Bronsted relations

Fig. 4.10. Bronsted relation for the hydrolysis of cyclohexenyl methyl ether. [Adapted from Ref 46 by permission of the American Chemical Society.]...

This is an example of a reversible reaction the standard electrode potential of the 2PS/PSSP + 2c couple is zero at pH 7. The oxidation kinetics are simple second-order and the presence of a radical intermediate (presumably PS-) was detected. Reaction occurs in the pH range 5 to 13 with a maximum rate at pH 6.2, and the activation energy above 22 °C is zero. The ionic strength dependence of 2 afforded a value for z Zg of 9 from the Bronsted relation... 

Important parameters involved in the Volmer-Butler equation are the transfer coefficients a and (1. They are closely related to the Bronsted relation [Eq. (14.5)] and can be rationalized in terms of the slopes of the potential energy surfaces [Eq. (14.9)]. Due to the latter, the transfer coefficients a and P are also called symmetry factors since they are related to the symmetry of the transitional configuration with respect to the initial and final configurations. 

ApA < 1. In Fig. 2 the region of curvature is much broader and extends beyond — 4 < ApA < + 4. One explanation for the poor agreement between the predictions in Fig. 3 and the behaviour observed for ionisation of acetic acid is that in the region around ApA = 0, the proton-transfer step in mechanism (8) is kinetically significant. In order to test this hypothesis and attempt to fit (9) and (10) to experimental data, it is necessary to assume values for the rate coefficients for the formation and breakdown of the hydrogen-bonded complexes in mechanism (8) and to propose a suitable relationship between the rate coefficients of the proton-transfer step and the equilibrium constant for the reaction. There are various ways in which the latter can be achieved. Experimental data for proton-transfer reactions are usually fitted quite well by the Bronsted relation (17). In (17), GB is a... 

Hydration and dehydration reactions have proved particularly convenient for studying catalysis by acids and bases over a wide range of structures and catalytic power. The results usually show a good correlation between acidic and basic catalytic constants and k ) and the of the catalyst, according to the usual Bronsted relations kjp = Ga qK /p) , ki, q = Gi, pjqKf, where p and q are statistical corrections. (These statistical corrections have not always been applied consistently, but the discrepancies thus introduced are not serious.) The information so far obtained is summarized in Table 3, and comments on the individual reactions follow. 

The Hammett and Taft equations are not the only linear free-energy relationships known. We shall encounter others—for example, the Bronsted relations, and the Grunwald-Winstein and Swain-Scott equations later in this book. 

Streitwieser and co-workers have extended their measurements of equilibrium acidities in cyclohexylamine to determination of exchange rates.69 They have made quantitative correlations between exchange rate and the pKa s determined by equilibrium methods for various aromatic compounds and have thus been able to verify that the Bronsted relation holds for these substances and to find Bronsted coefficients a for various types of compounds. A third method for evaluating p/Ca of weak acids, which has been used by Applequist70 and by Dessy,71 involves the study of exchange reactions of organometallic compounds (Equations 3.54 and 3.55). 

Lin, A. C. Chiang, Y. Dahlberg, D. B. Kresge, A. J. Base-catalyzed hydrogen exchange of phenylacetylene and chloroform. Bronsted relations and normal acid behavior. /. Am. Chem. Soc. 1983, 105, 5380-5386. 

The pKa value of imidazole (6-9) is comparable with that of H2POj" (pA = 7-2), but its reactivity is over two orders of magnitude higher. This demonstrates again a protonic acid that does not fit into Rabani s Bronsted relation (Rabani, 1965). It should be remembered that the reactivities of formic and acetic acids included in Rabani s treatment have been shown to be accounted for by their carbonylic groups. Thus the suggested Bronsted relation may be adequate for certain inorganic protonic acids only. 

For heteroaromatics having a basicity which can be measured precisely by conventional potentiometric or spectrophotometric methods, a pKa value is easily obtained. Owing to the very small size of the proton, the pKa is considered free from steric effects. Thus, the nucleophilicity of a series of heteroaromatic molecules, say in quaternization reactions, may be compared to the pKa within the same series this is a Bronsted relation ... 

