Stoichiometric numbers greater than 1, reaction mechanisms

The effect of the occurrence, within a generalized reaction scheme, of chemical steps, multielectron transfers, or an rds that is a dissociation or combination step (i.e., one that involves a change of stoichiometric coefficients) wiU be examined as well as mechanisms where the rds (and hence the ovCTaU reaction) has a stoichiometric number greater than 1. This latter case is more complicated than these others and, since it is the only mechanistic situation in a consecutive reaction scheme that can give... 

Reaction Mechanisms Involving a Stoichiometric Number Greater than 1... 

This limitation was recognized by Milner (5), who introduced the concept of direct paths, each of which is unique in the sense that it cannot be considered to result from the superposition of any other member of the set of elementary reactions. Milner applied this idea to the enumeration of mechanisms for a number of simple overall reactions involving electrochemistry. He arrived at the rule that for such a reaction the number of nonzero stoichiometric numbers specifying a direct path can be no more than one greater than the number of intermediates. By a trial-and-error procedure he was able to count all mechanisms consistent with a given choice of possible unit steps. 

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. 

Tafel slopes that are not infinite but are substantially greater than 118 mV dec- can be explained by (1) an arbitrary and trivial assumption that P < 1/2 (2) the effect (footnote f) of barrier-layer films such as oxide on Zr02 or Ti0242 (but this is usually only in the case of anodic reactions, particularly those involving valve-metal barrier oxide films) and (3) an electrochemical reaction mechanism where the rds is a chemical step and has a stoichiometric number, v, greater than 2 [refer to Eq. (1)]. This latter possibility will be developed in the next section in terms of a general multistep reaction mechanism. 

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