Question

Two liquids X and Y form an ideal solution at 300K, vapour pressure of the solution containing 1 mole of X and 3 moles of Y is 550 mm Hg. At the same temperature, if 1 mole of V is further added to this solution, vapour pressure of the solution increases by 10 mm Hg. Vapour pressure (in mm Hg) of X and V 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

Answer: (C)

$ {{\rho }_{total}}=p_{A}^{o}.{{x}_{A}}+p_{B}^{o}.{{x}_{B}} $
$ 550=p_{A}^{o}\times \frac{1}{4}+p_{B}^{o}\times \frac{3}{4} $
$ p_{A}^{o}+3p_{B}^{o}=2200 $ ?(i) When 1 mole 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}+4p_{B}^{o}=2800 $ ...(ii)
On subtraction, (ii) - (i)
$ p_{B}^{o}=2800-200=600 $
On putting the value of
$ p_{B}^{o} $ Eq. (i)
$ p_{A}^{o}+3\times 600=220 $
$ p_{A}^{o}=2200-1800=400 $
On putting the value of
$ p_{B}^{o} $ in Eq. (i)
$ p_{A}^{o}+3\times 600=220 $
$ {{p}_{{{A}_{0}}}}=2200-1800=400 $