DISSOLUTION RATES OF SILVER IN FERRIC-FERROUS SYSTEMS.

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13-5M.314LD3907 •G7 Salzberg, Hugh Henry William, 192119^0 Dissolution rates of silver in »s3 ferric-ferrous systems. New York c19^ 0 a i,71 ,c23 typewritten leaves. tables,diagrs. 29cm. Thesis (Ph.D.) - New York Univer­ sity, Graduate School, 19^0. Bibliography: p.c72-733 C50675

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T H IS D IS S E R T A T IO N HAS BEEN M IC R O F IL M E D E X A C T L Y AS R E C E IV E D .

library Of M W TORK UMIYBRSITI UBimSITT HEIGHTS

DISSOLUTION RATES OF SILVER IN FERRIC-FERROUS SYSTEMS

By Hugh Henry William Salzberg

A dissertation in the department of chemistry submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Graduate School of Arts and Science, New York University I

To Professor Cecil V. King in both gratitude and respect.

His infinite patience made this work possible.

TABLE OF CONTENTS

Introduction ........................................ CHAPTER I Experimentation and Observations ..................... Procedure - Apparatus - Materials - Errors Observations - Surface area - Time of Runs Surface condition - Anion present - Temperature Rotational speed - Acid concentration - Ionic Strength - Concentration of ferric ion - Concen­ tration of Ferrous ion - Concentration of Silver ion - Product of silver concentration and ferrous concentration - Emf between cylinder and solution CHAPTER II ...................... Theory and Conclusions Historical - Discussion of Results and Formulation of Reaction Mechanism - Derivation of Rate Equation CHAPTER III Application of Equation ............................ Variation of Rates with Concentration - Rates in absence of ferrous and silver ion - Rates in absence of ferrous ion, ferric ion constant Rates in absence of silver ion, ferric ion constant Rates in presence of all three ionic species Variation of Rates with Stirring Speed - Variation of Rates with Temperature - Variation of Rates with Neutral Anions - Variation of Rates with EMF. CHAPTER IV Summary

............................

.............

Bibliography ........................................

/

INTRODUCTION

This thesis is based upon an investigation of the dis­ solution of metallic silver by solutions containing ferric ion. The study was initially undertaken to provide data for the comparison of the observed rates with those predicted by the classical diffusion theory, to attempt to correlate reaction rate and oxidation potential and to attempt to arrive at a mechanism of reaction. The specific system was chosen because of previous obser­ vations that ferric ions oxidize many metals quantitatively and with rates agreeing with the diffusion layer theory.

With

silver, however, the reaction does not go to completion, but reaches a state of equilibrium, at which point both the dis­ solution rate and the relative oxidation potential of the silver metal become zero.

This reaction could therefore be ex­

pected to vary in rate with wide latitude and could therefore show both diffusion and chemical control, each of which could be correlated with oxidation potential. The reaction is reversible and nay be expressed stoichimetrically as

Fe^

Ag

:

Fe^

-i-

-f- Ag* .

CHAPTER I

EXPERIMENTATION

Procedure A silver cylinder of known diameter and surface area was im­ mersed in reagent solutions for measured time intervals at con­ trolled rotational speeds and temperatures.

The amount of silver

dissolving was determined by weighing the cylinder both before and after each run. To insure the correspondence between reaction time and measured interval and to prevent weighing of the reaction products, on removal from the reacting solutions, the cylinder was immediate­ ly immersed in distilled water, wiped dry with filter paper and then weighed to constant weight. Before each run, the cylinder was polished to brightness using a fine grade of jeweler's rouge paper, the excess rouge being removed with filter paper.

The amount of silver lost during

polishing was only several tenths of a milligram. Each cylinder used weighed in the neighborhood of thirty grams and was weighed to a tenth of a milligram.

To improve the precision,

it was proposed to use thin silver sleeves instead of cylinders and weigh them on a microbalance.

However, in no case was the error of

the measurements less than or even equal to the balance error.

-1-

Apparatus The time intervals were ct* first measured with a stop watch or an electric timer. The cylinders were about 2 cms long and 1.5 cms in diameter and were rotated on a steel shaft mounted on an electric motor. The shaft was insulated from the solution by a bakelite sleeve above the cylinder and rubber washers and a bakelite cap below the cylinder.

The motor was a surplus Air Corps motor, weighing

less than a pound and operating on both AC and DC at speeds between one and fifteen thousand revolutions per minute without overheating.

The motor was mounted shaft downward upon an or­

dinary laboratory tripod and the cylinder was immersed merely by lifting the tripod off the table top and placing it down upon a sponge rubber mat with the beaker of solution in the center. The motor was operated by constant voltage AC, obtained by pass­ ing the incoming current through a voltage regulator.

Changes

in speed were produced by a variac in series with the motor.

A

rotational speed of 1,000 RPM was equal to a peripheral speed of 76 cms per second. Rotational speed was measured by means of a stroboscope which had been calibrated by a synchronous motor. Temperature control was by means of a heater and regulator operating through a relay.

The heater consisted of a length of

coiled nichrome wire in a loop of pyrex glass and was suspended in the solution.

The regulator was a six inch metastatic

-2-

mercury-in-glass type.

A good deal of difficulty was experienced

due to liquid splashing up and shotting out the contacts of the regulator, causing the reaction to be run at lower temperatures. Also, due to motor vibration, bubbles were formed in the capil­ lary at times, thus giving rise to higher temperatures.

To do

away with the latter condition, it was merely necessary to see that at no time did the motor touch the regulator.

However, al­

though several expedients were tried to prevent shorting, none was really successful.

These included coating the regulator with nail

polish, paraffin and covering it with rubber sheathing.

The most

satisfactory of these was found to be covering with a rubber sheath coated with shellac.

No cooling device was included since

the reactions were run at thirty degrees centigrade, several degrees above anticipated room temperature.

During one hot spell,

however, it was necessary to apply cold compresses to the sides of the beaker.

In light of the above experience, it is suggested

that any further work be conducted in a conventional type of thermostat in which the reaction vessel is immersed or suspended. Potentials were measured with a student type potentiometer, which had a precision limit of a hundredth of a millivolt.

How­

ever, due to both changes in working cell and in actual potential between the reacting electrodes as the reaction proceeded, the actual precision was nowhere near this limit.

The emf measured

was that between the silver-silver ion electrode and the ferricferrous electrode.

