Example 08.08 SLE of the Non-Eutectic System Anthracene - Phenanthrene

problem:

Anthracene (1) and phenanthrene (2) are completely misciible in the solid phase. Calculate the solid-liquid-equilibrium at T = 430 K implying ideal behavior of both phases.

general

constants

and

definitions:

input data

Solution

For ideal behavior, activity coefficients are equal to unity:

The activity of the pure solid at the temperature T can be calculated from:

The solid activity in case of non-eutectic systems can be calculated as:

where xs is the mole fraction vector in the solid phase.

The sum of the solid activities of the components miscible in the liquid phase is equal to unity at the solid-liquid coexistence temperature:

In a binary system this leads to the following function:

and the result for T = 430K:

The liquid phase composition is then given by the activity of a component divided by the sum of the activities of all components:

This leads to the result:

Using the functions defined above, a plot over the whole composition range can be generated: