Atomic mass, molecular mass and the mole

Atoms are far too light to weigh in grams conveniently, so we compare them with a standard. One atomic mass unit is defined as exactly 1/12 of the mass of one carbon-12 atom: 1 amu = 1.66056 × 10⁻²⁴ g. Today 'amu' is written 'u' (unified mass).

Most elements are a mixture of isotopes: atoms of the same element with different masses (hydrogen has three). So the average atomic mass weights each isotope by how common it is (its abundance). For carbon: 0.98892 × 12 + 0.01108 × 13.00335 + … = 12.011 u. That is why atomic masses in the periodic table are rarely whole numbers.

Molecular mass is the sum of the atomic masses of the atoms in a molecule. Water, H₂O = 2 × 1.008 + 16.00 = 18.02 u. Ionic solids such as NaCl do not exist as separate molecules, so we speak of their formula mass (NaCl = 23.0 + 35.5 = 58.5 u).

Chemists count particles in moles. One mole contains exactly 6.02214076 × 10²³ particles (atoms, molecules or ions). This number is the Avogadro constant, Nₐ. A mole is like a dozen: a dozen always means 12, and a mole always means 6.022 × 10²³.

The beauty of the mole: the molar mass in grams per mole is numerically equal to the atomic, molecular or formula mass in u. Water is 18.02 u, so one mole of water has a mass of 18.02 g.

Two simple formulas link everything:

• Moles = mass ÷ molar mass. So 36 g of water is 36 ÷ 18 = 2 mol.
• Number of particles = moles × 6.022 × 10²³. So 2 mol of water contains 2 × 6.022 × 10²³ = 1.204 × 10²⁴ molecules.