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(9.8) Where f=F/RT. The first two factors in each of these expressions form a product that is independent of potential and equal to the rate constant at E=E0’. Now consider the special case in which the interface is at equilibrium with a solution in which C*O = C*R. In this situation, E=E0’ and kfC*O = kbC*R, so that kf = kb. Thus, E0’, is the potential where the forward and reverse rate constants have the same value. That value is called the standard rate constant, k0.5. The rate constants at other potentials can then be expressed simply in terms of k0: Insertion of these relations into Yields the complete current-potential characteristics: (9.9) (9.10) (9.11) (9.12) This relation is very important. It, or a variation derived from it, is used in the treatment of almost every problem requiring an account of heterogeneous kinetics. There results and the inferences derived from them are known broadly as the Butler-Volmer formulation of electrode kinetics, in honor of the pioneers in this area276,277. One can derive the Butler-Volmer kinetic expressions by an alternative method based on electrochemical potentials278–283. Such an approach can be more convenient for more complicated cases, such as requiring the inclusion of double- layer effects or sequences of reactions in a mechanism. 215PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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