JEE Advanced · Chemistry · 17. Electrochemistry

The electrochemical cell shown below is a concentration cell. \(\mathrm{M} \mid \mathrm{M}^{2+}\) (saturated solution of a sparingly soluble salt, \(\left.\mathrm{MX}_{2}\right) \| \mathrm{M}^{2 \perp}\left(0.001 \mathrm{~mol} \mathrm{dm}^{-3}\right) \mid \mathrm{M}\).
The emf of the cell depends on the difference in concentrations of \(\mathrm{M}^{2+}\) ions at the two electrodes. The emf of the cell at \(298 \mathrm{~K}\) is \(0.059 \mathrm{~V}\).
Question:
The value of \(\Delta \mathrm{G}\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)\) for the given cell is (take 1 \(\mathrm{F}=96500 \mathrm{Cmol}^{-1}\) )

A \(-5.7\)
B \(5.7\)
C \(11.4\)
D \(-11.4\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(-11.4\)

Step-by-step Solution

Detailed explanation

At anode : \(M(\mathrm{~s})+2 X^{-}(\mathrm{aq}) \longrightarrow M X_{2}(\mathrm{aq})+2 \mathrm{e}^{-}\)

At cathode \(: M^{+2}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow M(\mathrm{~s})\)

Thus, here \(n=2\)

\(\Delta G=-n F E_{\text {cell }}\)

\(=-2 \times 96500 \times 0.059 \times 10^{-3} \mathrm{~kJ} / \mathrm{mole}=\) \(-11.4 \mathrm{~kJ} / \mathrm{mole}\)

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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