Calculate the SLE diagram of the eutectic system CCl4 (1) – n-octane (2) with the help of the modified UNIFAC model and the Wilson model. Please take into account that CCl4 shows a phase transition at 225.35 K.
To calculate the equilibrium between the liquid and solid phase, expressions for the fugacity or activity of the components in both phases are required. Due to the existance of a solid phase transition point in case of CCl4, the function for the solid activity has to be extended:
The behavior of the pure solid activities as function of temperature is shown in the following plot. Both values are zero at the respective melting temperatures and the change in slope in case of the first components at its transition point is clearly visible.
To calculate the activity of the components in the liquid, the activity coefficient is required. In this example it is first calculated via the Wilson model:
Calculation of the activity coefficient as function of temperature and composition can be performed using the expression given in Table 5.6:
The solid liquid equilibrium for a given mole fraction can now be calculated using the following function:
In order to calculate the equilibrium using mod. UNIFAC, some information about the components as well as the required model parameters have to be defined first:
There are 3 different subgroups and 2 main groups involved in the calculation. These are shown together with their ID (group number) and (in case of subgrous) the R and Q values in the following vectors. In order to identify the main group that a subgroup belongs to, the index vector s2m is defined. s2mi yields the main group address in the main group vectors, that subgroup i belongs to. The matrix contains the frequency of subgroup i in component j. The matrices , and contain the coefficients for the temperature dependent interaction parameters.
The function for the SLE equilibrium temperature defined above can also be used for modified UNIFAC. Note that the lower bound for the root function was changed. With quadratic temperature dependence of the interaction parameters, it is possible that the activity coefficients decrease drastically at very low temperatures outside the range of applicability of the modified UNIFAC model. This can lead to a second solution of the solid-liquid equilibrium at very low temperatures.
Using the two functions for the SLE equilibrium temperature defined above, the results of both models can now be shown in one plot.