Forming the complete equation: combining two half-equations

Why combine two half-equations?

An electron half-reaction describes only half the picture: it shows a pair gaining or losing electrons, but these electrons cannot remain ‘free’ in solution. We must therefore pair it with another pair that captures exactly the electrons released by the first pair.

The rule of equal numbers of electrons

Let’s consider the reaction between iron(II) ions and permanganate ions in an acidic medium.

Fe³⁺/Fe²⁺ pair (oxidation):

Fe2+ = Fe3+ + e-

Check: charges on the left +2; on the right +3–1 = +2. Balanced.

MnO₄⁻/Mn²⁺ pair (reduction):

MnO4- + 8 H+ + 5 e- = Mn2+ + 4 H2O

Iron releases only one electron per ion, whilst manganese accepts five. To ensure the number of electrons exchanged is the same on both sides, we multiply the iron half-reaction by 5:

5 Fe2+ = 5 Fe3+ + 5 e-

Addition and simplification

We add the left-hand sides together, then cancel out the electrons (5 e⁻ on each side):

MnO4- + 8 H+ + 5 Fe2+ -> Mn2+ + 4 H2O + 5 Fe3+

Let’s check one last time. Elements: Mn 1=1, O 4=4, H 8=8, Fe 5=5. Charges on the left: (-1) + 8×(+1) + 5×(+2) = -1 + 8 + 10 = +17. Charges on the right: (+2) + 0 + 5×(+3) = 2 + 15 = +17. Both sides equal +17: the overall equation is balanced.

Common pitfall

A common pitfall is to add the two half-equations directly without multiplying them first: the number of electrons then does not match, and the resulting overall equation is incorrect. Always check that there are no ‘e–’ left over after addition: this is a sign that the electron balance is correct.