Lesson 9 · 25 min

Mass spectrometry: isotope clusters and fragments

Ionise molecules and sort them by mass-to-charge: chlorine’s 3 : 1 and bromine’s 1 : 1 clusters follow from isotope convolution, the base peak is often a fragment, and high resolution tells CO⁺ from N₂⁺.

In this lesson

Describe how a mass spectrometer ionises molecules, separates the ions by mass-to-charge ratio m/z and detects them
Predict the isotope clusters of Cl, Br and S compounds by convolving isotope abundances (the binomial expansion), and count those atoms from the M + 2 peaks
Read the molecular ion, the base peak and simple fragments (loss of a Cl atom, CH₃⁺ and so on)
Use exact masses and resolving power to tell apart ions of the same nominal mass

Dichloromethane, CH₂Cl₂, has a molar mass of 84.93 g/mol — yet its mass spectrum has no strong peak at m/z 85, and its tallest peak is not the molecular ion at all but m/z 49. Every line in a mass spectrum is a family of ions; learn to read them and a few micrograms of sample will tell you how many chlorine or bromine atoms a molecule holds, and even separate ions whose masses differ by a few thousandths.

Predict first

The molecular ion of CH₂Cl₂ gives peaks at m/z 84, 86 and 88. Roughly what are their relative heights?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Only 84; no 86 or 88 1 : 1 : 1 About 9 : 6 : 1 (100 : 64 : 10) 1 : 2 : 1

Ionise, separate, detect

Electron ionisation (EI) passes gaseous molecules through a 70 eV electron beam, knocking out one electron to give a singly charged radical cation M⁺·, the molecular ion. Its excess energy breaks it into fragment ions and neutral pieces; only the charged ones are detected. A mass analyser sorts the ions by m/z: a quadrupole lets only one m/z through on a stable path; a time-of-flight (TOF) analyser gives every ion the same kinetic energy so that light ions arrive first; a magnetic sector bends them in a field. A detector (an electron multiplier) counts them one by one. Peak heights are usually given relative to the tallest peak, the base peak, set to 100.

“Soft” methods such as electrospray (ESI) and matrix-assisted laser desorption (MALDI) make almost no fragments and suit large molecules like proteins.

t = L\sqrt{\frac{m}{2zeU}}

Time-of-flight analyser: ions accelerated through a voltage U cross a field-free tube of length L in a time proportional to √(m/z).

$t$: flight time
$L$: length of the flight tube
$m, z$: ion mass and charge number
$e, U$: elementary charge and accelerating voltage

An isotope cluster is a probability problem

Each atom “draws lots” independently from the natural isotope mixture, so a molecule’s isotope distribution is the convolution of its atoms’ distributions — for a two-isotope element, a binomial expansion. Rules of thumb:

One Cl: M + 2 is about 32 % of M (3 : 1); two Cl: 100 : 64 : 10; three Cl: 100 : 96 : 31 : 3.
One Br: M and M + 2 almost equal; two Br: 1 : 2 : 1; three Br: 1 : 3 : 3 : 1.
One S: M + 2 about 4.4 % (³⁴S), the tell-tale of sulfur; every C adds about 1.1 % to M + 1 (¹³C).

Fragments carry their own isotope signatures: in CH₂Cl₂ the base peak at m/z 49 and its partner at 51 stand about 3 : 1, so that fragment kept only one chlorine — it is CH₂Cl⁺, formed by losing a Cl atom.

Electron ionisation 70 eV · isotope convolution · resolution

Mass spectra: isotope clusters and fragments

Formula

M + 1 = 6.5 %, M + 2 = 97.5 % (relative to the lightest peak)

Nominal mass	Exact mass / u	Relative / %
156	155.9575	100.0
157	156.9608	6.5
158	157.9554	97.5
159	158.9588	6.4

Type formulas into the isotope-pattern calculator: C6H5Br, CHCl3, SnCl4, C60, SO2 … Count the peaks in each cluster and read the height of M + 2. Then look at CCl₄ in the EI spectrum: there is no molecular ion at m/z 152, and the base peak is the CCl₃⁺ quartet. Finally raise R past about 2500 in the resolution tab and watch CO⁺ and N₂⁺ separate.

Worked example

The molecular-ion cluster of bromoform

CHBr₃ shows its molecular ion at m/z 250, 252, 254 and 256. With ⁷⁹Br 50.69 % and ⁸¹Br 49.31 %, compute the four relative heights (ignore ¹³C and ²H).

Exact mass. With ¹²C defined as exactly 12 u, no other nuclide has a whole-number mass: ¹H 1.00783, ¹⁴N 14.00307 and ¹⁶O 15.99491 u. So CO⁺ (27.9949), N₂⁺ (28.0061) and C₂H₄⁺ (28.0313) share the nominal mass 28 but not their exact masses. An instrument with enough resolving power R = m/Δm (about 2500 to separate CO from N₂) tells them apart, and an exact mass can be turned back into an elemental formula.

Concept check

A compound’s molecular-ion cluster is two peaks of almost equal height, 2 mass units apart. It most probably contains:

one chlorine atom one bromine atom two chlorine atoms one sulfur atom

Try the calculation

What resolving power R = m/Δm does a mass spectrometer need to separate CO⁺ (27.9949 u) from N₂⁺ (28.0061 u)?

Key takeaways

Electron ionisation makes the molecular ion M⁺·, which breaks into fragment ions; the analyser sorts them by m/z and heights are relative to the base peak = 100.
An isotope cluster is the convolution of each atom’s isotope distribution: Cl 3 : 1, Br 1 : 1, S an M + 2 of about 4 %, several atoms by binomial expansion.
The base peak is often a fragment (CH₂Cl⁺, CCl₃⁺, CH₃⁺); the molecular ion may be weak or missing.
Exact masses separate ions of the same nominal mass: CO⁺ and N₂⁺ need R ≈ 2500.

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Data and references

NIST Mass Spectrometry Data Center, EI mass spectra of Cl₂, Br₂, SO₂, CCl₄, CH₂Cl₂, CHBr₃ and CH₃Br, in the NIST Chemistry WebBook, NIST SRD 69 (P. J. Linstrom, W. G. Mallard, eds.).
J. Meija et al., “Isotopic compositions of the elements 2013 (IUPAC Technical Report)”, Pure Appl. Chem. 88, 293–306 (2016); M. Wang et al., “The AME 2020 atomic mass evaluation”, Chinese Phys. C 45, 030003 (2021).
F. W. McLafferty, F. Tureček, Interpretation of Mass Spectra, 4th ed., University Science Books (1993).
D. C. Harris, Quantitative Chemical Analysis, 9th ed. (2016), ch. 22 (mass spectrometry, resolving power).