Relative Atomic Mass and Relative Molecular Mass Revision Notes | A Level AQA Chemistry

1. Why We Need a Reference Standard

Atoms are extraordinarily small — a single hydrogen atom has a mass of roughly $1.67 \times 10^{-27}$ kg. Working with numbers like that in every calculation would be impractical. Chemists solved this by comparing atomic masses to a fixed reference, producing dimensionless ratios that are far easier to handle.

The chosen reference is the carbon-12 isotope, $^{12}_{6}$C. Its mass is defined as exactly 12 atomic mass units. Every relative mass in chemistry — whether for a single atom or an entire formula unit — is expressed as a ratio compared to one-twelfth of that carbon-12 mass.

Carbon-12 was selected because it is stable, abundant, and can be measured with exceptional precision in a mass spectrometer. This makes it the ideal anchor for the entire relative mass scale used across AQA A Level chemistry.

2. Relative Atomic Mass ($A_r$)

The word weighted is doing important work in that definition. Most elements exist as a mixture of isotopes, each with a different mass and a different natural abundance. The $A_r$ value accounts for both — heavier isotopes that are more abundant pull the weighted mean upward.

Chlorine is the classic example. About 75% of chlorine atoms are $^{35}$Cl and about 25% are $^{37}$Cl. The weighted mean works out to approximately 35.5 — which is why the periodic table shows 35.5 rather than a whole number for chlorine.

Worked example: Calculating $A_r$ from Isotope Data

A sample of boron contains 20% $^{10}$B and 80% $^{11}$B. Calculate the relative atomic mass of boron.

1. $$A_r = \frac{(\text{mass}_1 \times \text{abundance}_1) + (\text{mass}_2 \times \text{abundance}_2)}{100}$$ — Each isotope contributes proportionally to the overall mean mass.
2. $$A_r = \frac{(10 \times 20) + (11 \times 80)}{100}$$ — Isotope $^{10}$B has mass 10 and 20% abundance; $^{11}$B has mass 11 and 80% abundance.
3. $(10 \times 20) = 200$ and $(11 \times 80) = 880$, so numerator $= 200 + 880 = 1080$ — Work out each product separately before adding — this avoids arithmetic slips.
4. $$A_r = \frac{1080}{100} = 10.8$$ — The result is dimensionless. No units are written after the value.

Answer: $A_r$(B) = 10.8

3. Relative Molecular Mass ($M_r$)

Once you have $A_r$ values for individual elements, extending the idea to whole molecules is straightforward. The relative molecular mass ($M_r$) of a covalent compound is the sum of the relative atomic masses of every atom in its molecular formula.

The term relative molecular mass is reserved for covalent (molecular) compounds — substances that exist as discrete molecules. Water, carbon dioxide, ethanol, and glucose all qualify. The key is that the formula represents an actual molecule with a definite number of atoms bonded together.

Worked example: Calculating $M_r$ for Sulphuric Acid

Calculate the relative molecular mass of sulphuric acid, $\text{H}_2\text{SO}_4$. Use $A_r$: H = 1.0, S = 32.1, O = 16.0.

1. H: 2 atoms, S: 1 atom, O: 4 atoms — Read directly from the molecular formula $\text{H}_2\text{SO}_4$.
2. H: $2 \times 1.0 = 2.0$ S: $1 \times 32.1 = 32.1$ O: $4 \times 16.0 = 64.0$ — Each element's contribution is its $A_r$ scaled by how many atoms of it appear in the formula.
3. $M_r = 2.0 + 32.1 + 64.0 = 98.1$ — Add the three values: $2.0 + 32.1 = 34.1$, then $34.1 + 64.0 = 98.1$.
4. $M_r(\text{H}_2\text{SO}_4) = 98.1$ — $M_r$ is dimensionless — do not write g mol$^{-1}$ here. That notation belongs to molar mass.

Answer: $M_r$(H$_2$SO$_4$) = 98.1

4. Relative Formula Mass for Ionic Compounds

Here is where precision of language becomes important. Ionic compounds — such as sodium chloride, calcium carbonate, or magnesium sulphate — do not exist as discrete molecules. Their structures are giant ionic lattices, so there is no single molecule whose mass you can measure.

For this reason, AQA specifies that the term relative formula mass must be used for ionic compounds, not relative molecular mass. The calculation method is identical — sum the $A_r$ values of all atoms in one formula unit — but the terminology reflects the ionic nature of the compound.

