' 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 $=373 \mathrm{~K}$ )

(A) $\frac{1.3}{8} \times \frac{\mathrm{W}}{\mathrm{M}}$

(B) $\frac{16}{2.6} \times \frac{\mathrm{W}}{\mathrm{M}}$

(C) $\frac{2.6}{16} \times \frac{\mathrm{M}}{\mathrm{W}}$

(D) $\frac{1.3}{8} \times \frac{\mathrm{M}}{\mathrm{W}}$

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Solutions

' 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

)

(A) $\frac{1.3}{8} \times \frac{W}{M}$ ✓ Correct
(B) $\frac{16}{2.6} \times \frac{W}{M}$
(C) $\frac{2.6}{16} \times \frac{M}{W}$
(D) $\frac{1.3}{8} \times \frac{M}{W}$

Answer: (A)

Solution

Relative lowering of vapour pressure for the electrolyte gives

\frac{Δ P}{P ^{\circ}} = i x_{2}

, so

\frac{640 - 600}{640} = \frac{1}{16} = i x_{2}

. Elevation in boiling point gives

Δ T_{b} = i K_{b} m

, where

Δ T_{b} = 375 - 373 = 2 K

and the molality is

m = \frac{W / M}{0.1} = \frac{10 W}{M}

, so

2 = i \times 0.52 \times \frac{10 W}{M}

, giving

i = \frac{M}{2.6 W}

. Substituting this into the first relation,

x_{2} = \frac{1}{16 i} = \frac{1}{16} \times \frac{2.6 W}{M} = \frac{1.3}{8} \times \frac{W}{M}

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Single correct option

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JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Solutions

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