To balance the redox reaction in basic solution, follow these steps:
Assign oxidation numbers to each element in the reaction:
Cl in ClO₂: +4
Cl in CIO: +1
Ag in Ag⁺: +1
Ag in Ag: 0
Identify the elements undergoing oxidation and reduction:
Oxidation: Cl in ClO₂ is going from +4 to +1.
Reduction: Ag⁺ is going from +1 to 0.
Balance the number of atoms for each element except for H and O:
ClO₂ + Ag⁺ → CIO + Ag
Balance the oxygen atoms by adding water (H₂O) molecules:
ClO₂ + Ag⁺ → CIO + Ag + H₂O
Balance the hydrogen atoms by adding hydroxide ions (OH⁻):
ClO₂ + Ag⁺ + H₂O → CIO + Ag + OH⁻
Balance the charge by adding electrons (e⁻):
ClO₂ + 2Ag⁺ + 2H₂O → CIO + 2Ag + 2OH⁻ + 2e⁻
Make sure that the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction.
The balanced redox reaction in basic solution is:
ClO₂ + 2Ag⁺ + 2H₂O → CIO + 2Ag + 2OH⁻