The balanced equation for the reaction of ammonia (NH₃) and oxygen gas (O₂) yielding nitrogen gas (N₂) and water (H₂O) is:

4 NH₃ + 3 O₂ → 2 N₂ + 6 H₂O

Here's how we balance the equation:

1. Identify the reactants and products:

- Reactants: Ammonia (NH₃) and Oxygen (O₂)

- Products: Nitrogen (N₂) and Water (H₂O)

2. Count the atoms of each element on both sides:

| Element | Reactants | Products |

|---------|-----------|----------|

| N | 1 | 2 |

| H | 3 | 6 |

| O | 2 | 1 |

3. Adjust coefficients to balance the number of atoms:

- Start by balancing the nitrogen (N) atoms: Place a coefficient of 2 in front of N₂ on the product side.

- Balance the hydrogen (H) atoms: Place a coefficient of 6 in front of H₂O on the product side.

- Finally, balance the oxygen (O) atoms: Place a coefficient of 3 in front of O₂ on the reactant side.

4. Verify the final balanced equation:

4 NH₃ + 3 O₂ → 2 N₂ + 6 H₂O

Now, both sides of the equation have the same number of atoms of each element:

- 4 Nitrogen atoms (N)

- 12 Hydrogen atoms (H)

- 6 Oxygen atoms (O)