IB Chemistry — Structure 1.4: The Mole

This sub-topic is examined identically at SL and HL. The mole is the chemist's counting unit: one mole is 6.02 × 10²³ particles (the Avogadro constant, N_A). Because we can't count atoms directly, we count them by mass. Use the live calculators to see how mass, moles and particles connect.

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1. Mass ⇄ moles ⇄ particles S1.4.1–3

Molar mass (M) is the mass of one mole in g mol⁻¹ — numerically equal to the relative formula mass M_r. The key relationships: moles = mass ÷ M and particles = moles × N_A. Set a molar mass, then type any value below:

Live mole converter

Molar mass M (g mol⁻¹)

Mass (g)

Amount (mol)

Particles

moles = mass ÷ M · particles = moles × 6.02×10²³

2 mol of H₂O (M = 18) = 36 g = 1.20×10²⁴ molecules

2. Empirical & molecular formulae S1.4.4

The empirical formula is the simplest whole-number ratio of atoms; the molecular formula is the actual number. To find the empirical formula: turn each element's mass (or %) into moles by dividing by its A_r, then divide all by the smallest. Try it (the preset is 40.0% C, 6.7% H, 53.3% O):

Empirical formula finder

Element
Mass or %
Aᵣ
÷ smallest

—

CH₂Omoles → simplest ratio

3. Molar concentration S1.4.5

Concentration is amount of solute per volume of solution: c = n ÷ V, where V is in dm³ (1 dm³ = 1000 cm³) and c is in mol dm⁻³. Type any two values:

Concentration calculator · c = n ÷ V

Amount n (mol)

Volume V (dm³)

Concentration (mol dm⁻³)

0.5 mol ÷ 0.25 dm³ = 2 mol dm⁻³

4. Avogadro's law & gas volumes S1.4.6

Avogadro's law: equal volumes of all gases, at the same temperature and pressure, contain equal numbers of molecules. So for gases you can use volume ratios directly as mole ratios. At STP (273.15 K, 100 kPa) one mole of any ideal gas occupies 22.7 dm³ (the molar volume, V_m).

Same volume, same temperature and pressure → same number of molecules, whatever the gas. Their masses differ (different molar masses), but the count is equal.

Common mistakes examiners see

How do you convert mass to moles?✗ moles = mass × molar mass. ✓ moles = mass ÷ molar mass (n = m ÷ M).

Volume for concentration should be in…✗ cm³. ✓ dm³ for mol dm⁻³. Convert cm³ → dm³ by dividing by 1000 (250 cm³ = 0.250 dm³).

Is the empirical formula the same as the molecular formula?✗ Always yes. ✓ Not always. Empirical = simplest ratio (CH₂O); molecular = actual (e.g. glucose C₆H₁₂O₆ = 6 × CH₂O). They're equal only when the ratio can't be simplified.

Equal masses of two gases occupy equal volumes?✗ Yes. ✓ No — equal moles (not equal masses) give equal volumes at the same T and P (Avogadro's law).

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Counting Particles: The Mole