Balance the following by the method of half reactions and give the correct coefficients: ___ VO4^3- + ___ Fe2+ + ___ H+ --> ___ VO2+ + ___ Fe3+ + ___ H2O

Answer

To balance the redox reaction using the half-reaction method, we split the reaction into oxidation and reduction components. 1. Oxidation Half-Reaction: Fe^2+ -> Fe^3+. To balance the charge, add one electron to the product side: Fe^2+ -> Fe^3+ + e^-. 2. Reduction Half-Reaction: VO4^3- -> VO^2+. First, balance the oxygen atoms by adding 3 H2O to the product side: VO4^3- -> VO^2+ + 3 H2O. Next, balance the hydrogen atoms by adding 6 H+ to the reactant side: VO4^3- + 6 H+ -> VO^2+ + 3 H2O. Now, balance the charge. The total charge on the left is (-3 + 6) = +3, and on the right it is +2. Add one electron to the reactant side: VO4^3- + 6 H+ + e^- -> VO^2+ + 3 H2O. 3. Combine the half-reactions: Both half-reactions involve one electron, so we can add them directly: (Fe^2+ -> Fe^3+ + e^-) + (VO4^3- + 6 H+ + e^- -> VO^2+ + 3 H2O). The electrons cancel out, resulting in: VO4^3- + Fe^2+ + 6 H+ -> VO^2+ + Fe^3+ + 3 H2O. The coefficients are (1, 1, 6; 1, 1, 3). Looking at the options, this matches the fourth choice: (1,1,6; 1,1,3).