Two liquids $X$ and $Y$ form an ideal solution at $300 K$ , the vapour pressure of the solution containing $1 m o l e$ of $X$ and $3 m o l e s$ of $Y$ is $550$ mm Hg. At the same temperature, if $1 m o l e$ of $Y$ is further added to this solution, the vapour pressure of the solution increases by $10 m m H g$ . Vapour pressure (in mm Hg) of $X$ and $Y$ in their pure states will be respectively :

200

and

300

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300

and

400

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400

and

600

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500

and

600

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Solution

The correct option is B $400$ and $600$
$P_{t o t a l} = P_{A}^{o} \cdot X_{A} + P_{A}^{o} \cdot X_{B}$

$550 = P_{A}^{o} + \times \frac{1}{4} + P_{B}^{o} \times \frac{3}{4}$

$P_{A}^{o} + 3 P_{B}^{o} = 2200$ ...(i)

When $1 m o l$ of $y$ is further added to the solution
$560 = P_{A}^{o} \times \frac{1}{5} + P_{B}^{o} \times \frac{4}{5}$

$P_{A}^{o} + 4 P_{B}^{o} = 2800$ ...(ii)

On subtraction, (ii) - (i)

$P_{B}^{o} = 2800 - 2200 = 600$

On putting the value of $P_{B}^{o}$ in Eq. (i)

$P_{A}^{o} + 3 \times 600 = 2200$

$P_{A}^{o} = 2200 - 1800 = 400$

Hence, the correct option is $C$ .

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