When \(\mathrm{Na}_{3} \mathrm{PO}_{4}(a q)\) is added to a solution containing a metal ion and a precipitate forms, the precipitate generally could be one of two possibilities. What are the two possibilities?

In this problem, we have sodium phosphate (Na3PO4) and a solution containing a metal ion. When sodium phosphate dissociates in water, it forms sodium ions (Na+) and phosphate ions (PO4^3-). The metal ion in the solution would react with the phosphate ion to form a solid precipitate.

Most metal ions belong to one of the following groups: alkali metals, alkaline earth metals, or transition metals. The metal ion in the solution can be from any of these groups. We should consider the typical characteristics of each group while analyzing the possible precipitates.

When alkali metals react with phosphate ions, they usually form soluble compounds, such as sodium phosphate. Therefore, alkali metals are less likely to form precipitates. Alkaline earth metals, on the other hand, often form insoluble compounds with phosphate ions. For instance, calcium phosphate (Ca3(PO4)2) and barium phosphate (Ba3(PO4)2) are insoluble in water and can form precipitates. This makes alkaline earth metals a potential candidate for forming a precipitate with Na3PO4. Transition metals, like iron and copper, can also form insoluble compounds with phosphate ions. Examples include ferric phosphate (FePO4) and cupric phosphate (Cu3(PO4)2). Thus, transition metals can be another candidate for forming a precipitate with Na3PO4.

Based on the analysis, we find that two groups of metal ions can react with Na3PO4 to form insoluble precipitates: alkaline earth metals and transition metals. When Na3PO4 is added to the solution containing a metal ion, the two possible precipitates that can form are: 1. A precipitate formed by the reaction between the phosphate ion (PO4^3-) and an alkaline earth metal ion (such as calcium or barium ions). 2. A precipitate formed by the reaction between the phosphate ion (PO4^3-) and a transition metal ion (such as iron or copper ions). These are the two possibilities for the precipitate that could be formed when sodium phosphate is added to a solution containing a metal ion.