Electrochemical reactions with protonations at equilibrium: Part 14. The cubic scheme

Abstract

A theoretical study of the 1e −, 1H + square scheme is presented for the case when the molecule possesses an electro-inactive protonation site other than the electro-active site. The results are valid for a surface reaction (adsorbed species, Langmuir isotherm) or for a heterogeneous electrochemical reaction (semi-infinite linear diffusion) with protonations taking place in solution near the electrode. It is assumed, as in the other papers of this series, that the protonations are fast (at equilibrium) and that the symmetry factors of the electrochemical reactions are equal to O.5. The reaction can be described by using a cubic scheme consisting of two planar square schemes linked by protonations. The cubic scheme can itself be preceded and/or followed by a protonation. The mathematical treatment shows that it is globally equivalent to a simple monoelectronic reaction, with an apparent rate constant k 2app, which depends on the p K a and the pH, and an apparent standard potential E r2. The graph log k 2app = ƒ(pH) consists of rectilinear segments whose slopes depend on the number of protonations and deprotonations taking place before or after the electrochemical step. It can be shown very generally that, for a reduction, a prior protonation or posterior deprotonation gives a slope of −1 2 , whereas a prior deprotonation or a posterior protonation gives a slope of +1 2 . The reverse is true for an oxidation. The effects of successive reactions are additive, so that slopes of 0, ±1 2 , ±1, ±3 2 etc. can be obtained. Study of the graph log k 2app = ƒ(pH), with the help of the graph E r2 = ƒ(pH), allows the reaction sequence to be determined. The reaction sequence can be very complex, and the p K a values must be carefully assessed. The reaction path for the electro-active group can be determined by distinguishing the perturbations produced by the protonation of the electro-inactive site.