Vapor-Liquid Equilibrium Diagram for Non-Ideal Mixture

This Demonstration presents and diagrams for vapor-liquid equilibrium (VLE) of a benzene ()/ethanol () mixture. Drag the black dot to change the benzene mole fraction and the temperature or pressure. This liquid mixture is non-ideal and the system has an azeotrope (constant-boiling mixture) at the conditions used. The activity coefficients in the modified Raoult's law are calculated using the two-parameter Margules model. The corresponding bar chart displays the relative amounts of liquid (blue) and vapor (green) in equilibrium and the mole fraction of benzene in each phase ( for liquid phase, for vapor phase); the relative amounts are calculated using the lever rule. The blue line represents the liquid-phase boundary (bubble point), and the green line represents the vapor-phase boundary (dew point). You can also vary the temperature for the diagram.


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Antoine equation for saturation pressure of each component:
The constants , , and are different for benzene and ethanol; is the saturation pressure of each component in mm Hg, and is the temperature in °C.
For a non-ideal liquid mixture of benzene (B) and ethanol (E), the two-parameter Margules model (equations (3) and (4)) was used to calculate the activity coefficients. This model fits the excess Gibbs free energy according to equation (2)
, (2)
where is excess Gibbs energy and is the ideal gas constant.
The activity coefficients (γ1 and γ2) are given by
, (3)
, (4)
where is the liquid mole fraction of benzene, is the liquid mole fraction of ethanol, and and are the Margules parameters.
The modified Raoult's law was used to calculate the bubble-point and dew-point pressures using the -factors for benzene and ethanol:
, (5)
where is the vapor mole fraction, is the total pressure, and is the saturation pressure calculated from the Antoine equation (1).
Bubble-point pressure calculation:
Dew-point pressure calculation:
Lever rule:
is the molar composition at a selected point (black dot).
[1] J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, New York: Prentice Hall, 2012 pp. 372–377, 430.
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