e c i a l and r e l a t e d t o p i c s . Figure 6 i s an index to numerical compilations o f data according t o the c l a s s o f p r o p e r t y and type o f s o l u t e . Although an impressive number o f compilations have been p u b l i s h e d i n the past f i f t e e n years, o n l y a small f r a c t i o n o f the s c i e n t i f i c l i t e r a t u r e on aqueous s o l u t i o n s has been covered. In s p i t e o f the i n c r e a s i n g volume o f data on mixtures o f e l e c t r o l y t e and n o n e l e c t r o l y t e s o l u t e s which i s being produced, there are few comprehensive c o m p i l a t i o n h systems A c c o r d i n g l y th engineer who needs thermodynami o f t e n must s t i l l spend grea g primary literature.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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THERMODYNAMICS

OF AQUEOUS SYSTEMS WITH

INDUSTRIAL APPLICATIONS

BIBLIOGRAPHY ON THERMODYNAMIC PROPERTIES OF AQUEOUS SOLUTIONS BIBLIOGRAPHIES

1. Freeman, R. D., Ed. "Bulletin of Thermodynamics and Thermochemistry"; Thermochemistry Inc., University of Oklahoma, Stillwater, Oklahoma, 1955-1978. 2. Horvath, A. L. "Reference Literature to Solubility Data Between Halogenated Hydrocarbons and Water"; J. Chem.Doc.,1972, 12, 163. 3. Wichterle, I.; Linek, J.; Hala, E., Eds. "Vapor-Liquid Equilibrium Data Bibliography"; Elsevier Scientific Publishing Co., Amsterdam, 1973. Covers literature on electrolytes and non electrolytes to 1972 4. Hawkins, D. L. "Bibliography on the Physical and Chemical Propertie f Water 1969-1974" J Sol Chem. 1975, 4, 621. 5. Horvath, A. L. "Reference Literature to the Critical Properties of Aqueous Electrolyte Solutions"; J. Chem. Inf. & Computer Sci., 1975, 15, 245. 71 solutes indexed by compound name 6. Wichterle, I.; Linek, J.; Hala, E., Eds. "Vapor-Liquid Equilibrium Data Bibliography Supplement 1"; Elsevier Scientific Publishing Co., Amsterdam, 1976. Covers literature from 1973 to 1975 7. Armstrong, G. T.; Goldberg, R. N. "An Annotated Bibliography of Compiled Thermodynamic Data Sources for Biochemical and Aqueous Systems (1930-1975)"; Nat. Bur. Stand. Special Publ. No. 454, September 1976. Equilibrium, enthalpy, heat capacity and entropy data 8. Hicks, C. P., Ed., Chapter 9 "A Bibliography of Thermodynamic Quantities for Binary Fluid Mixtures in Specialist Periodical Report. Chemical Thermodynamics"; Vol. 2, McGlashan, M. L.; Senior Reporter, The Chemical Society, Burlington House, London, 1978. 9. Wisniak, J.; Tamir, A. "Mixing and Excess Thermodynamic Properties. A Literature Source Books"; Elsevier Scientific Publishing Co., New York, 1978. A review of correlations is given in the introduction. The bibliography includes inorganic and organic solutes and electrolytes and non-electrolytes 10. Smith-Magowan, D.; Goldberg, R. N. "A Bibliography of Sources of Experimental Data Leading to Thermal Properties of Binary Aqueous Electrolyte Solutions"; Nat. Bur. Stand. Special Publ. No. 537, March 1979. 11. Goldberg, R. N.; Staples, B. R.; Nuttall, R. L.; Arbuckle, R. "A Bibliography of Sources of Experimental Data Leading to Activity or Osmotic Coefficients for Polyvalent Electrolytes in Aqueous Solution"; Nat. Bur. Stand. Special Publ. No. 485, July 1979.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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COMPILATIONS OF DATA

12. Long, F. A.; McDevit, W. F. "Activity Coefficients of Nonelectrolyte Solutes in Aqueous Salt Solutions"; Chem. Rev., 1952, 51, 119. 13. Timmermans, J. "Systems with Metallic Compounds" in "The Physico-chemical Constants of Binary Systems in Concentrated Solutions"; Vol. 3, Interscience Publishers, Inc., New York, 1960. A compilation of various thermodynamic and transport properties, including aqueous electrolyte and non-electrolyte solutions 14. Timmermans, J. "Systems with Inorganic and Organic or Inorganic Compounds (Excepting Metallic Derivatives)" in "The Physico-chemical Constants Binary Systems in Concentrated Solutions" Vol 4 Interscience Publishers 15. Francis, A. W. "Critical Solution Temperatures"; Advances in Chemistry Series No. 31, American Chemical Soc., Washington, D.C., 1961. 16. Kortum, G.; Vogel, W.; Andrussow, K. "Dissociation Constants of Organic Acids in Aqueous Solution"; Pure Appl. Chem., 1961, 1, 190. 17. Parker, V. B. "Thermal Properties of Aqueous Uni-Univalent Electrolytes"; NSRDS-NBS 2, U.S. Department of Commerce, National Bureau of Standards, Washington, D.C., April 1965. 18. Hala, E.; Wichterle, I.; Polak, J.; Boublik, T. "Vapor-Liquid Equilibrium Data at Normal Pressures"; Pergamon Press, New York, 1968. Tables and correlating equations for 27 binary and ternary aqueous systems 19. Lindsay, W. T., Jr.; Liu, C. T. "Vapor Pressure Lowering of Aqueous Solutions at Elevated Temperatures"; Office of Saline Water, U.S. Government Printing Office, Cat. No. I 1.88:347, 1968· 20. Wagman, D. D.; Evans, W. H.; Parker, V. B.; Halow, I.; Bailey, S. M.; Schumm, R. H. "Selected Values of Chemical Thermodynamic Properties. Tables for the First Thirty-Four Elements in the Standard Order of Arrangement"; Nat. Bur. Stand. Tech. Note No. 270-3, January 1968. 21. Fabuss, B. M.; Korosi, A. "Properties of Sea Water and Solutions Contaning Sodium Chloride,PotassiumChloride, Sodium Sulfate and Magnesium Sulfate"; Office of Saline Water, Report No. 384, U. S. Department of the Interior, 1968. Tables and correlating equations for density, vapor pressure, thermal conductivity and viscosity of binary and ternary solutions

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

484

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

22. Wagman, D. D.; Evans, W. H.; Parker, V. B.; Halow, I.; Bailey, S. M.; Schumm, R. H. "Selected Values of Chemical Thermodynamic Properties. Tables for Elements 35 through 53 in the Standard Order of Arrangement"; Nat. Bur. Stand. Tech. Note No. 270-4, May 1969. 23. Wagman, D. D.; Evans, W. H.; Parker, V. B.; Halow, I.; Bailey, S. M.;.Schumm, R. H.;Churney,Κ, "Selected Values of Chemical Thermodynamic Properties. Tables for Elements 54 through 61 in the Standard Order of Arrangement"; Nat. Bur. Stand. Tech. Note No. 270-5, March 1971. 24. Parker, V. P.; Wagman, D. D.; Evans, W. H. "Selected Values of Chemical Thermodynamic Properties. Tables for the Alkaline Earth Elements (Elements 92 through 97 in the Standard Order of Arrangement)"; Nat. Bur. Stand. Tech. Note No. 270-6 November 1971 25. Hamer, W. J.; Wu Coefficients of Uni-Univalen Electrolyte 25°C"; J. Phys. Chem. Ref. Data, 1972, 1, 1047. Numerical data and coeffficients in smoothing equations for 80 compounds 26. Liu, C. T.; Lindsay, W. T., Jr. "Thermodynamics of Sodium Chloride Solutions at High Temperatures"; J. Sol. Chem., 1972, 1_, 45. 27. Horsley, L. H. "Azeotropic Data-Ill"; Advances in Chemistry Series 116, American Chemical Society, Washington, D.C., 1973. 28. Zdanovskii, A. B.; Solov'eva, E. F.; Lyakhovskaya, Ε. I. "Three Component Systems. Books 1 and 2" in "Handbook of Experimental Data on Solubility of Multicomponent Water-Salt Systems"; Vol. 1, Khimiya, Leningrad Otd., Leningrad, USSR, 1973. 29. Schumm, R. H.; Wagman, D. D.; Bailey, S.; Evans, W. H.; Parker, V. B. "Selected Values of Thermodynamic Properties. Table for the Lanthanide (Rare Earth) Elements (Elements 62 through 76 in the Standard Order of Arrangement)"; Nat. Bur. Stand. Tech. Note No. 270-7, April 1973. 30. Meites, L.; Zuman, P. "Organic, Organometallic Biochemical Substances" in "Electrochemical Data"; Part 1, John Wiley and Sons, New York, 1974. Oxidation-reduction potentials, polarographic data, etc. 31. Marcus, Y.; Kertes, A. S.; Yamir, E., Compilers, Introduction and Part 1 "Organophosphorus Extractants" in "Equilibrium Constants of Liquid-Liquid Distribution Reactions"; IUPAC Analytical Chemistry Division, Butterworths, London, 1974. 32. Kertes, A. S.; Marcus, Y.; Yamir, E., Compilers, Part 2 "Alkylammonium Salt Extractants" in "Equilibrium Constants of Liquid-Liquid Distribution Reactions"; IUPAC Analytical Chemistry Division, Butterworths, London, 1974.

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24. WILHOIT Thermodynamic Properties of Aqueous Solutions 485

33. Martell, A. E.; Smith, R. M., Eds. "Amino Acids" in "Critical Stability Constants"; Vol. 1, Plenum Press, New York, 1974. 34. Hi rata, M.; Ohe, S.; Nagahama, K. "Computer Aided Data Books of Vapor-Liquid Equilibria"; Kodanska Ltd., Tokyo, Elsevier Scientific Publishing Co., New York, 1975. Tables, charts and equations, including 30 aqueous solutions of non-electrolytes 35. Weishaupt, J., Part IV "Thermodynamic Equilibria in Boiling Mixtures" in "Landolt-Bornstein Numerical Data and Functional Relationships in Science and Technology"; Vol. 3, Hellwege, Κ. Η., Editor-in-Chief, Springer-Verlag, Berlin, 1975. Data for binary, ternary, and quaternary aqueous solutions 36. Zdanovskii, A. B. Solov'eva E F. Lyakovskaya Ε I. et al. "Four Componen "Handbook of Experimental Data on Solubility of Multicomponent Water-Salt Systems"; Vol. 2, Khimiya, Leningrad Otd., Leningrad, USSR, 1975. 37. Mackay, D.; Shiu, W-Y. "The Aqueous Solubility and Air-Water Exchange Characteristics of Hydrocarbons under Environmental Conditions" in "Chemistry and Physics of Aqueous Gas Solutions"; Adams, W. Α., Ed., Electrochemical Soc., Inc., Princeton, N.J., 1975. Data for 50 compounds in water and seawater 38. Jamieson, D. T.; Irving, J. B.; Tudhope, J. S. "Liquid Thermal Conductivity, A Data Survey to 1973"; Her Majesty's Stationery Office, Edinburgh, 1975. Tables of data for 18 non-electrolytes and 64 electrolytes in water 39. Christensen, J.J.; Eatouugh, D.J.; Izatt, R.M. "Handbook of Metal Ligand Heats and Related Thermodynamic Quantities"; Marcel Dekker, Inc., New York, 1975 A compilation of values of H, ∆S, and log Κ for reactions between metal ions and various ligands 40. Rard, J. A.; Habenschuss, Α.; Spedding, J. H. "A Review of the Osmotic Coefficients of Aqueous Η SO at 25 C"; J. Chem. Eng. Data, 1976, 21, 374. 41. Nemeth, B. A. "Chemical Tables"; Wiley/Hal s ted, New York, 1976. Extensive tables of solubility of inorganic compounds and densities of aqueous solutions 42. Silvester, L. P.; Pitzer, K. S. "Thermodynamics of Geothermal Brines I. Thermodynamic Properties of Vapor-Saturated NaCl (aq) Solutions from 0 to 300°C"; Lawrence Berkeley Laboratory Report LBL-4456, 1976. ∆

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

486 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

43. Freier, R. K. "Aqueous Solutions. Data for Inorganic and Organic Compounds"; Vol. 1, Walter de Gruyter, Berlin, New York, 1976. Density, ∆Gf , solubility, dissociation const, and standard potentials of oxidation-reduction reactions for aqueous species 44. Gerrard, W. "Solubility of Gases and Liquids"; Plenum Publishing Co., New York, 1976. 45. Tsonopoulos, C.; Coulson, D. M.; Inman, L. B. "Ionization Constants of Water Pollutants"; J. Chem. Eng. Data, 1976, 21, 190. Data for six weak acids up to 150 C 46. Christensen, J. J.; Hansen, L. D.; Izatt, R. M. "Handbook of Proton Ionization Heats and Related Thermodynamic Qunatities"; Wiley Interscience, New York, 1976. 47. Dellien, I.; Hall Molybdenum and Tungsten: Thermodynamic Properties, Chemical Equilibria, and Standard Potentials"; Chem. Rev., 1976, 76, 283. 48. "Saline Water Conversion Engineering Data Books - 1975"; U.S. Department of Interior, Office of Water Research and Technology, NTIS, PB-250 907, Washington, D. C. Engineering and technical properties of seawater and certain aqueous electrolyte solutions 49. Leyendekkers, J. V. "Thermodynamics of Seawater as a Multicomponent Electrolyte Solution. Part 1. Entropy, Volume, Expansibility, Compressibility"; Marcel Dekker, Inc., New York, 1976. Discussion of thermodynamics, including many tables and correlation equations 50. Gmehling, J.; Onken, V., Part 1 "Aqueous-Organic Systems" in "DECHEMA Chemistry Data Series, Vol. 1, Vapor-Liquid Equilibrium Data Collection"; Deutsche Gesellschaft fur Chemisches. Frankfurt, 1977. Data for 73 binary and 53 ternary systems 51. D'ans, J.; Surawski, H.; Synowietz, C.; Schafer, Κ., Ed., Part IV "Densities of Liquid Systems and Their Heat Capacities. Part B. Densities of Binary Aqueous Systems and Heat Capacities of Liquid System" in "Landolt-Bornstein. Numerical Data and Functional Relationships in Science and Technology"; Vol. 1, Hellwege, Κ. Η., Editor-in-Chief, Springer-Verlag, Berlin, 1977. 52. Staples, B. R.; Nuttall, R. L. "The Activity and Osmotic Coefficients of Aqueous Calcium Chloride at 298.15 K"; J. Phys. Chem. Ref. Data, 1977, 6, 385. 53. Rard, J. Α.; Habenschuss, Α.; Spedding, F. H. "A Review of the Osmotic Coefficients of Aqueous CaC12 at 25 C"; J. Chem. Eng. Data, 1977, 22, 180.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

24. WILHOIT Thermodynamic Properties of Aqueous Solutions 487

54. Wilhelm, E.; Battino R.; Wilcock R.-J. "Low Pressure Solubility of Gases in Liquid Water"; Chem. Rev., 1977, 77, 219. Review of theory. Tables of data and parameters in smoothing equations for 57 solutes in water 55. Marcus, Y.; Yamir, E.; Kertes, A. S., Compilers, Part III "Compound Forming Extractants, Solvating Solvents, and Inert Solvents" in "Equilibrium Constants of Liquid-Liquid Distribution Reactions"; IUPAC Chemical Data Series No. 15, Pergamon Press, Oxford, 1977. 56. Larkin, J. Α., Ed. "International Data Series B. Thermodynamic Properties of Aqueous Organic Systems"; Engineering Sciences Data Unit, Ltd., London, 1978-79. 57. Freir, R. K. "Aqueous Solutions. Data for Inorganic and Organic Compounds"; Vol. 2, Walter de Gruyter, Berlin, New York, 1978. Tables and graph pressure activity coefficient, corrosion, and other prop. 58. Barner, H. E.; Scheuerman, R. V. "Handbook of Thermochemical Data for Compounds and Aqueous Species"; John Wiley and Sons, New York, 1978. Computer generated tables of ΔHf, ΔGf, Η - H ,S for inorganic compounds and some aqueous species as a function of temperature 59. Goldberg, R. N.; Nuttall, R. L. "Evaluated Activity and Osmotic Coefficients for Aqueous Solutions: The Alkaline Earth Metal Halides"; J. Phys. Chem. Ref. Data, 1978, 7, 263. Tables and parameters for smoothing equations for 11 com­ pounds at 250C 60. Milazzo, G.; Caroli, S. "Tables of Standard Electrode Potentials"; John Wiley and Sons, New York, 1978 61. Stary, J.; Freiser, Η., Compilers, Part IV "Chelating Extractants" in "Equilibrium Constants of Liquid-Liquid Distribution Reactions"; IUPAC Chemical Data Series No. 18, Pergamon Press, Oxford, 1978. 62. Kragten, J. "Atlas of Metal-Ligand Equilibria in Aqueous Solution"; Ellis Horwood Ltd., Chichester, England, 1978 (distributed by John Wiley and Sons). 63. Staples, B. R. "Ionic Equilibrium Constants of Aqueous Alkaline Earth Salts"; Environ. Sci. Technol., 1978, 12, 339. 64. "Coal Conversion Systems Technical Data Books"; U.S. Department of Energy, National Technical Information Service, U.S. Dept. of Commerce, HCP/T2286-01 UC-90, 1978. Technical data on coal and coal products. Subsequent issues include data on the sour water system and salting out coefficients for gases in water f

r

298

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THERMODYNAMICS

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SYSTEMS W I T H INDUSTRIAL APPLICATIONS

65. Pytkowicz, R. M. "Activity Coefficients in Electrolyte Solutions"; Vol. I, CRC Press, Cleveland, 1979. 66. Pytkowicz, R. M. "Activity Coefficients in Electrolyte Solutions"; Vol. II, CRC Press, Cleveland, 1979. 67. Lorimer, J. W. "Alkaline-Earth Sulfates in All Solvents" in "Solubility Data Series"; Vol 6, Kertes, A. S., Editor-in-Chief, Pergamon Press, New York, 1979. 68. Farrell, P. "Mono- and -Disaccharides in Water" in "Solubility Data Series"; Vol. 6, Kertes, A. S., Editor-in-Chief, Pergamon Press, New York, 1979. 69. Serjeant, E. P.; Dempsey, B. "Ionization Constants of Organic Acids in Aqueous Solution"; IUPAC Chemical Data Series No. 23, Pergamon Press, Oxford, 1979. Supplement to reference 16. Covers literature through 1970 70. Bauman, J. E. "Alkali- and Alkaline-Earth Metal Oxides and Hydroxides in Water" i "Solubilit Dat Series" Vol. 10, Kertes, A New York, 1980 (in press). 71. Goldberg, R. N. "Evaluated Activity and Osmotic Coefficients for Aqueous Solutions: Bi-Univalent Compounds of Lead, Copper, Manganese and Uranium"; J. Phys. Chem. Ref. Data, in press. 72. Goldberg, R. N., Nuttall, R. L.; Staples, B. R. "Evaluated Activity and Osmotic Coeffcients for Aqueous Solutions: Iron Chloride, and the Bi-Univalent Compounds of Nickel and Cobalt"; J. Phys. Chem. Ref. Data, in press. 73. Staples, B. R. "Activity and Osmotic Coefficients of Aqueous Sulfuric Acid"; J. Phys. Chem. Ref. Data, in press. 74. Wagman, D. D.; Parker, V. P.; Evans, W. H.; Schumm, R. H.; Bailey, S. "Selected Values of Thermodynamic Properties. Tables for the Alkali Metals (Elements 98 through 103 in the Standard Order of Arrangement)"; Nat. Bur. Stand. Tech. Note No. 270-8, 1980 (in press). TREATISES AND REVIEWS 75. Redlich, O.; Meyer, D. M. "The Molal Volumes of Electrolytes"; Chem. Rev., 1964, 64, 221. 76. Stokes, R. H.; Mills, R. "Viscosity of Electrolytes and Related Properties" in "The International Encyclopedia of Physical Chemistry and Chemical Physics: Topic 16, Transport Properties of Electrolytes"; Vol. 3, Stokes, R. H., Ed., Pergamon Press, Oxford, 1965. 77. Conway, B. E.; Barrodas, R. G., Eds. "The Chemical Physics of Ionic Solutions"; John Wiley and Sons, New York, 1966. Papers presented at the International Symposium of the

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24. WILHOIT Thermodynamic Properties of Aqueous Solutions 489

Electrochemical Society, Toronto, Canada, 1964 78· King, E. J. "Acid-Base Equilibria" in "The International Encyclopedia of Physical Chemistry and Chemical Physics: Topic 15, Equilibrium Properties of Electrolyte Solutions"; Vol. 4, Robinson, R. Α., Ed., Pergamon Press, 1965 (distributed by The MacMillan Co., New York). 79. Prue, J. E. "Ionic Equilibria" in "The International Encyclopedia of Physical Chemistry and Chemical Physics: Topic 15, Equilibrium Properties of Electrolyte Solutions"; Vol. 3, Robinson, R. Α., Ed., Pergamon Press, Oxford, 1966. 80. Nancollas, G. H. "Interactions in Electrolyte Solutions (Metal Complex and Ion Pair Formation in Solution)"; Elsevier Publishing Co., Amsterdam, 1966. 81. Dyrssen, D.; Liljezin, J. O.; Rydberg, J., Eds. "Solvent Extraction Chemistry" John Wile and Sons Inc. New York, 1967. 82. Harned, H. S.; Robinson, R. A. "Multicomponent Electrolyte Solutions" in "The International Encyclopedia of Physical Chemistry and Chemical Physics: Topic 15, Equilibrium Properties of Electrolyte Solutions"; Vol. 2, Robinson, R. Α., Ed., Pergamon Press, Oxford, 1968. 83. Covington, A. K.; Jones, P., Ed. "Hydrogen-Bonded Solvent Systems"; Taylor & Francis Ltd., London, 1968. 84. Eisenberg, D.; Kauzmann, W. "The Structure and Properties of Water"; Oxford University Press, Oxford, 1969. 85. Coetzee, J. F.; Ritchie, C. D., Ed. "Solute-Solvent Interactions"; Vol. 1, Marcel Dekker, Inc., New York, 1969. 86. Wood, R. H.; Reilly, P. J. "Electrolytes" in "Annual Review of Physical Chemistry"; Vol. 21, Eyring, H.; Christensen, C. J.; Johnston, H. S.; Eds., Annual Reviews Inc., Palo Alto, CA, 1970. 87. Robinson, R. A.; Stokes, R. H. "Electrolyte Solutions"; 3rd ed., Butterworths, London, 1970. 88. Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. "Regular and Related Solutions. The Solubility of Gases, Liquids and Solids"; Van Nostrand Reinhold, New York, 1970. 89. Conway, Β. Ε., Chapter 1 "Some Aspects of the Thermodynamic and Transport Behaviour of Electrolytes" in "Physical Chemistry an Advanced Treatise. Vol. IXA Electrochemistry"; Eyring, H., Ed., Academic Press, New York, 1970. 90. Franks, F., Ed. "The Physics and Chemistry of Water" in "Water: A Comprehensive Treatise"; Vol. 1, Plenum Publishing Corp., New York, 1972. 91. Home, R. Α., Ed. "Structure and Transport Processes in Water and Aqueous Solutions"; Wiley-Interscience, New York, 1972.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

490 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

92. Kay, R. L., Ed. "The Physical Chemistry of Aqueous Systems"; Plenum Press, New York, 1973. A symposiumin honor of Henry S. Frank, 1972 93. Franks, F., Ed. "Water in Crystalline Hydrates of Aqueous Solution of Simple Non-Electrolytes" in "Water: A Comprehensive Treatise"; Vol. 2, Plenum Publishing Corp., New York, 1973. 94. Franks, F., Ed. "Aqueous Solutions of Simple Electrolytes" in "Water: A Comprehensive Treatise"; Vol. 3, Plenum Publishing Corp., New York, 1973. 95. Covington, A. K.; Dickinson, T., Ed. "Physical Chemistry of Organic Solvent Systems"; Plenum Press, New York, 1973. 96. Tanford, C. "The Hydrophobic Effect"; John Wiley and Sons, New York, 1973. 97. Luck, W. A. P., Ed "Structure of Water and Aqueous Solutions"; Verla 1974. 98. Ben-Nairn, A. "Water and Aqueous Solutions. Introduction to a Molecular Theory"; Plenum Press, New York, 1974. 99. Franck, Ε. U. "Selected Properties of Aqueous Solutions at High Temperatures and Pressures"; 8th International Conference on the Properties of Water and Steam, 1974. 100. Erdeg-Gruz, T. "Transport Phenomena in Aqueous Solutions"; John Wiley and Sons, New York, 1974. 101. Franks, F., Ed. "Aqueous Solutions of Amphiphiles and Macromolecules" in "Water: A Comprehensive Treatise"; Vol. 4, Plenum Publishing Corp., New York, 1974. 102. Adams, W. Α., Ed. "The Chemistry and Physics of Aqueous Gas Solutions"; The Electrochemical Society, Inc., Princeton, N.J., 1975. 103. Clever, H. L.; Battino, R., Chapter VII "The Solubility of Gases in Liquids" in "Techniques of Chemistry, Vol. VIII, Solutions and Solubilities, Part I"; Dack, M. R. J., Ed., John Wiley and Sons, New York, 1975, pp. 379-441. 104. McMeekin, T. L., Chapter VIII "The Solubility of Biological Compounds" in "Techniques of Chemistry, Vol. VIII, Solutions and Solubilities, Part I"; Dack, M. R. J . , Ed., John Wiley and Sons, New York, 1975, pp. 443-465. 105. Francks, F., Ed. "Water in Disperse Systems" in "Water: A Comprehensive Treatise"; Vol. 5, Plenum Publishing Corp., New York, 1975. 106. Riley, J. P.; Skirrow, G., Eds. "Chemical Oceanography"; Vols. 1 and 2, 2nd ed., Academic Press, New York, 1975. 107. Scatchard, G. "Equilibrium in Solutions. Surface and Colloid Chemistry"; Harvard University Press, Cambridge, Mass., 1976.

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24. WILHOIT Thermodynamic Properties of Aqueous Solutions

491

108· Furter, Wm. F., Ed. "Thermodynamics Behaviour of Electrolytes in Mixed Solvents"; Advances in Chemistry Series 155"; American Chemical Soc., Washington, D.C., 1976. 109. Coetzee, J. F.; Ritchie, C. D., Ed. "Solute-Solvent Interactions"; Vol. 2, Marcel Dekker, Inc., New York, 1976. 110. Pierotti, R. A. "A Scaled Particle Theory of Aqueous and Nonaqueous Solution"; Chem. Rev. 1976, 76, 717. 111. Getzen, F. W., Chapter XV "Structure of Water and Aqueous Solubility" in "Techniques of Chemistry, Vol. VIII, Solutions and Solubilities, Part II"; Dack, M. R. J., Ed., John Wiley and Sons, New York, 1976, pp. 363-436. 112. Kruus, P. "Liquids and Solutions. Structure and Dynamics"; Marcel Dekker, Inc., New York, 1977. 113. Kebarle, P. "Ion Thermochemistr on Solvation from Gas Phase Ion Equilibria Chemistry"; Vol. 28, Rabinovitch, B. S.; Schurr, J. M.; Strauss, H. L., Eds., Annual Reviews, Inc., Palo Alto, CA, 1977, p. 445. 114. Conway, Β. E.; Bockris, J. O'M. "Modern Aspects of Electrochemistry"; No. 12, Plenum Publishing Corp., New York, 1977. 115. Burgess, J. "Metal Ions in Solutions"; John Wiley and Sons, New York, 1978. 116. Franks, F., Ed. "Recent Advances" in "Water: A Comprehensive Treatise"; Vol. 6, Plenum Publishing Corp., New York, 1979. 117. Jenne, Ε. Α., Ed. "Chemical Modeling in Aqueous Systems"; ACS Symposium Series No. 93, SIS/American Chemical Soc., 1979. 118. Ritcey, G. M.; Ashbrook, A. W. "Solvent Extraction. Principles and Application to Process Metallurgy. Part II"; Elsevier Scientific Publishing Co., New York, 1979. MISCELLANEOUS REPORTS 119. Criss, C. M.; Cobble, J. W. "The Thermodynamic Properties of High Temperature Aqueous Solutions. IV. Entropies of Ions up to 200 and the Correspondence Principle"; J. Am. Chem. Soc., 1964, 86, 5385. 120. Criss, C. M.; Cobble, J. W. "The Thermodynamic Properties of High Temperature Aqueous Solutions. V. The Calculation of Ionic Heat Capacities up to 200C. Entropies and Heat Capacities above 200 C"; J. Am. Chem.Soc.,1964, 86, 5390. 121. Cobble, J. W. "Thermodynamic Properties of High Temperature Aqueous Solutions. VT. Applications of Entropy Correspondence to Thermodynamics and Kinetics"; J. Am. Chem. Soc., 1964, 86, 5394. o

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

492 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

122. Hamer, W. J. "Theoretical Mean Activity Coefficients of Strong Electrolytes in Aqueous Solution from 0 to 100 C"; NSRDS-NBS 24, U.S. Department of Commerce, National Bureau of Standards, December 1968. 123. Shoar, S. K.; Gubbins, Κ. E. "Solubility of Nonpolar Gases in Concentrated Electrolyte Solutions"; J. Phys. Chem., 1969, 73, 498. Prediction of salting out effect based on scaled particle theory 124. Sada, E.; Kobayashi, T.; Kito, S.; Ito, K. "Salting Out Parameters of Gas Solubility in Aqueous Salt Solutions"; J. Chem. Eng. Jpn., 1970, 3, 18. 125. Wilhoit, R.C. "Recent Developments in Calorimetry", pp 200225 in "Topics in Chemical Instrumentation", G.W.Ewing, Ed., Chemical Education Publishing Co., Easton, Pa., 1971 126. Tassios, D. P. "Extractive and Azeotropic Distillation"; Advances in Chemistr Society, Washington, D.C, 1972. 127 Tiepel, E. W.; Gubbins, Κ. E. "Thermodynamic Properties of Gases Dissolved in Electrolyte Solutions"; Ind. Eng. Chem. Fundam., 1973, 12, 18. Comparison of observed and predicited salting out coefficient for 50 systems 128. Chen, H.; Sangster, J.; Eng. J. J.; Lenzi, F. "General Method of Predicting Activity of Ternary Aqueous Solutions from Binary Data"; Can. J. Chem. Eng., 1973, 51, 234. 129. Pitzer, K. S. "Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations"; J. Phys. Chem., 1973, 77, 268. 130. Pitzer, K. S.; Mayorga, G. "Thermodynamics of Electrolytes. II. Activity and Osmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent"; J. Phys. Chem., 1973, 77, 2300. Parameters listed for 227 aqueous electrolytes 131. Pitzer, K. S.; Mayorga, G. "Thermodynamics of Electrolytes. III. Activity and Osmotic Coefficients for 2-2 Electrolytes"; J. Sol. Chem., 1974, 3, 539. 132. Ross, A. B.; Nedo, P. "Rate Constants for Reactions of Inorganic Radicals in Aqueous Solution"; NSRDS-NBS 65, U.S. Bureau of Commerce, Washington, D.C, 1974. 133. Zudkevitch, D.; Zarember, I., Eds. "Thermodynamics - Data and Correlations"; Vol. 70, AICHE Symposium Series No. 140, Am. Inst. Chem. Eng., New York, 1974. 134. Pitzer, K. S.; Kim, J. J. "Thermodynamics of Electrolytes. IV. Activity and Osmotic Coefficients for Mixed Electrolytes"; J. Am. Chem.Soc.,1974, 96, 5701. 135. Pitzer, K. S. "Thermodynamics of Electrolytes. V. Effects of Higher-order Electrostatic Terms"; J. Sol. Chem., 1975, 4, 249.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

24. WILHOIT Thermodynamic Properties of Aqueous Solutions

493

136. Le Neindre, B; Vodar B. "Experimental Thermodynamics Volume II. Experimental Thermodynamics of Non-Reacting Fluids", International Union of Pure and Applied Chemistry, Butterworths, London, 1975 137. Amidon, G. L.; Yalkowsky, S. H.; Anik, S. T.; Valvani, S. C. "Solubility of Nonelectrolytes in Polar Solvents. V. Estimation of the Solubility of Aliphatic Monofunctional Compounds in Water Using a Molecular Surface Approach"; J. Phys. Chem., 1975, 79, 2239. 138. Benson, B. B.; Krause, D., Jr. "Empirical Laws for Dilute Solutions of Non Polar Gases"; J. Chem. Phys., 1976, 64, 689. 139. Staples, B. R.; Nuttall, R. L. "Computer Programs for the Evaluation of Activity and Osmotic Coefficients"; Nat. Bur. Stand. Tech. Note No. 928, December 1976. 140. Fredenslund, A.; Gmehling J.; Rasmussen P "Vapor-Liquid Equilibria Using Elsevier Scientifi g , , Correlation of thermodynamic properties of non-electrolytes including aqueous systems. Listing of computer programs given. 141. Silvester, L. F.; Pitzer, K. S. "Thermodynamics of Electrolytes. 8. High-Temperature Properties, Including Enthalpy and Heat Capacity with Application to Sodium Chloride"; J. Phys. Chem., 1977, 81, 1822. 142. Franck, Ε. U. "Equilibrium in Aqueous Electrolyte Systems at High Temperatures and Pressures" in "Phase Equilibria and Fluid Properties in the Chemical Industry"; Storvick, F. S.; Sandler, S. I., Eds., ACS Symposium Series 60, American Chemical Society, Washington, D.C, 1977. 143. Pitzer, K. S.; Peterson, J. R.; Silvester, L. F. "Thermodynamics of Electrolytes. IX. Rare Earth Chlorides, Nitrates and Perchlorates"; J. Sol. Chem., 1978, 7, 45. 144. Silvester, L. F.; Pitzer, K. S. "Thermodynamics of Electrolytes. X. Enthalpy and the Effect of Temperature on the Activity Coefficients"; J. Sol. Chem., 1978, 7, 327. 145. Conway, Β. E. "The Evaluation and Use of Properties of Individual Ions"; J. Sol. Chem., 1978, 7, 722. f

RECEIVED

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

25 Prediction of Activity Coefficients of Strong Electrolytes in Aqueous Systems H. P. MEISSNER Chemical Engineering Department, Massachusetts Institute of Technology, Cambridge, M A 02139

In planning the processing of an aqueous solution containing more than one strong electrolyte a) upon evaporation, whic b) at what concentration will precipitation start, c) how much precipitation will occur as evaporation proceeds before a second electrolyte starts to co-precipitate, and d) what is the effect of temperature on this behavior. Answers require information on the activity coefficients of the solution components over the composition and temerature ranges of interest. The object here is to review a simple empirical method for predicting these activity coefficients, which involves the use of a single charac­ teristic constant for each cation-anion combination present. This constant is unchanged by the presence of other electrolytes, and is readily derived from experimental measurements. Electrolyte Characterization. The generalized dissociation of a strong electrolyte is as follows: (1) where subscripts i and j designate the cation A and the anion Β respectively, with z and z being the ion charges, andv and i

j

i

v the s t o i c h i o m e t r i c c o e f f i c i e n t s , whose sum ( v . + v . ) i s d e s i g n J ι J nated as ν... The i o n charges ζ. and ζ. are used t o c h a r a c t e r i z e ij J ι e l e c t r o l y t e s ; thus NaCl, NH^NO^ e t c are 1:1 e l e c t r o l y t e s , MgCl^ i s a 2:1 e l e c t r o l y t e , e t c . E l e c t r o l y t e s l i k e MgC^ forming an j

ion having a charge g r e a t e r than u n i t y are c a l l e d h i g h e r e l e c t r o ­ l y t e s . Values of ζ and ν f o r t y p i c a l e l e c t r o l y t e s are l i s t e d i n Table 1. In a s o l u t i o n of a s i n g l e e l e c t r o l y t e , here c a l l e d a "pure s o l u t i o n " , s u b s c r i p t s 1 and 2 are used t o designate c a t i o n s and anions r e s p e c t i v e l y . When more than two ions are p r e s e n t , then 0-8412-0569-8/80/47-133-495$05.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

496

OF

AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

the s o l u t i o n i s c a l l e d a "mixed" s o l u t i o n , w i t h c a t i o n s i d e n t i f i e d by the odd i n t e g e r s 1,3,5, e t c . , and anions by the even i n t e g e r s 2,4,6, e t c . Concentrations are expressed both i n m o l a l i t i e s and i n i o n i c s t r e n g t h u n i t s , r e l a t e d as f o l l o w s f o r i o n s : 2

I . = O.Sim.z. ); The

1. = 0 . 5 ( m

2 jZj

t o t a l i o n i c s t r e n g t h of s o l u t i o n s I

T

= 0.5(m z 1

2 1

+ m z 2

2 2

+ m^z^

2

)

(2) i s defined as I , where T

+ ...)

(3)

A s u p e r s c r i p t " ° " w i l l be used t o designate a pure s o l u t i o n , f o r which I t h e r e f o r e becomes I ° . I t i s e a s i l y shown (1_) that f o r T

2

a pure s o l u t i o n , I ° i a p p l i c a t i o n of these equations strengths f o r pure s o l u t i o n s of t y p i c a l e l e c t r o l y t e s having a m o l a l i t y of u n i t y are shown i n Table 2. 2

A c t i v i t y C o e f f i c i e n t s . The mean i o n i c a c t i v i t y c o e f f i c i e n t s of a c a t i o n - a n i o n p a i r (here shortened t o " a c t i v i t y c o e f f i c i e n t " f o r convenience) are d i r e c t l y measureable i n pure and o c c a s i o n a l ­ l y i n mixed s o l u t i o n s . The mean i o n i c a c t i v i t y c o e f f i c i e n t i s designated as γ?. i n pure s o l u t i o n and γ.. i n mixed s o l u t i o n . In t h i s development, a t t e n t i o n i s focused e x c l u s i v e l y on a c t i v i ­ ty c o e f f i c i e n t s of c a t i o n - a n i o n p a i r s , w i t h no use being made of a c t i v i t y c o e f f i c i e n t s of i n d i v i d u a l ions. E l e c t r o l y t e s i n Pure S o l u t i o n . I t has been found t h a t i n pure s o l u t i o n (2) at any constant temperature, e x p e r i m e n t a l l y 1/z ζ determined values of the term ( Ύ ^ ) 1 2 , when p l o t t e d against I° f o r v a r i o u s e l e c t r o l y t e s , form the curve f a m i l y of f i g u r e 1. 2

„ . χ 1 / ζ ζ i s designated as Γ° and c a l l e d the For convenience, (γ ) 1 2 12 "reduced a c t i v i t y c o e f f i c i e n t " . The data p o i n t s a t 25°C f o r s i x d i f f e r e n t e l e c t r o l y t e s are p l o t t e d on F i g . 1 t o show t y p i c a l agreement w i t h the isotherms presented. These curves are drawn from an a n a l y t i c a l equation which was f i t t e d t o p u b l i s h e d a c t i v i t y c o e f f i c i e n t data i n pure s o l u t i o n s a t 25°C f o r about 100 d i f f e r e n t e l e c t r o l y t e s (3). By t h i s equation, γ ° a t a given /

Ο

1

0

&

2

temperature i s uniquely determined by two f a c t o r s , namely the t o t a l i o n i c s t r e n g t h I ° and the q u a n t i t y q° « The term q° i s a 2

2

constant f o r each curve i n f i g u r e 1, but d i f f e r s from one curve to the next. Each e l e c t r o l y t e , t h e r e f o r e , can be c h a r a c t e r i z e d by i t s q° value a t 25°C The a n a l y t i c a l equation i n v o l v e d i s presented below, and i s a p p l i e d t o pure s o l u t i o n s by u s i n g 1°.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

25.

MEISSNER

497

Activity Coefficients of Strong Electrolytes

Table I I l l u s t r a t i v e Values of ν and ζ V. 1

NaCl CaCl

2

(NH ) S0 4

MgS0

2

4

4

A1 (S0 ) 2

4

3

ν.

ζ.

_J

1

ζ. _J

ζ . :ζ. 1 1

1

2

3

2

1

2:1

2

1

3

1

2

1:2

1

1

2

2

2

2:2

2

3

5

3

2

3:2

Table I I Values of 1° i n Pure S o l u t i o n f o r a M o l a l i t y (m. . ) of U n i t y _ i l NaCl CaCl

2

(NH ) S0 4

MgS0

2

4

4

A1 (S0 ) 2

Na.PO.

4

3

_

i

l

_ J L

_

!

1 1

1 3

1 1 / 2 1 2

1

3

2

1

4

1

1

15

2

1

6

3

1 2 9

_J_ 1 2 1

_J_ 1/2 1 2

1

2

3

6

11/2 1

4 1/2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

498

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

Ionic

Strength , I American Institute of Chemical Engineering

Figure 1. Typical isotherms for various electrolytes of the reduced activity coefficients vs. the total ionic strength (data points presented at 25°C): (0) LiBr; Ο HCI; (%) LiCl; (U) CaCl,; (*) Pb(ClO h; (O) Ca(N0 ) ; (+ ) ΝΗ>Ν0 ; (Q)AgNO, (3) h

3

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

3

25.

MEISSNER

for

I , and

499

Activity Coefficients of Strong Electrolytes

f o r l:l

( 7 )

A general t e s t of Equations ( 4 ) , (5) and (6) i n v o l v e s c a l c u l a t i n g the a c t i v i t y of water at some convenient i o n i c s t r e n g t h f o r a pure s o l u t i o n at 100°C, knowing only the q° value at 25°C f o r the e l e c t r o l y t e at i s s u e . Values of (a°) calculated i n this w z f a s h i o n f o r v a r i o u s e l e c t r o l y t e s are l i s t e d i n t a b l e 3, along w i t h experimental values f o r the same c o n d i t i o n . I n s p e c t i o n shows agreement i s t y p i c a l l y w e l l w i t h i n 10%. Greater success i s i n v a r i a b l y a t t a i n e d at lower i o n i c strengths than those l i s t e d . The same r e s u l t s would, of course, be a t t a i n e d by the use of F i g u r e 2 i n p l a c e of equation ( 6 ) . Mixed S o l u t i o n s . A mixed s o l u t i o n i s prepared by d i s s o l v i n g 12' 23' 34' * °l °f i n d i c a t e d e l e c t r o l y t e s i n t o at l e a s t enough water t o b r i n g then a l l i n t o s o l u t i o n . The t o t a l i o n i c s t r e n g t h I a t t a i n e d depends on how much water i s used. However, r e g a r d l e s s of the amount of water added, f o r a given set of values of N^ , N,^, , e t c . , the composition on a dry b a s i s of a l l the s o l u t i o n s made and a l s o the r a t i o s I ^ / I , I^/I^y I^/I^ Z l

Ν

Ν

N

e t c

m

e s

2

t n e

2

T

e t c . , o b v i o u s l y remain constant. For a set of s o l u t i o n s of constant dry composition, prepared as j u s t i n d i c a t e d , the values of Γ . p l o t t e d a g a i n s t I _ at lz,mix 1 1 0

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

9

25.

