Clausius-Clapeyron Equation Calculator

Calculate vapor pressure at any temperature using the Clausius-Clapeyron equation.

1 atm=101325 Pa
Water boils at 373K (100°C)
Water: 40,700 J/mol
Lower T = lower vapor pressure
Please check your inputs and try again.

Vapor Pressure Rises Rapidly with Temperature

The Clausius-Clapeyron relation connects the temperature dependence of saturation vapor pressure to latent heat of phase change. For vaporization with approximately constant enthalpy ΔHvap and ideal vapor behavior, integrating gives ln(P2/P1)=−ΔHvap/R(1/T2−1/T1). Because 1/T decreases as temperature rises, vapor pressure increases exponentially with temperature.

Temperatures must be absolute Kelvin values. The approximation is most reliable over a moderate temperature range where latent heat does not change too much and the vapor behaves nearly ideally. Near the critical point or across large ranges, more detailed vapor-pressure correlations are preferable.

ln(P2/P1)=−(ΔHvap/R)(1/T2−1/T1)
SymbolMeaningWhy it appears / units
PSaturation vapor pressureAny consistent pressure unit because only a ratio appears.
TAbsolute temperatureK; never Celsius in reciprocal-temperature terms.
ΔHvapMolar enthalpy of vaporizationJ/mol when R=8.314J/(mol·K).
RGas constant8.314J/(mol·K).

A plot of lnP versus 1/T is approximately linear with slope −ΔHvap/R under the assumptions. Larger enthalpy of vaporization produces a steeper temperature sensitivity in that plot.

Vapor pressure should rise with temperature for ordinary vaporization. With positive ΔHvap, raising T must increase the predicted equilibrium vapor pressure. If the result decreases, inspect the order of 1/T terms and the sign in the exponent before blaming rounding.

Worked Examples

Example 1: Water at 90°C (363K): ΔH=40700
P₂=101325×exp(-40700/8.314×(1/363-1/373))
Result: 70.1 kPa — water boils at 90°C here
At 3000m altitude: air pressure ~70 kPa
Example 2: Ethanol: P₁=101325 at 351K, ΔH=38600
P at 300K
Result: 8,180 Pa = 0.081 atm
Ethanol vapor pressure at room temperature
Example 3: Doubling pressure estimate
ΔH=40kJ/mol, T1=300K, find T2 for P2/P1=2
Result: T2≈313.5K
A modest temperature rise can cause a large vapor-pressure change.
Example 4: Unit consistency
ΔH=40kJ/mol
Result: use 40000J/mol with R=8.314J/(mol·K)
Matching joules with the gas constant avoids a factor-of-1000 error.

Common Mistakes

⚠️
Using Celsius in 1/T

Reciprocal temperature requires an absolute scale. Convert °C to K by adding 273.15.

⚠️
Combining kJ/mol with R in J/(mol·K)

Convert latent heat to joules per mole or use a gas constant expressed in matching energy units.

⚠️
Assuming ΔHvap is constant over any temperature range

Latent heat decreases with temperature and approaches zero at the critical point, so the integrated approximation has a limited range.

Frequently Asked Questions

Why does water boil at lower temp at altitude?
Boiling occurs when vapor pressure equals atmospheric pressure. At high altitude, atmospheric pressure is lower, so water boils at a lower temperature where its vapor pressure matches. Mt. Everest: water boils at ~69°C.
Engineering applications?
Refrigeration cycles (select refrigerant vapor pressure at operating temperatures), distillation (separation by vapor pressure differences), vacuum evaporation, and cryogenic system design.
Why is vapor pressure so sensitive to temperature?
Raising temperature increases the fraction of molecules with enough energy to escape the liquid phase, and the integrated thermodynamic relation gives an approximately exponential pressure response.
Can pressure be entered in kPa instead of Pa?
Yes, if both P1 and P2 use the same unit, because the equation contains only their ratio. The logarithm must act on a dimensionless ratio.
What does the slope of lnP versus 1/T represent?
Under the constant-enthalpy approximation, the slope is −ΔHvap/R. Experimental vapor-pressure data can therefore be used to estimate enthalpy of vaporization.
Is Clausius-Clapeyron valid for sublimation?
A similar integrated form can be used with the enthalpy of sublimation when solid-vapor equilibrium and the same idealizing assumptions are appropriate.
Why must temperature be absolute in Clausius–Clapeyron calculations?
The integrated Clausius–Clapeyron relation contains reciprocal temperature, 1/T, derived from thermodynamic equations that require an absolute scale. Use kelvin, not Celsius or Fahrenheit. The constant-ΔH approximation is most reliable over a moderate temperature range where latent heat does not vary strongly.

Formula Explorer connections

Interpretation: This formula tracks heat, temperature, work, entropy or transport in a thermodynamic system. Assumption: Use absolute temperature where required and consistent energy units. Constant properties, equilibrium, ideal gases or negligible losses may be assumed.

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