Fundamental harmonic a.c. polarography with disproportionation following the charge transfer step

A theoretical and experimental study is presented for the small amplitude a.c. polarographic response with systems involving second-order disproportionation following the charge transfer step. The theoretical derivation combines wellestablished analytical procedures for solving the a.c. boundary value problem with various nummerical methods to account for effects of d.c. polarization. The resulting rate law predicts significant influences of the disproportionation step on a.c. polarographic observables, including several novel effects not predicted or observed with first-order coupled chemical reactions. The basis for kinetic assessment of rate parameters associated with the heterogeneous charge transfer step and the homogenous disproportionation mechanism is clearly indicated by the theoretical rate law. The computer programs developed on the basis of the derivation provide the means for calculating predicted responses on the basis of most commonly-used mathematical models for the DME, including the expanding sphere model. The electrode reduction of UO22+ at the mercury-aqueous 6 M HClO4 interface is used as a model for the mechanism in question in an experimental assay of the theory's fidelity. Various predicted trends are verified experimentally. Analysis of the experimental data using the theoretical rate law generated rate parameters for the heterogeneous electrode reaction, the homogeneous disproportionation step and the diffusion process. Agreement between theory and experiment obtained with this set of rate parameters is quite satisfactory for a variety of observables. Finally, the disproportionation rate constant obtained is consistent with previous measurements by a variety of authors using both electrochemical and non-electrochemical methods.