Richard’s rule

Again, it would be good to note some reference values. For monoatomic substances, the increase of entropy in a melting process is about 10 Ct moP (Richards s rule), while for all substances boiling at normal pressure, it is around 100 Ct moU (Pictet-Trouton s rule). 

We can consolidate the values in Table 34.2 with Richard s rule by considering the processes involved when a compound, AB, melts. The overall melting reaction is... 

The first three members of the series with n = 1-3 illustrate Richards s rule with methane, a close to spherical molecule, and Walden s rule with ethane and propane, two non-spherical, rigid molecules. The threefold increase in the entropy of fusion of ethane and propane is caused by the added orientational motion. The linear increase of mass with the number of C-atoms also increases the interaction-energy and, thus, keeps T almost constant... 

On the other hand, the latent enthalpy of melting for a pure metal can be approximated by Richard s rule ... 

A more detailed empirical rule for the entropy of melting is listed at the bottom of Fig. 3.7. Three types of disorder make up the change on fusion positional (pos), orientational (or), and conformational (conf). The approximate contributions to AS are listed in brackets. The first term represents Richards s rule. It is the only contribution for spherical motifs. Irregular motifs can, in addition, show orientational disorder, and thus gain an extra 20-50 J/(K mol) on fusion. Flexible molecules, finally, have a third contribution to the entropy of fusion of 7 -12 J/(K mol) for each flexible bead within the molecule. 

Table 5.2 illustrates a collection of entropies of fusion for crystals with spherical motifs. Motifs are the building blocks, such as atoms, ions, molecules, or parts of molecules, which, by repetition, make up the crystal. One recognizes immediately that all data fit into the limit of Richards s rule (see Sect. 3.4.2). It is thus not the monatomic nature of the motifs, as initially thought by Richards, that is of importance, but rather their spherical nature. Crystals of noble gases and metals are listed in the top portion of the table and fit Richards s rule well. The more complicated inorganic and organic molecules in the two bottom portions are similarly described by Richards s rule. The entropy contribution of 7-14 J/(K mol) seems only a little dependent on the chemical nature of the motif. Size is also not of importance,... 

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