Relative atomic mass for A-Level Chemistry
Relative atomic mass (Ar) is the weighted mean mass of an atom of an element compared to one twelfth of the mass of an atom of carbon-12. Because most elements exist as a mixture of isotopes, the Ar value on the periodic table is rarely a whole number. Chlorine, for example, has an Ar of 35.5 because it is a mixture of chlorine-35 and chlorine-37 in roughly a 3:1 ratio.
This guide covers the formal AQA definition, how to calculate Ar from isotopic abundance, the role of mass spectrometry, and the common errors that lose Paper 1 marks every year.
Weighted mean, not simple mean
Each isotope's contribution is scaled by its relative abundance. Chlorine-35 is more abundant than chlorine-37, so it pulls the average closer to 35.
Compared to carbon-12
The reference standard is 1/12 the mass of a carbon-12 atom, defined as exactly 1.000. All other masses are expressed relative to this.
Measured with mass spectrometry
A mass spectrometer separates isotopes by their mass-to-charge ratio and measures their abundance, giving the data needed to calculate Ar.
The formal AQA definition
The AQA mark-scheme definition of relative atomic mass is: The weighted mean mass of an atom of an element compared to one twelfth of the mass of an atom of carbon-12. Every word in that definition can carry a mark.
Weighted mean gives one mark, of an atom of an element gives another, one twelfth of the mass of carbon-12 gives the third. Skipping any of those phrases is the easiest way to drop marks on a three-mark definition question.
Why one twelfth of carbon-12 Carbon-12 was chosen as the reference standard in 1961 because it gave whole-number masses for common isotopes and was easy to obtain in pure form. One twelfth of carbon-12 weighs about one atomic mass unit, so hydrogen-1 comes out at roughly 1.000.
Related mass terms you need to know
The AQA specification expects you to define five different mass terms. They sound similar but examiners are strict on the distinction between them. Mixing them up is one of the most common sources of dropped marks across the topic.
| Term | Symbol | Definition |
|---|---|---|
| Relative atomic mass | Ar | Weighted mean mass of an atom of an element compared to 1/12 the mass of a carbon-12 atom |
| Relative isotopic mass | (none) | Mass of an atom of a specific isotope compared to 1/12 the mass of a carbon-12 atom |
| Relative molecular mass | Mr | Sum of the Ar values of the atoms in a molecule (used for simple molecules) |
| Relative formula mass | Mr | Sum of the Ar values of the atoms in one formula unit (used for ionic compounds) |
| Relative molar mass | M | Mass of one mole of a substance in grams, numerically equal to Mr |
Calculating Ar from isotopic abundance
To calculate the relative atomic mass of an element from isotopic abundances, multiply each isotopic mass by its relative abundance, add the results together, and divide by the total abundance. In symbols: Ar = Σ(isotopic mass × abundance) / Σ(abundance).
If the abundances are given as percentages, the total is 100, so you divide by 100 at the end. If they are given as relative peak heights from a mass spectrum, divide by the sum of those peak heights. The method is the same either way.
Worked example: Chlorine
Chlorine has two isotopes: Chlorine-35 with an abundance of 75.0% and chlorine-37 with an abundance of 25.0%. Calculate the relative atomic mass.
Step 1: Multiply each isotopic mass by its abundance. (35 × 75) + (37 × 25) = 2625 + 925 = 3550.
Step 2: Divide by the total abundance. 3550 / 100 = 35.5.
The relative atomic mass of chlorine is 35.5. This matches the value on the periodic table, which is why chlorine's Ar is never quoted as a whole number even though no individual atom of chlorine actually weighs 35.5 atomic mass units.
Worked example: Boron from a mass spectrum
A mass spectrum of boron shows two peaks: One at m/z = 10 with a height of 18.7, and one at m/z = 11 with a height of 81.3. Calculate the Ar of boron.
Step 1: Multiply each m/z by its peak height. (10 × 18.7) + (11 × 81.3) = 187 + 894.3 = 1081.3.
Step 2: Divide by the total of the peak heights. 1081.3 / (18.7 + 81.3) = 1081.3 / 100 = 10.813.
Step 3: Round to a sensible number of significant figures. Ar(B) = 10.8 (to 3 s.f.).
The accepted value on the periodic table is 10.8, so the calculation matches. Always check the question for the required number of significant figures – AQA often asks for 1, 2, or 3 decimal places.
When peak heights do not add to 100 Mass spectra give you peak heights, not percentages. The peak heights can add to any total, so you must divide by the actual sum. Forgetting to do this and dividing by 100 instead is one of the most common mistakes on the topic.
How a mass spectrometer measures Ar
A time-of-flight (TOF) mass spectrometer ionises the sample, accelerates the ions through an electric field, lets them drift through a flight tube, and times their arrival at a detector. Lighter ions reach the detector first, heavier ions arrive later.
The output is a graph of relative abundance against mass-to-charge ratio (m/z). Each isotope shows up as a separate peak, and the height of the peak gives the abundance. The Ar is then calculated using the formula above, treating m/z as the isotopic mass for singly charged ions.
Where students lose marks on Ar questions
Examiner reports for AQA A-Level Chemistry flag the same handful of slips year after year. Almost all of them come down to imprecise wording in the definition or careless arithmetic in the calculation.
Common mistakes that cost easy marks Forgetting the word "weighted" in the definition (just writing "mean mass" loses a mark). Comparing to carbon-12 instead of *one twelfth of* carbon-12. Confusing relative atomic mass with relative isotopic mass. Dividing peak heights by 100 instead of by the actual sum of the peaks. Forgetting that m/z is mass divided by charge, so for a 2+ ion the actual mass is twice the m/z. Rounding to the wrong number of significant figures.
Key facts to memorise for the exam
- Definition: Weighted mean mass of an atom of an element compared to 1/12 the mass of a carbon-12 atom
- Reference standard: One twelfth of the mass of a carbon-12 atom is defined as exactly 1.000
- Formula: Ar = Σ(isotopic mass × abundance) / Σ(abundance)
- Mass spectrometer: Time-of-flight method, ions sorted by mass-to-charge ratio (m/z)
- Peak heights: Divide by the actual sum, not by 100, unless the data is given as percentages
- Distinguish: Relative atomic mass is for elements; relative molecular mass is for molecules; relative formula mass is for ionic compounds
- Units: Ar has no units because it is a ratio of masses
- Why most Ar values are not whole numbers: Because elements are a mixture of isotopes with different masses
