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The mole fraction of liquid A in a binary liquid solution of $A (p_{A}^{} = 300 Torr)$ and $B (p_{B}^{} = 800 Torr)$ is 0.6. The pressure at which last droplet of liquid is vapouried and the mole fraction of A in this last droplet, respectively, are

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detailed solution

Correct option is B

When the last droplet of liquid is vapourized, the composition of vapour formed will be $y_{A} = 0.60$ (given composition of the liquid solution).

Hence, $y_{A} = \frac{p_{A}}{p} = \frac{x_{A} p_{A}^{*}}{x_{A} p_{A}^{*} + x_{B} p_{B}^{*}} = \frac{x_{A} p_{A}^{*}}{p_{B}^{*} + (p_{A}^{*} - p_{B}^{*}) x_{A}}$

i.e. $0.60 = \frac{x_{A} (300 Torr)}{800 Torr + (300 Torr - 800 Torr) x_{A}}$

Solving for $x_{A}$ , we get $x_{A} = 0.80$ .

The pressure of the vapour will be $p = x_{A} p_{A}^{*} + x_{B} p_{B}^{*} = (0.80) (300 Torr) + (0.20) (800 Torr) = 400 Torr$

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The mole fraction of liquid A in a binary liquid solution of ApA∗=300 Torr and BpB∗=800 Torr is 0.6. The pressure at which last droplet of liquid is vapouried and the mole fraction of A in this last droplet, respectively, are