Everything in mole calculations passes through the mole. Convert to moles first, then convert out to the quantity the question wants: mass, number of particles or volume.
This lesson is part of moles, formulas and equations. It prepares you for reacting-mass and gas-volume calculations.
What is the route between mass, moles and particles?
Moles sit in the middle. Mass ÷ molar mass gives moles, and moles × 6.02 × 10²³ gives the number of particles.
| Start | Step | Result |
|---|---|---|
| Mass in g | ÷ molar mass (g mol⁻¹) | moles |
| Moles | × 6.02 × 10²³ | number of particles |
| Number of particles | ÷ 6.02 × 10²³ | moles |
| Moles | × molar mass | mass in g |
You never jump straight from mass to particles. Go through moles every time.
Worked example: molecules and atoms in water
How many molecules, and how many atoms, are in 9.0 g of water? (H = 1, O = 16.)
- Molar mass of H₂O = 2 × 1 + 16 = 18 g mol⁻¹.
- Moles = 9.0 ÷ 18 = 0.50 mol.
- Molecules = 0.50 × 6.02 × 10²³ = 3.01 × 10²³.
- Each molecule has 3 atoms, so atoms = 3 × 3.01 × 10²³ = 9.03 × 10²³.
The question asked for two different things, and the final multiplication by 3 is where students lose the second mark.
Working backwards from a count
How many grams are there in 2.41 × 10²³ atoms of magnesium? (Mg = 24.)
Moles = 2.41 × 10²³ ÷ 6.02 × 10²³ = 0.400 mol. Mass = 0.400 × 24 = 9.60 g.
Here the particles are already atoms, so no extra multiplication is needed. Reading what the particle is decides the last step.
The mistake that costs marks
A common slip is to stop at molecules when the question asks for atoms, or to give the atom count when it asks for molecules. Another is to divide by 6.02 × 10²³ when you should multiply.
| Question | Wrong answer | Why | Right answer |
|---|---|---|---|
| Atoms in 0.50 mol H₂O | 3.01 × 10²³ | Stopped at molecules | 9.03 × 10²³ |
| Molecules in 0.50 mol H₂O | 9.03 × 10²³ | Counted atoms | 3.01 × 10²³ |
| Mass of 2.41 × 10²³ Mg atoms | 14.4 g | Used 0.60 mol | 9.60 g |
Write the particle type beside each number, such as “0.50 mol of molecules”, and the confusion goes away. The mole and stoichiometry steps tool lets you check each conversion.
Check yourself
Find the mass of 0.25 mol of carbon dioxide, then the number of molecules and the total number of atoms. (C = 12, O = 16.)
Answer
Molar mass of CO₂ = 12 + 2 × 16 = 44 g mol⁻¹. Mass = 0.25 × 44 = 11 g.
Molecules = 0.25 × 6.02 × 10²³ = 1.505 × 10²³, which rounds to 1.51 × 10²³.
Each CO₂ molecule has 3 atoms, so atoms = 3 × 1.505 × 10²³ = 4.515 × 10²³, or 4.52 × 10²³.
What to study next
Go on to finding empirical and molecular formulas, where mass ratios become mole ratios. Then test yourself with the moles practice set.
If you want a teacher to go through these conversions with your own questions, see online one-to-one Chemistry tuition.