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
Correct Answer: E
Solution :
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 \[p_{X}^{o}=550\,mm\] \[P_{Y}^{o}=250\,mm\]
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