Clausius–Clapeyron Equation

The Clausius–Clapeyron equation is a fundamental relation in physical chemistry that explains how the vapour pressure of a liquid varies with temperature. This equation plays a vital role in understanding evaporation, boiling point, volatility, and phase transitions, and is frequently asked in JEE, NEET, and Class 11–12 board exams.

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What is the Clausius–Clapeyron Equation?

The Clausius–Clapeyron equation mathematically expresses the relationship between vapour pressure and temperature for a liquid in equilibrium with its vapour.

It is derived from the more general Clapeyron equation and is applicable when:

• The vapour behaves as an ideal gas
• The molar volume of liquid is negligible compared to vapour
• The enthalpy of vaporization remains constant

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Mathematical Form of Clausius–Clapeyron Equation

The integrated form of the Clausius–Clapeyron equation is:

ln P = − (ΔH_vap / RT) + C

Where:

• P = Vapour pressure
• ΔH_vap = Enthalpy of vaporization
• R = Universal gas constant
• T = Absolute temperature (Kelvin)
• C = Integration constant

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Two-Temperature Form (Most Used in Numericals)

For vapour pressures at two different temperatures, the equation becomes:

ln (P₂/P₁) = − (ΔH_vap/R) (1/T₂ − 1/T₁)

This form is extremely important for solving numerical problems in JEE and NEET.

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Derivation (Conceptual Understanding)

The derivation starts from the Clapeyron equation:

dP/dT = ΔH / TΔV

For liquid–vapour equilibrium:

• ΔV ≈ volume of vapour
• Vapour follows ideal gas equation: V = RT/P

Substituting and integrating gives the Clausius–Clapeyron equation. The negative sign indicates that vapour pressure increases exponentially with temperature.

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Graphical Representation

When ln P is plotted against 1/T, a straight line is obtained.

• Slope = − ΔH_vap / R
• Intercept = constant

This graph helps experimentally determine the enthalpy of vaporization.

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Physical Significance

The Clausius–Clapeyron equation explains why:

• Vapour pressure increases rapidly with temperature
• Volatile liquids have low boiling points
• Liquids evaporate faster at higher temperatures

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Applications of Clausius–Clapeyron Equation

• Calculation of vapour pressure at different temperatures
• Determination of enthalpy of vaporization
• Understanding boiling point variation
• Used in meteorology and atmospheric chemistry
• Important in distillation and refrigeration processes

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Exam-Oriented Important Points

• Valid only for liquid–vapour equilibrium
• Assumes ideal behaviour of vapour
• ΔH_vap is temperature independent
• Higher ΔH_vap → lower vapour pressure

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Common Mistakes Students Make

• Using temperature in Celsius instead of Kelvin
• Ignoring the negative sign in the equation
• Confusing Clapeyron with Clausius–Clapeyron equation

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Conclusion

The Clausius–Clapeyron equation is a powerful tool that connects thermodynamics, vapour pressure, and phase equilibrium. A clear understanding of this equation helps students solve numerical problems efficiently and strengthens conceptual clarity in physical chemistry.

At Chemca – Chemistry Made Easy, our goal is to simplify such important concepts so that learning chemistry becomes logical and enjoyable.

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