Pxy and Txy Diagrams for Vapor-Liquid Equilibrium (VLE)

The vapor-liquid equilibrium (VLE) behavior of a mixture of benzene () and toluene () is explored in and diagrams. Click the diagram to move the black point that represents the two variables: mole fraction of benzene and temperature or pressure. This system is modeled by Raoult's law, because ideal solution behavior is expected in the liquid phase for such similar molecules. The corresponding bar chart displays the relative amounts of liquid (blue) and vapor (green) that are 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 vary the temperature for the diagram and the pressure for the diagram.

where , , and are the Antoine constants for the relevant compounds. is the saturation pressure () of the components in mmHg. Temperature is in °C.

Raoult's law states that

. (1)

Equation (1) can be simplified by rewriting the toluene liquid composition in terms of the benzene liquid composition

(2)

This is the bubble-point pressure (BP) calculation:

is used to calculate the bubble-point pressure; is the ratio of component ; for Raoult's law, is the ratio of the component partial pressure to the total pressure .

(3)

Multiplying both sides of equation (3) by returns equation (1).

Dew-point pressure (DP) calculation:

is used to calculate the pressure at the dew point.

(4)

Rearranging equation (4) to solve for pressure as a function of benzene vapor composition :

(5)

Lever rule:

,

where is the molar composition at the point selected using the locator (the black point).

Reference

[1] J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, New York: Prentice Hall, 2012 pp. 372–377.