Brpnsted relationships

Citing amine basicity according to the of the conjugate acid permits acid-base reac tions involving amines to be analyzed according to the usual Brpnsted relationships For example we see that amines are converted to ammonium ions by acids even as weak as acetic acid... 

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/... 

The hnear part of the Brpnsted relationship represents a segment of a curved line. The theory for the deviations from linearity was provided by Marcus . ... 

Second, rate constants for intermolecular proton transfer obey the Brpnsted relationship, and the rates can be strongly influenced by electrostatics as well as the difference in the p/ a s for the two acids. Third, proton transfer can proceed at slower than diffusion-limited values with compounds forming weak hydrogen bonds in water. 

Figure 2.9 A Brpnsted plot for the attack of oxyanion nucleophiles onp-nitrophenyl acetate. As in Figure 2.8, the -effect nucleophiles ( ) are unusually reactive. Note how the linear plot breaks down with increasing pKa for the more reacdve nucleophiles. In general, the Brpnsted relationships hold only over a limited range of pk s in these reactions. The curvature is not often seen in practice because of the limited range of bases used.

The substituent effect on the equilibrium pXr+ forming diarylmethyl carboca-tions plays an important role in the extended Brpnsted relationship (19) by giving the extreme limit of the substituent effect on the transition state of the corresponding benzhydryl solvolysis. 

The identity of r values for solvolysis reactivities and the gas-phase stabilities of the corresponding carbocations implies the generality of the extended Brpnsted relationship or Hammond-Leffler rate-equilibrium relationship for benzylic solvolyses, i.e. (37a,b),... 

McEwen, J., Yates, K., Photohydration of Styrenes and Phenylacetylenes General Acid Catalysis and Brpnsted Relationships, J. Am. Chem. Soc. 1987, 109, 5800 5808. 

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. 

Leffler and reactivity-selectivity postulates, which predict that the selectivity should decrease and the Brpnsted (5 approach unity as the reactions become more endergonic. The curvature in this plot is much greater than predicted by the Marcus equation (equation 6) (22), however, and is believed to be an artifact caused by enhanced solvation of 7r-acceptor para substituents such as CN, COC6H5, and N02 (21). [The Marcus equation, which has gained wide acceptance in the interpretation of electron-transfer reactions, is represented in equation 6 as a Brpnsted relationship with an exponential term added to take into account curvature (23)]. 

Figure 3.27 is plot of the Brpnsted relationship for hydrolysis of a vinyl ether. The plot shows that the effectiveness of the various carboxylic acids as catalysts is related to their dissociation constants. In this particular case, the value of a is 0.79. ... 

The Brpnsted relationship (see Section 3.7.1.2 to review the Brpnsted catalysis law) shows a correlation with the identity of the alkoxy group. The alkoxy groups derived from more acidic alcohols have lower Brpnsted coefficients a. 

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