Phase equilibria and the Clausius-Clapeyron equation

A pure substance's phase diagram maps out which phase — solid, liquid, or gas — is thermodynamically stable at each combination of temperature and pressure, and the lines separating these regions are not arbitrary: each boundary line is the set of temperature-pressure pairs at which two phases have exactly equal molar Gibbs energy, and can therefore coexist in equilibrium. Move off the boundary in either direction and one phase's Gibbs energy drops below the other's, and the system converts entirely to the lower-energy phase; this is exactly why a pure substance's melting or boiling point is not a single fixed number but a whole curve of temperature-pressure pairs — "the boiling point of water" implicitly means "at standard atmospheric pressure," and at any other pressure the liquid-vapour boundary specifies a different equilibrium temperature.

The Clausius-Clapeyron equation makes this pressure-temperature relationship quantitative by working out the slope of the phase boundary directly from the requirement of equal Gibbs energy along it. For the liquid-vapour boundary specifically, treating the vapour as an ideal gas and assuming its molar volume vastly exceeds the liquid's (an excellent approximation, since gases are far less dense than liquids), the equation simplifies to d(ln P)/dT = ΔHvap/(RT²), relating the slope of the vapour pressure curve to the molar enthalpy of vaporisation, ΔHvap. Integrating this relation shows that vapour pressure rises with temperature, exponentially in the simplest approximation — which is exactly consistent with the everyday fact that liquids evaporate faster and boil at a lower external pressure requirement as temperature increases, and, read the other way, why boiling point rises with increasing external pressure, as in a pressure cooker, and falls at the reduced pressure of high altitude.

The magnitude of the enthalpy of vaporisation directly controls how steeply vapour pressure changes with temperature: substances with weak intermolecular forces and a small ΔHvap have vapour pressure curves that respond only mildly to temperature changes, while substances with strong intermolecular forces and a large ΔHvap show vapour pressure that changes dramatically over the same temperature range — a direct, quantitative link between a substance's microscopic intermolecular forces and its macroscopic phase behaviour.