MEISSNER

503

Activity Coefficients of Strong Electrolytes

any f i x e d temperature, again are found t o form a curve f a l l i n g i n t o the curve f a m i l y of F i g u r e 2. This curve i s i d e n t i f i e d by 12 mix ^ s u b s c r i p t 12,mix showing t h a t the i n d i c a t e d q

w

t

n t

n

e

e l e c t r o l y t e e x i s t s i n a mixed s o l u t i o n . A l l other i o n p a i r s i n t h i s mixed s o l u t i o n behave s i m i l a r l y , i n that the curves of Γ . versus I _ , Γ . versus I , e t c . , again f a l l i n t o the 23,mix T' 34,mix Τ ' curve f a l m i l y of Figure 1. Thus, i f q . i s known f o r t h i s ' U2,mix m i x t u r e , then the value of Γ _ . at any d e s i r e d I _ can again 12,mix Τ be read d i r e c t l y from the a p p r o p r i a t e curve of F i g u r e 2, o r a l t e r n a t i v e l y c a l c u l a t e d from equation ( 4 ) . Note t h e r e f o r e t h a t equation (4) a p p l i e s to a mixed s o l u t i o n a f t e r s u b s t i t u t i n g Γ . , I , and q_ . f o r Γ° and q ° 12,mix' T' ^12,mix 12' 12 12. I t i s found that f o r a given i o n p a i r at any temperature, q . i n a mixture i , mix l s o l u t i o n . On the othe , qy weighte 12,mix 0 0

0 /

J

m

&

1 0

&

1

0

0

0

n

1 ?

0

average of the q°_. values of s e l e c t e d i o n p a i r s present, c a l c u ­ l a t e d w i t h the f o l l o w i n g i s o t h e r m a l ecmation:

h

h

h

-*-0 ι - ' Ο ι

_ «12.mix

^

«112

+

«32

ι

- ' ο

Ζ

+

h

«52

+

h ι

Ο

^~

«12

+

_Ο

1^ «14

This equation a p p l i e s to any system of three c a t i o n s and three anions between 0°C and 120°C Terms are added or removed from equation (8) as ions are added or e l i m i n a t e d from the s o l u t i o n under study. Thus when a f o u r t h c a t i o n i s present, then the term ! — q° i s added. S i m i l a r l y i n a three i o n s o l u t i o n c o n t a i n i n g Τ 7

only M g C l

2

and NaCl, w i t h q° values at 25°C of 2.90

and

2.23

r e s p e c t i v e l y , equation (8) reduces t o : _ V++ M

S

C 1

2,mix~

» M

*T

8

+

C 1

2

h ^ : X

T

In t h i s mixed s o l u t i o n , when ro^^ S

a

o

N

a

+

C

1

o e s t

o

± ç n

*T

n

(9)

o M g C 1

2

zero r e l a t i v e t o ro^g^2

then by equation ( 9 ) , q., . i s c o r r e c t l y shown to equal MgCl ,mix n

J

2

q° . A f u r t h e r t e s t of t h i s r e l a t i o n i n v o l v e s the c a l c u l a t i o n ^MgCl η Λ

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

504

OF AQUEOUS

SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

at 25°C of the a c t i v i t y c o e f f i c i e n t s o f t r a c e amounts of MgCl^in a s t r o n g s o l u t i o n of NaCl, and the r e v e r s e , as f o l l o w s : a) Trace M g C l i n NaCl. In 3 m o l a l N a C l ( I = 3 ) , by equations 2

T

e

(8) or ( 9 ) , q ^ . Is à x 2 . 9 + ^ x2.23+ ^ x 2 . 9 ) , namely MgCl ,mix J J J 2

t race From equation 4, T „, . i s 0.77 and so by d e f i n i MgCl ,mix

2,57.

w

M

2

T

e

t i o n , y* *, . i s (0.77) MgCl ,mix

2

o r 0.59, versus 0.63 by e x p e r i -

2

ment ( 4 ) . b)

Trace NaCl i n MgCl -

a t r a c e of NaCl, I

In 1 m o l a l M g C l

2

C 1

_/I

T

i s 0.33.

i s 0.67,

1 ^ + + / ! ^

B

equatio

(8)

(I =3) c o n t a i n i n g

2

T

i s zero and

1 ^ + / ! ^

q j ' g ^ i

(0x2.33+0.67x2.90+0.33x2.33) , g ,ir ' ' NaCl,mix equal t o 0.78 by equation ( 4 ) . By d e f i n i t i o n , Ύ 5 Ο ? · i s then a l s o 0.78, versus 0.77 by experiment ( 4 ) . NaCl,mix ' — b

Γ

Θ

J

τ

r

E l e c t r o l y t e A c t i v i t i e s . The a c t i v i t y of a s o l i d e l e c t r o l y t e i n e q u i l i b r i u m w i t h i t s pure s a t u r a t e d s o l u t i o n , by d e f i n i t i o n is :

(a

i2>Sat

=

^Psat^Psat^)"

1 2

( 1 0 )

^^

S i m i l a r l y , the a c t i v i t y o f t h i s same s o l i d e l e c t r o l y t e i n e q u i l i b ­ rium w i t h any one o f i t s s a t u r a t e d mixed s o l u t i o n s i s : V

^ m i x ^ a t

=

V

V

l 2 12 ^iWVsat^mix*

( a

η w Sat }

When the s o l i d e l e c t r o l y t e c a r r i e s no water o f c r y s t a l l i z a t i o n , as w i t h NaCl and K C l , then η i s zero. Obviously, i f the a c t i v i t y c o e f f i c i e n t s used i n these equations a r e c o r r e c t l y p r e d i c t e d , then f o r any given temperature, the l e f t s i d e s of these equations must be equal* I f the value of ( a - . ) c a l c u l a t e d from equation 1Z,mix (11) f o r a given mixed s o l u t i o n i s found t o be g r e a t e r than v>°12^Sat from equation (10) then the s o l u t i o n i s s u p e r s a t u r a t e d , w h i l e i s the reverse i s found, then the s o l u t i o n i s not s a t u r a t e d . A simple t e s t of these r e l a t i o n s i s presented i n Table 4, i n which a r e l i s t e d s e v e r a l a r b i t r a r i l y chosen mixed s o l u t i o n s o f NaCl and K C l (q° values a t 25°C r e s p e c t i v e l y o f 2.23 and 0.91) s a t u r a t e d w i t h one or both s a l t s . The f i r s t column shows the s o l i d phase(s) p r e s e n t , the next two columns l i s t the 0

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

25.

MEISSNER

505

Activity Coefficients of Strong Electrolytes

m o l a l i t i e s of NaCl and K C l , reported i n the l i t e r a t u r e ( 5 ) , the next two present q.. . values c a l c u l a t e d from equation ( 8 ) , the ij,mix next two l i s t Γ._ . and Γ„_, . c a l c u l a t e d from equation (4) NaCl,mix KCl,mix w h i l e the l a s t two columns present ( a . ) _ and ( a ^ - . )« «_ NaCl,mix Sat KCl,mix Sat c a l c u l a t e d f o r the mixtures by Eq. (11). I n s p e c t i o n shows t h a t for pure NaCl s o l u t i o n , ( a ^ ) · ° · at 100°C. S i m i l a r l y , (a° ) a t 25°C i s 8.2 and a t 100°C i s 18.6. KCl Further i n s p e c t i o n shows t h a t , a s expected, a) as long as s o l i d NaCl i s present at 25°C,(a„ . )„ c a l c u l a t e d form equation NaCl,mix Sat (11) i s (approximately) equal to 33.3, and as long as s o l i d K C l i s present, ( ^ ^ i ) s t l c u l a t e d from equation (11) i s again (approximately saturated w i t h NaCl a, NaClmi l e s s than 33.6, w h i l e when not s a t u r a t e d w i t h K C l , r

n

M

n

XT

n

v

7

i

a C 1

s

3 3

3

a

t

2 5

c

a

n

d

3 8

8

S a t

Λ

a

c a

m

x

a

m

x

c a l c u l a t e d form equation (11), i s l e s s than 8.3; c) i n s p e c t i o n of the data f o r 100°C show t h a t analogous c o n c l u s i o n s can be drawn a t t h i s temperature. I t f o l l o w s that by these c a l c u l a t i o n s , the presence or absence of the s o l i d phases l i s t e d i n the f i r s t column are c o r r e c t l y p r e d i c t e d . S o l u b i l i t y . Assume now that the s o l u b i l i t y of K C l i s t o be p r e d i c t e d a t 100°C i n 3.48 m o l a l NaCl which when s a t u r a t e d w i t h KCl i s known t o be 5.34 m o l a l i n t h i s l a t t e r s a l t . To p r e d i c t t h i s m o l a l i t y , i t i s merely necessary t o know q^ ^ ^ci 25°C, and the s o l u b i l i t y of K C l a t 100°C. Thus a t 100°C, q^J a

n

d

a

t

aC

c

q

NaCl

a

n

d q

KCl

a

r

e f o u n d

t

o b

e 2

,

0

3a

n

d0

,

7

2

l

r e s p e c t i v e l y by a

i

equation ( 5 ) , hence by equation (10), ( ^Qi^

at

n

P

u r e

solution

i s 18.6. By equation (11): 18.6=

(^(3.48 + V > < 4 l . . i *

)

(

1

2

)

S o l u t i o n of t h i s equation i s by t r i a l , assuming a v a l u e of ^ C l mix * l l i 8 following i n turn: ionic strengths from equations (2) and ( 3 ) , q ^ ^ from equation ( 8 ) , anc

t n e n

c

a

c

u

a

t

n

t

n

e

KC

and Γ . from equation ( 4 ) . KCi,mix Ί

the proper value of n^ç^

n

a

s

m

x

When equation (12) "balances",

been found.

By such a procedure,

rn^ç,^ i s found t o be 5.1, versus the experimental value of 5.34, which represents good agreement. Vapor Pressures of Mixed S o l u t i o n s . I t has been pointed

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

506

THERMODYNAMICS

OF AQUEOUS SYSTEMS

W I T H INDUSTRIAL

APPLICATIONS

Table IV S a l t A c t i v i t i e s i n Saturated S o l u t i o n s of NaCl and K C l Literature r Eq(4) a Eq (11) m Values (5) From Eq. (8) _m N a C l ^ C C l % a C l , m i x K C l , m i x NaCl K C l NaCl K C l m

S o l i d Phase

m

q

25°C NaCl NaCl NaCl NaCl + K C l KCl KCl KCl

6.17 5.84 5.64 5.11 3.14 1.07 0.0

0.0 0.67 1.07 2.19 3.0 4.1 4.93

2.23 2.16 2.12 2.03

1.57 1.50 1.46 1.37

0.94 0.95 0.94 0.96

0.75 0.73 0.74 0.74

33.3* 33.8 33.7 34.3

0.0 2.35 4.0 8.69

1.57

0.91 0.70 0.58 0.0 8.19*

6.78 5.75 4.71 3.48 1.75 0.0

0.0 2.05 4.74 5.34 6.32 7.56

2.03 1.86 1.70 1.64 1.52 1.38

1.38 1.20 1.04 0.98 0.86 0.72

100 °C NaCl NaCl NaCl + K C l KCl KCl KCl

0.92 0.93 0.96 0.90 0.82 0.75

0.72 0.71 0.70 0.66 0.61 0.57

38.8* 0 38.9 8.0 41.5 21.4 26.0 20.0 9.5 19.0 0.0 18.6*

*From Eq. (10) Table V M g C l S o l u t i o n at 25°C Saturated w i t h MgSO^-7H 0 2

2

ExperiMgS0 ,r mental m(7) Τ Eq(8) MgSO, M g C l Eq(3) 4

4

0

a) b) c) d)

0.59 1.21 2.5 3.06

4.00 2.06 0.44 0.0

14.36 11.12 11.33 12.24

0.92 0.66 0.26 0.15

q

A

MgCl ,m MgS0 ,m 2

4

Eq(8)

Eq(4)

2.67 2.29 1.69 -

0.74 0.59 0.47 0.44

w,m

Eq(13) E q ( l l ) 0.57 0.76 .89 .93

A l l s o l u t i o n s saturated w i t h MgS0 *7H 0; s o l u t i o n " a " 4

2

a l s o s a t u r a t e d w i t h MgCl *6H 0. 2

Ep,m

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

.0048 .0085 .0078 .0079

25.

MEISSNER

507

Activity Coefficients of Strong Electrolytes

out above t h a t , f o r mixed s o l u t i o n s having the same d r y composi­ t i o n , curves of Γ ,Γ ,r , e t c . versus I each l i e 12,m 23,m 34,m' m on a separate q l i n e on F i g u r e 2. Values of water a c t i v i t y a t any i o n i c s t r e n g t h can be c a l c u l a t e d from these l i n e s , assuming each l i n e t o represent a h y p o t h e t i c a l pure e l e c t r o l y t e whose q , value i s i d e n t i c a l w i t h that of q for this line. 12,hypo. 12,m These h y p o t h e t i c a l water a c t i v i t i e s a r e l a b e l e d A, w i t h appro­ p r i a t e s u b s c r i p t s , and can be used t o c a l c u l a t e a . the t o t a l w,mix water a c t i v i t y over t h i s mixed s o l u t i o n , as f o l l o w s : 1 0

0 0

o /

1 0

n

n

M

a

2

3

. =A^ ·A^ ·> w,mix 12 23 34

...

(13)

where Ν

R

12 12 " N + N + N_, + 12 23 34 1 0

R

O Q

Ν _ 23 2 3 N- + N _ + N . + 12 23 34 =

0

e t C

Q

'

Values o f A . a t the d e s i r e d t o t a l i o n i c s t r e n g t h I a r e 12 ,mix m obtained as u s u a l from equation (6) a f t e r s u b s t i t u t i n g A ^ 1 0

&

m

a

f o r ( ^)-L2 ^

nt n

i

s

equation, or from Figure 2 p l u s equation ( 7 ) .

To i l l u s t r a t e a p p l i c a t i o n of equation (13), c o n s i d e r a mixed (unsaturated) s o l u t i o n at 25°C, 4.11 m o l a l i n NaCl (q° i s 2.23) and 8.55 m o l a l i n NaNO^ (q° i s -0.39), making I equal t o 12.66. T

By equation ( 8 ) , q by equation ( 6 ) , (13),

a^

i s 1.35 and q

N a C 1 > m i x

A N a C

^ i s 0.57 and

i s 0.04, hence

K C 1 > m i x

i s 0.67.

From equation

as p r e d i c t e d equals the experimental v a l u e of 0.64

s o l u t i o n , by equation ( 8 ) , q . is LâoU^,mix sa

w

2 Ι " · ' ' ' 4 2 When I i s 6.31, Γ . i s 0.64 by equation ( 4 ) , making Τ Gyp,mix 0/

m

Y

Gyp mix

3.69

J

e c

*

χ 10"

5

u a l

t c

0.168.

n

S u b s t i t u t i n g i n t o equation (11): 2

= m^ (0.168) (0.77)

2

yp

S o l v i n g Gypsum's s o l u b i l i t y m

i s found to be 0.047 m o l a l , Gyp

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

25.

MEISSNER

509

Activity Coefficients of Strong Electrolytes

versus an experimental value of 0.048 ( 6 ) . 2. In 0.178 m o l a l K^SO^. Over t h i s s o l u t i o n , s i n c e q

„ i s -0.25 and I i s 0.534, a° i s 0.997 by equation ( 6 ) . K b0. Τ w 2 4 Gypsum s o l u b i l i t y i s again minute, hence iç ++ mix i s negligible, =/ i s 2/3 and I + / I i s 1/3, making v

n

o

a

I

I

S 0

T

K

T

4

2 1 q^ . equal t o (-0.25x=- - O.lSx^) or -0.22 by equation ( 8 ) . Gyp,mix ^ 3 3 ^ trace Using t h i s q v a l u e , when I i s 0.534, Γ ™ . i s 0.594 Τ ' CaSO^mix trace 4 by equation ( 4 ) , making γ . equal t o (0.594) o r 0.124. n

J

m

n

0

uabu^,mix

By equation (11): 5

3.69 χ 1 0 " = in (π G G S o l v i n g , m i s 0.013, versus an experimental m o l a l i t y of G 0.011 ( 7 ) . 3. I n 3.0 m o l a l (NH^^SO^. C a l c u l a t i n g as above, Gypsum s o l u b i l i t y i n t h i s s o l u t i o n i d found t o be 0.043 m o l a l , v e r ­ sus an experimental v a l u e of 0.039 ( 7 ) . D i s c u s s i o n . The approach t o mixtures d i s c u s s e d here i s based on the f i n d i n g that f o r a s o l u t i o n of constant dry composi­ t i o n , a l l curves of Γ.„ . , Γ . , e t c . versus the t o t a l i o n i c 12,mix 32,mix s t r e n g t h f a l l i n t o the curve f a m i l y of F i g u r e 2, and t h e r e f o r e a l s o conform to equation ( 4 ) . This i s a d i r e c t consequence of the form of equations (8) and (9) of r e f e r e n c e ( 8 ) , showing the r e l a t i o n between Γ . , and Γ° , Γ° , e t c . and I . These i z ,mix 1Z ΖJ l e a r l i e r equations, of course, do not i n v o l v e " ^ ^ χ " their 0 0

Ί Ο

m

a

n

d

replacement by equaiton (4) f o r l o c a t i n g the mixture curve i s l a r g e l y a matter of convenience. Equation (13) f o r c a l c u l a t i n g a . over a mixed s o l u t i o n w,mix i s d e r i v e d from the modified Gibbs equation f o r a mixture ( 7 ) , namely n

&

-55.5 d i n a

W j m i x

= v^dm^ + v^dn^... + m ^ v ^ d l n y ^ + n. v dlnY3 2 3

2 3

2 m

+ ...

By combination w i t h equation ( 3 ) , terms i n v o l v i n g m and ν a r e replaced by terms i n v o l v i n g I and Z. Recognizing t h a t Γ 1/z

equals

ζ

IZ,mix

-j[^> then f o r a mixture of constant dry composition,

m

equation (13) f o l l o w s d i r e c t l y . I t i s evident t h a t the examples presented here show c o n s i d e r ­ able success. S i m i l a r r e s u l t s have been obtained w i t h other

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

510

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

systems, i n c l u d i n g some i n v o l v i n g double s a l t s (9,10). S u l f u r i c a c i d and some cadmium and z i n c s a l t s , however, so do not conform t o these r e l a t i o n s . I n view of the many u n c e r t a i n t i e s i n v o l v e d , t h e r e f o r e , c a l c u l a t e d compositions of saturated s o l u t i o n s should be t r e a t e d w i t h c a u t i o n and, where p o s s i b l e , checked by experiment. Nomenclature A.. 1 J

H y p o t h e t i c a l water vapor a c t i v i t y f o r a h y p o t h e t i c a l s o l u t i o n of e l e c t r o l y t e i j , f o r which ( q ° j ) i

pure

h y p o t h e t i c a l

i s assumed equal t o q.. . f o r the mixture under c o n s i d e r a ­ ble ,mix tion. ' a c t i v i t y (a°^) f ° e l e c t r o l y t e i j i n pure s o l u t i o n , J

a^j

i s

r

(a.. . ) i s f o r t h i s e l e c t r o l y t e i n mixed s o l u t i o n , (a° ) i j ,mix w i s f o r water i n a J

mixed s o l u t i o n . I

i o n i c s t r e n g t h , equations (2) and ( 3 ) ; I

m N_. η

T

i s the t o t a l i o n i c r

strength

f o r mixed s o l u t i o n s , and equals 1 ° ^ f ° pure

solutions. m o l a l i t y ; gram moles per 1000 grams water. gram moles of e l e c t r o l y t e i j added t o water t o make up a s o l u t i water o n system. moles of h y d r a t i o n per formula weight of an e l e c t r o ­ l y t e : Α Β · nH 0 ν . ν. 2 o

q^.

c h a r a c t e r i s t i c constant as i n equations ( 4 ) , ( 5 ) , and ( 8 ) .

R t

see equation (14) °C

ζ

i o n charge Greek.

ν γ., Γ 1 J

s t o c h i o m e t r i c c o e f f i c i e n t , equation (1). mean i o n i c a c t i v i t y c o e f f i c i e n t of i j i n s o l u t i o n l 2. "Reduced a c t i v i t y c o e f f i c i e n t , namely γ 1 / z

z

11

Subscripts

and S u p e r s c r i p t s .

° i j mix sat Τ

denotes a "pure" s o l u t i o n r e f e r s t o c a t i o n i , stands f o r odd i n t e g e r s 1,3,5 e t c . r e f e r s t o c a t i o n j , stands f o r even i n t e g e r s 2,4,6 e t c . denotes a mixed s o l u t i o n denotes a saturated s o l u t i o n r e f e r s t o " t o t a l " s o l u t i o n , as i n I

w

r e f e r s t o water i n the s o l u t i o n .

T

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

25.

MEISSNER

Activity Coefficients of Strong Electrolytes

511

Literature Cited

1. Kusik, C.L.; Meissner, H.P., Ind. Eng. Chem., Proc. Des. Dev. 1973, 12, 112. 2. Meissner, H.P., Tester, J.P. Ind. Eng. Chem., Proc. Des. Dev. 1972, 11, 128. 3. Kusik, C.L.; Meissner, H.P., AIChE Symp. Ser. 1978, 173, 74 14. 4. Meissner, H.P.; Kusik, C.L., AIChE J1. 1972, 18, 294. 5. D'Ans, J . , "Die Lösungsgleichewichte der Systeme der Salze Ozeanischer Salzablagerungen," Ver. für Ackerbau, Berlin, 1933. 6. International Critical Tables, McGraw Hill Book Co., NY 1933, III end IV. 7. Seidell, Α.; Linke, W.F., "Solubilities of Inorganic and Metal Organic Compounds", 4th Ed. van Nostrand & Co., Princeton, NJ, 1958. 8. Meissner, H.P.; Kusik 1973, 12, 205. 9. Meissner, H.P.; Kusik, C.L. Ind. Eng. Chem, Proc. Des. Pev. 1979, 18, 391. 10. Kusik, C.L.; Meissner, H.P.; Field, E.L., Ind. Eng. Chem., Proc. Pes. Pev., 1979, 18. 11. Meissner, H.P.; Peppas, N.A., AIChE J1. 1973, 19, 806. 12. Smithsonian Tables, 9th Rev. Ed. Washington, 1954. 13. Harned, H.S. and Owen, H.H., "Physical Chemistry of Electro­ lyte Solutions," 3rd Ed. Rheinhold, NY, 1958. RECEIVED January 31,

1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

26 The Solubility of Gases in Water from 350 600 Κ Η. LAWRENCE C L E V E R and C H U L H. H A N Department of Chemistry, Emory University, Atlanta, GA 30322

Two recent events allow a more detailed picture of the solubility o the noble gases in been given even a year ago. First, a careful compila­ tion and evaluation of the gas solubility values in water at a gas partial pressure of one atm between the temperatures of 273.15 and about 350 Κ was car­ ried out by Battino [1-5]. Second, an experimental study of the solubility "of the noble gases in water at moderate pressures and at temperatures up to 561 Κ by a new method was reported by Potter and Clynne [6]. Battino's selected values between 273 and about 350 K, Potter and Clynne's new values, and selected older literature data on the solubility of gases in water at temperatures up to 600 Κ have been combined, and fitted to an equation to give the inverse of the limiting low pressure value of Henry's constant over t h e t e m p e r a t u r e i n t e r v a l o f 273 t o 600 K . Battino's equations [^-5] a r e r e c o m m e n d e d f o r u s e o v e r t h e 273 t o 350 Κ r a n g e a n d t h e e q u a t i o n s o f t h e p r e s e n t w o r k a r e t e n t a t i v e e q u a t i o n s f o r the 350-600 Κ range o f temperature. Henry's constant is defined, H

2,l =

X

2 ^

( P

2/ 2 X

)

" V ? 2 = 02 2 2 2 Ρ

/ Ύ

Χ

(

1

)

w h e r e H2 η i s t h e H e n r y c o n s t a n t , P2 t h e g a s p r e s s u r e , t h e m o l e f r a c t i o n g a s s o l u b i l i t y , ±2 t h e g a s f u g a ­ c i t y , a 2 t h e d i s s o l v e d g a s a c t i v i t y , 02 t h e fugacity coefficient, a n d y2 t h e d i s s o l v e d g a s a c t i v i t y c o e f ­ ficient. In the H e n r y ' s law r e g i o n the d i s s o l v e d gas activity coefficient, 72 = 1/ b y d e f i n i t i o n . For the gases d i s c u s s e d i n t h i s paper the f u g a c i t y c o e f ­ f i c i e n t , 0 , d i f f e r s l i t t l e from u n i t y at the moder­ ate pressures at which s o l u b i l i t i e s are normally reported. A t u n i t gas p r e s s u r e (atm), t h e mole f r a c 2

0-8412-0569-8/80/47-133-513$06.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

514

THERMODYNAMICS

OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

t i o n s o l u b i l i t y i s equal to the i n v e r s e of Henry's constant, X = I/H2 assuming u n i t values of 0 and Ύ · A l i n e a r r e g r e s s i o n on a l l o f t h e s e l e c t e d d a t a f o r a g i v e n g a s was r u n t o o b t a i n t h e c o n s t a n t s o f a n equation o f the form 2

2

2

ln A

X +

l

2

= In

1/H

2

A /(T/100) 2

=

±

+ A

3

ln

(T/100)

+ A (T/100)

(2)

4

The u s e o f ( T / 1 0 0 ) a s a v a r i a b l e h a s t h e a d v a n t a g e o f m a k i n g t h e p a r a m e t e r s A - , , A , A 3 , a n d A4 o f s i m i l a r magnitude. The a p p l i c a t i o n o f s t a n d a r d thermodynamic d e f i n i t i o n s to the equation allows the equation p a r a ­ m e t e r s t o be u s e d t c h a r a c t e r i s t i c s of th in Table I. When a l l f o u r p a r a m e t e r s o f t h e e q u a t i o n 2

Table

I.

In

= A

AG

Χ

λ

C

S o l u b i l i t y equation definitions.

= -RT

1

+ A /(T/100)

= -RA-j^T AS°

= - R T in

λ

100RA

= -OAG°/3T)

2

-

= RA

d / H

RA T 3

1

2

£n

thermodynamic

(T/100) +

+ A3 in

2

In Χ

and

χ

A (T/100) 4

)

(T/100) -• R A T / 1 0 0

+ RA3 £ n

2

4

(T/100) + RA3 +

ΔΗ

c

= -100RA

AC; =

2RA4T/IOO

4- RA3T + R D T / 1 0 0 = AG° + ΤΔ§*° 2

2

(3ΔΗ°/3Τ)

= RA

3

+ 2RA T/100 4

= a + bT

a r e e v a l u a t e d , a h e a t c a p a c i t y change f o r the disso­ l u t i o n process that i s l i n e a r i n temperature is ob­ tained. When o n l y t h e f i r s t t h r e e c o n s t a n t s o f t h e e q u a t i o n a r e e v a l u a t e d , a heat c a p a c i t y change i n d e ­ pendent of temperature i s o b t a i n e d . Although a t e m p e r a t u r e d e p e n d e n t h e a t c a p a c i t y change i s more r e a l i s t i c , the s o l u b i l i t y d a t a are o f t e n not a c c u ­ r a t e enough t o j u s t i f y the e v a l u a t i o n o f the f o u r constants. The 273

solubility a n d 350 Κ .

of

gases

between

the

temperature

of

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

26.

CLEVER AND HAN

515

Solubility of Gases in Water

B a t t i n o has used the above e q u a t i o n i n h i s e v a l ­ u a t i o n o f the s o l u b i l i t y o f gases i n water a t one atmosphere gas p r e s s u r e a t temperatures between 2 7 3 and about 3 5 0 K. T a b l e s I I and I I I and F i g u r e 1 summarize h i s e v a l u a t i o n o f the s o l u b i l i t y d a t a . T a b l e I I g i v e s the temperature i n t e r v a l , the number o f l a b o r a t o r i e s t h a t B a t t i n o judges have p u b l i s h e d r e l i a b l e s o l u b i l i t y d a t a , the number o f e x p e r i m e n t a l v a l u e s used i n the l i n e a r r e g r e s s i o n , the l i n e a r r e g r e s s i o n s t a n d a r d d e v i a t i o n a t the m i d p o i n t tempera­ t u r e , and the temperature o f minimum mole f r a c t i o n s o l u b i l i t y (maximum v a l u e o f Henry's c o n s t a n t ) a t one atmosphere p a r t i a l p r e s s u r e o f the gas. For a l l o f the gases except oxygen o n l y a t h r e e c o n s t a n t e q u a t i o n was used. The temperatur l i t y a t one atmospher c u l a t e d from the t h r e e c o n s t a n t e q u a t i o n . The d i f f e r e n t i a t i o n o f e q u a t i o n ( 2 ) w i t h r e s p e c t t o tempera­ t u r e g i v e s T ^ = 1 0 0 A2/A3. The v a l u e s t h a t f a l l o u t s i d e the temperature range o f the e x p e r i m e n t a l d a t a used i n the r e g r e s s i o n must be l o o k e d on as o n l y t e n ­ t a t i v e v a l u e s o f the temperature o f minimum s o l u b i ­ lity. T a b l e I I I g i v e s v a l u e s o f the changes i n Gibbs energy, e n t h a l p y , e n t r o p y , and heat c a p a c i t y o f the s o l u t i o n p r o c e s s as c a l c u l a t e d from the e q u a t i o n s o f T a b l e I . F i g u r e 1 shows the recommended n o b l e gas mole f r a c t i o n s o l u b i l i t i e s a t u n i t gas p a r t i a l p r e s ­ sure (atm) as a f u n c t i o n o f temperature. The tempera­ t u r e o f minimum s o l u b i l i t y i s marked. The o r d e r o f i n c r e a s e i n the s o l u b i l i t y o f the gases a t any g i v e n temperature i n the 2 7 3 - 3 5 0 Κ range p a r a l l e l s , t o a f i r s t a p p r o x i m a t i o n , the p o l a r i z a b i l i t y o f the gas. T a b l e IV summarizes the p o l a r i z a b i l i t i e s and the molar volumes a t 2 7 3 . 1 5 Κ and 1 atm o f the gases. The gases are l i s t e d i n the o r d e r o f de­ c r e a s i n g molar volume which g i v e s some i n d i c a t i o n o f t h e i r n o n - i d e a l c h a r a c t e r . The p o l a r i z a b i l i t y i n d i ­ c a t e s the magnitude o f the London d i s p e r s i o n energy between the gas and a g i v e n s o l v e n t . m

n

The

s o l u b i l i t y o f the gases i n water from

600

K.

350 to

The l i t e r a t u r e was s e a r c h e d , and the d a t a on the s o l u b i l i t y o f gases i n water between the temperatures of 3 5 0 and 6 0 0 Κ were c o m p i l e d . The measurements i n the 3 5 0 t o 6 0 0 Κ temperature range were u s u a l l y made at moderate gas p a r t i a l p r e s s u r e s . The s o l u b i l i t y a t

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

273 278

273

273

273

273

Ar

Kr

Xe

Rn

2

2

H

N

four

348

348

-

5/73

9/74

9/69

3/40

5/20

3/30

11/42 3/13

9/59

9/59

Labs/Exp. Values

equation

348

348

348

373

348

353

318

_ 348

constant

273

273

273

Ne

-

Temperature Range/K

273

°2*

II

0.34

0.72

0.52

1.02

0.35

0.32

0.26 0.69

0.47

0.54

Standard Deviation a t M i d T/%

365.2

348.1

327.6

371.5

383.0

375.8

-

371.2

322.7

304.1

Temperature o f Minimum S o l y / K

t h e E v a l u a t i o n o f Gas S o l u b i l i t y i n Water a t 101.325 kPa (1 Atm) a n d Low T e m p e r a t u r e s ( B a t t i n o , [1-5])

He

Gas

Summary o f

Table

CLEVER

AND HAN

517

Solubility of Gases in Water

rH I

1

0 rH g rH 1

vo

h)

rH rH

\

o Çh U

LO rH

vo rH

rH

O

CN

00 CN CN

vo

ro

rH CT> CN

00 ro rH

vo o

o

CN rH

CN rH

o

vo o

o

rH 1

CN rH 1

CN

O

o

CN

rH 1

rH 1

σ»

ro ro

σ\

rH CN 1

1

CN

vo in

σ\ vo

CN rH

00

rH CN

CN

00 CN

vo

l

l

Ϊ2'···'£Ν

=

)

Σ

pairs

U

( r

ij ij °

}

( 3 )

°

where the p a r t i c l e i n d i c e monatomic p a r t i c l e s or coordinates must i n general i n c l u d e o r i e n t a t i o n a l and other i n t e r n a l coordinates as w e l l as the c e n t e r - t o - c e n t e r distance r

u ·

The program of c a l c u l a t i n g the B 0 - l e v e l p o t e n t i a l s from Schroedinger l e v e l cannot o f t e n be c a r r i e d through w i t h the accuracy r e q u i r e d f o r the i n t e r m o l e c u l a r forces i n s o l u t i o n theory. (9.) F o r t u n a t e l y a great deal can be l e a r n e d through the study o f B 0 - l e v e l models i n which the N-body p o t e n t i a l i s p a i r wise a d d i t i v e (as i n Eq. ( 3 ) ) and i n which the p a i r p o t e n t i a l s have very simple forms. (2_ 3_,6_) Thus f o r the hard sphere f l u i d we have, w i t h a=sphere diameter, 5

u(r)=GD

if

=0

ra

w h i l e f o r the 6-12

(h)

f l u i d we have 1 2

u(r) = e [ ( a / r ) - 2 ( a / r ) ] 6

0

(5)

The 6-12 p o t e n t i a l i s only q u a l i t a t i v e l y l i k e the r e a l i s t i c p o t e n t i a l s t h a t can be d e r i v e d by c a l c u l a t i o n s at Schroedinger l e v e l f o r , say, Ar-Ar i n t e r a c t i o n s . But i t r e q u i r e s c a r e f u l and d e t a i l e d study to see how r e a l simple f l u i d s ( i . e . one component f l u i d s w i t h monatomic p a r t i c l e s ) deviate from the behavior c a l ­ c u l a t e d from the 6-12 model. Moreover the p r i n c i p a l s t r u c t u r a l features o f simple f l u i d s are already q u i t e r e a l i s t i c a l l y given by the hard sphere f l u i d . The l e s s o n , t h a t d r a s t i c a l l y simple Hamiltonian models are adequate t o generate q u i t e r e a l i s t i c f l u i d p r o p e r t i e s and hence t o understand the s t r u c t u r e o f f l u i d s , can be r e i n f o r c e d by many other examples. For the present Symposium the most important may be the S t i l l i n g e r - R a h m a n s e r i e s o f s t u d i e s o f a B 0 - l e v e l

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

28.

Fundamental Theory of Ionic Solutions

FRIEDMAN

Hamiltonian model f o r water.

551

(10,11)

In a McMillan-Mayer l e v e l model (MM-level) f o r a s o l u t i o n , the p a r t i c l e s are the s o l u t e p a r t i c l e s ( i . e . t h e ions w i t h p o s i ­ t i v e , n e g a t i v e , or zero charge). The i o n - i o n p o t e n t i a l s can, i n p r i n c i p l e , be generated by c a l c u l a t i o n s i n which one averages over the s o l v e n t coordinates i n a BO-level model which sees the solvent p a r t i c l e s . ( ^ , 5 . ,12) P a i r w i s e a d d i t i v i t y (we use overbars f o r solvent-averaged p o t e n t i a l s ) r

°N l' 2 ' - " ' N

Σ

1

(

6

)

V- ^ p a i r s o r ions i s not so accurate o r r e a l i s t i c as at B O - l e v e l , but i s perhaps r e a l i s t i c enough f o r s o l u t i o n s i n which the i o n i c concentrations do not much exceed IM . (r

r

)

=

The s i m p l e s t mode the p r i m i t i v e model, (13>1^ HS + e.e ,/er (7) u. = u.. iJ î J' HS i j where Uj_j i s the p o t e n t i a l given i n Eq. ( U ) , w i t h cr-hjij , and where ε i s the d i e l e c t r i c constant o f the s o l v e n t medium. This i s i m p l i c i t l y the model s t u d i e d by Debye and H i i c k e l , and i n most l a t e r s t u d i e s o f i o n i c s o l u t i o n theory as w e l l . T h e i r w e l l known r e s u l t f o r the p o t e n t i a l o f average f o r c e , w..(r) = u?*? ( r ) + e . e . e ~ -^•J îj i J

Kr

/ετ ,

(8)

1

where κ i s the Debye s h i e l d i n g l e n g t h , i s not very a c c u r a t e , even f o r t h i s model, compared t o some o f the l a t e r r e s u l t s . Some of t h e advances are i n c o r p o r a t e d i n the system o f equations f o r the thermodynamic excess p r o p e r t i e s developed by K. S. P i t z e r . (15) In S e c t i o n k we discuss some more r e f i n e d MM-level models. 3.

MM-LEVEL

û _(r) +

FROM BO LEVEL

U n t i l very r e c e n t l y there was no i n f o r m a t i o n about how an MM p a i r p o t e n t i a l should l o o k , based upon c a l c u l a t i o n s from the deeper BO l e v e l . I n the s i m p l e s t BO l e v e l model f o r an i o n i c s o l u t i o n the s o l v e n t molecules are represented as hard spheres w i t h centered p o i n t d i p o l e s and the ions as hard spheres w i t h centered charges. Now there are two sets o f c a l c u l a t i o n s , ( 1 6 , 1 7 ) by very d i f f e r e n t approximation methods, f o r t h i s model where a l l of the spheres are 3 A i n diameter, where the d i p o l e moments are near 1 Debye, and where the ions are s i n g l y charged. The temperature i s 2 5 ° and the solvent c o n c e n t r a t i o n i s about 50M, corresponding t o a l i q u i d s t a t e . The d i e l e c t r i c constant o f the model s o l v e n t i s b e l i e v e d t o be near 9 · 6 · As shown i n F i g . 2 the p r i m i t i v e model w i t h

ε=9·6 i s

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

552

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

Figure 2. Solvent-averaged potential for charged hard-sphere ions in a dipolar hard-sphere solvent. MC approximation by Patey and Valleau (\6) and LHNC approximation by Levesque, Weis, and Patey (11). Also shown are the primitive model functions for solvent dielectric constants 9.6 and 6.

only very c l o s e t o t h e c a l c u l a t e d û+_(r) f o r r>72 . At r=3S , corresponding t o a c o n f i g u r a t i o n i n which t h e ions are i n c o n t a c t , t h e d e v i a t i o n o f ù+_ /kgT from the p r i m i t i v e model i s about 11 u n i t s . About 1 u n i t i s expected on the b a s i s o f s o - c a l l e d l i q u i d s t r u c t u r e e f f e c t s . Thus i f t h e charges and d i p o l e moments were made v a n i s h i n g l y s m a l l one would f i n d u+./k-gT - - 1 . The remaining 10 u n i t s i s a s s o c i a t e d w i t h the poor s h i e l d i n g o f the i o n i c charges by the s o l v e n t d i p o l e s when the ions a r e i n contact. Indeed the contact value observed f o r û+_/kgT corresponds t o a p r i m i t i v e model w i t h ε-6 and t h e same i o n s i z e s as the a c t u a l model, as shown i n the f i g u r e . The s m a l l - r behavior i n F i g . 2 i s q u i t e s u r p r i s i n g from the f o l l o w i n g p o i n t o f view. For r e a l 1-1 e l e c t r o l y t e s i n s o l ­ vents w i t h ε - 1 0 , e.g. tetrabutylammonium p i c r a t e i n ethylene

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

28.

FRIEDMAN

Fundamental Theory of Ionic Solutions

553

d i c h l o r i d e , the mass a c t i o n constant f o r forming +- i o n p a i r s , as estimated from the c o n d u c t i v i t y data, i s r a t h e r c l o s e t o what may be c a l c u l a t e d from the p r i m i t i v e model, w i t h a r e a l i s t i c i o n s i z e parameter, u s i n g the theory of Bjerrum ( l 8 ) . However the mass a c t i o n constant f o r forming i o n p a i r s estimated from the n o n - p r i m i t i v e model curve i n F i g . 2 i s l a r g e r than the p r i m i t i v e model r e s u l t by about three orders o f magnitude. This comparison suggests t h a t the p a r t i c u l a r B O - l e v e l model t r e a t e d i n F i g . 2 i s not very r e a l i s t i c . One does not yet know what a d d i t i o n a l features are r e q u i r e d t o improve the model. Another method o f c a l c u l a t i o n developed by Adelman and a p p l i e d by him t o a model f o r a 1-1 e l e c t r o l y t e i n water eives much s m a l l e r d e v i a t i o n s from the p r i m i t i v e model. ( 1 9 ) We t u r n t o w-j_j(r) i n the case t h a t both i and j a r e hydrophobic s o l u t e p a r t i c l e bond (20) corresponds t corresponding g i j ( r ) . From a B O - l e v e l model f o r a s o l u t i o n o f two Ne atoms i n water,with the B j e r r u m - l i k e ST2 model f o r water (10), Geiger, Rahman, and S t i l l i n g e r (ll) f i n d t h a t t h e i r c a l c u l a t i o n s suggest t h a t % , N e ( ) has a minimum at an r value t h a t corresponds t o a solvent-separated hydrophobic bond. In a more d e t a i l e d and s p e c i a l i z e d c a l c u l a t i o n along s i m i l a r l i n e s but f o r a model f o r Xe i n ST2 water, P a n g a l i , Rao, and Berne (21) f i n d t h a t ûxe?xe(r) has two w e l l s , one near k%. t h a t corresponds t o the u s u a l i d e a o f contact hydrophobic bonds and one near 7^ t h a t corresponds very c l o s e l y t o the type o f s o l v e n t - s e p a r a t e d hydrophobic bond t h a t one can get i f the water near the hydrophobic species has the c h a r a c t e r i s t i c hydrogen bonded s t r u c t u r e of water i n the c l a t h r a t e hydrates. Moreover the û x (r) p o t e n t i a l f u n c t i o n i s i n e x c e l l e n t agreement w i t h that c a l c u l a t e d by P r a t t and Chandler (22) by means o f a very d i f f e r e n t a p p r o x i mation method and a l s o a somewhat d i f f e r e n t model. Thus P r a t t and Chandler are able t o f i n e s s e the s p e c i f i c a t i o n o f the waterwater p a i r p o t e n t i a l i n the B O - l e v e l model by i n t r o d u c i n g , at an appropriate p o i n t i n the t h e o r y , the experimental (x-ray) d i s t r i p bution function (essentially p u r water. r

e

Xe

goo())

f

o

r

e

e

The e a r l i e r r a t h e r complicated evidence f o r c l a t h r a t e s t r u c t u r e s enforced by hydrophobic p a i r s (from EPR l i n e s h a p e phenomena f o r paramagnetic hydrophobic s o l u t e s , (23)) and f o r two s t a t e s o f the hydrophobic bond (from thermodynamic excess f u n c t i o n s (2^,25)) i s p r o v i d e d w i t h a d e t a i l e d background by these important t h e o r e t i c a l developments. k.

REFINED MM-LEVEL MODELS

Extensive s t u d i e s have been made o f MM-level models w i t h the p o t e n t i a l (26) Û..(r) = COR..

+ CAV.. + e.e./er

+ GUR..

