In a chemical reaction, atoms are rearranged into new substances. They are not created and they are not destroyed. That is the law of conservation of mass, and it is the reason chemical equations must be balanced: the same number of each kind of atom has to appear on both sides. In Chemistry you are asked to use mathematical representations to support the claim that atoms, and therefore mass, are conserved in a reaction. Balancing is how you do it.
What an equation tells you
In 2 H₂ + O₂ → 2 H₂O, the coefficients (the big numbers in front) say how many molecules of each substance take part. The subscripts (the small numbers) say how many atoms are in one molecule. Subscripts define what a substance is, so they never change. Only coefficients can change.
A method that works
- Write the correct formula for every reactant and product.
- Make a table of each element and count its atoms on each side. Treat a polyatomic ion, such as OH, as a unit if it stays together.
- Balance elements that appear in only one substance on each side first. Leave hydrogen and oxygen for last if they appear in several places.
- Adjust coefficients one element at a time, and recount after every change.
- If you get fractions, multiply everything by the smallest number that clears them.
- Do a final count of every element.
Worked example 1: burning methane
CH₄ + O₂ → CO₂ + H₂O
- Carbon: 1 on each side, already balanced.
- Hydrogen: 4 on the left, 2 on the right. Put a 2 in front of H₂O to get 4.
- Oxygen: the right side now has 2 (in CO₂) + 2 (in 2 H₂O) = 4. Put a 2 in front of O₂ to get 4 on the left.
Result: CH₄ + 2 O₂ → CO₂ + 2 H₂O. Count: C 1 and 1, H 4 and 4, O 4 and 4.
Worked example 2: rusting iron
Fe + O₂ → Fe₂O₃
Oxygen is 2 on the left and 3 on the right. The smallest number that both 2 and 3 divide into is 6, so use 3 O₂ on the left and 2 Fe₂O₃ on the right: 6 oxygen atoms each side. Now the right side has 4 iron atoms, so put a 4 in front of Fe.
Result: 4 Fe + 3 O₂ → 2 Fe₂O₃. Count: Fe 4 and 4, O 6 and 6.
Worked example 3: groups that stay together
Mg(OH)₂ + HCl → MgCl₂ + H₂O
Magnesium is balanced (1 and 1). Chlorine is 1 on the left and 2 on the right, so use 2 HCl. Now count hydrogen: the left has 2 (in Mg(OH)₂) + 2 (in 2 HCl) = 4, and oxygen has 2. The right needs 4 hydrogen and 2 oxygen, which 2 H₂O supplies.
Result: Mg(OH)₂ + 2 HCl → MgCl₂ + 2 H₂O. Count: Mg 1 and 1, O 2 and 2, H 4 and 4, Cl 2 and 2.
Checking conservation of mass with numbers
Take the balanced equation for burning propane: C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O. Molar masses in g/mol: C₃H₈ is 44.1, O₂ is 32.0, CO₂ is 44.0 and H₂O is 18.0.
- Reactants: 1 × 44.1 + 5 × 32.0 = 44.1 + 160.0 = 204.1 g
- Products: 3 × 44.0 + 4 × 18.0 = 132.0 + 72.0 = 204.0 g
The two totals agree to the precision of the data (the 0.1 g difference is rounding). If you ever found a clear gap, it would mean a miscount, or a product, such as a gas, that escaped your measurement. That second case is why a reaction in an open container can seem to lose mass: the missing mass left as gas.
A quick way to check any answer
Add up each element on the left, add up each element on the right, and compare. For 4 Fe + 3 O₂ → 2 Fe₂O₃, multiply each coefficient by the subscripts in its formula: the left has 4 Fe and 3 × 2 = 6 O, and the right has 2 × 2 = 4 Fe and 2 × 3 = 6 O. If every pair matches and the coefficients share no common factor (here 4, 3 and 2 do not), the equation is in its simplest balanced form.
Common mistakes
- Changing a subscript to balance. Turning H₂O into H₂O₂ gives a different substance. Only change coefficients.
- Forgetting that a coefficient multiplies the whole formula. In 2 Fe₂O₃ there are 4 iron atoms and 6 oxygen atoms.
- Not recounting. Each coefficient change affects every element in that substance, so recount after each step.
- Miscounting inside parentheses. In Mg(OH)₂ the subscript 2 applies to both O and H.
- Starting with an unbalanced formula. The formulas, such as MgCl₂, come from the charges of the ions. Balancing cannot fix a wrong formula.
Practice Chemistry questions with an explanation for every answer, or read the guide to California Chemistry practice.
Source: the California Next Generation Science Standards (CA NGSS), as set out in the California Science Framework, HS-PS1-7.