COMEDK · Chemistry · 17. Solutions

For a 1.0 molal solution containing the non-volatile solute Urea, the elevation in boiling point is 2.0 K while the depression in freezing point in a 3.0 molal solution having the same solvent is \(4.0 K\). If the ratio \(\dfrac{K_b}{K_f}=\dfrac{1}{X}\), what is the value of \(X\) ?

A \(\dfrac{2}{3}\)
B \(\dfrac{3}{2}\)
C \(\dfrac{1}{2}\)
D \(\dfrac{1}{4}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\dfrac{2}{3}\)

Step-by-step Solution

Detailed explanation

The elevation in boiling point is given by \(\Delta T_b = K_b \times m_1\), where \(m_1 = 1.0\) molal and \(\Delta T_b = 2.0\) K. Thus, \(2.0 = K_b \times 1.0\), which implies \(K_b = 2.0\) K kg mol\(^{-1}\). The depression in freezing point is given by…

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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