Question

For a \( \text{Mg} | \text{Mg}^{2+} (aq) || \text{Ag}^+ (aq) | \text{Ag} \), the correct Nernst Equation is:

• A. \( E_{\text{cell}} = E^\circ_{\text{cell}} + \frac{RT}{2F} \ln \left( \frac{[\text{Ag}^+]}{[\text{Mg}^{2+}]} \right) \)
• B. \( E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{2F} \ln \left( \frac{[\text{Ag}^+]}{[\text{Mg}^{2+}]} \right) \)
• C. \( E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{2F} \ln \left( \frac{[\text{Mg}^{2+}]}{[\text{Ag}^+]} \right) \)
• D. \( E_{\text{cell}} = E^\circ_{\text{cell}} + \frac{RT}{2F} \ln [\text{Ag}^+]^2 \)

Hint:

When writing the Nernst equation, ensure that the ion concentrations are correctly placed in the logarithmic expression.

Answer 1

The Correct Option is C

Using the Nernst equation, the relationship between cell potential and ion concentrations is given by: \[ E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{2F} \ln \left( \frac{[\text{Mg}^{2+}]}{[\text{Ag}^+]} \right) \] Thus, the correct Nernst equation is \( E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{2F} \ln \left( \frac{[\text{Mg}^{2+}]}{[\text{Ag}^+]} \right) \).