Question

The standard EMF of the cell \(Mg(s)\,|\,Mg^{2+}(0.01\,M)\,||\,Ag^{+}(0.0001\,M)\,|\,Ag(s)\) is 3.17 V at \(25^{\circ}C\). The EMF of the cell at the same temperature is (2.303RT/F at \(25^{\circ}C\) is 0.06 V).

• A. 3.17 V
• B. 2.81 V
• C. 3.35 V
• D. 6.70 V
• E. 3.0 V

Hint:

Don't forget to square the concentration if the coefficient is 2.

Answer 1

Answer: (E)

Step 1: Concept
Nernst Equation: $E_{cell} = E^0 - \frac{0.06}{n} \log Q$.

Step 2: Meaning
Reaction: $Mg + 2Ag^+ \rightarrow Mg^{2+} + 2Ag$. Here $n=2$. $Q = \frac{[Mg^{2+}]}{[Ag^+]^2}$.

Step 3: Analysis
$Q = \frac{10^{-2}}{(10^{-4})^2} = \frac{10^{-2}}{10^{-8}} = 10^6$.
$E_{cell} = 3.17 - \frac{0.06}{2} \log(10^6) = 3.17 - 0.03(6) = 3.17 - 0.18 = 2.99 \text{ V}$.

Step 4: Conclusion
Rounding 2.99 V gives 3.0 V. Correct answer is (E).
Final Answer: (E)