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Question

The boiling point of an aqueous urea solution is 101.04 C. The density of solution is 1.12 g/mL. Which of the following is/are correct statement(s) regarding this solution?
[Given: For water, Kb=0.52 K kg mol1,Kf=1.86 K kg mol1]

A
The molarity of solution is 2 M
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B
The freezing point of solution is 3.72 C
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C
If the solution is cooled to 1.86 C, no ice will form
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D
At any temperature, the relative lowering of vapour pressure is (9259)
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Solution

The correct option is D At any temperature, the relative lowering of vapour pressure is (9259)
A) ΔTb=Kbm
Here,
ΔTb is the elevation in boiling point =101.04 C100 C=1.04 C
kb is molal elevation in boling point constant and m is the molality
Hence,
1.04=0.52×mm=2
2 moles of urea is present in 1000 g solvent.
number of moles of the solute nB=2

mass of the solute wB=2×60=120 g
mass of the solvent wA=1000 g
mass of the solution wS=1120 g/mL
density of the solution dS=1.12 g/mL
volume of the solution vS=1000 mL

Molartiy =molesvolume of the solution (L)
M=21000×1000=2 M

B) ΔTf=Kfm
Here,
ΔTf is the depression in freezing point
Kf is the molal depression freezing point constant
=1.86×2=3.72
Freezing pointTf=0 C3.72 C=3.72 C

C) If the solution is cooled to 1.86 C, ice will not form. This is because the freezing point of the solution is 3.72 C.

d) Relative lowering of vapor pressure = mole fraction of the solute
number of moles of the solute = 2
number of moles of the solvent =100018

mole fraction=22+100018=2×181036=9259

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