Question

Two liquids $ X $ and $ Y $ form an ideal solution. The mixture has a vapour pressure of $ 400\, mm $ at $ 300\, K $ when mixed in the molar ratio of $ 1:1 $ and a vapour pressure of $ 350\, mm $ when mixed in the molar ratio of $ 1:2 $ at the same temperature. The vapour pressures of the two pure liquids $ X $ and $ Y $ respectively are

• A. $250\, mm, 550\, mm$
• B. $350\, mm, 450 \,mm$
• C. $350\, mm, 700\, mm$
• D. $500\, mm, 500\, mm$
• E. $550\, mm, 250 \,mm$

Answer 1

Answer: (E)

In 1st case, When two liquids X and Y are mixed in the molar ratio $ 1:1 $ .
Moles of $ X=1 $ Moles of $ Y=1 $
Mole fraction of $ X({{\chi }_{X}})=\frac{1}{2} $
Mole fraction of $ Y({{\chi }_{Y}})=\frac{1}{2} $
We know that $ P=P_{X}^{o}{{\chi }_{X}}+p_{Y}^{o}{{\chi }_{y}} $ (P = total pressure of mixture)
$400=\frac{1}{2}p_{X}^{o}+\frac{1}{2}p_{Y}^{o} $
$ 400\times 2=p_{X}^{o}+p_{Y}^{o} $ .. (i)
For case $ I{{I}^{nd}}, $ When liquids are mixed in the molar ratio of $ 1:2 $
Moles of $ X=1 $
Moles of $ Y=2 $
Mole fraction of $ X({{\chi }_{X}})=\frac{1}{3} $
Mole fraction of $ Y({{\chi }_{Y}})=\frac{2}{3} $
$ P=p_{X}^{o}{{\chi }_{X}}+P_{Y}^{o}{{\chi }_{Y}} $
$ 350=\frac{1}{3}p_{X}^{o}+\frac{2}{3}P_{Y}^{o} $
$ 350\times 3=p_{X}^{o}+2P_{Y}^{o} $ ...(ii)
From Eqs (i) and (ii), we get
$ p_{X}^{o}=550\,mm $
$ P_{Y}^{o}=250\,mm $