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Question
Balance the following redox equation by half-reaction method.
\[\ce{H2C2O_{4(aq)} + MnO^-_{4(aq)}->CO2_{(g)} + Mn^2+_{( aq)}(acidic)}\]
Solution
\[\ce{H2C2O_{4(aq)} + MnO^-_{4(aq)}->CO2_{(g)} + Mn^2+_{( aq)}}\]
Step 1: Write the unbalanced equation for the redox reaction. Assign the oxidation number to all the atoms in reactants and products. Divide the equation into two half equations.
- Oxidation half-reaction: \[\ce{H2C2O_{4(aq)}->CO2_{(g)}}\]
- Reduction half-reaction: \[\ce{MnO^-_{4(aq)}->Mn^2+_{( aq)}}\]
Step 2: Balance the atoms except O and H in each half equation. Balance half equation for O atoms by adding 4H2O to the right side of the reduction half equation.
- Oxidation: \[\ce{H2C2O_{4(aq)}->2CO2_{(g)}}\]
- Reduction: \[\ce{MnO^-_{4(aq)}->Mn^2+_{( aq)} + 4H2O_{(l)}}\]
Step 3: Balance H atoms by adding H+ ions to the side with less H. Hence, add 2H+ ions to the right side of the oxidation half equation and 8H+ ions to the left side of the reduction half equation.
- Oxidation: \[\ce{H2C2O_{4(aq)}->2CO2_{(g)} + 2H^+_{( aq)}}\]
- Reduction: \[\ce{MnO^-_{4(aq)} + 8H^+_{( aq)}->Mn^2+_{( aq)} + 4H2O_{(l)}}\]
Step 4: Now add 2 electrons to the right side of the oxidation half equation and 5 electrons to the left side of the reduction half equation to balance the charges.
- Oxidation: \[\ce{H2C2O_{4(aq)}->2CO2_{(g)} + 2H^+_{( aq)} + 2e^-}\]
- Reduction: \[\ce{MnO^-_{4(aq)} + 8H^+_{( aq)} + 5e^-->Mn^2+_{( aq)} + 4H2O_{(l)}}\]
Step 5: Multiply oxidation half equation by 5 and reduction half equation by 2 to equalize the number of electrons in two half equations. Then add two half equations.
- Oxidation: \[\ce{5H2C2O_{4(aq)}->10CO2_{(g)} + 10H^+_{( aq)} + 10e^-}\]
- Reduction: \[\ce{2MnO^-_{4(aq)} + 16H^+_{( aq)} + 10e^-->2Mn^2+_{( aq)} + 8H2O_{(l)}}\]
Add two half equations:
\[\ce{5H2C2O_{4(aq)} + 2MnO^-_{4(aq)} + 6H^+_{( aq)}->10CO2 + 2Mn^2+_{( aq)} + 8H2O_{(l)}}\]
The equation is balanced in terms of the number of atoms and the charges.
Hence, balanced equation: \[\ce{5H2C2O_{4(aq)} + 2MnO^-_{4(aq)} + 6H^+_{( aq)}->10CO2 + 2Mn^2+_{( aq)} + 8H2O_{(l)}}\]
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