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

(9)

554

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

The COR t e r n represents the short range r e p u l s i o n between the i o n s , e i t h e r by a power law (o±^/r)9 o r by an exponential f u n c t i o n e ~ ' i j . I t s parameters are c a l c u l a t e d from the known s i z e s , e.g. c r y s t a l r a d i i , o f p a r t i c l e s i and j . The CAV term, which v a r i e s l i k e l / r ^ , accounts f o r a p a r t i c u l a r d i e l e c t r i c e f f e c t , something l i k e the one i n the s a l t i n g - out theory o f Debye and McAulay. (2j) I t turns out t o be n u m e r i c a l l y unimportant even f o r Setchenow c o e f f i c i e n t s . The Coulomb term i s w e l l known. The GUR term i s intended t o account f o r an e f f e c t p o i n t e d out some time ago by Gurney (2_8) and by H. S. Frank. (29) Thus i f there i s a region (the cosphere) around each i o n w i t h i n which the solvent i s modified by the i o n , then the force between two ions w i l l have a c o n t r i b u t i o n from the f r e e energy changes when the cospheres overlap. This idea i s q u a n t i f i e d i n the form r

a

(26)

GUR..(r) = Α..V

IJ

I

(10)

(r)/V

where V i s the molecula (r) the mutual volume o f the cospheres o f i and j when the distance between t h e i r centers i s r . The amplitude o f the e f f e c t , A^j , the only parameter i n Eq. ( 9 ) t h a t i s adjusted t o f i t the s o l u t i o n data, has the s i g n i f i c a n c e o f the f r e e energy change per molecule o f water d i s p l a c e d from the overlapping cospheres. Most o f t e n the cospheres are assumed t o i n c l u d e one molecular l a y e r o f s o l v e n t . w

m u

The osmotic c o e f f i c i e n t s c a l c u l a t e d from Eq. (9) can be brought i n t o good agreement w i t h s o l u t i o n data up t o about IM f o r aqueous s o l u t i o n s o f a l k a l i (26) and a l k a l i n e e a r t h h a l i d e s , (30) t e t r a a l k y l ammonium h a l i d e s , T3l) mixed e l e c t r o l y t e s , where the Harned c o e f f i c i e n t s are measured, (32) and e l e c t r o l y t e - n o n e l e c t r o l y t e mixtures, where Setchenow c o e f f i c i e n t s are measured. (33) E q u a l l y good r e s u l t s have been found f o r excess e n t h a l p i e s and volumes when these have been attempted. C o n t r i b u t i n g t o AJ;J a r e , i n a d d i t i o n t o the solvent s t r u c t u r a l e f f e c t s e x p l i c i t l y considered, c o n t r i b u t i o n s from d i e l e c t r i c s a t u r a t i o n , from the l i q u i d s t r u c t u r e e f f e c t s one has even i n simple f l u i d s , from solvent-mediated d i s p e r s i o n i n t e r ­ a c t i o n s o f the i o n s , from c h a r g e - p o l a r i z a b i l i t y i n t e r a c t i o n s o f the i o n s , and so on. I t i s d i f f i c u l t t o t e l l a - p r i o r i which e f f e c t s are dominant o r how b i g they are. However the c o l l e c t i o n of A j i c o e f f i c i e n t s has c h a r a c t e r i s t i c s t h a t are c o n s i s t e n t w i t h the f i r s t named e f f e c t being dominant. We f i n d , from the models that f i t the experimental data, t h a t -A-ij/kgT i s most o f t e n i n the range from - 0 . 3 t o 0 . I t v a r i e s q u i t e r e g u l a r l y w i t h v a r i a t i o n o f species i n a manner t h a t i s c o n s i s t e n t w i t h the conclusion t h a t the important e f f e c t s o f ion s i z e are e x p l i c i t l y accounted f o r i n Eq. ( 9 ) . (.33*34.) The most s t r i k i n g r e g u l a r i t y i s that i f i and j are both species that are a l l o r l a r g e l y hydrophobic then Aj_j tends t o be n e a r l y

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

28.

FRIEDMAN

Fundamental Theory of Ionic Solutions

555

independent o f species. This behavior makes i t r e l a t i v e l y easy to p r e d i c t the thermodynamic excess f u n c t i o n s o f aqueous s o l u t i o n s of hydrophobic s o l u t e s w i t h a c e r t a i n accuracy, which doubtless could be improved by f u r t h e r work. (35) One o f t h e f u r t h e r refinements which seems d e s i r a b l e i s t o modify Eq. ( 9 ) so that i t has wiggles (damped o s c i l l a t o r y b e h a v i o r ) . Wiggles are expected i n any r e a l i s t i c MM-level p a i r p o t e n t i a l as a consequence o f t h e molecular s t r u c t u r e o f t h e s o l v e n t ; ( 2 , 3 , 1 0 , 1 1 , 2 1 , 2 2 ) they would be found even f o r two hard sphere s o l u t e p a r t i c l e s i n a hard-sphere l i q u i d o r f o r two E2^0 s o l u t e molecules i n o r d i n a r y l i q u i d H 2 O , and are found i n s i m u l a t i o n s t u d i e s o f s o l u t i o n s based on BO-level models. I n i o n i c s o l u t i o n s i n a p o l a r solvent another source o f w i g g l e s , evidenced i n F i g . 2 , may be a s s o c i a t e d w i t h an o s c i l l a t o r y nonl o c a l d i e l e c t r i c f u n c t i o n s ( r ) . (_36) These v a r i o u s s t u d i e s may be used t o guide the i n t r o d u c t i o r e a l i s t i c way. 5.

NON-THERMODYNAMIC DATA

E l e c t r i c a l c o n d u c t i v i t i e s are much e a s i e r t o measure than thermodynamic c o e f f i c i e n t s and,of courseware a f f e c t e d by the solvent-averaged i o n - i o n f o r c e s . Using charged hard sphere models r e f i n e d by i n c o r p o r a t i o n o f a Gurney-like term E b e l i n g and coworkers ( 3 7 , 3 8 ) and J u s t i c e and J u s t i c e ( 3 9 , ^ 0 ) have adjusted Gurney parameters f o r aqueous a l k a l i h a l i d e s and some other systems t o f i t the c o n d u c t i v i t y data. Quite remarkably the Gurney parameters adjusted t o f i t t h e c o n d u c t i v i t y data are very w e l l c o r r e l a t e d w i t h the Gurney parameters adjusted t o f i t t h e thermodynamic excess f u n c t i o n s . ( F i g . 3) On t h i s b a s i s one c o u l d use c o n d u c t i v i t y data t o f i n d Gurney parameters i n cases i n which the thermodynamic data were incomplete and then use t h e r e s u l t s t o p r e d i c t thermodynamic excess f u n c t i o n s which otherwise would be poorly known. A u s e f u l and s i g n i f i c a n t c o r r e l a t i o n between t h e Gurney parameters and the s o l v a t i o n free energies a l s o has been reported. (38) Next we describe some work t h a t i s d i r e c t e d at t h e question, does the agreement w i t h experiment o f model p o t e n t i a l s l i k e t h e one i n Eq. ( 9 ) imply that t h e models are r i g h t ? I t seems u n l i k e l y that the answer i s a f f i r m a t i v e because o f the great v a r i e t y o f equations which, over the y e a r s , have been reported to give p r e c i s i o n f i t s t o t h e thermodynamic excess f u n c t i o n data; apparently there i s r e l a t i v e l y l i t t l e information i n these data. More d i r e c t l y , we f i n d that we can change some important aspects of the models w i t h i n the scope o f Eq. ( 9 ) and s t i l l f i t the data f o r thermodynamic·excess f u n c t i o n s . T y p i c a l examples are given below. For t h e r a t e constant k ^ o f an a c t i v a t i o n c o n t r o l l e d r e a c t i o n o f a s o l u t e p a r t i c l e o f species a w i t h one o f species a

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

556

THERMODYNAMICS OF AQUEOUS SYSTEMS

W I T H INDUSTRIAL

APPLICATIONS

0.5 h

Figure 3.

Gurney parameters for + — pairs determined by fitting data for osmotic

coefficient φ and conductivity Λ (3$). The line in the figure represents ideal correlation. The data are for alkali halides, except fluorides, in water. The parameter d+_ is defined for a simpler MM-level model than Equation 9; in Ref. 38 it is reported that d+./k/T = 0.75 + 3.6 A . / k T . These correlations have been found by Justice and Justice as well (39, 40). +

b

B

one has k

ab = K b

(

r

)

i

a b

(

r

)

d

(11)

'

where kàb(r) i s t h e r a t e when the distance between t h e reactants i s r . Comparing c a l c u l a t e d and experimental is a much b e t t e r way t o t e s t models than comparison o f t h e thermodynamic excess f u n c t i o n s because k -^ depends only on gat, whereas the thermodynamic excess f u n c t i o n s depend on a l l o f t h e s o l u t e - s o l u t e g^j , weighted by the concentration product i j · (3^»^l) While t h e t h e o r y f o r o r d i n a r y chemical k i n e t i c s i s not s u f f i c i e n t l y advanced so t h a t one knows enough about ab( ) "this purpose,the s i t u a t i o n i s much b e t t e r f o r s p i n r e l a x a t i o n induced by the d i p o l a r s p i n - s p i n i n t e r a c t i o n , as i n the process a

c

k

c

r

f

o

r

7

+

Li (m) + N i

2 +

7

+

= Li (m') + Ni

2+

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

28.

FRIEDMAN

557

Fundamental Theory of Ionic Solutions

f

where m-*m represents a change i n n u c l e a r s p i n s t a t e o f the T L i , i n t h i s case due t o c o l l i s i o n w i t h the paramagnetic N i . The r a t e constant i s determined by measuring Τη_ o f ÎLi as a f u n c t i o n of N i ^ concentration i n aqueous s o l u t i o n s o f L i C l and N i C l 2 * w i t h added MgCl2 t o keep the i o n i c s t r e n g t h f i x e d . The r a t e cons t a n t i s c a l c u l a t e d f o r models based on Eq. (9) f o r each one of the f o l l o w i n g cases. A. N i ^ and L i both are r i g i d l y hydrated so t h a t the i o n i c r a d i i used i n Eq. (9) are r e s p e c t i v e l y , 0.7+2.76 S and 0.6+2.762 . B. N i i s r i g i d l y hydrated but L i i s not; i t s r a d i u s i n Eq. (9) i s only 0.6 8 , C. N e i t h e r N i ^ nor L i i s r i g i d l y hydrated. A l l three models may be f i t t o the thermodynamic data f o r aqueous s o l u t i o n s o f N i C l 2 , L i C l , and t h e i r mixtures by a d j u s t i n g t h e i r Gurney parameters. Thus i i d i f f i c u l dynamic data whether on However only model Β i s i n s a t i s f a c t o r y agreement w i t h the s p i n r e l a x a t i o n data. (kl) 2 +

+

+

+

+

+

+

At t h i s time d i f f r a c t i o n data f o r i o n - i o n d i s t r i b u t i o n s i n aqueous s o l u t i o n s o f moderate c o n c e n t r a t i o n are beginning t o become a v a i l a b l e . In aqueous N1CI2 s o l u t i o n s very r e f i n e d neutron d i f f r a c t i o n s t u d i e s i n d i c a t e t h a t the N i - C l ~ p a i r c o r r e l a t i o n f u n c t i o n has a peak near 3 . l S under c o n d i t i o n s i n which the C l ~ does not penetrate the N i ( H 2 0 ) g u n i t . (h2) I t i s r e p o r t e d that EXAFS s t u d i e s give the same r e s u l t . (h3) While the i n f o r m a t i o n i s most welcome i t i s p u z z l i n g because a geometrical c a l c u l a t i o n i n d i c a t e s t h a t the c l o s e s t center t o center distance f o r the N i and a C l ~ that does not penetrate the h y d r a t i o n s h e l l i s c l o s e r t o 3.98. (1) 2 +

2 +

2 +

6.

CORRESPONDING STATES FOR IONIC SYSTEMS

I t has been proposed t o define a reduced temperature T f o r a s o l u t i o n o f a s i n g l e e l e c t r o l y t e as the r a t i o o f kgT t o the work r e q u i r e d t o separate a contact +- i o n p a i r , and the reduced d e n s i t y p as the f r a c t i o n o f the space occupied by the i o n s , (kk) The p r i n c i p a l f e a t u r e on the T , p corresponding s t a t e s diagram i s a coexistence curve f o r two phases, w i t h an upper c r i t i c a l p o i n t as f o r the l i q u i d - v a p o r e q u i l i b r i u m o f a simple f l u i d , but w i t h a markedly lower reduced temperature at the c r i t i c a l p o i n t than f o r a simple f l u i d (with the corresponding d e f i n i t i o n o f the reduced temperature, i . e . the r a t i o o f kgT t o the work r e q u i r e d t o separate a van der Waals p a i r . ) In the case o f a plasma, an i o n i c f l u i d without a s o l v e n t , the coexistence curve i s f o r the l i q u i d - v a p o r e q u i l i b r i u m , w h i l e f o r s o l u t i o n s i t corresponds t o two s o l u t i o n phases o f d i f f e r e n t concentrations i n e q u i l i b r i u m . Some non-aqueous s o l u t i o n s are known which do unmix t o form two l i q u i d phases o f s l i g h t l y d i f f e r e n t c o n c e n t r a t i o n s . While no examples i n aqueous s o l u t i o n are known, the corresponding r

r

r

r

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

558

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

s t a t e s p r i n c i p l e f o r i o n i c f l u i d s suggests t h a t s o l u t i o n s o f even 1-1 e l e c t r o l y t e s i n water might unmix above 300°C i n some c o n c e n t r a t i o n range. I t i s d i f f i c u l t t o be more p r e c i s e because the coexistence curve apparently i s s e n s i t i v e t o d e t a i l s i n t h e p a i r p o t e n t i a l s . (36) 7.

MIXING COEFFICIENTS

In a symposium concerning i n d u s t r i a l a p p l i c a t i o n s one expects s o l u t i o n s o f s i n g l e e l e c t r o l y t e s t o take second p l a c e i n importance behind s o l u t i o n s o f mixed e l e c t r o l y t e s . The l a t t e r have s c a r c e l y been mentioned i n t h i s review. To redress the balance we r e c a l l here an i n t e r e s t i n g question r e g a r d i n g the mixing c o e f f i c i e n t gj_ t h a t appears i n t h e expansion o f t h e excess f r e e energy o f mixing two e l e c t r o l y t e s w i t h a common i o n at constant molal i o n i s t r e n g t h I e X

A G (y,l) = y(l-y)l WRT[g (l) m

0

(l-2y)

g ; L

(l)

] (12)

Here y i s the f r a c t i o n o f the i o n i c s t r e n g t h due t o one o f t h e e l e c t r o l y t e s and W i s the mass (kg) o f solvent i n the mixture. I t i s w e l l known {h) t h a t h i g h e r order l i m i t i n g laws, depending upon o n l y the charge type and ε , determine t h e behavior o f gQ at very low I . Recently i t was found e x p e r i m e n t a l l y by Cassel and Wood {k5) t h a t i n mixtures o f d i f f e r e n t charge types at low I the c o e f f i c i e n t g ( a c t u a l l y 3(g;j/T)/3(l/T) ) seemed t o be d i v e r g i n g as I-K) and, moreover, t h a t the species-dependence of the divergence i n d i c a t e d t h a t t h e divergence was a l i m i t i n g law phenomenon. C a l c u l a t i o n s by two approximation methods (k6) showed t h a t g j would indeed appear t o diverge i n the range s t u d i e d by Cas s e l and Wood, and t h a t t h e e f f e c t was indeed due t o the l o n g range Coulomb i n t e r a c t i o n s , but t h e c a l c u l a t e d and experimental c o e f f i c i e n t s disagreed i n both s i g n and magnitude! On the other hand, more recent measurements i n a d i f f e r e n t system by Khoo and coworkers (hj) seem c o n s i s t e n t w i t h t h e t h e o r y , although the comparison has yet t o be c a r e f u l l y developed. ±

8.

ACKNOWLEDGEMENT

We are g r a t e f u l f o r the support o f the present work by the N a t i o n a l Science Foundation. LITERATURE CITED

1. Hill, T. L. "Statistical Mechanics," McGraw-Hill, New York, 1956. 2. Hansen, J. P. and McDonald, I. R., "Theory of Simple Liquids," Academic Press, N.Y., 1976. 3. Watts, R. O. and McGee, I. J. "Liquid State Physics," J. Wiley and Sons, N.Y., 1976.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

28. FRIEDMAN Fundamental Theory of Ionic Solutions

559

4. Friedman, H. L., "Ionic Solution Theory," Interscience Publishers, N.Y., 1962. 5. Friedman, H. L. and Dale, W. D. T., in "Modern Theoretical Chemistry, Vol. V, Statistical Mechanics," Plenum Press, N.Y., 1977, Editor, Berne, Bruce J., pp. 85-135. 6. Andersen, H. C., Ann. Revs. Phys. Chem., 1975, 26, l45. 7. Friedman, H. L., Jour. Electrochem. Soc., 1977, 124, 421C. 8. Friedman, H. L., in "Protons and ions involved in fast dynamic phenomena," Elsevier, N.Y., 1978. Laszlo, P., editor. 9. Lie, G. C., Clementi, Ε., and Yoshimine, Ν., J. Chem. Phys., 1976, 64, 2314. 10. Rahman, A. and Stillinger, F. Η., J. Chem. Phys., 1971, 55, 3336. 11. Geiger, Α., Rahman, , Stillinger, , Phys., 1979, 70, 263. 12. McMillan, W. G. and Mayer, J. Ε., J. Chem. Phys.., 1945, 13, 276. 13. Friedman, H. L., J. Chem. Phys., 1960, 32, 1134. 14. Stell, G. R. and Høye, J., Faraday Discuss. Chem. Soc., 1977, 64, 16. 15. Pitzer, K. S., Accts. Chem. Res., 1977, 10, 371. 16. Patey, G. N. and Valleau, J. P., J. Chem. Phys., 1975, 63, 2334. 17. Levesque, D., Weis, J. J., and Patey, G. Ν., Physics Letters, 1978, 66A, 115. 18. Kraus, C. Α., J. Phys. Chem., 1956, 60, 129. 19. Adelman, S. and Chen, J.-H., J. Chem. Phys., 1979, 70, 4291. 20. Kauzmann, W., Adv. Protein Chem., 1959, 14, 1. 21. Pangali, C., Rao, Μ., and Berne, B. J., J. Chem. Phys., 1979, 71, 2975. 22. Pratt, L. and Chandler, D., J. Chem. Phys., 1977, 67, 3683. 23. Jolicoeur, C. and Friedman, H. L., Ber. Bunsenges., 1971, 75, 248. 24. F. Franks in "Water, A Comprehensive Treatise," Plenum Press, N.Y.. 1974, Vol. 4, Ch. 1. Franks, F., editor. 25. Clarke, Α. Η., Franks, F., Pedley, M. D., and Reid, D. S., Faraday Trans. Chem. Soc. I, 1977, 73, 290. 26. Ramanathan, P. S. and Friedman, H. L., J. Chem. Phys., 1971, 54, 1086. 27. Debye, P. and McAulay, J., Physik. Z., 1925, 26, 22.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

560 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

28. Gurney, R. W., "Ionic Processes in Solution," Dover, N.Y., 1953. 29. Frank, H. S., in "Chemical Physics of Ionic Solutions, edited by Conway, Β. E. and Barradas, R. G., Wiley, N.Y., 1966, Z. Physik Chem. (Leipzig), 1965, 228, 364. 30. Friedman, H. L., Smitherman, Α., and De Santis, R., J. Solution Chem., 1973, 2, 59. 31. Ramanathan, P. S., Krishnan, C. V., and Friedman, H. L., J. Solution Chem., 1972, 1, 237. 32. Friedman, H. L. and Ramanathan, P. S., J. Phys. Chem., 1970,74,3756. 33. Krishnan, C. V. and Friedman, H. L., J. Solution Chem., 1974, 3, 727. 34. Friedman, H. L., Krishnan "Structure of Water and Aqueous Solutions, Luck, W., editor, Verlag Chemies Gmbh,1974,p. 169. 35. Rossky, P. J. and Friedman, H. L., J. Phys. Chem., 1979, submitted. 36. Dogonadze, R. R. and Kornyshev, Α. Α., J. Chem. Soc. Faraday Trans., 1974, 70, 2. 37. Bich, Ε., Ebeling, W., and Krienke, Η., Z. Phys. Chem., Leipzig, 1976, 257, 549. 38. Wiechert, Η., Krienke, Η., Feistel, R., and Ebeling, W., Z. Phys. Chem. Leipzig, 1978, 251, 1057· 39· Justice, J.-C. and Justice, M.-C., Faraday Discuss. Chem. Soc., 1977, 64, 265. 40. Justice, M.-C. and Justice, J . - C , Pure and Applied Chem., 1979, 51, 1681. 41. Hirata, F., Holz, Μ., Hertz, H. G., and Friedman, H. L., to be submitted. 42. Soper, Α. Κ., Neilson, G. W., Enderby, J. E. and Howe, R. Α., J. Phys. C, 1977, 10, 1793. 43. Sandstrom, D. R., J. Chem. Phys., 1979, 71, 2381. 44. Friedman, H. L. and Larsen, Β., J. Chem. Phys., 1978, 69, 92. 45. Wood, R. H. and Cassel, R. Β., J. Phys. Chem., 1974, 78, 1924. 46. Friedman, H. L. and Krishnan, C. V., J. Phys. Chem., 1974, 78, 1927. 47. Khoo, Κ. Η., Lim, Τ. Κ., and Chan, C. Υ., Faraday Trans. Chem. Soc. I, 1978, 74, 2037. RECEIVED

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

29 Activity Coefficients, Ionic Media, and Equilibrium Constants R. M . PYTKOWICZ Oregon State University, Corvallis, OR 97330

In this work the concepts of ionic medium effective ionic strength and free versu ined. Then they are applie y permissibl incorrect translations of equilibrium constants from one medium to another. Ionic Media Ionic media are solutions of background electrolytes which are concentrated enough so that the activity coefficients of the electrolytes of interest do not change during processes which are occurring. Typical ionic media are a 1 m HClO or NaClO solution and seawater. Let us consider the dissolution-precipitation process in seawater in the following example. The normal concentrations of calcium and of carbonate in the near-surface oceanic waters are about [Ca+] = 0.01 and [C03 -] = 2X10 M. The CaC0 in solution is metastable and roughly 2u0% saturated (1). Should precipitation occur due to an abundance of nuclei, [C03 -] will drop to 10 M but [Ca ] will change by no more than 2%. There­ fore, the ionic strength of the ionic medium seawater will remain essentially constant at 0.7 M. The major ion composition will also remain constant. We shall see later what the implications are for equilibrium constants. 4

2

2

4

-4

3

2

-4

2+

I t i s i m p o r t a n t t o r e a l i z e t h a t one must t a k e i n t o c o n s i d e r a t i o n i o n a s s o c i a t i o n o f t h e i o n i c media e l e c t r o l y t e s b e c a u s e i t a f f e c t s t h e e f f e c t i v e i o n i c s t r e n g t h ( 2 ) . T h i s i n t u r n changes the a c t i v i t y c o e f f i c i e n t s o f t h e i o n s under s t u d y . The e f f e c t i v e i o n i c s t r e n g t h , I , o f a 2-1 e l e c t r o l y t e C A w h i c h a s s o c i a t e s i s g i v e n by e

I

e

2

=0.5{4[C

2 +

]

p

+ [ A - ] + [CA ]} F

where t h e s u b s c r i p t F r e f e r s t o f r e e s p e c i e s . I p l a y s a key r o l e i n e q u i l i b r i a .

(1)

+

We s h a l l

see t h a t

e

0-8412-0569-8/80/47-133-561$05.00/0 © 1980 American Chemical Society In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

562

APPLICATIONS

E l e c t r o l y t e s w h i c h o f t e n a r e c o n s i d e r e d t o be c o m p l e t e l y d i s s o c i a t e d b u t i n e f f e c t a r e n o t a r e NaCl and NaClO^ ( 3 ) . Ion-Pairing In t h e p r e c e e d i n g s e c t i o n m e n t i o n was made o f i o n a s s o c i a t i o n ( i o n - p a i r i n g ) w h i c h , f o r the purposes o f t h i s paper, w i l l r e f e r to coulombic e n t i t i e s with o r without cosphere o v e r l a p . Experim e n t a l s u p p o r t f o r i o n - p a i r i n g has come from sound a t t e n u a t i o n ( 4 J , Raman s p e c t r o s c o p y [5) and p o t e n t i o m e t r y ( 2 , 3). Credibility has r e s u l t e d from t h e model o f Fuoss {§) a p p l i e c T by K e s t e r and Pytkowicz (7). Our method a t p r e s e n t i s n o t based upon t h e o r e t i c a l m o d e l s o r d e p a r t u r e s from i d e a l b e h a v i o r . I t c o n s i s t s i n the use o f p o t e n t i o m e t r i c d e t e r m i n a t i o n s and l i t e r a t u r e v a l u e s o f a c t i v i t y coefficients, starting h HCI-HCI0 e l e c t r o l y t d with the assumption tha t h e a s s o c i a t i o n c o n s t a n t pK = 7 i s e x t r e m e l y s m a l l i n t h i s c a s e . A c o m p a r i s o n o f e x p e r i m e n t a l r e s u l t s w i t h t h o s e c a l c u l a t e d from t h e Fuoss (6>) t h e o r y i s p r e s e n t e d i n T a b l e I. The t h e o r y i s o n l y v a l i d a p p r o x i m a t e l y so t h a t t h e o r d e r o f m a g n i t u d e agreement i s f a i r l y g o o d , e x c e p t i n t h e c a s e s o f MgC0 ° and C a C 0 ° . Stoichiom e t r i c a s s o c i a t i o n c o n s t a n t s K* a r e t h e n o b t a i n e d from t h e a c t i v i t y c o e f f i c i e n t s , e x p r e s s i o n s f o r K*, and from e q u a t i o n s f o r t h e c o n s e r v a t i o n o f mass. The l a t t e r e x p r e s s t h e t o t a l c o n c e n t r a t i o n o f a g i v e n i o n as t h e sum o f t h e c o n c e n t r a t i o n s o f t h e f r e e i o n and o f t h e i o n - p a i r s . V a l u e s o f K* and o f t h e a c t i v i t y c o e f f i c i e n t s o f f r e e i o n s i n i o n i c media depend o n l y upon t h e e f f e c t i v e i o n i c s t r e n g t h a s i s shown l a t e r . 3

3

T a b l e I. A comparison o f s t o i c h i o m e t r i c a s s o c i a t i o n constants c a l c u l a t e d from t h e Fuoss [6) model w i t h Debye r a d i i and from t h e measurements o f J o h n s o n and P y t k o w i c z ( 3 ) . Ion

Pair

NaS 1 0 " i s 3

3

3

log γ

= -

(3)

C

1

B a l0.s

+

D

D

h o w e v e r , i t i s e n t i r e l y e m p i r i c a l b e c a u s e F r a n k and Thompson ( 9 ) showed t h a t t h e i o n i c a t m o s p h e r e i s t h e n c o a r s e - g r a i n e d . The s p h e r e o f r a d i u s l/κ may c o n t a i n o n l y one o r a f r a c t i o n o f an i o n in c o n t r a s t to the requirement i s u s e d t h e n a has t o the e l e c t r o l y t e o f i n t e r e s t . T h i s f i t t o e x p e r i m e n t a l d a t a means t h a t y+j r a t h e r t h a n γ+p i s b e i n g d e t e r m i n e d . I n t e r m s o f e m p i r i c a l e q u a t i o n s , t h e f o l l o w i n g one p r o v i d e s good f i t s f r o m 1 0 " t o I.0 m s o l u t i o n s a c c o r d i n g t o o u r w o r k . The Davies e q u a t i o n (10) D

3

log

Ζ Ζ

Α I · 0

= - JLi_Ç

γ ±

5

+

,

C

1 + B l0-5

C

+

Q T 1.5 + Ε 12 C

(4)

C

c

i n c o n t r a s t t o t h e above e q u a t i o n s , i s a p r e d i c t i v e t o o l t h a t w o r k s w e l l up t o I = 0 . 1 . Note s h o u l d be made, h o w e v e r , t o t h e e f f e c t t h a t , i f i o n - p a i r i n g o r complexing o c c u r s , then the Davies e q u a t i o n o n l y works i f γ+ i s c o r r e c t e d f o r a s s o c i a t i o n . Thus, t h i s e q u a t i o n y i e l d s ( γ + ) = ( γ + ) when t h e r e i s no a s s o c i a t i o n and ( γ ) ρ when i o n - p a i r i n g o c c u r s . S e v e r a l approaches a r e a v a i l a b l e i n the case o f mixed electrolyte solutions. The G u n t e l b e r g e q u a t i o n c a n be u s e d a t v e r y h i g h d i l u t i o n s t o a v o i d t h e a m b i g u i t y i n t h e meaning o f a , t h e d i s t a n c e o f c l o s e s t a p p r o a c h , when s e v e r a l e l e c t r o l y t e s a r e present. T h i s e q u a t i o n i s e m p i r i c a l and has f e w e r t e r m s t h a n t h e Debye-Huckel e x t e n d e d e q u a t i o n . I found i t t o y i e l d poor a g r e e ­ ment w i t h e x p e r i m e n t a l r e s u l t s even a t m = 0.01 f o r NaCl a t 25°C (γ ] = 0 . 8 9 8 5 and γ = 0.9024). For the Davies equation f o r m = 0 . 2 0 one o b t a i n s γ+ i = 0 . 7 5 2 and γ = 0.735 a l s o f o r NaCl a t 2 5 ° C . " An e x t e n d e d f o r m o f t h e Debye-Huckel e q u a t i o n i s t h e h y d r a ­ t i o n one o f R o b i n s o n and S t o k e s ( 1 1 ) . I t c o n t a i n s two a d j u s t a b l e p a r a m e t e r s , ar) and h , where h i s r e l a t e d t o t h e h y d r a t i o n number. I t c a n be f i t t e d t o γ f o r s e v e r a l e l e c t r o l y t e s f o r c o n c e n t r a t i o n s i n e x c e s s o f 1 m. T h e i r e q u a t i o n has t h e v a l u a b l e f e a t u r e o f d e s c r i b i n g not o n l y the s a l t i n g - i n but a l s o the s a l t i n g - o u t part of the γ versus m curve. I t s h o u l d be n o t e d , h o w e v e r , t h a t t h e τ

ρ

±

D

±

c

a

C

±

e

x

p

c

a

c

+ e

x

D

H

±

+

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

29.

Activity Coefficients and Equilibrium Constants

PYTKOWICZ

565

a r b i t r a r y a l l o c a t i o n o f n o n - h y d r a t i o n t e r m s t o t h e Debye-Huckel e q u a t i o n f o r t h e e s t i m a t e o f a n a t h i g h c o n c e n t r a t i o n s weakens t h e theoretical v a l i d i t y o f the hydration equation. Furthermore, i t i s an o v e r s i m p l i f i c a t i o n t o o n l y c o n s i d e r t h e n o n s p e c i f i c c o u l o m b i c and t h e h y d r a t i o n t e r m s . Note t h a t , u n l e s s o t h e r w i s e i n d i c a t e d , I am u s i n g I a n d (γ ) = (γ+) χρ ' t h i s review. Furthermore, the simple equations p r e s e n t e d so T a r do n o t i n c l u d e t e r m s f o r t h e c o s p h e r e o v e r l a p , the hard c o r e t e r m , and i o n - c a v i t y i n t e r a c t i o n s . Next, p r e d i c t i v e equations f o r a c t i v i t y c o e f f i c i e n t s i n m i x e d e l e c t r o l y t e s o l u t i o n s , based upon r e s u l t s i n s i m p l e r o n e s , w i l l be m e n t i o n e d . The work o f B r t f n s t e d ( 1 2 ) and o f Guggenheim (13) l e d t o t h e s p e c i f i c i n t e r a c t i o n e q u a t i o n e

±

τ

θ

log γ

± Β

Ί

= -

η

1 + 10

x / ( l - x ) i s t h e m o l a l r a t i o o f Β t o C where Β i s MX and C i s N Y . A s i m i l a r c o n d i t i o n a p p l i e s t o l o g γ + ç . One c a n d e r i v e H a r n e d ' s r u l e f r o m t h i s e x p r e s s i o n a l t h o u g h i t c a n a l s o be done f r o m t h e i o n p a i r i n g model ( 2_). The e q u a t i o n s work w e l l f o r I up t o 0.1 m and p e r m i t t h e c a l c u l a t i o n o f γ+β and y i n a m i x t u r e o f t h e two e l e c t r o l y t e s from data o b t a i n e d i n s i n g l e e l e c t r o l y t e s o l u t i o n s . The method s u f f e r s , h o w e v e r , b e c a u s e t h e Β c o e f f i c i e n t s a r e n o t allowed to vary with the i o n i c strength. The s t a t i s t i c a l t h e r m o d y n a m i c a p p r o a c h o f P i t z e r ( 1 4 ) , i n v o l v i n g s p e c i f i c i n t e r a c t i o n t e r m s on t h e b a s i s o f t h ê T k i n e t i c c o r e e f f e c t , has p r o v i d e d c o e f f i c i e n t s w h i c h a r e a f u n c t i o n o f the i o n i c s t r e n g t h . The c o e f f i c i e n t s , a s t h e s t o i c h i o m e t r i c association constants i n our ion-pairing model, a r e obtained e m p i r i c a l l y i n s i m p l e s o l u t i o n s and a r e t h e n used t o p r e d i c t t h e a c t i v i t y c o e f f i c i e n t s i n complex s o l u t i o n s . The P i t z e r a p p r o a c h u s e s , h o w e v e r , a f i r s t t e r m a k i n t o t h e Debye-Huckel o n e t o represent nonspecific effects a t a l l concentrations. This weakens somewhat i t s t h e o r e t i c a l f o u n d a t i o n . As most o t h e r m e t h o d s , i n c l u d i n g o u r i o n - p a i r i n g model w h i c h was d e s c r i b e d e a r l i e r , t h e P i t z e r a p p r o a c h i s e m p i r i c a l i n practice. The i n t e r a c t i o n c o e f f i c i e n t s i n t h i s c a s e a r e d e t e r m i n e d by c u r v e f i t t i n g i n s i n g l e e l e c t r o l y t e s o l u t i o n s . I n t h e e q u a t i o n s d e v e l o p e d by R e i l l y and Wood ( 1 5 ) f r o m t h e c l u s t e r i n t e g r a l model ( l j 5 ) , γ i s c a l c u l a t e d i n compTex s o l u t i o n s f r o m e x c e s s p r o p e r t i e s o f s i n g T e s a l t s o l u t i o n s . Note t h a t t h e c l u s t e r i n t e g r a l a p p r o a c h i s based upon t e r m s w h i c h r e p r e s e n t t h e c o n t r i b u t i o n s o f pair-wise i o n i n t e r a c t i o n s i n various types o f c l u s t e r s to the p o t e n t i a l i n t e r a c t i o n energy. Then, the p a r t i t i o n f u n c t i o n and t h e e x c e s s p r o p e r t i e s o f t h e s o l u t i o n c a n be evaluated. The p r o c e d u r e i s a k i n t o t h e v i r i a l e x p a n s i o n i n t e r m s of c l u s t e r s . The more r e c e n t s t a t i s t i c a l t h e r m o d y n a m i c work a p p r o a c h e s t h e ±

c

+

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

566

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS

W I T H INDUSTRIAL

APPLICATIONS

p r o b l e m from t h e s t a n d p o i n t o f t h e r a d i a l d i s t r i b u t i o n f u n c t i o n (17). In u s i n g t h i s m e t h o d , Ramanthan and Fridman (1J3), i n c o n ­ t r a s t t o t h e method o f P i t z e r , made t h e Gurney c o s p h e r e o v e r l a p , t h e i o n - c a v i t y r e p u l s i o n , and r e p u l s i v e c o r e p o t e n t i a l e x p l i c i t . The c u r v e f i t t i n g was done by means o f t h e Gurney t e r m . The most f e r t i l e a p p r o a c h e s so f a r , from t h e s t a n d p o i n t o f p r e d i c t i n g γ i n complex s o l u t i o n s from d a t a i n s i m p l e o n e s , have been t h a t o f P i t z e r ( 1 4 J , and t h e i o n - p a i r a p p r o a c h o f P y t k o w i c z and K e s t e r [2) and o f J o h n s o n and P y t k o w i c z (3). The l a t t i c e model o f P y t k o w i c z and J o h n s o n (19) i s , a t t h T s t i m e , an e x p l a n a ­ t o r y r a t h e r than a p r e d i c t i v e t o o f . The o n l y t h r e e methods w h i c h do n o t r e q u i r e c u r v e - f i t t i n g a t p r e s e n t a r e t h e u s e o f t h e Debye-Hiickel l i m i t i n g l a w and o f t h e e q u a t i o n s o f G u n t e l b e r g and o f D a v i e s . Unfortunately these e q u a t i o n s a r e o f v a l u e o n l y i n v e r y d i l u t e and s i m p l e s o l u t i o n s . ±

Equilibrium

Constants

L e t us examine t h e f o l l o w i n g t y p e s o f c o n s t a n t s n o w . i n u s e and t h e i r r e l a t i o n s h i p s t o t h e thermodynamic c o n s t a n t s Κ * * ) : a) Apparent d i s s o c i a t i o n c o n s t a n t s which a r e o f p r a c t i c a l use i n i o n i c media (20) ,(t) = K, ΉΑ b)

Stoichiometric

K ; S

c)

HA T ;

(6)

T7^~

s o l u b i l i t y p r o d u c t s , such as

= [C*+] [C03*-] T

T

- K^/(Y

± C a C 0 3

)i

(7)

Free s o l u b i l i t y product

K " s p

d)

l Y

= [o*+] [C03*-] = K Î J / ( Y ,

F

F

± C a C 0 3

)

(8)

2 F

Stoichiometric association constant f o r ion-pairs

(9)

e)

A f f i n i t y c o n s t a n t s f o r compl (10)

(γ ) d e p e n d s o n l y upon t h e e f f e c t i v e i o n i c s t r e n g t h o f t h e medium. T h u s , κ " , Κ*, and 3 c a n be d e t e r m i n e d i n one i o n i c ±

£

(j

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

29.

PYTKOWICZ

Activity Coefficients and Equilibrium Constants

567

medium s u c h a s HC104 and a p p l i e d i n a n o t h e r one s u c h a s s e a w a t e r , provided that I i s t h e same i n t h e two s o l u t i o n s . K u ' and K ' , on t h e o t h e r h a n d , must be d e t e r m i n e d and^ a p p l i e d i n t h e same medium b e c a u s e γγ depends upon t h e c o m p o s i t i o n of the solution. Note t h a t i o n - p a i r i n g m o d e l s a r e r e q u i r e d f o r both c l a s s e s o f c o n s t a n t s t o a s c e r t a i n t h a t I i s indeed the same. e

A

s p

e

Literature Cited

1. Pytkowicz, R.M., J. Geol., 1965, 73,196-199. 2. Pytkowicz, R.M.; Kester, D.R., Am. J. Sci., 1969, 267, 217-229. 3. Johnson, K.; Pytkowicz, R.M., Am. J. Sci., 1978, 278, 14281447. 4. Fisher, F.H., Science 1967 157 823 5. Daly, F.P.; Brown 76, 3664-3668. 6. Fuoss, R.M., J. Am. Chem.Soc.,1958, 80, 5059-5061. 7. Kester, D.R.; Pytkowicz, R.M., Mar. Chem., 1975, 3, 365-374. 8. Pitzer, K.S.; Kim, J.J., Am. Chem. Soc. Jour., 1974, 96,5701. 9. Frank, H.S.; Thompson, P.T., J. Chem. Phys., 1959,31,10861095. 10. Davies, C.W., "Ion Association", Butterworths, London, 1962. 11. Robinson, R.A.; Stokes, R.H., "Electrolyte Solutions", Butterworths, London, 1968. 12. Brønsted, J.N., J. Am. Chem.Soc.,1922, 44, 877-898. 13. Guggenheim, E.A., Philos. Mag., 1935, A, 588-643. 14. Pitzer, K.J., Phys. Chem., 1973, 77, 258-277. 15. Reilly, P.J.; Wood, R.H., J. Phys. Chem., 1969, 73, 4292-4297. 16. Friedman, H.L., "Ionic Solution Theory", Interscience, New York, 1952. 17. Vaslow, F., "Water and Aqueous Solutions", R.A. Home, ed., Interscience, New York, 1972, pp. 465-518. 18. Ramanathan, P.S.; Friedman, H.L., J. Chem. Phys., 1971, 54, 1086-1099. 19. Pytkowicz, R.M.; Johnson, K., "Activity Coefficients in Electrolyte Solutions", R.M. Pytkowicz, ed., CRC Press, Coral Gables, Florida, In press. 20. Pytkowicz, R.M.; Ingle, S.E.; Mehrback, C , Limnol. Oceanogr., 1974, 19, 665-669. RECEIVED February 11, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

30 Flow Calorimetry of Aqueous Solutions at Temperatures up to 325° C R. H . WOOD and D. SMITH-MAGOWAN University of Delaware, Newark, D E 19711

1) Need The fact that we ar gathere togethe "Thermodynamics on Aqueous Systems with Industrial Application" indicates the importance of thermodynamic data on aqueous solu­ tions. In particular, there is a great need for data on high temperature aqueous systems. Because of the experimental diffi­ culties, there are relatively few measurements on these systems and yet they are of very great industrial importance. As the temperature of water approaches the critical tempera­ ture, 374°C, it becomes a low dielectric constant solvent with the dielectric constant approaching one tenth its value at 25°C. This is about the same dielectric constant as 1,1 dichloroethane at 25°C. Because of this large change in solvent properties there are corresponding very large changes in the properties of electrolytes dissolved in water. The few data available indicate(1-4) that the heat capacities of dilute aqueous solution be­ come very large and negative as the temperature approaches the critical temperature and the data presented below will show that the relative apparent molal enthalpy, L , becomes very large and positive at higher temperatures. These very large changes in thermodynamic properties make it very difficult to predict high temperature properties of solutions from low temperature measure­ ments and increase the need for accurate measurements. Φ

2)

Information

Obtained

C a l o r i m e t r i c m e a s u r e m e n t s , when combined w i t h t h e n o r m a l l y a v a i l a b l e room t e m p e r a t u r e t h e r m o d y n a m i c p r o p e r t i e s , g i v e v a l u e s f o r f r e e e n e r g y , e n t h a l p y , h e a t c a p a c i t y and even volume a t h i g h temperatures. We have been a c t i v e l y d e v e l o p i n g two t y p e s o f c a l o r i m e t e r s w h i c h w i l l o p e r a t e a t e l e v a t e d t e m p e r a t u r e s and p r e s s u r e s . One t y p e i s a h e a t o f m i x i n g c a l o r i m e t e r t o measure e n t h a l p i e s o f d i l u t i o n i n order to obtain d i f f e r e n c e s i n p a r t i a l molal enthalpy 0-8412-0569-8/80/47-133-569$05.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

570

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

or heat c o n t e n t s :

This property simply considered i s the f i r s t temperature d e r i v a ­ t i v e o f t h e f r e e e n e r g y o r a c t i v i t y and c a n be u s e d t o o b t a i n o s ­ m o t i c c o e f f i c i e n t s and a c t i v i t y c o e f f i c i e n t s by t h e r e l a t i o n s h i p s : T Φ(ϋΙ,Ι) - 4>(m,T ) = {mV2vR}/ 2

3L (-£)d(i)

2

and £ny(m,T) = [(m,T)-l

ο

where ï i s a r e f e r e n c e t e m p e r a t u r e . We have a l s o d e v e l o p e d a h e a t c a p a c i t y c a l o r i m e t e r f o r these extreme c o n d i t i o n s . The h e a t c a p a c i t y i s t h e s e c o n d t e m p e r a t u r e d e r i v a t i v e o f t h e f r e e e n e r g y and c a n be u s e d t o c a l c u l a t e t h e t e m p e r a t u r e d e p e n d ence o f e q u i l i b r i a by t h e r e l a t i o n s h i p :

AGiLPi . ΔβίΙ,Ρΐ

+

Δ

Η

(

ΐ

>

ρ

)

[

| . V,

+

/

ζ

(

Δ

£

ρ

d T 1 1 )

d (

|

( )

S i m i l a r l y the temperature dependencies o f the r e l a t i v e apparent m o l a l h e a t c o n t e n t c a n be d e t e r m i n e d f r o m t h e h e a t c a p a c i t y b y : 1

1

V" ' ^

88

111

V »*)

/ (^(m,T)

+

2

- C °(0,T))dT p

These c a l o r i m e t e r s c a n be used t o d e t e r m i n e t h e s e t h e r m a l p r o p e r t i e s t h r o u g h o u t a w i d e r a n g e o f p r e s s u r e s . The p r e s s u r e dependence c a n be used t o c a l c u l a t e v o l u m e t r i c p r o p e r t i e s by means o f t h e r e l a t i o n s h i p s : τ

Φ - "(1τ> τ

+v

ρ

Φ* =- 4) T

3 P

3)

Τ

3Γ Ρ

Advantages In a f l o w c a l o r i m e t e r t h e t h e r m o d y n a m i c p r o p e r t i e s a r e mea-

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

30.

