Chapter

Correlation Analysis in Chemistry

pp 119-173

Multiparameter Extensions of the Hammett Equation

  • John ShorterAffiliated withThe University

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Abstract

The Hammett equation (1937)2,3,4 takes forms (4.1), (4.2), where k or K is the rate or equilibrium constant for a side-chain reaction of a meta- or
$$\log k^0 = \log k^0 + \rho \sigma $$
(4.1)
$$\log K^0 = \log K^0 + \rho \sigma $$
(4.2)
para-substituted benzene derivative. The symbol k 0 or K 0 denotes the statistical quantity approximating to k or K for the “unsubstituted” or “parent” compound. The substituent constant, σ, measures the polar effect relative to hydrogen of a substituent (in the meta- or para-position) and is, in principle, independent of the nature of the reaction. The reaction constant, ρ, depends on the nature of the reaction (including conditions such as solvent or temperature) and measures the susceptibility of the reaction to polar effects. The ionization of benzoic acids in water at 25°C is the standard process for which ρ is defined as 1.000. The value of σ for a given substituent is thus log (K a /K 0 a ), where K a is the ionization constant of the substituted benzoic acid and K 0 a that of benzoic acid itself.