Remark b. Because nucleophilicity is usually recorded in organic solvents and pKa in water (or water/methanol mixtures), this can make a large difference. Answer The nucleophilicities of a series of molecules in different organic solvents are correlated with excellent correlation coefficients (r). Furthermore, correlations of each series with pKa in the case of non-ortho substituents is also very good. That the slope, a, of the Bronsted relation is an estimate of transition state location may be questioned (78T2331). Deviations from the Bronsted a seem to be well established as a measure of steric effects. 

The Bronsted Relation Linear Free Energy Relations... 

Many similar examples of the application of the Bronsted relation may be cited, including the mutarotation of glucose, the iodination of acetone, the bromination of aceto-acetic ester, and the dehydration of 1,1-dihy-droxyethane to acetaldehyde- and many other closely related compounds (see R. P. Bell, loc, cit). It is usually found that on going from one acid to another structurally very different, the two acids will not fit the same... 

Bell has examined some of the reasons for expecting gross deviations from the Bronsted relation and has suggested that both positive and negative deviations may occur if the transition state represents a structure considerably different in its charge distribution than the base of the conjugate acid (or vice versa). 

By applying such an argument to the Bronsted relation we find the modified expressions... 

The Bronsted relation represents only one very successful example of what have come to be known as linear free energy relations. It is found that there exist linear relations between the free energy of activation of... 

As discussed in Vol. 2, pp. 354 and 372, logarithms of second-order rate coefficients for acid or base catalysis are linearly related to the pK values of the acids or bases, respectively (Bronsted relation). 

Since 1924, the Bronsted relation has been applied to many general acid and base catalysed reactions, such as those discussed in Sect. 2.2, as well as to proton transfer equilibria like (43)—(45). Over limited ranges of acid strength and for variation within a similar catalyst type, G and a or j3 are constant and the relation holds well. Different catalyst types in a reaction often do not fit on a single Bronsted plot, but give different Bronsted lines. This was observed for the decomposition of nitramide [68]. It has also been observed in proton transfer from l,4-dicyano-2-butene(51)... 

The Bronsted relation has proved to be a useful equation for correlating rate and equilibrium results for proton transfer reactions. However, following the analysis by Leffler and Grunwald [73] in 1963 considerable effort has been made to go further than this and understand why the relation should hold, and also to attach some significance to the values of a and 3 in terms of the structure of the transition state for proton transfer. An alternative approach from that to be discussed here interprets the Bronsted relation from molecular potential energy diagrams [74]. 

When the rate coefficient k, for reaction (43) is measured for reaction between a single carbon acid (RCH) and a series of bases (B) the Bronsted relations for the forward and reverse reactions are given by (54) and (55), respectively, viz. 

The Bronsted relation is accurately obeyed for the individual ketones in Table 2 with carboxylate ions as catalysts. However, the trend of j3 with reactivity implies that if one ketone could be studied over a wide range of catalyst strength, the Bronsted plot would be curved and the Bronsted exponent would vary. Proton transfer from acetylacetone [17] has been studied with bases covering a pK range of ca. 15 units using the temperature-jump method. The values of fef and kr for reaction between acetylacetone and carboxylate ions, phenolate ions, hydroxide ion, and water are shown in Fig. 3. The data refer to reaction (72)... 

Bronsted plots for other carbon acids may be curves but this is not detected because of the limited range of reactivity over which the reactions can be studied and the Bronsted relation is therefore a sufficiently good approximation. The demonstration of a sharply curved Bronsted plot for diazoacetate ion came shortly after a new rate-equilibrium equation for proton transfer reactions had been proposed by Marcus. This will be discussed fully in Sect. 5.2 but it should be noted here that with this new theory, Bronsted plot curvature is easily accounted for. 

However, the bimolecular rate constant changes as a function of the pK of the nucleophilic group according to the Bronsted relation (eq. 4.12) where y is a reaction constant which depends on the nature of the modification reaction and p describes the sensitivity of a series of nucleophiles on the pK. ... 

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