Here's how to determine the net ionic equation for the reaction between potassium phosphate (K₃PO₄) and barium bromide (BaBr₂):

1. Write the balanced molecular equation:

3BaBr₂(aq) + 2K₃PO₄(aq) → Ba₃(PO₄)₂(s) + 6KBr(aq)

2. Write the complete ionic equation:

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

3Ba²⁺(aq) + 6Br⁻(aq) + 6K⁺(aq) + 2PO₄³⁻(aq) → Ba₃(PO₄)₂(s) + 6K⁺(aq) + 6Br⁻(aq)

3. Identify the spectator ions:

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

4. Write the net ionic equation:

The net ionic equation shows only the species that directly participate in the reaction:

3Ba²⁺(aq) + 2PO₄³⁻(aq) → Ba₃(PO₄)₂(s)

This equation represents the formation of the solid barium phosphate precipitate.