A solution of urea (mol. mass 56 g mol $^{1}$ ) boils at 100.18 $^{\circ}$ C at the atmospheric pressure. If K $_{f}$ and K $_{b}$ for water are 1.86 and 0.512K kg mol $^{1}$ respectively, the above solution will freeze at:

-6.54

^{\circ}

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-0.654

^{\circ}

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6.54

^{\circ}

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0.654

^{\circ}

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Solution

The correct option is A -0.654 $^{\circ}$ C
${Δ T}_{b} = K_{b} \times m$

$w h e r e, K_{b} = E b u l l i o s c o p i c c o n s t a n t m = m o l a l i t y$

${Δ T}_{b} = m \times 0.512 = 0.18$

$m = \frac{0.18}{0.512}$

${Δ T}_{f} = K_{f} \times m$

$w h e r e, K_{f} = F r e e z i n g p o i n t d e p r e s s i o n c o n s t a n t m = m o l a l i t y$

${Δ T}_{f} = 1.86 \times \frac{0.18}{0.512} = 0.654$

$T_{f} = T^{0} - {Δ T}_{f} = 0 - 0.654 = - {0.654}^{0} C$

Hence, the correct option is $B$

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