A solution containing several metal ions is treated with dilute HCl; no precipitate forms. The pH is adjusted to about 1, and $\mathrm{H}_{2} \mathrm{~S}$ is bubbled through. Again, no precipitate forms. The \(\mathrm{pH}\) of the solution is then adjusted to about 8 . Again, \(\mathrm{H}_{2} \mathrm{~S}\) is bubbled through. This time a precipitate forms. The filtrate from this solution is treated with \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\). No precipitate forms. Which of these metal cations are either possibly present or definitely absent: \(\mathrm{Al}^{3+}, \mathrm{Na}^{+}, \mathrm{Ag}^{+}, \mathrm{Mg}^{2+}\) ?

The first thing is to understand what happens when we treat a solution containing metal ions with dilute HCl. Chlorides of certain metal ions are insoluble and will precipitate when HCl is added. However, no precipitate is formed in this case, which means that Al³⁺ and Ag⁺ ions are not present because AlCl₃ and AgCl are soluble in dilute HCl.

At a low pH (around 1), H₂S will react with metal ions to form metal sulfides. Since there is no precipitate formation, we can conclude that none of the metal sulfides are formed. Therefore, at this stage, we can't make any further conclusion about the presence or absence of Na⁺ or Mg²⁺ ions.

When we adjust the pH to about 8 and pass H₂S through the solution again, a precipitate is formed. This means that there are metal ions present that can form insoluble metal sulfides at this pH. MgS is insoluble at this pH, so Mg²⁺ ions could possibly be present. On the other hand, Na₂S is soluble at this pH which means Na⁺ ions are not forming a precipitate, but we still cannot confirm their absence.

Finally, after filtering the solution from step 3, (NH₄)₂HPO₄ is added and no precipitate is formed. This indicates that there are no metal ions present that can form insoluble metal phosphates. In our list of ions, Al³⁺ can form insoluble AlPO₄, but since no precipitate is observed, we can conclude that Al³⁺ ions are definitely absent. #Conclusion# In summary, based on the given exercise: - Al³⁺ is definitely absent, because no precipitate was formed in the presence of HCl and (NH₄)₂HPO₄. - Na⁺ is possibly present, as NaCl is soluble in dilute HCl, Na₂S is soluble at pH 8, and no precipitate was observed after adding (NH₄)₂HPO₄. - Ag⁺ is definitely absent, due to no precipitate formation after treating the solution with dilute HCl. - Mg²⁺ is possibly present, as MgCl₂ is soluble in dilute HCl, MgS is insoluble at pH 8, and no precipitate was observed after adding (NH₄)₂HPO₄.