The actual electrodes used were a shiny

-3-

platinum electrode immersed in the solution and the silver cylinder itself.

Contact was made with the rotating cylinder by means of a

mercury cup mounted on the shaft. The reaction vessel was a 600 cc beaker.

This size was

chosen because it could hold 500 cc of solution at such a height that the cylinder would be immersed to a sufficient depth to minimize cavitation.

The quantity 500 cc was chosen for con­

venience in calculations.

Materials The cylinder was purchased as pure silver from the American Platimum Company.

As a check, the silver was analyzed for zinc,

lead, copper and iron.

None of the first three was found and

only traces of iron were indicated.

The cylinder was prepared

by melting the silver metal in a silica cylinder in a glo-bar furnace. The silver sulfate used was prepared by addition of sulfuric acid to silver nitrate, followed by repeated washing and recrystaHization until free from nitrate ions. The ferric sulfate was purchased as CP hydrated ferric sulfate and dissolved in water with sufficient sulfuric acid present to prevent hydrolysis and formation of colloidal ferric hydroxide.

Analysis of this stock solution was by permangani-

metric titration of solution passed through a Jones reductor. The ferrous sulfate was CP anhydrous material.

Part of the

work wag performed adding crystalline material directly to the re­ acting solution.

Most of the work, however, was done using stock

ferrous sulfate in enough sulfuric acid to inhibit air oxidation, made up fresh every three days. The ferric perchlorate was made by addition of perchloric acid to solid ferric hydroxide. The ferric and silver nitrates were CP crystals and all acids were CP.

Errors Of the thirteen parameters, it was necessary to control seven during each experimental run.

These were temperature, speed, sur­

face condition, concentration of acid, and concentration of each of the ions. In addition to errors in the control of these factors, there was the possibility of balance error and of abrasion of the cylinder by filter paper or of deposition of rouge on the cylinder. Due to

the difficulty of controlling all of the above, the

experimental error was about 0.4- - 0.5 milligrams per run.

There­

fore, whenever possible, runs were made for periods of time suf­ ficient to remove large enough amounts of material to make the fixed experimental error a small percentage error. In any event, it will be noted that in the final rate equation the overall difference between calculated and observed rates is Q 0.03 m-gm/cm -min, which is for a two-minute run, of the order of

-5-

the experimental error.

Observations There were thirteen parameters upon which the rate of dis­ solution was observed to depend.

These were:

(l) surface area,

(2) total time of runs, (3) surface condition, (4.) anion present, (5) temperature, (6) rotational speed, (7) concentration of acid, (8) ionic strength, (9) concentration of ferric ion, (10) con­ centration of ferrous ion, (11) concentration of silver ion, (12) product of silver and ferrous concentration,(13) emf between cylinder and solution. The effects of each are hereinafter separately discussed. (1) Surface Area All other factors being held constant, it was observed that the rate, as expected, was directly proportional to the surface area of the cylinder.

Therefore, in the rest of this report,

reference to the rate will be understood to mean rate per square centimeter of surface.

62)

Total Time of Runs It was found that the rates of reaction were not large

enough to change appreciably the concentrations of reagents over the first 10-15 minutes.

In the sulfate system, or in the nitrate

and perchlorate systems with additional sulfate ion present, the rates were almost constant over this period, falling off only

-6-

after appreciable change in concentration.

In the nitrate and

perchlorate systems, however, the rate fell off very rapidly over the first fifteen minutes} thereafter remaining relatively con­ stant until significant changes had occurred in reagent concentra­ tion. Since the greater portion of the work was done in the sulfate system, the time of runs is found to have no effect on the rate, and was generally taken to be 1, 2 , 5, or 10 minutes, all of which gave the same rate per minute. The effects of time upon the various systems are shown in Table I and Figure 1.

TABLE I Rate Versus Time Rates given are milligrams dissolving per 2 minute run. Temperature is 30 degrees, rotational speed 4.,000 rpm or a peripheral speed of 304- centimeters per second. Ferric concentrations are in gram-Lons per liter. 500 cc of solution is used. Time 0.04 Fe

Rate (sulfate)

(0.05 Fe

2

10.8

4

10.4-

4-9

6 8 10

10.2

3.9

10.4 10.3

3.3 3.6

-7-

7.8

(nitrate)

I

Figure 1

16

Rate versus Time

12 a

8 js=m

2-min 4

0

0

2

4

6 Minutes

8

10

12

0.20 Figure 2

Rate versus Time

0.16 1C8 X

m«equ.

0.12 unpolished between runs 0.08 — — .polished between runs

0.04

0.00

12 Minutes -

9

-

16

24

28

(3) Surface Condition It was found that in the absence of reaction product, where rates were relatively high, the rate was independent of treatment of surface.

Rates with etched, mechanically polished, and electro­

polished surfaces were substantially the same. With low rates, under conditions approaching equilibrium, the rate was found to vary with the degree of polish of the cylinder. Rates with polished cylinders were much higher and more reproduc­ ible.

This is shown in Figure 2, where consecutive runs in the

same solution show a progressive diminution in rate if unpolished, but on being polished the rate increases to almost its original value. Composition of solution for Figure 2 was as follows: Fe+3 = 0.0.400,

Fe+2 = 0.083,

gm-ions per liter, the

silt

-9-

Ag" - 0.0060: m s

*Kf

All in

(A) Anions

A completely unexpected development in this work was the effect of anions upon the reaction velocity. The necessity of using an anion whose ferric, ferrous and silver salts were soluble and which would neither oxidize nor reduce the other reacting species, narrowed the choice down to sulfate, nitrate and perchlorate ionB. From the outset of the work it was observed that there were marked discrepancies

between the rates of the sulfate system and 44 the rates found by Reass using sterling silver and ferric

nitrate.

A comparison of rates using ferric nitrate, ferric

sulfate, and ferric perchlorate was therefore undertaken.

It was

found, as shown in Table III and Figure 3, that the results in perchlorate and nitrate systems are in agreement with each other, being much slower than that in the sulfate system.

Also, as shown

in Figure 1 above, the rates in nitrate and perchlorate solutions fall off much more rapidly, more rapidly in fact than changes in concentration would indicate. In addition to the above, it was found that addition of sulfate

ion to either of the other systems increased the rate,

while addition of nitrate or perchlorate ions to the sulfate system did not decrease the rate.

-11-

An attempt was also made to determine the effect of the chloride ion.

