Entropy−Enthalpy Compensation in Chemical Reactions and Adsorption: An Exactly Solvable Model

Abstract

The free energies of reaction or activation for many systems respond in a common fashion to a perturbing parameter, such as the concentration of an "inert" additive. Arrhenius plots as a function of the perturbing parameter display a "'compensation temperature" at which the free energy appears to be independent of the perturber, an entropy-enthalpy compensation process. Thus, as the perturber's concentration varies, Arrhenius plots of the rate constant or equilibrium constant exhibit a rotation about the fixed compensation temperature. While this (isokinetic/isoequilibrium) component of the phenomenon of entropy-enthalpy compensation appears in a huge number of situations of relevance to chemistry, biology, and materials science, statistical mechanical descriptions have been almost completely lacking. We provide the general statistical mechanical basis for solvent induced isokinetic/isoequilibrium entropy-enthalpy compensation in chemical reactions and adsorption, understanding that can be used to control of rate processes and binding constants in diverse applications. The general behavior is illustrated with an analytical solution for the dilute gas limit.

Evaluation of the three‐phase equilibrium method for measuring temperature dependence of internally consistent partition coefficients (KOW, KOA, and KAW) for volatile methylsiloxanes and trimethylsilanol

“…This kind of correlation between Δ H and Δ S is termed the enthalpy and entropy compensation effect , because of the cancellation of the 2 terms Δ H and −TΔ S in the Gibbs relationship for the physicochemical process of interest where Δ G OA is Gibbs free energy for the octanol‐to‐air partitioning process. These effects have been observed for many chemical and biological reactions for groups of similar compounds and Henry's law constants for PCBs . However, others have cautioned that such phenomena may be a statistical artifact in the experimental data .…”

“…where DG OA is Gibbs free energy for the octanol-to-air partitioning process. These effects have been observed for many chemical and biological reactions for groups of similar compounds [28][29][30][31] and Henry's law constants for PCBs [27]. However, others have cautioned that such phenomena may be a statistical artifact in the experimental data [32].…”

Experiments and Kinetic Modeling for Reduction of Ferric Oxide-biochar Composite Pellets

“…It can be seen that there is an obvious linear relation between ln(A) and E. The kinetic compensation effect was a widely phenomenon not only in the fields of science, notably heterogeneous catalysis 41,42) but also in chemistry. 43,44) Previous studies believed that kinetic compensation effect was resulted from pure mathematics treatment by the use of Arrhenius formula of free energy, 45) but many theories were developed to explain this effect in follow-up studies. Sosnovski 46) has considered that two kinds of materials which have different activation energies could be used to explain this phenomenon.…”

Extremely reactive carbenes: electrophiles and nucleophiles

“…The tandem changes in Δ H ‡ and Δ S ‡ are often referred to as compensation . One frequently observes linear correlations between changes in enthalpy and entropy for a set of related reactions . Parallel decreases in Δ H ‡ and Δ S ‡ in a reaction set are not uncommon, “for each mechanism of interaction between molecules…the maximum reduction in energy for the system is obtained if certain geometrical conditions are met.…”

“…One frequently observes linear correlations between changes in enthalpy and entropy for a set of related reactions. [13] Parallel decreases in ΔH ‡ and ΔS ‡ in a reaction set are not uncommon, [3] "for each mechanism of interaction between molecules…the maximum reduction in energy for the system is obtained if certain geometrical conditions are met. Ratner; subsequently, he held postdoctoral positions in the laboratories of Professors Paul v. R. Schleyer (Erlangen) and Lionel Goodman (Rutgers).…”