Ionic-molecular equation for d):
\[ 3\text{Ba}^{2+} + 6\text{Cl}^- + 6\text{K}^+ + 2\text{PO}_4^{3-} \rightarrow \text{Ba}_3\text{(PO}_4)_2 \downarrow + 6\text{K}^+ + 6\text{Cl}^- \]
Complete ionic equation:
\[ 3\text{Ba}^{2+} + 2\text{PO}_4^{3-} \rightarrow \text{Ba}_3\text{(PO}_4)_2 \downarrow \]
To identify the salts, we can use reactions that produce a precipitate or gas with one of the salts.
Proposed Identification Method:
\[ \text{Na}_2\text{CO}_3 + \text{BaCl}_2 \rightarrow \text{BaCO}_3 \downarrow + 2\text{NaCl} \]
\[ 3\text{Na}_2\text{SO}_4 + \text{BaCl}_2 \rightarrow \text{BaSO}_4 \downarrow + 2\text{NaCl} \]
\[ 3\text{Na}_3\text{PO}_4 + 2\text{BaCl}_2 \rightarrow \text{Ba}_3\text{(PO}_4)_2 \downarrow + 6\text{NaCl} \]
Distinguishing between BaCO3 and Ba3(PO4)2:
To distinguish between sodium carbonate and sodium phosphate, we can add an acid, for example, hydrochloric acid (HCl).
\[ \text{Na}_2\text{CO}_3 + 2\text{HCl} \rightarrow 2\text{NaCl} + \text{H}_2\text{O} + \text{CO}_2 \uparrow \]
Summary of identification:
Note: To definitively distinguish between sodium sulfate and sodium phosphate using barium chloride, it is important to note that barium sulfate (BaSO4) is insoluble in acids, while barium phosphate (Ba3(PO4)2) is also insoluble in water but can react with strong acids. However, the primary distinguishing feature with carbonate is gas evolution. If further distinction is needed between sulfate and phosphate, one could use a solution of calcium chloride (CaCl2). Calcium phosphate is insoluble, while calcium sulfate is sparingly soluble.
Answer: The reactions and identification steps are provided above.