Bronsted coefficients proton transfers

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... 

General base catalysis of the cyclization of ethyl 2-hydroxymethyl 4 nitrobenzoate [35], where the acyl group is further activated by electron withdrawal by the nitro-substituent, is characterized by a Bronsted coefficient of 0 97, i.e. unity within the limits of error, suggesting that proton transfer is a diffusion-controlled process (Fife... 

The final step of the convolution analysis is the determination of the transfer coefficient a. This coefficient, sometimes called the symmetry factor, describes how variations in the reaction free energy affect the activation free energy (equation 26). The value of a does not depend on whether the reaction is a heterogeneous or a homogeneous ET (or even a different type of reaction such as a proton transfer, where a is better known as the Bronsted coefficient). Since the ET rate constant may be described by equation (4), the experimental determination of a is carried out by derivatization of the ln/Chet-AG° and thus of the experimental Inkhei- plots (AG° = F E — E°)) (equation 27). 

If a proton-transfer reaction is visualized as a three-body process (Bell, 1959b), a linear free energy relationship is predicted between the acid dissociation constant, Aha, and the catalytic coefficient for the proton-transfer reaction, HA. Figure I shows the relationships between ground-state energies and transition-state energies. This is a particular case of the Bronsted Catalysis Law (Bronsted and Pedersen, 1924) shown in equation (9). The quantities p and q are, respectively, the number of... 

The results obtained for the catalyzed hydrolysis of p-nitrophenyl acetate obey a Bronsted type relationship there is a linear correlation between log feN and pK, with a slope of 1.6 [5, 29]. It is not surprising that the slope is much larger than 1, for the rate coefficients are referred to nucleophilic attack rather than proton transfer. 

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... 

For p-nitrobenzyl cyanide (pK° 13.4) [117] kinetic results were obtained [19] which are similar to the slow proton transfers described for nitroparaffins and ketones. In aqueous solution rate coefficients for amine catalysed detritiation give a Bronsted plot with slope 13 = 0.61 and the rates of the thermodynamically favourable recombination of the car-banion with ammonium ions vary between ca. 103 and 10s 1 mole-1 sec-1. In 80/20 (v/v) ethei ethanol at —77°, a value j3 = 0.49 was observed for catalysis by phenolate ions [12]. The p-nitrophenyl group in this cyanocarbon acid considerably alters the proton transfer behaviour. 

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. 

A number of other proton transfer reactions from carbon which have been studied using this approach are shown in Table 8. The results should be treated with reserve as it has not yet been established fully that the derived Bronsted exponents correspond exactly with those determined in the conventional way. One problem concerns the assumption that the activity coefficient ratios cancel, but doubts have also been raised by one of the originators of the method that, unless solvent effects on the transition state are intermediate between those on the reactants and products, anomalous Bronsted exponents will be obtained [172(c)]. The Bronsted exponents determined for menthone and the other ketones in Table 8 are roughly those expected by comparison with the values obtained for ketones using the conventional procedure (Table 2). For nitroethane the two values j3 = 0.72 and 0.65 which are shown in Table 8 result from the use of different H functions determined with amine and carbon acid indicators, respectively. Both values are roughly similar to the values (0.50 [103], 0.65 [104]), obtained by varying the base catalyst in aqueous solution. The result for 2-methyl-3-phenylpropionitrile fits in well with the exponents determined for malononitriles by general base catalysis but differs from the value j3 0.71 shown for l,4-dicyano-2-butene in Table 8. This latter result is also different from the values j3 = 0.94 and 0.98 determined for l,4-dicyano-2-butene in aqueous solution with phenolate ions and amines, respectively. However, the different results for l,4-dicyano-2-butene are to be expected, since hydroxide ion is the base catalyst used in the acidity function procedure and this does not fit the Bronsted plot observed for phenolate ions and amines. The primary kinetic isotope effects [114] also show that there are differences between the hydroxide ion catalysed reaction (feH/feD = 3.5) and the reaction catalysed by phenolate ions (kH /kP = 1.4). The result for chloroform, (3 = 0.98 shown in Table 8, fits in satisfactorily with the most recent results for amine catalysed detritiation [171(a)] from which a value 3 = 1.15 0.07 was obtained. 