WOOD AND SMITH-MAGOWAN

Calorimetry of Aqueous Solutions

571

sured i n a f l o w i n g stream contained i n a small diameter t u b i n g . F l o w c a l o r i m e t r i c t e c h n i q u e s have been u s e d f o r many y e a r s a t room t e m p e r a t u r e b e c a u s e o f t h e i r s p e e d a n d c o n v e n i e n c e ^ : ^ ' . For o p e r a t i o n s a t h i g h temperatures o r w i t h a h i g h vapor p r e s s u r e s o l v e n t , t h e advantages o f u s i n g f l o w c a l o r i m e t r i c techniques a r e overwhelming. I n t h e f i r s t p l a c e t h e r e i s no v a p o r s p a c e s o t h e r e i s no n e c e s s i t y f o r c o r r e c t i o n s f o r t h e change i n t h e v a p o r space c o m p o s i t i o n . Because o f t h e s m a l l d i a m e t e r t u b i n g u s e d , r e l a t i v e l y t h i n w a l l e d t u b i n g i s s t r o n g enough t o c o n t a i n t h e h i g h p r e s s u r e s and a s a r e s u l t t h e c a l o r i m e t e r c a n be c o n s t r u c t e d f o r very r a p i d thermal response. A t h i r d advantage i s t h a t e x ­ p e r i m e n t s c a n be r u n c o n s e c u t i v e l y w i t h o u t c o o l i n g a n d r e l o a d i n g the c a l o r i m e t e r . A l l t h a t i s n e c e s s a r y i s t o s t a r t pumping i n t o t h e c a l o r i m e t e r f r o m room t e m p e r a t u r e t h e f l u i d s f o r t h e n e x t measurement. I n t h e f o l l o w i n g s e c t i o n we w i l l show t h a t t h e s e advantages o f f l o w c a l o r i m e t r i p r a c t i c e f o r measurement by d i s c u s s i n g t h e o p e r a t i o n o f s e v e r a l i n s t r u m e n t s t h a t have been constructed i n our laboratory. 4)

Measurements

o f Δ^Η

The f i r s t a t t e m p t i n o u r l a b o r a t o r y t o a p p l y f l o w t e c h n i q u e s t o h i g h t e m p e r a t u r e o p e r a t i o n was t h e c o n s t r u c t i o n by D r . E . E . Messikomer o f a f l o w , h e a t - o f - m i x i n g calorimeter(12). Unfortu­ n a t e l y , because t h e t h e r m o p i l e s used i n t h i s i n s t r u m e n t d i d n o t work above 100°C t h e i n s t r u m e n t was l i m i t e d t o t h i s t e m p e r a t u r e . H o w e v e r , t h e r e s u l t s were e n c o u r a g i n g b e c a u s e t h e y showed t h a t v e r y r a p i d and a c c u r a t e t h e r m o d y n a m i c d a t a c o u l d be o b t a i n e d a n d t h a t t h e o p e r a t i o n o f t h e c a l o r i m e t e r was as e a s y a t 100°C a s i t was a t room t e m p e r a t u r e . Because o f t h e encouraging r e s u l t s o b t a i n e d w i t h t h e f i r s t c a l o r i m e t e r , D r . James M a y r a t h b u i l d a new v e r s i o n w h i c h was s u c ­ c e s s f u l l y o p e r a t e d up t o A schematic o f t h i s c a l o r i ­ m e t e r i s g i v e n i n f i g u r e 1. B a s i c a l l y i t i s a h e a t - f l o w c a l o r i ­ m e t e r i n w h i c h t h e two l i q u i d s t o be m i x e d a r e pumped a t room temperature i n t o a counter c u r r e n t heat exchanger, a f t e r which t h e y a r e e q u i l i b r a t e d w i t h an aluminum c a l o r i m e t r i c b l o c k . Next t h e two l i q u i d s a r e m i x e d , a n d t h e h e a t g e n e r a t e d by t h e m i x i n g p r o c e s s i s e x t r a c t e d f r o m t h e f l o w i n g s t r e a m by a s e r i e s o f t h e r ­ m o p i l e s w h i c h c a n measure t h e h e a t e x t r a c t e d . Using several heat e x t r a c t o r s g u a r a n t e e d t h a t most o f t h e h e a t g e n e r a t e d i s m e a s u r e d by t h e t h e r m o p i l e s a n d t h e sum o f t h e v o l t a g e on t h e t h e r m o p i l e s i s t h e n a measure o f t h e r a t e o f h e a t p r o d u c t i o n . A d i a g r a m o f a t y p i c a l r u n i s g i v e n i n f i g u r e 2 w h i c h shows t h e power g e n e r a t e d by m i x i n g o f magnesium c h l o r i d e w i t h w a t e r a t 200°C. I n t h i s c a l o r i m e t e r a h e a t o f d i l u t i o n t a k e s 30 m i n ­ u t e s a n d f r o m an i n i t i a l b a s e l i n e i t t a k e s a b o u t 15 m i n u t e s f o r the c a l o r i m e t e r t o reach a steady s t a t e . The s e n s i t i v i t y o f t h i s c a l o r i m e t e r was e q u i v a l e n t t o b e i n g a b l e t o d e t e c t a 2 X 1 0 ~ K

200°c(LU.

4

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

572

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Figure 1. Flow heat of mixing calorimeter: (a and b) solutions to be mixed; (c) calorimetric block; (d) thermopiles for detecting heatflow;(e) exit for mixture

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

30.

WOOD AND SMITH-MAGOWAN

τ

0

10

1

20

573

Calorimetry of Aqueous Solutions

1

30 T/mln

1

40

ι

SO

Γ

60

Figure 2. Results of an enthalpy of dilution run on aqueous MgCl at 473 Κ (thermopile voltage vs. time—maximum 1.23 zt 0.002; Q = 1.129 watts; Δ Τ = 12.8 K) 2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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APPLICATIONS

t e m p e r a t u r e r i s e on m i x i n g t h e c a l o r i m e t r i c f l u i d s . Some t y p i c a l r e s u l t s f r o m t h i s c a l o r i m e t e r a r e shown i n f i g u r e s 3 and 4 . It s h o u l d be n o t e d t h a t t h e h e a t o f d i l u t i o n o f magnesium c h l o r i d e a t 200°C i s 40 kJ m o l " and t h a t t h i s i s c l o s e t o t h e h e a t o f r e a c t i o n o f H w i t h OH*" a t room t e m p e r a t u r e . Thus, the heat e f ­ f e c t s i n w a t e r a t 200°C a r e e x t r e m e l y l a r g e and c h a n g i n g r a p i d l y with temperature. This i s a f u r t h e r reminder o f the d i f f i c u l t y o f p r e d i c t i n g t h e p r o p e r t i e s o f h i g h t e m p e r a t u r e aqueous s o l u t i o n s f r o m t h e i r p r o p e r t i e s a t room t e m p e r a t u r e s . 1

+

5)

Heat C a p a c i t y

Measurements

The s u c c e s s o f t h e m i x i n g c a l o r i m e t e r s f u r t h e r e n c o u r a g e d us to c o n s t r u c t a f l o w , heat-capacity c a l o r i m e t e r using the basic design p r i n c i p a l s o f Patrick Picker et A schematic d i a ­ gram o f o u r h e a t c a p a c i t calorimete i give i figur 5 Th operation o f the instrumen a h i g h p r e s s u r e l i q u i d c h r o m a t o g r a p h y pump t h r o u g h a 1.5 mm o u t s i d e d i a m e t e r h a s t a l l o y t u b e t h r o u g h a h e a t e x c h a n g e r and o n t o a c o p p e r c a l o r i m e t r i c b l o c k where i t i s e q u i l i b r a t e d a t t h e r e f e r ­ ence t e m p e r a t u r e . The f l u i d i n t h e t u b e i s t h e n h e a t e d a b o u t 2 ° Κ and t h e r e s u l t i n g t e m p e r a t u r e r i s e d e t e c t e d by a t h e r m i s t o r . The stream then l e a v e s t h e c a l o r i m e t r i c b l o c k through t h e c o u n t e r c u r ­ r e n t h e a t e x c h a n g e r and goes t o a s a m p l e i n j e c t i o n v a l v e w h i c h a l l o w s a s a m p l e l o o p ( c o n t a i n i n g 10 ml o f t h e s o l u t i o n t o be measured) t o be i n t e r j e c t e d i n t o t h e f l o w s t r e a m . The s t r e a m t h e n goes t h r o u g h a. s e c o n d c o u n t e r c u r r e n t h e a t e x c h a n g e r and i n t o an i d e n t i c a l Q l o r i m e t r i c u n i t w i t h h e a t e r and t h e r m i s t o r t o detect the temperature r i s e . A f t e r l e a v i n g the block through the counter c u r r e n t heat exchanger the s o l u t i o n e x i t s the system t h r o u g h a back p r e s s u r e r e g u l a t o r . I n o p e r a t i o n t h e pump and h e a t e r s a r e t u r n e d on w i t h w a t e r f l o w i n g t h r o u g h b o t h c a l o r i m e t r i c u n i t s and a w h e a t s t o n e b r i d g e c o n t a i n i n g t h e two t h e r m i s t o r s i n o p p o s i t e arms i s b a l a n c e d . A f t e r a steady s t a t e i s reached the s a m p l e l o o p v a l v e i s opened and t h e s a m p l e s o l u t i o n f l o w s t h r o u g h the second c a l o r i m e t r i c u n i t . When t h e sample h i t s t h e h e a t e r and t h e r m i s t o r on t h e s e c o n d u n i t t h e r e i s a change i n h e a t c a p a ­ c i t y and a c o n s e q u e n t change i n t e m p e r a t u r e . The h e a t e r on t h i s u n i t i s a d j u s t e d t o r e b a l a n c e t h e t h e r m i s t o r b r i d g e and t h u s t o keep t h e t e m p e r a t u r e r i s e e x a c t l y t h e same. The r a t i o o f t h e power a p p l i e d t o t h e h e a t e r w i t h w a t e r f l o w i n g and w i t h t h e sam­ p l e f l o w i n g i s then the r a t i o o f t h e v o l u m e t r i c heat c a p a c i t i e s o f t h e two s o l u t i o n s . The r a t i o o f t h e mass f l o w s t h r o u g h t h e c a l o r i m e t r i c u n i t s i n t h e two c a s e s i s j u s t t h e r a t i o o f t h e d e n ­ s i t i e s o f w a t e r and o f t h e s o l u t i o n t o be measured a t t h e t e m p e r a ­ t u r e o f t h e sample l o o p . T h i s c a n be e a s i l y shown u s i n g t h e a s s u m p t i o n s t h a t 1) a t c o n s t a n t c o m p o s i t i o n , t h e mass f l o w i s i n ­ d e p e n d e n t o f t e m p e r a t u r e 2) a t c o n s t a n t t e m p e r a t u r e , t h e v o l u m e ­ t r i c f l o w i s i n d e p e n d e n t o f t h e c o m p o s i t i o n and 3) t h e h e a t and volume o f m i x i n g a t t h e i n t e r f a c e between t h e two s o l u t i o n s p r o -

alW»

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

WOOD AND SMITH-MAGOWAN

Figure 3.

Calorimetry of Aqueous Solutions

Apparent molal enthalpy of aqueous NaCl as a function of molality and temperature

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

30.

WOOD AND SMITH-MAGOWAN

Calorimetry of Aqueous Solutions

SAMPLE

LOOP

BACK

PUMP

VACUUM CHAMBER

ADIABATIC SHEILD THERMISTOR

HEATER

Figure 5.

Schematic of flow, heat-capacity calorimeter

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

577

578

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

d u c e s a n e g l i g i b l e change i n v o l u m e . Experience with the Picker i n s t r u m e n t has shown t h a t t h i s l a t t e r a s s u m p t i o n i s q u i t e a c c u r ­ ate. The r e s u l t i n g e q u a t i o n f o r t h e h e a t c a p a c i t i e s o f t h e two solutions is P

S,2 P'

1

2

.

l

p

1

Λ

.

Where P. and P a r e t h e powers i n t h e h e a t e r w i t h s o l u t i o n s 1 and 2 f l o w i n g and p-| and p a r e t h e d e n s i t i e s o f t h e s o l u t i o n s a t t h e temperature o f t h e sample l o o p . The r e s u l t i n g i n s t r u m e n t has a r e s p o n s e t i m e f o r changes o f e l e c t r i c a l power i n p u t o f 50 s e c o n d s f o r 99% r e s p o n s e , a s e n s i ­ t i v i t y t o a change i n powe f about 0.005% d capabili ty of operating with t h i as 325°C. The r e s u l t s o f some measurements on s o d i u m c h l o r i d e s o l u ­ t i o n s a r e g i v e n i n f i g u r e 6 . The d i f f i c u l t y o f p r e d i c t i n g p r o ­ p e r t i e s o f s o l u t i o n s a t h i g h t e m p e r a t u r e s i s e m p h a s i z e d by t h e s e results. A t l o w c o n c e n t r a t i o n s t h e r e i s a v e r y l a r g e change i n h e a t c a p a c i t y as t e m p e r a t u r e i n c r e a s e s w h i c h i s n o t p r e s e n t a t higher concentrations. Indeed, the heat c a p a c i t y d i f f e r e n c e s a t 25°C seems a l m o s t n e g l i g i b l e compared w i t h t h e changes f o u n d w i t h c h a n g i n g t e m p e r a t u r e a t l o w m o l a l i t y and w i t h c h a n g i n g m o l a l i t y at high temperature. I t i s d i f f i c u l t t o compare t h e s e r e s u l t s w i t h t h e p r e v i o u s r e s u l t s o f o t h e r a u t h o r s s i n c e we c h o s e t o make measurements a l o n g an i s o b a r w h i c h was a c c e s s i b l e a t a l l t e m p e r a t u r e s . This a l l o w s c o n v e n i e n t d a t a r e d u c t i o n . O t h e r a u t h o r s have g e n e r a l l y measured a l o n g t h e s a t u r a t e d w a t e r v a p o r p r e s s u r e c u r v e w i t h c o n ­ sequent c o m p l i c a t i o n s i n data r e d u c t i o n . While a t p r e s e n t , o n l y t h i s one i s o b a r has been s y s t e m a t i c a l l y i n v e s t i g a t e d , a few measurements o f t h e p r e s s u r e dependence a t 320K and 572K have been made. These r e s u l t s show t h a t a t a l l t e m p e r a t u r e s t h e p r e s ­ s u r e dependence o f t h e h e a t c a p a c i t y i s a p p r e c i a b l e and needs t o be more f u l l y e v a l u a t e d , s i n c e t h e p r e s e n t body o f v o l u m e t r i c d a t a i s n o t s u f f i c i e n t l y p r e c i s e t o make t h e s e c o r r e c t i o n s a c ­ curately. In f a c t , o u r v e r y l i m i t e d r e s u l t s a t d i f f e r e n t p r e s ­ s u r e s s u g g e s t t h a t t h e p r e c i s i o n o f t h i s p r o c e d u r e may be s u f f i ­ c i e n t t o supplant volumetric determinations a t high temperature and p r e s s u r e s . 2

2

6)

Conclusion

These p r e l i m i n a r y r e s u l t s show t h a t t h e p r o m i s e o f f l o w c a l ­ o r i m e t r i c t e c h n i q u e s f o r i n v e s t i g a t i n g t h e thermodynamic p r o p e r ­ t i e s o f h i g h t e m p e r a t u r e aqueous s o l u t i o n s has been r e a l i z e d . A l t h o u g h t h e r e a r e many e x p e r i m e n t a l d i f f i c u l t i e s i n a d a p t i n g

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

WOOD AND SMITH-MAGOWAN

Calorimetry of Aqueous Solutions

579

T/K

1 Figure 6.

Apparent molal heat capacity of aqueous NaCl at 177 bars as a function of molality and temperature

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

580

THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

these t e c h n i q u e s t o high temperature o p e r a t i o n , these problems have now been s o l v e d and we have a r a p i d and s e n s i t i v e m e a s u r i n g instrument. As a r e s u l t we c a n now g e t down t o t h e b u s i n e s s o f e x p l o r i n g aqueous s o l u t i o n c h e m i s t r y a t t e m p e r a t u r e s up t o 325°C. Literature Cited

1. a) Gardner, W.L.; Mitchell, R.E.; Cobble, J.W. J. Phys. Chem., 1969, 73, 2025. b) Cobble, J.W. and Murray, Jr., R.C. Discussions Faraday Soc., 1977, 64. 2. C-Τ. Liu and W.T. Lindsay. J. Soln. Chem., 1972, 1, 45. 3. Likke, S. and Bromley, L.A. J. Chem. Eng. Data, 1973, 18, 189. 4. Puchkov, L.V.; Styazhkin, P.S.; Fedorova, M.K. J. Applied Chem. (Russ.), 1976, 49, 1268. 5. Monk, P. and Wadsö I Acta Chem Scand 1968 22 1842 6. Picker, P.; Jolicoeur dynamics, 1969, 1, 469. 7. Gill, S.J. and Chen, Y.-J. Rev. Sci. Instruments, 1972, 43, 774. 8. Picker, P.; Fortier, J.-L.; Philip, P.R; Desnoyers, J.E. J. Chem. Thermodyn., 1971, 3, 631. 9. Elliot, K.; Wormald, C.J. J. Chem. Thermodynamics, 1976, 8, 881. 10. Messikomer, E.E.; Wood, R.H. J. Chem. Thermodynamics, 1975, 7, 119. 11. Mayrath, J.E., "A Flow Microenthalpimetric Survey of Electro­ lyte Solution Thermodynamic Properties from 373K to 473K" Ph.D. Dissertation, University of Delaware, June, 1979. RECEIVED

January 30, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

31 Review of the Experimental and Analytical Methods for the Determination of the PressureVolume-Temperature Properties of Electrolytes FRANK J. MILLERO Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, F L 33149

The pressure-volume-temperature (PVT) properties of aqueous electrolyte and mixed electrolyt needed to make practica engineering exampl precise PVT properties of natural waters like seawater are required to determine the vertical stability, the circulation, and the mixing of waters in the oceans. Besides the practical interest, the PVT properties of aqueous electrolyte solutions can also yield information on the structure of solutions and the ionic interactions that occur in solution. The derived partial molal volumes of electrolytes yield information on ion-water and ion-ion interactions (1,2). The effect of pressure on chemical equilibria can also be derived from partial molal volume data (3). I. Experimental Methods The PVT properties of aqueous solutions can be determined by direct measurements or estimated using various models for the ionic interactions that occur in electrolyte solutions. In this paper a review will be made of the methods presently being used to determine the density and compressibility of electrolyte solutions. A brief review of high-pressure equations of state used to represent the experimental PVT properties will also be made. Simple a d d i t i v i t y methods o f estimating the d e n s i t y of mixed e l e c t r o l y t e s o l u t i o n s l i k e seawater and geothermal b r i n e s w i l l be presented. The p r e d i c t e d PVT p r o p e r t i e s f o r a number of mixed e l e c t r o l y t e s o l u t i o n s are found to be i n good agreement with d i r e c t measurements. A. One Atmosphere D e n s i t i e s . The d e n s i t i e s or volume prope r t i e s of s o l u t i o n s have been studied by a number of methods which are e x t e n s i v e l y reviewed elsewhere Qy^y^Z) °^ ^ °^ methods, only the magnetic f l o a t (7-14), the h y d r o s t a t i c balance (5,15-20), the v i b r a t i n g flow densimeter (2JL,22,), and d i l a t o m e t r i c (23,24,25) methods give data with s u f f i c i e n t p r e c i s i o n to study the d e n s i t i e s of d i l u t e s o l u t i o n s . For more concentrated a

0-8412-0569-8/80/47-133-581$10.50/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

582

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

s o l u t i o n s (above 1 m) the c l a s s i c a l pycnometer methods (4»J5,6) can a l s o be used t o o b t a i n r e l i a b l e d e n s i t i e s . I w i l l not d i s ­ cuss a l l of these methods, but w i l l b r i e f l y o u t l i n e the three systems ( h y d r o s t a t i c balance, magnetic f l o a t and v i b r a t i n g d e n s i ­ meters) that are p r e s e n t l y being used t o measure the d e n s i t i e s of s o l u t i o n s . Since the PVT p r o p e r t i e s of water are w e l l known (26-32) over a wide range of temperatures, most d e n s i t y measure­ ments are made r e l a t i v e to water. By making r e l a t i v e d e n s i t y measurements (Δρ = ρ - ρ ) , where ρ i s the d e n s i t y of pure water, i t i s p o s s i b l e t o make very p r e c i s e measurements w i t h r e l a t i v e ease. 1. H y d r o s t a t i c Balance. Many s t u d i e s u s i n g a h y d r o s t a t i c balance have been made of the d e n s i t i e s of s o l i d s and l i q u i d s ( 2 0 - 2 5 ) . By weighing s o l i d s of a known d e n s i t y (determined by independent measurement i s p o s s i b l e to determin a n a l y t i c a l balance can be adapted to a h i g h - p r e c i s i o n l i q u i d d e n s i t y apparatus by a t t a c h i n g a platinum w i r e or nylon s t r i n g w i t h a " s i n k e r " to the balance arm (Figure 1 ) . The s i n k e r and w i r e are weighed i n a i r and then i n the s o l u t i o n . The surface of the s o l u t i o n i s brought to the same mark on the w i r e each time so that i t c o n t r i b u t e s the same (small) amount to the t o t a l volume (V). The d i f f e r e n c e between the weight i n vacuum (W^) and i n water (W ) i s equal to the mass of d i s p l a c e d f l u i d . For r e l a ­ t i v e d e n s i t y measurements the system i s c a l i b r a t e d by weighing the s i n k e r i n a s o l u t i o n of known d e n s i t y (water). The volume of the s i n k e r i s determined from 0

V =

(W

- W )/p

v

o

(1)

o

where p i s the d e n s i t y of water ( 2 8 ) . Once the volume of the s i n k e r i s known, the d e n s i t y of an unknown s o l u t i o n can be d e t e r ­ mined from 0

Ρ - (W

(2)

- W)/V

v

where W i s the weight i n the s o l u t i o n of unknown d e n s i t y . r e l a t i v e d e n s i t y (Δρ) can be determined from A

P

= ρ _ p

0

(W

=

o

_

= ζξΐΐ)

W ) / V

p

o

The

(3)

The s p e c i f i c g r a v i t i e s (p/p ) can be determined from the r a t i o of the weights i n s o l u t i o n and water

P/P = (w - w)/(w - w) O

v

v

o

(4)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

31.

MiLLERO

Pressure-Volume-Temperature Properties of Electrolytes 583

Journal of Solution Chemistry

Figure 1. Sketch of the hydrostatic balance densitometer—-(A) magnetic stirrer; (B) glass float; (C) stirring motor; (D) constant temperature bath; (E) nickel thermometer; (F) lucite plug; (G) sample container; (H) nylon wire; (I) suspension hook; (J) Mettler H20 balance (33)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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A sketch of the h y d r o s t a t i c balance t h a t we have used (20,33,34) i n my l a b o r a t o r y i s shown i n F i g u r e 1. A 100g g l a s s f l o a t (66 cm* i n volume) i s suspended by a n y l o n l i n e (0.02 cm diameter) from a hook on the bottom pan o f a M e t t l e r (H-20) balance. The g l a s s sample c e l l has a L u c i t e top w i t h a h o l e i n the center t o accomodate the suspension l i n e and i s suspended i n a constant temperature bath c o n t r o l l e d t o ± 0.001°C. A submersible mag­ n e t i c s t i r r e r a g i t a t e s the s o l u t i o n i n s i d e the c e l l . A weight d i f f e r e n c e o f ± 8 χ 10~"^g g i v e s a p r e c i s i o n o f ± 1 ppm i n den­ s i t y . The accuracy of the system was checked by u s i n g NaCl s o l u ­ t i o n s and found t o be ± 2 ppm. The l a r g e s t u n c e r t a i n t y w i t h u s i n g t h i s method t o measure d e n s i t i e s a r i s e s from the s u r f a c e t e n s i o n e f f e c t between the l i q u i d s u r f a c e and the w i r e o r s t r i n g . To circumvent t h i s prob­ lem many workers (4) have p l a t i n i z e d the w i r e i n the r e g i o n at which i t contacts the l i q u i d s u r f a c e Anothe proble w i t h t h i method i s that i t i s d i f f i c u l s o l u t i o n being s t u d i e d precis y analyze an a l l o q u o t of s o l u t i o n a f t e r the d e n s i t y i s determined. 2. Magnetic F l o a t Densimeter. The f l o a t a t i o n method of determining the d e n s i t y of a l i q u i d i s a m o d i f i c a t i o n of the h y d r o s t a t i c method. I n the f l o a t a t i o n method, however, the f l o a t has no suspension thread or w i r e . E a r l i e r workers adjusted t h e buoyancy of t h e f l o a t by mixing two l i q u i d s , adding Pt weights and by changing the temperature (4 ,_7). I n a l l of these e a r l y a p p l i c a t i o n s , the accuracy was l i m i t e d by how a c c u r a t e l y the c o e f f i c i e n t of thermal expansion of the s o l u t i o n was known. Lamb and Lee (8) extended the accuracy and p r e c i s i o n of the method by imposing a magnetic f i e l d on a f l o a t c o n t a i n i n g a s o f t i r o n core. They showed that t h i s electromagnetic method of weighing was able to y i e l d a p r e c i s i o n of b e t t e r than 1 χ 10~^g cm~^ i n d e n s i t y . A number of workers (7,9-14) have modified t h i s method by u s i n g a magnetic core i n the f l o a t . A sketch of t h e magnetic f l o a t system which we have used f o r a number of years (7) i s shown i n F i g u r e 2. The densimeter c o n s i s t s of the f o l l o w i n g major compo­ nents: A) the s o l u t i o n c o n t a i n e r (110 cm^); B) the magnetic f l o a t (32.2 cm3); C) t h e pulldown s o l e n o i d ; D) the main s o l e n o i d ; and E) the support and l e v e l i n g p l a t f o r m . The magnetic f l o a t i s made of pyrex g l a s s and c o n t a i n s a magnetic core. The pulldown s o l e n o i d C i s used t o b r i n g t h e f l o a t i n t o the f i e l d of the main s o l e n o i d (^ 716 t u r n s of Cu w i r e ) . The e n t i r e system i s placed on the bottom of a constant temperature bath c o n t r o l l e d t o ± 0.001°C. I f a magnetic f o r c e from the main s o l e n o i d i s used which i s j u s t s u f f i c i e n t t o h o l d the f l o a t on the bottom of the s o l u t i o n c o n t a i n e r , the buoyancy f o r c e s g i v e pV = W + f i

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Figure 2. Sketch of the magnetic float densitometer: (A) solution container; (B) magnetic float; (C) pull down solenoid; (D) the main solenoid; (E) support and leveling platform (1)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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where ρ i s t h e d e n s i t y o f t h e s o l u t i o n , V i s t h e volume o f t h e f l o a t , W i s t h e w e i g h t o f t h e f l o a t , f_ i s a n i n t e r a c t i o n c o n s t a n t a n d jL i s t h e c u r r e n t t h r o u g h t h e s o l e n o i d . The system i s c a l i ­ brated by measuring the current which i s just s u f f i c i e n t to hold t h e f l o a t o n t h e b o t t o m i n w a t e r when v a r i o u s P t w e i g h t s (w) a r e added t o t h e f l o a t . The buoyancy e q u a t i o n i s p(V + w / p where p p obtains

t

i s the density

the linear w(l

which

can be used

an e l e c t r o l y t e

p t

)

= W + w + fi

of Pt.

By r e a r r a n g i n g

equation

- p/p

p t

)

(6) this

equation one

= - f i + ( ρ V - W)

to determine

f

and V.

s o l u t i o n can be determined

The r e l a t i v e from

(7) density

of

Δρ = ρ w h e n t h e same w e i g h t s a r e u s e d ( Δ 1 = i - i ) . The p r e c i s i o n o f t h e s y s t e m i s ± 0 . 3 ppm a n d t h e a c c u r a c y i n d i l u t e s o l u t i o n s i s ± 2 ppm. F o r more c o n c e n t r a t e d s o l u t i o n s t h e a c c u r a c y i s l i m i t e d by o u r p r e s e n t knowledge o f t h e d e n s i t y o f p l a t i n u m (21.483 ± 0 . 0 0 2 g c m " a t 2 5 ° C ) ( 1 1 ) . We h a v e u s e d t h i s m a g n e t i c f l o a t s y s t e m t o s t u d y t h e volume p r o p e r t i e s o f a number o f e l e c t r o l y t e solutions (7,35-52). B y p u t t i n g t h e s y s t e m i n t o a h i g h p r e s s u r e bomb ( 3 6 ) t h e magnetic system c a n be used t o measure t h e d e n s i t i e s o f aqueous s o l u t i o n s over a wide p r e s s u r e range w i t h a p r e c i s i o n o f ± 11 ppm. We p r e s e n t l y a r e d e v e l o p i n g a m a g n e t i c f l o a t s y s t e m t h a t can b e used t o measure t h e d e n s i t i e s a t l o w p r e s s u r e s t o h i g h temperatures (200°C). 3

3. V i b r a t i n g Flow Densimeter. One o f t h e m a j o r advances made i n m a k i n g d e n s i t y m e a s u r e m e n t s o f s o l u t i o n s w a s t h e s y s t e m d e v e l o p e d b y K r a t k y et^ a l . ( 2 1 ) w h i c h m e a s u r e s t h e n a t u r a l v i b r a ­ t i o n frequency of a tube containing a l i q u i d . The o s c i l l a t i n g f r e q u e n c y ( f ) o f t h e t u b e i s r e l a t e d t o i t s m a s s (m) b y f

= 1/2π ( k / m )

(9)

1 / 2

where k i s an instrument constant. Since t h e volume o f t h e tube i s constant, the density of a l i q u i d contained i n the tube i s d i r e c t l y related t o the period (τ) by ρ = A + Β τ

2

(10)

The p r i n c i p l e h a s b e e n known f o r a l o n g t i m e , h o w e v e r , t h e m o d i ­ f i c a t i o n made b y K r a t k y e t a l . ( 2 1 ) a n d P i c k e r e t a l . ( 2 2 ) h a v e l e d t o commercial instruments t h a t c a n be used t o measure

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Pressure-Volume-Temperature Properties of Electrolytes

—6 ~3 d e n s i t i e s r o u t i n e l y to a p r e c i s i o n of ± 3 χ 10 g cm . The system described by Kratky et_ a l . (21) ( a v a i l a b l e commercially from M e t t l e r ) r e q u i r e s small volumes, has a wide operating tem­ perature range, and a d i g i t a l readout. I t s major drawback i s that i t r e q u i r e s a long time to achieve thermal e q u i l i b r i u m . The flow densimeter developed by P i c k e r et a l . (22) r e q u i r e s only 5 to 7 cm of s o l u t i o n and gives d e n s i t i e s to a p r e c i s i o n of ± 2 ppm i n times of 5-10 minutes. A sketch of the P i c k e r e t a l . (22) system i s shown i n F i g u r e 3. A brass p l a t e holds the s t a i n ­ l e s s s t e e l v i b r a t i n g tube i n p l a c e . Magnetic pickups are used to keep the tube v i b r a t i n g a t i t s n a t u r a l frequency and sense the p e r i o d of the v i b r a t i o n . A thermoregulated j a c k e t surrounds the densimeter and the heat exchanger encompassing the l i q u i d i n t a k e l i n e s . The r e l a t i v e d e n s i t i e s are determined by measuring the p e r i o d i n a s o l u t i o n and solvent 3

Δρ The instrument constant Β can be determined by measuring the τ i n two f l u i d s of known d e n s i t y . A i r and water are used by most workers (22). In our l a b o r a t o r y we used seawater of known con­ d u c t i v i t y and pure water t o c a l i b r a t e our v i b r a t i n g flow systems (53). The system gives accurate d e n s i t i e s i n d i l u t e s o l u t i o n s , however, care must be taken when using the system i n concentrated s o l u t i o n s or i n s o l u t i o n s with l a r g e v i s c o s i t i e s . The development of commercial flow densimeters has caused a r a p i d i n c r e a s e i n the output of d e n s i t y measurements of s o l u t i o n s . Desnoyers, J o l i c o e u r and coworkers (54-69) have used t h i s system to measure the d e n s i ­ t i e s of numerous e l e c t r o l y t e s o l u t i o n s . We have used the system to study the d e n s i t i e s of e l e c t r o l y t e mixtures and n a t u r a l waters (53,70-81). We r o u t i n e l y take our system t o sea on océanographie c r u i s e s (79) and f i n d the system to perform very w e l l on a rocking ship. B. One Atmosphere C o m p r e s s i b i l i t i e s . Most isothermal comp r e s s i b i l i t y (3) measurements are made over extended pressure ranges and very few d i r e c t measurements have been made near 1 atm. It i s d i f f i c u l t to o b t a i n r e l i a b l e v a l u e s of β at 1 atm from high pressure PVT data due to the problems of e x t r a p o l a t i n g the com­ p r e s s i o n [k = ( v - v^)/v^P, where ν i s the s p e c i f i c volume] to zero a p p l i e d pressure. I f the compressions, volumes, or d e n s i t i e s are f i t to f u n c t i o n s of P, the c o m p r e s s i b i l i t y P

» • τ® • - *S>

21

at Ρ = 0 i s dependent upon the f u n c t i o n used. Since there i s no a p r i o r i method that can be used to o b t a i n the c o r r e c t pressure dependence, 1 atm c o m p r e s s i b i l i t i e s are more r e l i a b l y determined by u s i n g sound speed measurements (29,82,83,84,85,86).

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Sol ution Iη

Out

Journal of Solution Chemistry Figure 3.

Sketch of the Sodev vibrating densitometer (22)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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1. Piezometer Method. To measure the c o m p r e s s i b i l i t y of l i q u i d s near 1 atm we have developed a piezometer system (87). A s k e t c h of t h i s system i s shown i n F i g u r e 4. The piezometer, C, i s a c y l i n d r i c a l g l a s s v e s s e l w i t h a volume of ^ 450 cm . The piezometer c o n t a i n s the s o l u t i o n and ^ 330 gms of Hg. The top o f the piezometer i s f i t t e d w i t h a Taper j o i n t f o r f i l l i n g . A p r e c i s i o n bore c a p i l l a r y , E, (2mm i n diameter) i s f i t t e d t o the bottom of the piezometer. The piezometer i s suspended (B) i n a brass or s t a i n l e s s s t e e l pressure v e s s e l , H. A g l a s s b o i l e r tube, J , encloses the upper p o r t i o n of the c a p i l l a r y . The pressure v e s s e l i s f i l l e d w i t h ethylene g l y c o l which serves as a thermal and pressure medium. The e n t i r e apparatus i s submerged i n a con­ s t a n t temperature bath c o n t r o l l e d t o ± 0.001°C. The temperature i n s i d e the pressure v e s s e l i s monitored w i t h a Hewlett-Packard quartz c r y s t a l thermometer (to determine when thermal e q u i l i ­ brium i s reached a f t e r compressio d decompression) The c o m p r e s s i b i l i t the volume change of Hg capillary pressure are a p p l i e d t o the system. The change i n h e i g h t of the meniscus (Ah) and the pressure change (ΔΡ) are dependent upon the volume of mercury ( V ) , the volume of the s o l u t i o n ( V s i ) » and the i n s i d e volume of the g l a s s c o n t a i n e r to a r e f e r e n c e mark (Ah). The t o t a l volume of the system i s g i v e n by 3

0

H g

V

=

T

V

n

+ V + Ah Soin Hg

(13)

where A i s the cross s e c t i o n a l area of the c a p i l l a r y and h i s the i n i t i a l d i s t a n c e of the mercury meniscus below a r e f e r e n c e mark. The d i f f e r e n t i a t i o n of equation (13) w i t h r e s p e c t to pressure gives Τ

_

Soin 9P

3P

. dn 3P

Hg_ •_ 3A 5P 3P Ί

+

h

+

A

(

1

4

)

where the n e g a t i v e signs i n d i c a t e a decrease i n volume. S u b s t i ­ t u t i n g 3A/3P = - ( 2 / 3 ) A 8 , 3V /8P = - V 3 , ( 3 i s the compressi­ b i l i t y of g l a s s ) , β = -(1/V ) O V /3P7, an! 3 = " ο1η

2 f

2

n

(21)

7y

(f/f ) R

where i s the absorption per wavelength at the r e l a x a t i o n frequency, f_ i s the frequency of the measurement (^ 2 MHz), f i s the r e l a x a t i o n frequency, and u = u + Au i s the sound v e l o c ­ i t y at i n f i n i t e frequency. At concentrations of 0.5 m, equation (21) y i e l d s a value of Au = 1.0 m s e c " i n MgS04 s o l u t i o n s (105). A s h i f t of 1.0 m s e c " i n u w i l l s h i f t the a d i a b a t i c compressi­ b i l i t y by 0.06 χ 1 0 " ° bar""^ Since α has not been measured at high concentrations f o r many e l e c t r o l y t e s , an exact c o r r e c t i o n cannot be made at present to a l l the published data measured at a f i x e d frequency. R

a

0

1

1

C. High-Pressure PVT P r o p e r t i e s . Three methods are p r e s ­ e n t l y being used to measure the high-pressure PVT p r o p e r t i e s of electrolyte solutions: volumetric methods, (26,32,106) h i g h pressure magnetic f l o a t systems, (36,107,108) and high pressure speed of sound systems (109,110,111,112). I w i l l not attempt to review a l l the m o d i f i c a t i o n s made to these systems. 1. High Pressure PVT P r o p e r t i e s . The e a r l i e r v o l u m e t r i c methods (113,114) c o n s i s t e d of a piezometer, s i m i l a r to the one shown i n F i g u r e 6, which i s contained i n a pressure bomb. The

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Pressure-Volume-Temperature Properties of Electrolytes 593

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atmospheric pressure—(A) perature bath; (B) magnetic stirrer; (C) solution cell; (D) transmitting transducer; (E) reflector; (F) receiving transducer (85)

Soln Precision Bore Capillary

Hg

Figure 6.

Weight dilatometer

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Hg d i s p l a c e d a f t e r p r e s s u r i z a t i o n o f t h e s y s t e m i s w e i g h t e d a f t e r each measurement. The s e n s i t i v i t y o f t h e method i s l i m i t e d t o a b o u t 1 0 0 ppm b y t h e d i s c r e t e v o l u m e o f t h e m e r c u r y d r o p s a n d t h e s m a l l volume o f t h e piezometer. More r e c e n t workers (106) have determined t h e changes i n t h e volume o f t h e system by u s i n g i n ­ d i r e c t methods t o measure t h e h e i g h t o f Hg i n t h e p i e z o m e t e r . Bradshaw and S c h l e i c h e r (106) have designed a d i l a t o m e t e r system t h a t c a n measure t h e expansion and compression o f a s o l u t i o n under pressure. A s k e t c h o f t h e i r a p p a r a t u s i s shown i n F i g u r e 7. The volume change o f t h e sample w i t h temperature o r p r e s s u r e i s o b ­ t a i n e d by measuring t h e change i n h e i g h t o f mercury i n t h e p r e ­ c i s i o n bore tubing section of the dilatometer. The t u b i n g s e c t i o n i s separated from the dilatometer f l a s k by a tapered j o i n t . The r e l a t i v e height of the mercury i s determined by measuring the d i s t a n c e between a magnetic s t e e l c y l i n d e r f l o a t i n g on t h e t o p of t h e mercury ( f l o a t i n ) d anothe cylinde firml tached to the top of th d i l a t o m e t e r i s mounted pressur change d i s t a n c e between t h e cores i s measured b y u s i n g a l i n e a r d i f f e r ­ e n t i a l transformer with a micrometer head. The system was c a l i ­ b r a t e d b y making measurements on mercury. The p r e c i s i o n o f t h e s y s t e m i s ± 1 ppm/deg f r o m 0 t o 1 0 0 0 b a r s a p p l i e d p r e s s u r e . The s p e c i f i c volumes o f water determined w i t h the system from 0 t o 30°C a r e i n e x c e l l e n t agreement w i t h v a l u e s d e t e r m i n e d f r o m t h e sound d e r i v e d e q u a t i o n o f s t a t e o f Chen, F i n e and M i l l e r o (31) (see F i g u r e 8 ) . K e l l and W h a l l e y (26,32) have d e s c r i b e d a volumometer method ( F i g u r e 9) t o measure t h e volume o f l i q u i d s . A calibrated piston (see F i g u r e 9) i s used t o measure t h e change i n volume o f a s o l u ­ t i o n w i t h a change i n temperature o r p r e s s u r e . The system i s s i m i l a r i n p r i n c i p l e t o t h e apparatus d e s c r i b e d b y Keyes (115). The p r e s s u r e v e s s e l o f known v o l u m e i s immersed i n a t h e r m o s t a t . The p r e s s u r e o f t h e w a t e r i s m e a s u r e d b y means o f p r e s s u r e b a l ­ ances. The w a t e r i s s e p a r a t e d from t h e o i l b y mercury i n a U tube o r two l e g s o f a W t u b e . The change i n t h e volume o f water i n t h e p r e s s u r e v e s s e l due t o a change i n Τ o r Ρ i s measured by t h e change o f t h e p o s i t i o n o f t h e p i s t o n o f t h e volumometer. The c a l i b r a t e d p i s t o n was a d v a n c e d i n t o t h e c y l i n d e r b y means o f a screw t h r e a d and was b a l a n c e d by a s i m i l a r p i s t o n . The p r e s s u r e v e s s e l and c y l i n d e r o f t h e volumometer were j a c k e t e d by o t h e r pressure vessels t o prevent deformation. The b a l a n c i n g p r e s s u r e of t h e b a l a n c i n g water and t h e e x p e r i m e n t a l water was measured by a t h r e e l e g g e d o r W t u b e . The system was c a l i b r a t e d w i t h water at 1 atm and mercury a t h i g h p r e s s u r e s . The system was u s e d t o m e a s u r e t h e s p e c i f i c v o l u m e o f w a t e r f r o m 0 t o 150°C t o a p r e c i s i o n o f ± 1 0 ppm ( 2 6 ) a n d 1 5 0 t o 350°C t o a p r e c i s i o n o f 100 ppm ( 3 2 ) . F i n e a n d M i l l e r o ( 2 9 ) h a v e shown t h a t t h e h i g h p r e s s u r e v o l u m e m e a s u r e m e n t s o f K e l l a n d W h a l l e y f r o m 0 t o 100°C and 1 k b a r d i s a g r e e d f r o m v a l u e s d e r i v e d f r o m t h e sound speed measurements o f W i l s o n (109) b y * 120 ppm. K e l l and W h a l l e y (30)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Pressure-Volume-Temperature Properties of Electrolytes 595

Micrometer heod

Yoke Pressure vessel supported here

Bath lid

Reference core •Stainless steel (non-mag ne tic) pressure tubing Dilatometer—Tubing section (precision bore i.d.«

0.1875 inchtt) •Differential transformer -Floating core Pressure vessel Coil spring Taper joint Dilatometer- Flask section

Water sample Dilatometer support yolk Mercury

Pressure Inlet Deep-Sea Research Figure 7.

