Part 2: Mass spectrometry & isotope calculations

1. What a mass spectrometer is for

A time-of-flight (TOF) mass spectrometer is used to:

• identify elements from the masses of their isotopes
• measure isotope masses and their relative abundances, so that A_r can be calculated
• find the relative molecular mass (M_r) of molecules

The flight tube is evacuated to minimise collisions with residual gas. Collisions could change ion speed or direction and distort flight times.

There are four stages: ionisation → acceleration → ion drift → detection.

2. Stage 1: ionisation

Electron impact

The sample is vaporised. An electron gun fires high-energy electrons at the gaseous sample, and each impact knocks an electron out of a particle, forming a 1+ ion.

The net change can also be written as X(g) → X⁺(g) + e⁻. Electron impact is quite harsh, so molecules often break into fragments. It is mostly used for elements and for compounds with low M_r.

Electrospray ionisation

The sample is dissolved in a volatile, polar solvent and pushed through a fine needle held at a high positive voltage. This produces a fine aerosol of charged droplets. As the solvent evaporates, molecules gain a proton (H⁺):

Electrospray is a soft ionisation method that keeps fragmentation to a minimum. This makes it suitable for large molecules such as proteins. "Soft" does not mean you always get one single peak, though: isotope peaks still appear, and some molecules gain more than one proton.

3. Stages 2–3: acceleration and ion drift

Acceleration: positive ions are accelerated by an electric field. Ions of the same charge accelerated through the same potential difference gain the same kinetic energy; this includes the singly charged ions in the usual AQA model. Different charge magnitudes through the same voltage give different kinetic energies.

Ion drift: the ions then enter a flight tube with no electric field, where each moves at a roughly constant speed. For ions with the same kinetic energy (KE = ½mv²), a lighter ion moves faster and reaches the detector sooner.

More generally, ions accelerated through the same voltage have flight times proportional to √(m/z). Ions with different charge magnitudes do not gain the same kinetic energy through the same voltage.

4. Stage 4: detection

Give both parts: what happens to the ion (it gains electrons) and what is measured (a current). Answers that only say "the ion hits the detector" are not enough.

5. Mass-to-charge ratio (m/z)

The x-axis of a mass spectrum is m/z: the ion's mass divided by the size of its charge, where z is in units of the electron's charge.

When you identify the species that causes a peak, give both the isotope and the charge, e.g. 40 Ca+. Neutral atoms are not accelerated or detected, so every peak comes from an ion.

6. Flight-time equations and units

The most common mistakes are using the molar mass in g instead of the mass of one ion in kg, and forgetting the square root. Learn these equations: questions may not give them to you.

7. Worked example: flight time of an argon ion

An 40 Ar+ ion (take molar mass 40.0 g mol⁻¹) has KE = 2.00 × 10⁻¹⁶ J and travels along a 1.20 m flight tube. N_A = 6.022 × 10²³ mol⁻¹. Calculate the flight time.

1. Mass of one ion in kg: m = (40.0 × 10⁻³) ÷ (6.022 × 10²³) = 6.6423 × 10⁻²⁶ kg
2. Speed: v = √(2KE/m) = √((2 × 2.00 × 10⁻¹⁶) / (6.6423 × 10⁻²⁶)) = √(6.0220 × 10⁹) = 7.76015 × 10⁴ m s⁻¹
3. Time: t = d/v = 1.20 / (7.76015 × 10⁴) = 1.55 × 10⁻⁵ s (3 s.f.)

Keep the unrounded values in your calculator and only round at the end.

8. Reverse method: finding M_r from flight time

1. Convert t to seconds and d to metres.
2. Calculate the mass of one ion: m = 2KE × (t/d)² (in kg).
3. Convert to molar mass: m × N_A × 1000 gives the value in g mol⁻¹, which equals m/z for a 1+ ion.
4. If the ion is [M+H]⁺ from electrospray, subtract 1 to get M_r. Don't subtract 1 for an M⁺ ion from electron impact.

In a molecular spectrum, the molecular ion peak is not necessarily the tallest one or the one furthest to the right. The tallest peak (the base peak) is just the most abundant ion, and it may be a fragment. Small M+1 and M+2 peaks from heavier isotopes, or peaks from impurities, can sit to the right of the molecular ion.

9. Relative atomic mass

Mention both "average" and the carbon-12 reference. An isotope's isotopic mass is its actual relative mass, which is close to its mass number. The mass number is just the whole-number count of protons plus neutrons.

Divide by the total abundance. That total is only 100 when the abundances are percentages. Peak heights on a spectrum are relative and often won't add up to 100.

Worked example: element E (made-up data)

A_r = 510 ÷ 10 = 51.0. This makes sense: the answer is closest to 50, the most abundant isotope.

10. Finding missing abundances

Two isotopes: boron

Boron has A_r = 10.8 and two isotopes with masses of about 10 and 11. Let x be the fraction of ¹⁰B, so the fraction of ¹¹B is (1 − x).

So ¹⁰B is 20% and ¹¹B is 80%. Check: 20 + 80 = 100 ✓, and 10.8 is closer to 11 than to 10, which matches the heavier isotope being more common ✓.

Three isotopes (made-up data)

An element has isotopes of mass 90, 91 and 92 and A_r = 90.50. Isotope 90 makes up 70%, so the other two share the remaining 30%. Let x% be isotope 91, which makes isotope 92 (30 − x)%.

So isotope 91 is 10% and isotope 92 is 20%. Check: 70 + 10 + 20 = 100 ✓.

11. Extension: spectra of diatomic molecules

This goes beyond the core mononuclear-ion calculations. It is included in the Chemrevise guide.

Take chlorine as 75% ³⁵Cl and 25% ³⁷Cl. A Cl₂ molecule contains two atoms, so we combine their probabilities:

The mixed combination counts twice because it can happen two ways round. Bromine (50% ⁷⁹Br, 50% ⁸¹Br) gives Br₂⁺ peaks at m/z 158, 160 and 162 in a 1 : 2 : 1 ratio. Don't average these molecular peaks as if they were single atoms to find A_r.

12. Finesse practice

Original Finesse practice questions, not AQA past-paper questions.

13. Sources