Balancing chemical equations becomes much easier once you stop treating it as guesswork. The rule is simple: you must have the same number of each type of atom on both sides of the equation. You change the numbers in front of formulae, not the formulae themselves.
What does balancing an equation mean?
A chemical equation represents a reaction. Because atoms are not created or destroyed in an ordinary chemical reaction, the number of atoms of each element before the reaction must equal the number after it.
The key rule
Wrong: changing H2O into H3O to make the numbers fit.
Right: placing a coefficient in front, for example 2H2O.
A coefficient multiplies the whole formula. The small numbers inside a formula are part of the substance and must not be altered.
Worked example 1: hydrogen and oxygen
Start with:
H2 + O2 → H2O
There are two oxygen atoms on the left but only one on the right, so put a 2 in front of water:
H2 + O2 → 2H2O
Now there are four hydrogen atoms on the right, so put a 2 in front of hydrogen:
2H2 + O2 → 2H2O
A repeatable method
1. Write down the number of atoms of each element on both sides.
2. Balance one element at a time. Start with an element that appears in only one formula on each side if possible.
3. Leave hydrogen and oxygen until later when the equation is more complicated. They often appear in several substances.
4. Recount every atom at the end. A change that fixes one element can affect another.
Worked example 2: magnesium and oxygen
Mg + O2 → MgO
Oxygen is unbalanced: there are two oxygen atoms on the left and one on the right. Put a 2 in front of MgO, then balance magnesium:
2Mg + O2 → 2MgO
Common mistakes to avoid
Changing subscripts: this changes the substance itself. Only add or change coefficients.
Forgetting to multiply the whole formula: in 3H2O there are six hydrogen atoms and three oxygen atoms.
Stopping too early: always check every element again after the final change.
Using fractions when whole-number coefficients are expected: if a fraction appears during working, multiply every coefficient to obtain the smallest whole-number ratio.
Try these balancing equations
1. N2 + H2 → NH3
2. Al + O2 → Al2O3
3. CH4 + O2 → CO2 + H2O
Answers: 1. N2 + 3H2 → 2NH3 2. 4Al + 3O2 → 2Al2O3 3. CH4 + 2O2 → CO2 + 2H2O.
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Frequently asked questions
Can you change the small numbers in a chemical formula when balancing?
No. Changing a subscript changes the chemical formula and therefore the substance. Use coefficients in front of formulae instead.
Which element should you balance first?
There is no single rule for every equation, but it is often easiest to start with an element that appears in only one substance on each side and leave elements that appear in several compounds until later.
How do I check whether an equation is balanced?
Count the atoms of every element on the left and right. Each element must have the same total on both sides.