Compensation behavior enthalpy-entropy relationship

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 calculations yield S and AS° values of appreciable magnitude, +18 eu (cal moff and +10 eu, respectively, and in contrast to the free energies, calculated S and H quantities depart substantially from the quadratic relationship given by Eq. 112. In the case of small a and also small 7.,s-, one expects, from Eq. 112, the value of S /AS° to be approximately 0.5, whereas the calculations yield a ratio of approximately 2 (the distinction is pronounced even when the sizable estimated statistical uncertainties ( 5 eu) in the calculated entropies is taken account of). For this result to be compatible with Eq. 112, it would require a sizable positive value of /..S, but in fact the simulation results indicated a.s 0. Thus, for reaction 107, as represented by the simulation and model molecular Hamiltonian [36], we infer that near room temperature the separate entropy and enthalpy quantities are not well accounted for by a harmonic model, whereas, due to compensating effects, harmonic behavior is recovered when they are combined in the free-energy quantities. 

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