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:[1] When the activation energy is varied in the first instance, we may observe a related change in pre-exponential factors.
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.
Many of the more popular terms used in discussing the compensation effect are specific to their field or phenomena.
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.
(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.
At the isoequilibrium temperature β, all the reactions in the series should have the same equilibrium constant (Ki)
At the isokinetic temperature β, all the reactions in the series should have the same rate constant (ki)
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 ln σ0 is the preexponential factor, Ea is the activation energy, σ is the conductivity, and kB is the Boltzmann constant, and T is temperature.
LFERs are not always found to hold, and to see when one can expect them to, we examine the relationship between the free-energy differences for the two reactions under comparison.
The above equation may be rewritten as the difference (δ) in free-energy changes (ΔG):
[3] For most reactions the activation enthalpy and activation entropy are unknown, but, if these parameters have been measured and a linear relationship is found to exist (meaning an LFER was found to hold), the following equation describes the relationship between ΔH‡i and ΔS‡i:
[4] Alternately, the isokinetic (or isoequilibrium) temperature may be reached by observing that, if a linear relationship is found, then the difference between the ΔH‡s for any closely related reactants will be related to the difference between ΔS‡'s for the same reactants:
Constable described the linear relationship observed for the reaction parameters of the catalytic dehydrogenation of primary alcohols with copper-chromium oxide.
[5] The foundations of the compensation effect are still not fully understood though many theories have been brought forward.
Compensation of Arrhenius processes in solid-state materials and devices can be explained quite generally from the statistical physics of aggregating fundamental excitations from the thermal bath to surmount a barrier whose activation energy is significantly larger than the characteristic energy of the excitations used (e.g., optical phonons).
[6] To rationalize the occurrences of enthalpy-entropy compensation in protein folding and enzymatic reactions, a Carnot-cycle model in which a micro-phase transition plays a crucial role was proposed.
[7] In drug receptor binding, it has been suggested that enthalpy-entropy compensation arises due to an intrinsic property of hydrogen bonds.
[8] A mechanical basis for solvent-induced enthalpy-entropy compensation has been put forward and tested at the dilute gas limit.
[9] There is some evidence of enthalpy-entropy compensation in biochemical or metabolic networks particularly in the context of intermediate-free coupled reactions or processes.
[10] However, a single general statistical mechanical explanation applicable to all compensated processes has not yet been developed.
[14] Generally, chemists will talk about the isokinetic relation (IKR), from the importance of the isokinetic (or isoequilibrium) temperature, condensed matter physicists and material scientists use the Meyer-Neldel rule, and biologists will use the compensation effect or rule.
[15] An interesting homework problem appears following Chapter 7: Structure-Reactivity Relationships in Kenneth Connors's textbook Chemical Kinetics: The Study of Reaction Rates: The existence of any real compensation effect has been widely derided in recent years and attributed to the analysis of interdependent factors and chance.
[19][20] In response to the criticisms, investigators have stressed that compensatory phenomena are real, but appropriate and in-depth data analysis is always needed.
[22][23] W. Linert wrote in a 1983 paper: Common among all defenders is the agreement that stringent criteria for the assignment of true compensation effects must be adhered to.