Balancing a chemical equation means choosing coefficients so each element has the same number of atoms on both sides of the arrow. The reliable method is to count, adjust coefficients, and check again. You never change a chemical formula’s subscripts: that would change the substance itself.
What coefficients do
A coefficient is the number written before a formula. It multiplies every atom in that formula: 2H₂O represents four hydrogen atoms and two oxygen atoms. A subscript belongs to the formula, so H₂O and H₂O₂ are different substances. The equation is balanced when the total count of every element matches on the reactant and product sides. OpenStax explains this rule through conservation of matter and worked examples.
A four-step method
1. Write the correct formulas first. Put reactants on the left and products on the right. Check that each formula is correct before balancing; coefficients cannot fix an incorrect formula.
2. Count each element on both sides. A small table helps. If an element appears in more than one formula on a side, add those atoms together.
3. Change coefficients to fix one mismatch at a time. Start with an element that appears in just one formula on each side when possible. Leave an element that appears in several formulas until later; hydrogen and oxygen often fall into this group. Recount after every change because one coefficient affects all atoms in its formula.
4. Check every element and simplify. When all counts match, divide the coefficients by any common factor so they are the smallest whole numbers. Include an unwritten coefficient of 1 when checking.
Worked example: hydrogen and oxygen
Balance H₂ + O₂ → H₂O. Start by counting: the left has two H and two O atoms; the right has two H and one O. Put a 2 before H₂O to make oxygen counts equal: H₂ + O₂ → 2H₂O. Now the right has four H atoms, so put a 2 before H₂: 2H₂ + O₂ → 2H₂O.
Check the final counts: left H = 2 × 2 = 4 and O = 1 × 2 = 2; right H = 2 × 2 = 4 and O = 2 × 1 = 2. Each element matches.
Another example: iron oxide
For Fe + O₂ → Fe₂O₃, oxygen appears as groups of two on the left and three on the right. Six oxygen atoms is a shared total, so use 3O₂ and 2Fe₂O₃. That gives four Fe atoms on the right; add 4Fe on the left. The balanced equation is 4Fe + 3O₂ → 2Fe₂O₃. Check: Fe is 4 on each side and O is 6 on each side.
Common mistakes to avoid
Do not alter subscripts, even if changing one seems to balance the counts. Do not forget that a coefficient multiplies the whole formula: 3CO₂ has three carbon atoms and six oxygen atoms. Finally, do not stop after balancing the element you started with—recheck the full count table.
Practise and check your work
Try N₂ + H₂ → NH₃ before looking at the answer. One balanced result is N₂ + 3H₂ → 2NH₃: that gives two nitrogen atoms and six hydrogen atoms on each side. For more practice, use Khan Academy’s balancing-equations exercise. You can also turn missed equations into short prompts and retry them later with Prepo’s active-recall study method.
OpenStax Chemistry 2e: Writing and Balancing Chemical Equations