The solubility and diffusion coefficient of oxygen in potassium hydroxide solutions

Electrochimica Acta, 1967, Vol. 12. pp. 287 to 297. Pergamon Press Ltd. Printed in Northern Ireland

THE SOLUBILITY A N D D I F F U S I O N COEFFICIENT OF O X Y G E N IN POTASSIUM H Y D R O X I D E SOLUTIONS* R . E. DAVIS, G . L. HORVATH a n d C. W . TOBIAS Department of Chemical Engineering, University of California, Berkeley, California, U.S.A. Abstract--The solubility of oxygen in aqueous K O H solutions has been measured by a Van Slyke apparatus and by an adsorption technique developed by Hildebrand. In the range of concentration of K O H between 0 and 12 N, at 25°C, the two methods yielded identical results; at 760 torr oxygen partial pressure, log S = log 1.26 × 10-a -- 0.1746 C, where 0.1746 is the solubility coefficient, S the concentration of oxygen, g-mol/l, and C the concentration of KOH, g-mol/l. Between 0° and 60°C both the solubility and the solubility coefficient decrease with increasing temperature. Diffusion coefficients of oxygen in aqueous K O H were evaluated from the limiting current of oxygen on a rotating disk electrode, and also by a stagnant tube technique similar to that used by yon Stackelberg. The diffusivity drops sharply with increasing K O H concentration, and increases with temperature. At 25°C and for K O H concentrations between 2 and 4 N, the product of the diffusivity and the viscosity is constant: D/z ---- 1.3 × 10-7 g.cm/sL where D is the diffusivity, eroS/s, and ~ is the viscosity in poise. At 60°C and for 1 < N K O H < 8, the value of this product is D/~ = 1-9 x 10-7 g.cm/s ~. R6sum6--La solubilit6 de l'oxyg6ne darts les solutions aqueuses do K O H a 6t6 mesur6c au moycn d'un appareilVan Slyke et par une technique d'adsorption d6velopp6¢ par Hildebrand. Darts l'intervalle de concentration de K O H entre 0 et 12 N,/~ 25°C, les deux m6thodes ont donn6 des r6sultats identiques; /t 760 tort de pression partieUe d'oxyg6ne, log S = log 1,26 × 10 -3 -- 0,1746 C, oil 0,1746 est le coefficient de solubilit6, S la concentration d'oxyg6ne en mol/l et C la concentration de K O H en mol/l. Entre 0 ° et 60°C conjointement la solubilit6 et le coefficient de solubilit6 d6croisse avee l'augmentation de la temp6rature. Les coefficients de diffusion de l'oxyg6ne dans KOH, Aq ont 6t6 6valu6s d'apr6s le courant-limite d'oxyg6ne sur une 61ectrode/L disque tournant et aussi au moyen d'une technique/t tube statique similaire/~ eelle employ6e par yon Stackelberg. La diffusibilit6 tombe brutalement quand croit la concentration en K O H et augmente avec la temp6rature. A 25°C et pour des concentrations en K O H comprises entre 2 et 4 N, le produit de la diffusibilit6 par la viscosit6 est constant: D/~ = 1,3 X 10-~ g.cm/sL oi~ D est la diffusibilit6 en crn2/s et ~ la viscosit6 en poise. A 60°C et pour des concentrations en K O H comprises entre 1 et 8, la valeur de ce produit est D# = 1,9 × 10 -¢ g.cm/s s. Zusammenfassung--Die LOslichkeit von Sauerstoff in wasserigcr Kalilauge wurde nach Van Slyke und mitteis einer Adsorptionsmethodc nach Hildebrand bestimmt. Im Konzentrationsbereich yon 0 bis 12 N K O H ergcben beide Methoden iibercinstimmcnde Resultatc; bci 25°C und 760 torr Sauerstoffpartialdruck ist log S = log 1,26 × 10 -3 -- 0,1746 C wobei S = Sauerstoffkonzentration in g-reel/l, C = Konzentration der K O H in g-reel/l, 0,1746 L6slichkcitskoeffizient. Zwischcn 0 und 60°C nehmen sowohl die LSslichkeit des Sauerstoffs als auch dcr LSslichkeitskoeffizient mit steigendcr Temperatur ab. * Manuscript received 27 May 1965; in revised form 31 May 1966. 287

