Topic 15 · page 21 of 28

Accurate relative molecular mass

A high-resolution mass spectrometer measures the molecular ion peak to four decimal places. Atoms do not have whole-number masses, so the exact value tells you the molecular formula.

14 min read15.17(i)15.17(ii)

Why four decimal places help 15.17(ii)

In Topic 10 you used the molecular ion peak of a mass spectrum to find the relative molecular mass to the nearest whole number. Many different formulas share the same whole-number mass. For example, C₃H₄O₂, C₄H₈O and C₃H₈N₂ all have a relative molecular mass of 72.

A high-resolution mass spectrometer measures the mass of the molecular ion to four decimal places. The reason this separates the formulas is that individual isotopes do not have whole-number masses. Each element contributes a slightly different amount, so each formula has its own accurate mass.

Isotope Accurate relative atomic mass
¹H 1.0078
¹²C 12.0000
¹⁴N 14.0031
¹⁶O 15.9949

The question gives you these values to four decimal places. Carbon-12 is exactly 12.0000, because the scale is defined by it.

Calculating an accurate relative molecular mass 15.17(ii)

Add the accurate relative atomic mass of every atom in the molecular formula.

Worked exampleEthanol, C₂H₆O

  1. Carbon: 2 × 12.0000 = 24.0000
  2. Hydrogen: 6 × 1.0078 = 6.0468
  3. Oxygen: 1 × 15.9949 = 15.9949
  4. Total = 24.0000 + 6.0468 + 15.9949 = 46.0417

Worked exampleThree formulas with MrM_\text{r} near 72

Calculate the accurate relative molecular mass of C₃H₄O₂, C₄H₈O and C₃H₈N₂.

  1. C₃H₄O₂: 3 × 12.0000 + 4 × 1.0078 + 2 × 15.9949 = 36.0000 + 4.0312 + 31.9898 = 72.0210
  2. C₄H₈O: 4 × 12.0000 + 8 × 1.0078 + 15.9949 = 48.0000 + 8.0624 + 15.9949 = 72.0573
  3. C₃H₈N₂: 3 × 12.0000 + 8 × 1.0078 + 2 × 14.0031 = 36.0000 + 8.0624 + 28.0062 = 72.0686
A number line from 72.00 to 72.10 with three marked points: C3H4O2 at 72.0210, C4H8O at 72.0573 and C3H8N2 at 72.0686. A note says that a measured value of 72.0573 matches C4H8O only.
Three formulas that are all 72 to the nearest whole number have different accurate masses.

Keep all four decimal places in each step and give the final answer to four decimal places, as the question's data are given.

Suggesting a structure 15.17(i)

Compare the measured value with the calculated value for each possible formula. The one that matches (to about the fourth decimal place) is the molecular formula.

Worked exampleWhich formula?

The molecular ion peak of an organic compound is at m/z = 72.0573. Which of C₃H₄O₂, C₄H₈O and C₃H₈N₂ fits?

  1. The three calculated values are 72.0210, 72.0573 and 72.0686.
  2. The measured value 72.0573 matches only C₄H₈O.
  3. Possible structures with this formula include butanal and butanone (both C₄H₈O), so the accurate mass has given the formula and not yet the structure.

The accurate mass can only suggest possible structures, because isomers have exactly the same accurate mass. To choose between butanal and butanone you need more evidence: a test such as Tollens', or the NMR spectra later in this topic.

A second example shows how the method works for small molecules. Three different molecules all have a nominal mass of 28:

Formula Accurate relative molecular mass
CO 12.0000 + 15.9949 = 27.9949
N₂ 2 × 14.0031 = 28.0062
C₂H₄ 2 × 12.0000 + 4 × 1.0078 = 28.0312

Check yourself

  1. Why can a high-resolution mass spectrum distinguish between C₃H₄O₂ and C₃H₈N₂ when a low-resolution one cannot?
  2. Calculate the accurate relative molecular mass of C₂H₄O₂ using H = 1.0078, C = 12.0000 and O = 15.9949.
  3. Calculate the accurate relative molecular mass of C₃H₈O, and say how it differs from that of C₂H₄O₂.
  4. The molecular ion peak of a compound is at 60.0573. Decide between C₂H₄O₂, C₃H₈O and CH₄N₂O (accurate mass 60.0323) and suggest two possible structures.
  5. Calculate the accurate relative molecular mass of C₄H₈O₂ and state what extra information is needed to decide between ethyl ethanoate and methyl propanoate.

Answers cover these until you have tried the questions

  1. Isotopes do not have whole-number masses, so the two formulas have different accurate masses (72.0210 and 72.0686) even though both round to 72. Only a spectrometer reading to four decimal places can separate them.
  2. 2 × 12.0000 + 4 × 1.0078 + 2 × 15.9949 = 24.0000 + 4.0312 + 31.9898 = 60.0210
  3. 3 × 12.0000 + 8 × 1.0078 + 15.9949 = 36.0000 + 8.0624 + 15.9949 = 60.0573. It is 0.0363 higher than 60.0210.
  4. The measured 60.0573 matches C₃H₈O. Possible structures: propan-1-ol, propan-2-ol and methoxyethane (any two).
  5. 4 × 12.0000 + 8 × 1.0078 + 2 × 15.9949 = 48.0000 + 8.0624 + 31.9898 = 88.0522. Both esters are C₄H₈O₂ and have this same accurate mass, so you need other evidence, such as the proton NMR spectrum, to decide between them.