Thermodynamic Analysis of the Hammett Equation, the Temperature Dependence of ρ, and the Isoequilibrium (Isokinetic) Relationship

Abstract

Exact thermodynamic analysis of the Hammett equation has led to four differential equations relating δΔH0, δΔS0, δΔCp0, dρ/dT, and d2ρ/dT2. Similar equations can be obtained in terms of activation parameters ΔH≠, etc. For temperature independent δΔH0 and δΔS0 and therefore δΔCp0 = 0, two of these differential equations lead to ρ = ρ∞ [1–(β1/T)] and the familiar isoequilibrium (isokinetic) equation δΔH0 = β1δΔS0. The "isoequilibrium (isokinetic) temperature" represented here by β1 is a temperature independent constant of integration. For constant non-zero δΔCp0 we similarly obtain more complicated expressions for ρ and the "isoequilibrium (isokinetic) temperature." These findings are considered in relation to a model in which environmental contributions (due to solute–solvent interactions) to δΔH0 and δΔS0 are related by a parameter βc. The relationship between β1, and βc is established, and it is shown that in general β1 ≠ βc.