Clausius–Clapeyron equation calculator
Start from one known point — a vapor pressure at a temperature, such as water boiling at 101.325 kPa and 100 °C. Add the enthalpy of vaporization to get the vapor pressure at another temperature or the boiling point at another pressure, or add a second measured point to get the enthalpy of vaporization.
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How to use it
- Choose what to find: the vapor pressure P₂, the temperature T₂ or the enthalpy of vaporization.
- Enter a known point, P₁ at T₁.
- Enter T₂ and ΔHvap, or P₂ and ΔHvap, or a second point P₂ at T₂.
- Pick the pressure and temperature units; temperatures are converted to kelvin for the calculation.
ln(P₂ ÷ P₁) = −(ΔHvap ÷ R) × (1/T₂ − 1/T₁)
- P₂ = P₁ × e^(−ΔHvap/R × (1/T₂ − 1/T₁))
- 1/T₂ = 1/T₁ − R × ln(P₂ ÷ P₁) ÷ ΔHvap
- ΔHvap = R × ln(P₂ ÷ P₁) ÷ (1/T₁ − 1/T₂)
Worked example
Water: ΔHvap = 40.65 kJ/mol, P₁ = 101.325 kPa at 100 °C (373.15 K). Vapor pressure at 80 °C (353.15 K):
1/353.15 − 1/373.15 = 1.5177 × 10⁻⁴ K⁻¹; × 40,650 ÷ 8.314462618 = 0.742017.
P₂ = 101.325 × e^−0.742017 = 48.2462 kPa.
Two measured points of a liquid, 1 atm at 78.37 °C and 0.5 atm at 62.6 °C:
ΔHvap = 8.314462618 × ln 0.5 ÷ (1/351.52 − 1/335.75) = 43.131 kJ/mol.
Tips
- Kelvin only. The equation uses 1/T; °C values would give nonsense, so the calculator converts them.
- Stay close to the known point. The farther T₂ is from T₁, the more a constant ΔHvap matters.
- Altitude cooking. Lower air pressure means a lower boiling point, so food cooks more slowly in boiling water high up.
Frequently asked questions
What is the Clausius–Clapeyron equation?
ln(P₂ ÷ P₁) = −(ΔHvap ÷ R) × (1/T₂ − 1/T₁), with temperatures in kelvin and R = 8.314462618 J/(mol·K). It links the vapor pressure of a liquid at two temperatures through its enthalpy of vaporization.
How do I find the boiling point at a different pressure?
A liquid boils when its vapor pressure equals the surrounding pressure. Choose the temperature mode, enter the normal boiling point as the known point and the new pressure as P₂. Water at 70 kPa boils at about 89.76 °C by this equation.
How accurate is it?
It assumes ΔHvap stays constant and the vapor behaves as an ideal gas. Over a few tens of degrees it is close; water’s vapor pressure at 80 °C comes out 48.25 kPa against about 47.4 kPa measured, because ΔHvap grows as the temperature falls.
Which ΔHvap should I use for water?
40.65 kJ/mol is the value at the normal boiling point. Near room temperature water’s enthalpy of vaporization is higher, about 44 kJ/mol, so pick the value that matches your temperature range.
Does the pressure unit matter?
Only the ratio P₂ ÷ P₁ enters the equation, so any unit works as long as both pressures use it. The answer comes out in the unit you choose.