Brpnsted relationship measurements

There are a number of limitations on the Brpnsted relationship. First of aU, the relation holds only for similar types of acids (or bases). For example, carboxylic acids may have a different a values compared to sulfonic acids or phenols. Because charge, and likewise solvation, can greatly influence the reaction rate, deviations of net charge from one catalyst to another can also influence Brpnsted plots. Another limitation on this relationship relates to temperature. Reaction rates and the corresponding dissociation constants for the acids must all be measured at the same temperature (and, most rigorously, in the same solvent). For some systems, this may prove infeasible. A third limitation is that the reaction must indeed be subject to general acid (or base) catalysis. For certain catalysts, deviations from a linear relationship may indicate other modes of action beyond general acid/... 

From the results summarized in Table I, apparently the Brpnsted relationship will hold for all combinations of nucleophiles and electrophiles. Because, as pointed out previously, the Hammett equation is really a special case of the Brpnsted relationship, all the legion of nucleophile-electrophile, rate-equilibrium Hammett correlations that have been studied also fall under the scope of the Brpnsted relationship. For example, nucleophilicities of ArO , ArS , ArC(CN)2 , and the other families listed in footnote c of Table I have generally been correlated by the Hammett equation, where the acidities of benzoic acids in water are used as a model for substituent interactions with the reaction site (a), and the variable parameter p is used to define the sensitivity of the rate constants to these substituent effects. The Brpnsted equation (equation 3) offers a much more precise relationship of the same kind, because this equation does not depend on an arbitrary model and allows rate and equilibrium constants to be measured in the same solvent. Furthermore, the Brpnsted relationship is also applicable to families of aliphatic bases such as carboxylate ions (GCH2C02 ), alkoxide ions (GCH20 ), and amines (GCH2NH2). In addition, other correlations of a kinetic parameter (log fc, AGf, Ea, etc.) can be included with various thermodynamic parameters (pKfl, AG°, Eox, etc.) under the Brpnsted label. 

Brpnsted correlations for proton transfer and methyl transfer between pairs of mimicked 4-substituted pyridines have been simulated by means of AMI molecular-orbital calculations.The relationship to the Marcus equation is also considered. It is concluded that the Brpnsted coefficient fi provides an approximate measure of the position of the transition structure along the reaction coordinate between reactant and product encounter complexes. 

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