 Example 8.09 SLE of the System D-Carvoxime - L-Carvoxime With a Congruent Melting Point

problem:

Calculate the SLE diagram for the binary system d-carvoxime (1)–l-carvoxime (2) with a congruent melting point at a composition x1 = 0.5, Tmax = 365.15 K using
the Porter expression and the following pure component data:  general

constants

and

definitions:    input data     Solution

In a system with a congruent melting point, the components are completely miscible in both the solid and liquid phase. Again, equilibrium exists when the fugacities or activities of all components are identical in both phases. This means:  and

At the congruent melting point (maximum melting temperature of the mixture) shown in the following plot (Fig. 8.1e in the textbook) , The mole fractions of the components are identical in both phases: Using the following expression for the fugacity of the pure solid with the melting temperatures and heats of fusion given above leads to the ratio of the activity coefficients in the two phases: which means that the liquid activity coefficient is 1.432 times that in the solid phase.

We can use the simple Porter expression as a gE-model for both phases:  with the parameters AL and AS for the liquid and solid phase mixture.

It than holds that With the mole fraction at the congruent melting point equal to 0.5, we obtain:  For this mixture of optical isomers, we can safely assume ideal liquid mixture behavior, which leads to negative deviation from Raoult's law in the solid phase:  In this case the activity of a component in the liquid is identical to its liquid mole fraction and can be calculated as: At the correct equilibrium temperature, the summation condition for the mole fractions in the liquid must be met: (starting temperature for root function)  Using these functions, graphical representations of the phase equilibrium can be generated.    