Calculate empirical and molecular formulae
Convert composition data to mole ratios, distinguish empirical from molecular formulae, and interpret water of crystallisation.
AS Level; Cambridge International Chemistry 9701, 2025–2027 syllabus. Use the data and constants supplied for the question, show mole-ratio working, and report a justified number of significant figures. Written practice is self-checked
Before you begin
- Use common chemical symbols and formulae, and rearrange a simple equation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does an empirical formula show?
What you will learn
- Define empirical and molecular formulae
- Calculate formulae from composition or experimental data
- Use the terms anhydrous, hydrated and water of crystallisation
A formula records the simplest ratio or actual molecule
The empirical formula gives the simplest whole-number ratio of atoms in a compound. The molecular formula gives the actual number of each type of atom in one molecule; it is an integer multiple of the empirical formula.
Convert each element's mass or percentage to amount by dividing by Ar. Divide each amount by the smallest, then scale to whole numbers if needed. For a molecular formula, calculate the empirical formula mass and divide the supplied Mr by it; multiply every empirical subscript by that integer.
Water of crystallisation is part of a hydrated solid's formula
An anhydrous substance contains no water of crystallisation. A hydrated salt has water molecules incorporated in its crystal structure, written after a dot, for example CuSO₄·5H₂O. The number after the dot gives water molecules per formula unit.
If heating removes water, use the mass lost to find the amount of H₂O and the remaining anhydrous salt to find its amount. Divide by the smaller amount to obtain the simplest whole-number ratio. State what is assumed: for example, that heating removes only water and that the final mass is the anhydrous salt.
Pause and explain
A molecular formula is related to its empirical formula by what factor?
Worked example
A compound contains 40.0% carbon, 6.7% hydrogen and 53.3% oxygen by mass. Find its empirical formula. Use Ar(C,H,O) = 12.0, 1.0, 16.0.
Show the worked solution
- Assume 100 g: amounts are 40.0/12.0, 6.7/1.0 and 53.3/16.0 mol.
- Divide by the smallest amount to get approximately 1:2:1.
- Write the simplest whole-number ratio.
Answer CH₂O.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A compound has empirical formula CH₂ and Mr = 56.0. Find its molecular formula. Use Ar(C,H)=12.0,1.0.
Give me a hint
Find the empirical formula mass, then compare it with Mr.
Compare my reasoning
- Empirical formula mass = 12 + 2 = 14.
- Multiplier = 56/14.
- Multiply both subscripts by this integer.
C₄H₈.
Look for these in your work
- Empirical mass calculated
- Integer multiplier found
- All subscripts multiplied
A 2.50 g sample of hydrated magnesium sulfate loses 1.28 g when heated to constant mass. Find the simplest hydrate formula using Mr(MgSO₄)=120 and Mr(H₂O)=18.0.
Give me a hint
Find moles of water lost and moles of anhydrous MgSO₄ remaining.
Compare my reasoning
- Water amount = 1.28/18.0 = 0.0711 mol.
- Anhydrous MgSO₄ mass = 2.50 − 1.28 = 1.22 g; amount = 1.22/120 = 0.0102 mol.
- Divide both by 0.0102 to obtain the water-to-salt ratio.
MgSO₄·7H₂O approximately, since 0.0711/0.0102 ≈ 7.0.
Look for these in your work
- Mass loss treated as water under the stated heating assumption
- Anhydrous mass determined
- Whole-number hydrate ratio found
A student reports C₂H₄ as the empirical formula of a sample that is known only to have C:H mole ratio 1:2. What is wrong, and what additional data gives a molecular formula?
Give me a hint
Reduce the ratio before naming an empirical formula.
Compare my reasoning
- C₂H₄ reduces to CH₂.
- The ratio alone gives only an empirical formula.
- A molecular mass or Mr is needed to find the multiplier.
The empirical formula is CH₂, not C₂H₄, because the ratio reduces to 1:2. The molecular formula requires the compound's Mr so it can be compared with the empirical formula mass.
Look for these in your work
- Ratio reduced correctly
- Empirical and molecular meanings distinguished
- Additional datum identified
Common mistakes
- Rounding mole ratios too early
- Calling an empirical formula the molecule's actual formula without Mr evidence
- Treating the dot in a hydrate as multiplication of the entire salt formula
- Assuming a mass loss is water without stating the experimental assumption
What can you explain now?
What does an empirical formula show?
Compare with the explanation
The simplest whole-number ratio of atoms
It gives the simplest ratio, not necessarily a molecule's actual atom count.
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Make it stick
How do composition data become an empirical formula, and what extra information is needed for a molecular formula?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.