Balancing equations

Why this matters

A balanced equation is the recipe of a reaction. It tells a chemist how much of each reagent to order, tells an engineer how much carbon dioxide a furnace releases per kilogram of fuel, and is the starting point for every yield and dosing calculation in the next lessons. If the equation is not balanced, every number calculated from it is wrong.

The core idea: atoms are conserved

In a chemical reaction atoms are rearranged, not created or destroyed (the law of conservation of mass). So every element must appear the same number of times on the left (reactants) and the right (products).

reactants  ->  products
CH4 + O2   ->  CO2 + H2O        unbalanced

Count the atoms: left has 1 C, 4 H, 2 O; right has 1 C, 2 H, 3 O. Hydrogen and oxygen do not match.

Coefficients, not subscripts

You fix the count by putting coefficients (whole numbers) in front of formulas. You never change the subscripts inside a formula, because that changes the substance: H₂O is water, H₂O₂ is hydrogen peroxide.

2 H2O   = 2 molecules of water = 4 H and 2 O
H2O2    = a different chemical

A step-by-step method

1. Write correct formulas for every reactant and product.
2. Count each element on both sides (a small table helps).
3. Balance elements that appear in only one compound on each side first; save free elements (O₂, H₂, Fe) and hydrogen/oxygen for last.
4. Adjust one coefficient at a time and recount.
5. Reduce to the smallest whole-number set and check every element once more.

Worked example 1: burning methane

CH4 + O2 -> CO2 + H2O

• Carbon: 1 and 1. Already balanced.
• Hydrogen: 4 on the left, 2 on the right. Put a 2 in front of H₂O.

CH4 + O2 -> CO2 + 2 H2O

• Oxygen: right side now has 2 (in CO₂) + 2 (in 2 H₂O) = 4. Left has 2. Put a 2 in front of O₂.

CH4 + 2 O2 -> CO2 + 2 H2O

Balanced.

Worked example 2: burning propane

C3H8 + O2 -> CO2 + H2O

• Carbon: 3 on the left, so 3 CO₂.
• Hydrogen: 8 on the left, so 4 H₂O.
• Oxygen: right has 3 × 2 + 4 × 1 = 10, so 5 O₂.

C3H8 + 5 O2 -> 3 CO2 + 4 H2O

Worked example 3: making ammonia (the Haber process)

N2 + H2 -> NH3

Nitrogen: 2 on the left, so 2 NH₃. Hydrogen: now 6 on the right, so 3 H₂.

N2 + 3 H2 -> 2 NH3

Worked example 4: rusting iron

Fe + O2 -> Fe2O3

Oxygen comes in pairs on the left and threes on the right; the lowest common multiple is 6. So 3 O₂ and 2 Fe₂O₃, which needs 4 Fe:

4 Fe + 3 O2 -> 2 Fe2O3

Check: Fe 4 = 4, O 6 = 6.

Fractions are a useful trick

If you end with an odd count of oxygen, you can briefly use a fraction and then multiply everything by 2. For ethane, C2H6 + 7/2 O2 -> 2 CO2 + 3 H2O becomes 2 C2H6 + 7 O2 -> 4 CO2 + 6 H2O. The final answer must use whole numbers.

Reading what an equation tells you

N2 + 3 H2 -> 2 NH3 means:

• 1 molecule of nitrogen reacts with 3 molecules of hydrogen to make 2 molecules of ammonia, and
• 1 mole of N₂ reacts with 3 moles of H₂ to make 2 moles of NH₃.

The coefficients are a mole ratio, which is exactly what the next lesson uses to predict yields. State symbols are often added: (s) solid, (l) liquid, (g) gas, (aq) dissolved in water.

Common types of reaction

• Combustion: fuel + O₂ → CO₂ + H₂O (for hydrocarbons).
• Synthesis: A + B → AB (N₂ + 3H₂ → 2NH₃).
• Decomposition: AB → A + B (2H₂O₂ → 2H₂O + O₂).
• Single replacement: Zn + 2HCl → ZnCl₂ + H₂.
• Double replacement / precipitation: AgNO₃ + NaCl → AgCl(s) + NaNO₃.

Common mistakes

• Changing subscripts to force a balance. That changes the chemical.
• Forgetting to multiply through. In 3 CO₂ there are 6 oxygen atoms, not 2.
• Leaving a common factor. 2 CH₄ + 4 O₂ → 2 CO₂ + 4 H₂O balances, but reduce it to 1, 2, 1, 2.
• Not rechecking every element after the last change.

Quick recap

• Atoms are conserved, so each element must match on both sides.
• Change coefficients only; never change subscripts.
• Balance single-appearance elements first, then free elements, and recheck.
• Coefficients give the mole ratio used in stoichiometry.

Try it

Open the Do tab and take the quiz: you will choose the correct coefficients for several equations.