Balancing a Redox Equation by the Half-Reaction Method

Balancing a redox equation by the half-reaction method means splitting the reaction into separate oxidation and reduction half-reactions, balancing each for atoms and then for charge by adding electrons, and finally scaling and combining the two half-reactions so the electrons lost exactly cancel the electrons gained.

For Fe²⁺ + Cr2O7²⁻ → Fe³⁺ + Cr³⁺ in acidic solution, the oxidation half-reaction Fe²⁺ → Fe³⁺ + e⁻ is scaled by six to match the six electrons the reduction half-reaction Cr2O7²⁻ + 14 H⁺ + 6 e⁻ → 2 Cr³⁺ + 7 H2O requires, giving the balanced overall equation 6 Fe²⁺ + Cr2O7²⁻ + 14 H⁺ → 6 Fe³⁺ + 2 Cr³⁺ + 7 H2O.