Chimica

Balancing Chemical Equations: Solved Exercises Step by Step

How to balance a chemical equation using coefficients, step by step, with five solved exercises of increasing difficulty and verified answers.

Recommended for: Grade 9 · Grade 10

You balance a chemical reaction by placing coefficients in front of the formulas (never by changing subscripts) until every element has the same number of atoms on the left and right of the arrow. It is the practical version of the law of conservation of mass: in a reaction atoms are neither created nor destroyed, they simply rearrange.

Why we balance

The subscripts in a formula, such as the 2 in H₂O, say how many atoms are in a molecule and cannot be touched: they are part of the substance’s identity. The only thing you can change is the coefficient, the large number in front of the formula, which tells you how many molecules of that species take part in the reaction.

A three-step method

First pick an element that appears in only one compound per side and match it with a coefficient. Then move on to the other elements, saving hydrogen and oxygen for last because they usually appear in several molecules. Finally recheck every element and, if you are left with a fraction, multiply the whole reaction by the denominator to get back to whole-number coefficients.

In the exercises below the pattern is always the same, with increasing difficulty: they start with the formation of water and end with a combustion that has an odd number of oxygen atoms. Every answer is verified by counting the atoms of each element on both sides.

Solved exercises

1. Balance: H₂ + O₂ → H₂O base

Show solution
  1. Count the unbalanced atoms: the right side has 1 O, the left side has 2.
  2. Put a coefficient of 2 in front of H₂O to match the oxygen: H₂ + O₂ → 2H₂O.
  3. Now the right side has 4 H and the left only 2: put 2 in front of H₂.
  4. Reaction: 2H₂ + O₂ → 2H₂O.
  5. Check → H: 4 = 4 ; O: 2 = 2. It is balanced.

Answer: 2H₂ + O₂ → 2H₂O

2. Balance: N₂ + H₂ → NH₃ base

Show solution
  1. Nitrogen: 2 atoms on the left (N₂), 1 on the right, so put 2 in front of NH₃.
  2. N₂ + H₂ → 2NH₃ gives 6 H on the right but only 2 on the left.
  3. Put 3 in front of H₂ to get 6 H: N₂ + 3H₂ → 2NH₃.
  4. Check → N: 2 = 2 ; H: 6 = 6. It is balanced.

Answer: N₂ + 3H₂ → 2NH₃

3. Balance the combustion of methane: CH₄ + O₂ → CO₂ + H₂O intermedio

Show solution
  1. Carbon is already fine: 1 C on the left and 1 on the right.
  2. Hydrogen: 4 H on the left, so put 2 in front of H₂O to get 4 on the right.
  3. CH₄ + O₂ → CO₂ + 2H₂O: now the oxygen on the right is 2 (from CO₂) + 2 (from 2H₂O) = 4.
  4. Put 2 in front of O₂ to get 4 O on the left: CH₄ + 2O₂ → CO₂ + 2H₂O.
  5. Check → C: 1 = 1 ; H: 4 = 4 ; O: 4 = 4. It is balanced.

Answer: CH₄ + 2O₂ → CO₂ + 2H₂O

4. Balance: Fe + O₂ → Fe₂O₃ intermedio

Show solution
  1. Iron: 2 atoms on the right (Fe₂O₃), 1 on the left, so put 2 in front of Fe.
  2. Oxygen: 3 on the right, 2 on the left (O₂); the least common multiple of 3 and 2 is 6.
  3. You need 6 O per side: put 3 in front of O₂ (3×2 = 6) and 2 in front of Fe₂O₃ (2×3 = 6).
  4. Iron must be readjusted: 2 Fe₂O₃ contain 4 Fe, so put 4 in front of Fe.
  5. Reaction: 4Fe + 3O₂ → 2Fe₂O₃. Check → Fe: 4 = 4 ; O: 6 = 6. It is balanced.

Answer: 4Fe + 3O₂ → 2Fe₂O₃

5. Balance the combustion of ethane: C₂H₆ + O₂ → CO₂ + H₂O avanzato

Show solution
  1. Carbon: 2 on the left, so put 2 in front of CO₂.
  2. Hydrogen: 6 on the left, so put 3 in front of H₂O.
  3. Count the oxygen on the right: 2×2 (CO₂) + 3×1 (H₂O) = 7 atoms, an odd number.
  4. 7 O would require 7/2 O₂: to avoid fractions, multiply the whole reaction by 2.
  5. You get 2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O. Check → C: 4 = 4 ; H: 12 = 12 ; O: 14 = 14. It is balanced.

Answer: 2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O

FAQ

Why can't I change the subscripts to balance a reaction?

Because subscripts define the identity of the substance: changing H₂O into H₂O₂ turns water into hydrogen peroxide, a different compound. To balance you may only change the coefficients in front of the formulas, never the subscripts.

Which element should I start balancing from?

Start with elements that appear in only one compound on each side, often a metal or carbon, and leave hydrogen and especially oxygen for last, since they usually show up in several species at once.

Do the coefficients have to be as small as possible?

Yes. A reaction is correctly balanced when the coefficients are whole numbers reduced to the smallest ratio. If you end up with a fraction during the calculation, multiply the whole reaction by the denominator to clear it.