Bromate Anion Reduction at Rotating Disk Electrode in Steady State under Excess of Protons: Numerical Solution of the Convective Diffusion Equations at Equal Diffusion Coefficients of Components
Résumé
Process of bromate anion reduction at rotating disk electrode in steady state occurring owing to catalytic cycle is analyzed theoretically. The cycle consists of bromine/bromide reversible redox-couple and comproportionation irreversible reaction. Because of the cycle autocatalytic character (EC''-mechanism: Electrochim. Acta, 2015, 173, 779), the passing current can be enormously large at bromate high bulk concentration (up to the bromate limited diffusion current to electrode surface) even when the bromine concentration in the bulk solution is negligibly small. Unlike the previous theoretical studies of the problem (Electrochim. Acta, 2015, 173, 779; Doklady Chemistry, 2016, 468, 141; Russ. J. Electrochem., 2016, 52, No. 10, 925), in this work the component concentration distributions during the process at a prescribed value of the passing current are calculated on the basis of the convective diffusion equations for bromine and the bromate and bromide anions for the first time. Under the assumption that the component diffusion coefficients are equal, exact interrelations between these concentration profiles are derived, which allows reducing the problem to the solving of nonlinear equation of second order for the bromide concentration with boundary conditions at the electrode surface and in the solution bulk. Thus, obtained concentration profiles of all components for a corresponding set of current densities are used to calculate of steady-state polarization curves, as well, as the maximal current dependence on the rotating disk electrode velocity.