What is the relative atomic mass and how is it determined?

The relative atomic mass (Ar) is a measure of the mass of an atom compared to one-twelfth of the mass of a carbon-12 atom. It is a dimensionless quantity and is calculated based on the weighted average of the isotopic masses of an element's naturally occurring isotopes. This value is often found on the periodic table and is crucial for stoichiometric calculations in Chemistry, especially at the Cambridge International A Levels.

How do you calculate the relative molecular mass of a compound?

The relative molecular mass (Mr) of a compound is calculated by summing the relative atomic masses of all the atoms present in a molecule. For example, to find the Mr of water (H2O), you add the relative atomic masses of 2 hydrogen atoms (2 x 1) and 1 oxygen atom (16), resulting in an Mr of 18. This concept is fundamental in AS-Level Physical Chemistry for understanding molecular composition and stoichiometry.

Why is the concept of relative masses important in stoichiometry?

Relative masses are crucial in stoichiometry because they allow chemists to convert between moles and grams, facilitating the calculation of reactants and products in chemical reactions. By using relative atomic and molecular masses, students can accurately determine the proportions of substances involved in reactions, which is a key skill in Cambridge International A Levels Chemistry.

What is the difference between relative atomic mass and relative isotopic mass?

Relative atomic mass is the weighted average mass of an element's isotopes compared to one-twelfth of the mass of a carbon-12 atom, while relative isotopic mass refers to the mass of a specific isotope of an element. Understanding this distinction is important for students studying Atoms, molecules and stoichiometry in AS-Level Physical Chemistry, as it aids in comprehending the composition of elements and their isotopes.

How does the concept of relative formula mass apply to ionic compounds?

For ionic compounds, the relative formula mass is used instead of relative molecular mass because ionic compounds do not exist as discrete molecules. Instead, the relative formula mass is calculated by summing the relative atomic masses of the ions in the empirical formula. This concept is essential in Cambridge International A Levels Chemistry for analyzing the composition and stoichiometry of ionic substances.

Why is "Writing units (g) on Ar or Mr." a common mistake in Relative masses of atoms and molecules?

Why it happens: Confusing relative mass with molar mass. How to avoid it: Relative masses are ratios → no units. Molar mass (g mol⁻¹) is the one with units. Source: 9701 Examiner Reports

Why is "Not applying an outside subscript to every atom in a bracket." a common mistake in Relative masses of atoms and molecules?

Why it happens: Multiplying only the last atom or the metal. How to avoid it: In Ca(NO₃)₂ the ×2 applies to N and to all 3 O → 2 N and 6 O.

Why is "Omitting water of crystallisation in a hydrate's formula mass." a common mistake in Relative masses of atoms and molecules?

Why it happens: Treating the hydrate like the anhydrous salt. How to avoid it: Add n × 18.0 for n waters (e.g. +90.0 for ·5H₂O).

Why is "Calling NaCl's mass a 'relative molecular mass'." a common mistake in Relative masses of atoms and molecules?

Why it happens: Using Mr for everything. How to avoid it: Ionic/giant lattices have no molecules → use 'relative formula mass'. Reserve Mr for true molecules. Source: 9701 Examiner Reports 2022-2024

Why is "Defining Ar without 'weighted average' or 'relative to C-12'." a common mistake in Relative masses of atoms and molecules?

Why it happens: Giving a vague 'mass of an atom' answer. How to avoid it: Both ideas are needed: weighted average AND relative to 1/12 of carbon-12.

Atoms, molecules and stoichiometry(AS-Level Physical Chemistry)Cambridge International A Level Chemistry 9701

Relative masses of atoms and molecules

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Relative Masses of Atoms and Molecules — Cambridge International AS & A Level Chemistry 9701 (2025-2027 syllabus)

The unified atomic mass unit and the carbon-12 standard, and the precise definitions of relative atomic, isotopic, molecular and formula mass — the foundation every stoichiometry calculation rests on.

What you’ll learn

Mapped to the Cambridge International A Level 9701 syllabus (2025-2027).

2.1.1 — Define the unified atomic mass unit as one twelfth of the mass of a carbon-12 atom.
2.1.2 — Define relative atomic mass ( $A_r$ ), relative isotopic mass, relative molecular mass ( $M_r$ ) and relative formula mass in terms of the unified atomic mass unit.

The carbon-12 standard and the unified atomic mass unit

Atoms are too light to weigh in grams, so we compare them to a fixed standard: 1/12 of a carbon-12 atom.

