Identify the oxidation and reduction half-reactions. In this case, H₂O₂ is being oxidized to O₂, and ClO₂ is being reduced to ClO₂⁻.
Write the oxidation half-reaction: H₂O₂ → O₂. Balance the oxygen atoms by adding H₂O to the right side: H₂O₂ → O₂ + H₂O.
Balance the hydrogen atoms by adding H⁺ to the left side: H₂O₂ + 2H⁺ → O₂ + H₂O.
Write the reduction half-reaction: ClO₂ → ClO₂⁻. Balance the oxygen atoms by adding H₂O to the left side: ClO₂ + H₂O → ClO₂⁻.
Combine the balanced half-reactions, ensuring that the electrons cancel out, and adjust for basic conditions by adding OH⁻ to both sides to neutralize H⁺ and form water. The final balanced equation in basic solution is: H₂O₂ + ClO₂ + 2OH⁻ → ClO₂⁻ + O₂ + 2H₂O.