W ' g of a non-volatile electrolyte solid solute of molar mass ' M ' g mol -1 when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg . If aqueous solution of the electrolyte boils at 375 K and K b for water is 0.52 K kg mol -1 , then the mole fraction of the electrolyte solute ( x 2 ) in the solution can be expressed as (Given : density of water =1 g / mL and boiling point of water =373 K )

Chemistry · Solutions and Colligative Properties

JEE Main 2026 — 24 January, Morning Shift — Question 56

W ' g of a non-volatile electrolyte solid solute of molar mass ' M ' $\mathrm{g} \mathrm{mol}^{-1}$ when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg . If aqueous solution of the electrolyte boils at 375 K and $\mathrm{K}_{\mathrm{b}}$ for water is $0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ , then the mole fraction of the electrolyte solute ( $\mathrm{x}_{2}$ ) in the solution can be expressed as (Given : density of water $=1 \mathrm{~g} / \mathrm{mL}$ and boiling point of water $=373 \mathrm{~K}$ )

Option A:
$\frac{1.3}{8} \times \frac{\mathrm{W}}{\mathrm{M}}$
Correct
Option B:
$\frac{16}{2.6} \times \frac{\mathrm{W}}{\mathrm{M}}$
Option C:
$\frac{2.6}{16} \times \frac{\mathrm{M}}{\mathrm{W}}$
Option D:
$\frac{1.3}{8} \times \frac{\mathrm{M}}{\mathrm{W}}$

Answer: A

Step-by-step solution

$\mathrm{P}^{\circ}=640 \mathrm{~mm} \mathrm{Hg}$ $\mathrm{P}_{\mathrm{s}}=600 \mathrm{~mm} \mathrm{Hg}$ $\Delta \mathrm{P}=40 \mathrm{~mm} \mathrm{Hg}$ moles of solute $=\frac{W}{M}$ $\frac{\Delta \mathrm{P}}{\mathrm{P}^{\mathrm{o}}}=\mathrm{i} . \mathrm{X}_{\text {solute }}$ Again : $\Delta \mathrm{T}_{\mathrm{b}}=\mathrm{i} \times \mathrm{k}_{\mathrm{b}} \times \mathrm{m}$ $2=\mathrm{i} \times 0.52 \times \frac{\mathrm{W} / \mathrm{M}}{100} \times 1000$ $\mathrm{i}=\frac{2}{5.2} \times \frac{\mathrm{M}}{\mathrm{W}}$ $X_{\text {solute }}=\frac{40}{640} \times \frac{1}{i}=\frac{1}{16} \times \frac{5.2}{2} \times \frac{W}{M}$ $\mathrm{X}_{\text {solute }}=\frac{1.3}{8} \times \frac{\mathrm{W}}{\mathrm{M}}$

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Exam: JEE Main 2026
Paper: 24 January, Morning Shift
Subject: Chemistry
Chapter: Solutions and Colligative Properties
Topic: Abnormal Colligative Properties - van't Hoff Factor

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Answer: A

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