Kinetics of multiple-electron-transfer reactions—I. The transfer coefficient

Abstract

A theoretical approach to the evaluation of the transfer coefficients of multiple-electron-transfer reactions is developed. Methods of determination of α are critically examined and their limitations discussed. A distinction is drawn between the apparent transfer coefficient α′ and the true transfer coefficient α. The former is shown to include systematic errors due to the diffuse layer as treated by Frumkin and Gierst. The transfer coefficient for a one-electron-transfer reaction denoted by β, the symmetry factor, is shown to be 1 2 according to current theories of α. Statistical analysis of published experimental data for one-electron-transfer reactions show that α is 0·542 ± 0·119 (150 results); the departure from 1 2 of approximately 10% is attributed to the Frumkin-Gierst diffuse-layer effects. The Horiuti relationship between α and β is shown to be not valid for purely electron-transfer reactions that are devoid of catalytic steps. A theory is evolved for the evaluation of α for muli-electron-transfer reactions. Possible values of α, cathodic and anodic, are given for n = 2,3, and 4 and of nα e and nα a for multiple electron-transfer reactions and reactions involving oxidation or reduction of organic compounds. It is shown that the usually assumed formula α e + α a = 1 for the over-all reaction is valid only when the same stage is rate-determining in both directions. α e + α a ≷ 1, if the rate-determining steps in the forward and reverse are not the same, even though for individual electron-transfer steps α e = α a = 1 2 . For n = 3,5,7, etc it is shown that if the middle step is rate-determining in both directions then again α e = α a = 1 2 .