This was complicated by the fact,that on reaction,

an insoluble adherent film of silver chloride was formed at the interface, stopping the reaction. after several seconds. evolved.

This film was found to form

However, a technique of comparison was

The cylinder was rotated in the solution for several

seconds, then dipped in ammonia to remove the film, then in water to remove the ammonia.

The cylinder was then wiped with filter

paper and the process repeated until the time of rotation in the solution itself totalled a minute.

The chloride and perchlorate

systems were compared and it was found that the rates with chloride were much higher than perchlorate and almost as high as the rate with the sulfate ion. Because of its higher reaction rates and the ready avail­ ability of silver, ferric and ferrous sulfates, in contrast to ferrous nitrate and perchlorate, and silver and ferric perchlor­ ates, the sulfate system was selected.

The majority of this work

was done using sulfate ion and unless specified, all results refer to aqueous solutions of ferric, ferrous, and silver sulfates.

-12-

TABLE III Anion Versus Rates x ICS Rates are milli-equivalents per minute per square centimeter; Temperature is 30 degrees centigrade, and rotation is at 4.000 rpm. No ferrous or silver ions are present, initially. Cone Fe***

Sulfate

0.005 ^ 0 .G&0 0.020

0.216 O.44. 0.73

0.040

1.20

0.060

1.47

0.080

1.73

108 x Rate Nitrate

0.115 0.143 0.176 0.186 0.186 0.204 0.198 0.17 5 0.231 0.186

0.196

-13-

Perchlorate

0.120 0.138 0.186 0.231 0.236

0.302 0.318

2.0

Figure 3

Rate versus Anion

l.S

1.2 108 x rp^ecm

Ferric Sulfate Ferric Perchlorate Ferric Nitrate

cn-m

0.8

0.4

0.0 0

0.02

0.04 0.06 g-Ions of Fe

- i H "

0.08 0.10 per liter

(5) Temperatore It was found that where the reaction was presumably diffusion controlled, that is, with dilute ferric solutions containing no reaction products, there were temperature coefficients averaging about fifty per cent per ten degrees, as shown in Table IV and Figure 4*

This is in close agreement with the criterion of King 6 and Braverman. T4BLE IV Rate Versus Temperature (Diff Control) .Rate im-equ. cm^-min

Temp (’C)

1.01 1.20 1.70 1.7b 2.67 4.60

28.5 30.0 39.5

RPM

Fe^Sonc.

Coef/lO'C

4,000

0.04 M

1.5

40.0 50.0 67.5

1.54 2.34 3.66 5.22 6.73

30.0 39.0 49.0 60.0 70.0

7,000

0.04

1.5

2.04 2.98 4.67

30.0 40.0 50.0

4,000

0.10

1.5

2.82 3.84 6.65

30.0

7,000

0.10

1.4

40.0 49.0 Under conditions of slow reaction, which presumably are near

equilibrium, the reaction rate was much more sensitive to temperature change,

in increase of ten degrees in temperature increased 2 the rate by about 0.4 m-gjn/ cm -min, which, depending on the initial

-15-

rate was an increase of about 300-600 per cent.

This is shown in

Table V and Figure 5« TABLE V

IQoxRate

Rate Versus Temperature (Chemical Control) x Temp. Fe^^Conc Fe^Conc Ag'Conc RPM

0.050 0.389

30.0 39.0

1.02

48.5

1.88

59.0

0.0385 ^

0.0215«

-16-

0.0293 A) 4000

10

Figure 4

Rate versus Temperature (Diffusion Control)

*4*"I*4

Fe = Fe?7*= FeTTT= Fe =

25

2.0

35

55 65 45 Degrees Centigrade

Figure 5

0.10 0.10 0.04 0.04

Rate versus Temperature (Chemical Control)

cm^-m

1.6

1.2

0.8

0.4

35

RPM RPM RPM RPM

75

108xm-equ

0.0 • 25

7000 4000 7000 4000

45 55 Degrees Centigrade — /7 -

65

75

(b) Rotational Speed In the absence of reaction product and at low concentrations of ferric ion, the observed reaction rate is linear with stirring speed, as is the case with reactions known to be diffusion con5 trolled. However, at higher concentrations of reagent, even in the absence of product, there is a larger and larger deviation from linearity and therefore a smaller and smaller share of dif­ fusion control. At high concentrations of product, that is, with very low rates, stirring has still some slight effect, the rate increasing with increased stirring speed up to about 8,000 rpns or a per­ ipheral speed of 608 cms/ sec. The effects of stirring speed are shown in Table VI and Figure 6.

-18-

TABLE VI Rate Versus Stirring Speed 108 x Rate

RPMS

0.057 0.530 0.728

0 1000 2000

0.960

3000 4000

1.20 1.28 1.54 1.94

0.123 0.986

1.42 1.72 2.04 2.30 2.82 3.20 3.18 3.34 0.030 0.033 0.052 0.075 0.039 0.017

Fe^"^ Cone

F e ^ Cone

0.04 M

0 A)

Ag^Conc

Temp.

0 m

30*C

5000 7000 12000 0 1000 2000 3000 4000 5000 7000 9000 10000 12000

0.10

0

2000 3000

0.0387

0.0213

4000 6000 8000 12000

-19-

0

0.0291

4.0 Figure 6

Rate versus Rotational Speed

3.0 ■

2.0

1.0

T

I

Fe

Z.*

.w o u / ,

* 0.00213, Ag = 0.00291

0.0 0

2000

4000 6000 8000 Revolutions per Minute - *o-

10000

12000

(7) Concentration of Acid Although the hydrogen ion takes no part in the reaction, both ferric and ferrous salts hydrolyze to a considerable extent. It is veiy difficult to get an estimate of the extent of this hydrolysis, due to the tendency of ferric hydroxide to form col­ loidal suspensions instead of precipitating out of solution. Ferric hydroxide may be precipitated quantitatively from solutions with a pH as low as 3.

It was therefore felt that acid sufficient

in quantity to prevent hydrolysis and subsequent depletion of the ferric and ferrous concentrations could also be expected to be sufficient in quantity to cause considerable salt effect.

How­

ever, using dilute solutions, it was found that the addition of a small amount of acid was sufficient to depress the hydrolysis as measured by the observed reaction rates.