The formula unit is the simplest ratio of ions in the compound. For NaCl, that is one Na$^+$ and one Cl$^-$. For CaCl$_2$, it is one Ca$^{2+}$ and two Cl$^-$. You use the empirical formula as written, and the calculation proceeds in exactly the same way as for $M_r$.

Worked example: Calculating Relative Formula Mass for Calcium Carbonate

Calculate the relative formula mass of calcium carbonate, $\text{CaCO}_3$. Use $A_r$: Ca = 40.1, C = 12.0, O = 16.0.

1. Ca: 1 atom, C: 1 atom, O: 3 atoms — The formula unit of $\text{CaCO}_3$ contains one calcium, one carbon, and three oxygen atoms.
2. Ca: $1 \times 40.1 = 40.1$ C: $1 \times 12.0 = 12.0$ O: $3 \times 16.0 = 48.0$ — Three oxygen atoms each contribute 16.0: $3 \times 16.0 = 48.0$.
3. $40.1 + 12.0 + 48.0 = 100.1$ — $40.1 + 12.0 = 52.1$, then $52.1 + 48.0 = 100.1$.
4. Relative formula mass of $\text{CaCO}_3 = 100.1$ — Use 'relative formula mass', not 'relative molecular mass', because calcium carbonate is an ionic compound.

Answer: Relative formula mass of CaCO$_3$ = 100.1

Notice that the numerical process is the same in every row of that table. The distinction is purely terminological — but AQA mark schemes do penalise students who write 'relative molecular mass' for an ionic compound. Getting the language right costs you nothing and gains you marks.

5. Handling Brackets and Hydrated Salts

Formulae with brackets require one extra step: multiply everything inside the bracket by the subscript outside before summing. This is a frequent source of errors in calculation questions.

Worked example: Relative Formula Mass with Brackets: Calcium Hydroxide

Calculate the relative formula mass of calcium hydroxide, $\text{Ca(OH)}_2$. Use $A_r$: Ca = 40.1, O = 16.0, H = 1.0.

1. $\text{Ca(OH)}_2$ contains: Ca × 1, O × 2, H × 2 — The subscript 2 outside the bracket multiplies every atom inside: one O and one H each become two.
2. Ca: $1 \times 40.1 = 40.1$ O: $2 \times 16.0 = 32.0$ H: $2 \times 1.0 = 2.0$ — Each element's contribution is now calculated separately.
3. $40.1 + 32.0 + 2.0 = 74.1$ — $40.1 + 32.0 = 72.1$, then $72.1 + 2.0 = 74.1$.
4. Relative formula mass of $\text{Ca(OH)}_2 = 74.1$ — Calcium hydroxide is ionic, so 'relative formula mass' is the correct term.

Answer: Relative formula mass of Ca(OH)$_2$ = 74.1

Hydrated salts introduce water of crystallisation into the formula. Copper(II) sulphate pentahydrate, $\text{CuSO}_4 \cdot 5\text{H}_2\text{O}$, is a common example. You treat the dot as an addition: calculate the formula mass of $\text{CuSO}_4$ and add five times the $M_r$ of water.

6. Exam Technique and Common Mistakes

The definitions of $A_r$ and $M_r$ are high-value targets in AQA papers because they are frequently asked for 2 marks and frequently answered poorly. The two elements examiners look for are: (1) the phrase 'weighted mean mass' and (2) an explicit reference to the carbon-12 standard.

Writing 'average mass' instead of 'weighted mean mass' typically costs a mark. The word 'weighted' signals that you understand isotope abundances are factored in — a simple average would treat all isotopes as equally common, which they are not.

7. Bringing It Together: A Comparison Summary

All three terms — relative atomic mass, relative molecular mass, and relative formula mass — share the same underlying definition: a mass measured relative to one-twelfth of the mass of a carbon-12 atom. The differences lie in what is being measured and what type of substance is involved.

The carbon-12 standard underpins all three definitions. Whether you are describing a single chlorine atom, a molecule of glucose, or a lattice of sodium chloride, the reference point is always the same: one-twelfth of the mass of a $^{12}_{6}$C atom.

With these definitions secure, you have the foundation for every mole calculation in A Level chemistry. Molar mass (in g mol$^{-1}$) is numerically equal to $A_r$, $M_r$, or relative formula mass — so accuracy here pays dividends across the entire amount of substance topic.