When aqueous solutions of barium chloride (BaCl$_2$) and sodium sulfate (Na$_2$SO$_4$) are mixed, a double displacement reaction occurs, resulting in the formation of a white precipitate of barium sulfate (BaSO$_4$) and aqueous sodium chloride (NaCl).
Chemical equation:
\[\text{BaCl}_2\text{(aq)} + \text{Na}_2\text{SO}_4\text{(aq)} \rightarrow \text{BaSO}_4\text{(s)} + 2\text{NaCl(aq)}\]
Ions in the precipitate: Ba$^{2+}$ and SO$_4^{2-}$