Question

For a mixture of two volatile,completely miscible liquids A and B, with $\text{P}_{\text{A}}^{^\circ } = \text{500 torr and P}_{\text{B}}^{^\circ } = \text{800 torr}$ , What is the composition of last droplet of liquid remaining in equilibrium with vapour?

Provided the initial ideal solution has a composition of $\text{x}_{\text{A}} \, \text{=} \, \text{0} \text{.6}$ and $\text{x}_{\text{B}} \, \text{=} \, \text{0} \text{.4}$

• A. $\text{x}_{\text{A}} = \text{0.6} ; x_{\text{B}} = \text{0.4}$
• B. $\text{x}_{\text{A}} = \text{0.5} ; x_{\text{B}} = \text{0.5}$
• C. $\text{x}_{\text{A}} = \text{0.7} ; x_{\text{B}} = \text{0.3}$
• D. $\text{x}_{\text{A}} = \text{0.3} ; x_{\text{B}} = \text{0.7}$

Answer 1

Answer: (C)

$\text{P}_{\text{A}}^{\text{o}} = 5 0 0 torr ; P_{\text{B}}^{\text{o}} = 8 0 0 torr$



When most of the liquid has vaporized $x_{A}=0.6$ (given) would be $y_{A}=0.6$

$\mathrm{y}_{\mathrm{A}}=\frac{\mathrm{P}_{\mathrm{A}}^0 \mathrm{x}_{\mathrm{A}}}{\mathrm{P}_{\mathrm{A}}^0 \mathrm{x}_{\mathrm{A}}+\mathrm{P}_{\mathrm{B}}^0\left(1-\mathrm{x}_{\mathrm{A}}\right)}$

$\Rightarrow 0.6=\frac{500 \cdot \mathrm{x}_{\mathrm{A}}}{500 \mathrm{x}_{\mathrm{A}}+800\left(1-\mathrm{x}_{\mathrm{A}}\right)}$

$\text{x}_{\text{A}} = 0.70 ; \text{x}_{\text{B}} = \text{0.30}$