The balanced chemical equation for the decomposition of ammonium nitrite (NH₄NO₂) into water (H₂O) and nitrogen gas (N₂) is:

NH₄NO₂ → 2H₂O + N₂

Here's how the equation is balanced:

* Nitrogen (N): There are two nitrogen atoms on the product side (N₂) and one on the reactant side (NH₄NO₂). To balance this, we need to add a coefficient of 2 in front of the NH₄NO₂ on the reactant side.

* Hydrogen (H): There are eight hydrogen atoms on the reactant side (2 * 4 = 8) and four on the product side (2 * 2 = 4). To balance this, we need to add a coefficient of 2 in front of the H₂O on the product side.

* Oxygen (O): There are two oxygen atoms on the reactant side (NH₄NO₂) and two on the product side (2 * 1 = 2).

This gives us the final balanced equation:

NH₄NO₂ → 2H₂O + N₂