Half equations in chemistry

A half equation shows one half of a redox reaction: either the oxidation, where a species loses electrons, or the reduction, where a species gains them. Electrons are written in, as e⁻, so you can see them being transferred. For example, at the cathode in the electrolysis of copper(II) sulfate, Cu²⁺ + 2e⁻ → Cu: each copper ion gains two electrons and becomes a copper atom. A half equation must balance in atoms and in charge.

Oxidation and reduction: OIL RIG

AQA's GCSE specification defines oxidation as the loss of electrons and reduction as the gain of electrons. The memory aid is OIL RIG: Oxidation Is Loss, Reduction Is Gain.

• In a reduction half equation, the electrons are on the left, with the reactants: Cu²⁺ + 2e⁻ → Cu.
• In an oxidation half equation, the electrons are on the right, with the products: Zn → Zn²⁺ + 2e⁻.

Adding an oxidation half equation to a reduction half equation, so that the electrons cancel, gives the full redox equation. AQA's A-level specification describes exactly this: separate half equations are written for the oxidation and reduction processes, then combined to give an overall equation for any redox reaction.

How to write half equations

For simple ions and elements, which is most of GCSE:

1. Write the species before and after: Cl⁻ → Cl₂.
2. Balance the atoms: 2Cl⁻ → Cl₂.
3. Work out the total charge on each side: −2 on the left, 0 on the right.
4. Add electrons to the more positive side to make the charges equal: 2Cl⁻ → Cl₂ + 2e⁻.
5. Check: atoms balance, charges balance (−2 = 0 + (−2)).

Half equations in electrolysis

In electrolysis, AQA asks GCSE Higher students to write half equations for the reactions at the electrodes, and to complete and balance supplied ones.

• At the cathode (negative electrode), positive ions gain electrons: these are reductions.
• At the anode (positive electrode), negative ions lose electrons: these are oxidations.

Oxidation half equations can also be written with the electrons taken away on the left, such as 2Cl⁻ − 2e⁻ → Cl₂. AQA's specification shows both forms for the hydroxide ion. Our guide to electrolysis explains which product forms at each electrode.

Example 1: the oxygen half equation, step by step

Hydroxide ions form oxygen and water at the anode. Write the half equation.

Start with the species: OH⁻ → O₂ + H₂O. To make one O₂ you need oxygen atoms from several hydroxide ions, and each OH⁻ brings one hydrogen too. With 4OH⁻ there are 4 O and 4 H on the left, which make O₂ + 2H₂O on the right (2 + 2 = 4 O, and 4 H).

The charge is −4 on the left and 0 on the right, so add 4e⁻ to the right:

Half equations for displacement reactions

In a displacement reaction, the more reactive metal loses electrons and the ions of the less reactive metal gain them. Zinc in copper(II) sulfate solution:

Split it into its two halves:

• Oxidation: Zn → Zn²⁺ + 2e⁻ (zinc loses electrons)
• Reduction: Cu²⁺ + 2e⁻ → Cu (copper ions gain electrons)

The 2e⁻ lost by zinc is exactly the 2e⁻ gained by copper, so adding the halves cancels the electrons and gives back the ionic equation. Our ionic equations guide covers spectator ions.

Here is a quick check.

Balancing half equations in acid (A-level)

For ions containing oxygen, such as manganate(VII) or dichromate(VI), there is a set method. It works in acidic solution, where H⁺ ions and water are available.

1. Balance the atoms other than O and H.
2. Balance O by adding H₂O molecules.
3. Balance H by adding H⁺ ions.
4. Balance the charge by adding electrons.

Example 2: manganate(VII) to manganese(II)

Write the half equation for MnO₄⁻ → Mn²⁺ in acid.

• Mn: one on each side already.
• O: 4 on the left, so add 4H₂O on the right: MnO₄⁻ → Mn²⁺ + 4H₂O.
• H: now 8 on the right, so add 8H⁺ on the left: MnO₄⁻ + 8H⁺ → Mn²⁺ + 4H₂O.
• Charge: left −1 + 8 = +7, right +2. Add 5e⁻ to the left:

Electrons on the left, so this is a reduction. The oxidation state of Mn falls from +7 to +2, a change of 5, matching the 5 electrons gained. That is a useful check, and our guide to oxidation numbers shows how to work them out.

Example 3: hydrogen peroxide as an oxidising agent

Write the half equation for H₂O₂ → H₂O in acid.

O: 2 on the left, so 2H₂O on the right. H: 2 on the left, 4 on the right, so add 2H⁺ on the left. Charge: left +2, right 0, so add 2e⁻ on the left:

Combining half equations

To get the full equation, multiply one or both half equations so the electrons are equal, add them, and cancel anything on both sides.

Example 4: manganate(VII) and iron(II)

Combine MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O with Fe²⁺ → Fe³⁺ + e⁻.

The first gains 5 electrons and the second loses 1, so multiply the iron half equation by 5: 5Fe²⁺ → 5Fe³⁺ + 5e⁻. Add and cancel the 5e⁻:

Check the charge: left −1 + 8 + 10 = +17, right +2 + 15 = +17. It balances. This reaction is the basis of manganate(VII) titrations.

Example 5: hydrogen peroxide and iron(II)

Combine H₂O₂ + 2H⁺ + 2e⁻ → 2H₂O with Fe²⁺ → Fe³⁺ + e⁻. Double the iron half equation to match the 2 electrons:

The Equation Balancer balances half equations with electrons as well as full ionic equations, and shows the atom and charge counts, so you can check your own working.

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Half equations in a hydrogen fuel cell

A hydrogen fuel cell oxidises hydrogen to make water. AQA asks GCSE Higher students to write its electrode half equations. With an acidic electrolyte:

• At the negative electrode: H₂ → 2H⁺ + 2e⁻ (oxidation)
• At the positive electrode: O₂ + 4H⁺ + 4e⁻ → 2H₂O (reduction)

Doubling the first and adding gives 2H₂ + O₂ → 2H₂O: the same overall reaction as burning hydrogen, but releasing the energy as electricity.

Common mistakes

• Balancing atoms but not charge. Cl⁻ → Cl₂ + e⁻ has the wrong number of chlorines and the wrong charge. Count both.
• Electrons on the wrong side. Reduction: electrons are reactants. Oxidation: electrons are products.
• Writing Cl instead of Cl₂. Chlorine, bromine, oxygen and hydrogen gas are all diatomic.
• Adding electrons to the wrong side. Electrons are negative, so they go on the side that is more positive.
• Leaving electrons in a combined equation. Multiply the half equations until the electrons cancel completely.

Practise chemistry in a short timed paper

GCSE Chemistry Higher and A-level Chemistry: Year 1 each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course, so electrolysis and redox turn up regularly but not in every paper.

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