JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Solutions

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Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y . respectively in 1 kg of water. The ratio of depression in freezing points for A and B is found to be

1 : 4

. The ratio of molar masses of X and Y is :

(A) $1 : 4$
(B) $1 : 0.25$ ✓ Correct
(C) $1 : 0.20$
(D) $1 : 5$

Answer: (B)

Solution

Depression in freezing point is given by

Δ T_{f} = K_{f} \cdot m

, where

m

is molality.

For equal masses of solutes in equal masses of solvent:

\frac{Δ T _{f, X}}{Δ T _{f, Y}} = \frac{m _{X}}{m _{Y}} = \frac{1/ M _{X}}{1/ M _{Y}} = \frac{M _{Y}}{M _{X}}

Given

\frac{Δ T _{f, X}}{Δ T _{f, Y}} = \frac{1}{4}

\frac{1}{4} = \frac{M _{Y}}{M _{X}}

M_{X} : M_{Y} = 4 : 1 = 1 : 0.25

The ratio of molar masses is

1 : 0.25

JEE Main · 2022 · 25 Jul 2022 · Shift 2 · Single correct option

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