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case that looks simple at first glance is the deposition of silver from aqueous potassium nitrate: (9.33) However, there is evidence that this reduction involves at least a charge-transfer step, creating an adsorbed silver atom, and a crystallization step, in which the atom migrates across the surface until it finds a vacant lattice site. Electrode processes may also involve adsorption and desorption kinetics of primary reactants, intermediates, and products. Thus, electrode reactions generally can be expected to show complex behavior, and for each mechanistic sequence, one would obtain a distinct theoretical linkage between current and potential. That relation would have to take into account the potential dependences of all steps and the surface concentrations of all intermediates, in addition to the concentrations of the primary reactants and products. A great deal of effort has been spent in studying the mechanism of complex electrode reactions. One general approach is based on steady-state current- potential curves. Theoretical responses are derived on the basis of mechanistic alternatives, then one compares predicted behavior, such as the variation of exchange current with reactant concentration, with the behavior found experimentally. A number of excellent expositions of this approach are available in the literature278–280,291–295. More commonly, complex behavior is elucidated by studies of transient responses, such as cyclic voltammetry at different scan rates. 9.1.3.1 Rate-determining electron transfer In the study of chemical kinetics, one can often simplify the prediction and analysis of behavior by recognizing that a single step of a mechanism is much more sluggish than all the others, so that it controls the rate of the overall reaction. If the mechanism is an electrode process, this rate-determining step (RDS) can be a heterogeneous electron-transfer reaction. A widely held concept in electrochemistry is that truly elementary electron-transfer reactions always involve the exchange of one electron, so that an overall process involving a change of n electrons must involve n distinct electron-transfer steps. Of course, it may also involve other elementary reactions, such as adsorption, desorption, or various chemical reactions away from the interface. Within this view, a rate-determining electron transfer is always a one-electron-process, and the results that we derived above for the one-step, one-electron process can be used to describe the RSD, although the concentrations must often be understood as applying to intermediates, rather than to starting species or final products. For example, consider an overall process in which O and R are coupled in an overall multielectron process 224PDF Image | Redox Flow Batteries Vanadium to Earth Quinones
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