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After adding non-volatile solute freezing point of water decreases to \( -0.186^{\circ} \mathrm{C} . \) Calculate
\( \Delta T_{b} \) if \( K_{\mathrm{f}}=1.86 K \mathrm{~kg} \mathrm{~mol}^{-1} \) and \( K_{b}=0.521 K \mathrm{~kg} \mathrm{~mol}^{-1} \)

A \( 0.521 \mathrm{~K} \)
B \( 0.0521 \mathrm{~K} \)
C \( 1.86 \mathrm{~K} \)
D \( 0.0186 \mathrm{~K} \)

Verified Solution

Answer & Solution

Correct Answer

(B) \( 0.0521 \mathrm{~K} \)

Step-by-step Solution

Detailed explanation

Depression of freezing point for the water is,
\[
\begin{array}{l}
\Delta T_{f}=T_{f}^{\circ}-T_{f}=0-(-0.186)=0.186^{\circ} \mathrm{C} \\
\Delta T_{f}=K_{f} \times m
\end{array}
\]
Now, the molality of the solution,
\[
m=\frac{\Delta T_{f}}{K_{f}}=\frac{0.186}{1.86}=0.1 \mathrm{~m}
\]
Elevation of boiling point for water is,
\[
\begin{array}{l}
\Delta T_{b}=K_{b} \times m \\
=0.521 \times 0.1 \\
\Delta T_{b}=0.0521 K
\end{array}
\]

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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After adding non-volatile solute freezing point of water decreases to \( -0.186^{\circ} \mathrm{C} . \) Calculate\( \Delta T_{b} \) if \( K_{\mathrm{f}}=1.86 K \mathrm{~kg} \mathrm{~mol}^{-1} \) and \( K_{b}=0.521 K \mathrm{~kg} \mathrm{~mol}^{-1} \)

Step-by-step Solution

After adding non-volatile solute freezing point of water decreases to \( -0.186^{\circ} \mathrm{C} . \) Calculate
\( \Delta T_{b} \) if \( K_{\mathrm{f}}=1.86 K \mathrm{~kg} \mathrm{~mol}^{-1} \) and \( K_{b}=0.521 K \mathrm{~kg} \mathrm{~mol}^{-1} \)