What is a mole?
Atoms and molecules are too small to count one by one, so chemists group them into a package called the mole. One mole of any substance contains the same number of particles as there are atoms in 12 g of carbon-12. That number is the Avogadro constant, NA = 6.02 × 1023 per mole.
Key idea
Number of moles = mass (g) ÷ molar mass (g mol−1)
Number of particles = moles × 6.02 × 1023
Volume of gas = moles × molar volume (24 dm³ at room conditions; 22.4 dm³ at s.t.p.)
Molar mass and molar volume
The molar mass is the mass of one mole, numerically equal to Ar or Mr but with units g mol−1. So one mole of water (Mr = 18) has a mass of 18 g. For gases, one mole occupies the same volume at the same temperature and pressure — the molar volume — regardless of the type of gas.
Worked example
How many moles are in 8 g of methane, CH4? (Ar: C = 12, H = 1)
Molar mass = 12 + (4 × 1) = 16 g mol−1.
Moles = 8 ÷ 16 = 0.5 mol.
Number of molecules = 0.5 × 6.02 × 1023 = 3.01 × 1023.
Volume at room conditions = 0.5 × 24 = 12 dm³.
Moving between quantities
Always convert to moles first — moles are the central hub linking mass, particles and gas volume. Sketch the three-way triangle in your working so you never divide when you should multiply.
Remember
- 1 mole = 6.02 × 1023 particles.
- Molar mass in g mol−1 equals Ar or Mr.
- 1 mole of any gas = 24 dm³ at room conditions.