Antoine equation for saturation pressure of each component:

(1)

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 (

γ_{1} and

γ_{2}) 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:

(6)

Dew-point pressure calculation:

(7)

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.