Dilatometer system (106)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS

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W I T H INDUSTRIAL

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6

l0 V(Sound)-l0 V(B/S)

200

400

600

800

1000

P, bars Figure 8.

Comparisons of the specific volumes of water determined from sound speed measurements (3\) and direct measurements (106)

W A T E R FOR TEMPERATURE ^CONTROL j

HonnnooDOo

11

VACUUM AND F I L L

PRESSURE VESSEL AND THERMOSTAT

BALANCING WATER INJECTOR

Philosophical Transactions of the Royal Society of London

Figure 9. Diagram of the PVT apparatus (26) ((mm) balancing water; (ssm) experimental water; ( ) mercury)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

31.

MILLERO

Pressure-Volume-Temperature Properties of Electrolytes 597

a t t r i b u t e d t h i s d i f f e r e n c e t o an e r r o r i n the compression o f the pressure v e s s e l . They used sound derived d e n s i t i e s t o r e d e t e r ­ mine the compression of the v e s s e l and gave c o r r e c t e d values o f ν f o r water. Comparisons o f the s p e c i f i c volumes of water a t 1000 bar of v a r i o u s workers (29,30,106) w i t h those c a l c u l a t e d from the sound d e r i v e d equation of s t a t e o f Chen, F i n e and M i l l e r o (31) a r e shown i n F i g u r e 10. The r e s u l t s a r e i n good agreement and i n d i c a t e t h a t values o f ν f o r water a r e a c c u r a t e l y known t o ± 15 ppm from 0 t o 100°C a t 1000 b a r s . The d i f f e r e n c e s at lower pressures are s m a l l e r . The v o l u m e t r i c systems of Bradshaw and S c h l e i c h e r (106) and K e l l and Whalley (26,32) a r e the most p r e c i s e methods o f d i r e c t l y measuring the absolute d e n s i t i e s o r volumes a t high pressures. These methods, however, are not i d e a l l y s u i t a b l e f o r making s y s ­ tematic d e n s i t y s t u d i e s o f aqueous e l e c t r o l y t e s o l u t i o n s as a f u n c t i o n o f Ρ and Τ becaus experi mental work and t h e l o s 2. High Pressure Magnetic F l o a t Methods. As d i s c u s s e d e a r l i e r the magnetic f l o a t method can be used t o measure r e l a t i v e d e n s i t i e s (Δρ) w i t h great p r e c i s i o n . We have developed a h i g h pressure magnetic f l o a t system (36) t h a t i s i d e a l l y s u i t e d t o measure r e l a t i v e d e n s i t i e s as a f u n c t i o n o f pressure. A sketch of the h i g h pressure system i s shown i n F i g u r e 11. The pressure bomb (B) has o p t i c a l p o r t s f o r observing the motion o f the mag­ n e t i c f l o a t and i s made o f b e r y l i u m copper o r s t a i n l e s s s t e e l . The top (A) and Bottom (C) plugs were made o f s i m i l a r m a t e r i a l . The bottom plug contains an i n s e r t plug (D) t h a t supports the s o l e n o i d (G) which i s 300 turns o f No. 28 Cu w i r e . The window cones were machined from cast p l e x i g l a s r o d and have a p i t c h o f 30 degrees. The pressure i s t r a n s m i t t e d t o the contents through port (H). The magnetic f l o a t i s made o f t h i c k - w a l l (0.4 cm) pyrex g l a s s tube and contains a permanent magnet. A h i g h tem­ perature Apiezon wax was used t o hold the magnet i n p l a c e . The system i s c a l i b r a t e d w i t h water i n the same manner as the 1 atm magnetic f l o a t system. The d e n s i t y o f platinum as a f u n c t i o n of pressure was estimated from the c o m p r e s s i b i l i t y . Since t h e d e n s i t y o f P t decreases by only 0.009 g cm" from 0 t o 1200 b a r s , the e f f e c t o f pressure on the d e n s i t y o f P t can be neglected i f weights below 1 g are used. Both f and V were found to be f u n c t i o n s o f pressure (36). C a l i b r a t i o n s o f the f l o a t a t a g i v e n pressure i n d i c a t e t h a t the p r e c i s i o n o f t h e system i s ± 10 ppm w h i l e the a c c u r a c i e s a r e about ± 20 ppm (116). We have used t h i s system t o measure t h e r e l a t i v e d e n s i t i e s of D2O (117), seawater (116,118), and some major sea s a l t s Ç36, 119). The major d i f f i c u l t i e s we have had w i t h the h i g h pressure magnetic system i s t h a t the f l o a t s e a s i l y break due t o pressure shocks. This g r e a t l y d i s t u r b s one who has spent many hours c a l i b r a t i n g the f l o a t i n water a t v a r i o u s pressures. 3

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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T H E R M O D Y N A M I C S O F AQUEOUS SYSTEMS W I T H INDUSTRIAL

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100

Figure 10. Comparisons of the specific volumes of water at 1000 bars calculated from the sound derived equation of state of Chen, Fine, and Millero (31) and the data of various workers; (A) Bradshaw and Schleicher; (%) Kell and Whalley; (O) Fine and Millero

Figure 11.

High pressure magnetic float system (36)

Journal of Solution Chemistry

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

31.

Pressure-Volume-Temperature Properties of Electrolytes 599

MILLERO

3. High Pressure Sound V e l o c i m e t e r s . As discussed e a r l i e r , sound v e l o c i t y measurements can y i e l d p r e c i s e c o m p r e s s i b i l i t i e s of s o l u t i o n s . Wilson (109) was the f i r s t to develop a h i g h pres­ sure sound v e l o c i m e t e r that could be used over a wide range of pressures and temperatures. He used the " s i n g around" system to measure the h i g h pressure sound speeds of water (109), D 2 O (120), and seawater (121) to a p r e c i s i o n of ± 0.2 m s e c ~ l which i s e q u i v a l e n t to ± 0.012 χ ΙΟ"** b a r " i n &s» Barlow and Yazgan (111) have described a s i m i l a r system used to measure speed of sound i n water. D e l Grosso and Mader (110) have developed a more e l a b o r a t e inteferometer system and used i t to measure the h i g h pressure speed of sound i n seawater s o l u t i o n to a p r e c i s i o n o f ± 0.05 m sec*" (^ ± 0.006 χ 1 0 " b a r " i n B ) . A l l of these systems are capable of making absolute measurements on pure water. U n f o r t u n a t e l y , at present (112) the two sound s t u d i e s made on pure water d i f f e r by as much as 1.22 m s e c " at h i g h temperatures and pressures (P = 800 ba sound speeds of Wilson w i t h our independent s t u d i e s (122,123), we f e e l that at present Wilson's r e s u l t s f o r water are the best a v a i l a b l e . We have (112) reanalyzed the sound speed measurements of W i l s o n f o r water and d e r i v e d an equation f o r the speed of sound i n water from 0 to 100°C and 0 t o 1000 bars a p p l i e d pressure (with σ = 0.08 m s e c " ) . The 1 atm p o r t i o n of the equation i s based on the r e s u l t s of Del Grosso and Mader (95). We suggest that t h i s equation be used to c a l i b r a t e h i g h pressure sound v e l o c i m e t e r s u n t i l more r e l i a b l e r e s u l t s become a v a i l a b l e . We have designed a h i g h pressure sound v e l o c i m e t e r (112,123, 124). A sketch of the system i s shown i n F i g u r e 12. The v e l o c i ­ meter c o n s i s t s of a Nusonic h i g h p r e s s u r e s i n g l e transducer " s i n g around" system suspended i n a bomb. The h i g h pressure bomb i s made of s t a i n l e s s s t e e l and has a volume of ^ 500 cm . The bomb i s submerged i n a constant temperature bath c o n t r o l l e d to ± 0.001°C. A Harwood Engineering c o n t r o l l e d clearance p i s t o n gauge i s used to set the pressures (±0.1 bar a t 1000 bars a p p l i e d P ) . The system was c a l i b r a t e d w i t h water and the sound path (£) was found t o i n c r e a s e s l i g h t l y as the pressure i s increased (as­ suming τ i s independent of pressure) (112). Since we are i n t e r ­ ested i n measuring the r e l a t i v e speed of sound (Au) i n aqueous s o l u t i o n s , we use the v e l o c i m e t e r i n a d i f f e r e n t i a l mode. The v a l u e of _τ i s not a f u n c t i o n of pressure (or temperature), as the e l e c t r o n i c s are kept under ambient pressures. The v a l u e s of Au were determined from 1

1

6

1

g

1

1

3

(f - f )u A u

=

u

u

=

-o

f (1 - f x )

(

2

2

)

0

where f and f a r e , r e s p e c t i v e l y , the pulse r e p e t i t i o n r a t e s of the v e l o c i m e t e r i n the s o l u t i o n and pure water. The l e n g t h of

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

31.

Pressure-Volume-Temperature Properties of Electrolytes 601

MILLERO

the sound path i s not needed t o determine Au a t a g i v e n Ρ and T. The e l e c t r o n i c delay time i s determined a t 1 atm i n water a t v a r i o u s temperatures. The system has a p r e c i s i o n o f ± 0.19 m s e c " from 0 t o 50°C and 0 t o 1000 b a r s . We have used t h i s sys­ tem t o measure the speed of sound i n D 2 O (122), seawater (123), the major sea s a l t s (91), and mixtures of the major sea s a l t s (125). To generate i s o t h e r m a l c o m p r e s s i b i l i t i e s from sound speeds, i t i s necessary t o have r e l i a b l e e x p a n s i b i l i t y and heat c a p a c i t y data (equation 18). We have developed an i t e r a t i v e method t o convert h i g h pressure sound speed t o i s o t h e r m a l c o m p r e s s i b i l i t i e s (84). The e f f e c t o f pressure on the volume of a s o l u t i o n (3V/3P) a t a constant pressure i s g i v e n by 1

T

-(3v/3P)

P

P

= v /u

P

P

P

2

+ T(a v ) /C

P

(23)

p

where the s u p e r s c r i p t Ρ of pressure on the heat c a p a c i t y can be determined from C

P p

P

2

2

- C ° - T / (3 v/3T )dP p

(24)

Q

where C ^ i s t h e v a l u e at 1 atm (P = 0)· Since t h e second term i n equation (23) i s small compared t o v / u i t can be t r e a t e d as a p e r t u r b a t i o n term or a d i a b a t i c c o r r e c t i o n p

P

-(3v/3P)

P

2

P

2

= (v /u ) + A

(25)

s

To determine Ag i t i s necessary t o use an equation of s t a t e t o express the PVT p r o p e r t i e s . We have s e l e c t e d a second degree secant b u l k modulus t o represent the PVT p r o p e r t i e s o f aqueous s o l u t i o n s (84) P

Κ = Pv°/(v° - v ) = K° + AP + B P

2

(26)

where K^, A and Β a r e f u n c t i o n s of temperature and c o n c e n t r a t i o n . D i f f e r e n t i a t i n g t h i s equation w i t h respect t o pressure y i e l d s P

2

2

( 3 v / 3 P ) = v°(K° - BP )/(K° + AP + B P )

2

(27)

The term i s determined from the known 1 atm sound speeds ( u ^ ) , e x p a n s i b i l i t i e s (α^), s p e c i f i c volumes ( v ^ ) , and heat c a p a c i t i e s - Σ W K ( S )

(

M

X

)

(54)

and i s r e l a t e d to the a d i a b a t i c c o m p r e s s i b i l i t y ( 3 ) by Q

6

S

=

e

o(S)

+

Α

β

1

+

Β

β

l

3

/

2 +

°β

l

2

(55)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

616

where Α C

=

β

= [ ° $

-

( g )

B

ke

OF

6 q ( s )

AQUEOUS

$v

T b e

SYSTEMS

°]k, Β

s

3 ^ K ~ ^o(S)^V^ P the p r e d i c t e d Φ ζ £ ) u s i n g

e e c

*

o f

β

WITH

= [S - B R

s o u n

d

c a n

^

INDUSTRIAL

q ( s )

e

APPLICATIONS

S ^ k , and

estimated from

Κ

A/3

( s )

d

(56) anc

u

Comparisons of the p r e d i c t e d and measured values of $g * f ° seawater s o l u t i o n s u s i n g the a d d i t i v i t y method are shown i n Table V I . The agreement i s q u i t e good and s u f f i c i e n t f o r most needs. TABLE VI COMPARISONS OF THE MEASURED AND CALCULATED VALUES OF β FOR SEAWATE (u - U ) m sec q

a

S(°/oo)

Meas

5.024 10.057 15.142 20.000 24.943 30.031 35.003 35.005 40.025

5.50 10.96 16.44 21.60 26.91 32.41 37.72 37.72 43.18

-[β,, -

f

Calc

b

5.49 10.91 16.38 21.61 26.92 32.41 37.78 37.78 43.21

Meas

0.01 0.05 0.06 -0.01 -0.01 0.00 -0.06 -0.06 -0.03

0.495 0.980 1.461 1.910 2.364 2.827 3.270 3.270 3.716

Mean ± 0.03 a) b)

a

Δ

0

(ç) Calc

r

AND u

10 bar b

0.495 0.978 1.458 1.911 2.365 2.827 3.273 3.273 3.718

Δ 0.000 0.002 0.004 -0.001 -0.001 0.000 -0.003 -0.003 -0.002

Mean ± 0.002

From r e f . 85 From r e f . 86

Once the d e n s i t y and c o m p r e s s i b i l i t i e s of mixed e l e c t r o l y t e s o l u t i o n s a r e known a t 1 atm, values a t h i g h pressures can be made by u s i n g the secant b u l k modulus equation of s t a t e . The major d i f f i c u l t y , at p r e s e n t , w i t h u s i n g a d d i t i v i t y methods t o estimate the PVT p r o p e r t i e s of mixed e l e c t r o l y t e s i s the l a c k of experimental data f o r b i n a r y s o l u t i o n s over a wide range of con­ c e n t r a t i o n s and temperatures. H o p e f u l l y , i n the near f u t u r e we w i l l be able t o provide some of these data by measurements i n our l a b o r a t o r y i n Miami. Acknowledgement The author would l i k e t o acknowledge the support o f the O f f i c e of Naval Research (N00014-75-C-0173) and the Océanographie S e c t i o n of the N a t i o n a l Science Foundation (OCE77-28546) f o r t h i s study.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

31.

Pressure-Volume-Temperature Properties of Electrolytes 617

MILLERO

Abstract

A brief review is made of the methods that are currently being used to determine the density (ρ) and compressibility (ß) of electrolyte solutions as a function of pressure. The high pressure equations of state used to represent these properties are also discussed. The linear secant bulk modulus [K = Pρ /(ρ - ρ )] equation of state P

P

O

O

Κ =K +Β Ρ is shown to give a reasonable representation of the high pressure PVT properties of water from 0 to 350°C, where K° = 1/ß° the reciprocal of the 1 atm compressibility (applied pressure Ρ = 0) and Β is a constant. Since Β is not strongly dependent upon tem­ perature and concentration th equatio b dt estimate the high pressur reasonable accuracy, using 1 atm values of density and compres sibility. Simple additivity methods of estimating the density and compressibilities of mixed electrolytes like seawater and geothermal brines is presented. The predicted PVT properties for a number of mixed electrolytes are in good agreement with direct measurements. Literature Cited

1. Millero, F.J. Chem. Rev., 1971,71,147. 2. Millero, F.J., in "Water and Aqueous Solutions", R.A. Horne, Ed,, Wiley and Sons: New York, 1972; p. 519. 3. Millero, F.J., in "Activity Coefficients in Aqueous Electro­ lyte Solutions", R.M. Pytkowicz, Ed., CRC Press: W. Palm Beach, Fla., 1979, in press. 4. Bauer, N.; Lewin, S.Z., in "Techniques of Organic Chemistry", A. Weissberger, Ed., Interscience: New York, 1959, p. 167. 5. Bowman, H.A.; Schoonover, R.M, J„ Res. Nat. Bur. Stds., Sect. C, 1967, 71, 179. 6. Hidnert, P.; Peffer, E,L,, "Densities of Solids and Liquids", NBS Circ. 487, U,S. Govt. Print. Off., Washington, D.C., 1950. 7. Millero, F.J. Rev. Sci. Instrum., 1967, 38, 1441. 8. Lamb, A.B.; Lee, R.E. J. Am. Chem.Soc.,,1913, 35, 1666. 9. Geffcken, W.; Beckmann, Ch.; Kruis, A. Z. Phys. Chem. (Leipzig) Abt. B, 1933, 20, 398. 10. Hall, N.F.; Jones, T.O. J. Anu Chem.Soc.,1936, 58, 1915. 11. Ray, B.R.; Maclnnes, D.A. Rev. Sci. Instrum., 1951, 22, 642. 12. Spedding, F.H.; Pikal, M.J.; Ayer, B.O. J. Phys. Chem., 1966, 70, 2440. 13. Franks, F.; Smith, H.T. Trans. Faraday Soc., 1967, 63, 2586. 14. Ubrich, D.V.; Kupke, D.W.; Beams, J.W. Proc. Nat. Acad. Sci. U.S., 1964, 52, 349.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

618 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

15. Wirth, H.E. J. Am. Chem.Soc.,1937, 59, 2549. 16. Redlich, O.; Nielsen, L.E. J. Am. Chem. Soc., 1942, 64, 761. 17. Conway, B.E.; Verrall, R.E.; Desnoyers, J.E. Trans. Faraday Soc., 1966, 62, 2738. 18. Desnoyers, J.E.; Arel, M. Can. J. Chem., 1967, 45, 359. 19. Vaslow, F. J. Phys. Chem., 1966, 70, 2286. 20. Ward, G.K.; Millero, F.J, J. Soin. Chem., 1974, 3, 417. 21. Kratky, O.; Leopold, H,; Stabinger, H. Angew Phys., 1969, 2, 273, 22. Picker, P.; Tremblay, Ε.; Jolicoeur, C. J. Soln. Chem., 1974, 3, 377. 23. Geffcken, W.; Kruis, Α.; Solana, L. Z. Phys. Chem., (Leipzig) Abt. B, 1933, 23, 175. 24. Hepler, L.G.; Stokes, J.M.; Stokes, R.H. Trans. Faraday Soc., 1965, 61, 20. 25. Wirth, H.E.; Bangert F.K J Phys Chem. 1972 76 3488 26. Kell, G.S.; Whalley 258, 565. 27. Kell, G.S. J. Chem. Eng. Data, 1967, 12, 66; ibid., 1970, 15, 119. 28. Kell, G.S. J. Chem. Eng. Data, 1975, 20, 97. 29. Fine, R.A.; Millero, F.J. J. Chem. Phys., 1973,59,5529. 30. Kell, G.S.; Whalley, E. J. Chem. Phys., 1975, 62, 3496. 31. Chen, C.T.; Fine, R.A.; Millero, F.J. J. Chem.Phys.,1977, 66, 2142. 32. Kell, G.S.; McLaurin, G.E.; Whalley, E. Phil. Trans. R. Soc. Lond., 1978, A360, 389. 33. Ward, G.K.; Millero, F.J. J. Soln. Chem., 1974, 3, 431. 34. Ward, G.K.; Millero, F.J. Geochim. Cosmochim. Acta, 1975, 39, 1595. 35. Millero, F.J.; Gonzalez, Α.; Ward, G.K. J. Mar. Res., 1976, 34, 61. 36. Millero, F.J,; Knox, J.H.; Emmet, R.T. J. Soln. Chem., 1972, 1, 173. 37. Millero, F.J. J. Phys. Chem., 1967, 71, 4567. 38. Millero, F.J.; Drost-Hansen, W. J. Phys. Chem., 1968, 72, 1758. 39. Millero, F.J.; Drost-Hansen, W.; Korson, L. J. Phys. Chem., 1968, 721, 2251. 40. Millero, F.J. J. Phys. Chem., 1968, 72, 3209. 41. Millero, F.J.; Drost-Hansen, W. J. Chem. Eng. Data, 1968, 13, 330. 42. Millero, F.J. J. Phys. Chem., 1968, 72, 4589. 43. Millero, F.J. J. Phys. Chem., 1970, 74, 356. 44. Millero, F.J. J. Chem. Eng. Data, 1970, !L5, 562. 45. Millero, F.J. J. Chem. Eng. Data, 1971,16,229. 46. Millero, F.J.; Hoff, E.V.; Kahn, L.A. J. Soln. Chem., 1972, 1, 309. 47. Millero, F.J. J. Soln. Chem., 1973, 2, 1. 48. Millero, F.J.; Lepple, F.K. Mar. Chem., 1973, 1, 89.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

31. MILLERO Pressure-Volume-Temperature Properties of Electrolytes 619

49. Millero, F.J.; Knox, J.H. J. Chem. Eng. Data, 1973, 18, 407. 50. Masterton, W.L.; Welles, H.; Knox, J.H.; Millero, F.J. J. Soln. Chem., 1974, 3, 91. 51. Millero, F.J.; Emmet, R.T. J. Mar. Res., 1976, 34, 15. 52. Chen, C.-T.; Millero, F.J. J. Soln. Chem., 1977, 6, 589. 53. Millero, F.J.; Lawson, D.; Gonzalez, A. J. Geophys. Res., 1976, 81, 1177. 54. Desnoyers, J.E.; de Visser, C.; Perron, G.; Picker, P. J. Soln. Chem., 1976,5,605· 55. Jolicoeur, C.; Philip, P.R.; Perron, G.; Leduc, P.-Α.; Desnoyers, J.E. Can. J. Chem., 1972, 50, 3167, 56. Philip, P.R.; Desnoyers, J.E. J. Soln. Chem., 1972, 1, 353. 57. Leduc, P.-Α., Desnoyers, J.E. Can. J. Chem., 1973,51,2993. 58. Desnoyers, J.E.; Page, R.; Perron, G.; Fortier, J.-L.; Leduc, P.-A.; Platford, R.F. Can. J. Chem., 1973, 51, 2129. 59. Millero, F.J.; Perron G. Desnoyers J.E J Geophys Res. 1973, 78, 4499. 60. Perron, G.; Desnoyers, J.E.; Millero, F.J. Can. J. Chem., 1974, 52, 3738. 61. Fortier, J.-L.; Leduc, P.-A.; Desnoyers, J.E. J. Soln. Chem. Chem., 1974, 3, 523. 62. Leduc, P.-A.; Fortier, J.-L.; Desnoyers, J.E. J. Phys. Chem., 1974, 78, 1217. 63. Jolicoeur, C.; Boileau, J. J. Soln. Chem., 1974, 3, 889. 64. Perron, G.; Desnoyers, J.E.; Millero, F.J. Can. J. Chem., 1975, 53, 1134. 65. Perron, G.; Fortier, J.-L.; Desnoyers, J.E. J. Chem. Thermodyn., 1975, 7, 1177. 66. Jolicoeur, C.; Boileau, J.; Bazinet, S.; Picker, P. Can. J. Chem., 1975, 53, 716. 67. Desrosiers, N.; Desnoyers, J.E. Can. J. Chem., 1975, 53, 3206. 68. Perron, G.; Desrosiers, N.; Desnoyers, J.E. Can. J. Chem., 1976, 54, 2163. 69. Wen, W.-Y.; Lo Surdo, Α.; Jolicoeur, C.; Boileau, J. J. Phys. Chem., 1976, 80, 466. 70. Millero, F.J.; Ward, G.K.; Chetirkin, P.V. J. Biol. Chem., 1976, 251, 4001. 71. Millero, F.J.; Gonzalez, Α.; Brewer, P.G.; Bradshaw, A. Earth Planet. Sci. Lett., 1976, 32, 468. 72. Millero, F.J.; Kremling, K. Deep-Sea Res., 1976, 23, 1129. 73. Millero, F.J.; Chetirkin, P.V.; Culkin, F. Deep-Sea Res., 1977, 24, 315. 74. Millero, F.J.; Gombar, F.; Oster, J. J.Soln.Chem., 1977, 6, 269. 75. Millero, F.J.; Laferriere, Α.; Chetirkin, P.V. J. Phys. Chem., 1977, 81, 1737. 76. Millero, F.J.; Lo Surdo, Α.; Shin, C. J. Phys. Chem., 1978, 82, 784.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

620 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

77. Lo Surdo, A.; Shin, C.; Millero, F.J. J. Chem. Eng. Data, 1978, 23, 197. 78. Millero, F.J.; Forsht, D.; Means, D.; Gieskes, J.; Kenyon, K. J. Geophys. Res., 1978, 83, 2359. 79. Millero, F.J.; Means, D.; Miller, C.M. Deep-Sea Res., 1978, 25, 563. 80. Millero, F.J.; Lo Surdo, Α.; Chetirkin, P.V.; Guinasso, N.L. Limnol. Ocanogr., 1979, 24, 218. 81. Lo Surdo, Α.; Bernstrom, K.; Jonsson, C.-A.; Millero, F.J. J. Phys. Chem., 1979, 83, 1255. 82. Mathieson, J.G.; Conway, B.E. J. Soln. Chem., 1974, 3, 455. 83. Sakurai, M.; Nakajima, T.; Komatsu, T.; Nakagawa, T. Chem. Lett. (Japan), 1975, 971. 84. Wang, D.P.; Millero, F.J. J. Geophys. Res., 1973, 78, 7122. 85. Millero, F.J.; Kubinski T J Acoust Soc Am. 1975 57 312. 86. Millero, F.J.; Ward, G.K.; Chetirkin, P.V. J. Acoust. Soc. Am., 1977, 61, 1492. 87. Millero, F.J.; Curry, R.W.; Drost-Hansen, W. J. Chem. Eng. Data, 1969, 14, 422. 88. Lepple, F.K.; Millero, F.J. Deep-Sea Res., 1971, 18, 1233. 89. Millero, F.J., Lepple, F.K. J. Chem. Phys., 1971, 54, 946. 90. Millero, F.J.; Ward, G.K.; Lepple, F.K.; Hoff, E.V. J. Phys. Chem., 1974, 78, 1636. 91. Chen, C.-T.; Chen, L.-S.; Millero, F.J. J. Acoust. Soc. Am., 1978, 63, 1795. 92. Lo Surdo, Α.; Millero, F.J. J. Soln. Chem., 1979, in press. 93. Greenspan, M.; Tschiegg, CE. Rev. Sci. Instrum., 1957, 28, 897. 94. Garsey, R.; Roe, F.J.; Mahoney, R.; Litovitz, T.A. J. Chem. Phys., 1969, 50, 5222. 95. Del Grosso, V.A.; Mader, C.W. J. Acoust. Soc. Am., 1972, 52, 1442. 96. Hayward, A.T.J. Nature, 1969, 221, 1047. 97. Leonard, R.; Combs, P.; Stridmore, L. J. Acoust. Soc. Am., 1949, 21, 63. 98. Liebermann, L. J. Acoust. Soc. Am., 1948, 20, 868. 99. Bies, D. J. Chem. Phys., 1955, 23., 428. 100. Wilson, O.; Leonard, R. J. Acoust. Soc. Am., 1954,26,223. 101. Kurtze, G.; Tamm, K. Acustica, 1953,3,33. 102. Smith, W.C; Barrett, R.E.; Beyer, R.T. J. Acoust. Soc. Am., 1951, 23, 71. 103. Tamm, K.; Krutze, G.; Kaiser, R. Acustica, 1954, 4, 380. 104. Atkinson, G.; Petrucci, S. J. Phys. Chem., 1966, 70, 3122. 105. Atkinson, G., personal communication, 1976. 106. Bradshaw, Α.; Schleicher, K.E. Deep-Sea Res., 1970, 17, 691, ibid., 1976, 23, 583. 107. Fahey, P.F.; Kupke, D.W.; Beams, J.W. Proc. Nat. Acad. Sci. U.S., 1969, 63, 548.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

31. MILLERO Pressure-Volume-Temperature Properties of Electrolytes 621

108. Haynes, W.H.; Stewart, J.W. Rev. Sci. Instrum., 1971, 42, 1142. 109. Wilson, W.D. J. Acoust. Soc. Am., 1959, 31, 1067. 110. Del Grosso, V.A.; Mader, C.W. J. Acoust. Soc. Am., 1972, 52, 961. 111. Barlow, A.J.; Yazgan, E. Br. J. Appl. Phys., 1966, 17, 807; ibid., 1967, 18, 645. 112. Chen, C.-T.; Millero, F.J. J. Acoust. Soc. Am., 1976, 60, 1270. 113. Adams, L.H. J. Am. Chem.Soc.,1931, 53, 3769. 114. Gibson, R.E. J. Am. Chem.Soc.,1937, 59, 1521. 115. Keyes, F.G. Proc. Am. Acad. Arts Sci., U.S., 1933, 68, 505. 116. Chen, C.-T.; Millero, F.J. Deep-Sea Res., 1976, 221, 595. 117. Emmet, R.T.; Millero, F.J. J. Chem. Eng. Data, 1975, 20, 351. 118. Emmet, R.T.; Millero F.J J Geophys Res. 1974 79 3463. 119. Chen, C.-T.; Emmet, R.T.; Millero, F.J. J. Chem. Eng. Data, 1977, 22, 201. 120. Wilson, W.D. J. Acoust. Soc. Am., 1961, 33, 314. 121. Wilson, W.D. J. Acoust. Soc. Am., 1960, 32, 1357. 122. Chen, C.-T.; Millero, F.J. J. Acoust. Soc Am., 1977, 62, 553. 123. Chen, C.-T.; Millero, F.J. J. Acoust. Soc. Am., 1977, 62, 1129. 124. Chen, C.-T. Ph.D. Dissertation, University of Miami, Miami, Florida, 1977. 125. Chen, C.-T.; Millero, F.J., in preparation. 126. Fine, R.A.; Wang, D.-P.; Millero, F.J. J. Mar. Res., 1974, 32, 433. 127. Chen, C.-T.; Millero, F.J. J. Mar. Res., 1978,36,657. 128. Crease, J. Deep-Sea Res., 1962, 9, 209. 129. Picker, P.; Leduc, P.-A.; Philip, P.R.; Desnoyers, J.E. J. Chem. Thermodyn., 1971, 3, 631. 130. Ben-Naim, Α., in "Water - A Comprehensive Treatise", Vol. 1, Chapt. 11, F. Franks, Ed., Plenum Press: New York, 1972. 131. Weres, O.; Rice, S.A. Am. Chem.Soc.,1972, 94, 8983. 132. Gibbs, J.H.; Cohen, C.; Fleming, P.D. Ill; Porosoff, H. J. Soln. Chem., 1973, 2, 277. 133. Tait, P.G. "Voyage of H.M.S. Challenger HMSO", II, London, 1888; p. 1. 134. Hayward, A.T.J. Br. J. Appl. Phys., 1967, 18, 965. 135. Tammann, G. Zeit. Phys. Chem., 1895, 17, 620. 136. Tumlirz, O. Math. Naturwiss., K1., 1909, 118A, 203. 137. Gibson, R.E. J. Am. Chem.Soc.,1935, 57, 284. 138. Gibson, R.E.; Loeffler, O.H. J. Phys. Chem., 1939, 43, 207. 139. Gibson, R.E.; Loeffler, O.H. J. Am. Chem.Soc.,1941, 63, 898. 140. Murnaghan, F.D. Proc Nat. Acad. Sci. U.S., 1944, 30, 244. 141. Murnaghan, F.D. Proc. Symp. Appl. Math., 1949, 1, 158.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

622 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

142. Li, Y.-H. J. Geophys. Res., 1967, 72, 2665. 143. Ekman, V.W. Pubs. Circonst. Cons. Perm. Int. Explor. Mer., 1908, 43, 1.

144. Macdonald, J.R. Rev. Mod. Phys., 1969, 41, 316. 145. Millero, F.J., in "The Sea", Vol. 5, Chapter 1, E.D. Goldberg, Ed., Wiley: New York, 1974; pp. 3-80. 146. Millero, F.J. Ann. Rev. Earth Planet. Sci., 1974, 2, 101. 147. Millero, F.J. Deep-Sea Res., 1973, 20, 101. 148. Millero, F.J. J. Soln. Chem., 1973,2,1. 149. Millero, F.J., in "Structure of Water and Aqueous Solutions Solutions", W. Luck, Ed., Verlag Chemie, Weinheim, Bergstr., 1974; pp. 513-522. 150. Millero, F.J. Nav. Res. Rev., 1974, 27, 40. 151. Millero, F.J., in "Marine Chemistry in the Coastal Environment", Chapter 2, T.M. Chruch, Ed., ACS Symp. Ser. 18, Washington, D.C. 1975 25 152. Millero, F.J. Thalassi 153. Millero, F.J. Earth Planet. Sci. Lett., 1980, in press. 154. Young, T.F. Rec. Chem. Progr., 1951, 12, 81. 155. Wood, R.H.; Anderson, H.L. J. Phys. Chem., 1966, 70, 1877. 156. Reilly, P.J.; Wood, R.H. J. Phys. Chem., 1969, 73, 4292. 157. Wood, R.H.; Reilly, P.J. Ann. Rev. Phys. Chem., 1970, 21, 287. RECEIVED

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

32 Application of Thermodynamics in Hydrometallurgy A State-of-the-Art Review HERBERT E . BARNER Kennecott Copper Corp., Lexington, M A 02173 ROGER N. KUST Exxon Research and Engineering Co., Florham Park, NJ 07932

In the past several years interest i hydrometallurgica processing of ores has grown significantly. This growth can be attributed to several factors, among which are the necessity for environmental protection and pollution control, the increase in cost and decrease in availability of oil and natural gas, the increased complexity of ores processed, and the increased exploitation of non-sulf ide ores. Whether or not hydrometallurgical processing will provide satisfactory answers to many of the problems facing the minerals industry today is yet to be demonstrated. However, there have been several instances in recent years where hydrometallurgical processing, totally or in part, has proven to be advantageous. Hydrometallurgical processes involve the treating of a raw ore or concentrate with an aqueous solution of a chemical reagent in areaotor. The desired metal values are leached from the ore or concentrate, and the residue, after washing, is rejected as tailings. The leach liquor, containing one or more metal values in solution is then processed to the metals. The leaching reactor can be a conventional stirred tank or autoclave, or, as in the case of dump leaching, can be a large pile of rejected ore. In in-situ type leaching, the reactor is the ore-body itself, into which a suitable lixiviant is pumped. Hydro processes operate at lower temperatures than pyro processes, usually 50-250 C, and as a result the rates at which reactions occur are frequently several orders of magnitude slower. Consequently, in the development of such processes, kinetic studies become important. However, application of thermodynamics can still give valuable insight into the nature of various processes and should be used to determine process limitations. One important way in which thermodynamics is utilized in hydrometallurgical process development is as a guide to experimental planning and process selection and evaluation. A high degree of accuracy is not needed at this stage of process development. Estimates which are within 15 to 20% of the true value are frequently adequate for making feasibility calculations.

0-8412-0569-8/80/47-133-625$05.00/0 © 1980 American Chemical Society

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

There are numerous areas which can be treated by thermodynamic analysis. Some of them are: 1. Calculation of the solubility of simple and complex salts and gases, including estimation of "metal loading" in leach liquors 2. Estimation of vapor pressures of volatile components 3. Determination of the extent of reaction or position of equilibrium under various conditions of temperature, pressure and concentrations. 4. Estimation of extent of complex ion and ion pair formation. 5. Calculation of distribution coefficients for ion exchange processes. Earlier Reviews A number of earlier reviews on this subject have been published. MacDonald (1) has addressed the electrochemistry of metals in aqueous systems at high temperature ture data and the activity Two contributions from the Warren Spring Laboratory in England (2, 3) have reviewed pressure hydrolysis at high temperature and the extrapolation of potential-pH (Pourbaix) diagrams to high temperatures. Kwok and Robbins (4) have also considered the thermodynamics of high-temperature solutions with emphasis on separation of metal values from leach solutions; the CuS0 - H S 0 - H „ 0 was treated in some detail. Peters (5) has reviewed the leaching of copper, nickel, zinc, lead and molybdenum concentrates in terms of the thermodynamic stability of the sulfide minerals of these metals. Process developments associated with the most favorable decomposition paths are considered. From a geochemistry point of view, Helgeson 7, 8) has presented the properties of water at high temperature and pressure, Debye-Huckel parameters as a function of temperature and pressure, and the partial molal properties of electrolytes. Helgeson (9) has in addition published a comprehensive monograph on the thermodynamic aspects of hydrothermal ore-forming solutions. Barnes (10) has also presented a review of hydrothermal geochemistry with emphasis on thermodynamic interpretation and experimental measurements at high temperature and pressure. 4

2

4

Species in Solution Before any thermodynamic estimates can be made, there must be an assessment of the major solution, solid phase, and gaseous phase species present in a given system. In some instances physico-chemical measurements must be made to identify the species to be considered, but frequently chemical intuition and judgement flavored with experience are sufficient to provide a basis for initial estimating. Generally, for metal species in solution one needs to know how metal ions are hydrated, the number of ligands associated with the metal, the charges on the complex ions present, and whether or not the metal species are primarily mononuclear. For many metals such as copper, zinc, nickel, silver, etc. there is reasonable agreement as to what type of complexes are formed with the relatively simple ligands of interest to hydrometallurgy, e.g., hydroxide,

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

32.

BARNER AND KUST

Thermodynamics in Hydrometallurgy

627

chloride, sulfate, nitrate, cyanide, thiocyanate. For a few metals, such as molybdenum and tungsten, the species formed are extremely complex in nature and there is little agreement on their constitution, particularly in weak acid or neutral solutions. A recent report on the recovery of metal values from geothermal brine indicated the presence of lead, silver, copper, and iron in the cat ionic form. Because the brine contained 155 g/1 of chloride the metals must be present as chloroanions. The presence of chloroanions rather than aquated cations suggests a different type of processing and would certainly alter the results of thermodynamic estimates. Equilibrium Constants and Free Energy of Formation It is necessary to consider a number of equilibrium reactions in an analysis of a hydrometallurgical process. These include complexing reactions that occur in solution as wel for the dissolution and precipitatio analyzing the precipitation of iron compounds from sulfuric acid leach solutions, McAndrew, et al. (11) consider up to 32 hydroxyl and sulfate complexing reactions and 13 precipitation reactions. Within a restricted pH range only a few of these equilibria are relevant and need to be considered. Nevertheless, equilibrium constants for the relevant reactions must be known. Furthermore, since most processes operate at elevated temperatures, it is essential that these parameters be known over a range of temperatures. The availability of this information is discussed below. Data at 25°(^. Free energy of formation, equilibrium constants and related data at 25 C exist for a wide range of minerals, other solids, gases and aqueous species, including ions and complexes (see later discussion on data sources). Availability of data at this reference temperature is usually not a major stumbling block. On the other hand, new solution species are being identified. For example, some polynuclear species and some ion pair complexes are now recognized as being more significant in aqueous solutions than previously thought. There is therefore a need to develop, extend and up-date the data on new species which come to be recognized as significant. Temperature Effects. The most reliable source of information on the temperature dependence of a specific equilibrium constant is experimental measurement. Occasionally, sufficient experimental data are available. In the more usual situation, however, only sporadic high-temperature data, if any at all, are available. It is then necessary to use some form of extrapolation procedure to extend the 25 C data to higher temperatures. A number of approaches are available to extrapolate low-temperature equilibrium constants. Various aspects of this problem have been discussed and some comparisons to experimental data have been made. See, for example, Criss and Cobble (12), Helgeson (13), MacDonald (1), and Manning and Melling (3). We are not, however, aware of any recent comprehensive evaluation, error analysis or overall assessment. We summarize below what we believe to be the present situation.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

628

OF AQUEOUS

SYSTEMS WITH

INDUSTRIAL APPLICATIONS

The equation that relates the Gibbs free energy of a chemical reaction at temperature Τ to that at the reference temperature 298°C is given by + Δ 0

Τ. =

Δ 0

Δ8

298 " 298

Δ

Τ

Τ Δ

dT

Τ

^ 300 C) have been questioned (44) and there do seem to be unexplained d i f f e r e n c e s between s t u d i e s i n s t a i n l e s s s t e e l and t i t a n i u m v e s s e l s (45). The problem of measuring the thermodynamic p r o p e r t i e s of aqueous t r a n s i t i o n metal ions above 100 C has a l s o received_some a t t e n t i o n w i t h s t u d i e s on ¥e* complexing w i t h CI (46) , Br (47) and SO^" (48) up to 150°C and the formation of a n i o n i c hydroxy complexes of P b up to 300°C (49). P r e l i m i n a r y heats of s o l u t i o n of C0CI2 and CuCl2 have been measured up to 300 C by Cobble and Murray (50). H y d r o l y s i s was suppressed by HCI a d d i t i o n so that when the work i s completed and when the extent of CI complexing (and C u r e d u c t i o n ) can be allowed f o r the data w i l l extremel v a l u a b l e Preliminar concentration c e l l studie up to 170 C (51) suppor give complexing w i t h f i r s t row t r a n s i t i o n metal ions i s l i k e l y to be s i g n i f i c a n t by 300 C. The s o l u b i l i t y of Ye^O^ has been studied i n the temperature range 500-600°C by Chou and Eugster (52) using the HCI f u g a c i t y b u f f e r developed e a r l i e r (53). Under the c o n d i t i o n s used both HCI and the s o l u b l e i r o n species FeCl2 are completely a s s o c i a t e d . C l e a r l y the d e r i v e d thermodynamic data are a l s o of p o t e n t i a l value but more work on Cl~-complexing i s needed before they can throw l i g h t on the aqueous chemistry of F e under h i g h pressure b o i l e r conditions. Many of the 25 C o x i d a t i o n p o t e n t i a l estimates of Latimer (54) were obtained simply from a knowledge of what r e a c t i o n s proceed and what do not. Hence p r e p a r a t i v e and decomposition experiments i n simple autoclaves are a l s o of considerable v a l u e provided that f u l l experimental d e t a i l s are p u b l i s h e d . Swaddle's group has performed a number of such studies on the t r a n s i t i o n metals from which b o i l e r water c i r c u i t s are made (55,56,57) and a l s o on species of more d i r e c t relevance to l a b o r a t o r y s t u d i e s (58,59,60). Quite t r i v i a l unexpected observations i n autoclave s t u d i e s can be used to place l i m i t s on e q u i l i b r i u m constants. In complex systems, unique i n t e r p r e t a t i o n s w i l l u s u a l l y be impossible but the observations may s t i l l prove u s e f u l i f they can be supplemented by estimated data (H), 61). +

2 +

2 +

2 +

E s t i m a t i o n Procedures. There are b a s i c a l l y two ways which have been developed to d e a l w i t h the f a c t that heat c a p a c i t y terms are large i n r e a c t i o n s i n v o l v i n g i o n s . One i s based on e m p i r i c a l r e l a t i o n s h i p s (the entropy correspondence p r i n c i p l e ) between i o n i c entropies at d i f f e r e n t temperatures which C r i s s and Cobble (62) developed and checked to 200°C. Lewis (63) has checked a number of i t s p r e d i c t i o n s against a v a i l a b l e experimental evidence and has found the method reasonably s a t i s f a c t o r y f o r s e v e r a l

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

34.

