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Question

# A solution of urea in water has a boiling point of 100.18∘C. Calculate the freezing point of the same solution. Molal depression and elevation constants for water Kf and Kb are 1.86∘C kg mol−1 and 0.512∘C kg mol−1 respectively.

A
0.654C
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B
0.98C
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C
1.54C
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D
+0.101C
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Solution

## The correct option is A −0.654∘CBoiling point elevation of a solution is given by, △Tb=Kb×m where, △Tb is the elevation in boiling point. Kb is molal elevation constant. m is molality of solution. Freezing point depression of a solution is given by, △Tf=Kf×m where, △Tf is the depression in freezing point. Kf is molal depression constant. m is molality of solution. For a same solution of same molality m, we have, m=△TfKf=△TbKb ∴ △Tf=△TbKfKb; (△Tb=100.18−100=0.18∘C) =0.18×1.860.512=0.654∘C As the freezing point of pure water is 0∘C, The freezing point of the solution will be −0.654∘C.

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