Entropy of fusion and the freezing curve

Let us limit ourselves in this discussion to equation (22.5 ) which we write in the form  

On differentiation, we have, since Afh has been assumed to be independent of temperature, 

The sign of this derivative, which tells us the curvature of the line of co-existence of crystals and solution, depends upon the sign of the term 

These two cases are shown diagrammatically in figs. 22.1 and 22.2 they correspond to the entropy of fusion of the solvent at the melting point having a value greater or less than 2R, respectively. 

The dependence of the curvature of the freezing point curve at the origin upon the entropy of fusion of the solvent was first pointed out by van Laar. The most common case corresponds to (22.17) and fig. 22.1 (c/. chap. XIV, 5, table 14.6). On the other hand, for spherical solvent molecules (c/. table 14.5) for which the entropy of fusion is abnormally small, the case (22.18) is realized. The form of the freezing point curve at the origin is thus a useful criterion, in the absence of calorimetric data, for the identification of those compounds which have a low entropy of fusion, f 

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