Vapour Pressure of Binary Solutions of Liquid in Liquid

Consider a binary liquid solution formed by dissolving a volatile liquid solute A in a pure liquid solvent B, in a closed vessel. Both A and B can evaporate, so an equilibrium is eventually established between the liquid and vapour phases of both components at once.

Raoult's law, proposed by the French chemist Francois-Marie Raoult, gives the quantitative relationship: "in a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction." For component A:

At $x_A=1$ (i.e. pure A), $p_A$ must equal the vapour pressure of pure A, $p^\circ_A$; so the proportionality constant $k=p^\circ_A$, giving

and, by exactly the same reasoning for component B,

Total pressure. By Dalton's law of partial pressures, the total pressure above the closed vessel is the sum of the two partial pressures:

Substituting equations 9.4 and 9.5:

Using $x_A+x_B=1$, i.e. $x_A=1-x_B$:

which expands and regroups to

This last form is a straight line in the variable $x_B$: $y=mx+c$ with slope $(p^\circ_B-p^\circ_A)$ and $y$-intercept $p^\circ_A$. So a plot of $P_{total}$ against $x_B$ is linear, running from $p^\circ_A$ (at $x_B=0$) up (or down) to $p^\circ_B$ (at $x_B=1$).

Worked illustration -- toluene in benzene (Figure 9.5). For toluene (solute) dissolved in benzene (solvent), with pure vapour pressures $p^\circ_{toluene}=22.3$ mmHg and $p^\circ_{benzene}=74.7$ mmHg, the total-pressure equation becomes

$P_{solution} = p^\circ_{toluene} + x_{benzene}(p^\circ_{benzene}-p^\circ_{toluene}) \qquad (9.10)$ …