Physical Equilibria and Phase Diagrams

Two Phases in Balance

A physical equilibrium is a phase change running equally fast in both directions. At the melting point solid and liquid coexist; at the boiling point liquid and vapour do. At any such point $\Delta G = 0$, which gives a useful relation immediately:

$$\Delta S_{fus} = \frac{\Delta H_{fus}}{T_{fus}}$$

Vapour pressure is the pressure exerted by a vapour in equilibrium with its liquid. It depends only on temperature, never on the amount of liquid present, and it rises steeply as temperature climbs. A liquid boils when its vapour pressure equals the external pressure, which is why water boils below 100 °C on a mountain, and why a pressure cooker gets hotter than 100 °C.

The Clausius-Clapeyron equation describes that rise:

$$\ln \frac{P_2}{P_1} = -\frac{\Delta H_{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$$

A plot of $\ln P$ against $1/T$ is therefore a straight line of slope $-\Delta H_{vap}/R$, which is the standard way of measuring an enthalpy of vaporisation.

A phase diagram maps pressure against temperature, dividing the plane into solid, liquid and gas regions separated by coexistence curves. Two points matter especially. The triple point is the single condition where all three phases coexist. The critical point ends the liquid-vapour curve: above it liquid and gas become indistinguishable and the substance is a supercritical fluid.

Water's diagram is famously anomalous. Its solid-liquid boundary slopes backwards, because ice is less dense than liquid water, so raising the pressure on ice melts it. Almost every other substance has a forward-sloping boundary.

Common pitfall: thinking a bigger puddle has a higher vapour pressure. Vapour pressure is an intensive property fixed by temperature and the strength of the intermolecular forces. More liquid gives more vapour in total, at exactly the same pressure.