How to balance chemical equations

Why equations must balance

In a chemical reaction, atoms are rearranged into new substances, but no atoms are created or destroyed. This is the law of conservation of mass: the total mass of the products equals the total mass of the reactants. If you burn a candle in a sealed jar, the jar weighs the same afterwards.

A chemical equation is a record of that rearrangement, so it has to show the same number of each kind of atom on the left, the reactants, as on the right, the products. An unbalanced equation describes a reaction that cannot happen.

Coefficients and subscripts

A subscript is the small number inside a formula. In H₂O, the 2 says each water molecule has two hydrogen atoms and one oxygen atom. Subscripts are fixed by the substance's identity: change H₂O to H₂O₂ and you have hydrogen peroxide, a different chemical.

A coefficient is the large number in front of a formula. In 3H₂O, the 3 means three water molecules. To count atoms, multiply the coefficient by each subscript: 3H₂O contains 3 × 2 = 6 hydrogen atoms and 3 × 1 = 3 oxygen atoms. Coefficients are the only numbers you change when balancing; a missing coefficient means 1.

The step-by-step method

This method works for most equations you will meet in middle and high school:

• Write the correct formulas for every reactant and product. Get these right first; balancing cannot fix a wrong formula.
• Make an atom inventory: list each element and count its atoms on each side.
• Balance an element that appears in only one reactant and one product, usually a metal or carbon, by changing a coefficient.
• Update your counts after every change, since one coefficient changes every element in that formula.
• Balance hydrogen next and oxygen last, since they often appear in several compounds. Elements that appear on their own, like O₂ or Fe, are easiest to adjust last because changing them affects nothing else.
• If a polyatomic ion such as SO₄ or NO₃ appears unchanged on both sides, balance it as one unit.
• Reduce the coefficients to the smallest whole numbers, then recount every element on both sides.

Worked example: burning methane

Methane, CH₄, is the main gas in natural gas. When it burns, it reacts with oxygen to make carbon dioxide and water. This is the pattern for every hydrocarbon burning completely: hydrocarbon plus oxygen gives carbon dioxide plus water.

Worked example: iron rusting

Iron reacts with oxygen to form iron(III) oxide, Fe₂O₃, a major part of rust. Here oxygen has 2 atoms on one side and 3 on the other, so the trick is to find the lowest common multiple, 6.

Worked example: burning propane

Propane, C₃H₈, is the fuel in many gas grills. It follows the same pattern as methane, so use the same order: carbon, then hydrogen, then oxygen.

When oxygen will not come out even

Sometimes the oxygen needed is an odd number, which O₂ cannot supply with a whole number. Burning ethane, C₂H₆, is the classic case. Balancing carbon and hydrogen gives C₂H₆ + O₂ → 2CO₂ + 3H₂O, with 2 × 2 + 3 = 7 oxygen atoms on the right.

Use a fraction for a moment: 7/2 O₂ supplies 7 oxygen atoms. Then multiply every coefficient by 2 to clear the fraction: 2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O. Check: C 4 and 4, H 12 and 12, O 14 and 14.

Common mistakes

Most wrong answers come from one of these:

• Changing a subscript to make the numbers work, such as turning H₂O into H₂O₂. That changes the substance; change only coefficients.
• Putting a coefficient in the middle of a formula. A coefficient goes in front and multiplies the whole formula.
• Forgetting to multiply the coefficient by every subscript. 2Fe₂O₃ has 4 iron atoms and 6 oxygen atoms.
• Missing an element that appears in two products, like the oxygen in both CO₂ and H₂O.
• Not updating counts after each change, then finishing with one element out of balance.
• Leaving coefficients that share a factor, such as 2, 4, 2, 4, which should reduce to 1, 2, 1, 2.

How to check your work

Always finish with a full atom inventory. Write each element down the page with two columns, reactants and products, and fill in every count from scratch rather than trusting your earlier working. Every row must match.

Then check the coefficients have no common factor and that every formula is exactly as it was given. To practise, start with combustion of hydrocarbons such as methane, propane and butane, then move to reactions with polyatomic ions, like Na₂SO₄ + BaCl₂ → BaSO₄ + 2NaCl, where SO₄ moves as one unit.