Electrochemical reactions with protonations at equilibrium Part VIII. The 2 e, 2 H+ reaction (nine-member square scheme) for a surface or for a heterogeneous reaction in the absence of disproportionation and dimerization reactions

A theoretical study of the 2 e, 2H+ reaction (nine-member square scheme) is presented for a surface reaction (adsorbed species, Langmuir isotherm or monolayer-modified electrode), or for a heterogeneous electrochemical reaction with protonations taking place in solution near the electrode. The thermodynamic equilibrium diagrams are first examined. In the absence of dimerization, four types of diagrams (NN, SS, NS and SN) are possible, according to the order of the pKa's. The conditions for a direct apparent 2 e, 2H+ reaction are established; the limits pHs (low pH) and pHt (high pH) of the region in which it occurs are calculated. The radical formed after a 1 e, 1H+ reaction (AH in the case of a process AAH2) tends to exist in a broader potential range for the SS than for the NN type, the NS and SN cases being intermediate. The kinetic behaviour of the system is investigated by assuming that the symmetry factors of the electrochemical reactions are equal to 0.5, that the protonations are at equilibrium and that the radicals do not dimerize. The hypothesis is also made that the disproportionation reactions can be neglected; this hypothesis is discussed. In these conditions, when a direct 2 e, 2H+ reaction occurs, the system behaves as a simple reaction with two successive one-electron exchanges. Two apparent rate constants, which depend on the electrochemical rate constants, on the pKa's, on the pH and on the difference between the redox potentials can be defined. Both the protonations and the occurrence of a direct 2 e process cause a decrease, which can reach several orders of magnitude, in the apparent rate constants. The graphs of the logarithm of the rate constants as a function of pH are V-shaped, with slopes of ±0.5. The reaction sequence (order of addition of the electrons and protons) is discussed; for a reduction it is H+ eH+ e near pHs and eH+ eH+ near pH1 for all types. Between these sequences, the succession is eH+ H+ e for the NN case, H+ eeH+ for the SS case, and either or both for the NS and SN cases.