Short Notes - Relative masses of atoms and molecules
Detailed Study Notes
Detailed notes on Stoichiometry for Cambridge IGCSE Chemistry, covering key concepts, explanations, examples, and exam-focused revision points.
Relative Atomic and Molecular Mass — Cambridge IGCSE 0620 Chemistry Extended (2026)
Relative atomic mass (Ar), relative molecular mass (Mr), and percentage composition. The mass-bookkeeping skill that everything stoichiometric needs.
At a glance
Ar: weighted average mass of an element's atoms compared to 121 of 12C.
Mr: sum of Ar values for atoms in a formula unit.
No units for Ar or Mr — they're relative, not absolute.
Percentage by mass of element X: Mrn×Ar(X)×100%.
Use Ar values from the Periodic Table (rounded to whole numbers usually).
What you’ll learn
Mapped to the Cambridge IGCSE 0620 syllabus (2026-2028).
3.2 — Define relative atomic mass and relative molecular mass.
3.2 — Calculate Mr for a given formula.
3.2 — Calculate percentage composition by mass.
Ar and Mr
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Ar: per atom. Mr: per molecule (or formula unit).
Relative atomic mass (Ar). The weighted average mass of all the natural isotopes of an element, on a scale where 12C=12 exactly. No units (it's a ratio).
Ar values are on the Periodic Table. Common values:
H: 1
C: 12
N: 14
O: 16
Na: 23
Mg: 24
S: 32
Cl: 35.5
K: 39
Ca: 40
Fe: 56
Cu: 63.5
Relative molecular mass (Mr). Sum of the Ar values for all atoms in a formula unit.
Worked.Mr of H2O.
2×1+1×16=18.
Worked.Mr of CO2.
12+2×16=44.
Worked.Mr of Ca(OH)2.
Ca: 40. OH: 16+1=17. So 40+2×17=74.
Mr is just the Ar of every atom in the formula added together.
Worked.Mr of (NH4)2SO4.
NH₄: 14+4×1=18. SO₄: 32+4×16=96. So 2×18+96=132.
Compound
Atoms
Working
Mr
H₂O
2 H, 1 O
2 × 1 + 16
18
CO₂
1 C, 2 O
12 + 2 × 16
44
Ca(OH)₂
1 Ca, 2 O, 2 H
40 + 2 × 17
74
(NH₄)₂SO₄
2 N, 8 H, 1 S, 4 O
2 × 18 + 96
132
Tip. Take care with brackets. Subscript outside multiplies everything inside.
The subscript outside the bracket applies to every atom inside it — here both the N and all four H.
Ar: average isotope mass, no units.
Mr: sum of Ar for atoms in formula.
Brackets: subscript multiplies everything inside.
Look up Ar on Periodic Table.
Percentage composition by mass
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Find what fraction of a compound's mass is a particular element.
Formula.% of element X=Mr(number of atoms of X)×Ar(X)×100%.
Worked. Percentage of nitrogen in ammonium nitrate NH4NO3.
Mr: 14+4+14+48=80.
N atoms: 2 (one in NH₄, one in NO₃).
%N=(2×14)/80×100=35%.
Worked. Percentage of sulfur in sulfuric acid H2SO4.
Mr: 2+32+64=98.
%S=32/98×100≈32.7%.
Compound
Element
Atoms × Ar
Mr
% by mass
NH₄NO₃
N
2 × 14 = 28
80
35%
H₂SO₄
S
1 × 32 = 32
98
32.7%
Percentage composition splits the total Mr into each element's share.
Use. Percentage composition matters for fertilisers (you want high N percent), drug doses, food labels, and quality control.
Worked. A farmer wants high-nitrogen fertiliser. Compare ammonium nitrate (%N = 35%) and ammonium phosphate (NH4)3PO4.
Mr of (NH4)3PO4: 3×18+31+64=149.
%N = (3×14)/149×100≈28.2%.
