Question

how would you determine the standard Mg2+ | Mg ?

Answer 1

I would determine the standard
Mg2+1Mg->Mg3(or)3Mg

Answer 2

The standard electrode potential of $\sf{Mg^{2+}}$ can be measured with respect to the standard hydrogen electrode, represented by $\sf{Pt_(s)}$, $\sf{H_2{_(g)}}$(1atm) | $\sf{H^+{_(aq)}}$ (1M)

A cell consisting of Mg | $\sf{MgSO_4}$ (1M) as the anode and the standard hydrogen electrode as the cathode, is set up

Mg | $\sf{Mg^{2+}}$(aq, 1M) || $\sf{H^{+}}$ (aq, 1M) | $\sf{H_2}$ (g, 1bar), $\sf{Pt_(s)}$

Then, the emf of the cell is measured and this measured emf is the standard electrode potential of the magnessium electrode