Half Equations

When balancing half equations, you must ensure that both the number of atoms and the total electrical charge are identical on both sides of the arrow. For example, if the left side has a total charge of $2-$, the right side must also have a total net charge of $2-$.

Deriving Monatomic and Diatomic Products

Like balancing a seesaw, a half equation must have perfectly matched elements and charges, which requires different steps depending on the state of the final product. Metals form monatomic (single) neutral atoms, while hydrogen, oxygen, and halogens always form diatomic molecules (e.g., $Cl_2$, $O_2$).

Worked Example: Formation of sodium metal

Derive the half equation for the discharge of sodium ions ($Na^+$).

1. Identify the ion and its movement: Positive sodium ions ($Na^+$) are attracted to the negative cathode.
2. Write the unbalanced discharge process: $Na^+ \rightarrow Na$
3. Balance the charge by adding electrons: The $Na^+$ ion must gain one electron to become neutral.
   • $Na^+ + e^- \rightarrow Na$

Worked Example: Formation of chlorine gas

Derive the half equation for the discharge of chloride ions ($Cl^-$) to form chlorine gas.

1. Identify the ion and write the initial discharge process: Negative chloride ions ($Cl^-$) move to the anode to form diatomic chlorine ($Cl_2$).
   • $Cl^- \rightarrow Cl_2$
2. Balance the atoms: We need two chloride ions to form one diatomic molecule.
   • $2Cl^- \rightarrow Cl_2$
3. Balance the charge by adding electrons: The left side has a total charge of $2-$. The right side must match this by adding two electrons.
   • $2Cl^- \rightarrow Cl_2 + 2e^-$

Worked Example: Formation of oxygen gas

Derive the half equation for the formation of oxygen gas from hydroxide ions ($OH^-$).

1. Identify the reactants and products: Hydroxide ions ($OH^-$) react to form oxygen gas ($O_2$) and water ($H_2O$).
   • $OH^- \rightarrow O_2 + H_2O$
2. Balance the oxygen and hydrogen atoms: To make $O_2$ and $H_2O$ while balancing both elements, we require four hydroxide ions.
   • $4OH^- \rightarrow O_2 + 2H_2O$
3. Balance the total charge by adding electrons: The left side has a charge of $4-$. We must add four electrons to the right side to balance it.
   • $4OH^- \rightarrow 2H_2O + O_2 + 4e^-$