288

R.E. DAVIS, G. L. HORVATHand C. W. TOBIAS

Der Diffusionskoeffizientvon Sauerstoff in wiisseriger KOH wurde durch Messung des Grenzstromes der Sauerstoffreduktion sowohl an einer rotierenden Scheibenelektrode als auch nach der Methode von Cottrell/von Stackelberg ermittelt. Der Diffusionskoeffizientnimmt mit zunehmender KOH-Konzentration stark ab, erhSht sich jedoch mit steigender Temperatur. Bei 25°C und einer KOH-Konzentration zwischen 2 und 4 N, ist das Produkt aus Diffusionskoeflizient D (cm=/s) und Viskositiit # (poise) konstant: D# = 1,3 × 10-7 g.cm/ss Bei 60°C und KOH-Konzentrationen zwischen 1 bis 8 N ergibt sich das Produkt zu D/~ = 1,9.10 -~ g.cm]s~. INTRODUCTION THE dynamic behaviour of gas electrodes is strongly dependent on the solubility and diffusion coefficient of the reacting gas. Since these properties greatly influence transport processes, they should be known with a reasonable degree of accuracy over a wide range of tempertures and electrolyte concentrations. Of particular interest is the case of oxygen in aqueous potassium hydroxide solutions. The solubility of oxygen in distilled water has been determined by many workers, t and it is now generally agreed that the value at 25°C is 1.26 × 10-a molfl* 4- 1%. At the inception of the present investigation, the meagre published data on the solubility of oxygen in aqueous K O H 2-3 covered only the lower range of concentration, and even in this range the discrepancies between values reported by Geffckenz on one hand and by Pospigil and LuSh# 4 on the other, defy rational explanation. The solubility data reported quite recently by Knaster and Apel'baum, 5 and those by Walker et al, s for lower K O H concentrations, confirm Geffcken's values, but the two sets differ noticeably at higher concentrations. In this work the bulk of solubility measurements were made by the Van Slyke manometric technique. 7 These measurements involved the boiling off of the dissolved oxygen into a calibrated volume at known pressure. In view of the severe disagreement found between the solubilities obtained by this method and those reported recently by Pospigil and Lu~.n3~, an independent set of measurements was made employing the absorption principle and using the apparatus and technique developed by Kabatake and Hildebrand. s For the diffusivity of oxygen in pure water at 25°C, values ranging from 1.8 to 2.6 × 10-5 cmZ/s have been reported. 9'1° No data on the diffusivity of oxygen in aqueous K O H were found in the literature.l" In this work the experimental methods chosen for determining the diffusion coefficient of oxygen involved the measurement of limiting currents of oxygen at a rotating disk electrode11 and (at concentration of K O H higher than 2 N) in a stagnant diffusion cell. 2° Both methods have the distinct advantage of not requiring the application of empirical constants in the evaluation of the diffusivities from the rate data. SOLUBILITIES Experimental technique

Solutions were prepared from carefully degassed distilled water and reagent grade potassium hydroxide. Experiments were conducted in a constant temperature bath controlled to +0.2°C. 99.6 ~o pure oxygen was used in all measurements. * For an oxygen partial pressure of 760 torr. 1"Partial results of the investigations of Walker et al were reported 6 after the conclusion of our measurements.

