For a mathrmMg mid mathrmMg^2+$\mathrm{Mg} \mid \mathrm{Mg}^{2+}$ (aq) parallel mathrmAg^+(mathrmaq) mid mathrmAg$\parallel \mathrm{Ag}^{+}(\mathrm{aq}) \mid \mathrm{Ag}$ the correct Nernst Equation is :

### Related Formula E_textcell = E_textcell^circ - fracRTnF ln Q$$E_{\text{cell}} = E_{\text{cell}}^{\circ} - \frac{RT}{nF} \ln Q$$ ### Core Logic Let us explicitly formulate the complete chemical oxidation-reduction equations : Anode oxidation: mathrmMg_(s) rightarrow mathrmMg^2+_(aq) + 2e^-$\mathrm{Mg}_{(s)} \rightarrow \mathrm{Mg}^{2+}_{(aq)} + 2e^-$ Cathode reduction: 2mathrmAg^+_(aq) + 2e^- rightarrow 2mathrmAg_(s)$2\mathrm{Ag}^{+}_{(aq)} + 2e^- \rightarrow 2\mathrm{Ag}_{(s)}$ Net total equation : mathrmMg_(s) + 2mathrmAg^+_(aq) rightleftharpoons mathrmMg^2+_(aq) + 2mathrmAg_(s)$$\mathrm{Mg}_{(s)} + 2\mathrm{Ag}^{+}_{(aq)} \rightleftharpoons \mathrm{Mg}^{2+}_{(aq)} + 2\mathrm{Ag}_{(s)}$$ Total transferred moles of electrons n = 2$n = 2$ . Reaction quotient : Q = frac[mathrmMg^2+][mathrmAg^+]^2$$Q = \frac{[\mathrm{Mg}^{2+}]}{[\mathrm{Ag}^{+}]^2}$$ Substituting into Nernst form : E_textcell = E_textcell^circ - fracRT2F lnleft( frac[mathrmMg^2+][mathrmAg^+]^2 right)$$E_{\text{cell}} = E_{\text{cell}}^{\circ} - \frac{RT}{2F} \ln\left( \frac{[\mathrm{Mg}^{2+}]}{[\mathrm{Ag}^{+}]^2} \right)$$ Inverting the inside quotient changes the sign of the logarithm term from negative to positive: E_textcell = E_textcell^circ + fracRT2F lnleft( frac[mathrmAg^+]^2[mathrmMg^2+] right)$$E_{\text{cell}} = E_{\text{cell}}^{\circ} + \frac{RT}{2F} \ln\left( \frac{[\mathrm{Ag}^{+}]^2}{[\mathrm{Mg}^{2+}]} \right)$$ ### Pattern Recognition A standard negative logarithmic quotient can always toggle into an addition configuration by inverting the products/reactants variables concentration ratio.