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)

${\text{P}}_{\text{A}}^{\text{o}}=500torr;P_{\text{B}}^{\text{o}}=800torr$



When most of the liquid has vaporized $x_A=0.6$ (given) would be $y_A=0.6$

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

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

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