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

For a $Mg|Mg^{2+}(aq)||Ag^{+}(aq)|Ag$ the correct Nernst Equation is :
  1. \(\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]}{\left[\mathrm{Mg}^{2+}\right]}\)
  2. \(\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}+\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]^2}{\left[\mathrm{Mg}^{2+}\right]}\)
  3. \(\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]^2}{\left[\mathrm{Mg}^{2+}\right]}\)
  4. \(\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Mg}^{2+}\right]}{\left[\mathrm{Ag}^{+}\right]}\)

Solution

$\begin{array}{lll}\text { Cathode } & \left(\mathrm{Ag}+(\mathrm{aq})+\mathrm{e}^{-}\right. & \rightarrow \mathrm{Ag}) \times 2 \\ \text { Anode } & \mathrm{Mg} & \rightarrow \mathrm{Mg}^{2+}(\mathrm{aq})+2 \mathrm{e}^{-}\end{array}$

By Nernst equation
$\begin{aligned}
& \mathrm{E}_{\text {cell }}=\mathrm{E}_{\mathrm{cell}}^{\circ}-\frac{\mathrm{RT}}{\mathrm{nF}} \ln \mathrm{Q} \\
& \mathrm{E}_{\text {cell }}=\mathrm{E}_{\mathrm{cell}}^{\circ}-\frac{\mathrm{RT}}{\mathrm{nF}} \ln \frac{\left[\mathrm{Mg}^{2+}\right]}{\left[\mathrm{Ag}^{+}\right]^2} \\
& =\mathrm{E}_{\text {cell }}^{\circ}+\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]^2}{\left[\mathrm{Mg}^{2+}\right]}
\end{aligned}$

Asked in: JEE Main 2025 (29 Jan Shift 1)

Practice more Electrochemistry questions on Aicharya