Brpnsted slopes

Finally, in many cases the acidity equilibria cannot be measured but the rate of proton transfer or transmetallation can be measured to give an ionic or ion pair kinetic acidity. Studies using the rates of proton transfer have included the use of isotopes such as tritium and deuterium5,6. The rate is then used to calculate the Brpnsted slope, a, by plotting the logarithm of the proton transfer rate against the pK, as determined by the equilibrium acidity, for a series of compounds. From this plot, the approximate pKa of an unknown compound can be determined by comparison of the same type of compounds. 

Very similar results are found for reactions of quinuclidines with phos-phorylated pyridine, which follow a Brpnsted slope of Pnuc = —0.1. The less reactive phosphorylated 4-morpholinopyridine follows a slope of (3nuc = -0.01 (12). The changes in (3nuc for these phosphorylated pyridines and phosphate esters with a poorer leaving group (lg) represent Hammond effects that are described by the cross-interaction coefficient, pxy, of equation 3. This cross coefficient is larger than the direct coefficient that describes... 

Fig. 8 Schematic representation of how the Brpnsted slope (q ch) is lowered as a result of the 77-donor effect of the MeO group. (Figure taken from Ref. 184, by permission from the American Chemical Society.)...

Kinetic data17 with both phenols and carboxylic acids used as catalysts in reaction (10-27) are summarized in Table 10-6. The Brpnsted plot is shown in Fig. 10-6. The slope of the line gives a, which is 0.54. 

Transition state imbalance in the deprotonation of substituted 2-tetralones by hydroxide ions has been described. A Brpnsted plot of logA versus substrate pAfa is linear, with slope —a) of —0.60 0.01 but the negative deviation of the point for the 6-nitro derivative suggests that delocalization of charge lags behind proton transfer. ... 

The kinetics of the reactions of phthalic and maleic anhydrides with Z-substituted phenols (Z = H, m-Me, p-Me, m-Cl, p-C 1, and -CN) (Scheme 8) were studied in aqueous solution at pH 8.5. Two kinetic processes well separated in time were observed. The fast process was attributed to the formation of the aryl ester in equilibrium with the anhydride and allowed the determination of the rate of nucleophilic attack of the phenol on the anhydride. From the slow kinetic process, the equilibrium constant for this reaction was determined. The Brpnsted-type plots for the nucleophilic attack of substituted phenols on the anhydrides were linear with slopes /SNuc of 0.45 and 0.56 for phthalic and maleic anhydride, respectively. The results are consistent with a mechanism involving rate-determining nucleophilic attack and also with a concerted mechanism.27... 

The easiest test concerns Eq. (22a) describing the LJ-type dissociation. The equation establishes the linear correlation between the dissociation barrier A for a homonuclear admolecule A2 and the atomic heat of chemisorption Qh with the slope of k = 3/2. As seen from Table V, for H2, 02, and N2 dissociated on surfaces of metals as varied as Fe, Ni, Cu, W, and Pt, the experimental values of k lie within the range k = 1.4-1.7, that is, within 10-15% of the theoretical LJ value of k = 1.5. It should be stressed that, unlike similar linear relations between the activation barriers and the heats of reactions (Brpnsted, Polanyi, Frumkin-Temkin-Semye-nov, etc.), Eq. (22a) is not a postulate but a corollary of the general principle (BOC-MP) applied to the one-dimensional dissociation ABS As + Bs. 

Table II. Slope of Brpnsted—Bjerrum Plot for Some Horse-Heart Cytochrome c Reactions (25 °C)...

Although the value of the coefficient 1.16 in (20) does not have as direct a physical significance as the a-exponent in the extended Brpnsted equation (19) because the reaction, solvents and temperature are different, there is still a good linear rate-equilibrium relationship for benzhydryl carbocation formation the overall correlation embraces clearly concave partial correlations with varying slopes for the respective Y series. The whole pattern of substituent effects, pXr vs should be essentially identical (with only the ordinate scale being slightly different) to that of log (/ xy/Z hh) vs 2 a for the solvolyses shown in Fig. 8. 

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