JEE MAIN - Chemistry (2025 - 29th January Morning Shift - No. 2)
For a Mg | Mg2+ (aq) || Ag+ (aq) | Ag the correct Nernst Equation is :
$\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]^2}{\left[\mathrm{Mg}^{2+}\right]}$
$\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Mg}^{2+}\right]}{\left[\mathrm{Ag}^{+}\right]}$
$\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]}{\left[\mathrm{Mg}^{2+}\right]}$
$\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{o}}+\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \frac{\left[\mathrm{Ag}^{+}\right]^2}{\left[\mathrm{Mg}^{2+}\right]}$
Explanation
According to Nernst equation :-
$$\mathrm{E}=\mathrm{E}^{\circ}-\frac{\mathrm{RT}}{\mathrm{nF}} \ln \mathrm{Q}$$
Cell reaction :-
$$\begin{aligned} & \mathrm{Mg}_{(\mathrm{s})}+2 \mathrm{Ag}_{(\mathrm{aq})}^{+} \rightleftharpoons 2 \mathrm{Ag}_{(\mathrm{s})}+\mathrm{Mg}_{(\mathrm{aq})}^{+2} \\ & \Rightarrow \mathrm{Q}=\frac{\left[\mathrm{Mg}^{+2}\right]}{\left[\mathrm{Ag}^{+}\right]^2} \\ & \Rightarrow \mathrm{E}=\mathrm{E}_{\mathrm{Cell}}^{\mathrm{o}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} \ln \left[\frac{\left[\mathrm{Mg}^{+2}\right]}{\left[\mathrm{Ag}^{+}\right]^2}\right] \end{aligned}$$
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