Relative atomic mass — AQA GCSE Combined Science
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Relative atomic mass explained
Relative atomic mass, Aᵣ, is the average mass of the atoms of an element compared with 1/12 of the mass of a carbon-12 atom.
Read the full explanation
Because most elements exist as a mixture of isotopes with different abundances, the average must be weighted. For chlorine, about 75% is chlorine-35 and about 25% is chlorine-37, so Aᵣ = (75 × 35 + 25 × 37) ÷ 100 = 35.5. The value lies between the isotope masses and is closer to the more abundant isotope. A weighted mean is calculated by multiplying each isotope mass by its abundance, adding the products, then dividing by the total abundance.
Students should be able to calculate the relative atomic mass of an element given the percentage abundance of its isotopes.
Relative atomic mass (Ar) is a weighted mean of the masses of an element's isotopes, taking account of how common each isotope is. To calculate it, multiply each isotope's mass number by its percentage abundance, add these products, then divide by 100. For example, chlorine is 75% chlorine-35 and 25% chlorine-37, so Ar = (75 × 35 + 25 × 37) ÷ 100 = (2625 + 925) ÷ 100 = 3550 ÷ 100 = 35.5. The answer is not a whole number because it is an average, and it lies between the isotope mass numbers, closer to the more abundant isotope. Percentage abundances must total 100%; if they do not, check the data before calculating.
Your focus
- Define relative atomic mass in terms of carbon-12.
- Calculate a weighted mean relative atomic mass from isotope masses and abundances.
- Explain why the relative atomic mass of an element is usually not a whole number.
Show all 6 objectives
- Calculate relative atomic mass from isotope mass numbers and percentage abundances.
- Explain why relative atomic mass is a weighted mean rather than a simple average.
- Evaluate whether a calculated relative atomic mass is reasonable using the abundance data.
Relative atomic mass exam tips
Marking Points
- Defines relative atomic mass as an average mass compared with 1/12 of the mass of a carbon-12 atom.
- Explains that the average is weighted by the abundance of each isotope.
- Calculates a weighted mean using isotope masses and percentage or fractional abundances.
- Interprets an Aᵣ value as lying between the isotope masses and closer to the most abundant isotope.
- Uses data for chlorine, copper or another element to find Aᵣ from isotope abundances.
- State that relative atomic mass is a weighted mean of isotope masses, not a simple unweighted average.
- Multiply each isotope's mass number by its percentage abundance.
- Add the products and divide the total by 100 when abundances are percentages.
- Check that percentage abundances sum to 100% and that the final answer lies between the lowest and highest isotope mass numbers.
- Give the answer to an appropriate number of significant figures, usually the same as the data provided.
Examiner Tips
- 💡Write the weighted mean as a single expression before calculating, for example (75 × 35 + 25 × 37) ÷ 100.
- 💡Check that the answer lies between the isotope masses and nearer the more abundant isotope.
- 💡Show the abundance values you use, especially when they are given as percentages or decimals.
- 💡Write the calculation in one line before evaluating it, so the weighting is visible to the examiner.
- 💡Estimate first: the answer must lie between the isotope mass numbers and nearer the more abundant isotope.
- 💡If an answer looks like a whole number, check whether the data were already weighted or whether you divided by the wrong value.
Common Mistakes
- Averaging isotope masses without using abundances; correct this by weighting each mass by its abundance before dividing.
- Treating Aᵣ as the mass of a single atom; correct this by describing it as an average over the isotope mixture.
- Forgetting to divide by the total abundance, often 100 for percentages; correct this by completing the weighted mean calculation.
- Averaging the mass numbers without weighting: (35 + 37) ÷ 2 = 36. Correction: weight each mass number by its percentage abundance before dividing by 100.
- Dividing by the number of isotopes instead of 100. Correction: when abundances are percentages, the divisor is 100.
- Forgetting to convert a decimal abundance to a percentage, or mixing fractions and percentages. Correction: use one consistent form, such as percentages throughout.