The mole — chemistry's counting unit (HT)
Atoms and molecules are too small to count individually. Chemists use the mole to refer to a fixed, very large number of particles, just like a "dozen" means 12.
The mole and Avogadro's constant
One mole of any substance contains 6.02 × 10²³ particles of that substance — this number is Avogadro's constant (N_A).
- 1 mole of carbon atoms = 6.02 × 10²³ C atoms.
- 1 mole of water molecules = 6.02 × 10²³ H₂O molecules.
- 1 mole of NaCl formula units = 6.02 × 10²³ NaCl pairs (1 mole Na⁺ + 1 mole Cl⁻).
The link between mass and moles
The mass of one mole of any substance equals its A_r or M_r in grams.
- 1 mole of carbon = 12 g.
- 1 mole of water = 18 g.
- 1 mole of CO₂ = 44 g.
This gives the master equation:
moles = mass ÷ M_r (or A_r for elements)
Equivalently:
- mass = moles × M_r
- M_r = mass ÷ moles
✦Worked example— Worked examples
Example 1 — moles from mass
How many moles in 88 g of CO₂? (M_r = 44)
moles = 88 ÷ 44 = 2 mol
Example 2 — mass from moles
What mass is 0.25 mol of NaOH? (M_r = 40)
mass = 0.25 × 40 = 10 g
Example 3 — number of particles
How many molecules in 36 g of water?
- moles = 36 ÷ 18 = 2 mol
- molecules = 2 × 6.02 × 10²³ = 1.204 × 10²⁴
Example 4 — atoms from moles
How many oxygen atoms are in 1 mole of H₂O?
Each H₂O molecule contains 1 O atom. 1 mole H₂O = 6.02 × 10²³ molecules → 6.02 × 10²³ O atoms.
For 1 mole of CO₂: each molecule has 2 O atoms → 2 × 6.02 × 10²³ = 1.204 × 10²⁴ O atoms.
Why moles matter
The mole is the counting unit for chemistry: balanced equations describe mole ratios. So the mole is the bridge between the equation and any laboratory mass measurement.
For 2H₂ + O₂ → 2H₂O, the equation says "2 moles of H₂ react with 1 mole of O₂ to make 2 moles of H₂O" — those ratios let you turn any mass into the right amount of any other substance.
⚠Common mistakes
- Forgetting to divide by M_r when given a mass. moles = mass ÷ M_r, not mass × M_r.
- Wrong M_r — count atoms inside brackets correctly.
- Using Avogadro for moles, not number. Avogadro's constant converts between moles and number of particles, not between mass and moles.
- Mixing up atoms and molecules. Always state which kind of particle is the answer.
Links
Foundation for C3.5 (mole ratios), C3.6 (limiting reactants), C3.7 (concentration in mol/dm³), C3.8 (atom economy and yield), C3.9 (gas volumes).
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