Balancing redox equations

A balanced redox equation must balance both atoms and charge, and the electrons lost must equal the electrons gained. There are two methods.

Oxidation number method:

• Write the skeleton equation.
• Assign oxidation numbers and find which atoms change.
• Make the total increase in oxidation number equal the total decrease, by multiplying the species.
• Balance the charge with H⁺ (in acid) or OH⁻ (in base).
• Balance hydrogen by adding H₂O, and check the oxygens.

Half-reaction method:

• Split the reaction into an oxidation half and a reduction half.
• In each half, balance the atoms other than O and H.
• Balance O by adding H₂O, and balance H by adding H⁺ (not H₂).
• Balance the charge by adding electrons.
• Multiply the halves so that the electrons are the same in both, then add them; the electrons cancel.
• Check that atoms and charges balance.

For example, the reduction half of dichromate in acid: Cr₂O₇²⁻ → 2Cr³⁺. Balance O with 7H₂O, then H with 14H⁺, then charge: Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O. Each chromium goes from +6 to +3, so six electrons in all.

In a basic solution, first balance as if in acid. Then add as many OH⁻ to both sides as there are H⁺, and combine each H⁺ + OH⁻ into H₂O. No H⁺ should remain. An example in base: 2MnO₄⁻ + 6I⁻ + 4H₂O → 2MnO₂ + 3I₂ + 8OH⁻.