Chemistry · Ch 2 — Solutions

Raoult's Law

2.5.1

Raoult's Law

Raoult's law states that the partial vapour pressure of any volatile component of a solution is equal to the vapour pressure of the pure component multiplied by its mole fraction in the solution.

Suppose that for a binary solution of two volatile liquids $\mathrm{A_1}$ and $\mathrm{A_2}$ , $P_1$ and $P_2$ are their partial vapour pressures and $x_1$ and $x_2$ are their mole fractions in solution. Then according to Raoult's law we write

P_1 = x_1 P_1^0 \quad \text{and} \quad P_2 = x_2 P_2^0 \qquad \text{...(2.2)}

where $P_1^0$ and $P_2^0$ are the vapour pressures of the pure liquids $\mathrm{A_1}$ and $\mathrm{A_2}$ , respectively.

According to Dalton's law of partial pressures, the total pressure $P$ above the solution is

P = P_1 + P_2 = P_1^0 x_1 + P_2^0 x_2 \qquad \text{...(2.3)}

Since $x_1 = 1 - x_2$ , Eq. (2.2) can also be written as

P = P_1^0(1-x_2) + P_2^0 x_2 = P_1^0 - P_1^0 x_2 + P_2^0 x_2

= (P_2^0 - P_1^0)\,x_2 + P_1^0 \qquad \text{...(2.4)}

Because $P_1^0$ and $P_2^0$ are constants, a plot of $P$ versus $x_2$ is a straight line, as shown in Fig. 2.2. The figure also shows the plots of $P_1$ versus $x_1$ and $P_2$ versus $x_2$ according to equations (2.2): these are straight lines passing through the origin.

i. For $P$ versus $x_2$ (straight line), $P = P_1^0$ at $x_2 = 0$ and $P = P_2^0$ at $x_2 = 1$ .

ii. For $P_1$ versus $x_1$ (straight line), $P_1 = 0$ at $x_1 = 0$ and $P_1 = P_1^0$ at $x_1 = 1$ .

iii. For $P_2$ versus $x_2$ (straight line), $P_2 = 0$ at $x_2 = 0$ and $P_2 = P_2^0$ at $x_2 = 1$ .

Figure 2.2Raoult's-law diagram for an ideal binary solution: the two dashed partial-pressure lines P1 and P2 and the solid total-pressure line P_Total = P1 + P2 plotted against mole fraction, running between the pure-component vapour pressures P1-zero and P2-zero.

$Fig. 2.2 — Raoult's-law diagram for an ideal binary solution: the two dashed partial-pressure lines P1 and P2 and the solid total-pressure line P_Total = P1 + P2 plotted against mole fraction, running between the pure-component vapour pressures P1-zero and P2-zero.$

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. Vapour pressure (y-axis) against mole fraction $x_2$ (x-axis, from $x_1{=}1,\ x_2{=}0$ at the left edge to $x_1{=}0,\ x_2{=}1$ at the right). The dashed line I ( $P_1$ ) falls from $P_1^0$ at the left to zero at the right; the dashed line II ( $P_2$ ) rises from zero at the left to $P_2^0$ at the right; the solid line III is the total pressure $P_{Total} = P_1 + P_2$ , running from $P_1^0$ to $P_2^0$ . For an ideal solution the t …

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