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=0.52K kg mol−1,Kf=1.86K kg mol−1]
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∘C−100∘C=1.04∘C kb is molal elevation in boling point constant and m is the molality
Hence, 1.04=0.52×m⇒m=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=120g
mass of the solvent wA=1000g
mass of the solution wS=1120g/mL
density of the solution dS=1.12g/mL
volume of the solution vS=1000mL
Molartiy =molesvolume of the solution (L) M=21000×1000=2M
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∘C−3.72∘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