The unbalanced reaction is
a NH₄NO₃ ⇒ b N₂ + c O₂ + d H₂O
where a, b, c, and d are unknown constants.
Count how many times each element appears on either side of the reaction.
• reactants:
N = 2a, H = 4a, O = 3a
• products
N = 2b, O = 2c + d, H = 2d
Now we solve the system of equations,
2a = 2b … … … [1]
4a = 2d … … … [2]
3a = 2c + d … … … [3]
From [1] we immediately have
a = b
In [2], we get
2a = d
and substituting for d in [3] gives
3a = 2c + 2a
a = 2c
Let c = 1; then
• a = 2×1 = 2
• b = 2
• d = 2×2 = 4
So, the balanced reaction is
2 NH₄NO₃ ⇒ 2 N₂ + O₂ + 4 H₂O
