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Clausius–Clapeyron Calculator

Find vapor pressure P₂ at temperature T₂ from ΔH and P₁ at T₁

Parameters

J/molⓘ
Kⓘ
Kⓘ
barⓘ
Show Trail

Controls

xⓘ

Calculated Values

Final Pressure P₂:
1.95;bar1.95;bar
ln(P₂/P₁):
0.67;0.67;

Examples

Water vapor pressure

ΔH=40.7 kJ/mol, T₁=373 K, T₂=393 K, P₁=1 bar.

    Estimate P₂

    Lower T step.

      Visualization

      Clausius–Clapeyron Equation — Phase Equilibrium and Vapor Pressure

      The Clausius–Clapeyron equation describes how pressure changes along a phase coexistence curve (e.g. liquid–vapor boundary). From the second law and entropy balance at phase transition: dP/dT = ΔS/ΔV = ΔH/(T·ΔV), where ΔH is latent enthalpy and ΔV is volume change across the transition.

      For vaporization, ΔV ≈ V_vapor − V_liquid ≈ V_vapor (liquid volume negligible). Assuming ideal vapor and constant ΔH over a temperature range, integration gives the Clausius–Clapeyron equation: ln(P₂/P₁) = (ΔH_vap/R)(1/T₁ − 1/T₂), with R = 8.314 J/(mol·K) and ΔH_vap in J/mol.

      Higher temperature increases vapor pressure exponentially — more molecules have energy to escape the liquid surface. Near the critical point, the distinction between phases blurs and the equation breaks down. Far below critical T, it is very accurate for many substances.

      Practical uses: estimate boiling point at altitude (lower atmospheric P → lower boiling T; water boils ~95 °C in Denver vs 100 °C at sea level), estimate ΔH_vap from two vapor pressure measurements, and design distillation columns.

      For solid–liquid equilibrium (melting), use ΔH_fusion with typically much smaller ΔV — the same mathematical form applies. The slope dP/dT on a P–T phase diagram is steep for vaporization, shallow for melting (water is anomalous: ice–water line slopes backward).

      Entropy at phase transition: ΔS = ΔH/T. Clausius–Clapeyron connects measurable P(T) data to fundamental thermodynamic quantities and is essential in meteorology (saturation vapor pressure, humidity), chemistry, and chemical engineering.

      Key Concepts

      • dP/dT = ΔH/(T·ΔV) — coexistence curve slope
      • ln(P₂/P₁) = (ΔH/R)(1/T₁ − 1/T₂) — integrated form
      • ΔH: molar enthalpy of vaporization (J/mol)
      • T in kelvin; R = 8.314 J/(mol·K)
      • Higher T → higher vapor pressure P
      • ΔS = ΔH/T at phase transition

      Real-World Applications

      • Boiling point vs altitude and atmospheric pressure
      • Vapor pressure charts for solvents and refrigerants
      • Distillation and separation process design
      • Meteorology: saturation vapor pressure and humidity
      • Class 12 phase transitions and latent heat
      • Antoine equation (empirical fit) as engineering alternative

      Explore Further

      More thermodynamics tools

      Physics Equations

      Clausius–Clapeyron:
      ln⁡P2P1=ΔHR(1T1−1T2)\ln\frac{P_2}{P_1} = \frac{\Delta H}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)
      Solve:
      P2=P1exp⁡(ΔHR(1T1−1T2))P_2 = P_1 \exp\left(\frac{\Delta H}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)\right)

      Step-by-Step Solution

      See how the main results are calculated.

      1

      Step 1: Phase Equilibrium

      Vapor pressure vs temperature along coexistence curve.

      Equation:

      dPdT=ΔHTΔV\frac{dP}{dT} = \frac{\Delta H}{T \Delta V}

      Explanation:

      Clausius–Clapeyron from entropy balance.

      2

      Step 2: Integrated Form

      Equation:

      ln⁡P2P1=ΔHR(1T1−1T2)\ln\frac{P_2}{P_1} = \frac{\Delta H}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)

      Explanation:

      ΔH ≈ constant over temperature interval; R = 8.314 J/(mol·K).

      3

      Step 3: Exponent

      Calculation:

      ΔHR(1T1−1T2)=407008.314×(1373−1393)=0.6679\frac{\Delta H}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right) = \frac{40700}{8.314}\times\left(\frac{1}{373}-\frac{1}{393}\right) = 0.6679
      4

      Step 4: P₂

      Calculation:

      P2=P1×eexp=1×1.9501=1.9501P_2 = P_1 \times e^{\text{exp}} = 1 \times 1.9501 = 1.9501

      Result:

      P2=1.9501(sameunitsasP1)P₂ = 1.9501 (same units as P₁)
      5

      Step 5: ΔH Sign

      Vaporization: positive ΔH.

      Explanation:

      Higher T → higher vapor pressure P₂ > P₁.

      6

      Step 6: Validity

      Ideal vapor, negligible liquid volume.

      Explanation:

      Use ΔH in J/mol for R in J/(mol·K).

      Frequently Asked Questions (FAQ)

      Difference from ideal gas law?

      Clausius–Clapeyron is along phase boundary; ideal gas is single phase.

      Can use for melting?

      Yes with ΔH_fusion and solid–liquid equilibrium.

      Why ln P?

      Integrating dP/P from thermodynamic relation.

      Boiling at Denver?

      Lower P_boiling ≈ 95 °C due to lower atmospheric pressure.

      ΔH temperature dependent?

      Somewhat — equation assumes constant ΔH over interval.

      Practice MCQs

      1. Increasing T along liquid–vapor line:
      2. ΔH in equation is:
      3. T in Clausius–Clapeyron must be:
      4. At higher altitude, water boils at:
      5. ln(P₂/P₁) positive means:
      6. R used is typically:

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