Hammett-type plots equilibrium

The Hammett reaction constants p = 2.7138 and 3.0157 were determined for addition of water to meta-substituted l-(4-methoxyphenyl)ethyl carbocations (80-X, Scheme 44A) and 1-4-methoxybenzyl carbocations (p-Me-1 +-X), respectively. The value of p = 2.7 for addition of water to 80-X is 36% that of the value of = 7.6, the slope of Hammett-type plots equilibrium constants for addition of water to 80-X to form the alcohol.138 This shows that the addition of water proceeds through a transition state where partial bond formation to the nucleophile results in a 36% change in the interaction between the m-substituent and the cationic benzylic carbon, compared with the complete loss of this interaction at the water adduct. Scheme 44A therefore proceed through a transition state in which there is a 36% change in the interaction between the m-substituent and positive charge at the benzylic carbon due to partial bond formation to the water nucleophile. 

The rate constants for the solvent-recombination process of the carbocations [3C (X,Y,Z)] were determined by the use of the azide clock method (Richard etal., 1984 Richard and Jencks, 1984a,b,c McClelland et al., 1991) and the rate constant of the forward reaction was derived using (38b) as /Ch = /CwXr+ (McClelland et al., 1989,1991). While ordinary Hammett-type relationships were found to be inapplicable to the substituent effects on solvent recombination, there is a rate-equilibrium correlation for all available data on triarylmethyl cations, shown as the linear log/c , vs. p/Cr<- plot, in Fig. 34 with a slope of 0.64. Such a relationship was earlier suggested by Arnett and Hofelich (1983) and Ritchie (1986). The correlation of ky, with the cr scale was... 

The Hammett equation is the best-known and most widely studied of the various linear free energy relations for correlating reaction rate and equilibrium constant data. It was first proposed to correlate the rate constants and equilibrium constants for the side chain reactions of para and meta substituted benzene derivatives. Hammett (37-39) noted that for a large number of reactions of these compounds plots of log k (or log K) for one reaction versus log k (or log K) for a second reaction of the corresponding member of a series of such derivatives was reasonably linear. Figure 7.5 is a plot of this type involving the ionization constants for phenylacetic acid derivatives and for benzoic acid derivatives. The point labeled p-Cl has for its ordinate log Ka for p-chlorophenylacetic acid and for its abscissa log Ka for p-chloroben-zoic acid. The points approximate a straight line, which can be expressed as... 

---