Solubility and diffusion coefficient of O~ in KOHaq

289

The apparatus and experimental technique of both methods has been described in the literature. 7's However, the prodecure followed in saturating and degassing the solutions requires special attention. For the Van Slyke experiments, solutions were prepared by bubbling oxygen into the sample in a 250-ml Pyrex flask through a fritted glass tube for 15 min. The gas was presaturated with water vapour by first bubbling the oxygen through a solution of the same temperature and composition as the sample. After sparging for 15 min, and a 2-5 min period during which the bubbling was stopped and an oxygen blanket was maintained, the sample was withdrawn and analysed for oxygen content. Kabatake and Hildebrand s stated that the largest source of error in their experiments was the degassing process. Substantial improvement was made by the addition of a single stage vacuum distillation. For this purpose distilled water was frozen over K O H pellets under vacuum and the resulting solution boiled and cooled to 0°C under vacuum to ensure a gas-free sample. Supersaturation was believed to be a source of error la since the samples for the Van Slyke experiments were prepared by bubbling gas through the liquid. Experiments were conducted in which samples were taken from saturated liquid and the solubility determined as a function of time after sparglng was stopped. After 2-3 min, the solution had developed its equilibrium state and no change in the solubility could be detected within the limits of sensitivity of the Van Slyke apparatus. In addition, experiments were conducted in which the equilibrium solubility was attained by three different methods. The gas was sparged directly into the solution during the entire run for case 1. In case 2 oxygen was sparged into solution at 2°C. The solution temperature was then brought to 24°C and the sparging replaced with an oxygen blanket. For case 3, the degassed solvent was kept under an oxygen blanket and gently stirred with a magnetic bar. Typical results shown in Fig. 1 indicate that the standard 2"OxlO-a Jr~

I

I

I

I

1.8J--t °u

1.2

D

,.oYl I J

o,8 Jo/ 0

1 I0

I 20 Time,

1

I

30

40

50

h

FIG. 1. Saturation of distilled water as a function of time.

A, 02 spargcd through water at 24°C. [], Oi sparged through water at 2°C, at t = 0 sparging stopped, oxygen blanket maintained and temperature raised to 24°C. O, water provided with oxygen blanket, gently stirred.

290

R.E. DAvis, G. L. HORVATHand C. W. TOBIAS

saturation procedure followed in the Van Slyke runs was satisfactory and it was not necessary to employ more elaborate techniques. Livingston, Morgan, and Richardson 13 showed that the height of a short liquid column would have negligible effect on the solubility, especially when the liquid is agitated, as in the case of the Van Slyke experiments. Using Henry's law the data obtained in the present measurements were corrected to 760 torr oxygen partial pressure (from 760 torr total pressure) to allow comparison with results by others. The solubility of oxygen as well as numerous other gases in water follows Henry's law up to quite high pressures. 13 RESULTS

AND

DISCUSSIONS

The results of the Van Slyke experiments are presented in Fig. 2. This plot shows the variation of oxygen solubility as a function of potassium hydroxide concentration at a total pressure of 1 atm. Results obtained with the Hildebrand apparatus are

5x10-3L

I

t

I

1

i

I

(

760 T total pressure "~-O.o10-3~ cE" "~

6 0 ° C ~ ~

i 10_4

1°-~

0

2I

~ -'¢.',~'4I 6I 8I 10 12 Concentrationof KOH,tool/[

14

FIG. 2. Solubilities of oxygen in KOH at 0°C, 25°C and 60°C. Data points represent values obtained by Van Slyke method. plotted on Fig. 3 for 25°C. Included in the figure are data points reported by other investigators as well as results from the Van Slyke experiments corrected to a partial pressure of Oz of 760 torr. The line for 25°C in Fig. 3 corresponds to log S = log 1.26 × 10-3 -- 0.1746 C,

(1)

where S is the solubility of oxygen in g-mol/l and C the concentration of K O H in g-tool/1. The linear variation of the logarithm of oxygen concentration with K O H concentration is typical of the "salting out" of a non-electrolyte in an electrolyte solution. The vapour pressure of the solvent changes by 15 torr at 25°C over the range of K O H concentrations investigated; therefore, the partial pressure of the non-electrolyte is

Solubility and diffusion coefficientof 02 in KOH~q

291

very nearly constant. At 1 atm total pressure and at 0°C the difference in partial pressure of oxygen between dilute and concentrated K O H solutions is negligible, while at 60°C the change is in the order of 100 torr. For the Van Slyke apparatus, the sample volumes were measured with a maximum probable error of 4-1.0 per cent. The measurement of the gas volume and pressure introduces a probable error of 0.5 per cent with a maximum precision of 3 x 10-6 mol/1 of gas. The error in the absorption determinations was estimated to be less than I per cent for distilled water. 2 x 10 -3

l

I

I

1

I

I

10 -3

PO2 = 760 l"

!

