## Clausius Clapeyron Equation

We've discussed vapor pressures, and how you can calculate it if you know the number of mols, the volume and the temperature of the vapor. It would be tiresome to have to do this calculation every time you wanted to know what the partial pressure of a substance is at some temperature. The following equation, easily programmed into a spreadsheet, will give a value directly, allowing us to easily determine how a liquid/vapor or solid/vapor system behaves. The Clausius-Clapeyron Equation is:

where:

P is the vapor pressure at temperature T in degrees Kelvin (°K = 273 + °C) P0 is a known vapor pressure at temperature T0 °K

H is the LHV if the substance is a liquid or the enthalpy of sublimation if it's a solid R is the Universal Gas Constant (R = 8.3144 J/mol.K, or 8.3144x10-3 kJ/mol.K, or 1.9872 cal/mol.K)

All you have to do when using this equation is take care that the units you're using are consistent with each other.

For example, we know that the vapor pressure of water is 1000 mbar at its boiling point of 100°C The vapor pressure at 78.32°C (the boiling point of ethanol) is P78.32 in the following sum:

loge(1000/P78 32) = 40.639 (1/373 - 1/351.32) / 8.3144 x 10-3 