A solution containing several metal ions is treated with dilute HCl; no precipitate forms. The pH is adjusted to about 1, and H₂S is bubbled through. Again, no precipitate forms. The pH of the solution is then adjusted to about 8. Again, H₂S is bubbled through. This time a precipitate forms. The filtrate from this solution is treated with (NH₄)₂HPO₄. No precipitate forms. Which of these metal cations are either possibly present or definitely absent: Al³⁺, Na⁺, Ag⁺, Mg²⁺?

Verified step by step guidance

1. Step 1: Understand the behavior of metal ions with HCl. When dilute HCl is added and no precipitate forms, it suggests that metal ions like Ag^+ (which forms AgCl) are absent.
2. Step 2: Consider the effect of H2S at pH 1. At this pH, metal sulfides of Group II (like Cd^2+, Bi^3+, Cu^2+) would precipitate. Since no precipitate forms, these ions are likely absent.
3. Step 3: Analyze the effect of H2S at pH 8. At this pH, metal sulfides of Group III (like Co^2+, Ni^2+, Zn^2+, Mn^2+, Fe^2+) can precipitate. The formation of a precipitate suggests the presence of one or more of these ions.
4. Step 4: Evaluate the addition of (NH4)2HPO4. This reagent is used to precipitate Group IV cations like Mg^2+ as MgNH4PO4. Since no precipitate forms, Mg^2+ is likely absent.
5. Step 5: Conclude the presence or absence of the given ions. Al^3+ does not precipitate with H2S or (NH4)2HPO4, so it could be present. Na^+ does not form precipitates in these conditions, so it is likely present. Ag^+ and Mg^2+ are likely absent based on the lack of precipitates in earlier steps.

Key Concepts

Solubility and Precipitation Reactions

Solubility refers to the ability of a substance to dissolve in a solvent, while precipitation occurs when dissolved ions combine to form an insoluble compound. In this scenario, the formation of precipitates is influenced by the pH of the solution and the presence of specific ions. Understanding the solubility rules for various metal sulfides and phosphates is crucial for predicting whether a precipitate will form under different conditions.

pH and its Effect on Metal Ion Solubility

The pH of a solution significantly affects the solubility of metal ions and their corresponding compounds. At low pH (acidic conditions), many metal ions remain soluble, while at higher pH (alkaline conditions), certain metal hydroxides and sulfides may precipitate. This concept is essential for interpreting the results of the experiment, as the adjustments in pH determine which metal ions remain in solution or form precipitates.

Complex Ion Formation

Complex ion formation occurs when metal ions bind with ligands, which can affect their solubility and reactivity. In the context of this question, the presence of ammonium phosphate may influence the solubility of certain metal ions, such as Al³⁺, which can form soluble complexes. Recognizing how complexation alters the behavior of metal ions in solution is vital for determining which ions are present or absent after treatment with (NH₄)₂HPO₄.