How to Find an Empirical Formula in IGCSE Chemistry

You divide the amounts in moles by the smallest number and get a ratio of 1 : 2.5. The formula needs whole numbers. What should you do?

Double both parts of the ratio. That gives 2 : 5 and keeps the proportion the same. Rounding 2.5 to 3 would change the proportion and give a different formula.

What is an empirical formula?

An empirical formula gives the simplest whole-number ratio of the elements in a compound. A molecular formula tells you how many atoms of each element are in one molecule. For example, hydrogen peroxide has the molecular formula H₂O₂ and the empirical formula HO because its hydrogen-to-oxygen ratio simplifies from 2 : 2 to 1 : 1. Cambridge IGCSE Chemistry syllabus, Section 3

Worked example — find the empirical formula from masses

A sample contains 6.2 g of phosphorus and 8.0 g of oxygen. Find its empirical formula. Use relative atomic masses P = 31 and O = 16.

1. Convert each mass to moles

Divide each element’s mass by its molar mass. Phosphorus and oxygen atoms have molar masses of 31 g/mol and 16 g/mol, respectively.

This conversion matters because equal masses of two elements can contain different numbers of atoms. The formula comes from comparing amounts in moles.

2. Divide both values by the smallest

The smallest amount is 0.20 mol.

• Phosphorus: 0.20 ÷ 0.20 = 1

• Oxygen: 0.50 ÷ 0.20 = 2.5

The phosphorus-to-oxygen ratio is 1 : 2.5.

3. Multiply both parts to get whole numbers

Multiply both parts by 2. The ratio becomes 2 : 5, so the empirical formula is P₂O₅.

How do you find the molecular formula?

Suppose the question also gives the compound’s relative molecular mass, 284.

1. Find the relative mass of the empirical formula. For P₂O₅, that’s (2 × 31) + (5 × 16) = 142.

2. Divide the relative molecular mass by that value. 284 ÷ 142 = 2.

3. Multiply every subscript by 2. The molecular formula is P₄O₁₀.

You can check your answer in two ways. The subscripts 4 and 10 reduce to 2 and 5, and (4 × 31) + (10 × 16) = 284.

Try it yourself

An iron oxide sample contains 11.2 g of iron and 4.8 g of oxygen. Use relative atomic masses Fe = 56 and O = 16. What is its empirical formula?

Answer — Iron gives 0.20 mol and oxygen gives 0.30 mol. Divide both by 0.20 to get 1 : 1.5, then multiply both parts by 2. The empirical formula is Fe₂O₃.

Frequently asked questions

What if the question gives percentages instead of masses?

For percentages by mass, imagine a 100 g sample. An element that makes up 40% of the compound contributes 40 g in that sample. Convert those masses to moles and continue with the same method.

Why do I divide the oxygen mass by 16 instead of 32?

You’re counting oxygen atoms in the compound. Use 16 g/mol for oxygen atoms. Use 32 g/mol when the question asks for the amount of O₂ molecules.

For a broader study plan, read TheTuitionE’s IGCSE exam preparation guide for UAE parents.

If your child gets as far as the mole ratio but gets stuck turning it into a formula, bring a recent question to a free TheTuitionE demo class.