Excess Gibbs functions from experimental data

DETERMINATION OF NONELECTROLYTE ACTIVITIES AND EXCESS GIBBS FUNCTIONS FROM EXPERIMENTAL DATA... 

In this chapter, we shall consider the methods by which values of partial molar quantities and excess molar quantities can be obtained from experimental data. Most of the methods are applicable to any thermodynamic property J, but special emphasis will be placed on the partial molar volume and the partial molar enthalpy, which are needed to determine the pressure and temperature coefficients of the chemical potential, and on the excess molar volume and the excess molar enthalpy, which are needed to determine the pressure and temperature coefficients of the excess Gibbs function. Furthermore, the volume is tangible and easy to visualize hence, it serves well in an initial exposition of partial molar quantities and excess molar quantities. 

It is important to note that in the equation (6.19) G is excess Gibbs free energy. This function can be calculated accurately by means of liquid activity models. C is a constant depending on the particular type of EOS. Note also that in the mixing rules of Huron Vidal the parameters in the liquid activity model are not equal with those found at other pressures, and must be regressed again from experimental data. 

There are several ways of reporting experimental data on the deviations from ideal behavior. The most common ones are either the activity coefficients of each component, or the total excess Gibbs energy of the system. If the vapor above the liquid -mixture can be assumed to be an ideal gas, then it is also convenient to plot Pa/Pa as a function of xA where PA and PA are the partial pressure and the vapor pressure of A, respectively. 

An equation for the activity coefficient can be obtained by fitting an appropriate equation to the experimental data. Rather than fitting each individual activity coefficient to its own function, the preferred procedure is to fit the excess Gibbs energy as a function Xi. The activity coefficients are obtained from this fit by noting from eg. that In is in fact a partial molar property specifically, it is the partial molar... 

---