Dissociation as a Rate-Limiting Step

When an electrochemical combination or dissociation step is rate-limiting for a given reaction sequence, a unique potential dependence of the non-rds steps arises owing to the difference in stoichiometric coefficients between reactant and product of the rds. The simplest examples that can be envisaged are (1) where (O equivalents of some reactant combine to form a single product in an electrochemical reduction reaction (e.g., 2H+ + 2e H2) or (2) for the case where a single reactant splits into equivalents of some product (e.g., CI2 + 2e 2CT). 

Considering a hypothetical reaction in which a dissociation (in the cathodic reduction direction) step is rate-limiting, the equation for the net rate for a reaction, the rds of which involves the dissociation of 1 into entities, would be written as 

Note that the change in stoichiometric coefficients in this rate-limiting step (i.e., from 1 to (o) affects only the potential dependence of the surface activity of the product, Irds +1 which, in fact, is raised to the odh power in Eq. (45). If the potential dependence of the activities of the intermediates is expanded by the usual quasi-equilibrium approach [Eqs. (27)-(31)], the net rate equation for a reaction, the rds of which is a dissociation step, is 

It is at this point that we depart from the terminology used by Bockris and Reddy (Ref. 3, p. 1007) in their often-cited and generalized discussion of transfer coefficients [Eqs. (la) and (lb)] (i.e., and y ) and introduce the related terms y. and y p. The difference between these sets of electron-number parameters is that in the latter, an electron transferred in a step that occurs, say, v times (i.e., it has a stoichiometric number v greater than 1) is counted only once and not the v times it actually has to occur for one turnover of the overall reaction. This added complication of the electron accounting has the advantage of showing more clearly how stoichiometric coefficients and numbers enter into experimentally obtainable transfer coefficients and hence can demonstrate one of the links between mechanism and experiment. 

The transfer coefficients for an rds that is a dissocation (reductive or chemical) step are therefore 

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