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The **Nernst equation** for a half-cell reaction (M^n+ + n e⁻ → M) at 298 K can be written as:
A$E = E^0 / (n\log[M^{n+}])$
B$E = E^0 - \dfrac{0.0591}{n}\log[M^{n+}]$
C$E = E^0 - 0.0591 \, n \log[M^{n+}]$
D$E = E^0 + \dfrac{0.0591}{n}\log[M^{n+}]$
Answer & Solution
Correct answer: D. $E = E^0 + \dfrac{0.0591}{n}\log[M^{n+}]$
$E = E^0 - (0.0591/n)\log Q$ where $Q = 1/[M^{n+}]$ for the reduction $M^{n+} + ne^- \to M$ (since pure solid $M$ has activity 1). So $E = E^0 - (0.0591/n)\log(1/[M^{n+}]) = E^0 + (0.0591/n)\log[M^{n+}]$. Half-cell potential rises with $[M^{n+}]$.
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