A note on inner-sphere reactions

If the rate-determining step is the adsorption of an ion, the reaction obeys the laws for ion-transfer reactions (see Chapter 9), and again a Butler-Volmer-type law will hold. 

The reduced species of an outer-sphere electron-transfer reaction is generated by a chemical reaction of the form  

Denote the forward and backward rate constants of this reaction by ka and kb- When the reaction proceeds under stationary conditions, the rates of the chemical and of the electron-transfer reaction are equal. Derive the current-potential relationship for this case. Assume that the concentrations of A and of the oxidized species are constant. 

The Gibbs energy of activation in Eq. (5.4) can be split into an enthalpy and an entropy term AGjx = AH x - T AS]x. Define two transfer coefficients 

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