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by a mechanism having the following general character: ‐ (net result of steps preceding RDS) (RDS) (net result of steps following RDS) Obviously n’ + n’’ + 1 = n The current-potential characteristic can be written as (9.35) (9.36) (9.37) (9.38) ‐ (9.34) where k0rds, α, and E0’rds apply to the RDS. This relation is (9.12) written for the RDS and multiplied by n, because each net conversion of O’ to R’ result in the flow of n electrons, not just one electron, across the interface. The concentrations CO’(0,t) and CR’(0,t) are controlled not only by the interplay between mass transfer and the kinetics of heterogeneous electron transfer, as we found in the Butler- Volmer model for one-step, one-electron process, but also by the properties of the preceding and following reactions. The situation can become quite complicated, so we will make no attempt to discuss the general problem. However, a few important simple cases exist, and we will develop them briefly now. 9.1.3.2 Multistep Process at Equilibrium If a true equilibrium exists for the overall process, all the steps in the mechanism are individually at equilibrium. Thus, the surface concentrations of O’ and R’ are the values in equilibrium with the bulk concentrations of O and R, respectively. We designate them as (CO’)eq and (CR’)eq. Recognizing that i=0, we can proceed through the treatment leading to (9.14) to obtain the analogous relation (9.39) 225PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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