Statistical Treatment of Bronsted Plots

Scatter in free energy correlations may also be caused by a statistical effect when more than one reaction centre can be involved.The reactivity of a base or nucleophile possessing q identical basic or nucleophilic sites compared with a dissociation equilibrium where the conjugate acid possesses p identical acidic sites requires the following statistical correction to the simple Bronsted type relationship (Equations 23 and 24). 

A similar correction applies to reactivity of acid-catalysed reactions (Equations 25 and 26) 

These equations factor all the acid-base types in a series to that where p = = 1. For example, if triethylamine and diaminoethane monocation are to be interpreted in the same correlation they need corrections because the former has p = 1 and q = 1 whereas the latter has p = 2 and q = 1. The assignment of p and q is not satisfactory for acid-base pairs with uncertain structures (such as H3O and HO ) or species with multiple centres of differing reactivity hydronium and hydroxide ions almost always show anomalous reactivities in corrected Bronsted correlations, but these are partly due to solvation effects. The protons attached to a single atom such as ammonium (R-NHj or oxonium ion (R-OH2 ) are regarded as having p = 1 rather than the number of identical protons. A similar convention selects the q value for hydroxide ion as unity even though there are three lone pairs free to accept a proton. The statistical 

The statistical correction is important for correlations with small numbers of points over a small range when the range and number of points increases, the statistical correction becomes less important and the similarity coefficient shows very little difference between corrected and uncorrected treatments (see Problem 4). 

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