Clausius-Clapeyron Equation
Relating vapor pressure to temperature for phase transitions
The Clausius-Clapeyron Equation
For liquid-vapor equilibrium
Variables:
- P1, P2 = Vapor pressures at T1 and T2
- T1, T2 = Temperatures (Kelvin)
- DeltaHvap = Enthalpy of vaporization (J/mol)
- R = Gas constant (8.314 J/mol·K)
Applications:
- • Vapor pressure calculations
- • Boiling point estimation
- • Phase diagram construction
- • Distillation process design
Alternative Forms
Linear Form:
ln(P) = -DeltaHvap/RT + C
Plot ln(P) vs 1/T; slope = -DeltaHvap/R
Two-Point Form:
ln(P2/P1) = (DeltaHvap/R)(1/T1 - 1/T2)
Most common for comparing two temperatures
Step-by-Step Example
Problem:
The vapor pressure of water is 23.8 mmHg at 25 C. If DeltaHvap = 40.7 kJ/mol, what is the vapor pressure at 40 C?
1) Known values
- P1 = 23.8 mmHg
- T1 = 25 C = 298.15 K
- T2 = 40 C = 313.15 K
- DeltaHvap = 40.7 kJ/mol = 40700 J/mol
- R = 8.314 J/mol·K
- P2 = ?
2) Apply the equation
ln(P2/P1) = (DeltaHvap/R)(1/T1 - 1/T2)
3) Temperature term
1/T1 - 1/T2 = 1/298.15 - 1/313.15 = 0.000161 K^-1
4) Compute ln(P2/P1)
ln(P2/P1) = (40700/8.314) x 0.000161 = 0.788
5) Solve for P2
P2/P1 = e^0.788 = 2.20
P2 = 2.20 x 23.8 mmHg = 52.4 mmHg
Answer:
The vapor pressure of water at 40 C is about 52.4 mmHg.
Key Assumptions and Limits
Assumptions:
- • DeltaHvap roughly constant over range
- • Vapor behaves ideally
- • Liquid volume negligible vs vapor
- • System at equilibrium
Less Accurate When:
- • Very large temperature spans
- • Near critical temperature
- • High pressures (non-ideal vapor)
- • DeltaHvap strongly temperature dependent
Common DeltaHvap Values
| Substance | DeltaHvap (kJ/mol) | Boiling Point (C) |
|---|---|---|
| Water (H2O) | 40.7 | 100.0 |
| Ethanol (C2H5OH) | 38.6 | 78.4 |
| Benzene (C6H6) | 30.7 | 80.1 |
| Acetone (C3H6O) | 29.1 | 56.1 |
Common Mistakes to Avoid
Temperature units
Always use Kelvin, not Celsius.
Energy units
If R is in J/mol·K, use DeltaHvap in J/mol.
Log type
Use natural log (ln), not log10.
Order of temperatures
Use (1/T1 - 1/T2) exactly; reversing changes the sign.
Related Calculators
Frequently Asked Questions
When is the equation most accurate?
Over moderate temperature ranges away from the critical point.
Can I use it for sublimation?
Yes, replace DeltaHvap with Deltasub for solid-to-vapor transitions.
How to get DeltaHvap experimentally?
Measure vapor pressures at different T, plot ln(P) vs 1/T, slope = -DeltaHvap/R.
Why assume constant DeltaHvap?
It simplifies math; DeltaHvap changes slowly over small temperature ranges.