Here's how to balance the equation for the reaction of hydrogen and nitrogen monoxide to produce water and nitrogen:

Unbalanced Equation:

H₂ + NO → H₂O + N₂

Balancing the Equation:

1. Nitrogen (N): There's 1 N on the left and 2 on the right. Put a 2 in front of NO.

H₂ + 2NO → H₂O + N₂

2. Oxygen (O): There are 2 O on the left and 1 on the right. Put a 2 in front of H₂O.

H₂ + 2NO → 2H₂O + N₂

3. Hydrogen (H): There are 2 H on the left and 4 on the right. Put a 2 in front of H₂.

2H₂ + 2NO → 2H₂O + N₂

Balanced Equation:

2H₂ + 2NO → 2H₂O + N₂