Raoult's law

Remarks

For an ideal gas, $\mu_i^{\text{gas}} = \mu_i^{\circ}(T) + RT \ln(p_i/p^\circ)$ with a reference pressure $p^\circ$. Equality of chemical potentials for the mixture, and again for the pure liquid with $x_i = 1$ and $p_i = p_i^*$, gives $RT\ln x_i = RT \ln(p_i/p_i^*)$, which is the law. Mixtures of similar molecules, such as benzene and toluene, follow it closely. Without the ideal solution hypothesis the law fails: ethanol and water deviate strongly from it and form an azeotrope. For any real solution, the solvent still obeys the law in the limit of small solute fractions.

Going deeper

For a student

The law is the defining behaviour of an ideal solution, and real solutions are described by how far they deviate from it, through activity coefficients. It is the basis of the simplest models of distillation: the vapour is richer in the more volatile component, so repeated evaporation separates the two. For a dilute solute the companion law is Henry's law, which has the same linear form but a different constant.