The balanced equation for the reaction of hydrogen and nitrogen monoxide to yield water and nitrogen is:

2 H₂ + 2 NO → N₂ + 2 H₂O

Here's how it works:

* Reactants:

* Hydrogen (H₂)

* Nitrogen monoxide (NO)

* Products:

* Nitrogen (N₂)

* Water (H₂O)

Balancing the equation:

1. Nitrogen (N): There are two nitrogen atoms on the product side (N₂) and one on the reactant side (NO). To balance, we place a coefficient of 2 in front of NO.

2. Oxygen (O): Now, there are two oxygen atoms on the reactant side and two on the product side (2 H₂O), so oxygen is balanced.

3. Hydrogen (H): There are four hydrogen atoms on the product side (2 H₂O) and two on the reactant side (2 H₂). To balance, we place a coefficient of 2 in front of H₂.

This ensures that the number of atoms of each element is equal on both sides of the equation, making it a balanced chemical equation.