Entropy predicting relative values

Predicting Relative S° Values of a System Based on an understanding of systems at the molecular level and the effects of heat absorbed, we can often predict how the entropy of a substance is affected by temperature, physical state, dissolution, and atomic or molecular complexity. (All S° values in the following discussion have units of J/mohK and, unless stated otherwise, refer to the system at 298 K.)... 

SAMPLE PROBLEM 20.1 Predicting Relative Entropy Values... 

Analyze and Plan In part (a) we must predict the value for AG° relative to that for AH° on fhe basis of fhe balanced equation for fhe reaction. In parf (b) we musf calculafe fhe value for AG° and compare wifh our qualifafive prediction. The free-energy change incorporafes bofh fhe change in enfhalpy and the change in entropy for fhe reaction (Equation 19.11), so under sfandard conditions ... 

From such crude data as are to be found in the literature we can calculate approximate values of the equilibrium constants, and hence of the free energies of dissociation for the various hexaarylethanes. From our quantum-mechanical treatment, on the other hand, we obtain only the heats of dissociation, for which, except in the single case of hexaphenylethane, we have no experimental data. Thus, in order that we may compare our results with those of experiment, we must make the plausible assumption that the entropies of dissociation vary only slightly from ethane to ethane. Then at a given temperature the heats of dissociation run parallel to the free energies and can be used instead of the latter in predicting the relative degrees of dissociation of the different molecules. 

For purposes of comparison we list in Table XV.8 the entropy change for some ionic equilibria in water at 25°C. Despite the fact that the list includes species of covalent character for which the electrostatic model is a dubious approximation, the over-all entropy change parallels the value predicted from Eq. (XV. 12.2). The AF and Aff show much less correlation. Some idea of the relative importance of the specific character of the ion pair interaction is provided by the data shown in Table XV.9 on the ion-binding capacities of Fe +. 

Equation (6.7) predicts that the equilibrium number of vacancies increases exponentially with temperature. To understand why. it is instructive to compare Fig. 6.2a and 6, where Eq. (6.6) is plotted, on the same scale, for two different temperatures. At higher temperatures (Fig. 6.26), the configurational entropy term becomes more important relative to the enthalpy term, which in turn shifts eq to higher values. 

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