How do you balance a chemical equation?
Balancing a chemical equation means making sure there are the same number of atoms of each element on both sides of the arrow. You do it by placing whole-number coefficients in front of formulas, never by changing the subscripts. For example, hydrogen and oxygen form water in the balanced equation 2H₂ + O₂ → 2H₂O.
Why equations must balance
A chemical equation is a short way to describe a reaction. The starting substances, called reactants, go on the left, and the new substances, called products, go on the right. The arrow means “react to form.”
In a reaction, atoms are not created or destroyed; they only swap partners. This is the law of conservation of mass, which the French chemist Antoine Lavoisier demonstrated with careful experiments in the late 1700s. Every atom on the left must still be there on the right, so the number of atoms of each element, and the total mass, stay the same.
The golden rule: change coefficients, not subscripts
A coefficient is a number placed in front of a formula. It tells you how many molecules or units of that substance take part, so changing it simply changes how much of the substance there is.
Changing a subscript is never allowed, because it turns the substance into something else. H₂O is water, but H₂O₂ is hydrogen peroxide, a completely different chemical.
A step-by-step method
Step 1: write the correct formulas for all reactants and products. Step 2: count the atoms of each element on both sides. Step 3: add coefficients to balance one element at a time. Start with an element that appears in only one substance on each side. It often helps to adjust lone elements, such as O₂ or Fe, last, because changing their coefficients does not upset any other element. Step 4: count every element again. Step 5: make sure the coefficients are the smallest whole numbers possible.
Example 1: making water
Start with H₂ + O₂ → H₂O. The left side has 2 H and 2 O atoms, but the right side has 2 H and only 1 O. Put a 2 in front of H₂O to get 2 oxygen atoms on the right: H₂ + O₂ → 2H₂O.
Now the right side has 4 H, but the left has only 2, so put a 2 in front of H₂: 2H₂ + O₂ → 2H₂O. Check: 4 H and 2 O on each side. It is balanced.
The masses agree too. Two moles of H₂ (4.032 g) plus one mole of O₂ (31.998 g) make 36.030 g, exactly the mass of two moles of H₂O (2 × 18.015 = 36.030 g).
Example 2: burning methane
Methane, CH₄, is the main ingredient of natural gas. When it burns, it reacts with oxygen to make carbon dioxide and water: CH₄ + O₂ → CO₂ + H₂O.
Carbon is already balanced, with 1 atom on each side. Hydrogen is not: there are 4 on the left and 2 on the right, so write 2H₂O. Now count oxygen on the right: 2 in CO₂ plus 2 in 2H₂O makes 4. To get 4 oxygen atoms on the left, write 2O₂. The balanced equation is CH₄ + 2O₂ → CO₂ + 2H₂O, with 1 C, 4 H and 4 O on each side.
Example 3: rusting iron
Iron reacts with oxygen to form iron(III) oxide: Fe + O₂ → Fe₂O₃. Real rust also contains water, but this simpler equation shows the main reaction.
Both reactants are lone elements here, so begin with the trickier one, oxygen: O₂ has 2 oxygen atoms and Fe₂O₃ has 3. The smallest number that both 2 and 3 divide into is 6, so write 3O₂ (6 oxygen atoms) and 2Fe₂O₃ (6 oxygen atoms). The right side now has 2 × 2 = 4 iron atoms, so write 4Fe on the left. The balanced equation is 4Fe + 3O₂ → 2Fe₂O₃, with 4 Fe and 6 O on each side.
Key points
- A balanced equation has the same number of atoms of each element on both sides of the arrow.
- Atoms are rearranged, not created or destroyed, so mass is conserved in every reaction.
- Balance an equation by changing coefficients only, because changing a subscript changes the substance.
- Balance one element at a time, usually leaving lone elements such as O₂ and Fe for last, and then recount everything.
- Three balanced examples: 2H₂ + O₂ → 2H₂O, CH₄ + 2O₂ → CO₂ + 2H₂O and 4Fe + 3O₂ → 2Fe₂O₃.
Check yourself
Three quick questions on this lesson.
1. When you balance a chemical equation, what are you allowed to change?
Show the answer
The coefficients in front of the formulas — Only coefficients may change, because changing a subscript would turn a substance into a different one.2. In the balanced equation for burning methane, what coefficient goes in front of O₂?
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2 — The products contain 4 oxygen atoms (2 in CO₂ and 2 in 2H₂O), so 2O₂ is needed on the left.3. How many oxygen atoms are on each side of 4Fe + 3O₂ → 2Fe₂O₃?