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 ρ_o). The relationship between ρ_o and the customary (temperature dependent) ρ is

ρ_T = ρ_o(1/T-1/T^b_iso)/(1/T-1/T^b_iso)

where T^b_iso , 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 ρ_o, in that the σ value for the isokinetic substituent , i.e., the abscissa of the common point of intersection in the Hammett plot, is

σ_iso = (1/T-1/T^b_iso)E^(u)_a/(2.303Rρ_o) = E^(u)_a/(2630p_o)

Further, ρ_o I related to energies

ρ_o = 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.