S1.4
Counting particles by mass: The mole
7 SL (SL 1.4.1-1.4.6)
Unverified
← View on the mapParent topic: Models of the particulate nature of matter
Guiding question
Guiding questionHow do we quantify matter on the atomic scale?
The one big idea
The mole is the bridge between the atomic scale and the laboratory bench. It converts the mass you can weigh into the number of particles that actually react, via the Avogadro constant.
What this rests on
Our editorial judgement.The dependencies in this section are this site’s own assessment of what a sub-topic rests on. They have notbeen verified by a chemistry teacher and are not part of the official IB guide. By contrast, section 8 (Linking questions) reproduces the IB’s own wording verbatim.
- EditorialS1.2 The nuclear atomRelative atomic mass and isotopic abundance need the nuclear atom.
What rests on this
- EditorialS1.5 Ideal gases
- EditorialS3.1 The periodic table: Classification of elements
- EditorialR1.1 Measuring enthalpy changes
- EditorialR2.1 How much? The amount of chemical change
- EditorialR2.2 How fast? The rate of chemical change
- EditorialR2.3 How far? The extent of chemical change
- EditorialR3.1 Proton transfer reactions
- EditorialR3.2 Electron transfer reactions
Core concepts that must be mastered
- The mole and the Avogadro constant(1.4.1)You cannot weigh a single atom, but you can weigh a mole of them. The mole is the SI unit of amount of substance: one mole contains the Avogadro number N_A ≈ 6.02 × 10²³ of elementary entities. An entity may be an atom, molecule, ion, electron, or any specified group — "one mole of O₂ molecules" and "one mole of O atoms" are different amounts. The mole is an amount, not a mass: one mole of hydrogen atoms weighs 1.008 g, one mole of lead atoms weighs 207.2 g. The relationship between amount n and number of entities N is N = n × N_A.
- Relative masses and molar mass(1.4.2, 1.4.3)Atomic masses are compared on the ¹²C scale, where ¹²C is assigned a mass of exactly 12. Relative atomic mass Ar and relative formula mass Mr are both dimensionless ratios — they have no units. Mr is the sum of the Ar values in a formula. Molar mass M has units of g mol⁻¹ and links mass to amount through n = m/M. Use data-booklet Ar values to 2 d.p. For H₂SO₄: Mr = 2(1.01) + 32.07 + 4(16.00) = 98.11, so M = 98.11 g mol⁻¹. The chain of conversions is: mass ⇄ moles ⇄ number of particles, with M as the link in one direction and N_A in the other.
- Empirical and molecular formulas(1.4.4)The empirical formula is the simplest whole-number ratio of atoms in a compound; the molecular formula is the actual count. To find the empirical formula from percentage composition: convert each percentage to moles (treat % as grams), divide by the smallest, and round to the nearest whole number. To find the molecular formula: divide the molar mass by the empirical formula mass to get the multiplier, then multiply the empirical formula by it. For example, a compound with 40.0% C, 6.7% H, 53.3% O and M = 180 g mol⁻¹: empirical formula CH₂O (mass 30), multiplier 6, molecular formula C₆H₁₂O₆.
- Molar concentration(1.4.5)Molar concentration c = n/V measures the amount of solute per volume of solution. The standard unit is mol dm⁻³; square brackets [ ] denote molar concentration, so [H⁺] means "the molar concentration of hydrogen ions." To convert between g dm⁻³ and mol dm⁻³, divide by the molar mass. This relationship is the foundation of every titration, every equilibrium calculation, and every rate equation in the course. Concentration and amount are not the same thing: diluting a solution with more solvent changes the concentration but not the amount of solute — this matters enormously in equilibrium (R2.3) and titration work (R3.1). A common error is confusing the amount of solute (in moles) with the concentration of the solution (in mol dm⁻³): adding water to a solution keeps n constant but decreases c, while adding more solute increases both.
- Avogadro's law and gas volumes(1.4.6)Avogadro's law states that equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules. This means you can use volume ratios as mole ratios directly in gas reactions: if 1 volume of N₂ reacts with 3 volumes of H₂, then 1 mol of N₂ reacts with 3 mol of H₂. No conversion to moles is needed — the volumes do it for you. This works because the volume of a gas depends on the number of particles and the conditions (T, P), not on the identity of the gas. This law connects to the ideal gas equation (S1.5, PV = nRT) and to stoichiometric calculations in Reactivity 2.1.
- How this sub-topic connectsThe mole is the quantitative foundation for the entire course. Every stoichiometric calculation in Reactivity 2.1 rests on n = m/M and mole ratios from balanced equations. Concentration (n = cV) underpins equilibrium (R2.3), acids and bases (R3.1), and electrochemistry (R3.2). Avogadro's law connects to ideal gases (S1.5) and to gaseous equilibrium calculations. There is no HL extension — the mole is shared ground, and the reason S1.4 carries 7 SL hours is that this is the single most leveraged skill in the syllabus.
Quantitative non-negotiables
- Convert between mass, moles and number of particles in either direction using n = m/M and N = n × N_A.
- Interconvert percentage composition, empirical formula and molecular formula.
- Use n = cV for molar concentration (mol dm⁻³ and g dm⁻³).
- Apply Avogadro's law: equal volumes of gases at the same T and P contain equal numbers of molecules.
Common failure modes
M-05 — Relative atomic mass is the number of protons plus neutrons.
Confidence: verified
Why it’s wrong: That is the mass number of one isotope.
Correction: Ar is the weighted mean of isotope masses over natural abundance, on the ¹²C = 12 scale; that's why chlorine is 35.45.
M-23 — A mole is a mass / a mole is 1 g.
Confidence: verified
Why it’s wrong: A mole is an amount, not a mass.
Correction: A mole is 6.02 × 10²³ specified entities. Its mass depends on what the entities are.
M-26 — Concentration and amount are the same thing.
Confidence: likely
Why it’s wrong: Diluting a solution changes the concentration but not the amount of solute.
Correction: This matters enormously in equilibrium and titration calculations.
What "HL standard" actually looks like
No HL extension. The mole is shared SL and HL — every stoichiometric calculation in the course rests on it.
Linking questions
Official IB.The questions in this section are the IB’s own linking questions, reproduced verbatim from the guide. They are not this site’s editorial judgement — see section 3 for that distinction.
- Official IB
Atoms increase in mass as their position descends in the periodic table. What properties might be related to this trend?
- Official IB
How can molar masses be used with chemical equations to determine the masses of the products of a reaction?
- Official IB
What is the importance of approximation in the determination of an empirical formula?
- Official IB
Avogadro's law applies to ideal gases. Under what conditions might the behaviour of a real gas deviate most from an ideal gas?
- Official IB
In what ways does Avogadro's law help us to describe, but not explain, the behaviour of gases?
- Official IB
Why is the equivalence point sometimes referred to as the stoichiometric point?
3 further official linking questions target Tool, Inquiry or Nature of Science strands and are not drawn as edges on the map:
Editorial The decision to surface these off-graph questions here is our editorial judgement — the IB does not prescribe where they should appear.
- Official IB
How can experimental data on mass changes in combustion reactions be used to derive empirical formulas?
- Official IB
What are the considerations in the choice of glassware used in preparing a standard solution and a serial dilution?
- Official IB
How can a calibration curve be used to determine the concentration of a solution?
Bridge: GCSE → IB HL
Derived. These are the bridge items tagged to this sub-topic— places where the GCSE model gets redefined, genuinely new territory, or carry-over strengths. The tagging is this site’s editorial judgement.