Which redox pair cannot be used to make a voltaic cell?

• A. 2 Ga3+ + 3 Fe ⟶ 2 Ga + 3 Fe2+
• B. Mn2+ + 2e- ⟶ Mn
• C. Fe2+ + 2e- ⟶ Fe
• D. Sn2+ + 2e- ⟶ Sn

Answer: (A)

The key idea is that a voltaic cell must use two half-reactions that transfer the same number of electrons and together produce a positive cell potential (a spontaneous reaction). In the pair that combines Ga3+/Ga reduction with Fe/Fe2+ oxidation, the Ga3+/Ga couple consumes 3 electrons per Ga atom, while the Fe/Fe2+ couple releases 2 electrons per Fe atom. To balance electrons, you’d multiply the half-reactions appropriately (3 Fe oxidized to Fe2+ and 2 Ga3+ reduced to Ga), giving an overall cell reaction. However, when you look at the standard reduction potentials, Ga3+/Ga has a reduction potential around -0.56 V and Fe2+/Fe around -0.44 V. Using Ga3+/Ga as the cathode and Fe2+/Fe as the anode yields a cell potential E°cell ≈ (-0.56) - (-0.44) ≈ -0.11 V, which is negative. That means this arrangement would not proceed spontaneously as a galvanic (voltaic) cell.

The other reductions listed can be paired with an oxidation that yields a positive overall potential, so they can form voltaic cells with an appropriate partner. For example, Mn2+/Mn has a very negative reduction potential and can pair with an electrode couple with a higher (less negative) reduction potential to give a positive E°cell, and similarly for Fe and Sn reductions with suitable oxidants. Thus, the redox pair involving Ga3+/Ga with Fe/Fe2+ is the one that cannot function as a spontaneous voltaic cell in the orientation shown.