Question

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

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

Hint:

When using the Nernst equation, always ensure the correct concentrations of the species involved and the number of electrons transferred (\( n \)) are used.

Answer 1

The Correct Option is C

The Nernst equation is used to calculate the cell potential at non-standard conditions. The equation is given by: \[ E_{{cell}} = E_{{cell}}^o - \frac{RT}{nF} \ln \frac{[{products}]}{[{reactants}]} \] For the given reaction, the number of electrons (\( n \)) is 2. The cell potential depends on the ratio of concentrations of the ions involved. In this case, the correct form of the Nernst equation is: \[ E_{{cell}} = E_{{cell}}^o - \frac{RT}{2F} \ln \frac{[{Mg}^{2+}]}{[{Ag}^+]} \] Thus, the correct option is (3).