A solution of urea (molar mass of urea 60) boils at ${100.18}^{o} C$ at atmospheric pressure. If $K_{f}$ and $K_{b}$ for water are 1.86 and 0.512 K ${molality}^{- 1}$ respectively, the above solution will freeze at

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${6.54}^{o} C$

$- {6.54}^{o} C$

${0.654}^{o} C$

$- {0.654}^{o} C$

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{Δ T_{b}}{Δ T_{f}} = \frac{K_{b}}{K_{f}} \\ ∴ Δ T_{f} = \frac{K_{f}}{K_{b}} \times Δ T_{b} = \frac{1.86}{0.512} \times 0.18 = 0.654 \\ ∴ f.pt. = 0 - 0.654 = - {0.654}^{o} C \end{array}$

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