Half-Reaction Method in Acidic Solution

The half-reaction method balances a redox equation in acidic solution by splitting it into oxidation and reduction half-reactions, balancing atoms (using H₂O for oxygen and H⁺ for hydrogen) and charge (using electrons), equalizing the electrons and adding the halves. In brief: permanganate oxidizes iron(II) according to MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O, found by balancing MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O and Fe²⁺ → Fe³⁺ + e⁻.

The method is reliable for ionic reactions in water, where H⁺ and H₂O take part. This article lists the steps, works through four examples of increasing difficulty, includes a table of common half-reactions in acid, explains how to use the balanced equation in titration calculations and gives some history.

What are the steps?

1. Write the skeleton ionic equation and assign oxidation numbers to identify what is oxidized and reduced.
2. Write two unbalanced half-reactions.
3. For each half-reaction: balance all atoms except O and H; balance O by adding H₂O; balance H by adding H⁺; balance charge by adding electrons.
4. Multiply each half-reaction by an integer so that the electrons are equal.
5. Add the half-reactions and cancel electrons and any identical species on both sides.
6. Check atoms and charge.

Worked examples

1. MnO₄⁻ + Fe²⁺ → Mn²⁺ + Fe³⁺.
   Reduction: MnO₄⁻ → Mn²⁺. Add 4H₂O on the right for the oxygen: MnO₄⁻ → Mn²⁺ + 4H₂O. Add 8H⁺ on the left: MnO₄⁻ + 8H⁺ → Mn²⁺ + 4H₂O. Charge: left +7, right +2, so add 5e⁻ on the left.
   Oxidation: Fe²⁺ → Fe³⁺ + e⁻. Multiply by 5.
   Sum: MnO₄⁻ + 8H⁺ + 5Fe²⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺. Charge: +17 = +17.

2. Cr₂O₇²⁻ + Fe²⁺ → Cr³⁺ + Fe³⁺.
   Reduction: Cr₂O₇²⁻ → 2Cr³⁺ + 7H₂O; add 14H⁺ on the left; charge: left +12, right +6, so add 6e⁻ on the left.
   Oxidation: 6 × (Fe²⁺ → Fe³⁺ + e⁻).
   Sum: Cr₂O₇²⁻ + 14H⁺ + 6Fe²⁺ → 2Cr³⁺ + 7H₂O + 6Fe³⁺. Charge: +24 = +24.

3. MnO₄⁻ + H₂C₂O₄ → Mn²⁺ + CO₂.
   Reduction (×2): MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O.
   Oxidation (×5): H₂C₂O₄ → 2CO₂ + 2H⁺ + 2e⁻.
   Sum: 2MnO₄⁻ + 16H⁺ + 5H₂C₂O₄ → 2Mn²⁺ + 8H₂O + 10CO₂ + 10H⁺. Cancel 10H⁺: 2MnO₄⁻ + 6H⁺ + 5H₂C₂O₄ → 2Mn²⁺ + 8H₂O + 10CO₂.

4. Cu + NO₃⁻ → Cu²⁺ + NO (dilute nitric acid).
   Reduction (×2): NO₃⁻ + 4H⁺ + 3e⁻ → NO + 2H₂O.
   Oxidation (×3): Cu → Cu²⁺ + 2e⁻.
   Sum: 2NO₃⁻ + 8H⁺ + 3Cu → 2NO + 4H₂O + 3Cu²⁺. Charge: +6 = +6.

Common half-reactions in acid

How is the result used in a titration?

An iron tablet of mass 0.500 g is dissolved in acid and titrated with 0.0200 mol/L KMnO₄, which needs 18.50 mL. n(MnO₄⁻) = 0.01850 × 0.0200 = 3.70 × 10⁻⁴ mol. From the 1 : 5 ratio, n(Fe²⁺) = 1.85 × 10⁻³ mol, so m(Fe) = 1.85 × 10⁻³ × 55.845 = 0.1033 g, which is 20.7% of the tablet. Permanganate acts as its own indicator: the first persistent pink color shows the end point.

How do you check the result?

• Count the atoms of every element, including H and O.
• Add the charges on each side.
• Confirm that no electrons remain in the final equation.

How did the method develop?

The ion-electron (half-reaction) method became general in the early 20th century and was popular in analytical chemistry, where redox titrations with permanganate and dichromate were developed in the 19th century (Margueritte 1846; Penny 1850).

Which mistakes are common?

Mistake 1: Adding H⁺ before balancing oxygen

Use H₂O for oxygen first, then H⁺ for hydrogen.

Mistake 2: Forgetting the charge balance

Electrons balance charge, so check it in each half-reaction.

Mistake 3: Not cancelling common species

Cancel H⁺ and H₂O that appear on both sides.

Mistake 4: Using the method for basic solution without conversion

H⁺ cannot appear in a basic solution. See the next article.