The balanced chemical equation for the reaction of hydrazine (N₂H₄) with oxygen gas (O₂) to produce nitrogen gas (N₂) and steam (H₂O) is:

N₂H₄(l) + O₂(g) → N₂(g) + 2H₂O(g)

Here's how the equation is balanced:

* Nitrogen (N): There are 2 nitrogen atoms on both sides of the equation.

* Hydrogen (H): There are 4 hydrogen atoms on both sides of the equation.

* Oxygen (O): There are 2 oxygen atoms on both sides of the equation.

This equation shows that one mole of hydrazine reacts with one mole of oxygen to produce one mole of nitrogen and two moles of water.