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WASSCE Chemistry · The Mole Concept

The mole, molar mass and the Avogadro constant

By the WASSCE Tutor team

Updated 12 November 2026 · 7 min read · Prepared against the WASSCE syllabus.

Atoms are far too small to count one by one, so chemists count them in huge, fixed batches, just as traders count kola nuts by the hundred or eggs by the crate. The chemist's batch is the mole. Almost every calculation in WASSCE Chemistry passes through it, so this lesson is worth mastering.

Learning objectives

By the end of this lesson you should be able to:

  • define the mole and the Avogadro constant
  • calculate relative molecular mass and relative formula mass
  • define molar mass and convert between mass and moles
  • convert between moles and numbers of particles
  • use the mole "bridge" to move between quantities

The mole and the Avogadro constant

Definition
  • A mole is the amount of substance that contains as many particles (atoms, molecules, ions or electrons) as there are atoms in exactly 12 g of carbon-12.
  • That number is the Avogadro constant, L=6.02×1023L = 6.02 \times 10^{23} particles per mole.

One mole of anything contains 6.02×10236.02 \times 10^{23} particles:

  • 1 mol of carbon atoms = 6.02×10236.02 \times 10^{23} C atoms
  • 1 mol of water molecules = 6.02×10236.02 \times 10^{23} H₂O molecules
  • 1 mol of sodium chloride contains 6.02×10236.02 \times 10^{23} Na⁺ ions and 6.02×10236.02 \times 10^{23} Cl⁻ ions

Always say which particle you mean: one mole of oxygen atoms (O) is not the same as one mole of oxygen molecules (O₂).

Relative molecular mass and formula mass

  • Relative molecular mass (Mᵣ): the sum of the relative atomic masses of all the atoms in a molecule.
  • Relative formula mass: the same idea for ionic compounds, which have no molecules.
Worked example

Using H = 1, C = 12, O = 16, Na = 23, S = 32, Ca = 40, Cu = 64:

SubstanceWorkingMᵣ
H₂O2(1) + 1618
CO₂12 + 2(16)44
H₂SO₄2(1) + 32 + 4(16)98
CaCO₃40 + 12 + 3(16)100
Na₂CO₃2(23) + 12 + 3(16)106
CuSO₄·5H₂O64 + 32 + 4(16) + 5(18)250

Molar mass

Definition

The molar mass (M) of a substance is the mass of one mole of it, in g/mol (g mol⁻¹). It is numerically equal to the relative atomic, molecular or formula mass.

So the molar mass of water is 18 g/mol, of CO₂ 44 g/mol, of CaCO₃ 100 g/mol.

n=mMmoles=mass (g)molar mass (g/mol)n = \dfrac{m}{M} \qquad \text{moles} = \dfrac{\text{mass (g)}}{\text{molar mass (g/mol)}}
n=mMmoles=mass (g)molar mass (g/mol)\begin{gathered}n = \dfrac{m}{M} \\[6pt] \begin{aligned}&\text{moles} \\ &= \dfrac{\text{mass (g)}}{\text{molar mass (g/mol)}}\end{aligned}\end{gathered}
Worked example

Mass and moles.

  1. How many moles are in 25 g of calcium carbonate? n=25100=0.25n = \dfrac{25}{100} = 0.25 mol.
  2. What is the mass of 0.2 mol of sodium hydroxide, NaOH (M = 40)? m=n×M=0.2×40=8m = n \times M = 0.2 \times 40 = 8 g.
  3. 0.5 mol of a substance has a mass of 32 g. What is its molar mass? M=320.5=64M = \dfrac{32}{0.5} = 64 g/mol.

Moles and numbers of particles

N=n×Lnumber of particles=moles×6.02×1023N = n \times L \qquad \text{number of particles} = \text{moles} \times 6.02 \times 10^{23}
N=n×Lnumber of particles=moles×6.02×1023\begin{gathered}N = n \times L \\[6pt] \begin{aligned}&\text{number of particles} \\ &= \text{moles} \times 6.02 \times 10^{23}\end{aligned}\end{gathered}
Worked example

Counting particles.

