Bronsted exponents

Together with other workers in the field Jencks [10] has extended the Bronsted correlation to include a meaning for the exponents provided one is prepared to work within a given framework of assumptions. A model for the equihbrium between acyl esters and their hydrolysis products (Eqn. 16) might be the ionisation of the phenol where the charge on phenol and phenolate oxygen is defined as zero and — 1 respectively. 

Measurements of 8gQ may be made directly from a series of equilibrium constants the latter parameters are, however, quite rare owing to experimental difficulties but ySgg can be estimated without explicitly measuring equilibrium constants. The equilibrium constant for the esterification reaction (Eqn. 17) is related to that between phenyl acetates, phenol and acetic anhydride (Eqn. 18) by a simple equation (Eqn. 19). 

CH3CO2H + ArOH CHjCOOAr + CH3CO2H CH3CO-O-COCH3 + H2O 

Since K2 is substituent independent ySgg for K is identical with that for A ,. Ths approach is clearly very useful as the equilibrium of Eqn. 17 is not easily accessible whereas that of Eqn. 18 is. The approach is general and enables to be estimated for any constant donor acyl function. 

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It was concluded that while kinetic isotope effects are much more sensitive than Bronsted exponents to variations in pKa, the use of either quantity as an index of transition state symmetry may be doubtful. 

Ruasse and Dubois (1984). Rate data for styrenes and a-Me-styrenes (from Durand et al., 1966) and for methoxy- and hydroxystyrenes (from Loudon and Berke, 1974). "Values in parentheses are for bromination in water (Ruasse and Lefebvre, unpublished results). Grunwald-Winstein coefficients for solvent effects. Values in parentheses are for protonation in MeOH (Toullec, 1979 Dubois et al., 1981b). Bronsted exponents. 

In contrast, for a proton transfer from a hydrogen-bonded acid occurring by the mechanism in (24), the predicted dependence of kf and on the strength of the catalysing base is quite different. In this case, when the pA bh of the base and the p -value of the hydrogen-bonded acid are closely matched, that is at Ap 0, it would be predicted that the proton in the transition state will be roughly half-transferred and Bronsted exponents a and p of around 0.5 should be observed. 

Apparently, these results implied an inverse relationship between reactivity and selectivity, with the reactivity of the carbocation measured by the inverse of the rate constant for solvolysis. This indeed was not unexpected in the context of a general perception that highly reactive reagents, especially reactive intermediates such as carbocations, carbanions, or carbenes are unselective in their reactions.257 259 Such a relationship is consistent with a natural inference from the Hammond postulate258 and Bell-Evans-Polanyi relationship,260 and is illustrated experimentally by the dependence of the Bronsted exponent for base catalysis of the enolization of ketones upon the reactivity of the ketone,261,262 and other examples21,263 including Richard s careful study of the hydration of a-methoxystyrenes.229... 

Marcus rate theory is useful to rationalize the connection between reactivity and the slope a of Bronsted plots. The derivative of Equation (19) with respect to ArG° is the slope of the Marcus curve, which corresponds to the Bronsted exponent a for a given free energy of reaction ArG°, Equation (20).74 80... 

Kinetic isotope effects and Bronsted exponents / A i Ha, for the third-order rate constants for a set of carboxylic acid-carboxylate ion buffers seem to be... 

Whether, in general, the Bronsted exponent provides a guide to the degree of proton transfer is an important question, since one of the objects of reaction kinetics is to obtain information about the transition state. At present, the question is largely unanswered. One view [79] is that current studies show that the Bronsted exponent is a very poor guide , whereas others feel that with certain modifications to the theory... 

Some years ago Bell [86] noted that, for ketones 1, 2, 3, 4, 6,10,14 and 17 in Table 2, as the value of log10 R increases the Bronsted exponent decreases smoothly. A linear relation... 

