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 containing 6.022 140 76 × 10²³ entities (atoms, molecules, ions, electrons). This number is Avogadro's constant, written Nₐ. In practice, 6.022 × 10²³ is used.
Why this exact value? Since the 2019 redefinition of the International System of Units, it is no longer derived from anything: Nₐ is fixed by definition, exactly like the speed of light. It defines the mole, not the other way round.
Historically, the mole was defined as the number of atoms in 12 g of carbon-12. That older definition remains an excellent approximation — one mole of ¹²C weighs 11.999 999 996 g — but it is no longer the official one.
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.
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