Studies on Alternating Current Electrolysis. IV . Mathematical Treatment of Reversible Electron Transfer with Alternating Voltage Control and Distorted Current

Abstract

A mathematical treatment is developed which yields equations relating faradaic current, voltage, and time when an alternating voltage is applied to an electrolytic cell composed of a plane and auxiliary electrodes immersed in a solution containing initially supporting electrolyte and only reversibly oxidizable or reducible species. Both oxidant and reductant are taken to be soluble, and specific adsorption is assumed to be absent. The voltage across that branch of the equivalent circuit through which only faradaic current flows is assumed to be periodic with fixed amplitude and with or without an additional direct applied voltage component; the resultant current is distorted. Diffusion controlled kinetics is postulated, and it is assumed that equilibrium is essentially established at the electrode surface. The equations developed show that a “steady state” (i.e., a periodic state) is quickly attained, yield diagnostic tests of use in establishing the reversible mechanism, make it possible to determine the standard potential, and finally yield for the periodic state a relation between faradaic current and time. These results are then generalized so as to include systems in which the reversible electrochemical step is followed by a sufficiently slow secondary reaction step. One diagnostic result of interest in the latter connection is that the mean faradaic current vanishes in the periodic state, regardless of the amplitude or of the shape of the applied periodic potential, when the follow‐up reaction occurs to a negligible extent.