Here's how to break down the reaction between bromine and potassium iodide and write the balanced half-equations:

The Reaction:

Bromine (Br₂) reacts with potassium iodide (KI) to form iodine (I₂) and potassium bromide (KBr).

The Balanced Overall Equation:

Br₂ (l) + 2KI (aq) → 2KBr (aq) + I₂ (s)

Half-Equations:

1. Oxidation Half-Equation:

* Iodide ions (I⁻) are oxidized to iodine (I₂).

* 2I⁻ (aq) → I₂ (s) + 2e⁻

2. Reduction Half-Equation:

* Bromine molecules (Br₂) are reduced to bromide ions (Br⁻).

* Br₂ (l) + 2e⁻ → 2Br⁻ (aq)

Explanation:

* Oxidation: The iodide ions (I⁻) lose electrons and their oxidation state increases from -1 to 0.

* Reduction: The bromine molecules (Br₂) gain electrons and their oxidation state decreases from 0 to -1.

Important Notes:

* The number of electrons lost in the oxidation half-equation must equal the number of electrons gained in the reduction half-equation.

* This is why we multiplied the reduction half-equation by 2.

* These half-equations can be combined to get the overall balanced equation.