Chemical equations & balancing
The idea
A chemical equation is a before-and-after inventory of atoms: reactants on the left, products on the right, and an arrow for the transformation. Because atoms are never created or destroyed in a reaction — the conservation of mass you already know — every element must appear in equal numbers on both sides. Balancing means choosing whole-number coefficients (the multipliers in front of each formula) until the inventory matches.
Work systematically: balance one element at a time, start with elements that appear in only one substance per side, and save lone elements (like a bare metal or O₂) for last since their coefficients adjust freely without disturbing anything else. When an element comes in mismatched group sizes — say twos on one side and threes on the other — jump straight to the least common multiple instead of nudging coefficients one at a time.
The cardinal sin is changing a subscript to force a balance. Coefficients say how many units react; subscripts say what the substance is. Turning H₂O into H₂O₂ does not balance water — it silently swaps water for hydrogen peroxide, a different chemical entirely.
Worked example
Iron rusts in oxygen according to the unbalanced equation Fe + O₂ → Fe₂O₃. Balance it.
- Take inventory: the left has 1 Fe and 2 O; the right has 2 Fe and 3 O. Nothing matches yet.
- Tackle oxygen first because it appears in awkward group sizes — packets of 2 on the left and 3 on the right. The least common multiple is 6, so place a 2 before Fe₂O₃ (giving 6 O) and a 3 before O₂ (also 6 O).
- Now repair iron: 2 Fe₂O₃ contains 4 Fe, so put a 4 in front of the lone Fe on the left. Saving the lone element for last meant this fix disturbed nothing else.
- Final audit: 4 Fe + 3 O₂ → 2 Fe₂O₃ gives Fe: 4 = 4 and O: 6 = 6. Balanced, and the coefficients 4, 3, 2 share no common factor, so they are already in lowest terms.
- Read the result as a recipe: every 4 atoms (or moles) of iron consume 3 molecules (or moles) of O₂ to make 2 formula units (or moles) of Fe₂O₃ — the ratio holds at any scale.
Answer. The balanced equation is 4 Fe + 3 O₂ → 2 Fe₂O₃.
Check your understanding
- Why does changing a subscript break the chemistry even when it seems to fix the atom count?
- Why is it efficient to balance lone elements last, and what makes their coefficients safe to adjust?
- What do the final coefficients mean at the scale of individual particles versus the scale of moles?
- How would you quickly convince someone that a finished equation really is balanced?
Build the foundations first
Chemical equations & balancing builds on these concepts. If any feel shaky, start there.