Solutions Question 336

Question: A solution of urea (mol. mass $ 56gmo{l^{-1}} $ ) boils at $ 100.18{}^\circ C $ at the atmospheric pressure. If $ K_{f} $ and $ K_{b} $ for water are 1.86 and $ 0.512Kkgmo{l^{-1}} $ respectively, the above solution will freeze at

Options:

A) $ 0.654{}^\circ C $

B) $ -0.654{}^\circ C $

C) $ 6.54{}^\circ C $

D) $ -6.54{}^\circ C $

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Answer:

Correct Answer: B

Solution:

As $ \Delta T_{f}=K_{f}m $

$ \Delta T_{b}=K_{b}.m $ Hence, we have $ m=\frac{\Delta T_{f}}{K_{f}}=\frac{\Delta T_{b}}{K_{b}} $ or $ \Delta T_{f}=\Delta T_{b}\frac{K_{f}}{K_{b}} $

$ [ \Delta T_{b}=100.18-100=0.18{}^\circ C ] $

$ =0.18\times \frac{1.86}{0.512}=0.654{}^\circ C $ As the freezing point of pure water is $ 0{}^\circ C, $

$ \Delta T_{f}=0-T_{f} $

$ 0.654=0-T_{f} $
$ \therefore T_{f}=-0.654 $ Thus the freezing point of solution will be $ -0.654{}^\circ C. $



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