JEE Main 2025 Jan 29 Shift 1, Chemistry Q10: Electrochemical Cell And Nernst Equation

Balance the cell reaction to clear electrons:

${\mathrm{Mg}}_{(s)}+2{\mathrm{Ag}}_{(aq)}^{+}⟶{\mathrm{Mg}}_{(aq)}^{2+}+2{\mathrm{Ag}}_{(s)},n=2.$

The reaction quotient is $Q=\frac{[{\mathrm{Mg}}^{2+}]}{[{\mathrm{Ag}}^{+}{]}^2}.$

Nernst equation: $E_{\text{cell}}=E_{\text{cell}}^{\circ }-\frac{RT}{2F}\ln Q=E_{\text{cell}}^{\circ }-\frac{RT}{2F}\ln \frac{[{\mathrm{Mg}}^{2+}]}{[{\mathrm{Ag}}^{+}{]}^2}.$

Inverting the logarithm flips the sign: $E_{\text{cell}}=E_{\text{cell}}^{\circ }+\frac{RT}{2F}\ln \frac{[{\mathrm{Ag}}^{+}{]}^2}{[{\mathrm{Mg}}^{2+}]}.$