Relative atomic mass and the mass spectrometer
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Question
What is relative atomic mass, A_{r}?
Answer
The **weighted average** mass of an element's isotopes, relative to one-twelfth of a carbon-12 atom. It has **no units**.
Question
Why is A_{r} usually not a whole number?
Answer
Because it averages **isotopes of different masses**, weighted by their **abundance** (e.g. Cl = 35.5).
Question
What does a mass spectrometer do?
Answer
It separates the atoms/ions of a sample by **mass**, producing a **mass spectrum**.
Question
What is on the axes of a mass spectrum?
Answer
**m/z** (mass-to-charge ratio) on the x-axis; **relative abundance** on the y-axis.
Question
What does the m/z of a peak tell you?
Answer
For singly-charged ions, the **mass of that isotope**.
Question
What does the height of a peak tell you?
Answer
The **relative abundance** of that isotope — the taller the peak, the more common the isotope.
Question
How do you calculate A_{r} from a spectrum?
Answer
$A_{r} = \dfrac{\sum(\text{mass} \times \%\,\text{abundance})}{100}$ — weight each isotope mass by its abundance, sum, divide by 100.
Question
How many peaks for an element with 3 isotopes?
Answer
**Three** peaks — one peak per isotope.
Question
What if abundances are given as a ratio, not %?
Answer
Divide the weighted sum by the **total of the abundances** instead of by 100.
Question
Sanity check on a calculated A_{r}?
Answer
It must lie **between** the lightest and heaviest isotope masses, closest to the **most abundant** one.
Question
Is A_{r} = 35.5 a real chlorine atom's mass?
Answer
No — chlorine atoms are ³⁵Cl or ³⁷Cl; 35.5 is the **weighted average** (75% ³⁵Cl, 25% ³⁷Cl).
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