Step 1: Definition of Precipitation Reaction
A precipitation reaction occurs when two aqueous solutions combine to form an insoluble product, known as the precipitate. This occurs when the product is insoluble in water.
Step 2: Analyzing the options
- In option (A), barium sulfate (BaSO\(_4\)) is formed as a solid precipitate, which is insoluble in water. This makes it a precipitation reaction.
- In option (B), no precipitate is formed; the products are soluble in water, making it not a precipitation reaction.
- In option (C), magnesium sulfate (MgSO\(_4\)) is soluble in water, and thus no precipitate is formed. This is not a precipitation reaction.
- In option (D), sodium oxide (Na\(_2\)O) is formed, which is not a precipitation reaction because it is not insoluble in water.
Step 3: Conclusion
The correct answer is option (A), as it results in the formation of a solid precipitate (BaSO\(_4\)).
\[
\boxed{\text{BaCl}_2 (aq) + H_2SO_4 (aq) $\rightarrow$\text{BaSO}_4 (s) + 2HCl (aq)}
\]