How to balance chemical equations step by step: the five steps, six worked examples from easy to hard, the fastest order to balance in, what you may and may not change, and the mistakes that lose the marks in Class 10, GCSE and Grade 10

"How to balance chemical equations step by step" is typed by students in CBSE Class 10 (it is the first chapter of the book), in GCSE and IGCSE chemistry, and in Grade 9 and 10 chemistry in the US, Canada and Australia, and by parents who remember the idea and not the method. This page gives the five steps, the fastest order to balance in, six worked examples from the easiest to the kind that appears in the last question of a paper, the one rule you must never break, and the four mistakes examiners see most.

Why balance at all

Atoms are not made or destroyed in a chemical reaction; they are rearranged. So the number of atoms of each element before the reaction must equal the number after. An unbalanced equation like H2 + O2 → H2O claims two oxygen atoms became one, which cannot happen. Balancing is the arithmetic that makes the equation tell the truth: 2H2 + O2 → 2H2O.

The five steps

1. Write the formulas correctly. Word equation first (hydrogen + oxygen → water), then formulas (H2 + O2 → H2O). Most balancing "errors" are formula errors: writing NaCl2 or H2O2 for water. Check the formulas before touching the numbers.
2. Count the atoms of each element on each side. A small table helps: left column the elements, then "left" and "right" counts.
3. Put a coefficient in front of a formula to make one element balance. Start with the element that appears in the fewest formulas. A coefficient multiplies every atom in that formula: 2H2O means 4 H and 2 O.
4. Recount and repeat for the next element. Balancing one element often unbalances another; that is normal. Leave hydrogen and oxygen until last.
5. Check every element, and reduce. All counts equal on both sides, and the coefficients in the smallest whole numbers.

The one rule: change coefficients (the big numbers in front), never subscripts (the small numbers inside a formula). H2O is water; H2O2 is bleach.

The fastest order

Metals first, then non-metals other than H and O, then hydrogen, then oxygen. Oxygen last because it usually appears in the most formulas and often sorts itself out. For combustion equations (a hydrocarbon plus oxygen giving carbon dioxide and water), the order is always carbon, hydrogen, oxygen. If oxygen is left with an odd count on one side and even on the other, double every coefficient and finish.

Six worked examples

1. Hydrogen and oxygen: H2 + O2 → H2O. O: 2 on the left, 1 on the right. Put 2 in front of H2O: H2 + O2 → 2H2O. Now H: 2 left, 4 right. Put 2 in front of H2: 2H2 + O2 → 2H2O. Check: H 4 = 4, O 2 = 2.

2. Methane burning: CH4 + O2 → CO2 + H2O. C: 1 = 1. H: 4 left, 2 right, so 2H2O. O: 2 left, 2 + 2 = 4 right, so 2O2. CH4 + 2O2 → CO2 + 2H2O.

3. Iron rusting: Fe + O2 → Fe2O3. Metal first: Fe 1 left, 2 right, so 2Fe. O: 2 left, 3 right, an odd number. Double: 4Fe + O2 → 2Fe2O3 gives O 2 left, 6 right, so 3O2. 4Fe + 3O2 → 2Fe2O3. Check: Fe 4 = 4, O 6 = 6.

4. Aluminium and hydrochloric acid: Al + HCl → AlCl3 + H2. Metal first: Al 1 = 1. Cl: 1 left, 3 right, so 3HCl. H: 3 left, 2 right; the lowest common multiple is 6, so 6HCl and 3H2, and now Cl is 6 on the left, 3 on the right, so 2AlCl3, and Al is 1 left, 2 right, so 2Al. 2Al + 6HCl → 2AlCl3 + 3H2. Check: Al 2 = 2, H 6 = 6, Cl 6 = 6.

5. Propane burning: C3H8 + O2 → CO2 + H2O. Carbon: 3, so 3CO2. Hydrogen: 8, so 4H2O. Oxygen on the right: 6 + 4 = 10, so 5O2. C3H8 + 5O2 → 3CO2 + 4H2O. This is the combustion order (C, H, O) and it works for every hydrocarbon.

6. With brackets: Ca(OH)2 + H3PO4 → Ca3(PO4)2 + H2O. Count the brackets: Ca(OH)2 has 1 Ca, 2 O, 2 H; Ca3(PO4)2 has 3 Ca, 2 P, 8 O. Metal first: 3Ca(OH)2. Then P: 2 on the right, so 2H3PO4. Now H on the left: 6 (from 3Ca(OH)2) + 6 (from 2H3PO4) = 12, so 6H2O. Check O: left 6 + 8 = 14; right 8 + 6 = 14. 3Ca(OH)2 + 2H3PO4 → Ca3(PO4)2 + 6H2O. Treat a bracketed group as one unit while balancing and it stays manageable.

State symbols

(s) solid, (l) liquid, (g) gas, (aq) dissolved in water. They do not affect the balancing but GCSE and IGCSE papers award a mark for them, and CBSE Class 10 expects them in the first chapter: 2H2(g) + O2(g) → 2H2O(l).

The four mistakes examiners see most

1. Changing a subscript. H2 + O2 → H2O2 balances the atoms and describes a different reaction. Zero marks.
2. Wrong formula to begin with. Balancing Na + Cl2 → NaCl2 is impossible because NaCl2 does not exist; the formula must be NaCl (2Na + Cl2 → 2NaCl).
3. Forgetting the coefficient multiplies everything. 2Ca(OH)2 has 4 H, not 2.
4. Not reducing. 4H2 + 2O2 → 4H2O is balanced but not in the lowest terms; halve it.

Where it sits in the curriculum

Where to get help

A 1-on-1 online chemistry class with a tutor who holds a master's in chemistry: the five steps on the whiteboard, twenty equations from easy to bracketed, then the reaction types and the moles that follow. The recording and notes after every class, US$10 to $13 an hour. The chemistry page has the courses from Class 9 to A-level; the 118 elements list has every symbol you will need; and the free 30-minute first class is a real lesson on the equations that came home wrong.

Questions parents ask

See how we teach this, 1-on-1 online →