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For the mechanism in (9.35) and (9.37), Nerstian relationships define the equilibrium for the pre- and postreactions, and they can be written in the following forms: (9.40) where E0’pre and E0’post apply to (9.35) and (9.37), respectively. Substitution for the equilibrium concentrations of O’ and R’ in (9.39) gives Recognizing that n = n’ + n’’ + 1 and that E0’ for the overall process is it can be distilled (9.41) into (9.41) (9.42) (9.43) which the exponential form of the Nernst equation for the overall reaction is, (9.44) Of course, this is a required result if the kinetic model has any pretense to validity, and it is important that the BV model attains it for the limit of i=0, not only for the simple one-step, one-electron process, but also in the context of an arbitrary multistep mechanism. The derivation here was carried out for a mechanism in which the prereactions and postreactions involve net charge transfer; however the same outcome can be obtained by a similar method for any reaction sequence, as long as it is chemically reversible and a true equilibrium can be established. 226PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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