Rate-determining electron transfer, multistep mechanisms

The rate expression for the multistep consecutive electron-transfer reaction of Scheme 1 [i.e., Eq. (31)] is able to relate complex consecutive electron-transfer reaction mechanisms to experimental potential vs. logarithmic current-density relations. When p is assumed to be 1/2, the Tafel slopes (1/a/) predicted by this relation can only have values less than or equal to 118 mV dec i (at 25 °C) for electron-transfer limited reactions, since electrons transferred in non-rds steps will add integers (to P) in the expected a values and therefore decrease the Tafel slope below 118 mV dec 1. For instance, the usual cathodic Tafel slope of 118 mV dec-i for a one- electron transfer over a synunetric harrier is decreased to 39 mV dec for one preceding quasi-equilibrium electron transfer and to 24 mV dec for two, etc., and the anodic Tafel slopes are similarly decreased for one and two following (where the reaction steps are still written as reductions, as in Scheme 1) electron transfers, respectively. It should be noted that the Tafel slopes that are determined hy a values involving y-i- P differ substantially and discontinuously from the value for a = P = 1/2, and therefore should be easily distinguishable. 

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