Example P08.01 Solubility of Anthracene and Phenanthrene in Benzene and
Ethanol (Ideal and Modified UNIFAC)
Calculate the solubility of the isomeric compounds anthracene and phenanthrene in benzene and ethanol at 25 °C assuming ideal behavior and using the group contribution method modified UNIFAC.
First calculate the logarithm of the activity of the pure solid components anthracene and phenanthrene at 25°C:
In an ideal liquid mixture, the activity in the liquid phase is equal to the mole fraction (solubility).
In this case the nature of the solvent is not relevant. Note though, that this solubility is expressed as a mole fraction. Solvents with different molecular weight would yield different mass based solubilities.
In order to calculate the real liquid mixture behavior using mod. UNIFAC, the required information on the mixture and the UNIFAC parameters have to be defined:
There are 5 different subgroups and 3 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 activity coefficients of the two solutes in the two solvents can now easily be calculated at the ideal solubility (see above) and the solubility can be iteratively adjusted so that the activity is now equal to the ideal solubility: