Vapor Pressure (Clausius-Clapeyron Equation)
The Clausius-Clapeyron equation relates vapor pressure to temperature.
Learn how to calculate vapor pressure changes with examples.
The Formula
The Clausius-Clapeyron equation describes how the vapor pressure of a substance changes with temperature. Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase.
As temperature increases, more molecules have enough kinetic energy to escape the liquid surface, so vapor pressure rises. This equation was developed by Benoit Paul Emile Clapeyron in 1834 and later refined by Rudolf Clausius.
At the boiling point, the vapor pressure equals the external atmospheric pressure. This is why water boils at lower temperatures at high altitude, where atmospheric pressure is reduced.
Variables
| Symbol | Meaning |
|---|---|
| P₁ | Vapor pressure at temperature T₁ (in atm, Pa, or mmHg) |
| P₂ | Vapor pressure at temperature T₂ (same units as P₁) |
| ΔH_vap | Enthalpy of vaporization (in J/mol) |
| R | Gas constant = 8.314 J/(mol·K) |
| T₁, T₂ | Absolute temperatures (in Kelvin) |
Example 1
Water has a vapor pressure of 23.8 mmHg at 25°C (298 K). Its ΔH_vap = 40,700 J/mol. What is the vapor pressure at 35°C (308 K)?
Apply the formula: ln(P₂/23.8) = -(40,700/8.314) × (1/308 - 1/298)
Calculate: 1/308 - 1/298 = 0.003247 - 0.003356 = -0.000109
ln(P₂/23.8) = -4,893 × (-0.000109) = 0.5333
P₂/23.8 = e^0.5333 = 1.7046
P₂ ≈ 40.6 mmHg
Example 2
A liquid has vapor pressures of 100 mmHg at 50°C (323 K) and 400 mmHg at 80°C (353 K). What is ΔH_vap?
Rearrange: ΔH_vap = -R × ln(P₂/P₁) / (1/T₂ - 1/T₁)
ln(400/100) = ln(4) = 1.3863
1/T₂ - 1/T₁ = 1/353 - 1/323 = 0.002833 - 0.003096 = -0.000263
ΔH_vap = -8.314 × 1.3863 / (-0.000263)
ΔH_vap ≈ 43,800 J/mol (43.8 kJ/mol)
When to Use It
Use the Clausius-Clapeyron equation when you need to relate vapor pressure to temperature.
- Predicting boiling points at different altitudes or pressures
- Calculating enthalpy of vaporization from experimental data
- Designing distillation and evaporation processes
- Understanding weather phenomena involving humidity and dew point