Data are not available which permit a check of the assumption that similar Bronsted exponents are obtained by variation of either the base catalyst or the ketone (j3B and j3s, respectively). It was claimed recently [80] that Bronsted exponents for ketones obtained in these two ways are the same ( 3B = (3 ). This claim was based on an analysis of some of the data in Table 2, but is untenable. The values of 3S were calculated from values of log, 0 R and p caic. for compounds 1, 2, 3, 4, 6, 8, 14, 15, 16, 17 and 18 in Table 2 and compared with the values of (3 (= pB) shown in Table 2. Since the pKcaic. values were themselves calculated from these same kinetic data by assuming 3B = 3S (see earlier), the argument is circular. 

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)... 

The foregoing results indicate that it is difficult to obtain information about transition state structure from the size of the Bronsted exponent in the ionization of nitroparaffins. The current view is that proton transfer is about half-complete when the transition state is reached [76(b), 106]. It is difficult to reconcile the results for nitroparaffins with the hope that the Bronsted exponent may in general give an indication of transition state structure and there is a general tendency to treat nitroparaffins as exceptional and still use this concept in other cases. 

Similar Bronsted exponents, 0.94 0.02 for phenolate ions and 0.98 0.08 for secondary amines, were observed but the Bronsted plots for these two types of catalyst were separated by about half a unit in log 0 k. The values of the Bronsted exponents are close to the limiting values of unity expected for normal proton transfer. Reaction (78) is thermodynamically favourable in the reverse direction and for fully normal proton transfer the rate coefficients for recombination of the carbanions with phenols and ammonium ions should be around 101 0 1 mole"1 sec"1. Calculations using the approximate pif 21 for this acid measured [69] in dimethyl... 

The first mechanism (a) occurs if fe t < k2 and the observed rate coefficient is given by feobs = k1. The second mechanism (b) applies if fe i > fe2 and then kohs = k2 x K where K = fe1 /fe j. The two mechanisms which correspond, respectively, to a rate-determining proton transfer and a pre-equilibrium followed by a subsequent step have been discussed in detail for isotope exchange reactions in Sect. 2.2.1. The second possibility (b) is apparently favoured by Cram [120] for racemization of 2-methyl-3-phenylpropionitrile whereas Melander [119] has interpreted his results in terms of the first (a). From the variation of the rate coefficient for racemization in different solvent mixtures of methanol/ dimethylsulphoxide a Bronsted exponent j8 = 1.1 was calculated [119] using an acidity function method which will be described fully in Sect. 4.6. 

For the malononitriles and l,4-dicyano-2-butene, very low primary isotope effects are observed (Table 3). For 2-methyl-3-phenylpropionitrile reacting with methoxide ion in pure methanol, fcH/fcD = 1.15 [119]. Isotope effects [121] on proton transfer from ketones [89] and nitro-paraffins [5] are much higher than these values. It will now been shown that the low primary isotope effects observed for cyanocarbons support [113] the conclusion [64] reached from the high Bronsted exponents that proton transfer occurs through a transition state in which the proton is almost fully transferred. The equilibrium isotope effect (KH /KD = Kr /l) on the ionization of malononitriles (80)... 

A reaction with mechanism (99) should show general base catalysis but under some conditions this catalysis is difficult to detect and the rate may be dominated by hydroxide ion catalysis. However, recent work has now been carried out on the detritiation of chloroform in which general base catalysis by amines was observed [171(a)]. In the work with chloroform in which general base catalysis was not detected [114], since it was not possible to obtain a Bronsted exponent by measuring catalytic coefficients for a series of bases, an alternative procedure first suggested by Bell and Cox [172] was used. The rate of detritiation of chloroform was measured in a mixed solvent of water with varying amounts of dimethylsulphoxide and a constant concentration of hydroxide ion. As discussed briefly in Sect. 4.4 an acidity function (H ) has been determined for these solvent... 

The equilibrium constant for eqn. (100) varies with change in solvent composition and this variation is calculated from the acidity function. The effect of this variation in equilibrium constant on the measured value of fe, is used to calculate a Bronsted exponent. The rate coefficient for detritiation kT is related to fe, by a primary isotope effect (assuming mechanism (99) applies) and therefore a plot of log, 0 feT against H +... 

Bronsted exponents for base catalysed proton transfer from carbon acids determined by an acidity function technique in mixed solvents... 

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