3.2 Relative masses of atoms and molecules
- Syllabus
- 0620–2026–2027
- Topic
- 3.2
- Level
- —
Learning objectives
3.2.1Relative atomic mass, Ar, as the• Describe relative atomic mass, Ar, as the average mass of the isotopes of an element compared to 1/12th of the mass of an atom of 12C3.2.2Relative molecular mass, Mr, as the• Define relative molecular mass, Mr, as the sum of the relative atomic masses. Relative formula mass, Mr, will be used for ionic compounds3.2.3Reacting masses in simple proportions• Calculate reacting masses in simple proportions. Calculations will not involve the mole concept
Describe relative atomic mass
Relative atomic mass, Aᵣ, is the weighted average mass of the isotopes of an element compared with 1/12 of the mass of one carbon-12 atom.
| Part of the definition | Meaning |
|---|---|
| average of the isotopes | isotope masses contribute according to their relative abundance |
| relative scale | masses are compared, not measured directly in grams |
| reference | one carbon-12 atom is exactly 12 units, so the comparison unit is 1/12 of its mass |
Aᵣ can be non-integer, such as chlorine at about 35.5, because it is an abundance-weighted average of different isotopes.
Aᵣ is not the mass number of one isotope and is not compared with the mass of a whole carbon-12 atom; the reference is one twelfth of that mass.
Calculate relative molecular and formula mass
Relative molecular mass, Mᵣ, is the sum of the relative atomic masses of all atoms in one molecule. For an ionic compound, the same calculation is called relative formula mass because the solid has formula units rather than molecules.
| Step | Action |
|---|---|
| 1 | read every element and subscript in the formula |
| 2 | multiply each Aᵣ by the number of that atom |
| 3 | apply an outside bracket subscript to every atom inside |
| 4 | add all contributions |
For Pb(NO₃)₂: Mᵣ = 207 + 2 × (14 + 3 × 16) = 331. The bracket means two N atoms and six O atoms in the formula unit.
The same sum can be rearranged to find an unknown Aᵣ when the total relative mass and formula are given.
Relative molecular or formula mass is a ratio and has no unit. Do not call an ionic formula unit a molecule.
Calculate reacting masses by simple proportion
A balanced equation fixes the particle ratio. Multiplying each formula mass by its coefficient converts that ratio into a reacting-mass ratio—without using the mole concept.
| Step | Action |
|---|---|
| 1 | write or use the balanced equation |
| 2 | calculate the relative mass of the required reactant and product |
| 3 | multiply each relative mass by its equation coefficient |
| 4 | form the required mass ratio and scale both sides by the same factor |
CaCO₃ → CaO + CO₂ gives relative masses 100 → 56 + 44. Therefore 100 g CaCO₃ produces 56 g CaO, so 10.0 g produces 10.0 × 56/100 = 5.6 g CaO.
The calculated product masses must respect conservation of mass. If a reactant is in excess, base the maximum product on the amount that actually reacts.
Use coefficient-weighted formula masses, not coefficients alone. This objective uses direct mass proportions; amount in moles belongs to the next Topic.