On the influence of coupled homogeneous redox reactions on electrode processes in d.c. and a.c. polarography: I. Theory for two independent electrode reactions coupled with a homogeneous redox reaction

Abstract

A theoretical study of the d.c. and a.c. polarographic responses with the mechanism A+e⇌ks,1,α1BC+e⇌ks,2,α2DA+D⇌k2k1C+B is presented. It is found that the coupling of the two heterogeneous electrode processes by the homogeneous redox reaction under many conditions will lead to significant effects on the a.c. polarographic response which can be exploited to enable measurement of the rate parameters k1 and/or k2 of the homogeneous redox reaction. Other unique measurement possibilities also arise, such as deduction of the E0 and ks-values for totally irreversible electrode processes. In the extreme where k1≫k2, the theoretical predictions confirm the conclusions of Yamaoka regarding the enhancement of an irreversible a.c. polarographic wave by a second, more easily reduced, redox couple. In the opposite extreme (k1≪k2), which corresponds to the classical catalytic mechanism, the theory provides for the first time a.c. polarographic rate laws for the case where the homogeneous process is second-order. The theoretical equations are applicable to all combinations of homogeneous and heterogeneous kinetic-thermodynamic parameters, encompassing situations involving both resolved and unresolved polarographic waves. the usual assumption of equal diffusion coefficients is relaxed and the equations developed should account for moderate differences in diffusion coefficient under most circumstances, and large differences if the homogeneous redox reaction is reasonably rapid. Computer programs developed invoke the expanding sphere electrode model. Guidelines for experimental evaluation of various rate and thermodynamic parameters are presented. It is found that some rather simple measurement procedures based on appropriate theoretical working curves will permit evaluation of the homogeneous kinetic parameters. Implications of the results for a.c. polarographic analysis of multi-component systems are considered.