Ammonium nitrate is the better N source by mass.
%=(n×Ar)/Mr×100.
Useful for fertilisers, drugs, food.
Always sum atom counts FIRST.
Quick recap
Ar: per atom (weighted average of isotopes).
Mr: sum of Ar for the formula.
Brackets in formulae: subscript multiplies inside.
%=(n×Ar)/Mr×100.
Use for fertiliser comparisons, drug dosages, etc.
Memorise this
Verbatim phrases and definitions Cambridge mark schemes credit.
Relative atomic mass (Ar) — weighted average atomic mass relative to 121 of 12C.
Relative molecular mass (Mr) — sum of Ar values for atoms in a formula.
Percentage composition — mass fraction of each element in a compound, expressed as a percentage.
How it’s examined
Mr and percentage composition are foundational and appear most years on Paper 2 (2-3 marks: calculate Mr, percentage of element) and Paper 4 (4-6 marks: combined with stoichiometry). Examiner reports flag bracket-handling errors in formulae and missed atoms when counting elements.
Step-by-step worked examples — Relative masses of atoms and molecules
Step-by-step solutions to past-paper-style questions on relative masses of atoms and molecules, written exactly the way a tutor would explain them at the board.
1Mr of a simple molecule
Getting started• Mr
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Question
Calculate the relative molecular mass, Mr, of water, H2O. (Ar: H = 1, O = 16.)
Step-by-step solution
Step 1
Multiply each Ar by the number of those atoms in the formula. There are 2 H atoms and 1 O atom.
Mr=(2×1)+(1×16)
Step 2
Add the contributions together.
Mr=2+16=18
Answer
Mr(H2O)=18
Examiner tip
Mr has no units — it is a RATIO of masses on the carbon-12 scale.
2Mr of carbon dioxide
Getting started• Mr
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Question
Calculate the relative molecular mass of carbon dioxide, CO2. (Ar: C = 12, O = 16.)
Step-by-step solution
Step 1
One C atom plus two O atoms.
Mr=(1×12)+(2×16)
Step 2
Add up.
Mr=12+32=44
Answer
Mr(CO2)=44
Examiner tip
The subscript 2 belongs only to oxygen here — there is just one carbon atom.
3Mr of sulfuric acid
Building confidence• Mr
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Question
Calculate the relative molecular mass of sulfuric acid, H2SO4. (Ar: H = 1, S = 32, O = 16.)
Step-by-step solution
Step 1
Identify how many of each atom: 2 H, 1 S, 4 O.
Step 2
Multiply each Ar by its count.
Mr=(2×1)+(1×32)+(4×16)
Step 3
Add: 2+32+64.
Mr=2+32+64=98
Answer
Mr(H2SO4)=98
Examiner tip
Lay the calculation out term by term — most lost marks here come from miscounting the four oxygens (4×16=64).
4Relative formula mass with brackets
Building confidence• Adapted from 0620/42 May/Jun 2023 Q3• Mr, brackets, ionic
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Question
Calculate the relative formula mass of calcium nitrate, Ca(NO3)2. (Ar: Ca = 40, N = 14, O = 16.)
Step-by-step solution
Step 1
Work out the mass of ONE nitrate group, NO3, first.
Mr(NO3)=14+(3×16)=62
Step 2
The subscript 2 outside the bracket multiplies the WHOLE nitrate group, so there are two of them.
2×62=124
Step 3
Add the one calcium atom.
Mr=40+124=164
Answer
Mr(Ca(NO3)2)=164
Examiner tip
The bracket subscript multiplies EVERY atom inside it (so 2×3=6 oxygens in total). Forgetting this is the single most common error.
5Mr of a hydrated salt
Stretch• Adapted from 0620/41 Oct/Nov 2022 Q4• Mr, water of crystallisation
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Question
Calculate the relative formula mass of hydrated copper(II) sulfate, CuSO4⋅5H2O. (Ar: Cu = 64, S = 32, O = 16, H = 1.)