Further increases of

acidity above this showed the dependence of rate upon acid to be so slight that above the minimum acid concentrations wide vari­ ations produced only effects upon reaction rate of the order of magnitude of experimental error. Therefore, stock solutions of ferrous and ferric sulfates were made with enough acid to inhibit hydrolysis, as determined by optical inspection, and on dilution of aliquot portions to form reacting solutions, 4- cc of concentrated sulfuric acid were added to 500 cc of solution. The accompanying Figure 7 and Table VII illustrate the ef­ fect of addition of acid upon rate.

-21-

TABLE VII Rate VerBus Acidity

!C3xRate

Normality of Acid

0.172 0.188

0.0037 0.0096

0.220

0.241

0.209 0.225 0.209 0.214 0.209 0.204 0.230

0.0313 0.0313 0.0386 0.0453 0.0530 0.0675 0.105

0.220

0.112

0.220 0.204

0.294 0.294

i«i Fe

Cone

0.005 H

-22-

,, Fe** Cone 0

^

, Ae 0

Cone M

0.30 Figure 7

Rate versus Acidity

0.20

0.10

02 0.00

30 Normality of HaS0*

King compared the rates of dissol­ ution of zinc pipe in HCl with the rate of convection toward the

10

wall found by Fage and Townend

in their ultramicroscopic studies

of the motion of colloidal particles flowing through pipes.

The

rate of dissolution was found to be much greater than the rate of convection, suggesting that the effect of stirring is to decrease the thickness of the diffusion layer but that the final step in transport of material to the surface is a diffusion through a con­ centration gradient.

Therefore, Roller's equation for chemically-

controlled dissolution rates was found to be based upon a false premise. 13 Also in 1939 F. V. Durdin suggested a theory of dissolution whereby the rate is either the slower of two simultaneous processes, discharge of an electron (cathodic) or emission of an ion (anodic) or is diffusion controlled.

Unfortunately, the article is in

Russian and so the details of the theory have not been checked. In 194-0 Kimball,^- postulating an adsorbed layer of ions on the surface and a saturated layer next to the surface, derived an

-u-

equation for rate of solution in which the rate depended on the potential difference between the electrode and the solution and the effect of stirring on rate could be expressed as ks/(l / Ks) where k and K are constants and s is the stirring rate in rpms. As shown previously, the first of these predictions is in error and on examination of the rate versus stirring speed curve shows that the second is also in error. 16

Amis

in 194-8 postulated a mechanism for adsorption of re­

agent on the surface of a solid, derived an equation fir reaction rates in terms of concentration of materials at the interface and number of active sites covered and uncovered.

His equation applies

only to heterogeneous catalysis in solutions.

However, the method

he used is similar to that used here, which was independently ar­ rived at. Currently, the diffusion theory is accepted generally as giving the explanation of diffusion controlled heterogeneous re­ actions.

There has been offered no satisfactory theoiy for non-dif­

fusion controlled reactions, which are of greater interest in that they alone can give insight into the actual mechanism of reaction. Additional work on special aspects of the theory centered mainly around the effect of stirring and diffusion coefficient.

For outside

stirring with the metal fixed in position, Nemst and Merriam^ and 18 Brunner noted that the rate varied with the 0.8th power of stirring speed.

6

King and Braverman

found that for a rotating

cylinder, the diffusion controlled rate was linear with stirring speed.

-4-5-

.Kimball, as noted above, suggested that the effect of stirring could be expressed as rate equals ks/ 1 / Ks. tigators

19

*

20

*

21

Numerous inves-

attempted to find a stirring speed which would

completely dissipate the diffusion layer and cause the reaction to be completely chemically controlled, but have either been un­ able to do so or have been shown to be in e

r

r

o

r

.

^

26 As for diffusion coefficients, King and Cathcart found in the study of magnesium dissolving in acids that the rate was ap­ proximately proportional to the diffusion coefficient.

Inves­

tigators examining other reactions found the power to be anywhere 29 between 0.7 and 0.8,

with theoretical equations being derived 27 25 and giving powers of 3/A and 2/3. Also, attempts have been 26, 28 made to correlate rates of dissolution with rates of heat transfer.

It is now accepted that the dissolution rate in dif­

fusion controlled reactions is a fractional power (about 0.75), of the diffusion coefficient in the given solution. The dissolution rates of different crystal faces has been well studied and it has been shown that in diffusion controlled reactions 31 different crystal faces show the same rates, while in chemically controlled reactions different faces show markedly different 32, 33 rates. Not much work has been done on study of specific effects of sup34 posedly neutral ions, but King and Weidehammer found that copper dissolved in Fe Cl- much faster than in Fe (N0„1. King and

^

21 Abramson

found a variety of effects on rate of dissolution of

-46-

iron in acids on addition of differing neutral anions. Giacobe

35

Butts and

found silver dissolved slower in ferric nitrate than in

ferric sulfate.

Effects of different anions have been noted in 3b 37 38 39 40 studies of cadmium, iron, lead, magnesium and zinc. Also, Mouquin and Steitz^ have suggested that the rate of dis­ solution of metal in acid could depend on the charge on the metal. Specific work on silver has been done only by a few inves­ tigators. Giacobe.

35

of workers.

Semi-quantitative studies were done by Butts and The equilibrium constants were determined by a variety And, of course, Van Name and Hill were the first to

point out that dissolution of silver in ferric sulfate was not dif­ fusion controlled.

Discussion of Results and Formulation __________ of Reaction Mechanism. In the light of the above-mentioned experimental observations, the following conclusions have been reached,

(l) The dissolution

of a silver cylinder in ferric-ferrous systems at 30*C and 304 per second

centimeters^peripheral speed is diffusion controlled only in the absence of reaction products and at concentrations of ferric ion below 0.01 g-ion/liter.

(2) Increased stirring speed increases the

fraction of chemical control.

(3) This fraction of

chemical con­

trol is due to two factors: the backward reaction and adsorption of all three species of ion present upon the surface of the silver. Taking the above-mentioned points one by one, Figure 9 (Rate versus Ferric Concentration) shows that at low concentrations the

-47-

rate is indeed that of a diffusion controlled reaction.

At higher

concentrations the curve has increasing deviations from the straight line representative of diffusion control. concentrations of ferric

Also, at all

ion, the rate falls below the diffusion

controlled rate on addition of reaction product, as shown in Figures 10 and 11. That there is a backward reaction is attested to by the form­ ation of silver crystals on adding excess ferrous ion to silver ion.

