Enthalpy-entropy compensation

When a chemical reaction exhibits a linear relationship between enthalpy and entropy, one might observe what is known as an Enthalpy-Entropy Compensation, where the magnitude of change in the Gibbs free energy is less than one might expect. Mathematically, this is because of the Gibbs free energy equation (ΔG = ΔH – TΔS), where the change in enthalpy (ΔH) and the change in entropy (ΔS) have opposite signs—ΔG will change very little if both enthalpy and entropy increase. For instance, in a reaction where the chemical bonds become stronger or where chemical bonds are being formed throughout the course of a reaction a negative ΔH value will result. At the same time, this aforementioned act of forming or even strengthening a bond will limit the movement of the molecule (in terms of the molecule’s ability to rotate, vibrate, etc.) and hence decrease the molecule’s entropy. This leads to a fairly small ΔG value. This effect is frequently invoked in the discussion of the thermodynamics of proteins, ligands, and nucleic acids.

There are two variations on the usage of enthalpy-entropy compensation in explaining a reaction: the weak, and the strong form of compensation.

• The weak form of compensation is described when ΔH and ΔS have the same sign as a change occurs in some thermodynamic quantity excluding temperature. The weak form of compensation is a result of the rules of thermodynamics. Statistical mechanics shows qualitatively that as a system populates the lower energy levels, the enthalpy and entropy will both decrease.
• Given a regular change in some experimental variable (such as a series of homologous molecules, or a series of experimental conditions excluding temperature), the strong form of compensation occurs when ΔH and ΔS exhibit a linear correlation. In this case ΔG will be small relative to the range of values expected from the experiment.

Athel Cornish-Bowden^[1] has argued enthalpy-entropy is probably a statistical artifact, which could result in observing a relationship between two variables which may at first seem to be a trustworthy, but is false because the relationship being observed does not actually exist. Sometimes a graph that is plotted against temperature will be used to attain a value of enthalpy and entropy, when in fact this is not the proper way to measure these values. Assume a linear, Arrhenius plot of the natural log of the rate constant, ln(k), versus inverse temperature T⁻¹. Both the intercept and slope of this plot are used alongside transition-state theory to reveal a linear plot of ΔS^‡ versus ΔH^‡. This approach is fine for ΔH^‡. On the other hand, the ΔS‡ value is derived from an extrapolation that can be as high as twenty times the range of the measured data. One cannot hope for more than a broad idea of the true value of ΔS^‡.

Plots of ΔH^‡ vs. ΔS^‡ have been shown to exhibit an extremely strong linear relationship. Criticism of the enthalpy-entropy compensation arises from this strong correlation, which is “too good to be true.” It is believed these plots are a result of looking at the same variable in two different ways, and nothing experimentally significant is being shown.

Ideally, calorimetry experiments can yield the proper measurements of enthalpy and entropy.

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