Raoult's law

Raoult's law (/ˈrɑːuːlz/ law) is a relation of physical chemistry, with implications in thermodynamics. Proposed by French chemist François-Marie Raoult in 1887,^[1][2] it states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component (liquid or solid) multiplied by its mole fraction in the mixture. In consequence, the relative lowering of vapor pressure of a dilute solution of nonvolatile solute is equal to the mole fraction of solute in the solution.

Mathematically, Raoult's law for a single component in an ideal solution is stated as

${\displaystyle p_{i}=p_{i}^{\star }x_{i}}$

where ${\displaystyle p_{i}}$ is the partial pressure of the component ${\displaystyle i}$ in the gaseous mixture above the solution, ${\displaystyle p_{i}^{\star }}$ is the equilibrium vapor pressure of the pure component ${\displaystyle i}$, and ${\displaystyle x_{i}}$ is the mole fraction of the component ${\displaystyle i}$ in the liquid or solid solution.^[3]

Where two volatile liquids A and B are mixed with each other to form a solution, the vapor phase consists of both components of the solution. Once the components in the solution have reached equilibrium, the total vapor pressure of the solution can be determined by combining Raoult's law with Dalton's law of partial pressures to give

${\displaystyle p=p_{\text{A}}^{\star }x_{\text{A}}+p_{\text{B}}^{\star }x_{\text{B}}+\cdots .}$

In other words, the vapor pressure of the solution is the mole-weighted mean of the individual vapour pressures:

${\displaystyle p={\dfrac {p_{\text{A}}^{\star }n_{\text{A}}+p_{\text{B}}^{\star }n_{\text{B}}+\cdots }{n_{\text{A}}+n_{\text{B}}+\cdots }}}$

If a non-volatile solute B (it has zero vapor pressure, so does not evaporate) is dissolved into a solvent A to form an ideal solution, the vapor pressure of the solution will be lower than that of the solvent. In an ideal solution of a nonvolatile solute, the decrease in vapor pressure is directly proportional to the mole fraction of solute:

${\displaystyle p=p_{\text{A}}^{\star }x_{\text{A}},}$

${\displaystyle \Delta p=p_{\text{A}}^{\star }-p=p_{\text{A}}^{\star }(1-x_{\text{A}})=p_{\text{A}}^{\star }x_{\text{B}}.}$

If the solute associates or dissociates in the solution, the expression of the law includes the van 't Hoff factor as a correction factor.