A solution containing 62 g ethylene glycol in 250 g water is cooled to $-10^{\circ} \mathrm{C}$. If $\mathrm{K}_{\mathrm{f}}$ for water is $1.86 \mathrm{~K~kg~mol}^{-1}$, the amount of water(in g) separated as ice is

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Solutions

A solution containing 62 g ethylene glycol in 250 g water is cooled to

- 1 0^{\circ} C

. If

K_{f}

for water is

1.86 K kg mol^{- 1}

, the amount of water(in g) separated as ice is

(A)48
(B)32
(C)64✓ Correct
(D)16

Answer: (C)

Solution

The dissolved ethylene glycol (

M = 62

) amounts to

\frac{62}{62} = 1 mol

, and it stays in solution while some water freezes out. Cooling to

- 1 0^{\circ} C

fixes the depression at

Δ T_{f} = 10 K

, so the molality of the unfrozen solution must satisfy

10 = K_{f} m = 1.86 m

, giving

m \approx 5.38 mol/kg

. One mole of glycol then needs

\frac{1}{5.38} \approx 0.186 kg = 186 g

of liquid water remaining, so of the original

250 g

the ice separated is

250 - 186 = 64 g

JEE Main · 2019 · 09 Jan 2019 · Shift 2 · Single correct option

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