Solutions, associated excess entropy

Table III presents integral excess entropies of formation for some solid and liquid solutions obtained by means of equilibrium techniques. Except for the alloys marked by a letter b, the excess entropy can be taken as a measure of the effect of the change of the vibrational spectrum in the formation of the solution. The entropy change associated with the electrons, although a real effect as shown by Rayne s54 measurements of the electronic specific heat of a-brasses, is too small to be of importance in these numbers. Attention is directed to the very appreciable magnitude of the vibrational entropy contribution in many of these alloys, and to the fact that whether the alloy is solid or liquid is not of primary importance. It is difficult to relate even the sign of the excess entropy to the properties of the individual constituents.

This value is of the same order of magnitude as the number of nearest neighbours, and gives a reasonable interpretation of the entropy change. It seems therefore worthwhile attempting a more detailed discussion of the excess entropy of an associated solution. 

Equation (26.73) has a very simple interpretation. The excess entropy is made up first of a term related to the loss of orientations by the monomolecules on association to form the complex this term is always negative. The two other terms represent the differences between the configurational entropy of the solution and that of a perfect solution (c/. 20.19). It is readily shown, using Stirhng s formula, that the contribution of these two terms to the entropy is (i) positive if + (ii) zero if nj B= Ai+ Bi (iii) negative if... 

The lattice argument used above is oversimplified. It has been found that the excess entropies of mixing (beyond the ideal solution of Eqs. 3.7 and 3.8) can be quite large [ 12 to 16]. This is associated with volume changes in mixing. In 1937, Lennard-Jones and Devonshire [ 17]... 

SOLUTION In this example, we assume that all the nonideality is associated with a difference in energetics between the species in the mixture and the pure species that is, the excess entropy is zero. This assumption is valid for species of roughly the same size. Let s consider the difference in energetics between a andfc in a mixture vs. a andb as pure species. Figure E7.9A illustrates the possible interactions in the mixture and of pure a and pure b. Pure a and b exhibit only a-a interactions and h-h interactions, respectively. The mixture contains not only these like a-a and h-h interactions but also unlike a-h interactions. In fact, when species a and h are mixed, we can view the process in terms of intermolecular interactions. Some a-a interactions of pure a are replaced by a-h interactions, while some h-h interactions of pure h are also replaced by a-h interactions. To quantify the difference in energy of the mixture relative to the pure species and, therefore, the nonideality of the mixture, we compare the magnitude of the interactions in the mixture with those that existed as pure species. 

It is important to note that these data can be retrieved from measurements of IR spectra at room temperature in solution or even in the soUd state and need just a comparative analysis of the spectra of proton donor with and without base (Fig. 10). Application of Eqs. 12 does not require the knowledge of concentrations, but one should keep in mind that the base excess makes it easier to observe. Measurements at different temperatures provide not only the enthalpy (AHhb) but entropy (AShb) of hydrogen bond formation as the parameters of the temperature dependenee of hydrogen bond formation eonstant AThr. The AThr values (Eq. 4) can be obtained from the intensity drop of vah band (Fig. 10). In this case the knowledge of proton donor and proton acceptor concentrations is vital. In the absence of proton donor self-association (relatively low HA concentrations) the hydrogen bonded complexes have 1 1 composition (one HA molecule interacts with one molecule of proton acceptor) and calculations are straightforward. 

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