Discussion
The standard EMF of the following cell
Mg(s) | Mg+2 (0.01M) || Ag+(0.0001M) | Ag(s) is 3.17 V at 250C. The EMF of the cell at the same temperature is (2.303RT/F at 250C is 0.06V)
Answer: E
The EMF of the cell is 3.0 V (2.99 V).
The cell reaction is \(\mathrm{Mg + 2Ag^+ \rightarrow Mg^{2+} + 2Ag}\), so 2 electrons are transferred. Apply the Nernst equation:
\[ \begin{aligned} E &= E^\circ - \frac{0.06}{2}\log\frac{[\mathrm{Mg^{2+}}]}{[\mathrm{Ag^+}]^{2}} \\ &= 3.17 - 0.03\log\frac{10^{-2}}{(10^{-4})^{2}} \\ &= 3.17 - 0.03 \times 6 \\ &= 3.17 - 0.18 = 2.99 \approx 3.0 \text{ V} \end{aligned} \]
3.17 V is the standard value and ignores the concentrations. Forgetting to square [Ag+] gives \(\log 100 = 2\) and 3.11 V, and adding instead of subtracting the correction gives 3.35 V.
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