Writing simple half equations

What a half equation shows

• A half equation shows one half of a redox reaction — either the oxidation or the reduction — with the electrons written in.

• Together, the two half equations account for the whole reaction.

• The electrons show where they came from or went to, which is exactly what an ordinary equation hides.

The two simplest cases

A metal being oxidised — the metal loses electrons and becomes a positive ion:

$$\text{Mg}(s) \rightarrow \text{Mg}^{2+}(aq) + 2e^-$$

• The number of electrons equals the charge on the ion formed.

A metal ion being reduced — the ion gains electrons and becomes the metal:

$$\text{Cu}^{2+}(aq) + 2e^- \rightarrow \text{Cu}(s)$$

• Again the number of electrons equals the charge that disappears.

A non-metal being reduced — the atom gains electrons and becomes a negative ion:

$$\text{Cl}_2(aq) + 2e^- \rightarrow 2\text{Cl}^-(aq)$$

• Watch the two chlorine atoms. A diatomic molecule needs two ions on the right, and therefore two electrons.

The two things every half equation must balance

• Atoms — the same number of each element on both sides.

• Charge — the total charge must be the same on both sides, once the electrons are counted.

• Checking the charge is the fastest way to find an error. Add up the charges on the left, add up the charges on the right, and they must match.

For $\text{Fe}^{2+} \rightarrow \text{Fe}^{3+} + e^-$:

• Left: +2. Right: $(+3) + (-1) = +2$. Balanced.

Building one from scratch

• Write the species that changes, on the correct sides.

• Balance the atoms of the element being oxidised or reduced.

• Add electrons to whichever side makes the charges equal.

• Check both atoms and charge.

• If you find yourself adding electrons to both sides, you have made an error — every half equation has electrons on one side only.