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5.3.2.1Moles (HT only)

AQA GCSE Combined Science (8464), Higher tier · Chemistry › Quantitative chemistry › Use of amount of substance in relation to masses of pure

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Chemists measure amounts of substances in moles. One mole of any substance contains 6.02 × 1023 particles, and its mass in grams equals its relative formula mass. This subtopic is Higher tier only, and moles = mass ÷ Mr is used in almost every harder calculation.

Grade by grade

What you need to be able to do, from the first marks up to the top grade.

  1. 5
    State what one mole containsOne mole of any substance contains 6.02 × 1023 particles (the Avogadro constant).
  2. 5
    Recall the mass of one moleThe mass of one mole in grams equals the Ar or Mr, e.g. 1 mol of H2O has a mass of 18 g.
  3. 6
    Calculate moles from massmoles = mass (g) ÷ Mr.
  4. 7
    Calculate mass from molesmass (g) = moles × Mr.
  5. 8
    Calculate numbers of particlesnumber of particles = moles × 6.02 × 1023.
  6. 9
    Find Mr from mass and molesMr = mass ÷ moles, then use it to identify a substance or element.

Notes

What a mole is

  • Chemical amounts are measured in moles. The symbol for the unit is mol.
  • One mole of any substance contains the same number of particles (atoms, molecules or ions): 6.02 × 1023. This number is the Avogadro constant.
  • So 1 mol of carbon atoms (C) contains the same number of particles as 1 mol of carbon dioxide molecules (CO2).
  • The mass of one mole of a substance in grams is numerically equal to its Ar or Mr: 1 mol of Na = 23 g, and 1 mol of NaCl = 58.5 g.

Moles, mass and Mr

  • moles = mass (g) ÷ Mr
  • Rearranged: mass = moles × Mr, and Mr = mass ÷ moles.
  • Example: 11 g of CO2 (Mr 44) is 11 ÷ 44 = 0.25 mol.
  • Example: 0.40 mol of NaOH (Mr 40) has a mass of 0.40 × 40 = 16 g.
  • The mass must be in grams: multiply kilograms by 1000 first.

Numbers of particles

  • number of particles = moles × 6.02 × 1023
  • Example: 0.50 mol of water contains 0.50 × 6.02 × 1023 = 3.01 × 1023 molecules.
  • Each water molecule has 3 atoms, so the same sample contains 3 × 3.01 × 1023 = 9.03 × 1023 atoms.
  • Enter the Avogadro constant with your calculator's ×10x (or EXP) key.

Cheatsheet

  • 1 mole = 6.02 × 1023 particles (the Avogadro constant)
  • Mass of 1 mol in grams = Ar or Mr
  • moles = mass (g) ÷ Mr
  • mass (g) = moles × Mr
  • Mr = mass ÷ moles
  • number of particles = moles × 6.02 × 1023
  • Unit of amount of substance: mol

How to answer each type of question

Calculate the number of moles in a mass

2 marks6
  1. Work out or read the Mr.
  2. Divide the mass in grams by the Mr.
  3. Give the unit, mol.

Example. Calculate the amount, in moles, of calcium carbonate in 7.50 g.
Relative formula mass (Mr): CaCO3 = 100 [2 marks]

Show the model answer
7.50 ÷ 100 (1)
= 0.0750 mol (1)

Calculate the mass of an amount in moles

2 to 3 marks7
  1. Work out the Mr from the Ar values.
  2. Multiply the number of moles by the Mr.
  3. Give the unit, g.

Example. Calculate the mass of 0.150 mol of magnesium sulfate, MgSO4.
Ar: O = 16; Mg = 24; S = 32 [3 marks]

Show the model answer
Mr = 24 + 32 + (4 × 16) = 120 (1)
mass = 0.150 × 120 (1)
= 18.0 g (1)

Explain why samples contain the same number of particles

2 marks7
  1. Work out the number of moles in each sample.
  2. Say that equal numbers of moles contain equal numbers of particles (6.02 × 1023 per mole).

Example. A student has 24 g of magnesium and 40 g of calcium.
Explain why both samples contain the same number of atoms.
Ar: Mg = 24; Ca = 40 [2 marks]

Show the model answer
Each sample is 1 mol (24 ÷ 24 = 1 and 40 ÷ 40 = 1) (1). One mole of any element contains the same number of atoms, 6.02 × 1023 (1).

Calculate the number of particles

3 marks8
  1. Convert the mass to moles: mass ÷ Mr.
  2. Multiply the moles by 6.02 × 1023.
  3. If the question asks for atoms, multiply by the number of atoms in one formula.
  4. Give the answer in standard form.

Example. Calculate the number of molecules in 8.8 g of carbon dioxide.
Mr: CO2 = 44
The Avogadro constant is 6.02 × 1023 per mole. [3 marks]

Show the model answer
moles = 8.8 ÷ 44 = 0.20 mol (1)
molecules = 0.20 × 6.02 × 1023 (1)
= 1.20 × 1023 (1)

Identify a substance from its mass and amount

3 marks9
  1. Find the Mr: mass ÷ moles.
  2. Subtract the parts of the formula you know.
  3. Divide by the number of unknown atoms and match the Ar to an element.

