The mole and the Avogadro constant

AS Level Chemistry · Atoms, molecules and stoichiometry. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

The mole is the chemist's counting unit. One mole of a substance contains 6.02 × 1023 particles. This number is the Avogadro constant, L.

You must always say which particles you are counting: atoms, molecules, ions or electrons. One mole of O2 molecules contains two moles of oxygen atoms.

The mass of one mole of a substance in grams is equal to its Ar or Mr. This links the mass you can weigh to the number of particles you cannot see. Most questions take two steps: mass to moles, then moles to particles.

Rules to remember

Common mistake

Students stop at the number of molecules when the question asks for atoms or ions. Multiply by the number of those particles in one formula unit.

Worked example

How many atoms are there in 3.40 g of ammonia, NH3? (Mr = 17.0, L = 6.02 × 1023 mol−1)

  1. Moles of NH3 = 3.40 ÷ 17.0 = 0.200 mol.
  2. Each molecule has 4 atoms, so moles of atoms = 0.200 × 4 = 0.800 mol.
  3. Number of atoms = 0.800 × 6.02 × 1023 = 4.82 × 1023.

Answer: 4.82 × 1023 atoms.

Practice questions

Try each one, then open the answer.

1. Which sample contains the same number of atoms as 2.0 g of hydrogen gas, H2?

  1. A
    12.0 g of carbon
  2. B
    16.0 g of oxygen gas, O2
  3. C
    17.0 g of ammonia, NH3
  4. D
    32.0 g of oxygen gas, O2
Show answer

Answer: D. 2.0 g of H2 is 1.0 mol of molecules = 2.0 mol of atoms, and 32.0 g of O2 is also 2.0 mol of atoms. 12.0 g of C and 16.0 g of O2 contain 1.0 mol of atoms; 17.0 g of NH3 contains 4.0 mol.

2. How many hydrogen atoms are there in 4.60 g of ethanol, C2H5OH? (L = 6.02 × 1023 mol−1)

  1. A
    3.01 × 1023
  2. B
    3.61 × 1023
  3. C
    6.02 × 1022
  4. D
    5.42 × 1023
Show answer

Answer: B. Mr = 46.0, so 4.60 g is 0.100 mol. Each molecule has six H atoms (five on carbon, one on oxygen): 0.600 × 6.02 × 1023 = 3.61 × 1023.

3. How many ions in total are present in 0.100 mol of calcium chloride, CaCl2? (L = 6.02 × 1023 mol−1)

  1. A
    6.02 × 1022
  2. B
    1.20 × 1023
  3. C
    1.81 × 1023
  4. D
    3.61 × 1023
Show answer

Answer: C. Each CaCl2 contains one Ca2+ and two Cl− ions, so there are 0.100 × 3 = 0.300 mol of ions; 0.300 × 6.02 × 1023 = 1.81 × 1023.

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