Also, on placing the cylinder in an equilibrium mixture of

all four reagents, it gained in weight, indicating a dynamic equi­ librium with dissolution of small crystals and reprecipitation of silver out onto the cylinder. The evidence for the importance of adsorption is as follows. Addition of either silver or ferrous ions in the absence of the other reaction product lowered the dissolution rate.

This lower­

ing of the observed rate could not be due to a backward reaction since that would require the presence of both of the reacting ions in appreciable concentration.

Therefore, the rate lowering must

have been the result of either adsorption with a corresponding diminution of reacting surface, or diminished activity of reagent. Changes in activity depend on changes in ionic strength, and, as shown in Figure 8 , the influence of ionic strength is not sufficient to account for the decrease in rate on addition of either the silver or the ferrous ions.

Also, if the rate lowering depended exclusively

on the backward reaction, the rate should depend on the product of

silver ion and ferrous ion. case.

As shown in Figure 9, this is not the

Therefore, adsorption must be taken into consideration. Considering then the reaction as involving three consecutive

processes, namely transport to, reaction at and removal, from the surface, for both forward and backward reactions, this then is the picture which emerges. Parts of the surface are covered with either silver, ferric or ferrous ions and parts are bare.

Each species is adsorbed at a rate

depending on its concentration in solution and is desorbed at a definite rate depending on the temperature.

For the forward re­

action to occur, the ferric ion must strike a free silver atom. For the backward reaction to occur, the ferrous ion must strike an adsorbed silver ion, since any silver

atoms

produced must be

formed on the surface to add to the weight of the cylinder.

If a

silver ion were to strike an adsorbed ferrous ion and react, the silver atom would be formed one ionic diameter away from the surface and would not adhere, thus playing no part in the weight changes of the cylinder, and thus in the measured dissolution rate. Taking the three species of ion one at a time, ferric ion strikes the surface and either reacts immediately or is adsorbed and then desorbed at a rate depending on the surface covered and the number of collisions with solvent particles.

Ferrous ion is pro­

duced at the surface by adsorption of ions diffusing in from the interior of the solution.

Adsorbed ferrous ion is not produced by

the reaction of ferric ion at the surface since in this case the

-49-

newly formed ferrous ion has a silver ion between it and the surface. Ferrous ion is removed from the surface by desorption.

Silver ion

is formed at the surface by react!jn of ferric ion and silver, and by silver ions adsorbed on the surface from the interior of the solution.

It is removed from the surface by either desorption and

diffusion away or by being struck by a ferrous ion and being trans­ formed back into silver metal. In the above statement that ferric ion on striking the surface is either adsorbed or reacts is the implied statement that the ac­ tual chemical reaction, the transfer of an electron, is much more rapid than the adsorption-desorption process. reasons for making this statement.

There are two

The first is that the transfer

of an electron involves a small and rapidly moving particle and should therefore be more rapid

than the motions of an ion.

The

second is that when adsorption is at a minimum, which is when there is no reaction product initially in solution, and therefore the rate of desorption is at a maximum, and when there is no backward reaction, the observed rate curve still deviates from the straight line of diffusion control. Another way of explaining the situation is by means of the following diagram.

-50-

Figure 14

Adsorbed Activated Complex

Adsorl ed Reagent

> r.

Adsorbed Product

Ex Ea Ea E« E* E6

* + * • + *

Energy of adsorption of reagent Ex * Energy of Reaction Energy of reaction from adsorbed reagent to adsorbed product Energy of activation for forward reaction Ee * Energy of activation of adsorbed reagent Energy of desorption of product

It is seen in the diagram that of the ferric ions striking the surface, some have the energy for reaction, others for ad­ sorption.

The ones that do not have energy for reaction will

remain on the surface

until they pick up the en-.rgy for desorption

or reaction by inelastic collision with solvent particles, ferrous and silver ions and other ferric ions.

This will occur at a con­

stant rate at a given temperature and stirring speed.

Therefore,

we will be justified in saying that the desorption rate of ferric

2 ion equals Kq_9i where K]_ is the rate per cm

of surface covered

by ferric ion, and 9-j_ is the actual surface covered. The ferric ions that have energy sufficient for reaction will pass the energy barrier and form reaction productj the ferrous ion formed passing out into the solution with all or part of the kinetic energy and the silver ion being adsorbed on the surface.

Some silver

ion may leave the surface, also, depending on the energy of the par­ ticular ferric ion that initiated the reaction} but a large fraction will remain behind where the energy for desorption is picked up by means of inelastic collisions with ferric and silver ions and sol­ vent molecules, the rate being constant at a constant temperature, and stirring speed. When the rate of formation of silver ions is slow, the activa­ tion for desorption will occur at a rapid enough rate so that the surface is kept clear.

When the rate of arrival of ferric ions is

rapid, the surface will become clogged with silver ions and slow up the reaction even in the absence of initial ferrous and silver ions.

-52-

In the case of reactions that are diffusion controlled over all concentrations, E^, the energy difference between adsorbed reagent and adsorbed product is so great that desorption occurs immediately, or rather, all of the metal ions formed have sufficient energy for immediate desorption.

The surface is therefore kept

clear.

Derivation of Rate Equation Keeping the above picture in mind, we shall now derive a rate equation embodying all factors, with one further assumption.

The

extent of the adsorption of ferric ion shall be small in comparison to that of silver and ferrous ion.

This is justified on the basis

that silver ion will be most strongly adsorbed since there is little distinction between a silver ion on the surface and one in the in­ terior of the metal.

The silver cylinder, thus having much of its

surface covered by positively charged silver ions will then repell other positive particles, the force of the repulsion increasing with the magnitude of the positive charge.

Also, most of the ferric ion

that strikes the bare surface will react while the ferrous ion will merely be adsorbed, especially since at low ferric concentrations Fe'W’ ions react as fast as they arrive. To recapitulate, the forward reaction occurs when a ferric ion strikes the uncovered surface, the backward reaction occurs when a ferrous ion strikes an adsorbed silver ion, and the adsorption of

-53-

is

ferric ion^small in comparison to that of the other two.

Also, the

number of impacts of an ion upon the metal is proportional to its concentration in solution.

Let C^, C2 , and

refer to the concentration of Fe't"^, Ag^and

Fe++, in solution, respectively.

