Liquid-solid solution equilibria at constant pressure

When we consider the solubility of a solid component in a solvent, the emphasis is placed on obtaining the mole fraction or other composition variable as a function of the temperature. Thus, Equation (10.96) gives the solubility as a function of the temperature in this interpretation. The solubility in an ideal solution is given by 

14 Liquid-solid solution equilibria at constant pressure 

When a liquid solution and a solid solution are in equilibrium, both components exist in both phases. We again develop the pertinent equations for only one component, because the equations for the second component are identical except for the change of subscripts. The condition of equilibrium is the equality of the chemical potential of the component in the two phases, so 

It is apparent from this equation that we can determine only the difference between the two excess chemical potentials at the experimental conditions. If one is known from other studies, then the other can be determined. It must be pointed out that the difference is not isothermal and, if isothermal quantities are desired, the same corrections as discussed in Section 10.12 must be made by the use of Equation (10.87). 

The equilibrium temperature may be intermediate between the freezing points of the two components, or may be above or below both freezing points. Two special cases are worthy of additional comment. The mole fractions are equal at the composition of a maximum or minimum in the temperature-composition curve. Then, at such an extremum, 

---