Steady-state limiting currents determined by coupled diffusion, migration, and chemical equilibrium

A simple theoretical model is presented for the reduction of a singly charged cation under conditions where migration is important and the cation is coupled to a neutral species through a chemical equilibrium, AB = A(+) + B(-). Only the steady-state transport-limited current, I(l), is considered. Simple algebraic equations describe the ratio of I(l) to the diffusion-limited current, I(d), as it depends on the degree of dissociation, determined by the ratio of equilibrium constant to formal concentration, K(AB)/C*(AB). The ratio I(l)/I(d) is found to depend on the ratio of electrolyte to equilibrium concentration of A(+) in bulk solution just as for the well-known result for the case without the equilibrium (i.e., K(AB) → ∞). The results are in accord with published experimental data for weak acids. Agreement and disagreement with other theoretical treatments of this problem are discussed. The main results are for 1:1 supporting electrolytes; extensions are made to 2:1, 1:2, and 2:2 supporting electrolytes.