E

o c o

10 -4

8 o U

10 -s 2

4

6

8

I0

12

Concentration of KOH, tool/{

FIG. 3. Comparison of oxygen solubility data from different sources. ~ , Geffcken, 1904. $7, Knaster and Apel'baum, 1963. A, Walker et al, 1964. O, present work, Van Slyke method. D, present work, absorption method. In comparing the results of the present investigation with those by Geffcken,2 Pospigil and Lu~n~, 4 Knaster and Apel'baum, 5 and Walker et aL e one notes the very good agreement in pure water and at low K O H concentrations. However, already at 4 N K O H the values reported by Pospigil and Lu~n~ are some 200 per cent higher than those obtained in this work. In the higher K O H concentration range, the data of Knaster and Apel'baum fall somewhat above the line represented by (1), although for 10 molal K O H the solubility reported by these workers coincides with the value so predicted. Walker et al predict a levelling off of solubility to a constant value in concentrated K O H solutions. Such behaviour has not been substantiated by the other investigators. In view of the fact that the solubility of oxygen drops by about a factor of 100 as the concentration of K O H is increased from 0 to 12 molal, the limitation of gasometric apparatus for determining the very small concentrations o f oxygen at the

292

R.E. DAVIS, G. L. HORVATHand C. W. TOaIAS

high K O H concentrations does not allow sharp conclusions. It seems, however, reasonable to suggest that the simple, semilogarithmic relation given by (1) represents the solubility behaviour of O8 in K O H solutions with an acceptable degree of accuracy. The theoretical explanation of the "salting out" of a non-electrolyte by an electrolyte has been attempted by several workers. ~4-1~ Assumptions must be made which cannot be expected to be valid over a wide range of salt concentration. With the exception of the theory of McDevit and Long ~ (which is based on the "internal pressure" of the solution), the assumption was made that the principal effect of the non-electrolyte is on the dielectric constant of the solution. By assuming that the dielectric constant is a linear function of the non-electrolyte concentration, a logarthmic"salting out" behaviour is predicted. None of the available theories offer sufficiently reliable methods by which the system parameters can be evaluated to allow quantitative interpretation of these data. The temperature variation of the parameters is even less precisely known. However, for most systems experimentally investigated, the slope of the logarithm of the concentration of non-electrolyte vs salt-concentration line decreases with increasing temperature. 17 DIFFUSION COEFFICIENT Experimental methods

The rotating disk electrode has been considered by Levichxs in detail. Newman 19 has provided a correction which eliminates the approximation of infinite Schmidt number in the Levich statement. Applying the correction suggested by Newman, the equation used for the limiting current density is into 0-6205 Sc-2/s nF Cbum Co1/~ v1/~ = 1 -k 0"298 Sc-x/a + 0.14514 Sc-2/z '

(2)

where n is the number of electrons transferred per molecule, into the limiting current density in A/cm z, F the Faraday in C, Cbulk the bulk concentration in mol/cm3, oJ the angular velocity in rad/s, v the kinematic viscosity in cm2/s, D the diffusion coefficient in cm2/s, and Sc the Schmidt number (v/D). For the experiments with the rotating disk, limiting currents were determined as a function of rotational speed. Diffusion coefficients were calculated using (2) and the plot of limiting current vs the square root of the angular velocity. The case of diffusion through a stagnant liquid has been the subject of investigations, among others by Stackelberg, ~° Laitinen and Kolthoff~1 and Lingane.22 Since the absence of natural convection is essential to this method, diffusion in a capillary pore to a fiat electrode is the most attractive geometry. If natural convection does not occur during constant potential operation, and if this potential is high enough, the concentration of the diffusing species eventually becomes zero at the electrode, where it is consumed. The diffusion equation ac a~c a-~ = D ax--q

