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Solutions Part 2

Section: Chemistry

Question : 12 of 95

Marks: +1, -0

Two liquids

A

B

T K

T K

A

B

15 kNm ^{-2}

A

A

B

A

Solution:

Concept:

Raoult's law relates partial vapour pressures to liquid mole fractions; Dalton's law relates vapour-phase mole fractions to partial pressures.

Explanation:

Let

x_A

be the mole fraction of A in the liquid.

Then

x_B = 1 - x_A

Partial pressures:

p_A = x_A P_A^* = 55 x_A

p_B = x_B P_B^* = 15 (1 - x_A)

Total pressure:

P = p_A + p_B = 55x_A + 15 - 15x_A = 40x_A + 15

Vapour-phase mole fraction of A:

y_A = \frac{p_A}{P} = \frac{55x_A}{40x_A + 15} = 0.8

Solve:

55x_A = 0.8(40x_A + 15) = 32x_A + 12

55x_A - 32x_A = 12

⇒

23x_A = 12

Thus

x_A = \frac{12}{23} = 0.5217

Answer:

0.5217 (Option A)

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