Details

The Antoine equation is used to calculate the saturation pressure (bar) of each component:

,

where , , and are the Antoine constants, is temperature (°C), and the subscript identifies the component ( for benzene and for ethanol).

The fugacities and in the vapor and liquid phases (bar) are defined by:

,

,

where is the activity coefficient approximated by the two-parameter Margules equation, is the liquid mole fraction, is the vapor mole fraction, and is the total pressure (bar).

The fugacities are compared in order to determine the final phase of each component in the system. To have vapor-liquid equilibrium (VLE), the fugacities of each component must be equal in the liquid and vapor phases: and . After the addition of benzene or ethanol, components will either vaporize or condense in order to return to VLE. If the fugacity of the added component in the liquid phase is greater than that of the vapor phase, the components will vaporize:

.

Conversely, if the fugacity of the vapor phase is greater, the components will condense to return to VLE:

.

The total pressure is the sum of the partial pressures:

.

The activity coefficients are approximated by the two-parameter Margules equation:

,

,

where and are the Margules parameters.

Finally:

,

,

where and are the amounts of liquid and vapor in the system calculated from the lever rule and is the total mole fraction of a component.

The screencast video at [1] explains how to use this Demonstration.

Reference

[1] Add a Component to a Mixture with an Azeotrope [Video]. (Dec 16, 2020) www.learncheme.com/simulations/separations/add-a-component-to-a-mixture-with-an-azeotrope.