Analysis of the interfacial admittance in the case of a two-step two-electron electrode reaction with a diffusing intermediate, with application to the reduction of pyrazine

Abstract

A critical evaluation is presented of the analysis of impedance or admittance data in the case of an electrode reaction proceeding by two consecutive one-electron transfers with a stable, solution-soluble intermediate. It is shown that the expression for this case, as derived by Armstrong and Firman, has four limiting forms that have the same frequency dependence as the expression describing a single charge-transfer reaction (“pseudo-Randles behaviour”). Also, the conditions for another simplification, which leads to quarter circles in the complex plane diagram (“Amrstrong's equivalent circuit”), are considered. It follows that the special case, where the quarter circle is in the negative quadrant, cannot occur when the system is dc reversible or at equilibrium. For dc irreversible systems, this phenomenon can show up under rather narrow conditions. In addition, it is found that, if these limiting cases are not fulfilled, the general equation often has a frequency dependence that within the practically useful frequency range is hardly distinguishable from that of the single charge-transfer case (“apparent Randles behaviour”). Consequently, the presence of the consecutive mechanism has to be detected from the dc potential dependence of the admittance parameters rather than from the frequency dependence. Finally, it is shown that the general expression corresponds to an equivalent circuit consisting of five elements which, however, have no sensible physical meaning.

These views are applied to the reduction of pyrazine at a DME from 1 M aqueous NaClO4 solutions of pH 4.8, 5.4 and 6.1. Although only one wave is observed in the dc polarogram, the potential dependence of the transfer resistance and the Warburg coefficient (found as parameters in a case of “apparent Randles behaviour”) indicates two consecutive one-electron transfers. The standard rate constants and the transfer coefficients of these two electron transfers are calculated, as well as the rate constant of a homogeneous chemical reaction following the second electron transfer. It is concluded that slow protonation steps largely determine the kinetics of the electron transfers.

The reactants are found to be weakly adsorbed in contrast with the strong adsorption found earlier in strongly acidic solutions.