= Raoult's law
{c}
{title2=$p_i=x_i p_i^*$}
{wiki}
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>:
$$
p_i=x_i p_i^*(T),\qquad
P=\sum_i p_i=\sum_i x_i p_i^*(T),\qquad
y_i=\frac{p_i}{P}.
$$
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.<Thermodynamics and Chemistry by Howard DeVoe>[§9.4.1, printed pp. 248–249: partial-pressure form and its distinction from the general thermodynamic law; §9.4.2: ideal liquid mixture]{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
$$
\mu_i^{\rm v}=\mu_i^{\rm v,\circ}(T)+RT\ln\frac{p_i}{p^\circ},
\qquad
\mu_i^*(T,p_i^*)=\mu_i^{\rm v,\circ}(T)+RT\ln\frac{p_i^*}{p^\circ},
$$
where $p^\circ$ is a reference <pressure>. Approximate $\mu_i^*(T,P)$ by $\mu_i^*(T,p_i^*)$ 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>.<Thermodynamics and Chemistry by Howard DeVoe>[Printed p. 380, Biographical Sketch: François-Marie Raoult; experimental work on dilute solutions]{ref}
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