Final answer:
The white precipitate formed when PbI₂ is mixed with Na₂CO₃ is most likely PbCO₃ (lead carbonate), as it is known to be insoluble in water.
Step-by-step explanation:
When PbI₂ (solid) is added to Na₂CO₃ (aqueous), a white precipitate is formed. The white precipitate is most likely PbCO₃. This is derived from rules of solubility where lead carbonate, PbCO₃, is known to be insoluble, leading to the formation of a precipitate. On the contrary, sodium iodide, NaI, would be soluble in water and hence, does not precipitate. The other potential product from this reaction, NH₄NO₃, appears to be a mistake as no ammonium ions or nitrate ions are present in the reactants.