Reaction constants, Hammett

A plot against Hammett s cr-constants of the logarithms of the rate constants for the solvolysis of a series of Mz-substituted dimethylphenylcarbinyl chlorides, in which compounds direct resonance interaction with the substituent is not possible, yielded a reasonably straight line and gave a value for the reaction constant (p) of — 4 54. Using this value of the reaction constant, and with the data for the rates of solvolysis, a new set of substituent parameters (cr+) was defined. The procedure described above for the definition of cr+, was adopted for... 

The numerical values of the terms a and p are defined by specifying the ionization of benzoic acids as the standard reaction to which the reaction constant p = 1 is assigned. The substituent constant, a, can then be determined for a series of substituent groups by measurement of the acid dissociation constant of the substituted benzoic acids. The a values so defined are used in the correlation of other reaction series, and the p values of the reactions are thus determined. The relationship between Eqs. (4.12) and (4.14) is evident when the Hammett equation is expressed in terms of fiee energy. For the standard reaction, o%K/Kq = ap. Thus,... 

Table 7-2 lists 15 reactions whose rates are correlated by the Hammett equation. Besides the reaction constant p, the table gives a value for k° (from the fitted line), which provides all the information needed to estimate k for any member of the series, if the corresponding o is available, by means of Eq. (7-24). Note that kP in Table 7-2 is generally not identical to the experimental value of k for the ct = 0 member of the series, because this experimental point may deviate from the regression line. 

Equation (7-51), the Taft equation, provides good correlations for many aliphatic reactions. The scope of this relationship is illustrated by Table 7-10. The reaction constant p has been interpreted along the lines described for the Hammett p values. 

Some authors plot log k or AG against 1/e rather than against the Kirkwood function. Since 1/e is nearly linearly related to (e — 1)/(2e + 1), within the assumptions of a theory in which the solvent is treated as a continuum this substitution of variable is not serious. Another approach is to interpret the solvent dependence of the Hammett reaction constant p on a dielectric constant function. ... 

Following the early work by one of the authors and by Sixma on the evaluation of substituent and reaction constants by molecular orbital theory, little more has been done along these hnes. Reaction constants have further been treated theoretically with at least moderate success, and a complete theoretical treatment of the Hammett equation awaits detailed testing. 

A completely different approach has been taken by Hine, who has considered that the substituent and reaction center are not really distinct, both being substituents in a benzene nucleus, and has then related substituent and reaction constants. Although of considerable theoretical interest, Hine s work has little bearing on practical applications of the Hammett equation since he starts from the premise of unique, single-valued substituent constants. This premise is invalid whether we are utilizing the naive approach with three separate, well-defined sets or the more refined methods with a continuous range of para values. 

Finally, two sets of physical properties have been correlated by the Hammett equation. Sharpe and Walker have shown that changes in dipole moment are approximately linearly correlated with ct-values, and Snyder has recently correlated the free energies of adsorption of a series of substituted pyridines with u-values. All the reaction constants for the series discussed are summarized in Table V. 

In the manner outlined, a few attempts have been made to apply the Hammett equation to the transmission of substituent effects in the pyridine series. In the alkaline hydrolysis of 5-substituted ethyl picolinates (5-R-2-COOEt) in 85% ethanol at 25, 35, and 45°, the reaction constants are about 60% as large as those in the corresponding benzene series the overall fit to the Hammett equation, however, is at best fair, since out of four points (R = Et, H, I, Ac) one (Ac) deviates widely. 

In all cases where a sufficiently large number of substituents has been tested, a linear free-energy correlation is found with Hammett s reaction constants are fairly high, the values rang-... 

In Scheme 7-1 kx and kn refer to the rate constants for a benzene derivative, in our case the benzenediazonium ion, bearing a substituent X in the 3- or 4-position, and the corresponding unsubstituted benzene derivative respectively. The term p is Hammett s reaction constant for the reaction, and o is Hammett s substituent constant which is, at least in principle, independent of the nature of the reaction but different for the 3- and 4-positions. A plot of log kx (or log kx - log kH) versus o should give a straight line. Its slope (positive or negative) corresponds to the reaction constant p. Equilibrium relationships are treated analogously. 

