About the Clausius-Clapeyron Calculator
This Clausius-Clapeyron calculator uses the two-point form of the Clausius-Clapeyron equation to relate vapor pressure and temperature for a liquid. Give one known point (P₁, T₁) and solve for the vapor pressure at another temperature, the temperature at which the vapor pressure reaches a given value (such as the boiling point under reduced pressure), or the molar enthalpy of vaporization from two measured points.
It is meant for physical and general chemistry students, and for practical questions such as why water boils at a lower temperature at altitude, how much more volatile a solvent becomes when warmed, or estimating the boiling point under vacuum for a rotary evaporator. Any pressure unit works because only the ratio P₂/P₁ enters the equation; temperatures are converted to kelvin internally.
The equation assumes the enthalpy of vaporization is constant over the temperature range, the vapor behaves as an ideal gas and the liquid volume is negligible. It is accurate over modest ranges (tens of degrees) and becomes approximate over wide ranges or near the critical point. It also applies to sublimation if you enter the enthalpy of sublimation.
How to use the clausius-clapeyron calculator
- 1Choose what to solve for: a new vapor pressure, a temperature or ΔHvap.
- 2Pick your temperature and pressure units.
- 3Enter one known point (P₁ at T₁) — the normal boiling point at 1 atm is a convenient choice.
- 4Enter the remaining values and read the answer and the vapor pressure curve.
Formula and method
The Clausius-Clapeyron equation follows from the thermodynamics of a liquid–vapor equilibrium. Assuming the vapor is an ideal gas, the liquid volume is negligible and ΔHvap is constant, integrating between two states gives the two-point form above: the natural log of the pressure ratio is proportional to the change in reciprocal absolute temperature. A plot of ln P against 1/T is a straight line with slope −ΔHvap/R.
Solving for P₂ gives P₂ = P₁·exp[−ΔHvap/R·(1/T₂ − 1/T₁)]. Solving for T₂ gives 1/T₂ = 1/T₁ − R·ln(P₂/P₁)/ΔHvap, and the enthalpy is ΔHvap = R·ln(P₂/P₁) ÷ (1/T₁ − 1/T₂). Temperatures must be absolute (kelvin) and R = 8.314462618 J/(mol·K).
- P₁, P₂
- Vapor pressures at T₁ and T₂ (same unit)
- T₁, T₂
- Absolute temperatures (K)
- ΔHvap
- Molar enthalpy of vaporization (J/mol)
- R
- Gas constant, 8.314462618 J/(mol·K)
Worked examples
Vapor pressure of water at 80 °C
Starting from 101.325 kPa at 100 °C with ΔHvap = 40.66 kJ/mol, ln(P₂/P₁) = −(40,660 ÷ 8.3145) × (1/353.15 − 1/373.15) = −0.742, so P₂ ≈ 48.2 kPa. The measured value is 47.4 kPa — the small gap comes from ΔHvap rising as temperature falls.
Enthalpy of vaporization of water from two points
Water’s vapor pressure is 3.17 kPa at 25 °C and 101.325 kPa at 100 °C. ΔHvap = 8.3145 × ln(31.96) ÷ (1/298.15 − 1/373.15) ≈ 42.7 kJ/mol, an average over the range that sits between the 25 °C (44.0) and 100 °C (40.7) values.
Boiling point of water at 70 kPa (about 3,000 m altitude)
Using the normal boiling point (100 °C at 101.325 kPa) as P₁, T₁: 1/T₂ = 1/373.15 − 8.3145 × ln(70/101.325) ÷ 40,660, giving T₂ ≈ 362.9 K or about 89.8 °C. Food cooks noticeably slower at that altitude.
Frequently asked questions
What does the Clausius-Clapeyron equation calculate?+
It relates the vapor pressure of a substance to temperature. With one known point and the enthalpy of vaporization, you can predict the vapor pressure at another temperature, the boiling point at another pressure, or work out ΔHvap from two measurements.
Do I have to use kelvin?+
The equation itself needs absolute temperature, because it uses 1/T. This calculator lets you enter °C, °F or K and converts to kelvin internally. Pressures can be in any unit as long as P₁ and P₂ use the same one.
Why does water boil at a lower temperature at high altitude?+
Air pressure falls with altitude, and a liquid boils when its vapor pressure equals the surrounding pressure. At 70 kPa the vapor pressure of water reaches the outside pressure at about 89.8 °C instead of 100 °C.
How accurate is the Clausius-Clapeyron equation?+
It is usually within a few percent over ranges of a few tens of degrees. It assumes constant ΔHvap and ideal vapor, so accuracy drops over wide ranges or at high pressures; the empirical Antoine equation fits real data more closely.
What is the enthalpy of vaporization of water?+
About 40.66 kJ/mol at its normal boiling point of 100 °C and about 44.0 kJ/mol at 25 °C. It decreases as temperature rises and becomes zero at the critical point (374 °C).