Individual atoms have tiny absolute masses (a carbon atom is about $2 \times 10^{-23}\,\text{g}$ ), so chemists use relative masses — every atom's mass compared to a single agreed standard.

The unified atomic mass unit (u) is defined as one twelfth of the mass of one atom of carbon-12: $1\,\text{u} = \tfrac{1}{12} \times m(^{12}\text{C})$

Why carbon-12?

It is a single, well-defined isotope (6 protons + 6 neutrons), so the standard is exact and reproducible.
It gives almost every other atom a relative mass close to a whole number (e.g. H ≈ 1, O ≈ 16), which is convenient.

On this scale a carbon-12 atom has a mass of exactly 12 u by definition.

Absolute atomic masses are tiny → use relative masses.
1 u = 1/12 the mass of a carbon-12 atom.
C-12 has a mass of exactly 12 u by definition.

Relative atomic mass and relative isotopic mass

Isotopic mass is for a single isotope; Ar is the weighted average over the natural mixture.

Relative isotopic mass — the mass of one atom of a particular isotope compared to $\tfrac{1}{12}$ of a carbon-12 atom. These are very close to whole numbers (e.g. $^{35}\text{Cl} = 35$ , $^{37}\text{Cl} = 37$ ).

Relative atomic mass ( $A_r$ ) — the weighted average mass of the atoms of an element compared to $\tfrac{1}{12}$ of a carbon-12 atom. Because natural samples are a mixture of isotopes, $A_r$ is rarely a whole number.

$A_r = \frac{\sum(\text{relative isotopic mass} \times \text{abundance})}{\sum \text{abundance}}$

Worked. Chlorine: $75\%\;^{35}\text{Cl} + 25\%\;^{37}\text{Cl}$ → $A_r = \frac{(35 \times 75)+(37 \times 25)}{100} = 35.5$

(See Topic 1.2 Isotopes and Topic 22.2 Mass spectrometry for where abundances come from.)

Relative isotopic mass = one isotope vs 1/12 C-12.
Ar = weighted mean over all isotopes.
Ar is usually non-integer (e.g. Cl = 35.5).

Relative molecular mass and relative formula mass

Add up the Ar values. Use 'molecular' for molecules, 'formula' for ionic/giant structures.

Relative molecular mass ( $M_r$ ) — the sum of the relative atomic masses of all the atoms in a molecule, relative to $\tfrac{1}{12}$ of a carbon-12 atom.

$M_r(\text{H}_2\text{SO}_4) = (2 \times 1.0) + 32.1 + (4 \times 16.0) = 98.1$

Relative formula mass — exactly the same sum of $A_r$ values, but used for substances that are not molecular (ionic compounds, giant structures), where the formula is just a ratio of ions rather than a real molecule.

$\text{formula mass}(\text{CaCO}_3) = 40.1 + 12.0 + (3 \times 16.0) = 100.1$

Hydrated salts include the water of crystallisation: $\text{formula mass}(\text{CuSO}_4{\cdot}5\text{H}_2\text{O}) = 159.6 + 5(18.0) = 249.6$

Units. Relative masses are ratios, so they have no units — never write 'g' after an $A_r$ or $M_r$ value.

$M_r$ / formula mass = sum of $A_r$ values.
'Molecular' for molecules; 'formula' for ionic/giant solids.
Include water of crystallisation for hydrates.
Relative masses have no units.

How it’s examined

Definitions of $A_r$ and the unified atomic mass unit are standard Paper 2 openers (1-2 marks each), and $M_r$ /formula-mass calculations underpin every stoichiometry question on Papers 1, 2 and the practical papers. Examiner reports penalise definitions that omit 'relative to carbon-12' or 'weighted average', and answers that put units on relative masses.

Sources: Cambridge International AS & A Level Chemistry 9701 syllabus (2025-2027), section 2.1; 9701 Examiner Reports 2022-2024; 9701/21 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-20.

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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.