  1. How many molecules are in 0.5 mol of water?
N=0.5×6.02×1023=3.01×1023 moleculesN = 0.5 \times 6.02 \times 10^{23} = 3.01 \times 10^{23} \text{ molecules}
N=0.5×6.02×1023=3.01×1023 molecules\begin{aligned}N &= 0.5 \times 6.02 \times 10^{23} \\ &= 3.01 \times 10^{23} \text{ molecules}\end{aligned}
  1. How many atoms are in that water? Each H₂O molecule has 3 atoms:
3×3.01×1023=9.03×1023 atoms3 \times 3.01 \times 10^{23} = 9.03 \times 10^{23} \text{ atoms}
3×3.01×1023=9.03×1023 atoms\begin{aligned}&3 \times 3.01 \times 10^{23} \\ &= 9.03 \times 10^{23} \text{ atoms}\end{aligned}
  1. What is the mass of 1.204×10241.204 \times 10^{24} carbon atoms?
n=1.204×10246.02×1023=2 molm=2×12=24 gn = \dfrac{1.204 \times 10^{24}}{6.02 \times 10^{23}} = 2 \text{ mol} \qquad m = 2 \times 12 = 24 \text{ g}
n=1.204×10246.02×1023=2 molm=2×12=24 g\begin{gathered}\begin{aligned}n &= \dfrac{1.204 \times 10^{24}}{6.02 \times 10^{23}} \\ &= 2 \text{ mol}\end{aligned} \\[6pt] m = 2 \times 12 = 24 \text{ g}\end{gathered}

The mole bridge

The mole at the centre: mass divided by molar mass gives moles; moles times the Avogadro constant gives particles; gas volume divided by 22.4 dm³ gives moles; concentration times volume gives moles

Figure 1. Every conversion passes through moles. WASSCE Tutor diagram.

To change one quantity into another, go through moles:

  • mass → moles (÷ M) → particles (× L)
  • mass → moles (÷ M) → gas volume (× 22.4 dm³) (next lesson)
  • concentration and volume → moles (C × V) → mass (× M) (next lesson)
Worked example

How many oxygen molecules are in 8 g of oxygen gas, O₂?

  1. Molar mass of O₂ = 32 g/mol.
  2. Moles: n=8÷32=0.25n = 8 \div 32 = 0.25 mol.
  3. Molecules: 0.25×6.02×1023=1.505×10230.25 \times 6.02 \times 10^{23} = 1.505 \times 10^{23}.
In Sierra Leone

A trader selling sugar by the cup does not count the grains; the cup is a fixed "batch". Chemists do the same with the mole. One mole of table sugar, C₁₂H₂₂O₁₁ (M = 342 g/mol), is about 342 g, roughly a cupful, and holds 6.02×10236.02 \times 10^{23} sugar molecules.

Common mistake

Do not use 16 for the molar mass of oxygen gas. Oxygen gas is O₂, so its molar mass is 32 g/mol. The same applies to H₂ (2), N₂ (28) and Cl₂ (71).

Key points

  • One mole contains 6.02 × 10²³ particles (the Avogadro constant), the number of atoms in 12 g of carbon-12.
  • Mᵣ = sum of the relative atomic masses in the formula; molar mass has the same number in g/mol.
  • n=m÷Mn = m \div M and N=n×LN = n \times L.
  • Always state the particle (atoms, molecules, ions) and use the right formula (O₂, not O).
  • Convert any quantity to moles first.

WASSCE examination focus

WAEC tests this

Expect to define the mole, to calculate Mᵣ (including hydrated salts), and to convert between mass, moles and numbers of particles. Questions often ask for the number of atoms or ions, not molecules, so read carefully and multiply by the number in the formula.

Quick check

  1. Calculate the relative molecular mass of ammonium nitrate, NH₄NO₃ (N = 14, H = 1, O = 16).
  2. How many moles are in 9.8 g of H₂SO₄?
  3. How many molecules are in 0.1 mol of carbon dioxide?
  4. What is the mass of 3.01 × 10²³ atoms of sodium (Na = 23)?

Answers:

  1. 14+4+14+48=8014 + 4 + 14 + 48 = 80.
  2. 9.8÷98=0.19.8 \div 98 = 0.1 mol.
  3. 0.1×6.02×1023=6.02×10220.1 \times 6.02 \times 10^{23} = 6.02 \times 10^{22} molecules.
  4. 0.5 mol × 23 = 11.5 g.

Keep going with the mole concept

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More lessons in The Mole Concept

  1. Molar volume of gases and concentration of solutions🔒

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