In the ionization of chloroform it is not possible to calculate the rate of recombination of the carbanion with water because a pK value for chloroform is not available. However, since a Bronsted exponent of unity is observed for proton transfer to hydroxide ion it is not unreasonable to assume that the reverse recombination of the carbanion with water occurs at the diffusion limited rate (ca. 1010 1 mole-1 sec-1). Using this value and the forward rate coefficient for proton removal by hydroxide ion, a pTf value for chloroform of 24 is calculated [114]. 

The expected change in Bronsted exponent with change in reactivity is illustrated by the results [49] shown in Table 9 for the hydrolysis of vinyl ethers (mono alkoxy-activated olefins) which occurs by initial slow protonation of olefinic carbon as in mechanism (28). The value of R which is the catalytic coefficient for an acid of pK 4.0 calculated from results for carboxylic acids with pK around 4.0 is taken as a measure of the reactivity of the system. The correlation of a with reactivity is scattered but the trend is in the expected direction. The results are quite similar to those shown for the ionization of ketones in Table 2. For the proton transfers shown in Table 9 the Bronsted exponent has not reached the limiting value of zero or unity even when reaction in one direction is very strongly thermodynamically favourable. The rate coefficient in the favourable direction is probably well below the diffusion limit, although this cannot be checked for the vinyl ethers. Non-limiting values for the Bronsted exponent have also been measured in the hydrolysis of other vinyl ethers [176]. 

The main reaction in MeCN occurs through a base-catalyzed pathway involving formation of a zwitterionic intermediate, equilibrium formation of an anionic intermediate and a rate-limiting proton transfer to base, rate constant kc, followed by a fast leaving-group expulsion. The corresponding reactions in DMSO, however, are found to proceed by both uncatalyzed (via kh) and catalyzed pathways. Similar reactions in benzene show that the Hammett coefficient determined with substituted anilines for the catalyzed path is extremely large (p = —7.7) relative to that for the uncatalyzed path (p = —4.7). The Bronsted fix value (which may, however, be unreliable since the p fa(H20) values are... 

Figure 13 Curvature in a free energy relationship due to a positive Hammond coefficient for the proton transfer from >ff,-dimethyl (9-fluorenyl)sulfonium tetrafluoroborate. The dashed line is fit of the data to a linear Bronsted equation...

When the reaction is homonuclear (AG° = 0), the Bronsted coefficient is exactly equal to 1/2. Equations similar to equation (7.8.10) have also been used to estimate the Bronsted slope for proton and atom transfer reactions [46]. 

It remains to comment on a seeming contradiction for series 10 pi, + is small ( — 0.61), but the Bronsted a is 0.65. The Bronsted coefficient suggests that the proton is more than half transferred from the general acid to in reaction 15. To assess the significance... 

In Ch. 19 Williams describes theoretical simulations of free-energy-relation-ships in proton transfer processes. Both linear and non-linear relations are observed, usually described in terms of Bronsted coefficients or Marcus intrinsic barriers. Derived from empirical data, the phenomenological parameters of themselves do not lead to satisfying explanations at a fundamental molecular level. Theoretical simulations can fill in this gap. 

The numerical values of the forward and reverse Bronsted coefficients in a simple proton transfer should sum to unity. Neither a nor p should exceed unity or be less than zero. Bordwell and his co-workers [29] discovered that in the nitroalkane acid-base system (Eqn. 36) the introduction of electron-donating substituents into R lowered the rate constant for reaction but increased the overall equilibrium constant. 

The Bronsted coefficient, yS, (Table 10) suggests, as expected, that electron-withdrawing substituents in the beta phenyl ring promote increased proton transfer to the base in the transition state for elimination in the 2-phenylethyl series. A concomitant increase in ko Jk r is also observed , and an interpretation has been forwarded that increased beta hydrogen bond breaking is accompanied by increased C -X bond breaking. Consequently the ElcB mechanism is extremely rare and has been considered as a near-paradox - . Two peculiar features of these results warrant further comment. 

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