Relative Atomic Mass and Relative Formula Mass

This lesson covers relative atomic mass ($A_r$) and relative formula mass ($M_r$) as required by the AQA GCSE Combined Science Trilogy specification (8464). You need to understand what these quantities mean, how to read $A_r$ values from the periodic table, and how to calculate the $M_r$ of any compound from its formula.

---

What Is Relative Atomic Mass ($A_r$)?

The relative atomic mass ($A_r$) of an element is the average mass of one atom of the element compared to one-twelfth the mass of a carbon-12 atom.

• It is a weighted average that takes into account the masses and abundances of all the naturally occurring isotopes of that element.
• $A_r$ has no units — it is a ratio.
• You can read $A_r$ values directly from the periodic table (the larger number shown for each element).

Key $A_r$ Values to Know

Element	Symbol	$A_r$
Hydrogen	H	1
Carbon	C	12
Nitrogen	N	14
Oxygen	O	16
Sodium	Na	23
Magnesium	Mg	24
Aluminium	Al	27
Sulfur	S	32
Chlorine	Cl	35.5
Potassium	K	39
Calcium	Ca	40
Iron	Fe	56
Copper	Cu	63.5

Exam Tip: You do NOT need to memorise $A_r$ values — they are given on the periodic table in the AQA exam. But knowing the common ones speeds up your work enormously.

---

Why Is $A_r$ a Weighted Average?

Most elements exist as a mixture of isotopes — atoms with the same number of protons but different numbers of neutrons. The $A_r$ reflects this mixture.

Worked Example — Chlorine

Chlorine has two isotopes:

Isotope	Mass Number	Natural Abundance
$^{35}$Cl	35	75%
$^{37}$Cl	37	25%

$$A_r = \frac{(35 \times 75) + (37 \times 25)}{100} = \frac{2625 + 925}{100} = \frac{3550}{100} = 35.5$$

This is why the periodic table shows 35.5 for chlorine, not a whole number.

Worked Example — Copper

Copper has two isotopes:

Isotope	Mass Number	Natural Abundance
$^{63}$Cu	63	69%
$^{65}$Cu	65	31%

$$A_r = \frac{(63 \times 69) + (65 \times 31)}{100} = \frac{4347 + 2015}{100} = \frac{6362}{100} = 63.6$$

The periodic table rounds this to 63.5.

---

What Is Relative Formula Mass ($M_r$)?

The relative formula mass ($M_r$) of a substance is the sum of the relative atomic masses of all the atoms in its formula.

• For molecules (covalent compounds), it is sometimes called the relative molecular mass — but the calculation is identical.
• Like $A_r$, it has no units.

How to Calculate $M_r$

flowchart TD
    A["Write out the chemical formula"] --> B["Count the number of atoms\nof each element"]
    B --> C["Multiply each count\nby the element's Ar"]
    C --> D["Add up all the values"]
    D --> E["Result = Mr"]
    style A fill:#3b82f6,color:#fff,stroke:#2563eb
    style E fill:#f59e0b,color:#000,stroke:#d97706

1. Write out the formula.
2. Count the number of atoms of each element.
3. Multiply each count by the element's $A_r$.
4. Add up all the values.

---

Worked Examples

Example 1 — Water ($\text{H}_2\text{O}$)

Element	Number of Atoms	$A_r$	Contribution
H	2	1	$2 \times 1 = 2$
O	1	16	$1 \times 16 = 16$

$$M_r = 2 + 16 = 18$$

Example 2 — Carbon Dioxide ($\text{CO}_2$)

Element	Number of Atoms	$A_r$	Contribution
C	1	12	$1 \times 12 = 12$
O	2	16	$2 \times 16 = 32$

$$M_r = 12 + 32 = 44$$

Example 3 — Calcium Carbonate ($\text{CaCO}_3$)

Element	Number of Atoms	$A_r$	Contribution
Ca	1	40	$1 \times 40 = 40$
C	1	12	$1 \times 12 = 12$
O	3	16	$3 \times 16 = 48$

$$M_r = 40 + 12 + 48 = 100$$

Example 4 — Magnesium Hydroxide ($\text{Mg(OH)}_2$)

Watch out for brackets! The subscript 2 outside the bracket means there are two OH groups.

Element	Number of Atoms	$A_r$	Contribution
Mg	1	24	$1 \times 24 = 24$
O	2	16	$2 \times 16 = 32$
H	2	1	$2 \times 1 = 2$

$$M_r = 24 + 32 + 2 = 58$$

Example 5 — Sodium Carbonate ($\text{Na}_2\text{CO}_3$)

Element	Number of Atoms	$A_r$	Contribution
Na	2	23	$2 \times 23 = 46$
C	1	12	$1 \times 12 = 12$
O	3	16	$3 \times 16 = 48$

$$M_r = 46 + 12 + 48 = 106$$

Example 6 — Aluminium Sulfate ($\text{Al}_2(\text{SO}_4)_3$)

The subscript 3 outside the bracket means there are three $\text{SO}_4$ groups.

Element	Number of Atoms	$A_r$	Contribution
Al	2	27	$2 \times 27 = 54$
S	3	32	$3 \times 32 = 96$
O	12	16	$12 \times 16 = 192$

$$M_r = 54 + 96 + 192 = 342$$

Exam Tip (AQA 8464): Always lay your working out in a clear table or list. Show every step — you earn method marks even if you make an arithmetic error.

---

Common Mistakes to Avoid

Mistake	Correction
Forgetting to multiply inside brackets	In $\text{Ca(OH)}_2$, there are 2 O atoms and 2 H atoms, not 1 of each
Using mass number instead of $A_r$	Always use the periodic table value — $A_r$ may not be a whole number (e.g. Cl = 35.5)
Missing atoms in complex formulae	Count every atom carefully, especially with multiple brackets
Giving $M_r$ a unit	$M_r$ has no units — it is a dimensionless ratio

---

Summary

• Relative atomic mass ($A_r$) is the average mass of an atom of an element relative to one-twelfth the mass of a carbon-12 atom. It has no units and is found on the periodic table.
• $A_r$ is a weighted average because elements have different isotopes.
• Relative formula mass ($M_r$) is the sum of the $A_r$ values of all atoms in a formula.
• To calculate $M_r$: count atoms (including inside brackets), multiply by $A_r$, and add up.
• Always show your working clearly in a table or step-by-step list.
• This topic appears on both Foundation and Higher tier AQA papers.