Question

Liquids A and B form ideal solution for all compositions of A and B at 25℃. Two such solutions with 0.25 and 0.50 mole fractions of A have the total vapor pressures of 0.3 and 0.4 bar, respectively. What is the vapor pressure of pure liquid B in bar?

Answer 1

Step 1: Calculating the ${\mathrm{X}}_{\mathrm{B}}$ for the first case

As ${\mathrm{X}}_{\mathrm{A}}=0.25$, $\therefore {\mathrm{X}}_{\mathrm{B}}=0.75$

We know that,

$$\begin{gathered} {\mathrm{P}}_{\mathrm{total}}={\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{A}}+{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{B}} \\ \Rightarrow 0.3={\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}\times 0.25+{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}\times 0.75...........\left(\mathrm{i}\right) \end{gathered}$$

Step 2: Calculating the ${\mathrm{X}}_{\mathrm{B}}$ for the second case

As ${\mathrm{X}}_{\mathrm{A}}=0.50$, $\therefore {\mathrm{X}}_{\mathrm{B}}=0.50$

We know that,

$$\begin{gathered} {\mathrm{P}}_{\mathrm{total}}={\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{A}}+{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}{\mathrm{X}}_{\mathrm{B}} \\ \Rightarrow 0.4={\mathrm{P}}_{\mathrm{A}}^{\mathrm{o}}\times 0.50+{\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}\times 0.50...........\left(\mathrm{ii}\right) \end{gathered}$$

Step 3: Calculating the vapor pressure

From equations (i) and (ii) we get,

${\mathrm{P}}_{\mathrm{B}}^{\mathrm{o}}=0.2\mathrm{bar}$

Therefore, the vapor pressure of pure liquid B is 0.2 bar