Relative Atomic Mass, Formula Mass and Concentration
Two short but essential calculation skills that feed into every stoichiometry question: working out Mr, and expressing concentration correctly.
Part 1: Relative masses
Relative atomic mass (Ar)
Relative atomic mass (Ar) is the weighted average mass of an element’s atoms, compared with 1/12 the mass of a carbon-12 atom.
It is a ratio, so it has no units. Values are given in the Periodic Table.
Relative formula mass (Mr)
Relative formula mass (Mr) is the sum of the Ar values of all the atoms in a formula.
(For a compound made of molecules it is also called the relative molecular mass.)
Worked examples:
| Compound | Working | Mr |
|---|---|---|
| H₂O | (2 × 1) + 16 | 18 |
| NaOH | 23 + 16 + 1 | 40 |
| CaCO₃ | 40 + 12 + (3 × 16) | 100 |
| H₂SO₄ | (2 × 1) + 32 + (4 × 16) | 98 |
| Ca(OH)₂ | 40 + 2(16 + 1) | 74 |
| Al₂(SO₄)₃ | (2 × 27) + 3(32 + 64) | 342 |
| CuSO₄·5H₂O | 64 + 32 + 64 + 5 × 18 | 250 |
BRACKETS multiply everything inside them. For Ca(OH)₂ you need two oxygens and two hydrogens. Wrong Mr values for sodium hydroxide and other compounds were recorded, and brackets are the usual cause.
A dot means “plus that many water molecules” — for CuSO₄·5H₂O, add 5 × 18 = 90. This is the water of crystallisation.
Use ATOMIC masses, not diatomic. In a compound you have atoms: use H = 1 and O = 16, not 2 and 32. A recorded error used the diatomic values.
Percentage composition
% of an element = (total Ar of that element ÷ Mr of the compound) × 100
Example — the percentage of nitrogen in NH₄NO₃ (Mr = 80):
- There are 2 nitrogen atoms → total Ar = 28
- % N = (28 ÷ 80) × 100 = 35%
Count ALL the atoms of that element in the formula — in ammonium nitrate the nitrogen appears twice, in two different parts of the formula.
Part 2: Concentration
The two units
Concentration in mol/dm³ = moles ÷ volume in dm³ Concentration in g/dm³ = mass in grams ÷ volume in dm³
Converting between them:
g/dm³ = mol/dm³ × Mr mol/dm³ = g/dm³ ÷ Mr
Example: a 0.5 mol/dm³ solution of NaOH (Mr = 40)
= 0.5 × 40 = 20 g/dm³
The unit conversion that costs most marks
Volume MUST be in dm³. 1 dm³ = 1000 cm³, so cm³ → dm³ means DIVIDE by 1000.
Example: 25.0 cm³ = 0.025 dm³
This was the most frequent error in the whole stoichiometry area, recorded three separate times — not converting, and converting the wrong way. Make it the first line of your working.
A useful check: a volume in dm³ is almost always a small decimal for laboratory quantities. If you have 25 dm³ of solution in a conical flask, something is wrong.
Worked example
5.85 g of NaCl (Mr = 58.5) is dissolved to make 250 cm³ of solution.
- Moles = 5.85 ÷ 58.5 = 0.1 mol
- Volume = 250 ÷ 1000 = 0.25 dm³
- Concentration = 0.1 ÷ 0.25 = 0.4 mol/dm³
- In g/dm³: 0.4 × 58.5 = 23.4 g/dm³
Dilution
Diluting adds solvent, so the MOLES stay the same while the VOLUME increases — the concentration therefore falls.
c₁V₁ = c₂V₂
Example: 25 cm³ of 2.0 mol/dm³ solution diluted to 100 cm³:
- c₂ = (2.0 × 25) ÷ 100 = 0.5 mol/dm³
The volumes can be in cm³ here, provided both are in the same unit — they cancel.
Mistakes that cost marks
Ignoring brackets when calculating Mr.
Forgetting the water of crystallisation after a dot.
Using diatomic masses for atoms in a compound.
Missing an element that appears twice in a formula.
Not converting cm³ to dm³, or dividing the wrong way.
Confusing mol/dm³ with g/dm³.
Multiplying instead of dividing by Mr, or vice versa.
Forgetting that dilution keeps the moles constant.
Omitting units on the answer.
Frequently asked questions
What is relative atomic mass? The weighted average mass of an element’s atoms relative to 1/12 of carbon-12. It has no units.
How do I calculate Mr? Add the Ar values of every atom in the formula.
What is the Mr of Ca(OH)₂? 74 — the bracket means two O and two H.
What does the dot in CuSO₄·5H₂O mean? Add 5 water molecules — 5 × 18 = 90.
How do I find the percentage of an element? (total Ar of that element ÷ Mr) × 100.
What is the formula for concentration? Moles ÷ volume in dm³, giving mol/dm³.
How do I convert cm³ to dm³? Divide by 1000.
How do I convert mol/dm³ to g/dm³? Multiply by the Mr.
What happens to concentration on dilution? It decreases — the moles stay the same, the volume increases.
What is the dilution equation? c₁V₁ = c₂V₂.
Quick revision checklist
- I can define Ar and know it has no units
- I can calculate Mr, handling brackets correctly
- I include water of crystallisation after a dot
- I use atomic, not diatomic, masses
- I can calculate percentage composition, counting all atoms
- I know concentration = moles ÷ dm³
- I convert cm³ to dm³ by dividing by 1000
- I can convert between mol/dm³ and g/dm³
- I can use c₁V₁ = c₂V₂ for dilution
- I give the correct units every time
These notes cover relative masses and concentration in the Cambridge IGCSE Chemistry (0620) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Chemistry lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and data booklet for your own exam series.
Finished this topic?
Saved on this device — no account needed.