(3)

293

Solubility and diffusion coefficient of Oz in KOI-I~q solved for the b o u n d a r y conditions representing our experimental condition, I, c = Cbulk at all x for t = 0 II, c = 0 atx=0 fort>0 III, C=Cbulk a t x = oo f o r t > 0 yields the solution

C b ' l)l ; I D i = nFD l ~ . = o - - n F.V/(zr

) .

(4)

Thus if diffusion is unidirectional and the electrode is operating at limiting current, the current should d r o p in p r o p o r t i o n to t -1/2. The correction for the finite length o f the pore is found to be negligible for time periods of several hours. I f a first order rate equation is assumed such that i = k C e l e e t r o d e exp (7) (5) where r/ is a constant, corresponding to a dimensionless overpotential, b o u n d a r y condition II becomes

i nFD ac ac C--kexp(~)k(e~-(n)p'~x ~=0 k ~x ~=0 a t x = 0 for t > 0.

II',

A typical solution of(3) with b o u n d a r y condition I I ' is plotted in Fig. 4. Although it is not essential that the electrode should be at limiting current when the circuit is closed, the potential should be high enough so that limiting condition is reached within a reasonable period of time. -~'~'~-~-~,,.~ --

C. . . . .

" ' ~ /

,ration at elec,rode = 0

Concentration

at e l e c t r o d e = K a~xl

< •-2

~

~

C o n c e n t r a t i o n at electrode = 1

"o

i

t.

U

I

1 0 -7

01

I I I t1111 1'0

I

I I I Iilii 10

I

I I I III 100

Time, rain FIG. 4. Current vs time for unidirectional diffusion to a fiat electrode. (Curves constructed for Cbuak = 4"5 X 10-8 mol/cm8, D = 6-2 × 10-s cm2/s, K = 6"5 × 10-8 cm.) F o r the stagnant diffusion cell, the current was measured as a function o f time and each experiment continued until the curve representing i vs t converged to a straight line with a slope o f - - 1 / 2 on a log/log plot. Diffusion coefficients were evaluated using (4) and the straight portion of the experimental curve. PROCEDURE Solutions were prepared f r o m degassed distilled water and reagent-grade potassium hydroxide. Saturation with 99.6 ~ pure oxygen was achieved by sparging the gas into

294

R.E. DAVIS, G. L. HORVATHand C. W. TOBIAS

the solution through a fritted glass tube for 15 min prior to making a determination. Bulk saturations with oxygen were confirmed by Van Slyke analysis. All experiments were carried out in a constant temperature bath controlled to 0.2°C. Electrodes for both disk and stagnant diffusion measurements were pretreated by cathodic evolution of hydrogen. The disk electrode assemblies employed in this study have been described elsewhere by Gordon, Newman and Tobias. m Platinum, silver, nickel, amalgamated silver and gold-plated copper were tried as working electrodes. Only silver and platinum yielded reproducible results. The counter electrode was a platinum screen. The diameters of the disk were 0-30 + 0.00015 in. The speed was varied from 900 rpm to 3600 rpm, measured with a stroboscopic tachometer. Current was provided by a Lambda Electronic Model 28 constant current supply and measured by means of the voltage drop across a calibrated precision resistor. Electrode potentials were measured relative to a saturated mercury/mercury-oxide reference electrode and recorded by a Bausch and Lomb V.O.M.5 recorder. Limiting currents were determined at 3--4 rotational speeds for each concentration investigated.

