Brpnsted equation

The Brpnsted equations relate a rate eonstant k to an equilibrium constant K. In Chapter 6, we saw that the Marcus equation also relates a rate term (in that case AG ) to an equilibrium term AG°. When the Marcus treatment is applied to proton... 

Equation 2.13 is an example of the Brpnsted equation (see section A3). Here, the Brpnsted /3 value measures the sensitivity of the reaction to the pKa of the conjugate acid of the base. The A is a constant for the particular reaction. 

Brpnsted equations are also common in general-acid catalysis, as, for example, in the hydrolysis of certain acetals.8-10 In acid catalysis, a rather than /3 is used ... 

The variation in the p values in a closely related series of reactions can be related to the cationic charge developed at the reaction centre in the transition state. Thus, a corollary of the RSR is that the coefficient S should be a measure of whether the transition state occurs early or late on the reaction coordinate as a result of any structural perturbation of the energy of the transition state as well as of the intermediate in the reaction series. The S coefficient in an RSR should be intimately related to the a exponent in the extended Brpnsted equation (cf., Johnson, 1980). 

Although the value of the coefficient 1.16 in (20) does not have as direct a physical significance as the a-exponent in the extended Brpnsted equation (19) because the reaction, solvents and temperature are different, there is still a good linear rate-equilibrium relationship for benzhydryl carbocation formation the overall correlation embraces clearly concave partial correlations with varying slopes for the respective Y series. The whole pattern of substituent effects, pXr vs should be essentially identical (with only the ordinate scale being slightly different) to that of log (/ xy/Z hh) vs 2 a for the solvolyses shown in Fig. 8. 

The progress of the reaction at the transition state, a, is usually obtained from the coefficients of the extended Brpnsted equation (19) or of other rate-equilibrium relationships which compare substituent effects on kinetics and thermodynamics. Using (24) the p values can also express this position if Pk for rates and pe for equilibria of the same elementary step are available. 

Tables of MY and Nx values are given that permit calculation of a large number of reaction rates. The relationship of this expression to the formally similar, but empirical, Swain-Scott and Brpnsted equations is of much interest.

In an attempt to avoid the limitations of the one-parameter equations, Edwards (19, 20) in 1954 added polarizability (as measured by the oxidation potential of oxidative dimerization of nucleophiles, E°) as a second parameter to get a modified Brpnsted equation ... 

O"), as it is with experimental hydrogen basicities this finding suggests that the high solution reactivity of carbon nucleophiles toward carbon has a thermodynamic origin. The correlation between carbon and hydrogen basicity leads to the suggestion that this correlation is central to the operation of the Brpnsted equation. 

The final chapter of this section is by Rappoport and is concerned with nucleophilic reactions at vinylic carbon. Two reaction types are considered, those of neutral vinyl derivatives and those of vinyl cations. Correlation of rates for these reactions with both Ritchie and Swain-Scott equations was attempted without success. Rappoport concludes that these reactions are subject to a complex blend of polar, steric, and symbiotic effects and that a quantitative nucleophilicity scale toward vinylic carbon cannot be constructed . This conclusion is reminiscent of the earlier observation of Pearson (see the introduction to the section on the Brpnsted equation) and the later observation of Ritchie (Chapter 11) regarding the difficulty of correlating nucleophilic reactivity with a single equation. Rappoport finds another familiar situation when he explores the relationship between reactivity and selectivity for the vinyl substrates sometimes the RSP is obeyed and sometimes it is not. 

The term nucleophilicity refers to the relative rate of reaction of an electron donor with a given electrophile, as distinct from basicity, which refers to its relative affinity for a proton in an acid-base equilibrium. A quantitative relationship between rate and equilibrium constants was discovered by Brpnsted and Pedersen (1) in 1924. These authors found that the rate constants for the catalytic decomposition of nitramide by a family of bases, such as carboxylate ions (GCH2C02 ), could be linearly correlated with the acidities of their conjugate acids, pKHB. This observation led to the discovery of general base catalysis and the first linear free-energy relationship, which later became known as the Brpnsted equation ... 

It was soon realized, however, that this simple definition of nucleophilicity would not suffice. Shortly afterward, Edwards (6) attempted to define relative nucleophilicities in terms of two parameters, H (basicity) and Eox (oxidation potential), using the (variable) coefficients a and to relate these properties to changes in the electrophile (equation 5). Later, Edwards and Pearson substituted a polarizibility parameter, P, for Eox. In essence, equation 5 is a Brpnsted equation with a second parameter added. 

For other applications of the Brpnsted equation to SN2 reactions, see Smith, G. F. J. Chem. Soc. 1943, 521-523. Hudson, R. F. Klopman, G. J. Chem. Soc. 1962, 1062-1067. Hudson, R. F. Chemical Reactivity and Reaction Paths Klopman, G., Ed. Wiley-Interscience New York, 1974 Chapter 5. For applications of the Brpnsted equation to acyl transfer and other reactions, see Hammett (2) and Jencks, W. P. Catalysis in Chemistry and Enzymology McGraw-Hill New York, 1969. 

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. 

The main drawback of these linear free-energy relationships is that they do not relate to reaction mechanisms. Curiously enough, like the original Brpnsted equation, the main objective appeared to be the correlation of rate data rather than the interpretation of reaction mechanisms. This deficiency was partly remedied in the concept (8) of hard-soft acid-base (HSAB), which was in effect a qualitative extension of the Swain-Edwards equation but was more powerful in the sense that different types of reaction were related to the hard-soft classification, and the concept therefore has a wide application in organic synthesis and inorganic equilibria. 

The following data give the dissociation constants and rate of acetaldehyde hydration catalysis by each acid. Treat the data according to the Brpnsted equation and discuss the mechanistic significance of the results. 

The reduced reactivity here of o-methyl thiophenoxide may be ascribed to steric factors. In these and other examples, relatively good correlations with the Hammett and Brpnsted equations may be observed, and it has been noted [57] that when nucleophilic attack is rate limiting, the Brpnsted value is usually in the range 0.5-0.7. Studies of the substitution reactions of halogenonitrobenzenes with nucleophiles, including substituted fluorenide carbanions, such as (12), and phenothiazine nitranions (13) in DMSO solvent [53] indicated that for anions of the same basicity, the nucleophilic reactivity was in the order S >>C >0 >N. The high reactivity of thianions is most likely due to their high polarizability. 

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