Question

How would you determine the standard electrode potential of the system ${\text{Mg}}^{2+}|\text{Mg}$ ?

Answer 1

Standard electrode potential of ${\text{Mg}}^{2+}|\text{Mg}$

The standard electrode petential of ${\text{Mg}}^{2+}|\text{Mg}$ can be measured with respect to the standard hydrogen electrode, represented by $H^{+}(aq,1M)|Pt\left(s\right)|H_2\left(g\right),1\text{bar}$.

A cell, consisting of ${\text{Mg}}^{2+}|\text{Mg}(aq,1M)$ as the anode and the standard hydrogen electrode $H^{+}(aq,1M)|Pt\left(s\right)|H_2\left(g\right),1\text{bar}$ as the cathode.

The cell represented as
$Mg|mg(aq,1M)||H^{+}(aq,1M)|Pt\left(s\right)|H_2\left(g\right),1\text{bar}$

Thus, emf of cell, $E_{cell}^{\circ }=E_{right}^{\circ }-E_{left}^{\circ }$

The potential of standard hydrogen electrode is always zero.

Therefore,

$E_{right}^{\circ }=0$

Hence,
$E_{cell}^{\circ }=-E_{{\text{Mg}}^{2+}|\text{Mg}}^{\circ }$
$E_{{\text{Mg}}^{2+}|\text{Mg}}^{\circ }=-E_{cell}^{\circ }$