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 Incoming links: François-Marie Raoult

Raoult's law 2026-10-18

In the ideal solution and ideal gas vapor approximation, each component's partial pressure equals its liquid mole fraction times its pure-component vapor pressure at the same temperature:

p_{i} = x_{i} p_{i}^{*} (T), P = \sum_{i} p_{i} = \sum_{i} x_{i} p_{i}^{*} (T), y_{i} = \frac{p _{i}}{P} .

These pressure formulas neglect the change in the pure-liquid reference between its saturation pressure and

P

; appreciable real gas behavior also requires a more general treatment. The ideal solution definition in terms of chemical potentials does not require either approximation.^[ref]

A short derivation explains the reference choice. At vapor-liquid equilibrium, each component has the same chemical potential in the liquid and vapor. For an ideal gas mixture, chemical potential of an ideal gas gives

μ_{i}^{v} = μ_{i}^{v, \circ} (T) + RT ln \frac{p _{i}}{p ^{\circ}}, μ_{i}^{*} (T, p_{i}^{*}) = μ_{i}^{v, \circ} (T) + RT ln \frac{p _{i}^{*}}{p ^{\circ}},

where

p^{\circ}

is a reference pressure. Approximate

μ_{i}^{*} (T, P)

by

μ_{i}^{*} (T, p_{i}^{*})

and subtract the pure-component equation from the mixture equation:

RT ln x_{i} = RT ln \frac{p _{i}}{p _{i}^{*}} .

Taking the exponential function gives Raoult's law. Summing partial pressures and normalizing gives

P

and

y_{i}

; this last step uses the ideal gas vapor assumption separately from the liquid model.

The law is named after François-Marie Raoult, who measured vapor pressures and freezing behavior of chemical solutions.^[ref]

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