Bronsted plots curved

FIGURE 3.22. Endergonic homolytic dissociation of ion radicals, a Potential energy curves, b Bronsted plots combining the effect of diffusion and activation. kBT/h= 1013s-1, 4/= 1010 s-1, kdif = 1010M- s-1, Drx-w + 2o = 0.3eV, r = 298K. Dotted line log[Pg.225]

Data for the reactions of several cyclic tertiary amines with phenyl, 4-nitro-phenyl and 2,4-dinitrophenyl acetates, at 25°C and ionic strength 1.0, appear in Table 40, and as a Bronsted plot in Fig. 20. The usual irregularities of such plots for nucleophilic attack are evident. Linear relationships between log k and pKa are generally found for groups of compounds of closely similar structure, as for the substituted pyridines in Fig. 20. The data for the two tricyclic amines fall on separate curves, and the points for imidazole clearly fall on neither of the first two sets of lines. The separate lines for the reactions of particular classes of nucleophile are approximately parallel, as is usually found. 

For the reaction of MOH(n 1)+ with propionic anhydride,200 the Bronsted plot of log kMOH versus the pKa of MOH2n+ follows a smooth curve if the values for HzO and OH- are included (Figure 4). However, if the line is drawn to exclude the fcHj0 value, a Bronsted /3 of ca, 0.25 is obtained. Although kMOH for [Co(NH3)5OH]2+ (3 M s 1) is some 103-fold less than k0H, this reaction will compete favourably at neutral pH with base hydrolysis. At pH 7 where the cobalt(III) complex exists almost completely as the MOH2+ species the observed first order rate constant for nucleophilic attack by OH would be ca. 10-4 s 1. AIM solution of [Co(NH3)5OH]2+ would give a value of kobs 2.5 s 1, a rate acceleration of > 104-fold. Since the effective concentration of a nucleophile in the intramolecular reaction could be ca. 102 M, rate accelerations of 10° are possible. The role of the metal ion in such reactions is to provide an effective concentration of an efficient nucleophile at low pH. 

Buckingham and Engelhardt200 have studied the hydrolysis of propionic anhydride in the presence of kinetically inert complexes of the type [M(NH3)5OH]n+. These reactions occur by nucleophilic attack of coordinated hydroxide on the anhydride (Scheme 32). For reactions of M-OHl" l,+ with propionic anhydride, the Bronsted plot of log kMOH versus the p.Ka of M—OH2k+ is a smooth curve if values for reaction with HzO and OH- are included. Although Icmoh for [(NH3)5CoOH]2+ (3 M-1 s-1) is about 103-fold less than fcoH. its reaction will compete favourably at neutral pH with base hydrolysis. Such effects are considered in more detail in Section 61.4.2.2.3. 

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... 

Modern theoretical developments in the theory of proton-transfer reactions suggest that such linear Bronsted plots are only a first approximation when the range of the P-KHA-values is narrow. When a wider range of bases is used, the curve obtained should be such that the Gibbs free energy of activation AG fits the Marcus eqn (6). This equation was derived (Cohen and Marcus, 1968 ... 

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. 

While the equations above suggest that Bronsted plots should be linear, curved plots can arise in some circumstances, as discussed by Kresge, A. J. Chem. Soc. Rev. 1973,2,475. Curved Bronsted plots may also result when a change in the rate-limiting step of a two-step mechanism accompanies the change in base or acid catalyst. For a discussion, see reference 199. 

If the reaction of benzylpenicillin with alkoxide ions proceeded with rate-limiting attack, basic alkoxide ions would be expected to show a negative deviation from the Bronsted plot which is usually curved for such reactions (Hupe and Jencks, 1977 Jencks et al., 1982). 

Figure 1. Curved Bronsted plot for the reaction of carbonyl compounds with bases. [Reproduced by permission from The Proton in Chemistry (second edition), Cornell University Press, Ithaca,...

Fio. 3. Arrhenius plot of logarithm of retention time of 2,3-dimethylbutane versus reciprocal of absolute temperature on zeolite containing predominately Bronsted acid sites (upper curve) and zeolite containing predominately Lewis acid sites (lower curve). 

Then, with a fixed concentration of the acid (HA) and various concentrations of the corresponding salt, a plot of the mutarotation constants against the concentrations of the salt gives a linear curve. The slope of the curve gives kAe, and the intercept on the k axis is kHj0 + kHA [HA]. A plot from the work of Bronsted and Guggenheim189 is shown in Fig. 5. 

Interpretation of the slightly curved Bronsted correlations in terms of Marcus type theory is clouded by the curvature not being accurately defined. This is quite apart from any reservations about the validity of the energy-profile equations. The data can often be force fitted to a linear plot with little difference in correlation coefficient from that to the quadratic (Fig. 7). 

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