Here's how to determine the net ionic equation for the reaction of silver nitrate (AgNO₃) and ammonium sulfide ( (NH₄)₂S):

1. Write the balanced molecular equation:

2AgNO₃(aq) + (NH₄)₂S(aq) → Ag₂S(s) + 2NH₄NO₃(aq)

2. Identify the soluble and insoluble compounds:

* Soluble: Silver nitrate (AgNO₃), ammonium sulfide ((NH₄)₂S), and ammonium nitrate (NH₄NO₃)

* Insoluble: Silver sulfide (Ag₂S)

3. Write the complete ionic equation:

2Ag⁺(aq) + 2NO₃⁻(aq) + 2NH₄⁺(aq) + S²⁻(aq) → Ag₂S(s) + 2NH₄⁺(aq) + 2NO₃⁻(aq)

4. Cancel out the spectator ions:

Spectator ions are the ions that appear on both sides of the equation and do not participate in the reaction. In this case, NH₄⁺ and NO₃⁻ are spectator ions.

5. The net ionic equation is:

2Ag⁺(aq) + S²⁻(aq) → Ag₂S(s)