Thermodynamics of Non-Ideal Solutions

The starting point for developing the thermodynamics of non-ideal solutions is the same as that for ideal solutions. Thus, one considers the equilibrium between each component in the liquid solution and its vapor. It follows from section 1.6 that one may write in general for component A, 

This equation states that chemical potentials of component A in the liquid solution and vapor are equal and that each relates to the vapor pressure of A. However, one would like to have a way of relating the chemical potential of A to its mole fraction in solution. This is achieved by relating the vapor pressure of A to its mole fraction in the liquid solution using a correction factor to make the value of Pa predicted by Raoult s law equal to the true value. Thus, one writes 

It is interesting to evaluate the thermodynamic functions of mixing for the nonideal solution. On the basis of equations (1.8.3) and (1.8.6), 

In the case of non-ideal solutions the mixing functions are often referred to the value they would have in an ideal solution, thereby defining the excess 

In order to calculate the other excess functions one must know the temperature and pressure derivatives of the activity coefficients ya and Yg. The excess entropy of mixing is given by 

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