Example. 0.250 mol of a Group 1 metal carbonate, M2CO3, has a mass of 34.5 g.
Identify metal M.
Ar: C = 12; O = 16 [3 marks]

Show the model answer
Mr = 34.5 ÷ 0.250 = 138 (1)
2 × Ar of M = 138 − (12 + 3 × 16) = 78, so Ar of M = 39 (1)
M is potassium (1)

Shortcuts and memory tricks

  • Formula triangle: mass on top, moles × Mr underneath. Cover the one you want.
  • Sense check: a few grams of a substance with an Mr near 100 is well under 1 mol.
  • Moles to particles: multiply by 6.02 × 1023. Particles to moles: divide. A number of particles is always enormous.
  • Keep unrounded values in your calculator (use ANS) and round only at the end.

Where marks are lost

  • Dividing the Mr by the mass instead of the mass by the Mr.
  • Using a mass in kg or mg instead of grams.
  • Mixing up molecules and atoms: 1 mol of O2 has 6.02 × 1023 molecules but twice as many atoms.
  • Writing 6.0223 instead of 6.02 × 1023, or typing it into the calculator wrongly.
  • Rounding the number of moles too early, which makes the final answer wrong.

Exam technique

  • Write the equation you are using (e.g. moles = mass ÷ Mr) before putting numbers in.
  • Give very large or very small answers in standard form, to the significant figures asked for.
  • Include units: mol for amount and g for mass. Mr has no unit.
  • If the question gives you an Mr, use it rather than working it out again.

Quick recall

Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.

Calculate the number of moles in 8.8 g of carbon dioxide.
Mr of CO2 = 44
0.2 mol
Chemical amounts are measured in moles.
Relative atomic masses (Ar): C = 12, O = 16 Give the symbol for the unit mole.
mol

Sample questions

Written for this site in the style of AQA exam questions. They are not taken from real past papers.

Question 1Easy5 marks
The number of moles of a substance can be calculated using the equation:
number of moles = mass in g ÷ relative formula mass (Mr)
(a) Calculate the number of moles in 8.8 g of carbon dioxide.
Mr of CO2 = 44[2]
(b) Calculate the mass of 0.25 mol of sodium hydroxide.
Mr of NaOH = 40[2]
(c) Complete the sentence.
The mass of one mole of a substance in grams is numerically equal to its ....................[1]
Show the answer and mark scheme
(a) Answer: 0.2 mol
  • 8.8 ÷ 44
  • 0.2 (mol)
(b) Answer: 10 g
  • 0.25 × 40
  • 10 (g)
(c) Answer: relative formula mass (Mr)
  • relative formula mass / Mr
Question 2Medium7 marks
The Avogadro constant is 6.02 × 1023 per mole.
Relative atomic masses (Ar): C = 12, O = 16, Mg = 24
(a) How many atoms are there in 0.500 mol of magnesium?[1]
(b) Calculate the number of molecules in 13.2 g of carbon dioxide.
Give your answer in standard form to 3 significant figures.[2]
(c) Calculate the mass of 3.01 × 1022 atoms of carbon.[2]
(d) A student said: 'One mole of carbon dioxide contains 6.02 × 1023 atoms.'
Explain why the student is wrong.[2]
Show the answer and mark scheme
(a) Answer: 3.01 × 1023
  • 3.01 × 1023
(b) Answer: 1.81 × 1023
  • moles of CO2 = 13.2 ÷ 44 = 0.3
  • 0.3 × 6.02 × 1023 = 1.81 × 1023
(c) Answer: 0.6 g
  • moles = 3.01 × 1022 ÷ 6.02 × 1023 = 0.05
  • 0.05 × 12 = 0.6 (g)
(d)
  • one mole of CO2 contains 6.02 × 1023 molecules
  • each molecule contains 3 atoms, so there are 3 × 6.02 × 1023 / 1.806 × 1024 atoms
Question 3Hard6 marks
The Avogadro constant is 6.02 × 1023 per mole.
Relative atomic masses (Ar): H = 1, O = 16, S = 32
(a) Calculate the number of oxygen atoms in 4.90 g of sulfuric acid, H2SO4.
Give your answer in standard form to 3 significant figures.[3]
(b) Calculate the mass of sulfuric acid that contains 3.01 × 1023 hydrogen atoms.[3]
Show the answer and mark scheme
(a) Answer: 1.20 × 1023
  • moles of H2SO4 = 4.90 ÷ 98 = 0.05
  • moles of oxygen atoms = 0.05 × 4 = 0.2
  • 0.2 × 6.02 × 1023 = 1.20 × 1023
(b) Answer: 24.5 g
  • moles of H atoms = 3.01 × 1023 ÷ 6.02 × 1023 = 0.5
  • moles of H2SO4 = 0.5 ÷ 2 = 0.25
  • 0.25 × 98 = 24.5 (g)

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