Aggregation of Molecules to Solids and Liquids

When molecules pass from one phase to another, for example, from the solid to the gas, the intensity of the binding forces changes and the potential energy is altered. As the molecules become freer, energy is absorbed, and constitutes what is measured calorimetrically as latent heat. 

For the purposes of a statistical or thermodynamic treatment of phase equilibria the magnitude of the forces themselves is sufficiently characterized by the value of A17 or A f accompanying the transition from one phase to another. 

We may first examine the conditions under which two phases can coexist at constant pressure. Suppose dn gram molecules of substance pass from phase 1 to phase 2. The change in free energy is given by 

according to the convention explained above, is written AG, so that, under conditions of stable coexistence, AG — 0. 

Now AH and AS are both single-valued functions of temperature, and, therefore, AH, on the one hand, and TA8, on the other, when plotted against temperature are respectively represented by lines. Only at the intersection of these two curves can TAS = AH and AG — 0. Thus, for a given pressure, there exists a single equilibrium temperature at which G = G. At any other temperature these two quantities are not equal and no equilibrium is possible. 

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