Enthalpy–entropy compensation

In thermodynamics, enthalpy–entropy compensation is a specific example of the compensation effect. The compensation effect refers to the behavior of a series of closely related chemical reactions (e.g., reactants in different solvents or reactants differing only in a single substituent), which exhibit a linear relationship between one of the following kinetic or thermodynamic parameters for describing the reactions:

Between the logarithm of the pre-exponential factors (or prefactors) and the activation energies

ln

⁡

A

i

=

α

+

E

a

,

i

R

β

{\displaystyle \ln A_{i}=\alpha +{\frac {E_{{\text{a}},i}}{R\beta }}}

where the series of closely related reactions are indicated by the index i, Ai are the preexponential factors, Ea,i are the activation energies, R is the gas constant, and α, β are constants.

Between enthalpies and entropies of activation (enthalpy–entropy compensation)

Δ

H

i

‡

=

α

+

β

Δ

S

i

‡

{\displaystyle \Delta H_{i}^{\ddagger }=\alpha +\beta \Delta S_{i}^{\ddagger }}

where H‡i are the enthalpies of activation and S‡i are the entropies of activation.

Between the enthalpy and entropy changes of a series of similar reactions (enthalpy–entropy compensation)

Δ

H

i

=

α

+

β

Δ

S

i

{\displaystyle \Delta H_{i}=\alpha +\beta \Delta S_{i}}

where Hi are the enthalpy changes and Si are the entropy changes.

When the activation energy is varied in the first instance, we may observe a related change in pre-exponential factors. An increase in A tends to compensate for an increase in Ea,i, which is why we call this phenomenon a compensation effect. Similarly, for the second and third instances, in accordance with the Gibbs free energy equation, with which we derive the listed equations, ΔH scales proportionately with ΔS. The enthalpy and entropy compensate for each other because of their opposite algebraic signs in the Gibbs equation.

A correlation between enthalpy and entropy has been observed for a wide variety of reactions. The correlation is significant because, for linear free-energy relationships (LFERs) to hold, one of three conditions for the relationship between enthalpy and entropy for a series of reactions must be met, with the most common encountered scenario being that which describes enthalpy–entropy compensation. The empirical relations above were noticed by several investigators beginning in the 1920s, since which the compensatory effects they govern have been identified under different aliases.