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 where the series of closely related reactions are indicated by the index , are the preexponential factors, are the activation energies, is the gas constant, and are constants. Between enthalpies and entropies of activation (enthalpy–entropy compensation) where are the enthalpies of activation and are the entropies of activation. Between the enthalpy and entropy changes of a series of similar reactions (enthalpy–entropy compensation) where are the enthalpy changes and 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 tends to compensate for an increase in , 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, scales proportionately with . 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.
Related terms
Many of the more popular terms used in discussing the compensation effect are specific to their field or phenomena. In these contexts, the unambiguous terms are preferred. The misapplication of and frequent crosstalk between fields on this matter has, however, often led to the use of inappropriate terms and a confusing picture. For the purposes of this entry different terms may refer to what may seem to be the same effect, but that either a term is being used as a shorthand (isokinetic and isoequilibrium relationships are different, yet are often grouped together synecdochically as isokinetic relationships for the sake of brevity) or is the correct term in context. This section should aid in resolving any uncertainties. (see Criticism section for more on the variety of terms)
compensation effect/rule : umbrella term for the observed linear relationship between: (i) the logarithm of the preexponential factors and the activation energies, (ii) enthalpies and entropies of activation, or (iii) between the enthalpy and entropy changes of a series of similar reactions.
enthalpy-entropy compensation : the linear relationship between either the enthalpies and entropies of activation or the enthalpy and entropy changes of a series of similar reactions.
isoequilibrium relation (IER), isoequilibrium effect : On a Van 't Hoff plot, there exists a common intersection point describing the thermodynamics of the reactions. At the isoequilibrium temperature , all the reactions in the series should have the same equilibrium constant ()
isokinetic relation (IKR), isokinetic effect : On an Arrhenius plot, there exists a common intersection point describing the kinetics of the reactions. At the isokinetic temperature , all the reactions in the series should have the same rate constant ()
isoequilibrium temperature : used for thermodynamic LFERs; refers to in the equations where it possesses dimensions of temperature
isokinetic temperature : used for kinetic LFERs; refers to in the equations where it possesses dimensions of temperature
kinetic compensation : an increase in the preexponential factors tends to compensate for the increase in activation energy:
Meyer-Neldel rule (MNR) : primarily used in materials science and condensed matter physics; the MNR is often stated as the plot of the logarithm of the preexponential factor against activation energy is linear:
where is the preexponential factor, is the activation energy, σ is the conductivity, and is Boltzmann's constant, and is temperature.