JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Solutions

The vapour pressures of two volatile liquids A and B at

2 5^{\circ} C

are 50 Torr and 100 Torr, respectively. If the liquid mixture contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is

\frac{x}{17}

. The value of

x

is ______.

Answer: 14

Solution

For an ideal binary liquid mixture, the composition of the vapour phase is related to the liquid phase by Raoult's law. Using the relation:

\frac{y _{B}}{1 - y _{B}} = \frac{P _{B}^{o}}{P _{A}^{o}} \cdot \frac{X _{B}}{1 - X _{B}}

Given:

P_{A}^{o} = 50

Torr,

P_{B}^{o} = 100

Torr,

X_{A} = 0.3

, so

X_{B} = 0.7

.

Substituting:

\frac{y _{B}}{1 - y _{B}} = \frac{100}{50} \cdot \frac{0.7}{0.3} = 2 \times \frac{7}{3} = \frac{14}{3}

Solving for

y_{B}

3 y_{B} = 14 (1 - y_{B}) = 14 - 14 y_{B}

17 y_{B} = 14

y_{B} = \frac{14}{17}

Therefore,

x = 14

JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Integer answer

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JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Solutions

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