1Relative molecular mass of a compound (2 marks)
Getting started• Mr
Question
Calculate the relative molecular mass of ethanoic acid, $\text{CH}_3\text{COOH}$ . ( $A_r$ : H 1.0, C 12.0, O 16.0)
Step-by-step solution
1. Step 1
  Count atoms: 2 C, 4 H, 2 O.
  $M_r = (2 \times 12.0) + (4 \times 1.0) + (2 \times 16.0)$
2. Step 2
  Add up.
  $M_r = 24.0 + 4.0 + 32.0 = 60.0$
Answer
$M_r = 60.0$ (no units).
Examiner tip
Count every atom in the molecular formula — CH₃COOH has 2 C and 2 O, not 1 each.
2Formula mass with bracketed ions (2 marks)
Getting started• formula mass, brackets
Question
Calculate the relative formula mass of calcium nitrate, $\text{Ca(NO}_3)_2$ . ( $A_r$ : Ca 40.1, N 14.0, O 16.0)
Step-by-step solution
1. Step 1
  The subscript 2 multiplies everything inside the bracket → 2 N and 6 O.
  $M_r = 40.1 + 2 \times (14.0 + 3 \times 16.0)$
2. Step 2
  Evaluate the bracket, then add.
  $M_r = 40.1 + 2 \times 62.0 = 164.1$
Answer
Relative formula mass $= 164.1$ .
Examiner tip
Apply the outside subscript to every atom inside the bracket — a missed ×2 on oxygen is the classic slip here.
3Relative formula mass of a hydrate (2 marks)
Building confidence• formula mass, hydrate
Question
Calculate the relative formula mass of hydrated copper(II) sulfate, $\text{CuSO}_4{\cdot}5\text{H}_2\text{O}$ . ( $A_r$ : Cu 63.5, S 32.1, O 16.0, H 1.0)
Step-by-step solution
1. Step 1
  Anhydrous CuSO₄ first.
  $63.5 + 32.1 + (4 \times 16.0) = 159.6$
2. Step 2
  Add the five waters of crystallisation.
  $5 \times 18.0 = 90.0$
3. Step 3
  Total.
  $159.6 + 90.0 = 249.6$
Answer
Relative formula mass $= 249.6$ .
Examiner tip
Forgetting the 5 H₂O (a loss of 90) is the classic error in hydrate calculations.
4Ar from a three-isotope spectrum (3 marks)
Building confidence• Ar, isotopes
Question
Silicon is 92.2% $^{28}\text{Si}$ , 4.7% $^{29}\text{Si}$ and 3.1% $^{30}\text{Si}$ . Calculate $A_r$ to 1 d.p.
Step-by-step solution
1. Step 1
  Weighted mean.
  $A_r = \frac{(28 \times 92.2)+(29 \times 4.7)+(30 \times 3.1)}{100}$
2. Step 2
  Evaluate the numerator.
  $= \frac{2581.6 + 136.3 + 93.0}{100} = \frac{2810.9}{100}$
3. Step 3
  Divide.
  $A_r = 28.1$
Answer
$A_r = 28.1$ .
Examiner tip
Include the small isotopes too — dropping the 3.1% peak shifts the answer.
5Identifying an element from formula mass (3 marks)
Stretch• deduction, formula mass
Question
An oxide has the formula $\text{M}_2\text{O}_3$ and a relative formula mass of 102.0. Identify metal M. ( $A_r$ O = 16.0)
Step-by-step solution
1. Step 1
  Subtract the oxygen contribution.
  $2A_r(\text{M}) = 102.0 - (3 \times 16.0) = 54.0$
2. Step 2
  Divide by 2 to get $A_r$ of M.
  $A_r(\text{M}) = 27.0$
3. Step 3
  $A_r = 27.0$ is aluminium, consistent with $\text{Al}_2\text{O}_3$ .
Answer
M is aluminium (Al); the oxide is $\text{Al}_2\text{O}_3$ .
Examiner tip
Strip out the atoms you know first, then solve for the unknown Ar — and remember the subscript (÷2 here).
6Comparing percentage composition by mass (4 marks)
Stretch• percentage composition
Question
Which fertiliser has the higher percentage of nitrogen by mass: ammonium nitrate $\text{NH}_4\text{NO}_3$ or urea $\text{CO(NH}_2)_2$ ? ( $A_r$ : H 1.0, C 12.0, N 14.0, O 16.0)
Step-by-step solution
1. Step 1
  NH₄NO₃: $M_r = 80.0$ ; it contains 2 N (mass 28.0).
  $\%\,\text{N} = \frac{28.0}{80.0} \times 100 = 35.0\%$
2. Step 2
  Urea CO(NH₂)₂: $M_r = 60.0$ ; it contains 2 N (mass 28.0).
  $\%\,\text{N} = \frac{28.0}{60.0} \times 100 = 46.7\%$
3. Step 3
  Compare. Urea delivers more nitrogen per gram.
Answer
Urea (46.7% N) beats ammonium nitrate (35.0% N).
Examiner tip
Percentage by mass = (total mass of that element ÷ Mr) × 100 — count all atoms of the element.

