ENCH 445: Lecture 4 -- Thermodynamics of Phase Equilibrium

The basic items and concepts needed to describe phase equilibrium in this course are as follows:

    1.   Equation of state for a gas, including the ideal gas law and the virial equation of state for multicomponent gas mixtures.  

    2.  Three parameter Pitzer and Curl correlation for the second virial coefficient, including the multicomponent version of this correlation.

    3.  Fugacity and fugacity coefficient for components in a gas mixture, and the relation between the fugacity coefficient and the paramaters in the virial equation of state.

    4.  Fugacity, activity, and activity coefficient of a component in a liquid mixture.

    5.  Prediction of activity coefficients in a liquid mixture using regular solution theory.  

    6.  Prediction of vapor pressures of a pure liquid as a function of temperature using the Antoine equation.

    When performing enthalpy balances, a relation giving the heat of vaporization of a pure liquid as a function of temperature and a relation giving the heat capacity of a pure liquid as a function of temperature will be needed.  For the former we will use the Watson equation and for the later we will use a standard correlation in terms of the reduced temperature and the accentric factor.  

    If two phase are in equilibrium, then the fugacity of a component in one phase can be equated to the fugacity of that component in the other phase.  This relationship among component fugacities, together with the fact that the sum of the mole fractions in any phase are unity, permit the solution of phase equilibrium problems.  More specifically, consider the "bubble T" problem for a five component system where the five mole fractions in the liquid phase are specified along with the pressure.  The objective is to calculate the five mole fractions in the vapor phase and the temperature, i.e., there are six unknowns.  To solve for these unknowns, we can use the five equilibirum expressions for the five components where the fugacities are equated in the two phases.  The fact that the sum of the vapor phase mole fractions in unity is the sixth equation.   This system of equations can be solved using the numerical methods and software discussed in Lectures 2 and 3.