Estimate carbon count from the M+1 peak
Apply the syllabus ratio between M+1 and M⁺ abundances to estimate the number of carbon atoms.
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
Which peaks are compared in the carbon-count relationship?
What you will learn
- Use the supplied M+1 formula
- Calculate carbon count from relative peak abundance
- Check the estimate against the molecular formula
Apply the syllabus relationship carefully
The AS syllabus gives n = 100 × abundance of [M+1]⁺ / (1.1 × abundance of M⁺), where n is the number of carbon atoms. Use the two peak abundances on the same scale.
Keep the factor 1.1 in the denominator. It represents the approximate abundance contribution used in the syllabus relationship; do not replace the equation with a direct percentage reading.
Round only after checking the context
The calculation estimates an integer carbon count. If the result is close to a whole number, round appropriately and check it against the molecular formula or mass information supplied.
A result far from an integer can signal a copied peak, inconsistent intensity scale or arithmetic error. Do not infer a unique molecular structure from carbon count alone.
Pause and explain
Where does the factor 1.1 appear in the syllabus formula?
Worked example
A spectrum has M⁺ abundance 100 and [M+1]⁺ abundance 3.3. Estimate the number of carbon atoms.
Show the worked solution
- Use n = 100×[M+1]⁺/(1.1×M⁺).
- Substitute 3.3 and 100 on the same abundance scale.
- Evaluate and interpret the estimate as an integer count.
Answer n = 100×3.3/(1.1×100) = 3 carbon atoms.
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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.
M⁺ has abundance 80 and [M+1]⁺ has abundance 2.64. Estimate n.
Give me a hint
Substitute both peak abundances into the syllabus expression.
Compare my reasoning
- Calculate 100×2.64.
- Divide by 1.1×80.
- Interpret the result as a carbon count.
n = 100×2.64/(1.1×80) = 3 carbon atoms.
Look for these in your work
- Correct peaks used
- Factor and denominator correct
- Integer estimate interpreted
A spectrum has M⁺ abundance 120 and [M+1]⁺ abundance 5.28. Estimate the carbon count.
Give me a hint
Keep the same abundance scale in numerator and denominator.
Compare my reasoning
- Compute 100×5.28 = 528.
- Compute 1.1×120 = 132.
- Divide 528 by 132.
n = 4 carbon atoms.
Look for these in your work
- Scale is consistent
- Arithmetic correct
- Carbon count is integer
A student uses n = 100×M⁺/(1.1×[M+1]⁺). Explain why the formula is reversed and give the correct expression.
Give me a hint
The M+1 peak is the small signal whose abundance is compared with the molecular-ion peak.
Compare my reasoning
- The carbon estimate should rise when [M+1]⁺ abundance rises relative to M⁺.
- Place [M+1]⁺ in the numerator.
- Keep 1.1×M⁺ in the denominator.
Correct: n = 100×abundance([M+1]⁺)/(1.1×abundance(M⁺)). A larger M+1-to-M ratio indicates more carbon atoms.
Look for these in your work
- Direction of relationship explained
- Numerator corrected
- Denominator corrected
Common mistakes
- Putting M+1 in the denominator
- Dropping the factor 1.1
- Using peak values from different scales
- Reporting a non-integer without checking the data
What can you explain now?
Which peaks are compared in the carbon-count relationship?
Compare with the explanation
[M+1]⁺ and M⁺
The syllabus formula uses these two molecular-ion abundances.
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Make it stick
How do you use the [M+1]⁺ to M⁺ abundance ratio to estimate carbon count?
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.