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JEE Advanced 2026Paper 2
Exam
JEE Advanced
Year
2026
Paper
Paper 2
Subject
Chemistry
Chapter
Solutions

JEE Advanced 2026 · Paper 2 · Chemistry · Solutions

Passage: Two volatile liquids A and B form an ideal solution....

Passage: Two volatile liquids A and B form an ideal solution. Consider a 55 molal solution of B in A inside a closed container having a total vapour pressure of 100100 mm Hg at 300300 K. The vapour pressure of pure A at 300300 K is 105105 mm Hg. Assume that A and B behave as ideal gases in the vapour phase.
Given:
The gas constant R=0.08R = 0.08 L atm K−1^{-1} mol−1^{-1}
Molar mass of A is 5050 g mol−1^{-1}
Molar mass of B is 5757 g mol−1^{-1}
Density of liquid B at 300300 K is 0.50.5 g/mL
11 atm =760= 760 mm Hg

Question: At 300300 K, the ratio of the molar volume of pure B in vapour phase to its molar volume in liquid phase is ____.

Correct answer

0

Step-by-step solution

For a 55 molal solution of B in A, there are 55 moles of B in 10001000 g of A.

Moles of A =100050=20= \dfrac{1000}{50} = 20 mol.

Mole fraction of B, xB=520+5=0.2x_B = \dfrac{5}{20 + 5} = 0.2

Mole fraction of A, xA=1−0.2=0.8x_A = 1 - 0.2 = 0.8

Using Raoult's law for the total vapour pressure:

PT=PA∘xA+PB∘xBP_T = P_A^\circ x_A + P_B^\circ x_B

100=105×0.8+PB∘×0.2100 = 105 \times 0.8 + P_B^\circ \times 0.2

100=84+0.2PB∘100 = 84 + 0.2 P_B^\circ

0.2PB∘=16⇒PB∘=800.2 P_B^\circ = 16 \Rightarrow P_B^\circ = 80 mm Hg

The molar volume of pure B in the liquid phase (Vm,lV_{m,l}) is:

Vm,l=Molar mass of BDensity of liquid B=570.5=114V_{m,l} = \dfrac{\text{Molar mass of B}}{\text{Density of liquid B}} = \dfrac{57}{0.5} = 114 mL/mol =0.114= 0.114 L/mol

Assuming pure B behaves as an ideal gas in the vapour phase, its molar volume (Vm,vV_{m,v}) at its vapour pressure PB∘P_B^\circ is:

Vm,v=RTPB∘=0.08×300(80760)=24×76080=228V_{m,v} = \dfrac{RT}{P_B^\circ} = \dfrac{0.08 \times 300}{\left(\dfrac{80}{760}\right)} = \dfrac{24 \times 760}{80} = 228 L/mol

The ratio of the molar volume of pure B in the vapour phase to its molar volume in the liquid phase is:

Ratio=Vm,vVm,l=2280.114=2000\text{Ratio} = \dfrac{V_{m,v}}{V_{m,l}} = \dfrac{228}{0.114} = 2000

Answer: 20002000
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