MHT CET · Chemistry · Electrochemistry

Which from following equations represents a correct relationship between standard cell potential and equilibrium constant for cell reaction?

A \(\mathrm{E}_{\mathrm{cell}}^{\circ}=-\frac{2.303 \mathrm{RT}}{\mathrm{nF}}\)
B \(\mathrm{E}_{\text {cell }}^{\circ}=\frac{0.0592}{\mathrm{nF}} \log _{10} \mathrm{~K}\)
C \(\mathrm{E}_{\text {cell }}^{\circ}=\frac{0.0592}{\mathrm{n}} \log _{10} \mathrm{~K}\)
D \(\mathrm{E}_{\text {cell }}^{\circ}=\frac{0.0592}{\mathrm{n}} \ln \mathrm{K}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\mathrm{E}_{\text {cell }}^{\circ}=\frac{0.0592}{\mathrm{n}} \log _{10} \mathrm{~K}\)

Step-by-step Solution

Detailed explanation

The correct equation that represents the relationship between the standard cell potential and the equilibrium constant for the cell reaction is:
(3) \(E_{\text {cell }}^{\circ}=\frac{0.0592}{n} \log _{10}(K)\)
The general relationship between the standard cell potential \(E_{\text {cell }}^{\circ}\) and the equilibrium constant \(K\) is given by the Nernst equation, specifically in its standard form:
\(E_{\mathrm{cell}}^{\circ}=\frac{0.0592}{n} \log _{10}(K)\)

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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