Entropy entropic contributions

To conclude this section let us note that already, with this very simple model, we find a variety of behaviors. There is a clear effect of the asymmetry of the ions. We have obtained a simple description of the role of the major constituents of the phenomena—coulombic interaction, ideal entropy, and specific interaction. In the Lie group invariant (78) Coulombic attraction leads to the term -cr /2. Ideal entropy yields a contribution proportional to the kinetic pressure 2 g +g ) and the specific part yields a contribution which retains the bilinear form a g +a g g + a g. At high charge densities the asymptotic behavior is determined by the opposition of the coulombic and specific non-coulombic contributions. At low charge densities the entropic contribution is important and, in the case of a totally symmetric electrolyte, the effect of the specific non-coulombic interaction is cancelled so that the behavior of the system is determined by coulombic and entropic contributions. 

For the phosphoric anhydrides, and for most of the high-energy compounds discussed here, there is an additional entropic contribution to the free energy of hydrolysis. Most of the hydrolysis reactions of Table 3.3 result in an increase in the number of molecules in solution. As shown in Figure 3.11, the hydrolysis of ATP (as pH values above 7) creates three species—ADP, inorganic phosphate (Pi), and a hydrogen ion—from only two reactants (ATP and HgO). The entropy of the solution increases because the more particles, the more disordered the system. (This effect is ionization-dependent because, at low pH, the... 

This explains why the well-defined diffraction peaks up to the (004) plane are observed (see Figure 9.2). The entropic contribution of the intercalants, which leads to the entropy gain associated with the layer expansion after intercalation of the polymer chains, may not be significant because of the interdigitated layer structure. 

As pointed out in Ref. [4], no entropy variation appears in the description given by the harmonic model, apart from the weak contribution arising from the frequency shifts of the oscillators. The applications of this model are then a priori restricted to redox reactions in which entropic contributions can be neglected. We shall see in Sect. 3 that the current interpretations of most electron transfer processes which take place in bacterial reaction centers are based on this assumption. 

If greater precision is required in describing entropic contributions, the vibrational density of states for each material can be calculated as briefly described in Section 5.5. The entropy due to lattice vibrations can then be calculated. For more details on this concept, see the references associated with Section 5.5. 

Work from Sturtevant s laboratory detailed the kinetics and thermodynamics of zinc binding to apocarbonic anhydrase (carbonate dehydratase) selected data are recorded in Table II (Henkens and Sturtevant, 1968 Henkens etal., 1969). The thermodynamic entropy term A5 at pH 7.0 is 88 e.u. (1 e.u. = 1 cal/mol-K), and this is essentially matched by the binding of zinc to the hexadentate ligand cyclohexylenediamine tetraacetate where AS = 82 e.u. At pH 7.0 the enthalpy of zinc-protein association is 9.8 kcal/mol, but this unfavorable term is overwhelmed by the favorable entropic contribution to the free energy (AG = AH - T AS), where —TAS = -26.2 kcal/mol at 298 K (25°C). Hence, the kinetics and thermodynamics of protein-zinc interaction in this example are dominated by very favorable entropy effects. 

The conformational equilibria of three 2-substituted-l,3-dithianes 112-114 were studied by C NMR spectroscopy at various temperatures and in different solvents (Scheme 6), and both enthalpy and entropy differences were evaluated (Table 8) <1999T359>. The predominance of the axial conformers proved to be of enthalpic origin, in opposition to the entropic contribution which favors the equatorial conformers. The more polar solvent, on the other hand, stabilizes the more polar equatorial conformation. Parallel DFT calculations in the gas phase and in solution emphasized that both 2-substituents point outside the 1,3-dithiane ring system in the two conformations, for example 113-ax and 113-eq, and reproduce the experimentally observed conformational equilibria. Thus, the results of semi-empirical PM3 calculations <1997JMT(418)41> were able to be amended. 

Extreme cases were reactions of the least stabilized, most reactive carbene (Y = CF3, X = Br) with the more reactive alkene (CH3)2C=C(CH3)2, and the most stabilized, least reactive carbene (Y = CH3O, X = F) with the less reactive alkene (1-hexene). The rate constants, as measured by LFP, were 1.7 x 10 and 5.0 X lO M s, respectively, spanning an interval of 34,000. In agreement with Houk s ideas,the reactions were entropy dominated (A5 —22 to —29e.u.). The AG barriers were 5.0 kcal/mol for the faster reaction and 11 kcal/ mol for the slower reaction, mainly because of entropic contributions the AH components were only —1.6 and +2.5 kcal/mol, respectively. Despite the dominance of entropy in these reactive carbene addition reactions, a kind of de facto enthalpic control operates. The entropies of activation are all very similar, so that in any comparison of the reactivities of alkene pairs (i.e., ferei)> the rate constant ratios reflect differences in AA//t, which ultimately appear in AAG. Thus, car-benic philicity, which is the pattern created by carbenic reactivity, behaves in accord with our qualitative ideas about structure-reactivity relations, as modulated by substiment effects in both the carbene and alkene partners of the addition reactions. " Finally, volumes of activation were measured for the additions of CgHsCCl to (CH3)2C=C(CH3)2 and frani-pentene in both methylcyclohexane and acetonitrile. The measured absolute rate constants increased with increasing pressure Ayf ranged from —10 to —18 cm /mol and were independent of solvent. These results were consistent with an early, and not very polar transition state for the addition reaction. 

The conclusion from these experiments is that the associated ions [RXY]-are stereochemically related to the SN2 transition state. Furthermore, little variation occurs in the stability of the associated ions for CH3C1, CH3Br and CH3I, and steric hindrance is apparently of small consequence in the enthalpic and entropic contributions of these equilibria. These data can be compared directly to the solution values for enthalpy and entropy of activation to show that solvation effects on both parameters are indeed responsible for the large variations in rates observed in solution. 

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