Understanding Vapor Pressure
Vapor pressure is the equilibrium pressure at which a substance's molecules vaporize and condense at equal rates. Molecules with weak intermolecular bonds or low molar mass exhibit higher vapor pressures—they escape the liquid phase more readily. This property is temperature-dependent: as heat increases, molecular kinetic energy rises, causing more molecules to break free into the gas phase.
The magnitude of vapor pressure determines boiling behaviour. At sea level, water boils at 100 °C because its vapor pressure reaches 101.3 kPa—atmospheric pressure. At higher elevations where air pressure is lower, water boils at a reduced temperature. Conversely, in a sealed pressure vessel, boiling requires higher temperatures because the overlying vapor pressure must be overcome.
Common applications include:
- Predicting boiling points across different atmospheric conditions
- Designing refrigeration and air-conditioning cycles
- Assessing volatile organic compound (VOC) emissions
- Evaluating pump cavitation risk in fluid systems
Clausius-Clapeyron Equation
For a pure substance undergoing phase transition between two states, the Clausius-Clapeyron equation relates pressure and temperature changes to the molar enthalpy of vaporization. This logarithmic relationship holds across wide temperature ranges for most substances.
ln(P₁/P₂) = (ΔHᵥₐₚ/R) × (1/T₂ − 1/T₁)
where R = 8.3145 J/(mol·K)
P₁— Vapor pressure at initial temperature (Pa or atm)P₂— Vapor pressure at final temperature (Pa or atm)ΔHᵥₐₚ— Molar enthalpy of vaporization (J/mol)T₁— Initial temperature (K)T₂— Final temperature (K)R— Universal gas constant, 8.3145 J/(mol·K)
Enthalpy of Vaporization and Phase Diagrams
Enthalpy of vaporization (ΔHᵥₐₚ) is the thermal energy required to convert one mole of liquid into vapour at constant pressure and temperature. It reflects the strength of intermolecular forces: substances with strong hydrogen bonding or dispersion forces require more energy to vaporize.
Water's enthalpy of vaporization is approximately 40,660 J/mol at its normal boiling point. Organic solvents like ethanol (38,560 J/mol) and acetone (30,300 J/mol) require less energy because their intermolecular attractions are weaker.
Phase diagrams illustrate how pressure and temperature control whether a substance exists as solid, liquid, or gas. The vapour pressure curve—separating liquid and gas regions—shows that any point below the curve represents a liquid; points above represent a gas. The triple point marks where all three phases coexist, while the critical point defines conditions beyond which liquid and gas become indistinguishable.
Raoult's Law for Solutions
When a non-volatile solute dissolves in a solvent, the solution's vapor pressure decreases proportionally to the solvent's mole fraction. Raoult's law quantifies this colligative property, essential for understanding distillation efficiency and osmotic pressure.
P_solution = P_solvent × X_solvent
P_solution— Vapor pressure of the solution (Pa or atm)P_solvent— Vapor pressure of the pure solvent (Pa or atm)X_solvent— Mole fraction of solvent (dimensionless, 0 to 1)
Common Pitfalls and Practical Considerations
Accurate vapor pressure calculations require careful attention to units, reference conditions, and physical assumptions.
- Temperature must be in absolute scale — The Clausius-Clapeyron equation requires absolute temperature (Kelvin). Converting from Celsius: T(K) = T(°C) + 273.15. Using Celsius directly produces nonsensical results because the logarithmic relationship depends on ratios, which are meaningless with arbitrary zero points.
- Enthalpy of vaporization is temperature-dependent — Although often treated as constant over small ranges, ΔHᵥₐₚ actually decreases near the critical point. For high-precision work across wide temperature spans (>50 K), use temperature-dependent correlations. For classroom problems or engineering estimates, the constant value suffices.
- Cavitation risk in pumps and turbines — When a pump's suction pressure drops below a fluid's vapor pressure, the liquid vaporizes violently inside the pump, causing cavitation. This creates shock waves that pit metal surfaces and degrade performance. Designers must ensure inlet pressure stays above the fluid's vapor pressure at operating temperature.
- Raoult's law assumes ideal solutions — Real solutions deviate from Raoult's law due to solute-solvent interactions. Ionic solutions, strongly polar mixtures, and concentrated solutions show non-ideal behaviour. For approximate estimates, Raoult's law works; for rigorous design, use activity coefficients or experimental data.