KCET · Chemistry · Surface Chemistry

\(1 \mathrm{~g}\) of silver gets distributed between \(10 \mathrm{~cm}^{3}\) of molten zinc and \(100 \mathrm{~cm}^{3}\) of molten lead at \(800^{\circ} \mathrm{C}\). The percentage of silver still left in the lead layer is approximately

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Correct Answer

(C) 3

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Detailed explanation

Partition coefficient
\[
=\frac{\text { Conc. of } \mathrm{Ag} \text { in molten } \mathrm{Zn}}{\text { Conc. of } \mathrm{Ag} \text { in molten } \mathrm{Pb}}
\]
Mass of \(\mathrm{Ag}\) in lead at equilibrium \(=1-x\)
Mass of Ag in \(\mathrm{Zn}\) at equilibrium \(=x\)
\[
\begin{aligned}
300 &=\frac{x / 10}{1-x / 100}=\frac{10 x}{1-x} \\
10 x &=300(1-x) \\
10 x &=300-300 x \\
310 x &=300 \\
x &=\frac{300}{310} \\
x &=\frac{30}{31}
\end{aligned}
\]
Amount of silver in molten lead
\[
=1-x=1-\frac{30}{31}=\frac{31-30}{31}=\frac{1}{31}
\]
\(\therefore \quad \%\) of silver \(=\frac{1}{31} \times 100 \simeq 3 \%\)

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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