0 is the fraction of surface cov­

ered by adsorbed ions,

®3 are

fractions covered by

Fe’^ ’, Ag^ and F e ^ respectively. The rate of adsorption of an ion x is therefore Ax Cx (1-0) where Ax is fraction of ions with energy sufficient for adsorption and (1-0) is fraction of uncovered surface. The rate of desorption is Kx 0% . (1)

Ai

(1-0) =

0i + Rate of Reaction - Ki 0i + R.

This is true since Fe'H'+is used up by the reaction, or, more hit the surface than leave. (2)

Ag C2 (1-0) - K 2 ©2 -

since silver ion is produced by the

reaction, more leaving the surface than striking it. (3)

A^ C3 (1-0) =

03 , since adsorbed Fetf is neither used up

or produced by the reaction. (4 ) Since 0^ is much smaller than 62 and0^, let © = Therefore (5) Rate -

Ci (1-0) -

of adsorbed Fe+44 that react and

C3 02, where

for ©2 in (5), get

(6) R = K1 (1-0) Cx - K11 C 3 (a2 fe . t1"6! + (

is fraction

is fraction of Fe44 ions

striking adsorbed Ag+ that react. Substituting

+ 0^.

k2

-54-

| ) k 2)

Now, from (4), 9 = 02 + 63. Substitute values of 02 + 63 from (2) and (3) and get (7)

0

=

A2 C2 (1-6) +

R

k2

-

(1-0)

+

A3 C3 (1-0)

k2

( A2 C2

+

k3

A3 C3 ) +

(

R

K3 )

Therefore, (8) (1-0) = 1 - (1-0) (A2 c2 * (

=

A3 c3

k2

k3

R )

k2

1 - R K2____________ , +

A2 C2 K2

+

A3 °3

Inserting this value in (6), and solving, get (9)

R ( 1 + K11 Co) - (K1 Co - K11 C2 Con (

*2

>

(

K2

jl - r2 _____

J

[l +

AgCg I

\ A

k2

^

J

k3

Cross multiplying and factoring, etc (10)

R

= ( K1 Ci - K11 A2 C2 C 3 )

i_______*2___}_____________ _ ( 1 + K1 C1 (

+ A2 C2

k2

k2

+ K11 C3

+

k2

A3 C3

+

K11A3 C32)

k3

k 2 k3

)

Combining all constants, get the final form (11) Rate = %

CFejjj.

- K2

1 + K3 °Fe+++

+

CAg^.__________________ K4 CAg++

+ K5 CFe44

+ K6

C Fe++

This is the final form the equation takes and is the one which will be tested. Other initial assumptions are the following: (1) Assuming no adsorption of Fe+44 we get the same result. (2) Assuming Fe+++ adsorption is appreciable, we get two additional

-55-

terms in the denominator. *7 CFe++ CAg+ (3)

and K8 CF e*H CFe-f+

Assuming backward reactions due to Ag+ striking Fe-f-f, we get the

^7 ^Fe++ ^Ag+ ^erm

"^e denominator.

Therefore, if the equation 11 is obeyed by the experimental data, the assumption may be considered as valid..

-56-

CHAPTER III Applications of Equation

Variation of Rates with Concentration

1 . Rates in absence of ferrous and silver ion. When there is no reaction product present, the equation becomes simply, rate ions.

/ (l / k^Cj) where C

= concentration of F e ^ ^

This is the equation of a line that starts out as a straight

line with a positive slope, then falls off and eventually becomes a horizontal line.

According to this, when

is small in com­

parison to 1, the curve is a straight line of slope k^.

When C^

increases until 1 is negligible in comparison to k^C^, the curve flattens out at a value of k^/k^. The best test for the agreement of the data with this equation is to plot l/rate against the reciprocal of the concentration. equation for this is l/R = (l/k^) (l/C-^) -/ k^/k^. straight line.

The

This is a

Table XV and Figure 15 show that the reciprocal of

the observed rate when plotted against the concentration of ferric ion actually gives a straight line, which may be solved to give the two constants k^ and k^, by the method of least squares.

-57-

4

TABLE XV 1/Rate Versus 1/Ferric Concentration 1/Ct

1/Rate (obs) 108

200 100 50

'

25 20 16.6 12.5 10.0

2.

A.63 2.27 1.37 0.833 0.730 0.680 0.578 0.A90

h.

h.

04.33

13.5

1/Rate (Calc) 108

Difference 108

A-60

0.03 0.15

2.42 1.38 0.822 0.715 0.6A2 0.555 0.502

0.01 0.011 0.015 0.038 0.02 3 0.012 a.d 0.036 or ■U%

Rates in absence of ferrous ion, with ferric ion constant

with varying amounts of silver ion. If the ferric ion is held constant and the ferrous ion is initially equal to zero, the rate becomes equal to k^C-j/ (1 / ^3^1 / k^j) or ka/(kb / k^Cg) where C2 equals concentration of silver ions. This is seen by inspection to be a curve of decreasing value, level­ ing off to zero as C£ becomes infinite. A test for this equation would be to take the reciprocal of the rate and plot it against the C2 .

Taking the reciprocal it is seen

that l/Rate =■ k^/ka / k^C^Aaj which is a straight line.

-58-

5

r

j

Figure lb . l/Rate versus l/Pe

l/pe+"t+

^EJters/ g-ion

Concentration

200

Table XVI and Figure 1

show that this is actually the case.

Solving the straight line, by the least squares formula, gives the value for K^.

TABLE XVI l/Rate Versus Silver Ion Concentration l/Rate

Co

108 o.833 0 /Vl 0.84.30.001 ' 0.917 0.004 0.962 0.006 1.08 0.010 1.40 0.020

k>

0433

13.5

Ci

40

0.04

l/Rate (calc)

108 0.825 0.84.5 0.908 0.952 1.04 1.25

Difference

ISB 0.008 0.002 0.009 0.010 0.04 0.15 a.d. = 0.036 or %

-

(p o

•»

1.5

Figure 16

l/Rate versus

Ag+ Concentration

1.0

0.5

0.0 Ag+

0.010 g-1 / liter

_

(ml

0.020

3.

Rates in absence of silver ion, with ferric ion constant,

and varying amounts of If the ferric ion

added ferrous ions. is held constant in the absence of Bilver ion,

the equation becomes,

Rate = where

/ (1 /

/ k5C3 / k^Cj )

or k&/ (kfc / k ^ y ^ k^c| )

is the concentration of ferrous ion.

