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

Question

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

(1) \(\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{\circ}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} l n \frac{\left[\mathrm{Ag}^{+}\right]}{\left[\mathrm{Mg}^{2+}\right]}\)

(2) \(\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{\circ}}+\frac{\mathrm{RT}}{2 \mathrm{~F}} l n \frac{\left[\mathrm{Ag}^{+}\right]^{2}}{\left[\mathrm{Mg}^{2+}\right]}\)

(3) \(\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\circ}-\frac{\mathrm{RT}}{2 \mathrm{~F}} l n \frac{\left[\mathrm{Mg}^{2+}\right]}{\left[\mathrm{Ag}^{+}\right]}\)

(4) \( \mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{\circ}}-\frac{\mathrm{RT}}{2 \mathrm{~F}} l n \frac{\left[\mathrm{Ag}^{+}\right]^{2}}{\left[\mathrm{Mg}^{2+}\right]}\)  

Answer 1

Correct option is (2) \(\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\mathrm{\circ}}+\frac{\mathrm{RT}}{2 \mathrm{~F}}\ l n \frac{\left[\mathrm{Ag}^{+}\right]^{2}}{\left[\mathrm{Mg}^{2+}\right]}\)   

According to Nernst equation :-

\(\mathrm{E}=\mathrm{E}^{\circ}-\frac{\mathrm{RT}}{\mathrm{nF}}\ l n\ \mathrm{Q}.\)

Cell reaction :-

\(\mathrm{Mg}_{(\mathrm{s})}+2 \mathrm{Ag}_{(\mathrm{aq})}^{+} \rightleftharpoons 2 \mathrm{Ag}_{(\mathrm{s})}+\mathrm{Mg}_{(\mathrm{aq})}^{+2}\)

\(\Rightarrow \mathrm{Q}=\frac{\left[\mathrm{Mg}^{+2}\right]}{\left[\mathrm{Ag}^{+}\right]^{2}}\)

\(\Rightarrow \mathrm{E}=\mathrm{E}_{\mathrm{Cell}}^{\mathrm{\circ}}-\frac{\mathrm{RT}}{2 \mathrm{~F}}\ l n \left[\frac{\left[\mathrm{Mg}^{+2}\right]}{\left[\mathrm{Ag}^{+}\right]^{2}}\right]\)