TL;DR:
Atoms are not created or destroyed in a reaction, so each element must have the same count on both sides.
Change only the coefficients in front of formulas, never the subscripts inside them.
Propane burning balances as
C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O. Check each element, then the total mass.
Write down propane burning as C₃H₈ + O₂ → CO₂ + H₂O and it looks like a reaction. It is not yet correct, because the left side has 3 carbon atoms and the right side has 1. Atoms cannot vanish, so something is missing. Balancing is the fix.
Why equations have to balance
In a chemical reaction, atoms are rearranged into new combinations. They are not made or destroyed. That is the conservation of mass. So the number of atoms of each element has to match on both sides of the arrow.
A balanced equation also tells you the ratio in which substances react, which is the starting point for amounts in stoichiometry.
The one rule: coefficients, not subscripts
A subscript is the small number inside a formula, as in the 2 of H₂O. It says what the substance is. Change it and you change the substance: H₂O is water, but H₂O₂ is hydrogen peroxide, a different chemical.
A coefficient is the big number in front. It says how many molecules there are. 3 CO₂ means three molecules, each with 1 carbon and 2 oxygens, so 3 carbons and 6 oxygens in all. Balancing only ever changes coefficients.
Worked example: burning propane
Start from C₃H₈ + O₂ → CO₂ + H₂O. Use a tally of each element, and balance the elements that appear in one substance first. Leave oxygen, which appears in two products, until last.
Count the start. Left: C 3, H 8, O 2. Right: C 1, H 2, O 3.
Balance carbon: put 3 in front of CO₂. Right now has C 3, O 6 + 1 = 7.
Balance hydrogen: put 4 in front of H₂O, giving H 8. Right: C 3, H 8, O 6 + 4 = 10.
Balance oxygen: the right side has 10 oxygen atoms, and each O₂ supplies 2, so we need 5 O₂.
Write it:
C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O.
Now check every element from the final equation.
Element | Left | Right |
|---|---|---|
C | 3 (from C₃H₈) | 3 (3 × 1 in 3 CO₂) |
H | 8 (from C₃H₈) | 8 (4 × 2 in 4 H₂O) |
O | 10 (5 × 2 in 5 O₂) | 10 (3 × 2 in CO₂ plus 4 × 1 in H₂O) |
A second check uses masses. Using whole-number atomic masses of C 12, H 1 and O 16: C₃H₈ is 3 × 12 + 8 × 1 = 44 and O₂ is 32, so the left side is 44 + 5 × 32 = 204. On the right, CO₂ is 12 + 32 = 44 and H₂O is 2 + 16 = 18, so 3 × 44 + 4 × 18 = 132 + 72 = 204. Equal, as conservation of mass demands.
Burning fuels: Propane is a flammable gas. Do not test combustion at home. Gas appliances need ventilation, because burning in too little oxygen makes carbon monoxide, which is poisonous and has no smell.
What to do when odd numbers appear
Sometimes oxygen comes out as a fraction. Take ethane, C₂H₆ + O₂ → CO₂ + H₂O. Balance C with 2 CO₂ and H with 3 H₂O. The right side now has O: 2 × 2 + 3 = 7, so you would need 3.5 O₂.
A half molecule is not a real thing, so double everything: 2 C₂H₆ + 7 O₂ → 4 CO₂ + 6 H₂O. Check: C is 4 and 4, H is 12 and 12, O is 14 on the left and 8 + 6 = 14 on the right. Always finish with the smallest whole-number coefficients.
Here is a quick routine you can use on any equation. First, list each element down the side of the page. Second, count it on the left and on the right in a small table. Third, pick the element that shows up in the fewest formulas and fix it first. Fourth, update the table after every change, because changing one coefficient changes the counts of every element in that formula. Fifth, stop only when the table has no mismatches.
Polyatomic ions such as sulfate (SO₄) can be counted as one unit when they appear unchanged on both sides. In Ca(OH)₂, the subscript 2 outside the brackets multiplies everything inside, so there is 1 calcium, 2 oxygens and 2 hydrogens.
How to check your answer
Tally table. Count every element on both sides. All must match.
Smallest whole numbers. If all coefficients share a common factor, divide it out.
Mass check. Add the formula masses on each side and compare.
Subscripts unchanged. Compare each formula with the original to be sure none changed.
Mistakes that cost marks
Changing a subscript to make the count work, which turns one substance into another.
Forgetting to multiply a coefficient across every atom in a formula, such as the 2 in H₂O when the coefficient is 4.
Balancing oxygen first and having to start over.
Leaving a fractional coefficient in a final answer, unless the question allows it.
Stopping after carbon and hydrogen and not checking oxygen.
Where you will use it next
Once an equation is balanced, you can convert between amounts of substances using the ideas in the mole, explained with a dozen. Balanced equations also describe the neutralisation you meet in titration curves.
Frequently asked questions
Do coefficients of 1 get written?
No. A missing coefficient means 1. Writing C₃H₈ already means one propane molecule.
Is there only one way to balance an equation?
There is only one set of smallest whole-number coefficients. You can scale it up, such as doubling everything, but the ratios stay the same.
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