TURNER

665

High-Temperature Aqueous Systems

systems up to 250°C. He (64) and o t h e r s , f o r example Macdonald and colleagues (65,66) have used the method to estimate e q u i l i b r i u m constants to 300°C and above. I t cannot be claimed, however, that the method has been ο · · e x t e n s i v e l y checked above 250 C and i t appears that i t i n e v i t a b l y must become u n r e l i a b l e over 300 C. The average heat c a p a c i t i e s of ions c a l c u l a t e d by C r i s s and Cobble (67) show no s i g n that C values of ions are becoming i n c r e a s i n g l y negative w i t h temperature, although, as was seen i n S e c t i o n 2, the e f f e c t i s becoming considerable by 300 C. Nevertheless many e q u i l i b r i u m constants could probably be obtained to w i t h i n an order of magnitude a t 300 C i f a r e l i a b l e estimate could be made of the thermodynamic p r o p e r t i e s of any uncharged species or i o n p a i r s . U n f o r t u n a t e l y , there i s , as y e t , no r e l i a b l e method of c h a r a c t e r i s i n g such species i f (as w i l l f r e q u e n t l y be the case) they are only s t a b l e at high temperatures. Wit self-dissociatio thi i not, of course, a proble the entropy correspondence method only begins to manifest i t s underestimation of the magnitude of AC above 300 C. 2_ I t i s not a problem e i t h e r f o r the p r o t o n a t i o n constant of S ( i . e . the r e c i p r o c a l of the second d i s s o c i a t i o n constant of H2S) some estimates of which are shown i n F i g . 4. N e i t h e r Cobble's estimate (68), u s i n g the correspondence p r i n c i p l e (curve a) nor Pohl's (69) e x t r a p o l a t i o n (curve b) u s i n g an e m p i r i c a l equation due to Harned and Embree (70) i s showing any i n d i c a t i o n of the expected minimum i n K. The e x t r a p o l a t i o n used by Khodakovskii et a l (71) (curve c) i s based on the more f r e q u e n t l y used expression of Harned and Robinson (72) and a d i f f e r e n t s e l e c t i o n of low temperature data. While t h e i r r e s u l t looks more reasonable i t i s d i f f i c u l t to have much confidence i n any of the r e s u l t s even up to 200 C. The apparent f a i l u r e of the correspon­ dence p r i n c i p l e may a r i s e as much from the choice of low temperature data as a f a i l u r e of the r e l a t i o n s h i p i t s e l f . The disagreement between the c a l c u l a t e d standard f r e e energies of formation of aqueous F e and those deduced by Sweeton and Baes (23) has been commented on by the author (9) and by Tremaine, Van_Massow and Shierman (73). I n view of the problem at 300 C w i t h CI -complexing (discussed e a r l i e r ) i t seems u n l i k e l y to the author that the thermodynamics of d i s s o l u t i o n of magnetite i n a c i d s o l u t i o n are q u i t e as w e l l c h a r a c t e r i z e d as i s suggested by the c a l c u l a t i o n s of Tremaine et a l (73). The second method of e s t i m a t i o n which has so f a r been developed i s based on c o n s i d e r a t i o n of those AC values which were a v a i l a b l e i n 1967 when Helgeson developed i t ( 7 % ) . This method e s s e n t i a l l y separates e l e c t r o s t a t i c and n o n - e l e c t r o s t a t i c c o n t r i b u t i o n s to AS and. AC and Helgeson has compared the p r e ­ d i c t i o n s of a number of d i f f e r e n t assumptions concerning AC° w i t h published high temperature e q u i l i b r i u m constants. He concluded that the best one to make i s that ACp i s p r o p o r t i o n a l , at each temperature, to the e l e c t r o s t a t i c c o n t r i b u t i o n , AC . This p

p

2 +

p

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

666

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

34.

TURNER

661

High-Temperature Aqueous Systems

assumption, combined w i t h a simple e l e c t r o s t a t i c model, leads t o an e x p l i c i t r e l a t i o n s h i p between l o g Κ and temperature which i n c l u d e s i n i t the temperature dependence of the d i e l e c t r i c constant of water: A

ln Κ -

S

^

9

8

)

{298 " f (1 - exp [exp(b + aT) - C + (Τ - 298)/θ])} AH°(298) RT

m

'··

U

;

Here C(= exp (b + 298a)), ω(= 1 + aC6), b and θ are constants i n an e x p r e s s i o n f o r the temperature dependence of ε, the d i e l e c t r i c constant of water: ε = ε exp Q- exp (b + aT)

Τ/θ]

ο

(2)

Equation (1) was s i m p l i f i c a t i o more complete, but l e s s r e a d i l y usable equation:

g

S°(298) ln Κ = — ^ {298 - Τ +^ (1 - exp Qexp(b + aT) -C + (Τ- 298)/θ])} _ ^!g98)_

+

A S ^

+

a

[

l

n

(

T

/

2

9

8

)

.

1

+

2

9

8

/

T

]

+3(T-g8)

2

...

(3)

The f i r s t term represents how the e l e c t r o s t a t i c c o n t r i b u t i o n s d i f f e r from those at 2 5 ° C , A S ° (298) being the e l e c t r o s t a t i c c o n t r i b u t i o n to the r e a c t i o n ' s standard entropy a t 25 C . The l a s t two terms d e r i v e from the assumption that the n o n - e l e c t r o s t a t i c ο ο p a r t of AC , AC , can be represented by Ρ Ρ>η' AC°

ρ,η

= α

+ $T

...

(4)

2 F o l l o w i n g Helgeson (74) a term XT ( i n ( 4 ) ) i s ignored. On h i s model the c o n t r i b u t i o n of each i o n t o AS^ i s given by ... (5)

S° = -A [exp{exp(b + aT) } + Τ/θ] Ql/Θ + a exp(b + aT)] /ε

2 where A = (Ze) N/2r, Ze i s the charge on the i o n , r i t s r a d i u s and N, Avogadro's number. ε i s defined i n equation (2) and takes the v a l u e 3 0 5 . 7 . The e l e c t r o s t a t i c model i s crude and the choice of r t o be employed i s somewhat a r b i t r a r y , but Helgeson s model t o a c e r t a i n extent allows f o r t h i s by t a k i n g up u n c e r t a i n t i e s i n the e l e c t r o s t a t i c c o n t r i b u t i o n i n α and 3 . This was a q u i t e i n t e n t i o n a l f e a t u r e of the model because i t i s b e l i e v e d that much of the u n r e l i a b i l i t y of h y d r a t i o n models a r i s e s from non0

1

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

668

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e l e c t r o s t a t i c c o n t r i b u t i o n s . Helgeson used equation (3) t o curve f i t a l l s u f f i c i e n t l y r e l i a b l e experimental data and from t h i s obtained best f i t values of a, 8 and AS f o r a number of equilibria. The author has r e c e n t l y attempted to use t h i s method to estimate the e q u i l i b r i u m constant, K^, of the r e a c t i o n 3I

+ 3H 0

2

2

=

5 I ~ + I 0 + 6H

+

3

up to 300°C from experimental data at 25°C and 60°C (75). The r e a c t i o n i s , of course, a severe t e s t as i t produces 12 ions from 3 molecules of n e u t r a l s o l u t e . Equation (1) i s t o t a l l y u n s a t i s f a c t o r y s i n c e i t f a i l s to p r e d i c t the expected maximum i n the e q u i l i b r i u m constant as seen i n F i g . 5. Thus an attempt was made to use a c a l c u l a t e d AS ( v i a equation (5)) and see i f a b e t t e r estimate was p o s s i b l suggested were reasonabl t r i e d , one was that A C p i s independent of temperature - i . e . 3=0and the other made use of the o b s e r v a t i o n that i n Helgeson s Table 2 there i s an approximate r e l a t i o n s h i p between α and 3, α = -313 (±48). These estimates are a l s o shown i n F i g . 5 and i t i s c l e a r from the divergence of r e s u l t s above 100 C that the method i s too s e n s i t i v e t o the values of α and 3 to be of use at l e a s t i n t h i s case. The author b e l i e v e s (75) the correspondence p r i n c i p l e method (as used by Lewis (64) based on Cp ( I 2 ) = 65, although u n c e r t a i n due to lack of appropriate data on I 2 , provides the best estimate. Almost c e r t a i n l y f r e e energy approaches l i k e Helgeson s can be improved by b e t t e r i o n i c h y d r a t i o n models. To t h i s end a number have been q u a l i t a t i v e l y compared (76) and checked against experimental data on NaCl (77,78). More e x t e n s i v e c a l c u l a t i o n s based on one ( f i x e d hydration) model have a l s o been presented (79) and found to p r e d i c t i o n i c f r e e energies b e t t e r than the correspondence p r i n c i p l e between 150 and 275 C. At higher temperatures, however, the model i s l e s s s a t i s f a c t o r y . Much more work i s needed i n t h i s area s i n c e , i f such methods are to prove r e l i a b l e i n the d i f f i c u l t r e g i o n between 300 C and the c r i t i c a l p o i n t , the h y d r a t i o n models must be as free as p o s s i b l e from e m p i r i c a l f i t t i n g parameters. jn

1

1

3.Applications There f o l l o w some examples of attempts to apply thermodynamic arguments to a number of p l a n t problems. A t t e n t i o n i s d i r e c t e d as much to what can and cannot be done w i t h c u r r e n t l y a v a i l a b l e data as to the p r a c t i c a l s i g n i f i c a n c e of the r e s u l t s . Areas where work i s p a r t i c u l a r l y needed are s t r e s s e d . Generation of C o r r o s i v e Environments. The m a t e r i a l s of c o n s t r u c t i o n of a water c i r c u i t a r e , of course, s e l e c t e d t o be

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1000Q/K)"

Figure 5. Predictions of K : (1) Helgeson Equation 1; (2) Equation 5, β = 0; (3) entropy correspondence~C °(I (aq)) = 0; (4) entropy correspondence C °(I (aq)) == 65; (5) Equation 3,a= -313β h

p

2

p

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c o r r o s i o n r e s i s t a n t i n whatever s o l u t i o n s they are expected t o see. Most s e r i o u s problems a r i s e because i m p u r i t i e s i n or a d d i t i v e s t o the water are able to concentrate, sometimes by many orders of magnitude. This can occur where water i s b o i l i n g on t h i n porous oxide l a y e r s under high heat f l u x e s and i n regions of t u r b i n e s where the steam i s nominally dry but of such a pressure that concentrated s o l u t i o n s could be i n e q u i l i b r i u m w i t h i t . Simulations of the former occurrence have shown c o n c e n t r a t i o n f a c t o r s of ΙΟ» t o be p o s s i b l e while i n theory the l a t t e r s i t u a t i o n s cotfld r e s u l t i n even higher concentrations. I n PWR steam generators, e l e c t r o l y t e s can concentrate between the tubes and t h e i r support p l a t e s . The a c c e l e r a t e d production of c o r r o s i o n product leads t o "denting" by crushing of the supported tubes. I f the i m p u r i t y l e a k i n g ( v i a the condensers) t o a b o i l e r i s sea-water, the chemistry i s f a i r l y simple and i t i s easy t o pre­ d i c t roughly under wha go a c i d due t o M g h y d r o l y s i r e l i a b l e data on t h i s h y d r o l y s i s r e a c t i o n the best that can be hoped f o r i n e s t i m a t i n g the pH i s ±0.5 pH u n i t at 300°C (80). The much more complex s i t u a t i o n which a r i s e s when the condenser leak allows i n r i v e r or lake water can be d e a l t w i t h f o r m a l l y (82,83) but the u n c e r t a i n t i e s i n the data are u s u a l l y too large t o y i e l d r e l i a b l e pH estimates. We have been a b l e , however, on occasions to use a very simple model t o help understand s p e c i f i c p l a n t problems where r i v e r water analyses were a v a i l a b l e and on one occasion t o show that a t d i f f e r e n t times the b o i l e r water had (as c o r r o s i o n evidence suggested) a l t e r n a t e d between a c i d i c and a l k a l i n e c o n d i t i o n s . The model assumes that by 350 C any normally d i s s o c i a t e d multi-charged ions w i l l be s u f f i c i e n t l y unstable that they w i l l undergo whatever appropriate h y d r o l y s i s r e a c t i o n s can reduce t h e i r charge t o u n i t y . Whether the water goes a c i d o r a l k a l i n e then simply depends on whether the t o t a l (equivalent) concentration of m u l t i p l y charged c a t i o n s exceeds or i s smaller than the c o n c e n t r a t i o n of m u l t i p l y charged anions. When a 60 MW t u r b i n e a t Hinkley A power s t a t i o n d i s i n t e g r a t e d i n 1969 from s t r e s s c o r r o s i o n c r a c k i n g of a low pressure t u r b i n e d i s c (consequences shown i n P l a t e 1) i t was considered that Na^H s o l u t i o n s were most probably i n v o l v e d (84) and i t was soon found that i f NaOH were the s o l e e l e c t r o l y t e present i t s maximum concentration (based on vapour pressure depression) was s u f f i c i e n t t o have caused the c r a c k i n g . However, i t was a l s o found that i n mixtures i t was only the f r e e NaOH which l e d t o r a p i d s t r e s s c o r r o s i o n c r a c k i n g . Considerations of a c i d gas s o l u b i l i t y and s o l u t i o n thermodynamics showed that at the C O 2 and acetate l e v e l s present i t was most u n l i k e l y that f r e e NaOH was present i n s u f f i c i e n t q u a n t i t y to be r e s p o n s i b l e f o r the H i n k l e y f a i l u r e (85). Ammonium acetate and ammonium carbonate had a l s o been found to induce s t r e s s c o r r o s i o n c r a c k i n g of the appropriate s t e e l s but 2+

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s i m i l a r thermodynamic arguments showed that n e i t h e r e l e c t r o l y t e could i n p r a c t i c e approach the l e v e l s r e q u i r e d to cause c r a c k i n g (86,85). Subsequent attempts to improve the estimates (87) confirmed these f i n d i n g s . The e f f e c t o f a c i d gases l i k e C O 2 and a c e t i c a c i d on reducing the f r e e NaOH concentrations i n t u r b i n e s makes one wonder i f i t may be p o s s i b l e to p u r i f y b o i l e r water too much f o r the good of the t u r b i n e . I f t h i s i s so, then some of the observations r e c e n t l y made by Bussart, Curran and Gould (88) on the e f f e c t of water chemistry on modern large t u r b i n e s may not, a f t e r a l l , be " p a r a d o x i c a l " . I t was e v e n t u a l l y concluded that the most l i k e l y chemical c u l p r i t i n the Hinkley t u r b i n e s was molybdate which can be formed from the M0S2 l u b r i c a n t under the c o n d i t i o n s used during t u r b i n e assembly (89) o r leached from the s t e e l under stagnant c o n d i t i o n s i n s u f f i c i e n t q u a n t i t y to induce s t r e s s c o r r o s i o n (90). Understanding Corrosio Pourbaix diagrams to c o r r o s i o n problems i s w e l l known and w i l l not be considered here. Much e f f o r t has gone i n t o producing such diagrams f o r high temperature use. A recent paper (91) l i s t s 15 references to the s u b j e c t . The diagrams are p a r t i c u l a r l y u s e f u l i n i n t e r p r e t i n g c o r r o s i o n or e l e c t r o c h e m i c a l s t u d i e s conducted a t c o n t r o l l e d p o t e n t i a l . However, w i t h few exceptions (92) l i t t l e a t t e n t i o n has been given to the r o l e of s o l u t i o n phase a d d i t i v e s and i m p u r i t i e s i n i n f l u e n c i n g the composition o l the c o r r o s i o n f i l m , although q u i t e s u b t l e compositional d i f f e r e n c e s across a c o r r o s i o n f i l m have been discussed i n terms o f redox p o t e n t i a l (93,94). Since a l l chemical r e a c t i o n s w i l l be much f a s t e r above 300°C than at 25 C i t seems l i k e l y that redox b u f f e r i n g by s o l u t i o n components should be more p r e d i c t a b l e thermodynamically (once the data become a v a i l a b l e ) a t the higher temperatures. A f e a t u r e of c o r r o s i o n s t u d i e s which has been s t r e s s e d r e c e n t l y (2) i s the complete f a i l u r e of l a b o r a t o r y t e s t s on t h e i r own to p r e d i c t how r e l i a b l e operation of some nuclear steam generators can be maintained. At l e a s t a p a r t o f t h i s problem i s l i k e l y to a r i s e from d i f f e r e n t redox and/or pH c o n d i t i o n s imposed by the s o l u t i o n i n autoclave t e s t s and i n p l a n t c o n d i t i o n s and many low l e v e l contaminants could be i n v o l v e d . In view of what has been s a i d e a r l i e r concerning the r o l e of Mo(VI) i n stagnantwater i t i s c l e a r that some data, a t l e a s t on the thermodynamics of aqueous Mo s p e c i e s , should be sought at high temperatures. Some molybdate appears to be able to enter s o l u t i o n through the vapour at 250 C (61), so the contamination problem i s not n e c e s s a r i l y solved by the use of l i n e r s . Presumably other species capable of i n f l u e n c i n g redox p o t e n t i a l s and pH can a l s o contaminate s o l u t i o n s through the vapour. I t seems to the author that u n t i l some means i s a v a i l a b l e f o r e s t i m a t i n g the pH and redox p o t e n t i a l of s o l u t i o n s both i n autoclave s t u d i e s and under s p e c i f i c l o c a l p l a n t c o n d i t i o n s there w i l l always be doubt about the p r e d i c t i v e value of many c o r r o s i o n s t u d i e s c a r r i e d out i n autoclaves.

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Out of Core R a d i o a c t i v i t y . I n water r e a c t o r s the main source of out of core a c t i v i t y a r i s e s from the c o r r o s i o n products of the out of core c i r c u i t which are t r a n s p o r t e d i n t o the core and, a f t e r neutron i r r a d i a t i o n , subsequently t r a n s p o r t e d back. Since the core of a PWR w i l l i n e v i t a b l y be h o t t e r than the steam generator, there has been i n t e r e s t , p a r t i c u l a r l y a t Atomic Energy of Canada L t d . (A.E.C.L.), i n the e f f e c t of temperature on the s o l u b i l i t y of the v a r i o u s c o r r o s i o n products present and how t h i s i n f l u e n c e s t h e i r t r a n s p o r t a t i o n round the c i r c u i t (95). The s o l u b i l i t i e s c o u l d , even w i t h p e r f e c t data, only be t i e d down t o a range of l e v e l s f o r most elements because of the presence of r a d i o l y t i c a l l y produced H 2 and O 2 a t l e v e l s which are not at e q u i l i b r i u m . The system i s f u r t h e r complicated by the presence of mixed s p i n e l s as w e l l as pure oxides amongst the c o r r o s i o n products. Despite these c o m p l i c a t i o n s , however, a combination of d e t a i l e d sampling and thermodynamic r a t i o n a l i z a t i o 66) i s r e s u l t i n g i n a g r e a t l processes i n v o l v e d (96) . There i s l i t t l e doubt that the experimental programme being pursued by A.E.C.L. w i l l lead t o b e t t e r understanding o f the behaviour of c o r r o s i o n products i n a l l types of p l a n t . Thermodynamic arguments have a l s o been used i n support of work on decontaminating the c i r c u i t s of BWRs (11). I t was shown that c o n v e n t i o n a l c i t r i c a c i d c l e a n i n g s o l u t i o n s could not d i s s o l v e e i t h e r Fe2Û3 or important Co-containing s p i n e l s unless q u i t e strong reducing agents were present and i t was a l s o shown that the r i s k of e l e c t r o d e p o s i t i o n on s t e e l surfaces during the decontamination i s g r e a t l y reduced under s t r o n g l y reducing c o n d i t i o n s . There was some evidence from r e s u l t s on decontamination of the W i n f r i t h SGHWR (Steam Generating Heavy Water Reactor) that ^°Co may have been e l e c t r o d e p o s i t e d e i t h e r during e a r l y decontaminations or on load; the l a t t e r seems p o s s i b l e thermodynamically though u n l i k e l y k i n e t i c a l l y under normal ( r a d i a t i o n - f r e e ) c o n d i t i o n s . The high temperature thermodynamic data were, however, considered i n s u f f i c i e n t l y r e l i a b l e t o be c e r t a i n of the s i g n i f i c a n c e of some of the p l a n t o b s e r v a t i o n s . I t i s , however, c l e a r that e l e c t r o d e p o s i t i o n of ^ C o n load (as w e l l as d u r i n g decontamination) i s u n l i k e l y under s t r o n g l y reducing c o n d i t i o n s such as those which are nominally maintained i n PWR primary c i r c u i t s . The r e l e a s e of r a d i o a c t i v e i o d i n e s from BWR c i r c u i t s , f i r s t i n t o the steam phase and then i n t o the t u r b i n e h a l l , has a l s o been considered thermodynamically (75) . A r e - a n a l y s i s of some experimental data of S t y r i k o v i c h e t a l (97) , suggested that iodates were not, as had been t e n t a t i v e l y proposed, l i k e l y t o be present. S t y r i k o v i c h ' s p r e d i c t i o n of HIO as a p r i n c i p a l species under BWR c o n d i t i o n s was confirmed, but i t was concluded t h a t h i s experiments had not measured i t s steam/water p a r t i t i o n c o e f f i c i e n t . In view of the meagre experimental evidence, however, more work on t h i s system i s d e s i r a b l e . Q

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New Methods of Chemical Treatment, As d e s c r i b e d elsewhere (98) c o n s i d e r a b l e success has been achieved i n t r e a t i n g low pressure b o i l e r s w i t h polyamino-carboxylic a c i d type c h e l a t i n g agents. Some years ago the author suggested that weaker, but more thermally s t a b l e , c h e l a t i n g agents such as oxine (8 hydroxy q u i n o l i n e ) might f i n d a p p l i c a t i o n i n m a i n t a i n i n g once-through b o i l e r s f r e e of d e b r i s . The main doubt (98,99) was whether such b i d e n t a t e c h e l a t i n g agents are strong enough (thermodynamically) to be of any value and e a r l y estimates of magnetite s o l u b i l i t i e s up t o 200 C (14) were not encouraging. Apart from some recent work of Alexander (100) there i s s t i l l h a r d l y any data on metal ion c h e l a t i o n above 100 C. However i t has been p o s s i b l e t o estimate roughly some r e l e v a n t h i g h temperature s t a b i l i t y constants (12) and c r u d e l y c o r r e c t them on the b a s i s of measured i r o n l e v e l s d i s s o l v e d from Fe304 by oxine (101). On t h i s b a s i s the chances of u s i n g oxin look good, c a t e c h o l ma usable i n an adaption of a Russian method of t r e a t i n g super c r i t i c a l b o i l e r s (102) t o s u i t s u b - c r i t i c a l once-through b o i l e r s . E s t i m a t i o n i n t h i s f i e l d i s , at the moment, i n e v i t a b l y g r o s s l y approximate because of the lack of high temperature data and the l i k e l i h o o d (discussed i n S e c t i o n 2) of forming mixed hydroxy-chelate complexes at h i g h temperatures. Experimental work i n t h i s area i s p a r t i c u l a r l y needed. 4.Concluding Remarks There are many a d d i t i o n a l ways i n which thermodynamic arguments c o u l d , i n p r i n c i p l e , be used both f o r pure p r e d i c t i o n and f o r r a t i o n a l i z i n g p l a n t f i n d i n g s . I t i s a l s o necessary t o q u a n t i f y most of the r a t h e r q u a l i t a t i v e c o n c l u s i o n s discussed i n S e c t i o n 3. The l e a s t p r e d i c t a b l e systems i n v o l v e the behaviour of t r a n s i t i o n metal ions a t h i g h temperatures and u n t i l a good deal more work i s done to d i s e n t a n g l e t h e i r complexing and h y d r o l y s i s r e a c t i o n s i t i s u n l i k e l y that much progress can be made. The author very much hopes that the complexity of the t r a n s i t i o n metal systems w i l l not i n h i b i t work i n t h i s area. The l o s s to a user of thermodynamics i n my f i e l d would have been c o n s i d e r a b l e i f Sweeton and Baes had been put o f f beginning or r e p o r t i n g t h e i r (23) Fe3Û4 s o l u b i l i t y work by the f e a r t h a t on i t s own, i t might not y i e l d a complete answer t o the understanding of Fe304 s o l u b i l i t y . I n t h i s p a r t i c u l a r case the d e c i s i o n was probably not d i f f i c u l t as there may be no problem below 250-300 C. The q u e s t i o n which w o r r i e s me i s how people are to be encouraged to study systems which are o b v i o u s l y more complex, e x p e r i m e n t a l l y d i f f i c u l t and u n l i k e l y , on t h e i r own, to y i e l d r e l i a b l e thermodynamic r e a c t i o n f r e e e n e r g i e s , (e.g. Fe304 s o l u b i l i t y a t higher temperatures or s t u d i e s on mixed complexes). S i m i l a r l y , i f S t y r i k o v i c h e t a l (97) , had w o r r i e d about iodates and not given what the present author b e l i e v e s i s an q

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i n c o r r e c t i n t e r p r e t a t i o n of the r e s u l t s , the data might s t i l l be u n a v a i l a b l e . While a more d e t a i l e d t a b u l a t i o n of the raw data would have been b e t t e r , the data themselves are v a l u a b l e i n p r o v i d i n g the only a v a i l a b l e experimental work on the behaviour of i o d i n e i n h i g h temperature water. I t i s to be hoped t h a t , i n c r e a s i n g l y , J o u r n a l s w i l l provide f a c i l i t i e s f o r authors t o t a b u l a t e t h e i r raw data. The J o u r n a l of Chemical Thermodynamics i s t o be congratulated on the amount of data they p r i n t e d i n the paper of Sweeton and Baes (23). I f the formation constant of F e C l and r e l a t e d constants can e v e n t u a l l y be measured or estimated, and i f a r e a n a l y s i s proves necessary, the data are a l l there t o use. In view of the d i f f i c u l t i e s discussed i n S e c t i o n 2 i t seems that many of the more important e q u i l i b r i a of relevance t o power s t a t i o n o p e r a t i o n w i l l not be d i r e c t l y measurable. I t i s c e r t a i n , t h e r e f o r e , that great emphasi of e s t i m a t i n g high temperatur these are t o be checked up t o 350 C,a v a r i e t y of experimental techniques may w e l l prove necessary t o s o r t out usable thermodynamic data from experiments which, on t h e i r own, cannot give them. A l t e r n a t i v e l y , i f e s t i m a t i o n procedures can be developed which are s u b s t a n t i a l l y f r e e from e m p i r i c a l f i t t i n g parameters, they may not r e q u i r e extensive checking. +

This review was c a r r i e d out at the C e n t r a l E l e c t r i c i t y Research L a b o r a t o r i e s and i s p u b l i s h e d by permission of the C e n t r a l E l e c t r i c i t y Generating Board. 5.Literature Cited

1. Staehle, R.W., Corrosion, 1977, 33, 1 2. Faster, D., Kernenergie, 1979, 22, 118 3. Barnes, H.L., "High Temperature High Pressure Electrochemistry in Aqueous Solutions", N.A.C.E.-4, Houston, Texas, 1976, p.14 4. Freier, R.K., VGB-Speisewassertagung, 1969, p.11 5. Freier, R.K., VGB-Speisewassertagung, 1970, p.8 6. Turner, D.J., paper presented at symposium "Industrial Uses of Thermochemical Data", 1979, sponsored by NPL and Chemical Society, University of Surrey, Oct. 7. Liu, C. and Lindsay, W.T. Jr., J. Solution Chem., 1972, 1, 45 8. Choi, Y-S. and Criss, CM., Faraday Disc, of Chem. Soc., 1977, 64, 204

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

34. TURNER High-Temperature Aqueous Systems 675

9. Turner, D.J., C.E.R.L. Note, 1976, RD/L/N 165/76 10. Turner, D.J., C.E.R.L. Note, 1979, draft "Some Unexpected Reactions Between Metals and Aqueous Solutions at High Temperature; Part I. Gold and Platinum Dissolution" 11. Turner, D.J., C.E.R.L. Note, 1976, RD/L/N 213/76 12. Turner, D.J., C.E.R.L. Note, 1978, RD/L/N 11/78 13. Passell, T.O., E.P.R.I. Jnl., 1977, 2, 42 14. Bawden, R.J., C.E.R.L. Note, 1976, RD/L/N 72/76 15. Franck, E.U., "High Temperature Pressure Electrochemistry in Aqueous Solutions" N.A.C.E.-4 Houston Texas 1976 p.109 16. Marshall, W.L., ibid, p.117 17. Lindsay,W.T.and Liu, C., ibid, p. 139 18. Martynova, O.I., ibid, p.131 19. Lietzke, M.H., ibid, p.317 20. Mesmer, R.E., Sweeton, F.H., Hitch, B.F. and Baes, Jr.,C.F., ibid, p.365 21. Silvester, L.F. and Pitzer, K.S., J. Phys. Chem., 1977, 81, 1822 22. Helgeson, H.C. and Kirkham, D.H., Amer. J. Sci., 1976, 276, 97 23. Sweeton, F.H. and Baes, C.F., Jr., J. Chem. Thermodynamics, 1970, 2, 479 24. Nikolaeva, N.M., "High Temperature High Pressure Electro­ chemistry in Aqueous Solutions", N.A.CE.-4, Houston, Texas, 1976, p.146 25. Tremaine, P.R. and Leblanc, J.C., "The Solubility of Nickel Oxide and Hydrolysis of N i in Water to 573 K". In press 2+

26. Lüdemann, H.D. and Franck, E.U., Ber Bunsenges. physik. Chem., 1968, 72, 514 27. Lüdemann, H.D. and Franck, E.U., Ber Bunsenges. physik. Chem., 1967, 71, 455

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

676 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

28. Scholz, Β., Lüdemann, H.D. and Franck, E.U., Ber. Bunsenges. physik. Chem., 1972, 76, 406 29. Franck, E.U., "Phase Equilibria and Fluid Properties in the Chemical Industry", ed. T.S. Storvik and S.I. Sandler, A.C.S. Symposium, Series No. 60, Chap. 5, p.99 30. Broadbent, D., Lewis, G.G. and Wetton, E.A.M., J. Chem. Soc. Dalton Trans., 1977, 464 31. Hitch, B.F. and Mesmer, R.E., J. Soln. Chem., 1976, 5, 667 32. Holmes, H.F., Baes, Jr., CF. and Mesmer, R.E., J. Chem. Thermodynamics, 1978, 10, 983 33. Shoesmith, D.W. and Lee W. Can J Chem. 1976 54 3553 34. Mesmer, R.E. and Herting, D.L., J. Soln. Chem., 1978, 7, 90 35. Sweeton, F.H., Mesmer, R.E. and Baes Jr., CF., J. Soin. Chem., 1974, 3, 191 36. Fisher, J.R. and Barnes, H.L., J. Phys. Chem., 1972, 76, 90 37. Sirota, A.M. and Shviriaev, Yu.V., "High Temperature High Pressure Electrochemistry in Aqueous Solutions", N.A.C.E.-4, Houston, Texas, 1976, p.169 38. Marshall, W.L. and Franck, E.U., Paper presented at International Association for the Properties of Steam, Sept. 1979, Munich, West Germany 39. Marshall, W.L., J. Inorg. Nucl. Chem., 1975, 37, 2155 40. Marshall, W.L. and Slusher, R., J. Inorg. Nucl. Chem., 1975, 37, 2165 41. Marshall, W.L. and Slusher, R., J. Inorg. Nucl. Chem., 1975, 37, 2171 42. Marshall, W.L. and Jones, E.V., J. Inorg. Nucl. Chem., 1974, 36, 2313 43. Marshall, W.L. and Jones, E.V., J. Inorg. Nucl. Chem., 1974 36, 2319 44. Templeton, C.C., J. Chem. Thermodynamics, 1976, 8, 99 45. Marshall, W.L., ibid, p.100

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

34. TURNER High-Temperature Aqueous Systems 677

46. Nikolaeva, N.M. and Tsvelodub, L.D., Zh. Neorg. Khim., 1977, 22, 380 47. Nikolaeva, N.M., Zh. Neorg. Khim., 1977, 22, 2447 48. Nikolaeva, N.M. and Tsveladub, L.D., Zh. Neorg. Khim., 1975, 20, 3033 49. Tugarinov, I.Α., Ganeev, I.G. and Khodakovskii, I.L., Geokhimya, 1975, 9, 1345 50. Cobble, J.W. and Murray, Jr., R.C., Faraday Disc, of Chem. Soc., 1977, 64, 144 51. Bawden, R.J. and Turner, D.J., unpublished results 52. Chou, I.-M. and Eugster 53. Frantz, J.D. and Eugster, H.P., Amer. J. Sci., 1973, 273, 268 54. Latimer, W.L., "Oxidation Potentials", Prentice Hall Inc., New Jersey, 1952 55. Swaddle, T.W., Lipton, J.H., Guastalla,G. and Bayliss, P., Can. J. Chem., 1971, 49, 2433 56. Kong, P-C., Swaddle, T.W. and Bayliss, P., Can. J. Chem., 1971, 49, 2442 57. Gainsford, A.R., Sisley, M.J., Swaddle, T.W. and Bayliss, P., Can. J. Chem., 1975, 53, 12 58. Henderson, M.P., Miasek, V.I. and Swaddle, T.W., Can. J. Chem., 1971, 49, 317 59. Newton, A.M. and Swaddle, T.W., Can. J. Chem., 1974, 2751 60. Fabes, L. and Swaddle, T.W., Can. J. Chem., 1975, 53, 3053 61. Turner, D.J., C.E.R.L. Note, 1979, draft "Some Unexpected Reactions Between Metals and Aqueous Solutions at High Temperature. Part II. Steam Volatilization of Components from Stainless Steel" 62. Criss, C.M. and Cobble, J.W., J. Amer. Chem. Soc., 1964, 86, 5385 63. Lewis, D., Arkiv. Kemi., 1971, 32, 385 64. Lewis, D., Aktieb. Atomenergi Report, 1971, AE-436

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

678 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS

65. Macdonald, D.D., Shierman, G.R. and Butler, P., Atomic Energy of Canada Ltd. Reports, 1972, AECL-4136, 4137, 4138, 4139 66. Macdonald, D.D. and Rummery, T.E., Atomic Energy of Canada Ltd. Report, 1973, AECL-4140 67. Criss, CM. and Cobble, J.W., J. Amer. Chem. Soc., 1964, 86, 5390 68. Cobble, J.W., J. Amer. Chem. Soc., 1964, 86, 5394 69. Pohl, H.A., J. Chem. and Eng. Data, 1962, 7, 295 70. Harned, H.S. and Embree, N.D., J. Amer. Chem. Soc., 1934, 56, 1050 71. Khodakovskii, I.L. Geokhimiya, 1965, 827 72. Harned, H.S. and Robinson, R.A., Trans. Faraday Soc., 1940, 36, 973 73. Tremaine, P.R., Von Massow, R. and Shierman, G.R., Thermochimica Acta., 1977, 19, 287 74. Helgeson, H.C, J. Phys. Chem., 1967, 71, 3121 75. Turner, D.J., "Water Chemistry of Nuclear Reactor Systems", British Nuclear Energy Society, London, 1978, p.489 76. Turner, D.J., C.E.R.L. Note, 1969, RD/L/N 25/69 77. Bawden, R.J., C.E.R.L. Note, 1977, RD/L/N 85/77 78. Turner, D.J., Faraday Disc, of Chem. Soc., 1977, 64, 231 79. Tremaine, P.R. and Goldman, S., J. Phys. Chem., 1978, 82, 2317 80. Turner, D.J., "High Temperature High Pressure Electro­ chemistry in Aqueous Solutions", N.A.C.E.-4, Houston, Texas, 1976, p.188 81. Bawden, R.J., C.E.R.L. Note, 1973, RD/L/N 20/73 82. Bawden, R.J., C.E.R.L. Note, 1977, RD/L/N 87/77 83. Bawden, R.J., C.E.R.L. Note, 1979, RD/L/N 100/79 84. Hearn, B. and D. de G. Jones, C.E.R.L. Report, 1971, RD/L/R 1699

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

34. TURNER High-Temperature Aqueous Systems

679

85. Bawden, R.J. and Turner, D.J., C.E.R.L. Note, 1973, RD/L/N 213/73 86. Turner, D.J., C.E.R.L. Note, 1971, RD/L/N 269/71 87. Turner, D.J., C.E.R.L. Note, 1974, RD/L/N 238/74 88. Bussert, B.W., Curran, R.M. and Gould, G.C., Trans. ASME, 1978, Paper No. 78-JPGC-Pwr-9 89. Turner, D.J., C.E.R.L. Note, 1974, RD/L/N 204/74 90. Newman, J.F., C.E.R.L. Note, 1974, RD/L/N 215/74 91. Lewis, D., Chem. Scripta, 1974, 6, 49 92. Lewis, D., Aktieb 93. Bignold, G.J., Garnsey, R. and Mann, G.M.W., Corros. Sci., 1972, 12, 1325 94. Turner, D.J., C.E.R.L. Note, 1979, draft "Thermodynamics and the Nature of Oxides Formed on Iron-Chromium Alloys" 95. Tomlinson, Μ., "High Temperature High Pressure Electro­ chemistry in Aqueous Solutions", N.A.C.E.-4, Houston, Texas, 1976, p.221 96. Montford, B. and Rummery, T.E., Atomic Energy of Canada Ltd. Report, 1975, AECL-4444 97. Styrikovich, M.A., Martynova, O.I., Katkovskaya, K.Ya., Dubrovskii, I.Ya. and Smirnova, I.N., Atom Energya, 1964, 45 (transi, p.735) 98. Turner, D.J., J. Appl. Chem., 1972, 22, 983 99. Turner, D.J., "High Temperature High Pressure Electro­ chemistry in Aqueous Solutions", N.A.C.E.-4, Houston, Texas, 1976, p.256 100. Alexander, R.D., "Dissociation Constants in Water at High Temperatures: 1, 10-Phemanthroline, Related Bases and their Complexes with Iron (II)", Ph.D. Thesis, University of Surrey, 1976 101. Osborne, O., Wilson, J.S., Fried Jr., A.R. and Pryor Jr. W.M., Dow Chemical Co. Report, 1973, Final Report on ASME Contract C-9-2-D 102. Margulova, T.Kh., Yalova, R.Ya., Bulovko, A.Yu. and Krol' , A.Ya., Thermal Eng., 1972, 19, 114 RECEIVED

January 31, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

35 The Computation of Pourbaix Diagrams T. I. BARRY Chemical Standards Division, National Physical Laboratory, Teddington, Middlesex, TW11 OLW, UK

Pourbaix diagrams illustrat tion or precipitate species of a component or components as a function of pH and oxidation potential (1). They are particu­ larly useful for defining the conditions for selective precipita­ tion or solution in hydrometallurgical extraction (2) and for passivation of metals. However, they are tedious to produce manually, especially when a number of components are present. The purpose of this paper is to demonstrate the principles of automatic computation for simple and complex systems and to illus­ trate these by reference to the copper and sulphur systems both separately and combined. The same methods are applied to the delineation of the conditions under which various chloride com­ plexes of copper will predominate as a function of chloride activity rather than pH. Principles Figure 1 shows a Pourbaix diagram for sulphur compounds in water. The point of the diagram is to indicate which compound of sulphur has the highest activity at combinations of pH and oxidation potential. It shows for example that in oxidising, alkaline solutions the sulphate ion dominates, whereas in reducing, acid solutions aqueous hydrogen sulphide is the major sulphur compound. In acid conditions of intermediate oxidation potential a wedgeshaped region is found which defines the circumstances under which precipitation of sulphur can occur. An odd feature of the diagrams, as described here, is that unless the solution compounds have equal and constant activity coefficients, the concentrations of these compounds in their respective zones are not equal and could in principle be very different. To remove this anomaly the activity coefficients could readily be incorporated provided they were independent of pH and pE, the variables of the system. O-8412-0569-8/80/47-133-681$05.00/O Published 1980 American Chemical Society In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

OF AQUEOUS

SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

+

Figure 1. A pH-pE diagram for the S-H 0-H -e system at 298.15 K. The activities of the predominant sulphur compounds in solution are 10' . 2

1

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

35.

Computation of Pourbaix Diagrams

BARRY

683

The diagrams c a l c u l a t e d by the methods d e s c r i b e d d i f f e r t o some extent from many a v a i l a b l e i n the l i t e r a t u r e i n t h a t they omit the predominant s o l u t i o n compound i n areas where a condensed compound a l s o forms. This g r e a t l y s i m p l i f i e s t h e diagrams w i t h ­ out i m p a i r i n g t h e i r u s e f u l n e s s f o r most purposes. The system d e f i n e d by f i g u r e 1 has f o u r components, S - H 2 O - H - e. I t i s important t o note t h a t these f a l l i n t o two c l a s s e s . Sulphur w i l l be c l a s s i f i e d as a type 1 component to s i g n i f y t h a t we are i n t e r e s t e d i n what compounds i t forms. Condensed type 1 compounds, have an a c t i v i t y o f 1 i f present and > 1 i f absent. The a c t i v i t i e s o f the predominant type 1 compounds i n s o l u t i o n can be f i x e d at any d e s i r e d value. I n f i g u r e 1 they are s e t a t 1 C T . Thus t h e sulphate i o n has an a c t i v i t y o f 1 0 " i n i t s area and HS~ has an a c t i v i t y o f 1 C T i n i t s area. On t h e l i n e between these areas HS and the sulphate i o n c o e x i s t w i t h equal a c t i v i t i e s and t h these two compounds ca f o r the e q u i l i b r i u m +

1

1

1

so£~

=

HS

+

kK 0

-

2

9H

-

Be.

The remainder o f the components are o f type 2 . Their a c t i v i t i e s are e i t h e r f i x e d , as f o r H 0 , or they form the i n d e ­ pendent v a r i a b l e s o f the system, H and e. The a c t i v i t i e s o f H and t h e n o t i o n a l a c t i v i t y o f the e l e c t r o n are expressed i n l o g a ­ r i t h m i c form as pH and pE where pE i s r e l a t e d t o the o x i d a t i o n p o t e n t i a l , E , by t h e r e l a t i o n 2

+

h

RT I n F

10

pE

There are 6 sulphur compounds t o be considered and t h e r e f o r e 15 p o s s i b l e c o e x i s t e n c e l i n e s o f which o n l y 9 represent s t a b l e equilibria. Moreover, even these 9 l i n e s are v a l i d ( i . e . c o r r e s ­ pond t o s t a b l e coexistence) along only p a r t o f t h e i r p o s s i b l e extents. The problem then i s t o determine t h e equations f o r t h e l i n e s and the range over which they are v a l i d , and t o p r o v i d e a method f o r p l o t t i n g them. Methods f o r a simple case The p r i n c i p l e s o f t h e method become much c l e a r e r i f a p p l i e d to a p a r t i c u l a r r a t h e r than t h e general case. 1 The f i r s t step i s t o l i s t t h e compounds o f t h e type 1 compon­ ent together w i t h t h e i r Gibbs energies o f formation at t h e chosen temperature, o r t h e f u n c t i o n [ΔΗ°(f, 298) + G°(T) - H ° ( 2 9 8 ) ] which i s much e a s i e r t o c a l c u l a t e i n a data-bank. The two f u n c t i o n s must not be used f o r d i f f e r e n t substances i n the same c a l c u l a t i o n . The data used i n t h i s paper are taken from t h e monograph by Duby {3) on aqueous systems o f copper.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

684

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS

Table

WITH

Formula

1

S

2

HS0 ~

A G°(298) f

/kJ

1

-756.01

4

3

mole" 0

2

s t h e a c t i v i t y c o e f f i c i e n t o f w a t e r , f o r e a c h o f the binary systems. The Gibbs-Duhem e q u a t i o n f o r a b i n a r y aqueous e l e c t r o l y t e s o l u t i o n i s w r i t t e n :

l n

(15)

Γο·) •

Γ

where t h e a c t i v i t y c o e f f i c i e n t o f w a t e r i s n o r m a l i z e d such t h a t i t becomes u n i t y when t h e a c t i v i t y c o e f f i c i e n t o f t h e e l e c t r o l y t e is unity. S u b s t i t u t i o n o f E q u a t i o n 8 i n t o E q u a t i o n 15 g i v e s : In

ff

( 2 )

= (-59.56 + 0 . 1 7 9 t ) [ ( χ * - χ ) + Ι „ £

(16)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

37.

