Will a battery with magnesium (Mg) as the anode and aluminum (Al) work to power a flashlight? Why or why not?

Yes because magnesium has a more negative reduction potential than aluminum.

Explanation:

The single factor that will determine whether a battery with magnesium as anode and aluminium as cathode will work or not is the respective electrode potentials of the two elements.

Recall that in a battery, oxidation occur at the anode and reduction occurs that the cathode. The reduction potential shows the ease with which a metal is reduced or oxidized. The substance with the most negative reduction potential will function as the anode while the substance with the less negative electrode potential will function as the anode.

The reduction potential of Magnesium is - 2.37 V while that of aluminum is - 1.66 V. This implies that magnesium must function as the anode and aluminum as the cathode in order to have a spontaneous electrochemical process in the cell.