Balance the following redox equation, using either the oxidation-number-change method or the half-reaction method. You must show all your work, especially the total number of electrons transferred in the reaction. (In using the half-reaction method, assume that the reaction occurs in an aqueous acid solution.)
Fe2O3 + CO → Fe + CO2 (acid solution)
To balance a redox equation, we need to follow either the oxidation-number-change method or the half-reaction method. Let's use the half-reaction method to balance the given equation Fe2O3 + CO → Fe + CO2 in an acidic solution.
1. Separate the equation into two half-reactions: one for the oxidation half-reaction and one for the reduction half-reaction.
Fe2O3 → Fe (oxidation half-reaction)
CO → CO2 (reduction half-reaction)
2. Balance the atoms other than oxygen and hydrogen first.
Fe2O3 → 2Fe (oxidation half-reaction)
CO → CO2 (reduction half-reaction)
3. Balance oxygen atoms by adding water molecules (H2O) to the side that lacks oxygen atoms.
Fe2O3 + 3H2O → 2Fe (oxidation half-reaction)
CO → CO2 (reduction half-reaction)
4. Balance hydrogen atoms by adding hydrogen ions (H+) to the side that lacks hydrogen atoms. Since we're in an acidic solution, we can add H+ ions.
Fe2O3 + 3H2O → 2Fe + 6H+ (oxidation half-reaction)
CO + H2O → CO2 + 2H+ (reduction half-reaction)
5. Balance the charges by adding electrons.
Fe2O3 + 3H2O → 2Fe + 6H+ + 6e- (oxidation half-reaction)
CO + H2O → CO2 + 2H+ + 2e- (reduction half-reaction)
6. Multiply the two half-reactions by appropriate coefficients so that the number of electrons transferred in both reactions is equal.
2Fe2O3 + 6H2O → 4Fe + 12H+ + 12e- (oxidation half-reaction)
3CO + 3H2O → 3CO2 + 6H+ + 6e- (reduction half-reaction)
7. Combine the two half-reactions.
2Fe2O3 + 6H2O + 3CO + 3H2O → 4Fe + 12H+ + 12e- + 3CO2 + 6H+ + 6e-
8. Simplify the equation by canceling out common species.
2Fe2O3 + 3CO → 4Fe + 3CO2 + 6H2O
Thus, the balanced redox equation is:
2Fe2O3 + 3CO → 4Fe + 3CO2 + 6H2O
The total number of electrons transferred in the reaction is 12.