Clausius–Clapeyron Equation for Vaporization

The integrated Clausius–Clapeyron equation estimates how a liquid’s saturation vapor pressure changes with temperature. The relation is useful for Estimate vapor pressure at a nearby temperature or compare boiling conditions.. For water, use p₁=23.8 kPa at 298 K and ΔHvap=44.0 kJ/mol. At 308 K the estimate is p₂≈41.8 kPa. Check: saturation pressure rises as temperature rises. The final check tests a balance, direction or magnitude relevant to this formula. First map each quantity to the actual experiment, then substitute values. The result describes the modelled relationship; it does not automatically establish every mechanism in the real sample.

The symbols mean: p₁,p₂: saturation vapour pressures at T1 and T2 (Pa); T₁,T₂: absolute temperatures (K); ΔH_vap: molar enthalpy of vaporization (J/mol); R: universal gas constant (J·mol⁻¹·K⁻¹). Follow p₁ and p₂ in the same pressure unit · T in K · ΔHvap in J/mol · R in J·mol⁻¹·K⁻¹. Concentrations, activities, volumes and times must use compatible scales. A logarithm needs a dimensionless argument, and a balance must include all contributing species. State temperature and standard state whenever they are part of the definition; otherwise the result may refer to a different chemical condition. An amount is not a mass without molar mass, and activity is not an unnormalised concentration. Say whether inputs were measured or taken from a reference.

Assume ideal vapor, negligible liquid molar volume and nearly constant enthalpy of vaporization between the two temperatures. The approximation is less reliable near the critical point or across a broad temperature range. Check this assumption for the actual sample, temperature and phase. Nonideality, mass transport or side reactions can make a precise calculation systematically wrong. Compare the balanced reaction and the activity or concentration scale with the model, then state the assumption that most affects the result. Near model boundaries, check activities and phase state rather than extending a dilute-solution approximation. Different conditions require a fresh model check.

Recalculate the example: For water, use p₁=23.8 kPa at 298 K and ΔHvap=44.0 kJ/mol. At 308 K the estimate is p₂≈41.8 kPa. Check: saturation pressure rises as temperature rises. Check p₁ and p₂ in the same pressure unit · T in K · ΔHvap in J/mol · R in J·mol⁻¹·K⁻¹ and substitute the value back into the relation. Also ask whether its sign, balance or magnitude is chemically plausible. If a check fails, inspect units, coefficients and reference values before blaming rounding. Substitution checks the algebra; comparing assumptions with the experiment checks whether the model is appropriate.

Clausius–Clapeyron Equation for Vaporization is related to Raoult’s Law, Gibbs-Energie (Freie Enthalpie), van der Waals Equation, Kirchhoff’s Law for Reaction Enthalpy, Gibbs Phase Rule, but answers a distinct question: Estimate vapor pressure at a nearby temperature or compare boiling conditions.. Do not confuse it with a relation for a neighboring quantity or a different standard state. Name the target quantity and sample conditions first, then choose the equation containing that quantity. Similar-looking equations may use different stoichiometric bases or validity ranges. The linked entries may supply inputs for another step, but they do not replace this distinction. This keeps the interpretation auditable.