Hammett equation temperature dependence

Hammett equation. What form does TST give for the temperature dependence of Hammett s p for a series in which AS is essentially constant, as is often the case ... 

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... 

In order to gain an insight into the mechanism on the basis of the slope of a Type A correlation requires a more complicated procedure. Consider the Hammett equation. The usual statement that electrophilic reactions exhibit negative slopes and nucleophilic ones positive slopes may not be true, especially when the values of the slopes are low. The correct interpretation has to take the reference process into account, for example, the dissociation equilibrium of substituted benzoic acids at 25°C in water for which the slope was taken, by definition, as unity (p = 1). The precise characterization of the process under study is therefore that it is more or less nucleophilic than the reference process. However, one also must consider the possible influence of temperature on the value of the slope when the catalytic reaction has been studied under elevated temperatures there is disagreement in the literature over the extent of this influence (cf. 20,39). The sign and value of the slope also depend on the solvent. The situation is similar or a little more complex with the Taft equation, in which the separation of the molecule into the substituent, link, and reaction center may be arbitrary and may strongly influence the values of the slopes obtained. This problem has been discussed by Criado (33) with respect to catalytic reactions. 

The analysis of equation 64 offers important insight into the nature of p and a in the Hammett equation. Although the correct general dependence of p on temperature, as predicted from the isokinetic relationship between the enthalpy and the entropy of a reaction is (1, 79, 80)... 

Numerous lists are available in the literature that give the decomposition temperatures or the half-lives at certain elevated temperatures of many initiators. Decompositions of peroxides may proceed via concerted mechanisms and the rates are structure-dependent. This can be illustrated on benzoyl peroxide. The benzoyl groups, the two halves of the molecule, are dipoles. They are attached, yet they repel each other. Rupture of the peroxide link releases the electrostatic repulsion between the two dipoles. Presence of electron donating groups in the para position increases the repulsion, lowers the decomposition temperature, and increases the decomposition rate. The opposite can be expected from electron attracting groups in the same position. The effect of substituents on the rate of spontaneous cleavage of dibenzoyl peroxide was expressed in terms of the Hammett equation, log K/Ko) = pa. This is shown in Table 2.3. 

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