Here's how to determine the net ionic reaction for ammonium sulfate ((NH₄)₂SO₄) and barium chloride (BaCl₂):

1. Write the balanced molecular equation:

(NH₄)₂SO₄(aq) + BaCl₂(aq) → BaSO₄(s) + 2NH₄Cl(aq)

2. Write the complete ionic equation:

This involves breaking down all soluble ionic compounds into their respective ions:

2NH₄⁺(aq) + SO₄²⁻(aq) + Ba²⁺(aq) + 2Cl⁻(aq) → BaSO₄(s) + 2NH₄⁺(aq) + 2Cl⁻(aq)

3. Identify and cancel out spectator ions:

Spectator ions are ions that appear on both sides of the equation and do not participate in the reaction. In this case, NH₄⁺ and Cl⁻ are spectator ions.

4. Write the net ionic equation:

This is the equation after removing the spectator ions:

Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s)

Therefore, the net ionic equation for the reaction of ammonium sulfate and barium chloride is: Ba²⁺(aq) + SO₄²⁻(aq) → BaSO₄(s)