High-Resolution Mass Spectrometry

Introduction

A low-resolution spectrum tells you that a molecular ion has m/z 28 — but carbon monoxide, nitrogen and ethene all have a nominal mass of 28. How can you tell them apart without any other evidence? The answer is to weigh more precisely. High-resolution mass spectrometry measures m/z to four or more decimal places, and at that precision every molecular formula has its own unique mass. This single measurement is now the standard way chemists confirm the formula of a new compound.

Core explanation

Isotopic masses are not whole numbers. On the atomic mass scale, carbon-12 is defined as exactly 12.0000. Every other nuclide has a mass slightly different from its mass number, because when protons and neutrons bind into a nucleus a little mass is converted into binding energy, and because protons and neutrons themselves are not exactly 1 u each. The exact masses used in HRMS are:

Isotope Exact mass --- --- ¹H 1.0078 ¹²C 12.0000 ¹⁴N 14.0031 ¹⁶O 15.9949

Hydrogen and nitrogen are slightly heavier than their mass numbers; oxygen is slightly lighter.

Same nominal mass, different exact mass. Consider ions of nominal mass 28:

- CO: 12.0000 + 15.9949 = 27.9949 - N₂: 2 × 14.0031 = 28.0062 - C₂H₄: 24.0000 + 4 × 1.0078 = 28.0312

These differ in the second or third decimal place. A high-resolution instrument measuring the molecular ion as 28.0312 identifies ethene unambiguously.

How precise is precise enough? Modern instruments (time-of-flight with reflectrons, Orbitrap, or double-focusing magnetic sectors) achieve mass accuracy of a few parts per million (ppm) . At m/z 200, 5 ppm is ±0.001, easily enough to separate formulae that differ by 0.01 or more. Journals typically require the measured and calculated masses of a new compound to agree within 5 ppm.

Calculating exact masses. Always use the most abundant isotope of each element (¹²C, ¹H, ¹⁴N, ¹⁶O, ³⁵Cl, ⁷⁹Br), because the tallest molecular ion peak in the cluster is made of these. This is the monoisotopic mass , which is different from the average Mr calculated with relative atomic masses from a periodic table.

What HRMS does not tell you. An exact mass fixes the molecular formula, not the structure. Ethanol and methoxymethane are both C₂H₆O with exact mass 46.0417; IR and NMR are then needed to decide how the atoms are connected.

Formulae

Exact mass of ion = Σ(number of atoms × exact isotopic mass). Error in ppm = (measured − calculated) ÷ calculated × 10⁶.

Step-by-step reasoning

To determine a formula from an HRMS value:

1. Note the nominal mass (the value rounded to an integer). 2. List plausible formulae with that nominal mass, using the nitrogen rule. 3. Calculate the exact mass of each, using isotopic masses to four decimal places. 4. Compare with the measured value. 5. Choose the formula within the stated tolerance, typically a few ppm.

Visual explanation

Imagine zooming in on the single line at m/z 44 of a low-resolution spectrum. Under high magnification it separates into distinct thin lines at 43.9898 (CO₂), 44.0011 (N₂O), 44.0261 (C₂H₄O) and 44.0624 (C₃H₈) — one line for each formula that shares the nominal mass.

Real-world analogy

Two bags of sugar both labelled "1 kg" look identical on bathroom scales, but a laboratory balance reading to the milligram reveals that one is 1.0032 kg and the other 0.9987 kg. High-resolution mass spectrometry is the laboratory balance for molecules.

Real-world example

In metabolomics, researchers analyse blood or urine and detect thousands of small molecules at once. Exact masses let them assign a formula to each peak, helping to spot unusual metabolites linked to disease or to identify unknown drugs in toxicology screening without a reference sample.

Why?

Why does oxygen-16 have a mass less than 16 while hydrogen-1 has a mass greater than 1? The ¹H nucleus is a single proton with no binding energy, and a proton is slightly heavier than 1 u. In ¹⁶O, sixteen nucleons are strongly bound, and the mass equivalent of that binding energy (E = mc²) is lost, pulling the total below 16.

Common misconception

"High-resolution mass spectrometry gives the structure of the molecule." It gives only the molecular formula. Isomers have identical exact masses, so structural techniques are still required.

Worked example

Question: A compound gives a molecular ion at m/z 60.0211. Candidate formulae are C₂H₄O₂, C₃H₈O and CH₄N₂O. Which is correct?

Reasoning: C₂H₄O₂ = 24.0000 + 4.0312 + 31.9898 = 60.0210. C₃H₈O = 36.0000 + 8.0624 + 15.9949 = 60.0573. CH₄N₂O = 12.0000 + 4.0312 + 28.0062 + 15.9949 = 60.0323.

Answer: C₂H₄O₂, whose calculated mass matches the measured value.

Quick check

1. Why do CO and N₂ appear as a single peak at low resolution but as two separate peaks at high resolution? Answer: Both have nominal mass 28, but their exact masses, 27.9949 and 28.0062, differ in the second decimal place.

Exam focus

You will usually be given isotopic masses; show each addition clearly and keep four decimal places until the end. Say explicitly which formula "matches the measured m/z to four decimal places". Remember that HRMS distinguishes formulae with the same nominal mass but not isomers.

Advanced insight

The electron's mass (0.00055 u) matters at the highest precision: a positive ion is lighter than the neutral molecule by one electron mass, so careful workers subtract it. Chemists also use the "mass defect" of heteroatoms as a filter; compounds rich in hydrogen have large positive defects, while those containing chlorine, bromine or many oxygen atoms have negative defects.

Summary

High-resolution mass spectrometry measures m/z to four or more decimal places. Because isotopic masses are not whole numbers (¹H 1.0078, ¹⁴N 14.0031, ¹⁶O 15.9949, ¹²C 12.0000 exactly), formulae with the same nominal mass have different exact masses. Comparing a measured value with calculated monoisotopic masses fixes the molecular formula, though not the structure.

Practice questions

1. Calculate the exact mass of the molecular ion of methanol, CH₄O. Answer: 12.0000 + 4 × 1.0078 + 15.9949 = 32.0261. 2. A compound gives m/z 44.0262. Is it CO₂, C₃H₈ or C₂H₄O? Answer: C₂H₄O, whose exact mass is 24.0000 + 4.0312 + 15.9949 = 44.0261, matching within rounding. 3. A measured value of 150.0681 is compared with a calculated value of 150.0678. Calculate the error in ppm. Answer: (0.0003 ÷ 150.0678) × 10⁶ = 2.0 ppm, within a typical 5 ppm tolerance. 4. Explain why HRMS cannot distinguish propan-1-ol from propan-2-ol. Answer: Both have the same molecular formula, C₃H₈O, and therefore the same exact mass; HRMS only determines the formula.