The spectator ions in the reaction between Ba(OH)2 and K3PO4 are K+ and OH-. These ions appear on both sides of the complete ionic equation and do not participate in the creation of the precipitate, Ba3(PO4)2.
To identify the spectator ions in the reaction between aqueous solutions of Ba(OH)2 and K3PO4, we must first write out the balanced equation for the reaction and then the complete ionic equation. The balanced chemical equation is:
3Ba(OH)2 + 2K3PO4 → Ba3(PO4)2 + 6KOH
Now, the complete ionic equation, taking into account the solubility of the compounds, is:
3Ba2+ (aq) + 6OH− (aq) + 6K+ (aq) + 2PO43− (aq) → Ba3(PO4)2 (s) + 6K+ (aq) + 6OH− (aq)
From this we can determine that the spectator ions are K+ (aq) and OH− (aq), which appear on both sides of the equation and do not participate in the formation of the solid precipitate.
To finish, we can write the net ionic equation by removing these spectator ions from both sides. The net ionic equation is:
3Ba2+ (aq) + 2PO43− (aq) → Ba3(PO4)2 (s)