Chemistry · Ch 2 — Solutions

Raoult's Law for Solutions of Nonvolatile Solutes

2.7.1

Raoult's Law for Solutions of Nonvolatile Solutes

We saw in section 2.5.1 that Raoult's law expresses the quantitative relationship between the vapour pressure of a solution and the vapour pressure of the solvent. In solutions of nonvolatile solutes, the law is applicable only to the volatile solvent. The law states that the vapour pressure of the solvent over the solution is equal to the vapour pressure of the pure solvent multiplied by its mole fraction in the solution. Thus,

P_1 = P_1^0\,x_1

A plot of $P_1$ versus $x_1$ is a straight line, as shown in Fig. 2.5.

Figure 2.5Straight-line plot of the vapour pressure of the solvent against the mole fraction of solvent, rising from the origin at x = 0 to the pure-solvent vapour pressure at x = 1, illustrating Raoult's law for a nonvolatile solute.

$Fig. 2.5 — Straight-line plot of the vapour pressure of the solvent against the mole fraction of solvent, rising from the origin at x = 0 to the pure-solvent vapour pressure at x = 1, illustrating Raoult's law for a nonvolatile solute.$

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

What this figure shows. The vapour pressure of the solvent (y-axis) plotted against the mole fraction of solvent (x-axis, from $x = 0$ to $x = 1$ ). The plot is a single straight line through the origin, with small square data-point markers along it, illustrating $P_1 = P_1^0 x_1$ : the solvent's vapour pressure above the solution scales linearly with its own m …

For a binary solution containing one solute, $x_1 = 1 - x_2$ . It therefore follows that

P_1 = P_1^0\,x_1 = P_1^0(1 - x_2) = P_1^0 - P_1^0 x_2

\text{or} \qquad P_1^0 - P_1 = P_1^0\,x_2

Eq. (2.5) defines $P_1^0 - P_1$ as $\Delta P$ , the lowering of vapour pressure. Hence

$\Delta P = P_1^0\,x_2 \qquad \text{...(2.6)}$ …

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