Calculate relative atomic mass from isotope data
Use isotope masses weighted by their relative abundances and divide by the total abundance.
Section 22 · Analytical techniques
AS Level; Cambridge International Chemistry 9701, syllabus for 2028–2030. Use the functional-group data supplied by Cambridge; knowledge of how a mass spectrometer works is not required. Spectra and values in these questions are illustrative. Written practice is self-checked
Before you begin
- Recognise the functional groups from Topics 13–20 and calculate relative mass and weighted means.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How do relative abundances enter the relative atomic mass calculation?
What you will learn
- Set up a weighted mean for isotope masses
- Calculate relative atomic mass from abundances
- Check the result lies between isotope masses
Weight each isotope by its abundance
Relative atomic mass is the weighted mean of an element's isotope masses. Multiply each isotope mass by its relative abundance, add the products, and divide by the total abundance.
If percentages sum to 100, divide by 100. If the data are relative peak intensities that do not sum to 100, the same weighted-mean structure applies, but divide by their total instead.
Use the answer as a check on the data
The result should lie between the lightest and heaviest isotope masses. It will be closer to the isotope with the greater abundance.
Show the weighted calculation, not a simple average of the isotope masses unless their abundances are equal.
Pause and explain
If an isotope has the greater abundance, where should the weighted mean lie?
Worked example
An element has isotopes of masses 10 and 11 with abundances 20% and 80%. Calculate its relative atomic mass.
Show the worked solution
- Multiply each mass by its percentage: 10×20 and 11×80.
- Add the weighted values.
- Divide by 100.
Answer Aᵣ = (10×20 + 11×80)/100 = 10.8.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Isotopes of an element have masses 35 and 37 with abundances 75% and 25%. Calculate Aᵣ.
Give me a hint
Use the weighted sum and divide by 100.
Compare my reasoning
- Calculate 35×75 and 37×25.
- Add the products.
- Divide by 100.
Aᵣ = (35×75 + 37×25)/100 = 35.5.
Look for these in your work
- Both masses weighted
- Abundances combined correctly
- Answer checked between 35 and 37
A spectrum gives isotope peaks at masses 24 and 26 with intensities 90 and 10. Calculate the relative atomic mass.
Give me a hint
The intensities total 100, so use them as weights and divide by their sum.
Compare my reasoning
- Weighted total = 24×90 + 26×10.
- The intensities sum to 100.
- Divide the weighted total by 100.
Aᵣ = (24×90 + 26×10)/(90+10) = 24.2.
Look for these in your work
- Peak intensities used as weights
- Correct denominator
- Result nearer the more abundant isotope
A learner reports Aᵣ=36 for isotopes of masses 35 and 37 with abundances 75% and 25%. Identify the likely error and correct it.
Give me a hint
Check whether the answer is between the isotope masses and closer to the 75% isotope.
Compare my reasoning
- The answer must be between 35 and 37.
- It should be closer to 35 because that isotope is more abundant.
- Compute the weighted mean.
The correct value is 35.5. A value of 36 is the unweighted mean and ignores the 75:25 abundance ratio.
Look for these in your work
- Error identified
- Weighted calculation supplied
- Abundance used to check result
Common mistakes
- Taking an unweighted mean
- Dividing by 100 when the supplied intensities do not sum to 100
- Adding abundances rather than weighted masses
- Reporting a result outside the isotope mass range
What can you explain now?
How do relative abundances enter the relative atomic mass calculation?
Compare with the explanation
As weights on the isotope masses
More abundant isotopes contribute more to the weighted mean.
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Make it stick
How do you calculate a weighted isotope mean, and what quick check catches an implausible result?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.