Diffu 1"5-n

olivet

vlw~tlvuw

FIG. 5. Schematic of stagnant diffusion cell. The cross section of the 1.5-ram capillary appears exaggerated. The stagnant diffusion cell is shown in Fig. 5. The working electrode and counterelectrode were silver. The diameter of the diffusion pore was 1.5 ~ 0.02 ram. Current and potential measurements were made in the same manner as the disk experiments with an accuracy of + 0 . 5 %. A constant potential between 1.0 and 1-2 V was applied for 15-30 min to the cell during each experiment. Before each measurement, fresh solution was drawn into the

295

Solubility and diffusion coefficientof O= in KOH=q

pore from the bulk and 5-10 min was allowed for the solution to become quiescent before the potential was applied. The viscosity of solutions at 25°C was taken from the data of Mcllhenny ~5 and from the data of a Solvay Technical Service Bulletin 26 for 60°C. RESULTS AND DISCUSSION The diffusion coefficient of oxygen for 25 and 60°C is plotted as a function of potassium hydroxide concentration in Figs. 6 and 7. By extrapolation, the value in water is estimated to be between 1-9 and 2.0 × 10-5 cm2/s at 25°C and between 4.6 and 4-8 × 10-s cm2/s at 60°C. 2.0

I

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1

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l

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I

1m6 Y ~

M e t h o d of m e a s u r e m e n t

°'F: u 1.2

OR

,~ Silver rotating disk o Platinum r o t a t i n g disk

NN3

-

0.8

0.4

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2

1

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6

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I

10

Concentration of KOH, mol/L Fro. 6. Diffusion coefficients of oxygen in aqueousKOH at 25°C.

" T h e diffusivity at 25°C compares well with values between 1-9 and 2.0 × 10-5 cm2/s reported by Himmelbau z7 and 2.12 × 10-ScmZ/s reported by Jordan e t al. 1° The difference in diffusivity values at 25 and 60°C correspond to an average temperature coet~cient of 2-4 ~o per °C. This compares well with the data summary by Millington. ~a The product of the diffusion coefficient and the viscosity, shown in Fig. 8, indicates that the decrease in viscosity with increasing temperature does not account for the variation of tbe diffusion coefficient with temperature. The rapid decrease of the product D# in dilute solutions was also reported by Jordan e t al. 10 This decline which occurs more rapidly at the higher temperature may be attributed to the breakdown of the "ice-like" structure of the pure solvent due to the presence of the electrolyte. It should be noted, however, that at K O H concentration higher than 2 M and 1 M at 25 and 60°C, respectively, the D/~ product remains constant within experimental accuracy: at

25°C: D# = 1.3 × 10-7 cm 2 poise/s;

for

2-8 M K O H

at

60°C: D# = 1-9 × 10-Tcm2poise/s;

for

1-4 M K O H .

With silver rotating disk electrodes in dilute K O H solutions, the activation overpotential was low and the limiting current plateau well defined. The overpotential

296 5.0

R.E.

D A w s , G. L. HORVATH and C. W . TOBIAS

I

I

I

l

~

I

I

[

I

4.0 E

u

~

O

All points

by stagnant-diffuslon

cell

. 3.0

t~

/ 0

T

1 2

I

I I I ~ 4 6 Concentration of KC)H, tool/L

I 8

I

lO

F l a . 7. Diffusion coefficients of oxygen in aqueous K O H at 60°C.

was found to increase with increasing KOH concentration and the limiting current plateau became less distinct, rendering measurements impossible beyond 2 M KOH. With platinum electrodes the overpotential was found to vary with time at a constant current and rotational speed. As the concentration of KOH was increased the variation with time became more pronounced. In addition, the potential depended not only on time but also on the previous current setting, as was also noted by Palous and Buvet. ~ 2.6

I

i

t

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l

o2.2 o.

<

60 °C

.~uE 1.8 0

x ~

1.l

25oC

L0

0

[

I 2

I

I I I I 4 6 Concentration of KOH, tool / L

I 8

[

10

F l a . 8. D e p e n d e n c e o f the D # product o n K O H concentration for oxygen at 25 ° and 60°C.

