Vapor-Liquid Equilibrium Basics

Concept

Vapor-Liquid Equilibrium (VLE) dictates how a chemical mixture distributes itself between a liquid phase and a vapor phase at a specific temperature and pressure. Understanding VLE is fundamentally critical for designing separation processes like distillation. When a liquid mixture is in thermodynamic equilibrium with its vapor, the rate of evaporation equals the rate of condensation for all components. For an ideal mixture of chemically similar compounds (e.g., benzene and toluene), VLE can be accurately described by Raoult's Law.

Formula & Method

Raoult's Law states that the partial pressure ($p_i$) of a component in the vapor phase is proportional to its mole fraction in the liquid phase ($x_i$) and the pure substance vapor pressure ($P_i^*$) at the system's temperature:

By Dalton's law, the total pressure ($P$) of the vapor mixture is the sum of the partial pressures:

The mole fraction of a component in the vapor phase ($y_i$) is the ratio of its partial pressure to the total pressure:

Engineering Meaning

This example illustrates the core principle of distillation: the vapor phase becomes richer in the more volatile component ($A$, since $P_A^* > P_B^*$). While the liquid contains 40% A, the vapor boiling off contains 57.1% A. By continuously boiling and condensing this mixture across multiple stages, engineers can separate chemicals to high purities.

Engineering Check

Raoult's law strictly applies only to ideal solutions. Always verify that the mixture consists of non-polar, chemically similar molecules of roughly the same size. If the mixture deviates highly from ideality (like ethanol and water), Raoult's law will produce massive errors, and activity coefficients must be introduced. Always ensure that $\sum x_i = 1$ and $\sum y_i = 1$.

Explicit Exclusions

This fundamental article does not cover non-ideal VLE requiring activity coefficients (Modified Raoult's Law), fugacity coefficients, azeotrope formation, or equation-of-state methods.