Balancing equations in chemistry

Balancing equations means making sure a chemical equation has the same number of each type of atom on both sides. You do it by writing whole numbers, called coefficients, in front of the formulas. You never change the small numbers inside a formula. For example, H₂ + O₂ → H₂O is unbalanced, because there are 2 oxygen atoms on the left and 1 on the right. Putting a 2 in front of H₂O and of H₂ balances it: 2H₂ + O₂ → 2H₂O.

Why chemical equations must balance

Atoms are not created or destroyed in a chemical reaction; they are only rearranged. AQA's GCSE specification calls this the law of conservation of mass: no atoms are lost or made during a chemical reaction, so the mass of the products equals the mass of the reactants. A balanced equation shows that on paper. Every atom on the left turns up somewhere on the right.

Coefficients and subscripts

A formula has two kinds of number. AQA asks students to understand both: the multiplier written in normal script before a formula, and the subscript within it.

• The subscript, the small number in a formula, says how many atoms are in one particle. H₂O has 2 hydrogen atoms and 1 oxygen atom. Changing it changes the substance: H₂O₂ is hydrogen peroxide, not water.
• The coefficient, the big number in front, says how many particles there are. 2H₂O means two water molecules, so 4 hydrogen atoms and 2 oxygen atoms.

A coefficient multiplies everything in the formula after it. In 3Ca(OH)₂ there are 3 calcium atoms, 3 × 2 = 6 oxygen atoms and 6 hydrogen atoms.

How to balance chemical equations

1. Write the correct formulas for every reactant and product. Get these right first; you will not change them later.
2. Count the atoms of each element on both sides. A small table helps.
3. Balance one element at a time by changing coefficients. Start with an element that appears in only one substance on each side.
4. Leave elements on their own until last, such as O₂, H₂ or a metal like Fe. Their coefficient changes nothing else.
5. Recount everything. Fixing one element can unbalance another, so check again after every change.
6. Use the lowest whole numbers. If every coefficient is even, halve them all. Leave out a coefficient of 1.
7. Add state symbols if the question asks: (s) solid, (l) liquid, (g) gas and (aq) aqueous, meaning dissolved in water.

Balancing equations examples

Example 1: sodium burning in oxygen

Balance Na + O₂ → Na₂O.

Oxygen first: there are 2 on the left, so put a 2 in front of Na₂O. That gives 2 × 1 = 2 oxygen atoms on the right, but now 2 × 2 = 4 sodium atoms. Put a 4 in front of Na:

Check: Na 4 and 4, O 2 and 2. Balanced.

Example 2: making ammonia

Balance N₂ + H₂ → NH₃.

Nitrogen: 2 on the left, so 2NH₃ on the right. Hydrogen is now 2 × 3 = 6 on the right, so 3H₂ on the left:

Example 3: burning methane

Balance CH₄ + O₂ → CO₂ + H₂O.

For a hydrocarbon burning, balance carbon first, then hydrogen, then oxygen last, because O₂ is an element on its own.

• Carbon: 1 on each side already.
• Hydrogen: 4 on the left, so 2H₂O on the right.
• Oxygen: now 2 in CO₂ + 2 in 2H₂O = 4 on the right, so 2O₂ on the left.

Example 4: brackets and polyatomic ions

Balance Al₂(SO₄)₃ + NaOH → Al(OH)₃ + Na₂SO₄.

When a group of atoms such as SO₄ or OH stays together on both sides, treat it as one unit. That makes the counting much easier.

Put 2 in front of Al(OH)₃ for aluminium and 3 in front of Na₂SO₄ for sulfate. The right now has 6 OH and 6 Na, so put 6 in front of NaOH:

Example 5: the odd number trick

Balance C₂H₆ + O₂ → CO₂ + H₂O.

Carbon: 2CO₂. Hydrogen: 6 atoms, so 3H₂O. Oxygen on the right is now 2 × 2 + 3 × 1 = 7. You cannot get 7 oxygen atoms from whole O₂ molecules, so use 3½O₂ for now, then double every coefficient to clear the half:

Check: C 4 and 4, H 12 and 12, O 14 and 8 + 6 = 14.

Example 6: a decomposition

Balance KClO₃ → KCl + O₂.

K and Cl are already balanced, 1 each. Oxygen is 3 on the left and 2 on the right. The lowest common multiple of 3 and 2 is 6, so 2KClO₃ on the left and 3O₂ on the right. Then K and Cl need 2KCl:

Now try one in the course. Balance the combustion equation there, then come back for the harder methods.

The algebra method, for hard equations

When inspection gets confusing, give each coefficient a letter and write one equation for each element. Take a C₂H₆ + b O₂ → c CO₂ + d H₂O.

• Carbon: 2a = c
• Hydrogen: 6a = 2d
• Oxygen: 2b = 2c + d

Choose a = 2 to avoid fractions. Then c = 4, d = 6, and 2b = 8 + 6 = 14, so b = 7. That gives 2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O, the same as Example 5. The Equation Balancer uses the same idea for any equation you type in and shows the atom counts.

Try it

Equation Balancer

Balance chemical and ionic equations with the working shown

Open the calculatorGo to its page

Balancing ionic equations

An ionic equation shows only the ions that change. It must balance in two ways: atoms and charge. Take silver ions reacting with copper:

The atoms balance, with 2 silver and 1 copper on each side. The charges balance too: 2 × (+1) = +2 on the left and +2 on the right. Writing Ag⁺ + Cu → Ag + Cu²⁺ balances the atoms but not the charge, so it is wrong. AQA's GCSE specification asks Higher tier students to write balanced half equations and ionic equations where appropriate. Our guide to ionic equations goes further.

Using a balanced equation

Once an equation balances, its coefficients tell you the ratio in which substances react. 2H₂ + O₂ → 2H₂O means 2 moles of hydrogen react with 1 mole of oxygen to make 2 moles of water. That ratio is the starting point for reacting mass calculations, and the masses add up: in a balanced equation, the total relative formula mass of the reactants equals the total for the products. The Stoichiometry Calculator takes a balanced equation and works out reacting masses.

Common mistakes

• Changing a subscript. Turning H₂O into H₂O₂ to fix the oxygen makes a different chemical. Only change the big numbers in front.
• Putting a coefficient in the middle of a formula, such as H₂2O. Coefficients go in front.
• Forgetting that a coefficient multiplies the whole formula, including what is inside brackets.
• Not recounting. Balancing oxygen can unbalance hydrogen. Check every element at the end.
• Leaving a fraction or not simplifying. 4H₂ + 2O₂ → 4H₂O is balanced but should be 2H₂ + O₂ → 2H₂O.
• Writing oxygen as O. Oxygen gas is O₂, and so are hydrogen (H₂), nitrogen (N₂) and the halogens (Cl₂, Br₂, I₂).

Practise chemistry in a short timed paper

GCSE Chemistry Higher and GCSE Chemistry Foundation each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course, so you balance equations as part of real questions, not on their own.

Read next

Chemistry · Reactions and electrolysisHalf equations: how to write and balance them, examplesHow to write half equations for oxidation and reduction: electrolysis at each electrode, displacement, balancing in acid with H₂O and H⁺, and combining.