Liquid-pure solid equilibria at constant pressure

The differences between the standard states of the component in the condensed and gaseous states at the two temperatures cannot be evaluated without knowledge of the composition of standard states in the condensed phases. However, this requires prior knowledge of the excess chemical potentials. The experimental study of the isothermal vapor-liquid equilibria is therefore more convenient and yields the same information. 

The study of the elevation of the boiling point of a solvent by the addition of a nonvolatile solute is a special case of isopiestic vapor-liquid equilibria. The solvent is the only volatile component, and the standard state of the solvent is chosen as the pure solvent. Under these conditions Equation (10.81) may be written as 

This equation can be interpreted as giving the temperature of the equilibrium system as a function of the mole fraction of the liquid phase when A/r,[T, P, x] is known as a function of the temperature and mole fraction. For values of Xj very close to unity, A/r, may be taken as zero, and (H[(g) — / (/)) may be considered to be independent of the temperature and equal to the molar change of enthalpy on evaporation of the pure liquid at T. Then we obtain on integration 

Here R(T )2/A/fv ] is a property of the pure solvent. Equation (10.92) is the basic equation for the simpler expressions involving the mole fraction or molality of the solute of the equation for the boiling point elevation, but it must be emphasized that it is only an approximate equation, valid in the limit as xx approaches unity. Even for the approximation of ideal solutions, Equation (10.90) should be used for the calculation of the boiling point when Xj is removed from unity. 

12 Liquid-pure solid equilibria at constant pressure 

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