Antoine equation for saturation pressure of each component:
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)
is excess Gibbs energy and
is the ideal gas constant.
The activity coefficients (γ1
) are given by
is the liquid mole fraction of benzene,
is the liquid mole fraction of ethanol, 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:
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:
is the molar composition at a selected point (black dot).
 J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics
, New York: Prentice Hall, 2012 pp. 372–377, 430.