804
K. S. GURURAJA DOSS A S D H. P. AGARWAL
ROLE O F I S D I F F E R E S T ELECTROLYTES I S ELECTRODE KINETICS K . S. GURURAJA DOSS Indian Institute of Sugar Technology, Kanpur, India ASD
H. P.AGBRWAL
D . A . V . College, Kanpur, India Receiced July 18, 1949
d new and interesting method for studying the kinetics of electrode reactions has been worked out by Randles (2). The method is based on the application of an alternating potential of small amplitude to a microelectrode at which the relevant electrode reaction is in equilibrium. The microelectrode consists of a capillary dropping electrode similar to the polarographic electrode, except that a dilute amalgam of the metal under consideration replaces the mercury. The microelectrode is in contact with an aqueous solution containing an indifferent electrolyte like potassium nitrate, potassium bromide, etc. a t molar concentration (to avoid migration effects) in addition to the metal ions taking part in the electrode reaction. The theory of the method has been completely worked out by Randles. By combining (a) Fick's law of diffusion, ( b ) Faraday's laws of electrolysis, and (c) the theory of absolute reaction rates (l),as applied to electrodeprocesses, Randles has shown that the microelectrode system can be considered as equivalent to a capacity and a resistance in series, inasmuch as a phase shift is caused by the microelectrode in the alternating current passing through the system. B y measuring the phase shift and the alternating current passing through the system by the help of an oscillograph, it is possible to calculate the equivalent resistive and capacitative impedances of the system. Randles has worked out equations by means of which one can calculate the rate constants of electrode processes from the values of the impedances. He has applied the method to a number of systems and has obtained interesting correlations. One of the observations made by him is that the rate constant for the discharge of zinc ions a t the dropping amalgam electrode depends upon the nature of the indifferent electrolyte. He finds that the rate constant increases in the order: KSOs
< KCI < IIBr < IlCNS < 111
He attributes this to the increase in covalency of bondage between the metal ion and its addenda, which is supposed to lower the activation energy for discharge of the ion. It is the object of the present paper to examine critically the cause of this interesting phenomenon. Applying the theory of absolute reaction rates, Randles puts for the current i, i l~FA[K2&""F'RT - K ~ ~ O ~ - ( ~ - O ) V R. ~T F I
I
(1)
805
ELECTRODE K I N E T I C S
where cy and ci are the respective concentrations of the metal in the amalgam and that of the metal ion in the aqueous solution, close to the interface; K1 and K: are the rate constants for the two reactions; u is the potential of the aqueous solution relative to the mercury; CY is the fraction of the potential difference operative on the aqueous solution side of the energy barrier; n is the valency of the metal ion; F is the faraday; A is the area of the electrode; R is the gas constant; and T is the absolute temperature. Further Randles assumes that v = 0 for the equilibrium potential of the electrode when cy = ci = c, whence he gets K1 = K P = K , where K defines the rates of opposing reaction a t the equilibrium potential, as Kc moles per second per unit area of the electrode surface. The exact significance of K of Randles becomes clear by a careful consideration of the theory of absolute
K X
I N D I F F E R E N T ELECTROLYTES
10-1
~
- (u+ - u;)
~
so;. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3
i
mu.
0
reaction rates. According to the theory, the rates of the opposing reactions at equilibrium a t any electrode where cy = ci = c, are given by the expressions, ~
~
~
~ F (, I - -~~ ) / -r R
= v
~~ ~ n ~ ~ ~ ~ u e n F a / R T
(2)
where the first expression is for the rate of discharge and the latter is for the rate of conversion of the atom of the metal into an ion in solution. In these y1 and y2 are the activity coefficients of the metal in the amalgam and the metal ion in the solution, respectively. Therefore
K
= ~ . . ~ ~ ~ ~ - v ~ n RF T( l = - dK 2 y 2 e V e n F *
RT
(31
If for the system Zn, Hg 1 Zn++, S O , we represent the Randles rate constant by K' and the equilibrium potential by 2.: we get
K'
=
K ~ ~ , ~ - ( ~ - " ) ~ P " : / R T
(4)
and in the general case for the zinc amalgam electrode dipped in other media, n e put: K = K ~ ~ ~ ~ - ( I - - O R) T~ F L ~ (5) Combining equations 1 and 5 we get,
806
REYNOLD C. MERRILL AND ROBERT W. S P E N C E R
an important relation showing how the rate constants depend upon the equilibrium potential values. If oi is put equal to 0.5, it is possible to calculate the values of t e - c:; the values so obtained are given in table 1. Some of the rate constant values used in the calculations in table 1 were inadvertently left out in Randles' paper. Our thanks are due to Randles, who gave us all the details in a private communication. One can see from the values that they appear to be plausible and explain why the rate constants vary when the indifferent electrolyte is changed. I t is to be noted hon-ever that re - 8; is experimentally measurable, though, of course, there will be the interference by the liquid-junction potential. If the latter could be eliminated it would then be possible to calculate exactly the value of a . I t appears also possible to estimate the values of L ' ~ - r: by the knowledge of activity coefficients; but the time effects coming up a t the dropping electrode, combined with the fundamental difficulty in the evaluation of the activity coefficients of individual ions, may render this procedure difficult. SUMMARY
By studying the kinetics of electrode processes Randles observed that the rate constant for the discharge of the zinc ion depended upon the nature of the indifferent electrolyte used in the experiment. It is sho\\n that the variation in the rate constants can be interpreted plausibly on the basis of the variation of the equilibrium potential of the different systems. REFERENCES (1) GLASSTONE, LAIDLER,ASD EYRISG:Theory of Ente Processes, p . 575. McGraw-Hill Book Company, Inc., New York (1941). (2) RANDLES: Faraday Society Discussion 1, 11 (1947).
GELATIOS OF SODIUM SILIC.1TE
EFFECT OF
SULFCRIC
ACID, HYDROCHLORIC XCID, SODIUM ALEMIXATE
REYNOLD C. M E R R I L L
AND
h f h f O S I E M S U L F A T E , AXD
ROBERT W. SPENCER
Philadelphia Quartz Company, Philadelphia, Pennsylvania Received September 18, 1949
The addition to sodium silicate solutions of acids, acid-forming compounds, ammonium salts, and sodium aluminate produces a silica or silica alumina gel. Such gels are produced from a sodium silicate solution containing approximately 8.9 per cent sodium oxide and 28.7 per cent silica corresponding to a silica-toalkali (NapO) molecular ratio of 3.3, by reaction with an acid, usually sulfuric. Silica alumina gels may be made by reaction of the silicate with either an aluminum salt such as the sulfate or with sodium aluminate.
