Here's how to determine the net ionic equation for the reaction between silver acetate (AgC₂H₃O₂) and ammonium sulfate ((NH₄)₂SO₄):

1. Write the balanced molecular equation:

2 AgC₂H₃O₂(aq) + (NH₄)₂SO₄(aq) → Ag₂SO₄(s) + 2 NH₄C₂H₃O₂(aq)

2. Write the complete ionic equation:

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

2 Ag⁺(aq) + 2 C₂H₃O₂⁻(aq) + 2 NH₄⁺(aq) + SO₄²⁻(aq) → Ag₂SO₄(s) + 2 NH₄⁺(aq) + 2 C₂H₃O₂⁻(aq)

3. Identify and cancel spectator ions:

Spectator ions are ions that appear on both sides of the equation and do not participate in the reaction. In this case, the spectator ions are NH₄⁺ and C₂H₃O₂⁻.

4. Write the net ionic equation:

This includes only the ions that directly participate in the reaction:

2 Ag⁺(aq) + SO₄²⁻(aq) → Ag₂SO₄(s)

Therefore, the net ionic equation for the reaction between silver acetate and ammonium sulfate is:

2 Ag⁺(aq) + SO₄²⁻(aq) → Ag₂SO₄(s)