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# What is the Clausius-Clapeyron equation?

 Vocabulary Antoine equation Clausius-Clapeyron equation enthalpy of sublimation enthalpy of vaporization ideal gas law constant vapor pressure
Chemists often use the Clausius-Clapeyron equation to estimate the vapor pressures of pure liquids or solids:

 ln (P/P°) = HR ( 1T° - 1T )

where P is the vapor pressure, P° is a vapor pressure at a known temperature T°, H is an enthalpy of vaporization if the substance is a liquid or an enthalpy of sublimation if it's a solid, R is the ideal gas law constant, and T is the temperature (in kelvins).

The equation is easily derived from first principles. Several approximations are made to simplify the form of the equation:

• The change in volume that accompanies evaporation or sublimation is assumed to be equal to the volume of the vapor produced. This is a good assumption at moderate or low pressures. For example, water is about 1000 times more dense than its vapor around room temperature and pressure, so the volume change for complete evaporation of water equals the volume of vapor porduced to about three significant figures.
• The enthalpy of vaporization (or sublimation) is assumed to be constant over the temperature range of interest. This is never really true, but changes in these H's are very small at low and moderate pressures. As one approaches the critical point, this assumption will fail completely.
• The vapor is assumed to be an ideal gas. Again, this is a good assumption at moderate pressures for most substances.
• The external pressure doesn't affect the vapor pressure. There is a slight dependence on external pressure.

Several of the assumptions fail at high pressure and near the critical point, and under those conditions the Clausius-Clapeyron equation will give inaccurate results. Chemists still like to use the equation because it's good enough in most applications and because it's easy to derive and justify theoretically.

Chemical engineers often use the more accurate Antoine equation to predict vapor pressures.

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! What is the Clausius-Clapeyron equation?