Question

Two liquids X and Y form an ideal solution. At $300$K, vapour pressure of the solution containing $1$ mol of X and $3$ mol of Y is $550$ mm Hg. At the same temperature, if $1$ mol of Y is further added to this solution, vapour pressure of the solution increases by $10$ mmHg. Vapour pressure (in mm Hg) of X and Y in their pure states will be ________ respectively.

• A. $200$ and $300$
• B. $300$ and $400$
• C. $400$ and $600$
• D. $500$ and $600$

Answer 1

The correct option is C $400$ and $600$

Let

$P=x_x{P}_x^0+x_y{P}_y^0$

$\left(\frac{1}{1+3}\right)P_x^0+\left(\frac{3}{1+3}\right)P_y^0=550mmofHg$

$\left(\frac{1}{1+4}\right)P_x^0+\left(\frac{4}{1+4}\right)P_y^0=560mmofHg$

on solving for $P_y^0$ and $P_x^0$

We get,

$P_x^0=400mmofHg$

$P_y^0=600mmofHg$