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On mixing urea, the boiling point of $H_{2} O$ changed to $100.5 {}^{\circ}C .$ Calculate the freezing point of the solution, if $K_{f}$ of water is $1.87 K . kg . {mol}^{- 1}$ and $K_{b}$ of water is $0.52 K \cdot kg . {mol}^{- 1}$

A $- 1 {}^{\circ}C$
B $- 0.5 ° C$
C $- 1.8 ° C$
D $0 ° C$

Verified Solution

Answer & Solution

Correct Answer

(C) $- 1.8 ° C$

Step-by-step Solution

Detailed explanation

Elevation in boiling of solution: ∆Tb=i×kb×m100.5-100.0=1×0.52×mm =0.500.52 mol/kg Depression in freezing point of solution: ∆Tf=i×kf×m0-Tf=1×1.87×0.500.52Tf =-1.8oC

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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On mixing urea, the boiling point of H2O changed to 100.5C∘. Calculate the freezing point of the solution, if Kf of water is 1.87 K.kg.mol-1 and Kb of water is 0.52 K·kg.mol-1

Step-by-step Solution

On mixing urea, the boiling point of $H_{2} O$ changed to $100.5 {}^{\circ}C .$ Calculate the freezing point of the solution, if $K_{f}$ of water is $1.87 K . kg . {mol}^{- 1}$ and $K_{b}$ of water is $0.52 K \cdot kg . {mol}^{- 1}$