GCSE · Chemistry · Edexcel · Spec 1CH0

Empirical formulae from reacting masses or % composition

You can't see atoms or count them. But weigh the elements that reacted, grab a periodic table, and you can work out the formula. Detective work, with a calculator.

Masses in, formula out: iron and oxygen

Step through it. Imagine 5.6 g of iron reacts with 2.4 g of oxygen and you have no idea what the formula is. You only have the masses and a periodic table.

Predict, then check

Different route, same destination. No masses this time, just a model you can count.

A model of a glucose molecule has 6 carbon atoms, 12 hydrogen atoms and 6 oxygen atoms. What is glucose's empirical formula?

Ionic substances

Where does the formula of sodium oxide come from?

Sodium oxide is made of sodium ions, Na⁺, and oxide ions, O²⁻. Nobody has given you any masses.

How would you find its formula? Pick the idea closest to yours.

Balance the charges so they add up to zero.You always need a mass calculation first, like every other empirical formula.Write NaO, because there's one sodium and one oxygen.Na2O is the empirical formula, so the molecular formula must be something bigger.

How sure are you?

I'm sureI think soI'm guessing

Balance the charges so they add up to zero.

This matches the evidence

Yes. The substance has to be uncharged overall, so you need enough Na⁺ to cancel the O²⁻. Two Na⁺ (+2) balance one O²⁻ (−2), which gives Na2O. No masses needed, and Na2O is also the empirical formula.

You always need a mass calculation first, like every other empirical formula.

This is a common misconception

That's the shortcut people reach for because the mass method is the one they've just practised. The mass method is for when you're given masses or percentages. For an ionic substance the ion charges already tell you the ratio.

Write NaO, because there's one sodium and one oxygen.

This is a common misconception

Counting the elements isn't enough: the charges matter. One Na⁺ is +1 but one O²⁻ is −2, so they don't add up to zero. You need two Na⁺ for every O²⁻, giving Na2O.

Na2O is the empirical formula, so the molecular formula must be something bigger.

This is a common misconception

Empirical and molecular formulae are not always different. For an ionic substance the formula already shows the ratio of ions, so its chemical formula, Na2O, is its empirical formula. Nothing bigger is hiding behind it.

For an ionic substance, find how many of each ion make the charges add up to zero. That ratio is the formula, and it's the empirical formula too.

Empirical or molecular?

Sort the formulae

Tick every set each formula belongs to. Watch out: a formula can be in both.

A Empirical formula (simplest ratio)
B Molecular formula (actual atoms in a molecule)

H2O (water)
C2H6 (ethane)
C4H10 (butane)
CH3
C2H5
NaCl
SiO2

From empirical to molecular

Find the molecular formula

A compound has the empirical formula NO2 and a relative molecular mass of 92. What is its molecular formula? (Relative atomic masses: N = 14, O = 16.)

We know the empirical formula, NO2, and the relative molecular mass, 92. The empirical formula only gives the ratio, so we need to find how many NO2 units fit into the real molecule.
missing step

Which line is step 2?

Empirical formula mass: 14 + (16 × 2) = 46Empirical formula mass: 14 + 16 = 30Empirical formula mass: 14 × 16 × 2 = 448

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Turn masses into atoms, then tidy the ratio until it's as simple as it can be.

What you need to know

A molecular formula shows the actual number of atoms of each element in one molecule, like C2H6 for ethane.
An empirical formula is the simplest whole-number ratio of atoms or ions, and every substance has one.
H2O can't be reduced any further, so its empirical and molecular formulae match. Ethane's C2H6 reduces to CH3.
Have a goMaya says the empirical formula of C4H8 is just C4H8, because 'it's already a formula'. Is she right?
No. Divide both numbers by 4 and you get CH2.
A formula only stays the same when its numbers can't be reduced, like H2O. C4H8 is a 4 : 8 ratio, and that simplifies to 1 : 2.
Given masses or percentages, divide each by that element's relative atomic mass, using the periodic table.
Then divide every answer by the smallest one. That gives a unitary ratio, where at least one value is 1.
Have a goAfter dividing by relative atomic masses, a compound gives carbon 0.3 and hydrogen 0.9. What do you do next, and what ratio do you get?
Divide both by the smallest, 0.3: carbon 1, hydrogen 3.
Dividing by the smallest value is what forces at least one value to be exactly 1, giving the unitary ratio.
Values very close to whole numbers can be rounded. A value of roughly a half means multiply everything by 2: Fe 1 : O 1.5 becomes Fe2O3.
Have a goA unitary ratio comes out as nitrogen 1 : oxygen 2.5. Rounding 2.5 up to 3 sounds tidy. What should you do instead?
Multiply both by 2 to get N 2 : O 5, so N2O5.
2.5 isn't close to a whole number, so rounding would change the ratio. Multiplying every value by the same number keeps it.
Ones are never written in a formula: one calcium to one oxygen is CaO, not Ca1O1.
For an ionic substance, the ion charges must add up to zero. Two Na⁺ balance one O²⁻, so sodium oxide is Na2O.
Given a model, count the atoms of each element and divide by their highest common factor. Glucose's 6 : 12 : 6 gives CH2O.
To get a molecular formula, divide the relative formula mass by the empirical formula mass, then multiply every subscript by the answer.

