Marcus Theory and Butler-Volmer Kinetics

12 Marcus Theory and Butler-Volmer Kinetics Problem 

The Gibbs energy change between the reactant and the transition state, AG(t), (as discussed in Problem 2.11) may be described in terms of the reorganisation 

For a one-electron reduction, AG = F(E — Ef), and the rate of electron transfer ( k) is given in terms of AG( ) as shown below  

We know from Butler-Volmer kinetics that 

This result is important it shows us that a is predicted by Marcus theory to be 0.5 for a one-electron process if A AG, i.e. if the reaction is irreversible. Of further importance is the fact that AG as discussed above is not a standard Gibbs energy since it is dependent upon the electrode potential. Ckinsequently, a is not constant and this may lead to curved Tafel plots if a is measured over a wide potential range. 

---