The reaction between aluminum sulfide (Al₂S₃) and barium (Ba) is a metathesis reaction leading to the formation of barium sulfide (BaS) and aluminum (Al).

Here's the balanced chemical equation:

```

Al₂S₃ + 3Ba → 3BaS + 2Al

```

Explanation:

* Aluminum sulfide (Al₂S₃) is a compound with a higher electronegativity difference between aluminum and sulfur.

* Barium (Ba) is a highly reactive metal, readily reacting with sulfur to form barium sulfide (BaS).

* The reaction proceeds due to the higher reactivity of barium towards sulfur compared to aluminum.

* As a result, barium displaces aluminum from the sulfide, forming aluminum metal and barium sulfide.

Important Notes:

* This reaction is highly exothermic and generates significant heat.

* The reaction requires careful handling as it involves the production of highly reactive substances.

* The products of this reaction, barium sulfide and aluminum metal, are both solid at room temperature.

Please remember that these reactions are theoretical and should always be performed with proper safety precautions and under the guidance of an experienced chemist.