Vapor pressure and temperature
Every liquid gives off vapor, and the pressure of that vapor in equilibrium with the liquid rises steeply with temperature. When it reaches the pressure of the surrounding air, the liquid boils. The Clausius-Clapeyron equation links the two, and lets you predict a vapor pressure or a boiling point from a single known point and the enthalpy of vaporization.
The equation
Assuming the enthalpy of vaporization ΔHvap is constant over the range:
ln(P2 ÷ P1) = −(ΔHvap ÷ R) × (1/T2 − 1/T1)
- T1 and T2 are absolute temperatures in kelvins
- P1 is the vapor pressure at T1; for a liquid at its normal boiling point, P1 = 101.325 kPa
- R = 8.314 J/(mol·K)
Solved for the boiling point at a pressure P2:
1/T2 = 1/T1 − R × ln(P2 ÷ P1) ÷ ΔHvap
Example
For water, with ΔHvap = 40.65 kJ/mol and a normal boiling point of 100 °C:
- Vapor pressure at 90 °C: about 70.6 kPa, close to the measured 70.1 kPa
- Boiling point at 70 kPa, the air pressure around 10,000 ft: about 89.8 °C, or 193.6 °F
Built-in substances
The calculator includes water, ethanol, methanol, acetone, benzene, toluene and diethyl ether, each with its enthalpy of vaporization at the normal boiling point. Choose Other to enter any liquid’s ΔHvap and a known temperature and vapor pressure.
Limits of the approximation
ΔHvap decreases slowly as temperature rises and vanishes at the critical point. The equation is therefore most accurate within a few tens of degrees of the reference point. Far from it, the error grows: for water at 25 °C, starting from 100 °C, it predicts about 3.75 kPa while the measured value is 3.17 kPa. For precise work over wide ranges, chemists use the Antoine equation or tabulated data, which fit measured values with empirical constants.
Where it is used
- Predicting boiling points at altitude, in vacuum distillation and in pressure cookers
- Estimating the evaporation of solvents and fuels
- Meteorology, where a version of the equation gives the saturation vapor pressure of water in air