To balance the redox reaction in acidic solution, follow these steps:
Assign oxidation numbers to each element in the reaction:
Mn in MnO₂: +4
Mn in MnO: +2
Cu in Cu²⁺: +2
Cu in Cu⁺: +1
Identify the elements undergoing oxidation and reduction:
Oxidation: Mn in MnO₂ is going from +4 to +2.
Reduction: Cu²⁺ is going from +2 to +1.
Balance the number of atoms for each element except for H and O:
MnO₂ + Cu²⁺ → MnO + Cu⁺
Balance the oxygen atoms by adding water (H₂O) molecules:
MnO₂ + Cu²⁺ → MnO + Cu⁺ + H₂O
Balance the hydrogen atoms by adding hydrogen ions (H⁺):
MnO₂ + Cu²⁺ + 4H⁺ → MnO + Cu⁺ + 2H₂O
Balance the charge by adding electrons (e⁻):
MnO₂ + Cu²⁺ + 4H⁺ + 2e⁻ → MnO + Cu⁺ + 2H₂O
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 acidic solution is:
MnO₂ + Cu²⁺ + 4H⁺ → MnO + Cu⁺ + 2H₂O