How to Balance Chemical Equations

To balance a chemical equation, adjust the coefficients in front of the formulas until the number of atoms of each element is the same on both sides, without ever changing the subscripts in the formulas. In brief: for C3H8 + O2 → CO2 + H2O, balance carbon first (3CO2), then hydrogen (4H2O), then oxygen last (5O2), to get C3H8 + 5O2 → 3CO2 + 4H2O.

C₃H₈ + 5O₂ → 3CO₂ + 4H₂O C 3 = 3 H 8 = 8 O 10 = 10

Balanced equations are needed for every calculation of reacting amounts. The method is a matter of systematic bookkeeping. This article gives a step-by-step procedure, explains the useful tricks (treating polyatomic ions as units, balancing oxygen last, using fractions) and the algebraic method for harder cases, includes a table of examples, works through eight equations with full checks, and gives some history.

What are the steps for balancing by inspection?

  1. Write the correct formulas for all reactants and products. A wrong formula cannot be balanced into a correct equation.
  2. Count the atoms of each element on both sides. If polyatomic ions such as SO42− or OH− appear unchanged on both sides, count them as units.
  3. Start with the most complicated formula or with an element that appears in only one reactant and one product.
  4. Change the coefficients (never the subscripts) to balance one element at a time.
  5. Balance elements that appear in several substances last, especially oxygen and hydrogen, and free elements (such as O2) at the very end.
  6. If you end up with fractions, multiply all the coefficients by the smallest number that clears them.
  7. Check that each element has the same count on both sides and that the coefficients are the smallest whole numbers.

What tips make balancing easier?

Worked examples

  1. H2 + O2 → H2O. Oxygen: 2 on the left, 1 on the right, so use 2H2O. Hydrogen is then 4 on the right, so use 2H2. Result: 2H2 + O2 → 2H2O. Check: H 4 = 4, O 2 = 2.
  2. Fe + O2 → Fe2O3. Oxygen: 2 on the left and 3 on the right. The lowest common multiple is 6: 3O2 and 2Fe2O3. Iron: 4 on the right, so 4Fe. Result: 4Fe + 3O2 → 2Fe2O3. Check: Fe 4 = 2 × 2, O 6 = 2 × 3.
  3. Al + HCl → AlCl3 + H2. Chlorine is in HCl and AlCl3, and hydrogen is in HCl and H2, so choose coefficients that work for both. With 6HCl there are 6 Cl and 6 H on the left. Then 2AlCl3 gives 6 Cl and 3H2 gives 6 H on the right. Aluminum: 2Al. Result: 2Al + 6HCl → 2AlCl3 + 3H2.
  4. C2H6 + O2 → CO2 + H2O. Carbon: 2CO2. Hydrogen: 6 on the left, so 3H2O. Oxygen: 4 + 3 = 7 on the right, so 3.5O2. Multiply by 2: 2C2H6 + 7O2 → 4CO2 + 6H2O. Check: C 4 = 4, H 12 = 12, O 14 = 8 + 6.
  5. Ca(OH)2 + H3PO4 → Ca3(PO4)2 + H2O. Calcium: 3Ca(OH)2. Phosphate: 2H3PO4. Hydrogen on the left: 3 × 2 + 2 × 3 = 12, so 6H2O. Result: 3Ca(OH)2 + 2H3PO4 → Ca3(PO4)2 + 6H2O. Check oxygen: 6 + 8 = 14 on the left, 8 + 6 = 14 on the right.
  6. Fe2O3 + CO → Fe + CO2. Iron: 2Fe. Oxygen: 3 from Fe2O3 must go to CO2, and each CO2 needs one O from CO plus one more. Try 3CO and 3CO2: C 3 = 3, O 3 + 3 = 6 = 3 × 2. Result: Fe2O3 + 3CO → 2Fe + 3CO2.
  7. C6H12O6 + O2 → CO2 + H2O. C: 6CO2. H: 12 so 6H2O. O on the right: 12 + 6 = 18. On the left glucose has 6, so O2 must supply 12, which is 6O2. Result: C6H12O6 + 6O2 → 6CO2 + 6H2O.
  8. Al2(SO4)3 + Ca(OH)2 → Al(OH)3 + CaSO4. Treat sulfate and hydroxide as units. Aluminum: 2Al(OH)3. Sulfate: 3CaSO4. Calcium: 3Ca(OH)2. Hydroxide: 3 × 2 = 6 on the left and 2 × 3 = 6 on the right. Result: Al2(SO4)3 + 3Ca(OH)2 → 2Al(OH)3 + 3CaSO4.

How does the algebraic method work?

For difficult equations, assign a letter to each coefficient and write an equation for each element. Balance C4H10 + O2 → CO2 + H2O with a, b, c and d: a C4H10 + b O2 → c CO2 + d H2O.

  1. Carbon: 4a = c.
  2. Hydrogen: 10a = 2d, so d = 5a.
  3. Oxygen: 2b = 2c + d.
  4. Set a = 1. Then c = 4, d = 5, and 2b = 8 + 5 = 13, so b = 6.5.
  5. Multiply by 2 to clear the fraction: a = 2, b = 13, c = 8, d = 10.

Result: 2C4H10 + 13O2 → 8CO2 + 10H2O. Check: O 26 = 16 + 10.

2C₄H₁₀ + 13O₂ → 8CO₂ + 10H₂O C 8 = 8 H 20 = 20 O 26 = 16 + 10

Practice equations and answers

Unbalanced equations and balanced answers
Unbalanced Balanced
N2 + H2 → NH3N2 + 3H2 → 2NH3
Na + H2O → NaOH + H22Na + 2H2O → 2NaOH + H2
KClO3 → KCl + O22KClO3 → 2KCl + 3O2
C3H8 + O2 → CO2 + H2OC3H8 + 5O2 → 3CO2 + 4H2O
Mg + HNO3 → Mg(NO3)2 + H2Mg + 2HNO3 → Mg(NO3)2 + H2
NH3 + O2 → NO + H2O4NH3 + 5O2 → 4NO + 6H2O

How do you check an answer?

  1. Count each element on both sides using coefficient × subscript.
  2. Make sure that the coefficients have no common factor greater than 1, such as 4, 6, 8 and 4, 2, 2, 2.
  3. Check that you did not change any formula.
  4. For ionic equations, also check that the total charge is the same on both sides.

Where does balancing come from?

The practice of balancing equations follows from Lavoisier’s insistence on the conservation of mass in the 1780s. At first, equations expressed relative masses. After Dalton’s atomic theory and the development of reliable atomic masses in the 19th century, the coefficients were interpreted as numbers of molecules and moles. Today, balancing is automated by computer methods that solve the same linear algebra problem as the algebraic method.

Which mistakes are common?

Mistake 1: Changing subscripts

Changing H2O to H2O2 changes the substance. Only coefficients are changed.

Mistake 2: Balancing oxygen first in combustion

Oxygen appears in more than one product. Balance C and H first, and oxygen last.

Mistake 3: Forgetting to distribute a coefficient

3Ca(OH)2 contains 3 Ca, 6 O and 6 H atoms. The coefficient multiplies every element in the formula.

Mistake 4: Leaving a coefficient set that is not in the lowest terms

2H2 + 2O2 → 2H2O is not balanced, but 4H2 + 2O2 → 4H2O is balanced and can be reduced to 2H2 + O2 → 2H2O.