The vapour pressures of two liquids A and B in their pure states are in the ratio of 1 : 2. A binary solution of A and B contains A and B in the mole proportion of 1 : 2. The mole fraction of A in the vapour phase of the solution will be:

0.33

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0.2

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0.25

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0.52

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Solution

The correct option is B $0.2$
$\frac{P_{A}^{o}}{P_{B}^{o}} = \frac{1}{2}$

$\frac{x_{A}}{x_{B}} = \frac{1}{2}$

$P_{T} γ_{A} = P_{A}^{o} x_{A}$

$∴ \frac{γ_{A}}{γ_{B}} = \frac{P_{A}^{o}}{P_{B}^{o}} \frac{x_{A}}{x_{B}}$

We know $γ_{A} + γ_{B} = 1$

$∴ γ_{A} = 0.2$

Hence, the correct option is $B$

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The vapour pressures of two liquids A and B in their pure states are in the ratio of 1 : 2. A binary solution of A and B contains A and B in the mole proportion of 1 : 2. The mole fraction of A in the vapour phase of the solution will be:

The correct option is B 0.2PoAPoB=12xAxB=12PTγA= PoAxA∴γAγB=PoAPoBxAxBWe know γA+γB=1∴γA=0.2Hence, the correct option is B