Step-by-step solution
Step 1
Find Mr of the anhydrous part, CuSO4.
Mr(CuSO4)=64+32+(4×16)=160
Step 2
Find the mass of the water of crystallisation. The dot means '+ 5 water molecules', and Mr(H2O)=18.
5×18=90
Step 3
Add the two parts together.
Mr=160+90=250
Answer
Mr(CuSO4⋅5H2O)=250
Examiner tip
The dot (⋅) is an ADDITION of complete water molecules — multiply the whole 18 by 5, not just the hydrogens.
6Percentage by mass of an element
Stretch• Adapted from 0620/42 May/Jun 2024 Q9• %, composition
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Question
Calculate the percentage by mass of nitrogen in ammonium nitrate, NH4NO3. (Ar: N = 14, H = 1, O = 16.)
Step-by-step solution
Step 1
Calculate Mr of the whole compound: 2 N, 4 H, 3 O.
Mr=(2×14)+(4×1)+(3×16)=28+4+48=80
Step 2
Find the total mass of the element of interest. There are 2 nitrogen atoms.
mass of N=2×14=28
Step 3
Divide the element mass by Mr, THEN multiply by 100.
%N=8028×100=35%
Answer
%N=35%
Examiner tip
Use the TOTAL mass of that element (here 2×14, not just one N). Do the division first, then ×100.
Model Answers — Relative masses of atoms and molecules
High-scoring sample answers for relative masses of atoms and molecules on the Cambridge IGCSE 0620 paper, with examiner-style notes mapping each response to the mark scheme and assessment objectives.
Question 1
Paper 4 structured style2 marks
Define the term relative atomic mass, Ar. (2 marks)
Model answer
The relative atomic mass, Ar, is the average mass of the atoms of an element, compared with 121 of the mass of an atom of carbon-12 (12C). It is a weighted mean that takes the proportions of the different isotopes into account, so it has no units.
Why this scores
Two marks: (1) average mass of the atoms of the element; (2) on a scale where 12C (or 121 of a carbon-12 atom) is the reference. The word 'average' is essential because of isotopes.
Question 2
Paper 4 short-answer style1 mark
Calculate the relative molecular mass, Mr, of water, H2O. (Ar: H = 1, O = 16.) (1 mark)
Model answer
Mr=(2×1)+16=18.
Why this scores
One mark for the correct answer, 18. Always show the (2×1) for the two hydrogen atoms.
Question 3
Paper 4 structured style2 marks
Show that the relative molecular mass of sulfuric acid, H2SO4, is 98. (Ar: H = 1, S = 32, O = 16.) (2 marks)
Model answer
Add the contribution of each element: hydrogen 2×1=2, sulfur 1×32=32, oxygen 4×16=64. Total: Mr=2+32+64=98.
Why this scores
In a 'show that' question you must display the working. One mark for the correct contributions (2+32+64) and one for reaching 98.
Question 4
Paper 4 structured style3 marks
Calculate the relative formula mass of calcium hydroxide, Ca(OH)2, and of calcium nitrate, Ca(NO3)2. (Ar: Ca = 40, O = 16, H = 1, N = 14.) (3 marks)
Model answer
For Ca(OH)2, one hydroxide group is 16+1=17, and the subscript 2 doubles it: Mr=40+(2×17)=40+34=74. For Ca(NO3)2, one nitrate group is 14+(3×16)=62, and the subscript 2 doubles it: Mr=40+(2×62)=40+124=164.
Why this scores
Three marks: Ca(OH)2=74; correct nitrate group =62; Ca(NO3)2=164. The bracket subscript must multiply every atom inside it.
