Clausius-Clapeyron Calculator

Calculate vapor pressure at any temperature using the Clausius-Clapeyron equation. Find enthalpy of vaporization or predict boiling point at different pressures.

🌡️ Thermodynamics📐 ln(P2/P1) = -(ΔHvap/R)(1/T2 - 1/T1)🧪 Chemistry

P1 (mmHg or Pa)

T1 (K)

T2 (K)

ΔHvap (kJ/mol)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Clausius-Clapeyron Calculator	—	ln(P2/P1) = -(ΔHvap/R)(1/T2 - 1/T1)	Pa or mmHg

Step-by-Step Examples

Example 1

Water at 80 C

P1=760 mmHg at T1=373.15 K (100 C). Find P at T2=353.15 K (80 C). dHvap=40.7 kJ/mol.

ln(P2/760) = -(40700/8.314)(1/353.15 - 1/373.15)
= -4895 x (0.002832-0.002680) = -4895 x 1.52x10^-4
= -0.7440
P2 = 760 x e^-0.7440 = 760 x 0.4753 = 361.2 mmHg

✓ P(80C) = 361 mmHg (47.5% of atmospheric)

Example 2

Boiling at High Altitude

Water boils where P = 620 mmHg (high altitude). Find boiling point. P1=760 at T1=373 K.

ln(620/760) = -(40700/8.314)(1/T2-1/373)
Solve: 1/T2 = 1/373 + ln(620/760)/(-4895)
1/T2 = 0.002681 + 0.0000424 = 0.002723
T2 = 367.2 K = 94.0 C

✓ Water boils at ~94 C at high altitude

Example 3

Find dHvap

Measured: P(20 C)=17.5 mmHg, P(100 C)=760 mmHg. Find dHvap.

ln(760/17.5) = -(dH/8.314)(1/373-1/293)
ln(43.43) = 3.771 = -(dH/8.314)(-7.32x10^-4)
dH = 3.771/(8.314x7.32x10^-4) = 3.771/6.086x10^-3 = 619 J
Wait: 3.771 x 8.314/7.32x10^-4 = 42,870 J/mol = 42.9 kJ/mol

✓ dHvap = 42.9 kJ/mol (lit: 40.7 kJ/mol)

Real-World Applications

🏔️

Altitude Cooking

Lower atmospheric pressure at high altitude reduces water boiling point. Food cooks slower.

🧪

Physical Chemistry

Clausius-Clapeyron equation relates P-T behavior of phase transitions.

🏭

Chemical Engineering

Distillation design uses vapor pressure vs temperature relationships.

🌡️

Meteorology

Saturation vapor pressure over water and ice calculated using Clausius-Clapeyron.

Common Mistakes to Avoid

⚠️

T in Kelvin always

Must use Kelvin. T2=353 K for 80 C, not 80.

⚠️

dHvap in joules for R=8.314

dHvap usually given in kJ/mol. Multiply by 1000 before dividing by R=8.314 J/molK.

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Only valid near known data point

Clausius-Clapeyron assumes dHvap is constant with temperature. Works well for temperatures not too far from T1.

Frequently Asked Questions

What is the Clausius-Clapeyron equation? ▾

ln(P2/P1) = -(dHvap/R)(1/T2 - 1/T1). Relates vapor pressure at two temperatures via enthalpy of vaporization.

What is enthalpy of vaporization? ▾

Energy to convert 1 mol of liquid to gas at constant T and P. Water: 40.7 kJ/mol at 100 C. Smaller values: volatile liquids. Larger: strong intermolecular forces.

How does vapor pressure change with temperature? ▾

Always increases with temperature. Molecules gain more energy to escape liquid. Rule of thumb: vapor pressure roughly doubles per 10 C near boiling point.

What is normal boiling point? ▾

Temperature where vapor pressure equals 1 atm (760 mmHg). At higher altitudes, lower P means lower boiling point.

How does dHvap relate to intermolecular forces? ▾

Stronger intermolecular forces (high boiling point): higher dHvap. Water (H-bonding): 40.7 kJ/mol. Hexane (van der Waals): 28.9 kJ/mol.

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Formula Explorer connections

Interpretation: This relationship connects pressure, volume, temperature, amount or phase composition for gases and volatile mixtures. Assumption: Use absolute temperature and compatible pressure-volume units. Ideal behavior weakens at high pressure, low temperature, strong intermolecular attraction or near phase change.

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