You are working as a laboratory technician in a water quality testing laboratory. You have recently received some water samples believed to contain lead (Pb⁺²), barium (Ba⁺²), and/or magnesium (Mg⁺²) ions. Your laboratory has been asked to identify and separate the ions out of the water samples using precipitation reactions, and verify the identity of the metal ions using flame tests.

Your task is to design an experimental procedure to precipitate out each of the three metal ions from the water sample, separate the precipitate from the liquid supernatant after each precipitation, and then verify the identity of the metal ions in the precipitates using flame tests.

To conduct your precipitations you have aqueous solutions of sodium chloride, NaCl_(aq), sodium sulfide, Na₂S_(aq), and sodium hydroxide, NaOH_(aq).

Write 1-2 sentences explaining the purpose of the investigation. Share the possible results of the investigation and, more importantly, what they mean. This should include either a step-by-step procedure. Show the net ionic equations for the formation of the three precipitates.