1000g of 1 molal aqueous solution of sucrose is cooled and maintained at −3.72∘C . Calculate the weight of ice (in grams) that will separate out. (Kf for water=1.86 ∘C/molal )

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1000g of 1 molal aqueous solution of sucrose is cooled and maintained at $- {3.72}^{\circ} C$ . Calculate the weight of ice (in grams) that will separate out.
( $K_{f}$ for water $= 1.86^{\circ} C/molal$ )

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answer is 372.5.

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Detailed Solution

1342 g solution contains 342g sucrose
1000g solution contains $\frac{1000 \times 342}{1342} = 254.84 g sucrose$
Weight of water present $= 1000 - 254.84$
$= 745.16 g$
$Δ T_{f} = k_{f} . m$
$3.72 = 1.86 \times m$
$m = 2$
For molality to double, half the water in solution should separate out as ice.
i.e. $\frac{745.16}{2} = 372.58 g$