Adsorption of reactants is a common complication in electrode reactions. Unfortunately, theoretical consideration of adsorption becomes mathematically arduous when it is combined with diffusional mass transfer, especially in cases d.escribed by non-linear adsorption isotherms. Thus, exact results pertaining to potentiostatic conditions have been presented only for the case of a linear isotherm and reversible or totally irreversible reaction at stationary plane 1-3 and spherical 2'3 electrodes and of linear adsorption isotherm with irreversible charge transfer and quasi-reversible charge transfer involving the electrode material at an expanding electrode 4. While approximate treatments based on the Nernst diffusion layer model have been applied in the cases of more complicated adsorption isotherms 5'6, the results in one case 5 turned out to be at striking variance with those of more exact treatment 7. For this and other reasons it seemed desirable to extend exact treatment to other practically important cases, and to examine the basis of the diffusion-layer approximation more closely.
In recent work dealing with Langmuirian~,dsorption coupled with reversible charge transfer at a stationary plane 7 we noted that the Fick's Law boundary value problem describing the process can be converted to an integro-differential equation of exactly the same mathematical form as that arising in the description of diffusionlimited adsorption of a single species without electrode reaction. Thus previously published results for the simpler case s-11 could be transposed to the case of interest simply by change of definition of parameters. The purpose of the present work is to point out that this transposition can be applied for any isotherm at a stationary plane or expanding plane electrode provided only one of the reactants is adsorbed, and for an important class of isotherms if both reactants are adsorbed. It can also be applied to cases involving spherical electrodes when the diffusion coefficients of the reactants can be assumed equal. Thus previously published treatments for the Langmuir and Frumkin adsorption at stationary plane and spherical electrodes obtained by analogue 9'1° and digital computation x i as well as series solution for linear 4 and Langmuir 8 adsorption at an expanding plane constitute also treatments of the same cases with reversible charge transfer and adsorption of one or both reactants.
The work is divided into seven parts dealing in turn with stationary plane, stationary sphere, and expanding plane electrodes ; then with three features of the