Relative formula mass (Mr): how to calculate it

Calcium carbonate, CaCO₃

1. Count the atoms: 1 Ca, 1 C, 3 O.
2. Multiply by each $A_r$: Ca $= 40$, C $= 12$, O $= 3 \times 16 = 48$.
3. Add: $M_r = 40 + 12 + 48 = 100$.

In magnesium hydroxide, Mg(OH)₂, the 2 multiplies both O and H:

$M_r = 24 + 2 \times (16 + 1) = 24 + 34 = 58$

In aluminium sulfate, Al₂(SO₄)₃: 2 Al, 3 S and 12 O:

$M_r = (2 \times 27) + (3 \times 32) + (12 \times 16) = 54 + 96 + 192 = 342$

$$\% \text{ by mass} = \frac{A_r \times \text{number of atoms}}{M_r} \times 100$$

Oxygen in CaCO₃: $\dfrac{3 \times 16}{100} \times 100 = 48\%$.

Nitrogen in ammonium nitrate, NH₄NO₃ ($M_r = 80$): $\dfrac{2 \times 14}{80} \times 100 = 35\%$. Questions like this compare fertilisers.

Atoms aren't created or destroyed in a reaction, so the total mass of the products equals the total mass of the reactants. When calcium carbonate is heated:

$$\text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2$$

$100 = 56 + 44$. If a reaction seems to lose mass, a gas has usually escaped; if it gains mass, it has usually reacted with a gas such as oxygen from the air.

Element	Ar	Element	Ar
H	1	Na	23
C	12	Mg	24
N	14	S	32
O	16	Cl	35.5
Ca	40	Fe	56

You don't need to memorise them: a periodic table is provided in the exam. Use the values on it, because boards sometimes round differently (for example copper as 63.5 or 64).

• Multiplying only the first element after a bracket.
• Using atomic numbers (the smaller number) instead of relative atomic masses.
• Forgetting water of crystallisation, like the 5H₂O in CuSO₄·5H₂O.

Next, use $M_r$ to work with moles.

1. What is the $M_r$ of sodium hydroxide, NaOH?
2. What is the $M_r$ of hydrogen chloride, HCl?
3. What is the $M_r$ of calcium nitrate, Ca(NO₃)₂?
4. What percentage of ammonia, NH₃, is nitrogen by mass?

Answers: 40; 36.5; $40 + 2 \times (14 + 48) = 164$; $14 \div 17 \times 100 \approx 82.4\%$.