You cannot count atoms one by one — there are far too many in even the smallest sample. Chemists invented a dedicated unit: the mole.
Definition of the mole
One mole is the amount of substance that contains exactly 6.022 × 10²³ entities (atoms, molecules, ions, electrons). This number is Avogadro's constant, written Nₐ.
Why this exact value? Because it bridges the microscopic world (individual atoms) to the macroscopic world (measurable grams). It is defined so that:
1 mole of carbon-12 atoms weighs exactly 12 grams.
Molar mass
The molar mass M of a species is the mass of one mole of that species. It is given in g/mol.
For an atom, M is numerically equal to the relative atomic mass on the periodic table:
- M(H) = 1.008 g/mol
- M(C) = 12.01 g/mol
- M(O) = 16.00 g/mol
- M(Fe) = 55.85 g/mol
For a molecule, sum the atomic molar masses:
- M(H₂O) = 2 × 1.008 + 16.00 = 18.02 g/mol
- M(CO₂) = 12.01 + 2 × 16.00 = 44.01 g/mol
- M(C₆H₁₂O₆) = 6 × 12.01 + 12 × 1.008 + 6 × 16.00 = 180.16 g/mol
The central relation
Three quantities are linked by the formula:
n = m / M
where: - n: amount of substance (mol) - m: mass (g) - M: molar mass (g/mol)
It is one of the formulas you will use the most in high school.
Example
How many moles in 9.0 g of water?
n = m / M = 9.0 / 18.02 ≈ 0.50 mol.
That is about 3.0 × 10²³ water molecules. Three hundred thousand billion billion. For just 9 g.
Why it matters
The mole is what makes stoichiometry possible: predicting how many moles of B you obtain from so many moles of A in a reaction. Without the mole, chemistry would only be qualitative. With it, chemistry becomes a predictive science.