Before we close this section we make reference to an extended form of the Hammett equation in which the substituent constant and the reaction constant are separated into contributions from the field effect (F) and the mesomeric effect (R). This procedure was suggested by Taft in 1957 for 4-substituted benzene derivatives. It is called a dual substituent parameter (DSP) equation (Scheme 7-2). 

Figure 10-2 presents the Hammett plots for these two reactions. Each correlation is successful, in that a straight line results. The scatter in these plots is reasonably typical of these correlations, where 10-15 percent deviations are not uncommon. The slope for log k versus cr is +0.91. As one can see, this step accelerates with electron-withdrawing substituents, which are the X s with the positive values of a. A positive reaction constant means that the reaction center (here the carbonyl carbon) is more negative in the transition state. This finding supports the suggestion that the RCS is the addition of the semicarbazide to the carbonyl carbon. 

Hammett correlation. The rate constants for reactions of a group of para-substituted 2-nitrophenyl bromides with the base piperidine are given.40 Estimate the reaction constants p and a for COj. 

Effect on rate assuming no change in mechanism is caused steric factors upon substitution at C and rise to Cp have not been considered. The rate reductions are geared to substiment effects such as those giving rise to Hammett reaction constants on p- and a-aryl substitution. 

AS can be obtained. In most practical applications, the parameter is the solvent composition (41-44, 192-194) however, the functional relationships are of complicated form and have not been expressed algebraically. A slightly different approach makes use of the relationship between log k and the parameter usually the substituent constant a—at different temperatures. From the temperature dependence of the slope—the reaction constant p—the value of /3 is then obtained indirectly (3, 155). Consider the generalized Hammett equation (9, 17) in the form... 

It appeared to the author some years ago that, irrespective of the mechanism of the toxic action of DDT, there might be a correlation of structure and toxicity in analogous compounds. Hammett (13) has shown that the rate and equilibrium constants of over 50 side-chain reactions of meta and para substituted aromatic compounds may be correlated with the so-called substituent constant a, according to the equation log k — log k0 = pa, where k and k0 are rate (or equilibrium) constants for substituted and unsubstituted compounds, respectively, p is the reaction constant giving the slope of the linear relationship, and a is the substituent constant, which is determined by the nature and... 

Fig. 1—2 shows a Hammett diagram for 14 different imidazolides of benzoic acids with a wide range of substituents upon which the reactivity is strongly dependent for example, the difference in rate constants between jV-(4-nitrobenzoyl)imidazole and iV-(4-dimethylaminobenzoyl)imidazole under the same reaction conditions amounts to a factor of about 3000. The Hammett reaction constant p = + 1.85 for the series shown in Fig. 1—2 indicates clearly that the hydrolysis is following a nucleophilic addition-elimination reaction path. 

Pi Hammett reaction constant f refers to forward reaction... 

Fig. 8. Hammett pa correlations for the cycloheptaamylose-catalyzed ( ) and the uncatalyzed (O) decarboxylation of phenylcyanoacetic acid anions at pH 9.24. For the catalyzed reaction, the Hammett reaction constant p = 2.72. For the uncatalyzed reaction, p = 2.44.

The addition of two ortho-methyl groups to cumyl derivatives also results in a decrease in the Hammett reaction constant from p+ = —4.3 for cleavage of X-[8]-(4-nitrobenzoate) to p+ = —3.0 for cleavage of X-[10]-(4-methoxy-benzoate).27 This provides additional support for the conclusion that rotation about the CAr—Ca bond, which will minimize destabilizing steric interactions between methyl groups in the transition state, also reduces stabilizing resonance electron donation from the ring substituent to the benzylic carbon (Scheme 9). 

Table 2 Hammett reaction constants p and ring size for alkaline hydrolysis of ester systems in 70% (v/v) aqueous dioxan.

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