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# Pressure-Temperature Diagram for a Binary Mixture

This Demonstration shows a pressure-temperature (-) diagram for an ethane/heptane mixture in vapor-liquid equilibrium. The single-component plots of saturation pressure as a function of temperature are shown, as are - curves at six different ethane mole fractions; the liquid curve is shown in blue, the vapor curve in green. Use the slider to display an additional - curve (dashed) at the ethane mole fraction selected. The critical locus (black curve) represents the critical points for all mixtures of ethane and heptane. Uncheck "show all curves" to show only the selected mole fraction and the pure components.

### DETAILS

The bubble-point and dew-point pressures are calculated from Raoult's law:
,
,
,
where and are the liquid and vapor mole fractions of component ( for ethane and for heptane) and is the saturation pressure.
The saturation pressures are calculated using the Antoine equations:
,
where , and are Antoine constants and is temperature.
The Peng–Robinson equation of state for mixtures is used to determine the phase envelope and the critical locus. The critical point is where the bubble and dew curves meet; connecting these points is the critical locus. The -values are calculated:
,
.
The fugacity coefficient is calculated:
,
,
,
where is the compressibility factor, the superscript is for liquid and vapor, and are constants, and is pressure.
For a mixture:
,
,
,
,
,
,
where and are the attraction and repulsion factors for the mixture, and are the attraction and repulsion parameters for the pure component, is the binary interaction parameter, and are the critical temperature and pressure, is a simplification term, and is the acentric factor.
The equation is solved for the compressibility factor,
,
,
,
where , and are constants.
Reference
[1] J. R. Elliott and C. T. Lira, Introductory Chemical Engineering Thermodynamics, 2nd ed., Upper Saddle River, NJ: Prentice Hall, 2012 pp. 626–628.

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