Balancing Chemical Equations

Atoms are never created or destroyed in a reaction — balancing is just bookkeeping that respects that.

High schoolIntro Gen ChemUni Year 1
⏱️ About 20 min

A reaction rearranges atoms; it never makes or destroys them. So every atom that goes into a reaction must come out the other side — just recombined. Balancing an equation is how we honour that on paper: count the atoms on each side and make them match.

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The big idea: Mass is conserved: the same atoms exist before and after a reaction. We balance by placing coefficients in front of formulas — never by changing subscripts. Subscripts define what a substance is; coefficients only say how many units of it.
🎯 By the end, you'll be able to
  • State conservation of mass and why every equation must balance
  • Balance an equation by adjusting coefficients, leaving subscripts untouched
  • Follow a systematic order (metals, then non-metals, then H, then O)
📎 Helpful to know first

The rule: atoms in = atoms out

In a chemical reaction, bonds break and re-form, but the atoms themselves are only rearranged. This is the law of conservation of mass: the total mass — and the count of each kind of atom — is the same before and after.

So a correct equation must have the same number of each element on both sides. When it doesn't, it's unbalanced, and balancing it means adjusting how many of each molecule take part.

⚠️ Coefficients, not subscripts — the #1 rule
To balance, you change the big numbers in front of formulas (coefficients). You must never change the little numbers inside a formula (subscripts). Turning H₂O into H₂O₂ to get more oxygen doesn't balance the equation — it changes water into hydrogen peroxide, a completely different substance. Coefficients change amounts; subscripts change identity.
\[ \ce{2H2 + O2 -> 2H2O} \]
The coefficient 2 multiplies the whole formula: 2H₂O means 4 H atoms and 2 O atoms. Both sides now have 4 H and 2 O.
🔑 A reliable order to balance in
When it isn't obvious, follow this order and most equations fall into place: (1) balance metals first, (2) then other non-metals (like C), (3) then hydrogen, (4) and oxygen last. Leave elements that appear on their own (like O₂) until the end, since they're easiest to adjust without upsetting anything else.
📝 Worked example: Balance the combustion of methane: CH₄ + O₂ → CO₂ + H₂O.
  1. Balance carbon: 1 C on the left (CH₄), 1 C on the right (CO₂). Carbon is already balanced.
  2. Balance hydrogen: 4 H in CH₄, but only 2 H in one H₂O. Put a 2 in front of H₂O → 2H₂O, giving 4 H on each side.
  3. Balance oxygen last: the right now has 2 (from CO₂) + 2 (from 2H₂O) = 4 O. Put a 2 in front of O₂ → 2O₂ to supply 4 O.
  4. Final: CH₄ + 2O₂ → CO₂ + 2H₂O. Check: C 1 = 1, H 4 = 4, O 4 = 4. Balanced.
✓ CH₄ + 2O₂ → CO₂ + 2H₂O.
✨ Mass is conserved even when a gas escapes
Burn a log and the ash weighs far less than the wood — so where did the mass go? Into invisible gases (CO₂ and water vapour) that floated away. Nothing was destroyed. If you trapped and weighed every gas, the totals would match exactly. A disappearing solid or a bubbling gas never breaks conservation of mass; it just moves mass somewhere you weren't looking.
✏️ Practice: Balance the combustion of propane: C₃H₈ + O₂ → CO₂ + H₂O. What is the coefficient in front of O₂?
Solution
  1. Balance carbon: 3 C on the left → put 3 in front of CO₂ (3CO₂).
  2. Balance hydrogen: 8 H on the left → put 4 in front of H₂O (4H₂O), giving 8 H.
  3. Count oxygen on the right: 3(2) from CO₂ + 4(1) from H₂O = 6 + 4 = 10 O atoms.
  4. O₂ supplies them in pairs: 10 ÷ 2 = 5, so the coefficient of O₂ is 5. Balanced: C₃H₈ + 5O₂ → 3CO₂ + 4H₂O.
✏️ Practice: 12.0 g of carbon burns completely in 32.0 g of oxygen to form only carbon dioxide (C + O₂ → CO₂). By conservation of mass, what mass of CO₂ forms?
g
Solution
  1. No atoms are created or destroyed, so all the mass that goes in must come out as product.
  2. Mass of CO₂ = mass of carbon + mass of oxygen = 12.0 g + 32.0 g.
  3. = 44.0 g. (The CO₂ is an invisible gas, but its mass is fully accounted for.)

Check your understanding

1. To balance an equation, which numbers are you allowed to change?
Only coefficients (the numbers in front). Changing a subscript would change the substance itself into something different.
2. A student changes H₂O to H₂O₂ to get an extra oxygen. What's wrong?
Editing the subscript turns water into hydrogen peroxide — a different substance. Balance by adding a coefficient (e.g. 2H₂O), never by rewriting the formula.
3. Wood burns and the ash weighs much less than the original wood. This means:
The 'missing' mass floated off as invisible gases. Capture every gas and the before-and-after masses match — mass is always conserved.
🔎 Related lessons
Previous: Empirical & Molecular Formulas Next: Limiting Reactant & Percent Yield
✅ Key takeaways
  • Conservation of mass: the same atoms exist before and after — equations must have equal atoms on both sides.
  • Balance with coefficients (numbers in front); never change subscripts (that changes the substance).
  • A coefficient multiplies the whole formula: 2H₂O = 4 H and 2 O atoms.
  • Work in order: metals, then other non-metals, then hydrogen, then oxygen.
  • Mass is conserved even when a gas forms or escapes — it just moves out of sight.
➡️ A balanced equation is a recipe with exact proportions. But in a real lab you rarely have perfect proportions — one ingredient runs out first. That's the limiting reactant, and it sets how much product you can actually make.
Want to test yourself on this? Try the Chemistry practice test →