The mole and the Avogadro constant

· Mole (mol) = the SI unit for amount of substance.
· 1 mole contains exactly 6.02214076 × 10²³ elementary entities.
· This number is the Avogadro constant, usually written as L or N_A.
· For CIE calculations, use L = 6.02 × 10²³ mol⁻¹ unless a different value is given.
· Elementary entities can be atoms, molecules, ions, electrons or formula units.
· Always state the entity clearly: e.g. 1 mol of H₂ molecules is not the same as 1 mol of H atoms.

This diagram helps students visualise the mole as a counting unit linked to a fixed number of particles. It is useful for showing why 1 mol represents a very large number of atoms. Source

Using the Avogadro constant

· Core relationship: number of particles = amount in mol × Avogadro constant.
· Symbol form: N = nL or N = nN_A.
· Rearranged form: n = N ÷ L.
· N = number of particles; n = amount of substance in mol; L / N_A = 6.02 × 10²³ mol⁻¹.
· If n increases, N increases proportionally because L is constant.
· In exam answers, use standard form for very large particle numbers.

Particle conversions

· To convert mol → particles, multiply by 6.02 × 10²³.
· To convert particles → mol, divide by 6.02 × 10²³.
· Example: 0.500 mol of atoms = 0.500 × 6.02 × 10²³ = 3.01 × 10²³ atoms.
· Example: 1.204 × 10²⁴ molecules ÷ 6.02 × 10²³ = 2.00 mol of molecules.
· Keep the particle type in the answer: atoms, molecules, ions, electrons or formula units.
· Check powers of 10 carefully: answers are often around 10²²–10²⁴ particles.

Common exam traps

· Do not write “moles of atoms” if the question asks for molecules or ions.
· 1 mol of O₂ molecules contains 6.02 × 10²³ O₂ molecules but 1.204 × 10²⁴ O atoms.
· 1 mol of NaCl formula units contains 6.02 × 10²³ Na⁺ ions and 6.02 × 10²³ Cl⁻ ions.
· The Avogadro constant has units mol⁻¹; the number of particles has no unit but must name the entity.
· Give answers to an appropriate number of significant figures, usually matching the data given.

This figure shows that 1 mol of different elements contains the same number of atoms, but the masses are different. It helps students avoid the misconception that equal moles must have equal masses. Source