Half Equations (Higher Tier)

Definition of Half Equations

Half equations show either the oxidation or reduction part of a redox reaction separately. They represent what happens at each electrode during electrolysis. Half equations include electrons to balance the charge on both sides, as electrons are lost or gained during the reaction.

At the anode (positive electrode), oxidation occurs: electrons are lost by ions or atoms. At the cathode (negative electrode), reduction occurs: electrons are gained by ions or atoms.

Half equations focus on the species involved in the electrode reactions, showing the transfer of electrons explicitly. Note: Half equations are also used to represent oxidation and reduction in other redox reactions, not just electrolysis.

Writing Half Equations in Electrolysis

To write half equations for electrolysis:

• Identify the ions present in the electrolyte.
• Decide which ions are oxidised at the anode and which are reduced at the cathode.
• Write the oxidation half equation for the anode reaction.
• Write the reduction half equation for the cathode reaction.

For example, in the electrolysis of molten lead(II) bromide, the ions are Pb²⁺ and Br⁻. At the cathode, Pb²⁺ ions gain electrons (reduction), and at the anode, Br⁻ ions lose electrons (oxidation).

Remember, the anode is where oxidation happens (loss of electrons), and the cathode is where reduction happens (gain of electrons).

Example: Bromide ions lose electrons at the anode as shown in the half equation: $\mathrm{2Br^- \rightarrow Br_2 + 2e^-}$. This shows bromide ions being oxidised to bromine gas, releasing electrons.

Balancing Half Equations

Balancing half equations involves several steps to ensure both mass and charge are balanced:

1. Balance all atoms except hydrogen and oxygen.
2. Balance oxygen atoms by adding water molecules (H₂O).
3. Balance hydrogen atoms by adding hydrogen ions (H⁺).
4. Balance the charge by adding electrons (e⁻).

This method is especially useful for half equations in aqueous solutions, where H⁺ and H₂O are available to balance hydrogen and oxygen.

For example, consider the reduction of copper(II) ions:

$\mathrm{Cu^{2+} + 2e^- \rightarrow Cu}$

Here, copper ions gain two electrons to form copper metal. The atoms and charges are balanced.

Using Half Equations to Understand Electrolysis

Half equations can be combined to form the full equation for the electrolysis reaction. This shows the overall chemical change and electron transfer.

Electrons lost in oxidation equal electrons gained in reduction, ensuring charge conservation.

By writing half equations, you can predict the products formed at each electrode during electrolysis.

For example, in molten lead(II) bromide:

At the cathode (reduction):

$\mathrm{Pb^{2+} + 2e^- \rightarrow Pb}$

At the anode (oxidation):

$\mathrm{2Br^- \rightarrow Br_2 + 2e^-}$

Combining these gives the overall reaction:

$\mathrm{Pb^{2+} + 2Br^- \rightarrow Pb + Br_2}$

For instance, the half equation for the reduction of hydrogen ions to hydrogen gas is $\mathrm{2H^+ + 2e^- \rightarrow H_2}$. This shows hydrogen ions gaining electrons to form hydrogen gas.