# Add a Component to a Mixture with an Azeotrope

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Benzene and ethanol, which have an azeotrope at a benzene mole fraction of , are in vapor-liquid equilibrium (VLE) inside a cylinder fitted with a piston. Add either benzene or ethanol to the system by clicking the play button next to “inject isothermally”. The final state when the system returns to equilibrium after injection depends on which component is injected and how much is injected. The piston-cylinder shows the relative amounts of liquid and vapor, and the total moles in the liquid phase and in the vapor phase are displayed. The mole fraction of benzene in the liquid and the vapor are also displayed. The diagram shows the results of the mass balances and demonstrates why a given phase is the final state. To observe behavior for injecting a different number of moles or to inject the other component, click reset before clicking "inject isothermally" again.

Contributed by: Rachael L. Baumann (December 2014)
Additional contributions by: John L. Falconer and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA

## 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