A balanced equation has the same number of each kind of atom on both sides, because atoms are rearranged in a reaction and never created or destroyed. You balance by placing whole-number coefficients in front of formulas. This lesson follows constructing formulas from ion charges, since you must fix the formulas before you balance.
It belongs to the formulas and equations module. All examples here are original paper exercises on counting atoms.
What are coefficients and subscripts?
In 2H₂O, the 2 in front is a coefficient: two water molecules. The small 2 inside H₂O is a subscript: two hydrogen atoms in each molecule. Four hydrogen atoms and two oxygen atoms appear in total.
You may change the first kind and never the second.
How to balance, step by step
- Write the correct formulas for every substance. Do not alter them afterwards.
- Make an atom table: list each element and count it on the left and on the right.
- Pick an element that appears in one substance on each side, and balance it with a coefficient.
- Balance elements that exist alone last, such as O₂ or H₂, because changing them affects only one element.
- Recount everything. If all coefficients share a common factor, divide it out.
Worked example
Balance: C₃H₈ + O₂ → CO₂ + H₂O
| Element | Left | Right |
|---|---|---|
| C | 3 | 1 |
| H | 8 | 2 |
| O | 2 | 3 |
Step 1, carbon: put 3 before CO₂. The right side now has C = 3.
Step 2, hydrogen: put 4 before H₂O. The right side now has H = 8.
Step 3, oxygen: the right side has 3 × 2 = 6 from CO₂ plus 4 × 1 = 4 from H₂O, which is 10 O atoms. Each O₂ supplies 2, so put 5 before O₂ (5 × 2 = 10).
C₃H₈ + 5O₂ → 3CO₂ + 4H₂O
Check: C 3 = 3. H 8 = 8. O 10 = 10. All match.
The mistake to watch for
A common slip is to fix an oxygen count by editing a formula.
Mistaken answer: Mg + O₂ → MgO₂
The student wanted 2 O on each side and changed MgO into MgO₂.
MgO₂ is not magnesium oxide. The formula must stay MgO. Instead, balance with coefficients: two MgO give two O atoms, then two Mg are needed.
2Mg + O₂ → 2MgO
Check: Mg 2 = 2, O 2 = 2.
Check yourself
1. Balance: N₂ + H₂ → NH₃
Show answer
N: put 2 before NH₃ to give 2 N. H: that gives 6 H, so put 3 before H₂.
N₂ + 3H₂ → 2NH₃. Check: N 2 = 2, H 6 = 6.
2. Balance: Al + O₂ → Al₂O₃
Show answer
O needs an even total: use 3 O₂ (6 O) and 2 Al₂O₃ (6 O). Then Al: 2 × 2 = 4, so 4 Al.
4Al + 3O₂ → 2Al₂O₃. Check: Al 4 = 4, O 6 = 6.
3. Balance: Ca(OH)₂ + HCl → CaCl₂ + H₂O
Show answer
CaCl₂ needs 2 Cl, so put 2 before HCl. Then H on the left is 2 + 2 = 4 and O is 2, so put 2 before H₂O (4 H, 2 O).
Ca(OH)₂ + 2HCl → CaCl₂ + 2H₂O. Check: Ca 1, Cl 2, H 4, O 2 on both sides.
Where this leads next
Next, add state symbols from supplied evidence. Try your own equations in the equation balance reasoning trainer, and see how the coefficients become mole ratios in the mole and equation-ratio tutor.
Students who balance well with easy equations can stall on ones with brackets or extra products. A teacher in online one-to-one Chemistry tuition can work through those with you at your pace.