# Single-Component Fugacity

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This Demonstration plots fugacity of a hypothetical single component as a function of temperature or pressure. Use the dropdown menu to select the plot.

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The saturation point is where liquid and vapor have equal fugacities. Above or below the saturation point, the phase with the lower fugacity is the stable phase. The fugacity-versus-pressure plot is for low pressure, where the vapor phase is ideal and the fugacity versus pressure for the gas phase is linear.

When the "high pressure" box is checked, the vapor is assumed to be a real gas and the fugacity versus pressure for the vapor phase is not linear.

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Contributed by: Neil Hendren (October 2018)
Additional contributions by: Rachael L. Baumann and John L. Falconer
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA

## Details

Fugacity is used instead of Gibbs free energy to determine phase equilibrium because it is easier to use (the fugacity of a pure-component ideal gas is the same as the pressure). Fugacity is defined by:

(1)

where is the Gibbs energy, is specific volume, is pressure, is the gas constant, is temperature and is fugacity. When two phases are in equilibrium for a single component, the fugacity of the component is the same in each phase. When only one phase exists, it is the phase with the lower fugacity.

Equation (1) can be integrated, using the fact that the fugacity of an single-component ideal gas is the pressure, to yield:

(2)

where is the Gibbs energy of an ideal gas and is the fugacity coefficient. Equation (2) can be applied to solids, liquids or gases. Below the critical point, the Poynting correction is used to calculate the fugacity of a liquid or solid:

(3)

where is the fugacity coefficient at saturation conditions, is the saturation pressure and is the liquid or solid volume, which is assumed independent of pressure. For low pressure, we assume that

(4)

and

(5)

where the superscripts and represent liquid, solid and saturation properties.

## Permanent Citation

Neil Hendren

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