Br nsted plot

Figure 7-3. Br nsted plot for the decomposition of nitramide catalyzed by substituted anilines.

When a Br nsted plot includes acids or bases with different numbers of acidic or basic sites, statistical corrections are sometimes applied in effect, the rate and equilibrium constants are corrected to a per functional group basis. If an acid has p equivalent dissociable protons and its conjugate base has q equivalent sites for proton addition, the statistically corrected forms of the Br insted relationships are... 

Diffusion-limited rate control at high basicity may set in. This is more eommonly seen in a true Br nsted plot. If the rate-determining step is a proton transfer, and if this is diffusion controlled, then variation in base strength will not affect the rate of reaction. Thus, 3 may be zero at high basicity, whereas at low basicity a dependence on pK may be seen. ° Yang and Jencks ° show an example in the nucleophilic attack of aniline on methyl formate catalyzed by oxygen bases. 

This discussion of sources of curvature in Br insted-type plots should suggest caution in the interpretation of observed curvature. There is a related matter, concerning particularly item 5 in this list, namely, the effect of a change in transition state structure. Br nsted-type plots are sometimes linear over quite remarkable ranges, of the order 10 pK units, and this linearity has evoked interest because it seems to be incompatible with Marcus theory, which we reviewed in Section 5.3. The Marcus equation (Eq. 5-69) for the plot of log k against log K of the same reaction series requires curvature, the slope of the plot being the coefficient a. given by Eq. (5-67). A Brjinsted plot, however, is not a Marcus plot, because it correlates rates and equilibria of different reactions. The slope p of a Br nsted plot is defined p = d log kobs/d pK, which we can expand as... 

Make the Br nsted plot, calculate p, and discuss deviations from the line. 

It is traditional to treat H 0+ as an exceptional acid with unusual proton-transfer rate properties which preclude it from being included in such a Br nsted plot. In this case H O ... 

For the reactivity parameters Y, n, a+ (but not a) andN+ the lack of curvature is not unexpected. This is because these parameters are defined with respect to the rate of some standard reaction (solvolysis of t-butyl chloride, substitution of methyl iodide, solvolysis of cumyl chlorides, combination reaction of nucleophiles with a standard electrophile). Therefore the resultant plot is of the type log k vs. log k, while the curvature shown in a typical Br nsted plot (Figure 5) results from a plot of log k vs. log K. This curvature is due to a gradual change from a reactant-like transition state, which is insensitive to a perturbation in the reactivity parameter, to a product-like transition state in which equilibrium perturbations are largely reflected in the transition state (and hence the rate). A log k — log k plot is not expected to show this effect and hence is not expected to show curvature. 

Br nsted plot is found to be dependent on the intrinsic barrier to proton transfer. Fast reactions (small X/4) will show significant... 

Apart from these studies of curved Br nsted plots which have been utilized to verify Marcus theory, many additional examples of curved plots are known together they provide considerable evidence in support of an inverse relationship between reactivity and selectivity in proton transfer reactions. 

Jencks (1972, 1969b) has proposed a model which maintains the significance of a as a measure of transition state structure and yet provides a very elegant rationalization of the fact that linear Br nsted plots are often obtained over large reactivity ranges, both by variation in catalyst pKa and substrate reactivity. Jencks noted that the acid catalysed nucleophilic addition to carbonyl compounds (21) yielded linear Br nsted plots (in apparent violation of the reactivity-selectivity principle) yet as the basicity of the nucleophile N was increased the Br nsted slope decreased (in agreement with the... 

As stated on p. 151, curvature in Br nsted plots has become apparent from studies of fast proton transfer processes. Fundamental differences in Br nsted plots have been observed for reactions of... 

The curvature is large when the intrinsic barrier is low, which is in accord with the observation of curvature in fast reactions. The theory thus supports Kresge s (1973) statement that rapid proton transfers will give curved Br nsted plots and slow proton transfers will give linear plots, irrespective of the identity of the atoms involved. 

Bom-Oppenheimer approximation, 193 Br nsted acid catalysis, 265 Br nsted base catalysis, 265 Br nsted coefficient, 225, 345, 347 Br(nsted relationships, 345 Brj nsted-type plot, 350 curved, 351 Buffer, 24... 

It may be necessary and possible to achieve a good Br nsted relationship by adding another term to the equation, as Toney and Kirsch did in correlating the effects of various amines on the catalytic activity of a mutant enzyme. A simple Br nsted plot failed, but a multiple linear regression on the variables and molecular volume (of the amines) was successful. 

Make the Br nsted plot, calculate 3, and discuss deviations from the line. These data are for the nucleophilic catalysis of the hydrolysis of p-nitrophenyl acetate by imidazoles and benzimidazoles at pH 8.0. The apparent second-order catalytic rate constants are defined by... 

Roberts et al. (1982) concluded that the multistep mechanism involving an electron transfer process can be excluded, considering of the a-value of a Br nsted plot (a=0.5) observed over a wide range of cationic substrates, which agrees with the Marcus theory for atom transfer. The Br nsted a for an atom or group transfer depends on the position of a substituent and the tightness of the transition state (t) as well as on the resemblence of the transition state to reactants and/or products. The Marcus theory predicts that t can be related to the rates of symmetrical reactions. Rates and equilibrium constants were measured for the reactions of 10-methylacridane with a series of 1-benzyl-3-cyanopyridinium ions substituted in the... 

Linearity was demonstrated over a range of 8 pK units. We have now extended the correlation by an additional 2 pK units. Of particular significance is the extension to 1,3-diphenylindene, DPI, whose pKggQu is 13.6. The pK of this compound has been measured directly(13 the value of 19. is within 3 units of that for the solvent methanol, 16.9(14). Curvature is frequently observed in Br nsted plots as the ApK between acid and base tends towards zero(2). 

Fig, 3. Extended Br nsted plot for fluorenes and indenes from data of Table IV and ref, 12. The far left point is 1,3-diphenyl-indene the far right is 2,7 di-t-butylfluorene. 

Fig. 4. Br nsted plot for arylmethanes at 100°, The least squares line is that of the first five points (ref. 16). The last two are p-methylbiphenyl and toluene (Table IV).

The question remains why do two such closely related groups of compounds produce such markedly different Br nsted plots Fluorenes and indenes are derivatives of cyclopentadiene and one wonders if the magic properties of 4n + 2 ring systems are responsible. 

Fig. 5. Combined Br nsted plot including the phenalene derivatives (black squares).

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