Rate-equilibrium correlation, carbocation reactivity

A similar picture holds for other nucleophiles. As a consequence, there might seem little hope for a nucleophile-based reactivity relationship. Indeed this has been implicitly recognized in the popularity of Pearson s concept of hard and soft acids and bases, which provides a qualitative rationalization of, for example, the similar orders of reactivities of halide ions as both nucleophiles and leaving groups in (Sn2) substitution reactions, without attempting a quantitative analysis. Surprisingly, however, despite the failure of rate-equilibrium relationships, correlations between reactivities of nucleophiles, that is, comparisons of rates of reactions for one carbocation with those of another, are strikingly successful. In other words, correlations exist between rate constants and rate constants where correlations between rate and equilibrium constants fail. 

The starting point for most discussions of reactivity is a correlation of rate and equilibrium constants. One such correlation is shown in Fig. 1 of this chapter. It applies not to reactions of the carbocation with water as a nucleophile but to water acting as base, that is, the removal of a [3-proton from the carbocation to form an alkene or aromatic product. We will consider this reaction below, but here note that for most of the carbocations in Fig. 1 values of kH2o> the rate constants for reaction of the carbocation with water as a nucleophile are also available.25... 

It is not intended to pursue this discussion to a firmer conclusion. However, it is reasonable to infer that our understanding of reactivity and selectivity in carbocations has been brought to a point where the origins of differences in reactivities of hard and soft nucleophiles and of lack of correlation of rate and equilibrium constants have been greatly clarified. Particularly, in the hands of... 

On the basis of these considerations it has been concluded that under given reaction conditions (Lewis acid/solvent) the reactivity maximum is found for an alkylating system (RA7R+) that is approximately half-ionized [60,61]. Scheme 11 suggests that the electrophilic reactivity of RA" increases with increasing stabilization of R+ if only small equilibrium concentrations of carbocations are involved. In accord with this analysis, the relative alkylating abilities of alkyl chlorides have been found to be proportional to their ethanolysis rates (Fig. 2) [62]. The only compound that deviates from this correlation is trityl chloride which alkylates considerably more slowly than expected from its solvolysis rate. 

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