MnO₄^–(aq) + Br^–(aq) → Mn²⁺(aq) + Br₂(l)

acidic environment

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

[2 Br^–(aq) → Br₂(l) + 2 e^–] × 5

sum and eliminate common species

2 MnO₄^–(aq) + 10 Br^–(aq) + 16 H⁺(aq) → 2 Mn²⁺(aq) + 5 Br₂(l) + 8 H₂O(l)