Solubility and diffusion coefficient of O, in KOH,~,I

297

The stagnant diffusion cell offered special advantages over other methods in w o r k with the oxygen electrode in the higher K O H concentration range. I n cases where high charge-transfer overpotential prevents determination o f limiting current densities in the forced convection regime, the low current densities o f the stagnant diffusion cell are preferable. In chronopotentiometric measurements, any current which is not due to diffusion o f the species under investigation will increase the transition time and thus the apparent diffusion coefficient will be incorrect. During the constant overpotential operation o f a stagnant diffusion cell such effects are n o t important as long as the concentration o f the diffusing species becomes zero at the electrode. Walker et al e have recently measured the diffusion coefficient for 02 in K O H solutions at 25°C by the polarographic technique. The diffusivity was evaluated with the use o f the modified f o r m o f the Ilkovic equation, which employs an empirical constant. The reported values are 10-20 per cent higher than those obtained in this laboratory. Since some uncertainty is reflected in the literature s regarding the correct value o f the constant, no critical comparison will be m a d e with the results o f this work. Acknowledgement--This work was supported by the Advanced Research Projects Agency through the U.S. Army Electronic Research Laboratories.

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.

REFERENCES E. DOUGLAS,J. phys. Chem. 68, 169 (1964). G. GEwcr~N, Z. phys. Chem. 49, 257 (1904). A. M. COMEY,Dictionary of Chemical Solubility, p. 637. Macmillan, New York (1921). J. PosPigm, and Z. Lu~,~q, Coll. Czech. chem. Commun. 25, 589 (1960). M. B. KNASXERand L. A. APEL'BAUM,Zh.fiz. Khim. 38, 120 (1964). R. WALKERJR. et al, Diamond Laboratories Quarterly Progress Report, Fuel Cells, UFC6-13, July-September (1964); J. electrochem. Soc. 112, 469-471 (1965). D. D. VAN SLYKEand J. M. NEmL, J. bioL Chem. 61, 523 (1924). Y. KABATAKEand J. H. HILDEBRAND,.Jr.phys. Chem. 65, 331 (1961). G. SEMERANO,L. RICEOmNEand A. FAFFANI,Gazz. chim. ital. 79, 395 (1949). J. JOROAN,E. ACI~ERMANand E. L. BERGER,J. Am. chem. Soc. 78, 2979 (1956). D. P. GREGORYand A. C. RrDDIFORr),J. chem. Soc. 3756 (1956). H. P. Cat)Y, H. M. ErSEY and E. V. BERGER,J. Am. chem. Soc. 44, 1456 (1922). J. LrVINGSTON,R. MORGANand A. H. RICHARDSON,J. phys. Chem. 34, 2356 (1930). P. I)EBYEand J. MACAULEY,Phys. Z. 26, 22 (1925). P. DEe,/E, Z. phys. Chem. 130, 56 (1927). J. G. KIRKWOOD,Chem. Rev. 24, 233 (1939). W. F. McDEvrr and F. A. LoNe, Chem. Rev. 51, 131 (1952). V. G. LEVXCH,Acta Phys.-chim. URSS 17, 257 (1942). J. NEWMAN,J.phys. Chem. 70, 1327 (1966). H. YONSTACKELBERG,M. PILGRAMand V. TOOM~,Z. Elektrochem. 57, 342 (1953). H. A. Larn~N and I. M. KOLXrIOLL,J. Am. chem. Soc. 61, 3344 (1939). J. J. L~GA~, Electroanalytical Chemistry, Chap. 22. Interscience, New York (1958). S. L. GORDON,J. S. NEWMANand C. W. TOBIAS,Ber. Bunsenges. phys. Chem. 70, 414 (1966). S. PALOUSand R. Buwx, Bull. chem. Soc. Fr. 1606, (1962). L. B. HrrcHcOCK and J. S. M¢ILHEt~', Ind. Engng. Chem. 27, 466 (1935). Caustic Potash, Solway Technical Service, Bulletin 15 (1960). D. M. HIMMELBAU,Diffusion of Gases in Aqueous Solutions. University of Texas, Austin (1963). MmLrt.~GTON,Science 122, 1090 (1955).