Last updated: 2026-06-16

Understanding the Clausius-Clapeyron equation

The Clausius-Clapeyron equation describes how the vapor pressure of a liquid rises as it gets hotter. In its two-point form it connects the vapor pressures at two temperatures through the liquid's enthalpy of vaporization:

Because only the ratio $P_2/P_1$ appears, the two pressures can be given in atm, kPa, mmHg, or bar — whatever unit you choose simply carries through to the answer. Temperatures, however, must be absolute (kelvin), since the equation divides by them.

Worked example

Water boils at $T_1 = 373.15$ K, where its vapor pressure is $P_1 = 1$ atm. With an enthalpy of vaporization of $\Delta H_{vap} = 40.7$ kJ/mol, what is its vapor pressure at $T_2 = 350$ K (about 77 °C)?

Solving the two-point form for the unknown pressure gives:

Substituting the values, with ΔHvap converted to 40,700 J/mol:

So cooling water by about 23 K below its boiling point more than halves its vapor pressure — a steep response that reflects water's strong hydrogen bonding.

Solving for the enthalpy of vaporization

Run the same relationship backwards and two measured pressure–temperature points yield the enthalpy of vaporization:

This is how ΔHvap is often determined experimentally: measure the vapor pressure at several temperatures, plot $\ln P$ against $1/T$, and read ΔHvap from the slope, which equals $-\Delta H_{vap}/R$.

How vapor pressure climbs with temperature

The table below shows how the vapor pressure of water, anchored at 1 atm at its boiling point, falls as the temperature drops — computed from the same equation used above.

The proportional drop grows quickly because vapor pressure depends exponentially on the inverse temperature, not linearly on temperature itself.

When the equation applies

The integrated form assumes the vapor behaves as an ideal gas, that the liquid's molar volume is negligible next to the vapor's, and that ΔHvap is constant over the temperature range. These hold well over modest spans far below the critical point. Near the critical temperature, or across very wide temperature ranges where ΔHvap itself changes, the simple two-point form becomes less accurate and a temperature-dependent treatment is needed.