FUNK

121

Multicomponent Salt Systems

f o r t h e a c t i v i t y c o e f f i c i e n t o f w a t e r i n t h e HCl-h^O s y s t e m , where x * = 0 . 1 5 2 5 . F i g u r e 5 shows a c o m p a r i s o n between p r e d i c t e d and e x p e r i m e n t a l a c t i v i t y c o e f f i c i e n t s o f w a t e r i n t h e H C I - H O systçm a t 1 0 , 2 5 and 5 0 ° C ; E q u a t i o n 16 p r e d i c t s a c c u r a t e v a l u e s of f l ( 2 ) except i n very d i l u t e s o l u t i o n s . F o r such s o l u t i o n s , t h e B r o n s t e d - G u g g e n h e i m t h e o r y c a n be used t o c a l c u l a t e t h e a c t i v i t y c o e f f i c i e n t o f water. The a c t i v i t y c o e f f i c i e n t o f w a t e r i n t h e NaCl-H^O s y s t e m c a n be w e l l d e s c r i b e d b y s u b s t i t u t i o n o f o n l y t h e f i r s t t e r m o f E q u a t i o n 9 i n t o E q u a t i o n 1 5 . The r e s u l t i n g e x p r e s s i o n f o r t h e a c t i v i t y c o e f f i c i e n t o f water i s :

1ηΓ

1

(

3

= . 2 8 . 0 5 C(x§ - x )

)

3

+in

(17)

The s e c o n d t e r m o c a l c u l a t i o n o f t h e a c t i v i t y c o e f f i c i e n t o f NaCl a t l o w c o n c e n t r a t i o n s , and makes l i t t l e c o n t r i b u t i o n t o t h e i n t e g r a l i n E q u a t i o n 15. Equation 17 p r e d i c t s t h e a c t i v i t y c o e f f i c i e n t s o f water w i t h i n 1% o f t h e e x p e r i m e n t a l v a l u e s f o r m o l a l i t i e s above 0 . 2 . F o r t h e t e r n a r y s o l u t i o n , t h e Gibbs-Duhem e q u a t i o n c a n be e a s i l y i n t e g r a t e d t o c a l c u l a t e t h e a c t i v i t y c o e f f i c i e n t o f water when t h e e x p r e s s i o n s f o r t h e a c t i v i t y c o e f f i c i e n t s o f t h e e l e c t r o l y t e s are written at constant m o l a l i t y . For Harned's r u l e , i n t e g r a t i o n o f t h e Gibbs-Duhem e q u a t i o n g i v e s t h e a c t i v i t y o f water a s : -55.51 v m• ,r

Ί

l

o

„ 9

a

w 3 , , \ ο f v =n\ Q (ou- + o u ) - 2 oua (Y =0) • ' 3 2 3 3 2 ' 23 ( Y

)

=

a

n*\ (18)

v

Y

v u

q

u

9

u u

3

f o r a c o n s t a n t t o t a l m o l a l i t y o f m. The f r a c t i o n o f t o t a l e l e c t r o l y t e i n s o l u t i o n a s i i s e x p r e s s e d by Y . ; a ( Y ~ ) i s t h e a c t i v i t y o f w a t e r f o r a g i v e n v a l u e o f Y - . The s t a n d a r d s t a t e f o r w a t e r i s p u r e w a t e r a t t h e t e m p e r a t u r e o f t h e s y s t e m . The B r o n s t e d - G u g g e n h e i m e q u a t i o n s can a l s o be s u b s t i t u t e d i n t o t h e Gibbs-Duhem e q u a t i o n t o c a l c u l a t e t h e a c t i v i t y o f w a t e r i n d i l u t e solutions. Harned and R o b i n s o n (J3) g i v e t h e r e s u l t a n d a d e t a i l e d d i s c u s s i o n o f t h e Bronsted-Guggenheim e q u a t i o n s . E q u a t i o n s 11 and 12 a r e n o t w r i t t e n f o r c o n s t a n t m o l a l i t y , and c a n n o t be e a s i l y used w i t h the* Gibbs-Duhem e q u a t i o n t o o b ­ t a i n an a n a l y t i c a l e x p r e s s i o n f o r t h e a c t i v i t y o f w a t e r i n t h e ternary solution. However, i t i s p o s s i b l e t o p r o p o s e a s e p a r a t e equation f o r the a c t i v i t y c o e f f i c i e n t o f water that i s c o n s i s t e n t w i t h t h e p r o p o s e d model o f c o n c e n t r a t e d s o l u t i o n s . w

The a c t i v i t y Π (2 3 ) '

l

s

e

s

t

l

'

m

a

c o e f f i c i e n t o f water i n t h e t e r n a r y t

e

solution

d by:

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

728

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

(Ό.1525 — Χ * ) Figure 5.

Activity

coefficients

of water in the HCI-H 0 (A), and 50°C (%) 2

system at 10° (O),

25°

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

37.

1 Η

FUNK

Γ

1 ( 2

τ*ί(2

729

Multicomponent Salt Systems

, ) 3

=

Υ

2

Ί

η

^ ( 2 )

+

Υ

3

1

η

Γ

1

0

( 3 )

(

The s t a n d a r d - s t a t e f u g a c i t y o f w a t e r i n t h e t e r n a r y i s expressed s i m i l a r l y b y :

In f «

( 2 f 3 )

= Y In f » 2

( 2 )+

Y

3

In f °

(

3

)

1

9

>

solution,

(20)

where f ? / . > i s t h e s t a n d a r d - s t a t e f u g a c i t y o f w a t e r i n t h e b i n a r y s o l u t i o n ^ o r e l e c t r o l y t e i . The a c t i v i t y c o e f f i c i e n t Γ?/*\ i s c a l c u l a t e d u s i n g t h e mole f r a c t i o n o f i i n t h e t e r n a r y s o T u t i o n and e i t h e r E q u a t i o n 1 6 o r 1 7 . The s t a n d a r d - s t a t e f u g a c i t y o f w a t e r i n t h e t e r n a r y s o l u t i o n changes w i t h Y. s i n c e t h e s t a n d a r d s t a t e f u g a c i t y o f w a t e r i s d i f f e r e n t i n each b i n a r y s y s t e m . E q u a t i o n 20 i s s i m i l a r t t h e x p r e s s i o derived b O'Connell and P r a u s n i t z (KO f o constant i n a mixed s o l v e n t Equatio y c o e f f i c i e n t o f water i n t h e t e r n a r y s o l u t i o n using o n l y data f o r t h e b i n a r y m i x t u r e s ; t h e r e f o r e , i t c a n n o t be e x p e c t e d t o g i v e very precise r e s u l t s . V a p o r - l i q u i d e q u i l i b r i u m d a t a f o r t h e two b i n a r y s y s t e m s 0]_) were used t o c a l c u l a t e t h e s t a n d a r d - s t a t e f u g a c i t i e s r e q u i r e d i n E q u a t i o n s 6 and 2 0 . In t h e t e m p e r a t u r e r a n g e 0-50°C, t h e r e f u g a c i t i e s can be e x p r e s s e d b y : ln

f | = 1.332 + 0.781

In

f ^

In

ffjgj

2

)

(t/10)

(21)

= 0.885 + 0.610

(t/10)

(22)

= 1.485 + 0.591

(t/10)

(23)

where t h e f u g a c i t y i s i n mm. H g . F i g u r e 6 compares e x p e r i m e n t a l and c a l c u l a t e d a c t i v i t y c o e f f i c i e n t s o f w a t e r i n t h e t e r n a r y s y s t e m a t 25°C and a t o t a l m o l a l i t y o f 3.0. E q u a t i o n 18 was used t o e x p r e s s t h e e x p e r i m e n t a l activity coefficients. Agreement between e x p e r i m e n t a l and c a l c u ­ l a t e d v a l u e s i s s u r p r i s i n g l y good c o n s i d e r i n g t h a t E q u a t i o n 1 9 c o n t a i n s no t e r n a r y p a r a m e t e r s . The a c t i v i t y c o e f f i c i e n t o f w a t e r i n t h e HCI-NaCl-H^O s y s t e m i s n o t a s t r o n g f u n c t i o n o f c o m ­ p o s i t i o n , and E q u a t i o n T9 p r o v i d e s an a d e q u a t e d e s c r i p t i o n o f the a c t i v i t y c o e f f i c i e n t s . Vapor-Liquid E q u i l i b r i a E q u a t i o n s 11 and 1 9 e x p r e s s t h e n e c e s s a r y l i q u i d - p h a s e activity coefficients for the calculation o f vapor-liquid e q u i l i ­ b r i a i n t h e HCI-NaCl-H 0 system. E q u a t i o n 11 i s v e r y c o n v e n i e n t ?

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

730

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

Figure

6.

Activity

coefficients of water in the HCl-NaCl-H 0 and total molality of 3.0 ((%) experimental) 2

APPLICATIONS

system at

25°C

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

37.

FUNK

731

Multicomponent Salt Systems

f o r v a p o r - l i q u i d e q u i l i b r i u m c a l c u l a t i o n s , s i n c e HCI i s t r e a t e d as a n o n - e l e c t r o l y t e i n b o t h l i q u i d and v a p o r p h a s e s . This a v o i d s t h e c u s t o m a r y e q u a l i t y ( 1 2 ) between t h e f u g a c i t y o f HCI v a p o r and t h e mean i o n i c T u g a c i t y o f H C I . At moderate p r e s s u r e s , t h e v i r i a l e q u a t i o n o f s t a t e , t r u n c a ­ t e d a f t e r t h e s e c o n d v i r i a l c o e f f i c i e n t , can be used t o d e s c r i b e the vapor phase. As s u g g e s t e d b y H i r s c h f e l d e r , e t . a l . (1 3) t h e t e m p e r a t u r e dependence o f t h e v i r i a l c o e f f i c i e n t s i s e x p r e s s e d : B B

n

2 2

= 49.85 [ 1 . 0 - 0.328

e

= 77.43 [ 1 . 0 - 0.704

e

1

2

8

8

/

4 0 0 / T

]

T

]

where Τ i s t h e t e m p e r a t u r e i n ° K was used t o c a l c u l a t e t h and t h e e x p e r i m e n t a l d a t used t o c a l c u l a t e Β-μ f o r w a t e r . are estimated by: B

1 2

= 6 3 . 6 9 [ 1 . 0 - 0.516

e

7

3

5

/

T

(24) (25) The c o r r e l a t i o n o f P i t z e r ( 1 4 )

The c r o s s v i r i a l

coefficients

]

(26)

where s i m p l e m i x i n g r u l e s were used f o r t h e t h r e e p a r a m e t e r s i n E q u a t i o n s 24 a n d 2 5 . F i g u r e 7 shows t h e p r e d i c t e d v a p o r - p h a s e mole f r a c t i o n s o f HCI a t 25°C a s a f u n c t i o n o f t h e l i q u i d - p h a s e m o l a l i t y o f HCI f o r a c o n s t a n t NaCl m o l a l i t y o f 3. A l s o i n c l u d e d a r e p r e d i c t e d v a p o r phase mole f r a c t i o n s o f HCI when t h e i n t e r a c t i o n p a r a m e t e r A i s taken as z e r o . T h e r e a r e u n f o r t u n a t e l y no e x p e r i m e n t a l v a p o r l i q u i d e q u i l i b r i u m data a v a i l a b l e f o r t h e HCI-NaCl-H 0 system; however, c o n s i d e r i n g t h e e x c e l l e n t d e s c r i p t i o n o f t h e l i q u i d phase a c t i v i t y c o e f f i c i e n t s and t h e l o w t o t a l p r e s s u r e s , i t i s e x p e c t e d t h a t p r e d i c t e d mole f r a c t i o n s w o u l d be w i t h i n 2-3% o f t h e experimental values. 2

3

2

Solid-Liquid

Equilibria

The s o l i d - l i q u i d e q u i l i b r i u m f o r NaCl pressed b y : f

S

3

χ

ff " Γ 3

3

i s rigorously ex­

(27)

where f | i s t h e f u g a c i t y o f s o l i d s o d i u m c h l o r i d e . The r a t i o o f f u g a c i t i e s i n E q u a t i o n 2 7 i s t h e s o l u b i l i t y p r o d u c t o f NaCl and c a n be d e t e r m i n e d u s i n g s o l u b i l i t y d a t a . At saturation i n t h e NaCl-HpO s y s t e m , Ç° i s u n i t y and t h e s a t u r a t i o n mole f r a c -

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

732

THERMODYNAMICS

0.01

I 5

I

OF

I 5

AQUEOUS SYSTEMS

I

I

I

7 MOLALITY OF

W I T H INDUSTRIAL

I 9

I

APPLICATIONS

ι

t 11

I 13

MCI

Figure 7. Predicted vapor-liquid equilibria in the HCl-NaCl-H O for NaCl molality of 3.0 z

system at 25°C

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

37.

FUNK

733

Multicomponent Salt Systems

t i o n , x ^ , i s equal t o t h e s o l u b i l i t y p r o d u c t . T h e r e f o r e , Equa­ t i o n 1 0 c a n be used t o e x p r e s s t h e s o l u b i l i t y p r o d u c t o f NaCl as a f u n c t i o n o f t e m p e r a t u r e . The s e l e c t e d n o r m a l i z a t i o n o f t h e NaCl a c t i v i t y c o e f f i c i e n t has two p a r t i c u l a r a d v a n t a g e s f o r s o l i d - l i q u i d e q u i l i b r i a . First, the s o l u b i l i t y product i s c a l c u l a t e d d i r e c t l y from a v a i l a b l e s o l u b i l i t y d a t a ; no a c t i v i t y - c o e f f i c i e n t d a t a a r e r e q u i r e d . S e c o n d , t h e a c t i v i t y c o e f f i c i e n t o f NaCl h a s a c l e a r i n t e r p r e t a ­ t i o n ; i t p r o v i d e s a q u a n t i t a t i v e measure o f how HCI c h a n g e s t h e s o l u b i l i t y o f NaCl f r o m i t s s t a n d a r d - s t a t e v a l u e o f x i S o l i d - l i q u i d e q u i l i b r i u m d a t a (]6) f o r t h e HCI-NaCl H 0 s y s t e m a t 25°C were used w i t h E q u a t i o n 27 t o c a l c u l a t e experimental a c t i v i t y c o e f f i c i e n t s o f NaCl. Table 1 shows a c o m p a r i s o n between t h e e x p e r i m e n t a l a c t i v i t y c o e f f i c i e n t s and t h o s e c a l c u l a t e d u s i n g E q u a t i o n 1 2 . The agreement between e x p e r i m e n t a l and c a l c u l a t e and E q u a t i o n 12 s h o u l d e q u i l i b r i a at other temperatures. E q u a t i o n 27 i s s i m i l a r t o t h e s o l i d - l i q u i d e q u i l i b r i u m r e l a ­ t i o n used f o r n o n - e l e c t r o l y t e s . As i n t h e c a s e o f t h e v a p o r l i q u i d e q u i l i b r i u m r e l a t i o n f o r HCI, t h e s o l i d - l i q u i d e q u i l i b r i u m e x p r e s s i o n f o r NaCl i s s i m p l e s i n c e t h e e l e c t r o l y t e i s t r e a t e d t h e r m o d y n a m i c a l l y t h e same i n b o t h p h a s e s . 2

E x t e n s i o n o f T e c h n i q u e by V e r a and Co-Workers V e r a and c o - w o r k e r s (7,1_7,1JB) have e x t e n d e d t h e t h e r m o ­ d y n a m i c c o r r e l a t i o n and macTe two a d d i t i o n s . F i r s t , t h e y have developed a semi-empirical expression f o r t h e excess Gibbs energy i n place o f t h e simple e m p i r i c a l e q u a t i o n s o r i g i n a l l y used ( E q u a t i o n s 8 and 9 ) . A l s o , w h i l e t h e y use a s t a n d a r d s t a t e o f t h e e l e c t r o l y t e o f a s a t u r a t e d s o l u t i o n , t h e y change t h e s t a n d a r d s t a t e o f w a t e r back t o t h e c o n v e n t i o n a l one o f p u r e w a t e r . The e x p r e s s i o n f o r t h e e x c e s s G i b b s e n e r g y s u g g e s t e d b y C o r r e a and V e r a i s : g^./RT = Ax I n χ + B x

1 / 2

+ Kx + c x

3 / 2

+ Dx + . . . 2

(28)

t o d e s c r i b e a b i n a r y s y s t e m o f e l e c t r o l y t e i i n aqueous s o l u t i o n and where A , B, C , D, . . . a r e a d j u s t a b l e p a r a m e t e r s . Κ i s not an i n d e p e n d e n t p a r a m e t e r and i s d e t e r m i n e d by t h e n o r m a l i z a t i o n condition f o rthea c t i v i t y c o e f f i c i e n t . A p p l i c a t i o n o f standard thermodynamics l e a d s t o t h e f o l l o w i n g e x p r e s s i o n f o r t h e a c t i v i t y c o e f f i c i e n t o f water: l n P, = a x + b x

1 / 2

+cx

3 / 2

+dx + 2

(29)

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

734

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

TABLE

I

CALCULATED ACTIVITY VALUES OBTAINED FROM SOLID-LIQUID EQUILIBRIUM m

3

APPLICATIONS

DATA

T (Exp.)

P (Cal.)

3

3

0.00

6.126

1 .00

1.00

1.00

5.096

1 .20

1.24

2.00

4.054

1.51

1.53

3.00

3.100

1 .97

2.07

5.00

1.884

3.27

3.27

6.00

1.020

6.09

5.83

7.50

0.496

12.73

12.10

8.50

0.306

20.69

20.10

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

37.

FUNK

Multicomponent

Salt

735

Systems

where A = - a , B - 2 b , C=-2c, and D=-d. Use o f t h e Gibbs-Duhem e q u a t i o n and t h e n o r m a l i z a t i o n c o n d i t i o n l e a d s t o t h e e x p r e s s i o n for the a c t i v i t y c o e f f i c i e n t o f the e l e c t r o l y t e : ln Γ

= (K-a) - a l n χ + b x "

1

1 / 2

+ c^x + c y
14

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

38.

L i D D E L L AND

BAUTiSTA

Solid-Liquid

745

Reactions

where r i s a f u n c t i o n of c o n c e n t r a t i o n , temperature, e t c . , and t i s time. Equations (11-14) would give the number of moles of each substance formed d i r e c t l y as a f u n c t i o n of time but may be r a t h e r d i f f i c u l t to s o l v e . In order to make use of Equation (5) to o b t a i n c o n c e n t r a t i o n changes, moreover, a r e l a t i o n s h i p be­ tween ξ and t i s r e q u i r e d . The other p o s s i b i l i t y i s to remove a v a r i a b l e . D i v i d i n g each v a r i a b l e by -Ng gives g

moles

formed (15)

1

-Ng

moles S r e a c t i n g moles M„ formed

"M

~ 2

(16) -Ng

moles S r e a c t i n g

n moles D formed = — -Ν^ moles S r e a c t i n g D

«

D

(17)

The s i g n convention i m p l i c i t i n Equation (3) i s preserved; n. i s p o s i t i v e f o r a product and negative f o r a r e a c t a n t . Then Equations (11-13) become

0 = -ϋ

i

0 - -1 +

(18)

+ 2n

(19)

D

0 = -1 +

Once m^ and m^

(20)

are known, t h i s system i s easy to s o l v e .

Now suppose that under some c o n d i t i o n s formation of a t r i m e r may be important. There i s an a d d i t i o n a l r e a c t i o n to take i n t o account D + M

1

Τ

(21)

and an a d d i t i o n a l unknown n (or n ) . However, there i s a l s o an a d d i t i o n a l equation that can be w r i t t e n (and an e x t r a term to be added to Equation ( 1 9 ) ) . T

T

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

746

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

0 =— -— *T "D

APPLICATIONS

(22) \

Considering more species that are involved i n e q u i l i b r i u m r e a c t i o n s makes the, number o f unknowns l a r g e r , t h e r e f o r e , but an equation i s added t o the system along w i t h each new unknown. That i s not the case f o r species that p a r t i c i p a t e only i n i r r e v e r s i b l e r e a c t i o n s . Consider another s t r u c t u r a l form of the s o l i d , S , w i t h a d i f f e r e n t r e a c t i o n r a t e . T

S' + M

1

+ M

2

(23)

The unknown Ng appears i n the m a t e r i a l balance equations but there are no a d d i t i o n a l equation t b appended t th s e t Each i r r e v e r s i b l e number o f unknowns and equations, g (1) s c a l i n g o f the v a r i a b l e s , (2) use o f k i n e t i c data o r (3) both. S e t t i n g up the model equations f o r various s i t u a t i o n s i s discussed i n more d e t a i l below but we d i g r e s s here to o u t l i n e the steps i n v o l v e d i n a p p l y i n g the p a r t i a l e q u i l i b r i u m model. They are as f o l l o w s : (1)

(2) (3)

(4)

(5) (6)

Decide what r e a c t i o n s need t o be considered and which of them are i r r e v e r s i b l e and which are reversible. L i s t the unknowns. Write an equation o f the form o f Equation (8) f o r each r e v e r s i b l e r e a c t i o n . To o b t a i n the i n i t i a l f l u i d phase c o n c e n t r a t i o n nij, i t i s necessary t o know the a n a l y t i c a l concentrations i n the s o l u t i o n a t the s t a r t o f the heterogeneous r e a c t i o n as w e l l as e q u i l i b r i u m constants f o r the r e v e r s i b l e r e a c t i o n s . Write as many independent mass balances among the unknowns as p o s s i b l e . I f there are ions i n the f l u i d phase, a charge balance expressing e l e c t r o ­ n e u t r a l i t y can be w r i t t e n i f d e s i r e d . Check the equations w r i t t e n i n step (4) t o be sure they are a l l independent. Reduce the number o f equations by s c a l i n g them and/or s e l e c t k i n e t i c data. I f k i n e t i c data are t o be used, i t i s a d v i s a b l e t o change the v a r i a b l e s , r e p l a c i n g t by ξ and by ^ o r

A p p l i c a t i o n o f the P a r t i a l E q u i l i b r i u m Model We now consider the v a r i o u s f i n e p o i n t s i n the use o f the model and then discuss s e v e r a l a p p l i c a t i o n s .

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

38.

LIDDELL AND

BAUTISTA

141

Solid-Liquid Reactions

One d i f f e r e n c e between conducting and nonconducting media i s that i n the former case a charge balance may take the place of one of the m a t e r i a l balances. For the same number of s o l u t i o n s p e c i e s , however, the number of independent balance equations i s the same i n the two cases. M a t e r i a l balances can be w r i t t e n f o r m o i e t i e s which are conserved during the r e a c t i o n , such as the atoms of a p a r t i c u l a r element or the t o t a l charge, or f o r reactant or product species i f the s t o i c h i o m e t r y i s unambiguous. O x i d a t i o n - r e d u c t i o n reac­ t i o n s may be p a r t i c u l a r l y troublesome. In the f o l l o w i n g s i t u a t i o n , f o r example, one cannot w r i t e a m a t e r i a l balance r e ­ l a t i n g protons to water molecules. Consider the o x i d a t i o n of 0 to H 0 and the e q u i l i b r i u m d i s s o c i a t i o n of H^O. 2

2

... + 0 + 4 H

+

> ... + 2H 0

2

2H

+

2

(24)

+ 20H

+

The r a t i o of H to H 0 i s 2:1 i n Equation (24) and 1:1 i n Equation (25); i t i s not p o s s i b l e to w r i t e an equation that describes the o v e r a l l changes i n the amounts of these two species. Once the chemical r e a c t i o n s of the system have been i d e n ­ t i f i e d , the number of unknowns chosen a f f e c t s the s i z e of the set of equations but has no i n f l u e n c e on the number of equations that need to be used. To a c e r t a i n e x t e n t , the unknowns to be solved f o r can be s e l e c t e d a r b i t r a r i l y ; a v a r i a b l e may be ex­ cluded from the l i s t of unknowns as long as (1) i t i s not i t s e l f of p h y s i c a l i n t e r e s t and (2) i t appears only i n the i r r e v e r s i b l e r e a c t i o n s . Omitting such a v a r i a b l e does not a f f e c t the imbal­ ance between the number of unknowns and the t o t a l number of e q u i l i b r i u m and balance equations. Suppose the r e a c t i o n s of the system are the f o l l o w i n g : 2

S +R Ρ

+ χ

;

+

>

+P

*(P^)

(26)

2

0

(27)

for Material w e l l as a charge balance but t r i a l and e r r o r shows that i t i s impossible to do so without i n t r o d u c i n g n and n ~ . Ρ 2 need not appear, however. A set of three independent balances i s : +

R

S

A

5

\ + - " s - (P )0 l A

-n _

28

< > (29)

A

American Chemical Society Library 1155 16th St. N. W. In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; Washington, 0. C.Society: 20036 ACS Symposium Series; American Chemical Washington, DC, 1980.

748

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

n

R+

+

+

\

=

n

APPLICATIONS

( 3 0 )

A"

(Equation (30) assumes t h a t A was the only anion present before r e a c t i o n began.) The equation f o r the e q u i l i b r i u m r e a c t i o n i s "(Ρ,Α) ±

0

0

V

V-

+

-

(31)

i s

o

f

There are f o u r equations and f i v e unknowns. I f Ρ 2 physical i n t e r e s t , the unknown n can be i n c l u d e d ; an independent 2 m a t e r i a l balance f o r i t i s e a s i l y w r i t t e n : p

= -N

(32

s

There a r e now s i x unknowns and f i v e equations. The imbalance between the number of unknowns and the number o f equations i s unchanged. I f t h e r e i s no reason t o i n c l u d e the e x t r a v a r i a b l e , i t i s best t o leave i t o u t , thereby s i m p l i f y i n g the computation as much as p o s s i b l e . This example a l s o shows that the amount o f k i n e t i c i n f o r ­ mation needed t o complete the s e t o f equations (one equation i n t h i s case) depends on the number of independent i r r e v e r s i b l e r e a c t i o n s (one) and not on the number o f chemical species i n ­ v o l v e d only i n the i r r e v e r s i b l e r e a c t i o n s (two) o r on the number of these s p e c i e s appearing as unknowns. With an aqueous f l u i d phase o f high i o n i c s t r e n g t h , t h e problem o f o b t a i n i n g a c t i v i t y c o e f f i c i e n t s may be circumvented simply by u s i n g apparent e q u i l i b r i u m constants expressed i n terms of c o n c e n t r a t i o n s . This procedure i s recommended f o r hydrom e t a l l u r g i c a l systems i n which complexation r e a c t i o n s are impor­ t a n t , e.g., i n ammonia, c h l o r i d e , o r s u l f a t e s o l u t i o n s . Sometimes the e q u i l i b r i u m r e a c t i o n f o r the formation o f a species i n s o l u t i o n may be w r i t t e n i n more than one way. For example, the h y d r o l y s i s r e a c t i o n s o f f e r r i c i o n have t h i s c h a r a c t e r i s t i c ; the formation o f F e O H may be w r i t t e n as 2+

or

Fe

3 +

Fe

3 +

+ H 0 r—A FeOH

2+

+ 0H~ f==^ F e O H

2+

2

+ H

+

(33) (34)

Quite apart from the q u e s t i o n o f whether i t i s d e s i r a b l e t o take H 0 as a v a r i a b l e , i t may be best i n a s t r o n g l y a c i d s o l u t i o n t o work from Equation (33) r a t h e r than Equation (34). This i s be­ cause, i n such a s o l u t i o n , the hydroxide i o n c o n c e n t r a t i o n i s orders o f magnitude s m a l l e r than the c o n c e n t r a t i o n s o f the other 2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

38.

LIDDELL

A N D BAUTISTA

749

Solid-Liquid Reactions

species and the accuracy w i t h which the model equations can be solved becomes an important c o n s i d e r a t i o n . I f k i n e t i c data a r e t o be used, i t i s necessary t o transform the v a r i a b l e s t o conform w i t h those o f the p a r t i a l e q u i l i b r i u m model. The u n i t s used i n the model equations f o r R-^ and 5j a r e moles formed/kg of s o l u t i o n . Thus the mass of s o l u t i o n i n the r e a c t i n g system from which the k i n e t i c data comes must be known. Frequently, one w i l l know the volume and have t o approximate the d e n s i t y . A r e l a t i o n between ξ and t i s a l s o needed. For t h i s , the mass o f s o l i d o r i g i n a l l y present must be known. The amount of s o l i d r e a c i n g , -ANg, f o r a time i n t e r v a l At can be obtained from r a t e curves o r c a l c u l a t e d from an i n t e g r a t e d r a t e equation. The f r a c t i o n o f the o r i g i n a l mass r e a c t i n g i n the time i n t e r v a l gives an approximate v a l u e of ζ, e.g.,

Ν, S,0

- ξ av

where ξ i s i n t e r p r e t e d as the extent o f r e a c t i o n averaged over the time i n t e r v a l At and Ng s o l i d present b e f o r e the heterogeneous r e a c t i o n . I t i s then p o s s i b l e t o p l o t Ng versus ζ and t o r e l a t e v a r i a b l e s by an a l g e b r a i c equation. I t i s t h i s a l g e b r a i c equation that i s used t o complete the s e t of equations o f the p a r t i a l e q u i l i b r i u m model. Once the com­ p l e t e s e t i s s o l v e d , the c o n c e n t r a t i o n changes can be given as f u n c t i o n s o f time. This technique can be g e n e r a l i z e d i f two o r more indepen­ dent heterogeneous r e a c t i o n s occur. I n t h i s s i t u a t i o n , r a t e data must be a v a i l a b l e f o r each r e a c t i o n under comparable conditions. I f a s i n g l e s o l i d r e a c t s i r r e v e r s i b l y i n separate r e a c t i o n s , ANg i s t h e sum o f two or more c o n t r i b u t i o n s . I d e a l l y , t h e k i n e t i c data w i l l i n c l u d e o v e r a l l r e a c t i o n r a t e s under con­ d i t i o n s when a l l t h e i r r e v e r s i b l e r e a c t i o n s occur simultaneously as w e l l as the i n d i v i d u a l r a t e s o f the d i f f e r e n t r e a c t i o n s . Then the f r a c t i o n o f t h e t o t a l i r r e v e r s i b l e process due t o each of the r e a c t i o n s can be determined. L i k e ANg, C _ terms. For the same i n i t i a l mass o f s o l i d Ng^o» ÂNg ^ and are obtained from i n d i v i d u a l r a t e curves. Unless each ANg^i depends on i t s i n the same way, the r e l a t i v e importance o f the v a r i o u s heterogeneous r e a c t i o n s changes w i t h the t o t a l extent o f r e a c t i o n . I n any event, i t i s necessary t o express each ^ s,i function of ξ . We now d i s c u s s i n d e t a i l s e t t i n g up the p a r t i a l e q u i l i b r i u m model f o r a p a r t i c u l a r case. The d i s s o l u t i o n o f c h a l c o p y r i t e , CuFeS2, has been s t u d i e d e x t e n s i v e l y i n the l a b o r a t o r y ( 3 ^ , 5 ) and we have been i n t e r e s t e d i n i t because o f i t s importance i n dump l e a c h i n g . Under dump l e a c h i n g c o n d i t i o n s , two d i s s o l u t i o n r e a c t i o n s have been i d e n t i f i e d f o r t h i s m i n e r a l (3^4,j>): 3 ν

i

s

t

h

e

o

f

t

n

e

0

αν

a v

N

a

s

i s

a

s

u

m

o

f

a

α ν

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

750

THERMODYNAMICS

OF

CuFeS + 4 F e

AQUEOUS

3+

2

CuFeS + 0 2

2

+ Cu

+ 4H

+

2 +

SYSTEMS W I T H INDUSTRIAL

+ 5Fe

•> C u

2 +

2+

+ Fe

APPLICATIONS

+ 2S° 2 +

(36)

+ 2S° + 2H 0

(37)

£

The e q u i l i b r i u m constants f o r both r e a c t i o n s are very l a r g e : 6,76 χ 10 f o r Equation (36) and 8.62 χ 10 f o r Equation (37) (2). Concentration data from dump l e a c h i n g operations i n d i c a t e s that n e i t h e r r e a c t i o n i s c l o s e to e q u i l i b r i u m . Hence these are i r r e v e r s i b l e r e a c t i o n s . The leach s o l u t i o n i s a s u l f a t e medium and the s o l u t i o n chemistry i n v o l v e d a number of s p e c i e s . S u l ­ f a t e and b i s u l f a t e ions are i n e q u i l i b r i u m , F e ^ undergoes a s e r i e s of r e a c t i o n s producing hydroxo complexes and C u , F e and F e form a number of complex ions w i t h s u l f a t e and b i s u l ­ fate ions. The s o l i d s u l f u r produc Near room temperature, to s o l u b l e s u l f u r - c o n t a i n i n g a n i o n s ( 4 ) . I t can be assumed, t h e r e f o r e , that none of the s u l f u r atoms o r i g i n a l l y present i n the s o l i d c h a l c o p y r i t e enter the s o l u t i o n . The s u l f u r product i s not recovered i n the l e a c h i n g process and does not a f f e c t the s o l u t i o n chemistry. To a f i r s t approximation, the c o n c e n t r a t i o n and a c t i v i t y of the water molecules do not change during d i s s o l u t i o n so n j ^ o can be neglected. _ _ The unknown parameters of i n t e r e s t are N ^ ^ g , Q > Ή+ 20

54

+

2 +

J

2 +

n

n

,

2

a n d

the v a r i o u s F e ( I I I ) , F e ( I I ) and Cu(II) s p e c i e s , n ^ 2 so

n

e

HS0 To o b t a i n the i n i t i a l e q u i l i b r i u m concentrations of the v a r i o u s i o n s , the s o l u t i o n i s taken to c o n t a i n Fe2(804)3, 4, H2SO4 and a small amount of CuSO^. Leach l i q u o r i s r e c y c l e d a f t e r the recovery step so traces of CuSO^ are always present. A n a l y t i c a l concentrations of these substances and the e q u i l i b r i u m constants f o r each e q u i l i b r i u m r e a c t i o n must be known. Mass balances f o r F e ( I I I ) , F e ( I I ) , Cu(II) and SO4 - and a charge balance supplement the mass a c t i o n equations. This n o n l i n e a r set of equations can be solved by the well-known Newton-Raphson method ( 6 ) . In w r i t i n g balance equations f o r the p a r t i a l e q u i l i b r i u m model, two q u a n t i t i e s are a b s o l u t e l y conserved. These are the t o t a l number of s u l f a t e moieties and the net charge i n s o l u t i o n . The r e s u l t i n g equations are: 4

F e S 0

2

0

=

5

2

S 0 , 4"

+

W"

+

4

«FeSO,

+

2 5

4

Fe(SO.) ,"

4 2 < > 3 8

+

"FeHS0,2+ 4

+

n

FeS0 0 4

+

n

FeHS0+

+

4

n

CuS0,°

4

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

38.

LiDDELL AND BAUTISTA

0 = n j j - 2n

2- - \ 4

+

+

5

751

Solid-Liquid Reactions

+

Fe(OH) +

4ii

2

- + 3n 4

S

Q

Fe (OH)^+

+

+ 25,^2+

p e 3 +

^FeSO^

2

(39)

" Se(S0 ) 4

+

+

2i

2

"FeHSO+ 4

+

FeHS0 2+

+

2

4

25

n 2+ Fe

5

Cu2+ " OH"

M a t e r i a l balances can a l s o be w r i t t e n f o r F e ( I I I ) , F e ( I I ) and Cu(II) from the chemical equations f o r the two d i s s o l u t i o n r e a c t i o n s . Expressing other q u a n t i t i e s i n terms o f the amount of reactant consumed give W s

5

-

2

Fe(II)

=

1 / 4 5

-

Fe(III)

5 / 4 5

+

(

\

F e ( I I I ) " «0,,

4

)

(

4

1

)

(

4

2

)

S

"cu(II) - CuFeS

0

2

where n

Fe(III)

_

n

Fe + 5

5

H

Fe(II)

=

Cu(II)

=

3 + +

FeHS

V2+

H

*FeOH2+ + ··· + ^ ( S O ^ -

Cu2+

+

+

2 0 /

4

( 4 3 )

+

»FeS0 0

+

5

4

(

FeHS0 +

4

4

)

2

45

"cuSO 0

< > 4

These f i v e balance equations are a l l independent. 3 Among the s o l u t i o n phase species Η , SO^ , HSO4", Fe , FeOH +, F e ( O H ) , F e 9 ( 0 H ) , F e S 0 , Fe(S04> ", F e H S 0 , Fe +, FeS0 °, FeHS04* , C u , and CUSO4 , independent mass a c t i o n expressions can be w r i t t e n f o r the formation of HSO4"", FeOH , Fe(OH) +, F e ( O H ) , F e S 0 , F e ( S 0 ) - , FeHS0 +, FeS0 °, FeHS04^, 4 ° > g i v i n g an a d d i t o n a l 10 equations. There are a t o t a l of 15 equations and 17 unknowns. N Each unknown can be d i v i d e d by ~ C u F e s 2 reduce the +

2-

2

+

4 +

2

2

2

+

+

2+

4

2

2 +

4

0

4

4 +

2

2

a

n

2

+

4

2

4

2

4

4

d C u S 0

t

o

number of unknowns by one but c l e a r l y the use of k i n e t i c

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

752

THERMODYNAMICS

OF

AQUEOUS

SYSTEMS

W I T H INDUSTRIAL

APPLICATIONS

i n f o m a t ion cannot be avoided. The only k i n e t i c data that permits d i r e c t comparison of the r a t e s of Reactions (36) and (37) i s that of Baur, Gibbs and Wadsworth ( 3 ) . A f t e r a very b r i e f i n i t i a l p e r i o d of r a p i d reac­ t i o n , Reactions (36) and (37) a r e f o l l o w e d . E x t r a p o l a t i o n of the data of Baur, Gibbs and Wadsworth t o long times and t r a n s ­ formation of v a r i a b l e s i n d i c a t e t h a t a f t e r t h e i n i t i a l r a p i d r e a c t i o n , c h a l c o p y r i t e and oxygen r e a c t i n a constant r a t i o , i . e . , the f r a c t i o n of the t o t a l copper d i s s o l v e d due t o 0 i s a constant. A constant value can then be assigned f o r η ; 2 f o r t u i t o u s l y , the completed set of a l g e b r a i c p a r t i a l e q u i l i b r i u m equations i s l i n e a r i n t h i s case. 2

Λ

ϋ

Summary and Conclusion We have solved th model f o r a number of d i f f e r e n t i n i t i a l a n a l y t i c a l concentrations and choices o f η . The r e s u l t s of t h e greatest immediate °2 p r a c t i c a l importance concern the e f f e c t s of the i n i t i a l a n a l y t i ­ c a l F e ( 8 0 4 ) 3 c o n c e n t r a t i o n and t h e f r a c t i o n o f copper d i s s o l v e d by 0 and IT*". I t was assumed t h a t the d i s s o l v e d oxygen concen­ t r a t i o n d i d not l i m i t the r e a c t i o n , i . e . , oxygen entered the s o l u t i o n as f a s t as i t was used up i n the r e a c t i o n so t h a t a constant d i s s o l v e d oxygen l e v e l was maintained. The model equa­ t i o n s were solved f o r s u c c e s s i v e r e a c t i o n increments u n t i l e i t h e r the t o t a l F e ( I I I ) c o n c e n t r a t i o n had dropped t o 1 0 ~ o r the s o l u b i l i t y product f o r p r e c i p i t a t i o n of amorphous F e ( 0 H ) 3 was exceeded. P r e c i p i t a t i o n o f F e ^ i s a major problem i n dump l e a c h i n g operations and should be prevented i f p o s s i b l e . T y p i c a l r e s u l t s are shown i n F i g u r e 1 . At the same value o f |no«|, the f i n a l copper recovery i s increased by i n c r e a s i n g the i n i t i a l F e ( S 0 4 ) ^ c o n c e n t r a t i o n . For a given F e ( S Û 4 ) 3 concent r a t i o n , i n c r e a s i n g the f r a c t i o n d i s s o l v e d by 0 and causes an i n c r e a s e i n the f i n a l Cu(II) c o n c e n t r a t i o n but the curve e v e n t u a l l y drops o f f s h a r p l y as F e ( 0 H ) 3 p r e c i p i t a t e s . Moreover, the d e c l i n e i n copper recovery occurs a t s m a l l e r values of | η | f o r higher f e r r i c s u l f a t e c o n c e n t r a t i o n s . Λ

2

2

4

m

+

2

2

2

θ 2

The complete r e s u l t s of the c a l c u l a t i o n s a p p l y i n g the par­ t i a l e q u i l i b r i u m model t o the ambient temperature d i s s o l u t i o n of c h a l c o p y r i t e by f e r r i c i o n and by oxygen and a c i d are b e i n g reported i n another p u b l i c a t i o n ( 7 ) . The c o n c e n t r a t i o n changes o c c u r r i n g during the c h a l c o p y r i t e d i s s o l u t i o n i n the dump can be p r e d i c t e d by the model. This i n e f f e c t i n d i c a t e s how the i n f l u e n t l e a c h i n g s o l u t i o n c o n c e n t r a t i o n should be changed i n order t o maximize copper d i s s o l u t i o n and prevent the p r e c i p i ­ t a t i o n o f t r i v a l e n t i r o n . This can best be a t t a i n e d by main­ t a i n i n g a high F e ( I I I ) c o n c e n t r a t i o n and by h i g h a c i d concen­ t r a t i o n s . A very low c o n c e n t r a t i o n o f d i s s o l v e d oxygen i s

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

38.