This is also the equation

of a curve decreasing as the concentration of ferrous ion increases and approaching zero at infinite concentration. The constants for

this equation may be

evaluated by again plot­

ting

the reciprocal of the rate against the concentration. This 2 gives a parabola of type y = ax / bx . Table and Figure 17 show that this type of equation is obeyed and from it the values of k^ and k^ may be obtained. TABLE XVII l/Rate Versus Ferrous Ion Concentration kn

l/Rate 108

0.562 0.640 0.776 0.902

1.04 1.03 1.17 1.26 1.50 1.54

0.00 0.0203 0.0432 0.063b 0.0835 0.0838 0.0950 0.121 0.139 0.149

O H 33

kc; 13.5

}£5_ 20.8

kh

24.2

l/Rate (calc) 108

0.567 0.661 0.810 0.936 1.07 1.07 1.14 1.32

1.40 1.53

Difference 103

0.005 0.021 0.034 0.034 0.03 0.01 0.03 0.06 0.10 0.01 a.d. - 0.03 or 3%

-62-

2.0 Figure 17

l/Rate versus Fe++ Concentration

1.5

1.0

0.5

0.0 .

Fe

++

°*05

0.10

0.15

g-i / liter « 4

4.. Rate in the Presence of All Three Ions. From the equation it is seen that since there is a square term in the denominator involving the concentration of ferrous ion, even where the product of silver and ferrous ions remain the same, the observed rate will be lower the higher the ferrous concentration. From the above derived constants, on finally substituting all values into the equation, the value of done below in Table XVIII.

may be obtained.

This is

It will be noticed that there is a

greater percentage of error in this constant than in the others. This is true because all the errors are being lumped together here, and, also, the final expression has a different quantity in the numerator and so the percentage of error should be higher.

Never­

theless, it should be noted that the a.d. is 5% and in only four cases out of twenty-one is there a deviation greater than 10% and these occur in places where a small deviation has a high percentage error.

This is excellent agreement, considering the high experimental

error and the error involved in determining six constants. Perhaps another way of estimating the accuracy of this equation o

is to consider the absolute error.

This amounts to 0.03 m-gm/min-cm 2

area

or, for a two minute run with a cylinder of 10 crn^, about 0.6 m-grn. • This is within the limit of experimental error and, if one value, marked with an asterisk, be removed, as is permissible, the average error becomes equal to the experimental error.

Considering that this

is an equation involving six experimentally determined constants and applies to a reaction with thirteen parameters, with some seven of

them experimentally variable, this is excellent agreement. convin6ingj

Even moreA perhaps, than the indirect evidence used to support the postulates of the derivation, is this fact that the results ob­ tained by using the equation obtained on the basis of these postulates are in agreement with observed rates.

-65-

TABLE XVIII Rates in Presence of All. Three Ions Cx

C2

C3

0 .00191'*! 0.02 n 0.00^23 0.00574

0.00850 0.0127 0.0144 0.0169 0.00182* 0.04 0.00396 0.00600 0.0100 0.0120 0.014 0.015 0.016 0.002

0.004 0.006 0.008 0.010

0.06

1CS^iate fobs) lO&Rate (Calc)

DiffereneeilOS 0.06

0.93 0.828 0.710 0.617 0.495 O .446 0.395 0.790 0.645 0.498 0.289 0.263 0.150 0.148 0.061

0.875 0.778 0.722 0.626 0.499 0.454 0.388 0.680 0.574 0.480 0.310 0.232 0.159 0.156 0.089

0.009 0.004 0.008 O'.007 0.110 * 0.071 0.018 0.021 0.031 0.009 0.008 0.028

0.500 0.423 0.286 0.172 0.109

0.531 0.419 0.312 0.172 0.114

0.031 0.004 0.026 0.038 0.005

0.050 0.012

a.d. or

0.03 7%

Variation of Rates with Stirring Speed Where the rate is diffusion controlled, the first effect of increase in stirring speed is to decrease the extent of the dif­ fusion zone and therefore increase the rate of reaction.

This is

roughly equivalent to an increase in concentration. Where the rate is not diffusion controlled, the rate of arrival of ferric particles is increased and the rate of departure of silver and ferrous particles is increased.

Therefore, although the dif­

fusion gradient is less under these conditions and the effect of

-66-

stirring could be expected to be slight, there will nevertheless be some increase of rate with stirring all the way down to equil­ ibrium. It was noted that the observed rate fell off as stirring speed increased past 8000 rpms.

This it is felt is due to cavitation

which could not be completely avoided.

The Effect of Temperature An increase in temperature increases the rate of diffusion to anddesorption from the surface, due to both increased kinetic energies of all particles and to increased numbers of impacts. In the case of diffusion controlled reactions the only effect is to increase the rate of diffusion toward the surface.

In the

case of non-diffusion controlled reactions, however, the effect is far greater, since the positive term in the numerator is increasing and the negative term is decreasing, due to more rapid desorption. It must be emphasized that there is no immediately apparent way of plotting rates to arrive at activation energies.

Effect of Anions The above equation was derived from considerations of the rates in the sulfate system and strictly speaking applies only to this system.

However, consideration of the overall process here furnishes

the clue to the difference between anion systems. In the nitrate and perchlorate systems, there is sufficient acid to prevent hydrolysis and the anion does not form complexes.

-67-

Consequently, the ferric ion is a hydrated triply positive ion.

In

the sulfate and chloride systems, the anions form negatively charged complexes.

Since the surface of the silver is partially covered

with positive ferrous and silver ion, the positively charged par­ ticles are repelled, while the negatively charged complexes are not. This accounts for the difference in rates and also for the fact that in the case of the nitrate and perchloric systems with no initial ferrous or silver ion in solution, the rate is much higher but as the reaction proceeds the rate falls off very rapidly.

This last

is explained by the formation, as the reaction proceeds, of an ad­ sorbed layer of positive ions, rapidly building up a charge and ef­ fectively slowing down the rate.

The negatively charged complexes

are not influenced by this increase in positive charge of the cylinder.

Variation of Rate with EMF Between Cylinder and Solution In diffusion controlled reactions, the rate is observed to be independent of the IMF between cylinder and solution.

This is to be

expected since under these conditions the particles react as rapidly as they arrive at the surface.

The rate determining step is the dif­

fusion to the surface upon which the EMF should have no effect. Another way of looking at the lack of correspondence between rate and EMF here is to state that since rate depends upon actual concen­ trations and EMF only upon the ratio of concentrations, where the concentrations are low, slight variations should affect the latter

-68-

much more than the former. In the nitrate and perchlorate systems, although the rate was lower, the EMF was higher. plexes.

