Phase Diagrams (Pure Substance & Binary) Cheat Sheet

Key Facts

• For a pure substance phase diagram, each region represents one stable phase, such as solid, liquid, gas, or supercritical fluid.
• A phase boundary shows two phases in equilibrium, so points on the liquid vapor line represent liquid and gas coexisting.
• The triple point is the unique condition where solid, liquid, and gas coexist in equilibrium at one $P$ and one $T$.
• The critical point is the end of the liquid vapor boundary, above which the substance is a supercritical fluid and liquid gas distinction disappears.
• The Gibbs phase rule is $F = C - P + 2$, where $F$ is degrees of freedom, $C$ is components, and $P$ is phases.
• For a binary phase diagram at constant pressure, the condensed phase rule is $F = C - P + 1$, so for $C = 2$, $F = 3 - P$.
• In a two phase region of a binary diagram, a horizontal tie line gives the compositions of the two phases at that temperature.
• The lever rule for two phases is $\frac{m_{\alpha}}{m_{\beta}} = \frac{x_{\beta} - x_0}{x_0 - x_{\alpha}}$, where $x_0$ is the overall composition.

Vocabulary

Phase diagram

A graph that shows the stable phases of a substance or mixture under different conditions such as temperature, pressure, and composition.

Triple point

The temperature and pressure where solid, liquid, and gas phases of a pure substance coexist in equilibrium.

Critical point

The end of the liquid vapor equilibrium curve where the liquid and gas phases become indistinguishable.

Eutectic point

The lowest melting temperature in a binary system where a liquid transforms into two solid phases at a fixed composition.

Tie line

A horizontal line across a two phase region of a binary phase diagram used to read the compositions of coexisting phases.

Lever rule

A method for calculating the relative amounts of two coexisting phases from distances along a tie line.