Concerning the Problem of the Isokinetic Relationship. III. The Temperature-Dependance of the hammett Equation

Abstract

It is shown that the temperature-dependence of the Hammett equation is, in contrast to tradition, both physically and experimentally better described by means of temperature-dependent σ and temperature- independent ρ (termed ρo). The relationship between ρo and the customary (temperature dependent) ρ is ρT = ρo(1/T-1/Tbiso)/(1/T-1/Tbiso) where Tbiso , is the isoequilibrium temperature of the benzoic acid ionization, for which the present analysis suggests a value of -255 K, and T is 298 K. In these terms, the temperature variation of the Hammett equation can be evaluated by supplying merely E(u)a (the activation energy for the reaction of the unsubstituted reactant) and ρo, in that the σ value for the isokinetic substituent , i.e., the abscissa of the common point of intersection in the Hammett plot, is σiso = (1/T-1/Tbiso)E(u)a/(2.303Rρo) = E(u)a/(2630po) Further, ρo I related to energies ρo = E(u)a/(ΔH°u-ΔH°s(iso))where ΔH°u and ΔH°s(iso) are the ionization enthalpies of the parent benzoic acid and that bearing the isokinetic substituent , respectively. Analogous equations apply to thermodynamic reaction series when substituting E(u)a for ΔH°u(series). Along these lines the interpretation of the customary Hammett plot is advanced.