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Question

A solution of urea in water has a boiling point of 100.18C. Calculate the freezing point of the same solution. Molal depression and elevation constants for water Kf and Kb are 1.86C kg mol1 and 0.512C kg mol1 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 0.654C
Boiling 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=100.18100=0.18C)
=0.18×1.860.512=0.654C
As the freezing point of pure water is 0C,
The freezing point of the solution will be 0.654C.

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