A half-equation shows you what happens at one of the electrodes during electrolysis. Electrons are shown as e–. A half-equation is balanced by adding, or taking away, a number of electrons equal to the total number of charges on the ions in the equation.
When positive metal ions (cations) arrive at the negative electrode (the cathode), they gain electrons to form neutral metal atoms. This is called reduction. For example:
Pb2+ + 2e– → Pb
When negative non-metal ions (anions) arrive at the positive electrode (the anode), they lose electrons to form neutral atoms or molecules. This loss of electrons is called oxidation. For example:
2Br– → Br2 + 2e– OR 2Br– - 2e– → Br2
One way to remember this is by using the mnemonic OIL RIG:
Oxidation Is Loss of electrons, Reduction Is Gain of electrons.
Cations go to the cathode (negative electrode). They need to gain enough electrons to make them neutral. So an Al3+ ion needs to gain three electrons:
Al3+ + 3e– → Al
Half-equations for non-metal anions are more difficult to balance. For example, chloride ions make chlorine gas. Most non-metal elements formed in electrolysis are diatomic molecules (eg Cl2). For example:
2Cl– → Cl2
Add in two electrons to balance the charge so that both sides have the same charge. The two electrons need to go on the right-hand side, so that both sides have an overall charge of –2. For example:
2Cl– → Cl2 + 2e–