Question 5
Paper 4 (Extended) structured style4 marks
Hydrated copper(II) sulfate has the formula CuSO4⋅5H2O. Calculate its relative formula mass. (Ar: Cu = 64, S = 32, O = 16, H = 1.) (4 marks)
Model answer
First find the anhydrous part: Mr(CuSO4)=64+32+(4×16)=64+32+64=160. Next find the water of crystallisation, where each H2O has Mr=18, so five of them give 5×18=90. The dot in the formula means these are added on, so the total is Mr=160+90=250.
Why this scores
Four marks: Mr(CuSO4)=160; Mr(H2O)=18; 5×18=90; final total 250. The dot means '+ 5 whole water molecules'.
Question 6
Paper 4 (Extended) structured style5 marks
Ammonium nitrate, NH4NO3, is used as a fertiliser because of its high nitrogen content. Calculate the percentage by mass of nitrogen in ammonium nitrate. (Ar: N = 14, H = 1, O = 16.) (5 marks)
Model answer
First calculate the relative formula mass of the whole compound. There are 2 nitrogen, 4 hydrogen and 3 oxygen atoms, so Mr=(2×14)+(4×1)+(3×16)=28+4+48=80. Next find the total mass contributed by nitrogen: there are two nitrogen atoms, giving 2×14=28. Finally, divide the mass of nitrogen by the total Mr and multiply by 100: %N=8028×100=35%.
Why this scores
Five marks across: correct count of atoms; Mr=80; mass of nitrogen =28; correct formula Mrmass of element×100; final answer 35%. Use the TOTAL nitrogen mass (2×14), not one atom.
Key Definitions and Keywords — Relative masses of atoms and molecules
Definitions to memorise and the exact keywords mark schemes credit for relative masses of atoms and molecules answers — sharpened from recent examiner reports for the 2026 0620 sitting.
Relative atomic mass (Ar)
Examiner keyword▼
The average mass of the atoms of an element, on a scale where an atom of carbon-12 (12C) has a mass of exactly 12 (i.e. compared with 121 of a carbon-12 atom). It is a weighted mean over the isotopes.
Relative molecular / formula mass (Mr)
Examiner keyword▼
The sum of the relative atomic masses of all the atoms shown in the formula of a substance. 'Relative molecular mass' is used for molecules; 'relative formula mass' is used for ionic compounds.
Percentage composition by mass
Examiner keyword▼
The percentage of the total mass of a compound contributed by a given element: %element=Mr(number of atoms)×Ar×100.
Water of crystallisation
Examiner keyword▼
Water molecules chemically bound into a crystal structure, shown after a dot in the formula (e.g. CuSO4⋅5H2O). Each H2O (Mr=18) is added to the Mr of the salt.
Common Mistakes and Misconceptions — Relative masses of atoms and molecules
The traps other students keep falling into on relative masses of atoms and molecules questions — taken from recent Cambridge IGCSE 0620 examiner reports and mark schemes — and how to avoid them.
✕Forgetting to multiply every atom inside a bracket
0620/42 — recurring error in examiner reports
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Why it happens
The subscript outside the bracket is easy to overlook when working quickly.
How to avoid it
In Ca(NO3)2 the subscript 2 multiplies the WHOLE NO3 group, giving 2 N and 6 O atoms. Work out the bracket's mass first, then multiply.
✕Mishandling the dot in hydrated salts (e.g. only adding the hydrogens)
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Why it happens
Students treat ⋅5H2O as loose atoms instead of 5 whole water molecules.
How to avoid it
Add 5×Mr(H2O)=5×18=90 to the Mr of the anhydrous salt.
✕Multiplying by 100 at the wrong stage of a percentage calculation
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Why it happens
Operations are carried out in the wrong order.
How to avoid it
Always do Mrmass of element FIRST, and only then multiply by 100.
✕Using the mass of a single atom instead of all atoms of that element
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Why it happens
Forgetting that an element can appear more than once in a formula.
How to avoid it
Count every atom of the element. In NH4NO3 there are TWO nitrogens, so use 2×14=28.
Relative masses of atoms and molecules — frequently asked questions
The things students keep getting wrong in this sub-topic, answered.