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Vapor pressure calculation of pure substances

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Section summary
1. Definition
2. Calculation
3. Use

1. Definition

The presence of a liquid always involve the presence of vapor. Part of the molecules constituting the liquid vaporize and part of the vapor condenses. If the vapor is swept away, for example with an open container, the liquid will keep vaporizing and finally dry out. However, if the container is closed, an equilibrium can be reached where the number of molecules vaporized equal the number of molecules that condense. The corresponding pressure is said to be the vapor pressure of the liquid.

The vapor pressure is dependent on the liquid but also on the temperature, the higher the temperature, the higher will be the vapor pressure - also called saturation pressure. The vapor pressure is often noted Ps.

The Calculation methods given below are valid for pure substances, mixtures can lead to more complex laws.

Saturation pressure

Figure 1 : Saturation pressure of a pure substance

2. Calculation

The simpler law, and one of the most used, is the Antoine law. This law represents the evolution of the saturation pressure as a function of the temperature thanks to 3 coefficients A,B and C. Those coefficients are tabulated for many substances now and can be found in the litterature or on internet. For substances whose coefficients are not tabulated, it is possible to carry out experiences where pressure is measured as function of the temperature and to identify the different coefficients.

The Antoine equation is however well representative at low pressures - less than 2 bar abs, when reaching higher pressure, other equations should be used - note that for very quick orders of magnitudes, Antoine equation is often used outside its domain of validity, but this should be done with care.

Antoine equation for vapor pressure

Equation 1 : Antoine Equation

At higher pressure and up to the critical point, Harlacher equation can be an alternative. The expression is however not explicit, requiring more calculation to use.

Harlacher equation for saturation pressure

Equation 2 : Harlacher Equation

Note that the coefficient of the Harlacher equation are different than the coefficient of the Antoine law.

Log is here the natural logarithm. Please pay attention to the unit in which is expressed the pressure from the tables you use for the coeffcients.

3. Use

The vapor pressure of pure substances is one of the most important data in Chemical and Process Engineering. It is used in many applications, one of them being to calculate liquid vapor equilibria and especially flash calculations.