The big picture

An empirical formula is the simplest whole-number ratio of atoms or ions. From masses or percentages you divide by relative atomic mass, divide by the smallest, then round or multiply to get whole numbers. Ionic formulae come from balancing charges, and models from counting atoms. A molecular formula is the empirical formula multiplied up using the relative formula mass.

Key points

1An empirical formula is the simplest whole-number ratio. A molecular formula is the actual number of atoms in a molecule. Sometimes they match, as in H2O.

2From masses or percentages: divide by relative atomic mass, divide by the smallest, round or multiply to whole numbers, then write the formula without ones.

3Ionic substances: the charges add up to zero. A model: divide the atom counts by their highest common factor.

4Molecular formula = empirical formula with every subscript multiplied by (relative formula mass ÷ empirical formula mass).

.we-_R_18slubsnpfiv5ubrb_ [data-we-step]{display:flex !important}.we-_R_18slubsnpfiv5ubrb_ [data-we-solution]{display:block !important}.we-_R_18slubsnpfiv5ubrb_ [data-we-reveal]{display:none !important}

Worked example

Problem

A compound of carbon and hydrogen only is 85.7% carbon and 14.3% hydrogen by mass. Find its empirical formula. (Relative atomic masses: C = 12, H = 1.)

⚠ Watch out

Rounding 1.5 to 2 (or to 1) because it's 'close enough'. A half isn't close to a whole number. Multiply every value by 2 instead, so the ratio stays the same.

🧠

Memory hook

Three moves: divide by Ar, divide by the smallest, make it whole. Then drop the ones. Ar always goes first because atoms weigh different amounts.

✓

Check yourself

Try this cold: 4.8 g of magnesium reacts with 3.2 g of oxygen (Mg = 24, O = 16). Find the empirical formula, then say how you decided between rounding and multiplying.

Flashcards

(13)

What does a molecular formula show?

The actual number of atoms of each element in one molecule. Ethane's is C2H6.

What is an empirical formula?

The simplest whole-number ratio of atoms or ions in a substance. Every substance has one.

Why is water's empirical formula the same as its molecular formula?

H2O cannot be reduced any further, so the simplest ratio and the actual count are identical.

What is the empirical formula of ethane, C2H6?

CH3, because C2H6 reduces to a 1 : 3 ratio.

Butane has the empirical formula C2H5. What is its molecular formula?

C4H10, the actual number of atoms in a butane molecule.

Empirical formula from masses or percentages: what is step one?

Divide each mass or percentage by the relative atomic mass of that element.

What is step two, and what does it give you?

Divide every answer from step one by the smallest. The result is a unitary ratio, with at least one value equal to 1.

A unitary ratio has a value close to a whole number, or one that is roughly a half. What now?

Close to whole: round it. Roughly a half: multiply every value by 2. Fe 1 : O 1.5 becomes Fe2O3.

Why is a formula never written as Ca1O1?

Ones are not written in formulae. One calcium to one oxygen is CaO.

How do you find the empirical formula of an ionic substance?

Balance the ion charges so they add up to zero. Two Na⁺ cancel one O²⁻, giving Na2O.

You are given a model of a substance. How do you get its empirical formula?

Count the atoms of each element, then divide all the numbers by their highest common factor.

What is the relative formula mass of a substance?

The sum of the relative atomic masses of all the atoms in its formula.

How do you find a molecular formula from the empirical formula and the relative formula mass?

Find the empirical formula mass, divide the relative formula mass by it to get the multiplier, then multiply every subscript by the multiplier.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

Learning with Lightbulb is opening soon

You can use this lesson now. Join the waitlist and we'll let you know when the full Lightbulb experience is ready.

Keep me posted

Where does the formula of sodium oxide come from?

Sort the formulae

Find the molecular formula

More Edexcel GCSE Chemistry topics