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MCQMediumJEE 2026Raoult's Law & Vapour Pressure

JEE Chemistry 2026 Question with Solution

Two liquids A and B form an ideal solution at temperature T KT \, \text{K}. At T KT \, \text{K}, the vapour pressures of pure A and pure B are 55 kPa55 \, \text{kPa} and 15 kPa15 \, \text{kPa} respectively. What is the mole fraction of A in solution of A and B in equilibrium with a vapour in which the mole fraction of A is 0.80.8?

  • A

    0.3400.340

  • B

    0.6630.663

  • C

    0.4800.480

  • D

    0.52170.5217

Answer

Correct answer:D

Step-by-step solution

Standard Method

Given: Two liquids A and B form an ideal solution. Vapour pressures of pure components are PA0=55 kPaP_A^0 = 55 \, \text{kPa} and PB0=15 kPaP_B^0 = 15 \, \text{kPa}. The mole fraction of A in vapour phase is yA=0.8y_A = 0.8.

Find: The mole fraction of A in the liquid phase, xAx_A.

For an ideal solution, apply Raoult’s law:

pA=xAPA0p_A = x_A P_A^0

and

pB=(1−xA)PB0p_B = (1-x_A) P_B^0

Using Dalton’s law for the vapour phase:

yA=pApA+pB=0.8y_A = \frac{p_A}{p_A + p_B} = 0.8

Substitute the given values:

pA=55xAp_A = 55x_A pB=15(1−xA)p_B = 15(1-x_A)

So,

0.8=55xA55xA+15(1−xA)0.8 = \frac{55x_A}{55x_A + 15(1-x_A)}

Now solve the equation:

0.8(55xA+15−15xA)=55xA0.8(55x_A + 15 - 15x_A) = 55x_A 0.8(40xA+15)=55xA0.8(40x_A + 15) = 55x_A 32xA+12=55xA32x_A + 12 = 55x_A 23xA=1223x_A = 12 xA=0.5217x_A = 0.5217

Therefore, the mole fraction of A in the liquid phase is 0.52170.5217. The correct option is D.

Common mistakes

  • Using only Raoult’s law and taking yA=xAy_A = x_A directly is incorrect because vapour composition is not the same as liquid composition unless the components have identical vapour pressures. Use Dalton’s law together with Raoult’s law.

  • Writing pB=15xAp_B = 15x_A is wrong because the mole fraction of B in the liquid phase is 1−xA1-x_A, not xAx_A. The correct expression is pB=15(1−xA)p_B = 15(1-x_A).

  • Substituting the vapour pressures in the denominator incorrectly, such as omitting one component, gives a wrong total pressure. The denominator must be the total vapour pressure pA+pBp_A + p_B.

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