H₂O₂(aq) + Mn²⁺(aq) → MnO₄^–(aq) + H₂O(l)

acidic environment

[H₂O₂(aq) + 2 H⁺(aq) + 2 e^– → 2 H₂O(l)] × 5

[Mn²⁺(aq) + 4 H₂O(l) → MnO₄^–(aq) + 8 H⁺(aq) + 5 e^–]× 2

sum and eliminate common species

5 H₂O₂(aq) + 2 Mn²⁺(aq) → 2 MnO₄^–(aq) + 2 H₂O(l) + 6 H⁺(aq)