The EMF depends

This was due to the formation of com­ upon the concentration of ferric ion,

while the rate depends upon the number of whatever reducible par­ ticles arrive at the surface. Increased stirring increased the rate and decreased the EMF, since the increased rate meant a greater number of silver ions im­ mediately adjacent to the surface, thus lowering the EMF. The correspondence of rate with EMF near equilibrium for fixed stirring speeds, area, and ferric-ferrous ratios is explained by the fact that the EMF depends upon the free energy of reaction. This equals the difference between heat of reaction and entropy of reaction.

If the latter remains constant, an increase in EMF

therefore increases the heat of reaction which increases the rate of desorption, and thus the reaction rate.

-69-

CHAPTER IV Summary

The parameters upon which the observed rate of reaction was found to depend were surface area, temperature, rotational speed, concentration of reagents and products, specific anion present, and, under certain conditions, concentration of acid, condition of surface and EMF between cylinder and solution. Consideration of the effects of the above parameters upon the rate give rise to the following mechanism of reaction.

The surface

of the silver is partially covered by all three ionic species.

When

ferric ion strikes bare surface it reacts to form ferrous ion and adsorbed silver ion.

When silver ion strikes the surface it is ad­

sorbed, but when it strikes a ferrous ion, nothing occurs.

When

ferrous ion strikes the surface it is adsorbed, but when it strikes a silver ion, a backward reaction occurs.

The observed rate of re­

action is the difference between a forward rate, dependent upon the concentration of ferric ions and the amount of uncovered surface, and a backward rate, dependent upon the concentration of ferrous ions and the amount of the surface covered by silver ions.

The rate of

the actual transfer of the electron is more rapid than any of the processes involving transport or movement of ions. Consideration of the above mechanism gives rise to the equation for rate at constant temperature and stirring speed, the rate being

-70-

expressed as

equivalent per square centimeter of surface per minute. A Rate = (klCFe+44 “ k2°Fe++cAg+) / ^

/

k3°FefH- ^ k4°Ag+ / k5cF e + H / k6°2Fe4-+ )

For the special case where the stirring speed is 4-000 rpm and the temperature is 30*0, the constants are as follows:

p

-433x10. liter/cm -min. = 13.5 liters/equiv. k^ - 20.8 liters/equiv.

2

2

k£ -.0233 liters /equiv-cm -min.

k^ - 40.0 liters/equiv. o o k^ = 24.2 liters /equiv.

The above equation shows the variation of rates with concentra­ tion over the whole range between diffusion control and chemical, control, almost to equilibrium. Equations have not been developed for the variations of rates with the other parameters, but it is felt that the postulated mechanism will qualitatively explain these. It is suggested that such a mechanism and perhaps a similar equation could be applied to other cases of dissolution of metals in oxidizing solutions.

-71-

BIBLIOGRAPHY

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14, 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

Noyes and V/hitney Nernst Brunner Van Name and Hill Van Name and Hill King and Braverman Moelwyn-Hughes Roller King Fage and Townend Kilpatrick and Rushton Kilpatrick and Rushton Durdin Kimball Kimball Amis Nernst and Merriam Brunner Centnerszwer and Heller V/ilderman King and Abramson King and Eroudy King and Burger King and Schwer King King and Cathcart King King and Ho'ffard King, Roehl and Kipness King and Schack

Z. Physik. Chem.

22

639

(1897)

Ibid. Ibid. Am. J. .Science, 4-th Series

42 42 22

52 56 543

(19C4) (1904) (1913)

42

3C7

(1916)

24

1744

(1932)

Ibid.

4th Series

J. Am. Chem, Soc,

,

Kinetics of Reactions in Solution Oxford Press (1934) J. Phys. Chem. 221 (1935) 25 J. Am. Chem. Soc. 828 (1935) 21 656 (1932) Proc. Roy. Soc. AI 35 J. Phys. Chem.

24

2180

(1930)

Ibid.

22

269

(1934)

Ser. Khim. Nauk J. Chem. Phys. Ibid. Kinetics of Chemical Change in Solution Z. Physik. Chem.

3 (1939) 4(40) 8 199 (194C) 8 815 (1940) Macf.iillen 276 (1949)

22

235

(1905)

42 A161

56 113

(1904) (1932)

Ibid. J. Am. Chem. Soc.

66 61

445 2290

(1909) (1939)

Ibid.

25

1375

(1937)

Trans. Electrchem. Soc.

6 2

403

(1934)

Ibid. Ibid.

F . Schwer, -Master1s Thesis, II.Y.U.

(1949)

Unpublished, Univ. Conf. Corrosion. J. Am. Chem. Soc. 25

63

(1947) (1937)

Trans. N.Y. Acad. Sci,, Series 2 10 Ind. Eng. Chem. 22

262 75

(1948) (1937)

J. Am. Chem. Soc,

62

284

(1941)

Ibid.

22

1212

(1935)

King and Trans. Electrochem. Soc. 219 11 Appleton Ibid. 32. Gwathmey and 211 77 Benton Z.'Krystallographie 33. Glauner and 80 ill Glocker J. Am. Chem. Soc. 34-. King and 602 18 Weidehamner Chem. Met. Eng. 35. Butts and £8 76 Giacobe 36. Soaerberg Trans. Electrochem. Soc. 62 39 37. Bauer, Krohnke Die Korrosion Metalischer iVerkstoffe , Vol I and Masing 38. Aneregg and Purdue University Exp. Sta. Bull, lo Achatz 39. Uhlig Corrosion handbook John Y/iley & sons, 40. Friend and J. Inst. Met. 177 21 Tidmus *3s King and 574 2k Violton 42. Koyes and Ibid. 1016 21 Brann ASPRP Sixth Report, Kat. Bur. Stand • 43. ^e Lier chi and Fink 44. King and Reass Unpublished 45. Pittsburgh International Conference on Surface Reactions, Corrosion Publishing Co, Pittsburg, Pa 31.

47.

67

LIBRARZ 0? ■It I0RK UHITSRSIJI IIHITIRSITT MTIOHTa

t

■S3?

(1940) (1940) (1931) (1936) (1941) (1932) 241 (1924) (1948) (1924) /i r~\ » \ c x 94 t 9

(1912) (1942)

(1948)