Single Quality Factor for Enthalpy‐Entropy Compensation, Isoequilibrium and Isokinetic Relationships

Abstract

Enthalpy‐entropy compensation (EEC) is very often encountered in chemistry, biology and physics. Its origin is widely discussed since it would allow, for example, a very accurate tuning of the thermodynamic properties as a function of the reactants. However, EEC is often discarded as a statistical artefact, especially when only a limited temperature range is considered. We show that the likeliness of a statistical origin of an EEC can be established with a compensation quality factor (CQF) that depends only on the measured enthalpies and entropies and the experimental temperature range. This is directly derived from a comparison of the CQF with threshold values obtained from a large number of simulations with randomly generated Van ‘t Hoff plots. The value of CQF is furthermore a direct measure of the existence of a genuine isoequilibrium or isokinetic relationship.

Simple Accurate Verification of Enthalpy‐Entropy Compensation and Isoequilibrium Relationship

“…One must therefore conclude that although the coalescence of the Van ‘t Hoff plots is low ( CQF =0.3437 means that there is only a ratio of 2 : 3 between the smallest and largest LnP_Spread ) the origin of the Enthalpy‐Entropy Compensation is not due to a statistical effect. This is at variance with the conclusion in our previous article [33] . It shows that it is not sufficient to look only at the value of CQF to draw a conclusion about the origin of an EEC .…”

“…By means of the hypothetical example shown in Figure 1 we introduce all the relevant input parameters of our model. In the spirit of our previous article [33] we consider the absorption of hydrogen in a set of N =8 samples. From the hypothetic hydrogen pressure‐composition isotherms the equilibrium plateau pressures P i arising from the coexistence of a dilute and a concentrated hydride phase are obtained as a function of temperature within the temperature interval [ T low , T high ].…”

“…On the other hand, the CQF ‐histogram also shows that only 0.15 % of the simulations have CQF <0.1. This means that the probability to generate randomly a situation where all the Van ‘t Hoff plots are essentially parallel to each other is very low (This property of the Compensation Quality Factor was omitted in our previous article [33] ).…”

“…This is at variance with the conclusion in our previous article. [33] It shows that it is not sufficient to look only at the value of CQF to draw a conclusion about the origin of an EEC . Taking K into account is essential for a correct analysis.…”

“…The purpose of the present article is an essential improvement of the method described in our previous article [33] as it takes explicitly the relation between T comp and T hm into account. It aims to provide a very simple, yet accurate verification scheme addressing the nature of both the Enthalpy‐Entropy Compensation and the Isoequilibrium Relationship.…”