LiDDELL

AND BAUTISTA

753

Solid-Liquid Reactions

0020

0002 h

Ql

02

03

04

05

06

FRACTION DISSOLVED BY REACTION WITH 0 . Figure 1. Final Cu(II) concentration as a function of the fraction of chalcopyrite dissolved by 0 and H for various initial Fe (SO ) concentrations: C ) : (O) 0.025m; Ο 0.010m; (A) 0.005m; C —0.2m; C so —-0.001m; C . 0.01m +

2

2

FcSOi

k

3

Fc2(80i

Cu

u

S

h 28Ol

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

754 THERMODYNAMICS OF AQUEOUS SYSTEMS WITH INDUSTRIAL APPLICATIONS indicated since high levels of dissolved oxygen have a delete­ rious effect on the acid concentrations. This in turn affects the precipitation of ferric hydroxide. Abstract In many solid-liquid systems of practical interest, the heterogeneous reactions do not reach equilibrium. Reactions among dissolved species, however, generally are faster. Hence it is often possible to regard the heterogeneous reactions in such a system as producing changes in the concentrations of some of the liquid phase species, thereby causing the equilibria in the solution to shift. Classifying the reactions in such a system as reversible or irreversible makes possible the develop­ ment of a mathematical model of the changes in solution concen­ tration accompanying a heterogeneous process The derivation and use of the model equation that would be needed to equilib ruim liquid phase system must be supplemented by kinetic infor­ mation in order to make the heterogeneous problem determinate. The information needed includes: (1) the stoichiometry of each reaction, reversible or irreversible, taking place; (2) analyt­ ical concentrations in the solution phase at the start of the heterogeneous reactions; (3) equilibrium constants for the reversible reactions, which may be either true thermodynamic or apparent constants; and (4) kinetic data in the heterogeneous reactions. A set of equations is obtained that includes a linear equation for each reversible liquid phase reaction, material balances and, in the case of an aqueous liquid phase, a charge balance; following a change of variable, kinetic equations complete the set. The equations are algebraic in form and in favorable cases may all be linear. This type of model may readily be applied to various hydrometallurgical systems. Mineral leaching is discussed in detail. Terms and Solutions aj

activity of solute species

Κ equilibrium constant mj molality of solution phase species sj; moles/kg solution n. number of moles of solution phase species s. formed _ per mole of solid reacting nj number of moles of solution phase species s. formed per _ kg of solution ^ number of moles of solid S. formed per kg of solution Yj activity coefficient of solution phase species s_. stoichiometric coefficient of species 1 in equilibrium J

J

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

38. LiDDELL AND BAUTiSTA ξ

Solid-Liquid Reactions

755

constant progress variable for extent of reaction; fraction reacted

Acknowledgment This research was supported in part through the financial support of Monsanto, Union Carbide and Phillips Petroleum Corporations in the form of graduate fellowships, the National Science Foundation Energy Traineeship, and Graduate Assistantship from the Engineering Research Institute and the Ames Laboratory, USDOE to one of the authors (K.C.L.). This work was also supported by the U.S. Department of Energy, contract No. W-7405-Eng-82, Division of Basic Energy Sciences, Chemical Sciences Program. Literature Cited 1 Helgeson, H. C., Geochim. Cesmochim. Acta, 1968, 32, 853. 2 Liddell, K. C., A Mathematical Model of the Chemistry of the Dump Leaching of Chalcopyrite, 1979, Ph.D. Thesis, Iowa State University, Ames, Iowa. 3 Baur, J. P.; Gibbs, H. L.; Wadsworth, M. E., Initial-Stage Sulfuric Acid Leaching Kinetics of Chalcopyrite Using Radio­ -chemical Techniques, 1974, United States Bureau of Mines Report of Investigations 7823, Washington, D.C. 4 Dutrizac, J. E., Met. Trans. B, 1978, 9B, 431. 5 Munoz, P. B.; Miller, J. D.; Wadsworth, M. E., Met. Trans. B, 1979, 10B, 149. 6 Carnahan, B.; Luther, Η. Α.; Wilkes, J. O., "Applied Numerical Methods", 1969, John Wiley and Sons, New York, NY. 7 Liddell, K. C.; Bautista, R. G., Met. Trans. B, 1980. RECEIVED

January 30, 1980.

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

INDEX A Absorbent availability 36 Absorber/stripper, sour-water 4/ Absorption-oxidation processes 17 Absorption/stripping, design calculations for 284-289 Acetic acid-water mixture 174 Activity coefficient(s) 248-250 563-566 complete expressions for 166/ effect of temperature on of ammonia in water 109/ of carbon dioxide in water 111/ of gas in binary mixture with water 113/ of hydrogen sulfide in water .. 111/ equations for estimating individual ions 633 of HCI 723/ - N a C l - H 0 system, mean ionic 719/ at high concentrations in multicomponent salt systems .717-738 of ions 182 ionic media and equilibrium constants 561-567 models for the vapor-liquid equilibrium of electrolyte systems 61-87 of NaCl 725/, 734 of neutral solutes 233 for non-electrolytes in solutions of electrolytes 233 parameters 98/ of a pure salt in water 230 trace mean 563 of water in concentrated solutions ...726-729 in the HC1-H 0 system 728/ in the HCl-NaCl-H 0 system 730/ and osmotic coefficient data, correlations of 541 of the solvent (water) in a solution of pure electrolyte dissolved in water 232 of water 182 Acid(s) gas(es) lit removal 15-23 -water systems, N H 174-180 2

2

2

3

Addition processes, hydrogen 299-302 Absorption isotherm, representative .. 368/ Alkali processes, dual 91 Alkali salt solutions 17 Alkalinity, calculation of dissolved 102-103 Alkanolamine solutions, application to 53-57 Aluminosilicates, crystalline metal 22 Ammoni 2 3 5 306-307 in ammonium salts with radius of the anion 123/ correlation equations for salting-out of 127/ effect of temperature on salting out of 128/ mixtures with C 0 / H S / N H , pH of water207/-209/, 216/-218/ CO2/NH3, pH of water- ... 203/-206/, 214/, 215/ H0S/NH3, pH of water- .201/, 202/, 211/, 212/, 213/ molar volumes 112/ pH of water-, mixtures 201/-218/ volatility 187-226 effect of electrolytes on 187-226 effect of sodium hydroxide electrolyte on 223/ -water system 398 compositions for 402/ vapor-liquid equilibrium measurements 193/, 194/ vapor-liquid equilibrium runs 196/ in water, effect of temperature on the activity coefficient of 109/ in water, solubility of 109/ Ammonium salts, salting-out coefficients and parameters for 121/ Anion concentration, dependence of pH on total 274/ Anion pair, interaction coefficient of a cation231 Antimony-containing solutions, effect of glue addition on current efficiency of zinc electrowinning for 713/ Argon + water 521,525/ Association constants, stoichiometric 562 Association, degree of 420 2

2

3

757

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

758

T H E R M O D Y N A M I C S OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

Β Balance densitometer, hydrostatic 583/ Balance, hydrostatic 582-584 Binary(ies) hydrocarbon-water 398 mixture with water, effect of tem­ perature on the activity coeffi­ cient of the gas in 113/ nonhydrocarbon-water 395 steam mixtures, excess enthalpies of some 435-446 Boiler tubing, corrosion damage of ... 657/ Biodegradability of the organics 44 Biological treatment 37 Biomass, synthetic natural gas from 329-331 Block case run 235 data entry 236 data estimation 23 FRACHEM 23 Brines 165 Bubble point pressures for methanol-carbon dioxide system 345/ for methanol-hydrogen sulfide system 345/ for the nitrogen-carbon dioxidehydrogen sulfide-methanol system 346/ Buffers, heat of reaction of H with concentrated sodium citrate 277/ Buffer solutions with dissolved S0 , S0 vapor pressure and pH of sodium citrate 269-291 /i-Butane, H 0 426/ system 406, 425/, 426/ along the three-phase locus 408/ +

2

2

2

APPLICATIONS

Calcium (continued) sulfite and gypsum, magnesium concentration for liquors saturated with 255/, 259/ Calorimeter, flow heat-capacity 577/ Calorimeter, flow mixing 437/ heat of 572/ Calorimetric apparatus, outline of the flow 436, 437/ Calorimetry of aqueous solutions at temperatures up to 325°C, flow 569-580 Carbamate reaction 142 Carbon, activated 22 treatment, powdered 37 removal processes 297-299 Carbon dioxide (C0 ) 3, 5 aqueous solution, N H 68/ 2

3

dependent interaction param­ eters, nitrogen, 411/ mole of N H , pH of waterammonia mixtures 203/-218/ partial pressures of 153/ salting out correlation equations for 127/ effect of temperature on 128/ by sodium chloride and calcium chloride solutions 126/ solubility in aqueous solutions 79/ effect of H S on 58/ in water 110/ phase, effect of methanol on predicted 355/ on the solubility of H S, effect of .... 58/ system, bubble point pressures for methanol 345/ system H 0 429/, 430/ in water, effect of temperature on the activity coefficients of 111/ in water, effect of temperature on Marbules constant 110/ —water mixtures, pH of NH -H S198-222 —water system 395 compositions for 399/ NH 152-155,228,236 model summary for singlestage flash 240/ problem, input to ECES to describe 239/ C 0 - H S - H 0 , system N H 159, 161 Carbon monoxide (CO) 5 conversion of 390/ with excess H 0 , critical lines in reacting mixtures of 387/ 3

2

2

C Calcium and chloride 250-252 chloride solutions, salting-out of carbon dioxide by sodium chloride and 126/ concentration 251/ as a function of chloride-tomagnesium ratio for liquors saturated with calcium sulfite and gypsum 257/ gypsum saturation from measure­ ments of dissolved 258-260 seawater 650 and S0 species, dissolved concen­ trations of 256-258 sulfite and gypsum, for liquors satu­ rated with chloride-to-mag­ nesium ratio 257/ 2

2

3

2

3

2

2

2

3

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

759

INDEX

Cation-anion pair, interaction coefficient of 231 Cation on salting-out coefficient, effect of 120/ Cathode deposit morphology 707 Chalcopyrite dissolved, final Cu(II) concentration as a function of the fraction of 753/ Chemical model, formulation and verification of 248-252 Chloride calcium and 250-252 complexes of copper 693, 698/ -to-magnesium ratio for liquors saturated with calcium sulfite and gypsum 257/ calcium concentration as a function of 257/ Chromatography, consideration affecting observation of inter action second virial coefficient by 361-377 C P - H . O - H - e system, C u 694/, 695/ Claus process(es) 27, 29/ extended 28 gas-phase oxidation 23 of low H S gases 29-30 CO (see Carbon monoxide) C 0 (see Carbon dioxide) Coal conversion basic methods of 296-297 chemical reaction 303/ principles of 295-304 liquefaction processes,flowchartof 300/ processing, correlation of vaporliquid equilibria of aqueous condensates from 107-132 synthetic natural gas from 327 Cobalt concentration, zinc electrowinning vs 716/ Coefficients data, correlations of activity and osmotic 541 mixing 558 salting out at 25°C, 113-124 experimental 118/-119/ effect of temperature on 124-129 and parameters for ammonium salts 121/ Commercial status 23 Complete mix activated sludge (CMAS) 43 Composition, down to ppm levels, pH vs 187-226 Composition model, local 70-71 application of 74-85 development of 71-74 2

2

Compressibilities, one atmosphere 587-592 Compressibilities apparatus, isothermal 590/ Computational methods 99—101 Computer programs 634 Condensates from coal processing, correlation of vapor-liquid equilibria of aqueous 107-132 Conductance studies 661 Contact absorber, S 0 removal for the Shawnee turbulent 262/ Conversion processes, independent .... 28 Copper chloride complexes of 698/ deposit 710/ electrolysis 707 Correction parameter as a function of magnesium concentrations 2

environments, generation of 668-671 processes, understanding 671 Cresol-type components 307 Critical lines in reacting mixtures of CO with excess H 0 387/ water-gas shift 386 binary pairs 385/ points 380-383 binary 383-386 an equilibrium, calculated 388-391 evaluating 383 pressure 390 temperature 390/ Cross-dimers for various systems 430 Cu(II) concentration as a function of the fraction of chalcopyrite dissolved, final 753/ Cu-Cr-H.O-IT-e system 694/, 695/ C u - H 0 - H - e system at 689/ C u - S - H 0 - H - e system 692/ Cupric ion, chloride complexes of 693 2

2

+

2

Data, analysis of ternary and quaternary 131 Data compilations for hydrometallurgical applications, useful ...635-636 Densimeter, magnetic float 584-586 Densimeter, vibrating flow 586-587 Densities, one atmosphere 581-587 Densitometer hydrostatic balance 583/ magnetic float 585/ Sodev vibrating 588/

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

760

THERMODYNAMICS

OF AQUEOUS

Design calculations for absorption/ stripping 284-289 Design data charts 4/ Desulfurization processes, solution equilibria in aqueous fuel gas .... 93 Dielectric effects 165/, 177/ Dilatometer system 595/ Dilatometer, weight 593/ Dilute solutions,* thermodynamics of 718-720 Dissociation(s) constant(s) 195 extrapolation of HS0 629/ first 141 ionic 467 4

Ε Ebulliometer, recirculating 471 ECES to describe N H - C 0 - H problem, input to 239 ECES system overall structure of 234-236 to predict vapor-liquid equilibria, using 236-242 for vapor-liquid-solid equilibria, using 242 Edwards constants 176/ Efficiency consideration 302-304 heat recovery 302 tail gas cleanup process 30 Electricity generating industry 653-674 Electrode, S0 272 vapor pressure obtained by dynamic saturation of 279/-281/ Electrolysis of water 467 Electrolyte(s) 49-53 acidified zinc sulfate 708/, 709/, 712/, 715/ activity(ies) 504-505 coefficients for non-electrolytes 233 on ammonia volatility effect of 187-226 effect of sodium acetate 224/ sodium hydroxide 223/ in aqueous solutions, solubility of volatile weak 139-171 in aqueous systems, prediction of activity coefficients of strong 495-510 bi-bivalent 77/, 82/ characterization 495-496 correlation of thermodynamic prop­ erties of aqueous polyvalent 537-544 dissolved in water, activity of the solvent (water) in a solution of pure 232 3

2

2

SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

Electrolyte(s) (continued) miscible 453-456 in pure solution 496-499 pressure-volume-temperature properties of 581-617 previous applications of the Pitzer equation to weak 64-65 solutions 610/ equilibrium and kinetic problems in mixed 643-652 estimation of the PVT properties of mixed 612-616 high pressure equation of state of 602-612 phase equilibria in aqueous 49-59 systems, activity coefficient models for the vapor-liquid equilib­ rium of 61-87 f 62 effect on the vapor pressure of methanol 78/ vapor-liquid equilibrium in an aqueous system of volatile weak 140/ vapor-liquid equilibria, Beutier's model of volatile weak 181 at various temperatures, pressures, and compositions, thermody­ namics of aqueous 451-464 virial coefficient equations for ... 456-464 Electrometallurgy, applications and needs of thermodynamics in . .701-714 Electroneutrality 56, 181 Electrowinning for antimony-containing solutions, effect of glue addition on current efficiency of zinc 713/ effect of nickel concentration on the incubation period in 706/ versus cobalt concentration, zinc .... 716/ Enthalpy(ies) 576/ of aqueous MgCl , molal 576/ of aqueous NaCl, molal 575/ of some binary steam mixtures, excess 435-446 departures for an equimolar steam-methane mixture 10/ for pure methane 7/ for pure steam 8/ diagram for steam 8/ of dilution run on aqueous MgCl .. 573/ for NaCl, standard partial molal .... 630/ of steam-containing mixtures 5-10 -temperature diagram for steam .... 5 2

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

INDEX

761

Entropy of the anion, correlation of salting-out coefficients for ammonia in ammonium salts with 123/ Equalization and neutralization 37 Equations, models and correlating .537-540 Equation of state for aqueous systems with low mutual solubility, phase equilibrium calculations by 415-435 of electrolyte solutions, high pressure 602-612 studies on the 604 to synthetic and natural gas systems, application of the P F G C MES 333-358 Equilibrium(a) 248-250 in aqueous electrolyte solutions, phase 49-59 in aqueous fuel gas desulfurizatio processes, solution 9 calculations for coal gasification and related processes, two- and threephase 393-413 by equation of state for aqueous systems with low mutual solubility, phase 415-435 chemical 418-419 combined physical and 419 in solid-liquid reactions—application to leaching of ores, modeling 741-755 on wet scrubbing of S0 with magnesia-enhanced limestone, effects of aqueous .247-266 constants 176/, 249/, 566-567 activity coefficients, ionic media, and 561-567 coefficients for 163/ and free energy of formation .627-632 critical points at reaction 389/ dissociation 181 for estimating individual ion activity coefficient 633 in flue gas scrubbing slurries 91-105 and kinetic problems in mixed electrolyte solutions 643-652 liquid-liquid 423 model, application of the partial 746-752 model, development of the partial 742-746 in multicomponent aqueous solutions of electrolytes, predicting vapor-liquid-solid 227-245 physical 418 points, calculated critical and ... 388-391 2

Equilibrium(a) (continued) present in flue gas scrubbing slurries for the lime or limestone processes 94/ reaction 386-388 relations 55 solid-liquid 731-733 for the HCl-NaCl system 737/ sour water 187-226 triangular solid solution-aqueous solution 647/ types of 656-659 using the ECES system for vaporliquid-solid 242 vapor-liquid 181, 729-731 of aqueous condensates from coal processing, correlation of 107-132 dat 192-198 in the HCl-NaCl-H 0 system .... 732/ measurements, ammoniawater 193/, 194/, 196/ using the ECES system to predict 236-242 of weak electrolytes 173/ in an aqueous system of volatile 140/ Beutier's model of 181 Estimation procedures 664-668 Ethane-water system 403 compositions for 405/ Experimental methods 581-602 procedure 367-371 techniques 540 Extraction processes 702-705 Extrapolation to zero peak area 370/ 2

F

FeCl -HCl-H 0 242 Feed composition 348/ Float methods, high pressure magnetic 597-598 Float system, high pressure magnetic 598/ Flue gas desulfurization processes, solution equilibria in aqueous .... 93 Flue gas scrubbing slurries calculation of supersaturation ratios of 101-102 chemical equilibria in 91-105 for the lime or limestone processes, equilibria present in 94/ Fluidized-bed coal gasifier with typical reactor temperature profiles 298/ 2

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

762

THERMODYNAMICS

OF AQUEOUS SYSTEMS W I T H INDUSTRIAL APPLICATIONS

Flow calorimetric apparatus, outline of 436,437/ cell method 193/, 194/ densimeter, vibrating 586-587 heat-capacity calorimeter 577/ heat of mixing calorimeter 572/ Fossil fuel(s) characteristics 295-296 H / C ratios for various 298/ heating values of selected 296/ Free energy of formation, equilibrium constants and 627-632 Fuel(s) fossil characteristics 295-296 H / C ratios for various 298/ heating values of selected 296/

G Gas(es) in binary mixture with water, effect of temperature on the activity coefficient of 113/ Claus processing of low H S 29-30 cleanup, tail 27 process efficiency 30 -processors association research on substitute gas thermody­ namics 317-321 reducing 36 and related systems, thermodynamic data for synthesis 305-315 removal, acid 15-23 research institute, gas supply research program at 323-331 salting out of 113-131 shift, water 303/ critical lines 386 binary pairs, critical lines in 385/ mixtures 383 in sodium chloride solution, correla­ tion of salting-out coefficients of various 130/ solid hydrate 318 supply program 325-326 research at the gas research institute 323-331 systems, application of the P F G C MES equation of state to synthetic and natural 333-358 thermodynamics, gas processors association research on substitute 317-321 unconventional natural 326-327 in water partial molal volumes of 533 solubility of 108-113 2

Gas(es) (continued) in water (continued) solubility of (continued) from 350-600 Κ 513-534 noble 518/ Gasification 297-299 Gasifier with typical reactor tempera­ ture profiles, coal entrained-flow 300/ fluidized-bed 298/ moving-bed 298/ GLC apparatus, modified 370/ Glue addition on current efficiency of zinc electrowinning for antimonycontaining solutions, effect of 713/ GPA projects involving water 318-320 GRI history 323-324 R&D budget f 325/ calcium sulfite and calcium concentration as a function of chloride-to-magnesium ratio 257/ chloride-to-magnesium ratios 257/ magnesium concentration 255/, 259/ Gypsum saturation equations for calculating the degree of 258-260 from measurements of dissolved calcium 258-260 from measurements of dissolved S0 260 2

Η +

H -e system Cu-Cl^-HoO694/, Cu-HoOCu-S-H 0S-H 0H mixture vapor phase water con­ centrations, N HBr in halide solutions, mean ionic activity coefficients of HCI and .. H / C ratios for various fossil fuels HCI activity coefficient of and HBr in hailed solutions, mean ionic activity coefficients of .... and KCl aqueous solution, ionic activity coefficient of HC1-H 0, FeCl HC1-H 0 system, activity coefficients of water in HCl-NaCl system, solid-liquid equilibria for 2

2

695/ 689/ 692/ 682/

2

2

2

2

340/ 79/ 298/ 723/ 79/ 84/ 242

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

728/ 737/

INDEX

763

HCl-NaCl-H 0 activity coefficients of water in 730/ mean ionic activity coefficients for .. 719/ vapor-liquid equilibria in the 732/ H 0 n-butane 425/, 426/ critical lines in reacting mixtures of CO with excess 387/ FeCl -HCl242 methane 424/ mixtures, pH of N H - H S - C 0 - 198-222 NH -H S156/ -nitrogen, system 428/ problem, input to ECES to describe NH -C0 239/ -propane, system 424/, 425/ system activity coefficients of water in the HCI728 NaCl730 mean ionic activity coefficient for the HCl-NaCl719/ H 0 429/ NH -C0 152-155,228,236 model summary for single stage flash 240/ NH -C0 -HoS159, 161 NH -H S155-159, 161, 178/ NH -S0 159 vapor liquid equilibria in the HCl-NaCl732/ H 0 - C 0 system 429/, 430/ H 0 - H - e system Cu689/ Cu-Cl 694/, 695/ Cu-S692/ S682/ HoS-COo-H 0 mixtures, pH of NH 198-222 HoS-Η,ό, N H 156/ system 155-159, 161 C0 161 H 0-H S, system 429/ Hamiltonian models at various levels 549-551 Harned's rule 720-722 interaction parameters for 721/ Heat capacity of aqueous NaCl, molal 579/ calorimeter, flow 577/ measurements 574-578 exchangers 5 of reaction of H with concentrated sodium citrate buffers 277/ recovery efficiency 302 theoretical methane yield and .... 304/ values of selected fossil fuels 296/ 2

2

2

3

3

2

3

2

2

3

2

3

2

3

2

3

2

2

2

+

2

1

2

3

3

2

2

2

2

2

Helium + water 521, Henry's constants coefficients for for solubility of hydrogen sulfide in water Az-Heptane, enthalpy steam 438/, Η-Heptane, results for the mixture steam + /i-Hexane-water system Hydrocarbon flash dry wet -methanolsolubility in water phase, effect of methanol on predicted -water systems, other -water systems, ternary

522/ 176/ 164/ 111/ 440/ 436 406 350/ 351/ 352/ 354/ 409 341/

with concentrated sodium citrate buffers, heat of reaction of .... 277/ conversion 303/ sulfide 2,3 correlation equations for salting-out 127/ effect of C 0 on the solubility of 58/ first ionization constant of 115/ methanol system, bubble point pressure for the nitrogencarbon dioxide 346/ molar volumes of 112/ partial pressures of N H 156/, 158/ on the solubility of C 0 , effect of 58/ system, bubble point pressures for methanol 345/ temperature-dependent interac­ tion parameters, nitrogen, carbon dioxide 411/ in tower bottoms If in water, effect of temperature on the activity coefficients of .. 111/ in water, Henry's constant for solubility of 111/ -water system 395 compositions for 396/, 397/ Hydrogen + water 527, 529/ Hydrometallurgical applications, useful data compilations for .635-636 Hydrometallurgy, application of ther­ modynamics in 625-637 Hydrophobic bonding 468 2

3

2

+

I Ideality, deviations to Immiscible liquids and solids separation

181-183

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

37

764

THERMODYNAMICS

OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

Inert components, mixtures of water and 421-427 Incubation period in zinc electrowinning, effect of nickel concen­ tration on 706/ Industrial processes utilizing thermodynamic data 469/ Industrial waste treatment processes, survey of some 15-44 Integrated processing 30 sulfuric acid 29/ Interactions 17k between molecular and ionic species, parameters for 17 h solute molecules, water and 468 water molecules 468 coefficient of a cation-anion pair .... 231 model, separated associated fluid 445/ model for polar + nonpola mixtures 44 parameters 384/, 442 binary ion-ion 168/ molecule-molecule 168/ as determined from isothermal fits 83/ for Harned's rule 721/ Pitzer ionic 177/ tenary 168/ second virial coefficients by chroma­ tography, considerations affect­ ing observation of 361-377 solid-solution 644-650 in solution, chemical 711 Intercept as a function of temperature, predicted 375/ Intermodular forces and structure, techniques for studying 477/ Iodines, release of radioactive 672 Ions activity coefficients of 182 interactions between 182 and ion-pair activity coefficients, calculations of 93-99 pair-complex competition 650 pairing 562-563 product of water, temperature dependence of molal 662/ Ionic characterization factor 50 media and equilibrium constants, activity coefficients 561-567 systems, corresponding states for .... 557 Ionization constants 113 effect of temperature on 141/ of hydrogen sulfide, first 115/ Iron oxide 22

APPLICATIONS

Isotherms representative absorption values of the slope and intercept predicted for each for various electrolytes, typical Isothermal fits, interaction parameters as determined from

368/ 373/ 498/ 83/

Κ KBr solutions, aqueous 78/ KC1 aqueous solution, ionic activity coefficient of HC1 and 84/ Kinetic problems in mixed electrolyte solutions, equilibrium and 643-652 Krypton + water 524, 526/ L Land availability

34 44

reactions—application to 741-755 Lead speciation in seawater 651/ LiCl system, methanol-water81/ Locus(i), three-phase 409 H-Butane-water system along 408/ propane-water system along 407/ for selected paraffin-water binary systems 412/ Limestone, effects of aqueous chem­ ical equilibria on wet scrubbing of S0 with magnesiaenhanced 247-266 Limestone processes, equilibria present in flue gas scrubbing slurries for the lime or 94/ Linearization methods 99 Liquefaction 299-301 processes,flowchartfor coal 300/ Liquid membrane processes 22 Liquor composition, equilibrium S0 partial pressure and 252-258 Liquors saturated with calcium sulfite and gypsum calcium concentration as a function of chloride-to-magnesium ratios for 257/ chloride-to-magnesium ratios for . 257/ magnesium concentration for 255/, 259/ 2

2

M Magnesium 459/ chloride solution, osmotic coeffi­ cient for 459/ concentration for liquors saturated with calcium sulfite and gypsum 255/, 259/

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

765

INDEX

Magnesium (continued) Method(s) (continued) concentration (continued) of Edwards et al 169-171 and pH, correction parameter as a isopiestic 471 by Van Krevelen, Hoftijzer, and function of 254/ sulfite concentration as a func­ Huntjens 143-145 tion of 257/ piezometer 589-591 ratio for liquors saturated with cal­ MgCl 506 cium sulfite and gypsum, enthalpy of dilution run on aqueous 573/ molal enthalpy of aqueous 576/ chloride-to257/ calcium concentration as a MgS0 · 7H 0 506 function 257/ Models 416 Magnetic float 584-586 association 416 densimeter 585/ continuum 416 methods, high pressure 597-598 and correlating equations 537-540 system, high pressure 598/ validation 339-344 Margules constant for carbon dioxide at various levels, Hamiltonian ... 549-551 in water, effect of temperature of volatile weak electrolytes vaporliquid equilibrium, Beutier's .. 181 on 110/ Mass balances 56, 181,248-250 Moving-bed l gasifie with typical Metals and additives in electro­ deposition, trace 705-71 aqueous solutions of electrolytes, Metal ions, role of 705-707 predicting vapor-liquid-solid Methanation 303/ equilibria in 227-245 Methane 5 mixture composition, experimental 342/ effect of temperature on 338/ enthalpy departures for pure 7/ salt solutions 232 systems, water contents of 343/ mixture, enthalpy departures for an equimolar steam 10/ -water system 398,424/ compositions for 404/ Ν solubilities for 340/ N - H mixture vapor phase water yield and heat recovery efficiency, concentrations 340/ theoretical 304/ NH Methanol -acid gases-water systems 174-180 carbon dioxide system, bubble point and C 0 , calculated partial pressures for 345/ pressures of 149/ concentration profile, vapor phase .. 354/ concentration 197 hydrocarbon flash, wet352/ and H S, partial pressures of 158/ hydrogen sulfide system, bubble partial pressures of 153/, 156/ point pressures for 345/ pH of water-ammonia mixtures on predicted C 0 solubility in water with 203/-218/ phase, effect of 355/ N H - C 0 aqueous solution 68/ on predicted hydrocarbon solubility in water phase, effect of 354/ N H - C 0 - H 0 problem, input to ECES to describe 239/ salt effect on the vapor pressure of 83/ N H - C 0 - H 0 system 152-155, 228, 236 system model summary for single stage bubble point pressure for the flash 240/ nitrogen-carbon dioxide159, 161 hydrogen sulfide 346/ N H - C 0 - H S - H 0 - system -water-LiCl 81/ NH -Ho£-COo-H 0 mixtures, pHof 198-222 -water-NaBr 80/ NH -HoS-H 0 156/ uni-univalent electrolyte effect on system 155-159,161 the vapor pressure of 78/ partial pressures in 6/ Method(s) 178/ of Beutier and Renon 162-168 NH -SHo-H 0 system 159 for more complex diagrams 688-691 N H - S 0 - H 0 , system 80/ of data development 307-310 NaBr system, methanol-water2

4

2

2

2

3

2

2

2

3

2

3

2

2

3

2

2

3

2

2

2

3

2

3

3

2

2

3

2

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

766

OF AQUEOUS SYSTEMS W I T H INDUSTRIAL APPLICATIONS

NaCl 506/ activity coefficients of 725/ calculated 734 aqueous molal enthalpy of 575/ molal heat capacity of 579/ solutions 78/ standard partial molal entropy for . 630/ system, solid-liquid equilibria for the HC1737/ NaCl-H 0 system, in the HC1activity coefficients of water 730/ mean ionic activity coefficients 719/ vapor-liquid equilibria 732/ Natural gas systems, application of the PFGC-MES equation of state to synthetic and 333-358 Natural gas, unconventional 326-327 Neon -f water 521 523/ Neutral species, interaction betwee Neutralization, equalization an Neutralization, fraction P o prediction vs 283/ titration with HC1 or S0 , dependence of pH on 276/ titration with NaOH, dependence of pH on 276/ Nickel concentration on the incubation period, in zinc electrowinning, effect of 706/ Nitrogen -carbon dioxide-hydrogen sulfidemethanol system, bubble point pressure for 346/ -carbon dioxide-hydrogen sulfide, temperature-dependent inter­ action parameters 411/ -water system 398, 527, 528/, 530/ compositions for 400 Non-thermodynamic data 555 2

SO

2

Oil sands 363 Oil shale, synthetic natural gas from .. 329 Ores, modeling the chemical equilibria in solid-liquid reactions—appli­ cation to leaching of 741-755 Osmotic coefficient for magnesium chloride solution 459/ Osmotic coefficient for sodium chloride solutions 459/ Oxidation gas-phase (Claus process) 23 liquid-phase (Stretford process) .... 23 processes, absorption17 Oxygen conversion 303/ Oxygen + water 527, 531/

Psoo prediction vs. fraction neutralization Po solution composition, dependence of Parameters binary ion-ion for dielectric effects interaction Pitzer ionic temperature sensitive £jj Parameters for interactions between molecular and ionic species Paraffin-water binary systems, threephase loci for selected Peng-Robinson equation o

S

283/

n

2

286/ 170/ 177/ 384/ 177/ 176/ 171/ 412/ 442/

behavior 272-275 correction parameter as a function of magnesium concentration and 254/ equilibrium 648 S0 partial pressure as a func­ tion of 255/ on fraction neutralization, titration with HC1 or S0 , dependence of 272/ on fraction neutralization, titration with NaOH, dependence of .... 276/ measurements 270-271 of N H - H S - C 0 - H 0 mixtures 198-222 SOo concentration as a function of .. 259/ of sodium citrate buffer solutions with dissolved S0 , S0 vapor pressure and 269-291 on total anion concentration, dependence of 274/ vs. composition, down to ppm levels 187-226 of water ammonia mixture with C O , - H S - N H . 207/-209/, 216/-218/ C0 -NH 2Ό3/-206/, 214/, 215/ H S-NH 201/, 202/, 211/-213/ no acid gas present 200/, 210/ Phase equilibria 319 Phase rule 643-644 Piezometer method 589-591 Pipeline conditions, process 349/ Pitzer equation 62-64 application of the extended 66-69 extension of 65-66 2

2

3

2

2

2

2

2

2

2

2

3

3

3

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

INDEX

767

Pitzer equation (continued) limitations of 70 to weak electrolytes, previous applications of 64-65 Pitzer ionic interaction parameters .... 177/ Polar components, mixtures with .310-315 Polarizability and molar volume 519/ Pourbaix diagrams, computation of 681-699 Power station water circuits 654-656 Precipitation, controls of 649/ Predictions of K 669/ Pressures analysis of the results at high ... 439-441 over aqueous solutions 157/ in N H - H S - H 0 system, partial .. 6/ processing 23 Procedure of Beutier and Renon 145-148 of Edwards, Maurer, Newman Prausnitz 148-15 of van Krevelen et al. for calculating V L E 161-162 Process(es) alternatives 15-28,31-36 pipeline conditions 349/ installations 37 regenerative 91 selection 22-23, 28-30, 36-37, 44 throwaway 91 Processing steps, typical 37-44 Program builder 235 comparisons 697-699 generator 235 Propane-water system 403, 424/, 425/ along the three-phase locus 407/ Protein additives, role of 707-711 Protonation constant of S " 666/ Purification processes, hot-gas 22 PVT apparatus, diagrammatic sketch of 596/ properties, high-pressure 592-602 properties of mixed electrolyte solutions, estimation of 612-616 Pyrolysis 297 h

3

2

Ratio, solid/water 647/ Reacting mixtures, critical points in 379-391 Reaction coal conversion chemical 303/ equilibrium 386-388 step 317 Reactor(s) 5 boiling water 654 pressurized water 654 Recovery processes 33 Recycle processes 28, 704 Research program at the gas research institute, gas supply 323-331

2

2

Quench step

317

S

SHo-H 0 system, N H

so

2

3

159, 178/

2

concentration as a function of pH .. 259 electrode 272 S0 vapor pressure obtained by dynamic saturation of . 279/-281/ gypsum saturation from measurements of dissolved 260 with magnesia-enhanced limestone, effects of aqueous chemical equilibria on wet scrubbing of 247-266 partial pressure equilibrium 253-255 as a function of pH 255/ and liquor composition 252-258 removal enhancement effect of magnesiainduced dissolved sulfite on 260 as a function of dissolved sulfite concentration and slurry flow rate 263/ for the Shawnee turbulent contact absorber 262/ species, dissolved concentrations of calcium and 256-258 vapor pressure 275-284 obtained by dynamic saturation .. 278/ of the S0 electrode 279/-281/ and pH of sodium citrate buffer solutions with dissolved SOo 269-291 Salt(s) effect on the vapor pressure of methanol 83/ for low solubility 508-509 2

2

R

Radioactivity, out of core Radius of the anion, correlation of salting-out coefficients for ammonia in ammonium salts with

672

123/

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

THERMODYNAMICS

768

OF AQUEOUS SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

Salt(s) (continued) Seawater (continued) solutions speciation 650 activity of water for water455/ lead 651 alkali 17 using pure water high pressure, multicomponent 232 volumes of 611 systems, activity coefficients at high Separation equipment 5 concentrations in multicom­ Setschenow equation 65 ponent 717-738 Sieves, molecular 22 in water, activity coefficient of a Slopes, experimental data for pure 230 determination of 374/ Sludge, complete mix activated Salting-out (CMAS) 43 of ammonia, correlation equations 91 for 127/ Sludge, waste Slurry flow rate, S0 removal as a of ammonia, effect of temperature function of dissolved sulfite on 128/ concentration and 263/ of carbon dioxide correlation equations for 127/ Sodium acetate effect on Ν Η volatility, effect of temperature on 128/ sodiu hydroxid d 222-225 by sodium chloride and calciu chloride solutions 126 coefficients chloride 458 at 25°C 113-124 and calcium chloride solutions, experimental 118/-119/ salting-out of carbon correlation of dioxide by 126/ for ammonia in ammonium solutions, osmotic coefficient for 459/ salts with radius of the solution, correlation of saltinganion 123/ out coefficients of various for ammonia in ammonium gases in 130/ salts with entropy of the buffer solutions with dissolved S0 , anion 123/ SO » vapor pressure and pH of various gases in sodium of 269-291 chloride solution 130/ citrate buffers, heat of reaction of effect of cation on 120/ PP with concentrated 277/ effect of temperature on 124-129 hydroxide electrolyte on ammonia and parameters for ammonium volatility 223/ salts 121/ hydroxide and sodium acetate effect of gases 113-131 on N H volatility 222-225 of hydrogen sulfide, correlation Solubility(ies) 505 equations for 127/ the effect of pressure on gas 532-534 Saturation, dynamic 271-272 equation and thermodynamic apparatus for 274/ definitions 514 of the S 0 electrode, SO> vapor of gases in water from 350pressure obtained by 279/-281/ 600 Κ 513-534 S0 vapor pressure obtained by 278/ for methane-water systems 340/ Scrubbing slurries of the noble gases in water 518/ calculation of supersaturation phase equilibrium calculations by ratios of flue gas 101-102 equation of state for aqueous chemical equilibria in flue 91-105 systems with low mutual for the lime or limestone processes, solubility 415-435 equilibria present in flue gas 94/ of volatile weak electrolytes in Scrubbing of S0 with magnesiaaqueous solutions 139-171 enhanced limestone, effects of Solute molecules, interactions between aqueous chemical equilibria on water and 468 wet 247-266 Solutes, activity coefficients of neutral 182 Sea salt 613 Solutions Seawater 614/, 615, 616, 648 current trends in the fundamental calcium 650 theory of ionic 547-558 solutions 609/ mixed 502-504 sound speed data 606/ preparation 270 2

Λ

2

3

2

L

2

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

INDEX

769

Solvent extraction 470 physical 17 type 22 (water) in a solution of pure electro­ lyte dissolved in water, activity of 232 Sorption calculations 3 Sound velocimeters, high pressure 599-602 Sour gas treating 318 Sour-water absorber/stripper 4/ strippers 2, 3 thermodynamic data 2-5 treating 318 Speed data, sound 606/ seawater 606/ Speed measurements, sound 591-592 direct 596 Separation, immiscible liquids an solids 3 Steam -containing mixtures, enthalpies of 5-10 conversion 303/ enthalpy diagram for 8/ + Ai-heptane, enthalpy 438/, 440/ + /i-heptane, results for the mixture 436 methane mixture, enthalpy depar­ tures for an equimolar 10/ mixtures, excess enthalpies of some binary 435-446 pure 9 enthalpy departures for 8/ requirements, actual 288/ requirements, minimum 287/, 289/ Stoichiometry 379-380 Stress corrosion cracking 670 Stretford process (liquid-phase oxidation) 23 Stretford tail gas processes 29/ Strippers, sour-water 2, 3, 4/ Stripping calculations 3 design calculations for absorption 284-289 wastewater 37 Structure breaking 468 Structure making 468 Sulfite concentration, dissolved 256 and slurry flow rate, S0 removal as a function of 263/ Sulfite concentration as a function of magnesium concentration 257/ Sulfite on S0 removal, enhancement effect of magnesia-induced dissolved 260 Sulfur dioxide removal 30-37 Sulfur recovery 23-30 processes, guidelines for selection .. 29/ 2

2

Sulfuric acid 28 integrated processing 29/ options 30 Supersaturation ratios of flue gas scrubbing slurries, calculations of 101-102 Supersaturations, seeded runs at several initial 645 Supply program, gas 325-326 Syngas processing 5 Synthesis gas production 357 Synthesis gas and related systems, thermodynamic data for 305-315 Synthetic natural gas from biomass 329-331 from coal 327 from oil shale 329 Synthetic and natural gas systems,

Τ Temperature(s) -dependent interaction parameters for nitrogen, carbon dioxide, and hydrogen sulfide 411/ -dependent interaction parameters for paraffin-water binary systems 410/ diagram for steam, enthalpy5 difficulties at high 659-660 effects 499,627-632 predicted intercept as a function of 375/ predicted slope as a function of 376/ on salting-out coefficients, effect of 124-129 by Vera and co-workers, extension of 733-735 Theory 334-339 Thermodynamics 139-142 of aqueous electrolytes at various temperatures, pressures, and compositions 451-464 of concentrated solutions 722-726 considerations 656-668 data available 660-664 industrial processes utilizing 469/ sour-water 2-5 for synthesis gas and related systems 305-315 definitions, solubility equation and 514 of dilute solutions 718-720 in electrometallurgy, applications and needs of 701-714 framework 229-234 gas processors association research on substitute gas 317-321

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

770

THERMODYNAMICS

OF AQUEOUS

Thermodynamics (continued) of high temperature aqueous systems 653-674 properties of aqueous polyvalent electrolytes, correlation of .537-544 of aqueous solutions 467-481 techniques for measuring 472/ of solution, water + gas 517 and structure 548-549 Throwaway processes 31 Transition indicator, phase 372/ Turbine disc failure, consequences of 655/ V Vapor pressures 502 of mixed solutions 505-508 Variables search 10 specified and calculated 24 state 100 Velocimeter, sound 593/ high pressure 599-602, 600/ Virial coefficient equations for electrolytes 456-464 Virial coefficient equations, parameters for 463 V L E , procedure of van Krevelen et al. for calculating 161-162 Volume and partial molar volume, relationship between saturated liquid 368/ Volume, polarizability and molar 519 W Waste sludge 91 Waste treatment processes, survey of some industrial 15-44 Wastewater streams, other process 36 stripping 37 treatment 37-44, 575 Water 307 activity(ies) 182, 500/ in pure solutions 501 -ammonia mixtures with no acid gas present, pH of 200/ CO>-H>S-NH , pH of 207/-209/, 216/-218/ CO>-NH , pH of 203/-206/, 214/, 215/ HoS-NH,, pH of 201/, 202/, 211/-213/ argon + 521, 525/ binary systems, temperaturedependent interaction parameters 410/ s

s

SYSTEMS W I T H INDUSTRIAL

APPLICATIONS

Water (continued) binary systems, three-phase loci for selected paraffin 412/ circuit for a high-pressure boiler, a simplified 658/ circuits, power station 654-656 in concentrated solutions, activity coefficient of 726-729 concentration profile, vapor phase .. 353/ concentrations, N - H mixture vapor phase 340/ contents of multicomponent systems 343/ density dielectric constant and compressibility of 662/ determination of the parameters of pure 419-421 dilatometer 593/ dissociation of 142 electrolysi f 467 2

2

critical lines 386 binary pairs 385/ mixtures 383 in the HC1-H 0 system, activity coefficient of 728/ in the HCl-NaCl-H 0 system, activity coefficients of 730/ helium + 521, 522/ hydrogen + 527, 529/ and inert components, mixtures of 421^27 from 350-600 K, the solubility of gases in 513-534 krypton + 524, 526/ LiCl system, methanol81/ mixture, acetic acid174 molecules, interactions between 468 -NaBr system, methanol80/ neon + 521,523/ nitrogen + 527, 530/ oxygen + 527, 531/ parameters for the assumed species in 420 salt solutions, activity of water for .. 455/ solubility of 428/ specific volumes of 598/ system(s) along the three-phase locus, «-butane 408/ along the three-phase locus, propane 407/ ammonia 398 H-butane 406 carbon dioxide 395 compositions for 399/ compositions for the ammonia402/ for the ethane405/ 2

2

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

771

INDEX

Water (continued) system(s) (continued) compositions (continued) for the hydrogen396/ sulfide 397/ for methane 398, 404/ solubilities for 340/ for the nitrogen 400 ethane 403 n-hexane 406 hydrogen sulfide395 N H acid gases 174-180 nitrogen 398 other hydrocarbon 409 n-pentane 406 propane 403 treating step 317 vapor-liquid equilibrim measurement method, ammonia .193/ 194/ vapor-liquid equilibrium runs ammonia196 3

Water (continued) for water-salt solutions, activity of.. 455/ xenon + 527, 528/

Xenon + water

527, 528/

Zinc electrowinning for antimony-containing solutions, effect of glue addition on current efficiency effect of nickel concentration on the incubation period in vs. cobalt concentration flow sheet block diagram morphologie

In Thermodynamics of Aqueous Systems with Industrial Applications; Newman, S., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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