To determine if the reaction provided is electrically possible, we can first separate the overall reaction into its half-reactions:
Mg (s) + Br₂ (l) → MgBr₂
Mg → Mg²⁺ + 2e⁻ E = -2.37 V
Br₂ + 2e⁻ → 2Br⁻ E = 1.09 V
Looking at the half-reactions, we can see that magnesium loses electrons in the process which means that magnesium is oxidized.
Since bromine is gaining electrons, Br₂ is being reduced.
Now to determine if this reaction is taking place, we must find the reduction potentials for each half-reaction. To final the overall potential of the cell, we take the difference in the cathode (reduction) and anode (oxidation) potentials.
Ecell = Ecathode - Eanode
Ecell = 1.09 V - (-2.37 V)
Ecell = 3.46 V
A positive value of Ecell means that the reaction will happen spontaneously. Therefore, this reaction is electrically possible and will take place.