Enthalpy-entropy compensation relationship

Certainly, one should be careful in selecting high-quality experimental data for an enthalpy-entropy compensation plot, particularly when limited sets of data are available, since an apparent compensation plot may arise from the experimental errors in measurement, as emphasized by Houk et al. [108]. However, the review of reliable experimental data by Williams et al. [109], as well as the theoretical consideration by Gilson et al. [110, 111] discussed below in detail, leave no doubts about the validity of the enthalpy-entropy compensation relationship itself. 

The relationship of thermodynamic functions of selective bonding of Hb to a series of carboxylic CP in the variation of the degree of ionization of carboxylic groups is expressed by the effect of enthalpy-entropy compensation (Fig. 18). The compensation effect of enthalpy and entropy components is the most wide-spread characteristic of many reactions in aqueous solutions for systems with a cooperative change in structure [78],... 

Enthalpy—Entropy Compensation Effect as Extrathermodynamic Relationship. 64... 

ENTHALPY-ENTROPY COMPENSATION EFFECT AS EXTRATHERMODYNAMIC RELATIONSHIP... 

It would be somewhat surprising that the enthalpy-entropy compensation, though never derived from the fundamental thermodynamic relationships, is found so abundantly in various reactions and equilibria and that the reaction rate and equilibrium are independent of any perturbing factors at the specific temperature. However, it seems natural at the same time that chemical events are not controlled exclusively by a single factor but are rather governed by multiple factors correlating each other. 

Liu L (2001) Q.-X Guo, Isokinetic relationship, isoequilibiium relationship, and enthalpy-entropy compensation. Chem Rev 101 673... 

L. Liu and Q-X. Guo, Isokinetic Relationship, Isoequilibrium Relationship, and Enthalpy-Entropy Compensation, Chem. Rev., 2001,101, 673. R.A. Marcus, Skiing the Reaction Rate Slopes, Science, 1992, 256, 1523. 

Enthalpy-entropy compensation The free energy of equilibria can be decomposed into an enthalpic and entropic component. In biochemical equilibria, there often is a linear relationship between the enthalpy and the entropy, most intuitively explained by the loss of conformational entropy as binding enthalpy increases the stronger the binding the more rigid the complex. There is still controversy on this topic, however, because it is difficult to measure enthalpy and entropy independently and it is even more difficult to explain thermodynamic phenomena with atomistic models. 

Linear enthalpy-entropy compensation is well known to physical organic chemists and has been the subject of controversy since the relationship was first discovered experimentally. We have discussed the complications elsewhere and will only note here that the linearity found by Beetlestone et al. is statistically reliable for most of their examples. The most extensively studied set of small-solute compensation processes in water are the ionizations of weak acids. When acids such as acetic acid or benzoic acid are substituted in their nonpolar parts to form homologous series, the standard enthalpies and entropies of ionization are found to demonstrate compensation behavior with 7], values in the 280-290°K range but only after extraction of all the contributions to these quantities from the electronic rearrangements using methods developed by Hepler and Ives and their coworkers. The obvious conclusion is that this behavior in small-solute processes is due to solvation effects and thus a manifestation of some property of water. As a result of the comparison of their data with these small-solute examples, Beetlestone et al. suggested that bulk water also plays an important role in the protein processes they studied. 

The enthalpy-entropy compensation effect has long been a hot topic in chemical literature, because in principle no explicit relationship between the enthalpy change and the entropy change can be derived from fundamental thermodynamics. Nevertheless, the compensatory enthalpy-entropy relationship has often been observed in both activation and thermodynamic quantities determined for a very wide variety of reactions and equilibria. 

This relationship is often termed enthalpy-entropy compensation, and such correlations have been reported for a wide variety of reactions. For example. Figure 6.83 shows the correlation of AH with - AS for the oxidation of a series of o- and p-substituted anilines by percarbonate in glacial acetic acid. One possible explanation for such correlations is that variations in the enthalpy of the transition state might be reflected in the extent to which transition structures become more or less ordered than the reactants. ... 

Figure 5.7. Enthalpy/entropy plot (AH /AS ) according to Equ. 5.11 exhibiting a linear relationship ( linear enthalpy/entropy compensation law ). From the slope of the line the isokinetic temperature Tp can be estimated.

The slope of this straight line is referred to as the isokinetic temperature, Tp (Barnes, Vogel, and Gordon, 1969 Leffler, 1966). This relationship with a linear thermodynamic compensation of rates is called enthalpy/entropy compensation it is important for the physiological stability of proteins (Lumry and Eyring, 1954). The value Tp is generally between 270°K and 320°K for the thermal destruction of cells Tp is between 320°K and 350°K. The importance of this fact is the possible implication of a uniform mechanism for cell death through protein denaturation. 

Liu L, Guo OX (2001) Isokinetic relationship isoequilibrium relationship, and enthalpy - entropy compensation. Chem Rev 101 673-695... 

The mathematics of the Lewis acid/base concept is that of a data matrix of m rows and n columns. Data are complexation constants, as logA" or AG. Each row corresponds to a Lewis acidity scale towards a reference base B° (/ = 1 to m) and each column corresponds to a Lewis basicity scale towards a reference acid A°j (J = I to n). For a rigorous treatment, the data measured in different media cannot be mixed in the same data matrix. In the matrix measuring Lewis affinity, the data are complexation enthalpies. There are extrathermodynamic relationships (isoequilibrium relationships or enthalpy-entropy compensation law) which allow transformations between blocks of the affinity and basicity matrices. In the principal component analysis of Lewis basicity, this justifies, somewhat, the mixing of affinity columns and basicity columns in a unified basicity-affinity matrix. 

FIGURE 1. Isokinetic relationship derived from an enthalpy/entropy plot compensation effect... 

---