Key Formulae — Relative masses of atoms and molecules

The formulae you need to memorise for relative masses of atoms and molecules on the Cambridge International A Level 9701 paper, with every variable defined in plain English and a note on when to use it.

Relative atomic mass (weighted mean)
$A_r = \frac{\sum(\text{isotopic mass} \times \text{abundance})}{\sum \text{abundance}}$
$isotopic mass$
relative mass of each isotope
$abundance$
relative or % abundance
When to use
Finding Ar from isotopic abundances or a mass spectrum.
Relative molecular / formula mass
$M_r = \sum A_r(\text{all atoms in the formula})$
$A_r$
relative atomic mass of each element
When to use
Any time you need the mass of one mole; include water of crystallisation for hydrates.
Percentage composition by mass
$\%\,\text{element} = \frac{(\text{atoms of element}) \times A_r}{M_r} \times 100$
$atoms of element$
number of that atom in the formula
$M_r$
relative formula mass of the whole compound
When to use
Comparing how much of an element a compound contains (e.g. % N in fertilisers).

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 Cambridge International A Level 9701 sitting.

Unified atomic mass unit (u)
Examiner keyword
One twelfth of the mass of one atom of carbon-12.
Relative isotopic mass
Examiner keyword
The mass of one atom of an isotope relative to 1/12 of the mass of a carbon-12 atom.
Relative atomic mass (Ar)
Examiner keyword
The weighted average mass of the atoms of an element relative to 1/12 of the mass of a carbon-12 atom.
Relative molecular mass (Mr)
Examiner keyword
The sum of the relative atomic masses of the atoms in a molecule, relative to 1/12 of a carbon-12 atom.
Relative formula mass
Examiner keyword
The same sum of relative atomic masses, used for ionic or giant structures that do not exist as discrete molecules (e.g. NaCl, SiO₂).

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 International A Level 9701 examiner reports and mark schemes — and how to avoid them.

✕Writing units (g) on Ar or Mr.
9701 Examiner Reports
Why it happens
Confusing relative mass with molar mass.
How to avoid it
Relative masses are ratios → no units. Molar mass (g mol⁻¹) is the one with units.
✕Not applying an outside subscript to every atom in a bracket.
Why it happens
Multiplying only the last atom or the metal.
How to avoid it
In Ca(NO₃)₂ the ×2 applies to N and to all 3 O → 2 N and 6 O.
✕Omitting water of crystallisation in a hydrate's formula mass.
Why it happens
Treating the hydrate like the anhydrous salt.
How to avoid it
Add n × 18.0 for n waters (e.g. +90.0 for ·5H₂O).
✕Calling NaCl's mass a 'relative molecular mass'.
9701 Examiner Reports 2022-2024
Why it happens
Using Mr for everything.
How to avoid it
Ionic/giant lattices have no molecules → use 'relative formula mass'. Reserve Mr for true molecules.
✕Defining Ar without 'weighted average' or 'relative to C-12'.
Why it happens
Giving a vague 'mass of an atom' answer.
How to avoid it
Both ideas are needed: weighted average AND relative to 1/12 of carbon-12.

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Relative masses of atoms and molecules

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Short Study Notes — Relative masses of atoms and molecules

Detailed Notes

What you’ll learn

How it’s examined

1Relative molecular mass of a compound (2 marks)

2Formula mass with bracketed ions (2 marks)

3Relative formula mass of a hydrate (2 marks)

4Ar from a three-isotope spectrum (3 marks)

5Identifying an element from formula mass (3 marks)

6Comparing percentage composition by mass (4 marks)

Relative atomic mass (weighted mean)

Relative molecular / formula mass

Percentage composition by mass

Unified atomic mass unit (u)

Relative isotopic mass

Relative atomic mass (Ar)

Relative molecular mass (Mr)

Relative formula mass

✕Writing units (g) on Ar or Mr.

✕Not applying an outside subscript to every atom in a bracket.

✕Omitting water of crystallisation in a hydrate's formula mass.

✕Calling NaCl's mass a 'relative molecular mass'.

✕Defining Ar without 'weighted average' or 'relative to C-12'.

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Relative masses of atoms and molecules — frequently asked questions