Final answer:
The answer to which option illustrates a double replacement reaction is option b: BaCl₂ + K₂CO₃ → BaCO₃ + 2KCl, where barium and potassium ions exchange anions to form new compounds.
Step-by-step explanation:
An example of a double replacement reaction is option b: BaCl₂ + K₂CO₃ → BaCO₃ + 2KCl. In this reaction, the cations Ba²⁺ and K⁺ swap places with each other's anions, Cl⁻ and CO₃²⁻, forming new compounds BaCO₃ and KCl. This is characteristic of double replacement reactions, where two compounds react and their constituent ions exchange partners, typically resulting in the formation of a new precipitate, gas, or neutral molecule.