An aqueous solution is known to contain $\text{Ag}^+, \text{Mg}^{2+},$ and $\text{Sr}^{2+}$ ions. Which reagent should be used to selectively precipitate the $\text{Ag}^+$?

${ \textbf{(A)}\ 0.20 \text{M NaCl} \qquad\textbf{(B)}\ 0.20 \text{M NaOH} \qquad\textbf{(C)}\ 0.20 \text{M Na}_2\text{SO}_4 \qquad\textbf{(D)}\ 0.20 \text{M Na}_3\text{PO}_4 }$
1. To selectively precipitate $\text{Ag}^+$ ions from an aqueous solution containing $\text{Ag}^+$, $\text{Mg}^{2+}$, and $\text{Sr}^{2+}$ ions, we need to choose a reagent that forms an insoluble compound with $\text{Ag}^+$ but remains soluble with $\text{Mg}^{2+}$ and $\text{Sr}^{2+}$.

2. Let's analyze the solubility of the possible precipitates formed with each reagent:
   - **Option A: $0.20 \text{M NaCl}$**
     - $\text{Ag}^+ + \text{Cl}^- \rightarrow \text{AgCl}$ (Silver chloride)
     - $\text{Mg}^{2+} + 2\text{Cl}^- \rightarrow \text{MgCl}_2$ (Magnesium chloride)
     - $\text{Sr}^{2+} + 2\text{Cl}^- \rightarrow \text{SrCl}_2$ (Strontium chloride)
     - Silver chloride ($\text{AgCl}$) is known to be insoluble in water, while magnesium chloride ($\text{MgCl}_2$) and strontium chloride ($\text{SrCl}_2$) are soluble in water.

   - **Option B: $0.20 \text{M NaOH}$**
     - $\text{Ag}^+ + \text{OH}^- \rightarrow \text{AgOH}$ (Silver hydroxide)
     - $\text{Mg}^{2+} + 2\text{OH}^- \rightarrow \text{Mg(OH)}_2$ (Magnesium hydroxide)
     - $\text{Sr}^{2+} + 2\text{OH}^- \rightarrow \text{Sr(OH)}_2$ (Strontium hydroxide)
     - Both silver hydroxide ($\text{AgOH}$) and magnesium hydroxide ($\text{Mg(OH)}_2$) are insoluble in water, while strontium hydroxide ($\text{Sr(OH)}_2$) is slightly soluble.

   - **Option C: $0.20 \text{M Na}_2\text{SO}_4$**
     - $\text{Ag}^+ + \text{SO}_4^{2-} \rightarrow \text{Ag}_2\text{SO}_4$ (Silver sulfate)
     - $\text{Mg}^{2+} + \text{SO}_4^{2-} \rightarrow \text{MgSO}_4$ (Magnesium sulfate)
     - $\text{Sr}^{2+} + \text{SO}_4^{2-} \rightarrow \text{SrSO}_4$ (Strontium sulfate)
     - Silver sulfate ($\text{Ag}_2\text{SO}_4$) is slightly soluble in water, magnesium sulfate ($\text{MgSO}_4$) is soluble, and strontium sulfate ($\text{SrSO}_4$) is slightly soluble.

   - **Option D: $0.20 \text{M Na}_3\text{PO}_4$**
     - $3\text{Ag}^+ + \text{PO}_4^{3-} \rightarrow \text{Ag}_3\text{PO}_4$ (Silver phosphate)
     - $3\text{Mg}^{2+} + 2\text{PO}_4^{3-} \rightarrow \text{Mg}_3(\text{PO}_4)_2$ (Magnesium phosphate)
     - $3\text{Sr}^{2+} + 2\text{PO}_4^{3-} \rightarrow \text{Sr}_3(\text{PO}_4)_2$ (Strontium phosphate)
     - Silver phosphate ($\text{Ag}_3\text{PO}_4$), magnesium phosphate ($\text{Mg}_3(\text{PO}_4)_2$), and strontium phosphate ($\text{Sr}_3(\text{PO}_4)_2$) are all insoluble in water.

3. Based on the solubility rules, the best reagent to selectively precipitate $\text{Ag}^+$ ions is $0.20 \text{M NaCl}$ because $\text{AgCl}$ is insoluble in water, while $\text{MgCl}_2$ and $\text{SrCl}_2$ are soluble.

The final answer is $\boxed{\text{A}}$