MnO₄^–(aq) + Cr³⁺(aq) → Mn²⁺(aq) + Cr₂O₇^2–(aq) (pH = 1)

oxidation/reduction under acidic conditions

[MnO₄^–(aq) + 8 H⁺(aq) + 5 e^– → Mn²⁺(aq) + 4 H₂O(l)] × 6

[2 Cr³⁺(aq) + 7 H₂O(l) → Cr₂O₇^2–(aq) + 14 H⁺(aq) + 6 e^–] × 5

6 MnO₄^–(aq) + 10 Cr³⁺(aq) + 11 H₂O(l) → 6 Mn²⁺(aq) + 5 Cr₂O₇^2–(aq) + 22 H⁺(aq)