Half equations in electrolysis are critical representations that illustrate the loss or gain of electrons during redox (reduction-oxidation) reactions.

In the context of electrolysis, a redox reaction involves the transfer of electrons between different species. Half equations serve to depict these individual processes, clearly indicating the number of electrons either lost or gained by the involved species.

The half equation for oxidation represents the loss of electrons. Oxidation occurs when a substance loses electrons, and this is illustrated in the half equation by placing the substance on the left-hand side and the resulting product, along with the lost electrons, on the right-hand side. For instance, the oxidation of sodium can be expressed as:

This equation indicates that sodium ($\text{Na}$) loses one electron ($e^-$) to form a sodium ion ($\text{Na}^+$).

Conversely, the half equation for reduction illustrates the gain of electrons. Reduction occurs when a substance gains electrons, which is represented by positioning the substance and the gained electrons on the left-hand side, while the resulting product is placed on the right-hand side. For example, the reduction of chlorine can be represented as:

This equation demonstrates that chlorine ($\text{Cl}_2$) gains two electrons ($2e^-$) to produce two chloride ions ($2\text{Cl}^-$).

In electrolysis, the electrode where oxidation occurs is referred to as the anode, while the electrode where reduction takes place is known as the cathode. The half equations provide valuable insights into the reactions occurring at each electrode during the electrolysis process. They are essential tools for understanding and analyzing the underlying mechanisms of electrochemical reactions in electrolysis.