Mass Spectrometry: Isotope Effects

Figure 1 and the isotope abundance data from Table 1, we can see that there are 1.08 ¹³C atoms for every 100 ¹²C atoms, and the ¹³C peak will be 1.08% as large as the ¹²C peak.

The example above is simple, but the same methods can be applied to determine isotope peaks in more complicated molecules as well. The molecule C₄Br₁O₂H₅ has several isotope effects: ¹³C, ²H, ⁸¹Br, ¹⁷O, and ¹⁸O all must be taken into account. First we will look at the (M+1)⁺ peak in comparison with the M⁺ peak. Only isotopes that will increase the value of M by 1 must be taken into consideration here – since ⁸¹Br and ¹⁸O would both increase M by 2, they can be ignored (the most abundant isotopes for Br and O are ⁷⁹Br and ¹⁶O). Like the previous example, there are 1.08 ¹³C atoms for every 100 ¹²C atoms. However, there are 4 carbon atoms in our molecule, and any one of them being a ¹³C atom would result in a molecule with mass (M+1). So it is necessary to multiply the probability of an atom being a ¹³C atom by the number of C atoms in the molecule. Therefore, we have:

4C * 1.08 = 4.32 = molecules with a ¹³C atom per 100 molecules

We can repeat this analysis for ²H and ¹⁷O:

5H * 0.015 = 0.075 = molecules with a ²H atom per 100 molecules

2O * 0.04 = 0.08 = molecules with a ¹⁷O atom per 100 molecules

Any of the three isotopes, ¹³C, ²H, or ¹⁷O occurring in our molecule would result in an (M+1)⁺ peak. To get the ratio of (M+1)⁺/M⁺, we need to add all three probabilities:

4.32 + 0.075 + 0.08 = 4.475 = (M+ 1)⁺ molecules per 100 M⁺ molecules

We can say then that the (M+1)⁺ peak is 4.475% as high as the M⁺ peak.

A similar analysis can be easily repeated for (M+2)⁺:

1Br * 98 = 98 = molecules with an ⁸¹Br molecule per 100 molecules

2O * 0.2 = 0.4 = molecules with an ¹⁸O molecule per 100 molecules

98 + 0.4 = 98.4 = (M+2)⁺ molecules per 100 M⁺ molecules

The (M + 2)⁺ peak is therefore 98.4% as tall as the M⁺ peak.

This method is useful because using isotopic differences, it is possible to differentiate two molecules of identical mass numbers.

References

1. Skoog, DA. Holler, FJ. Crouch, SR. Principles of Instrumental Analysis, 6^th Edition. Thomson Brooks/Cole (2007).
2. Coursey, J. S., Schwab, D. J., Dragoset, R. A. (2001). Atomic Weights and Isotopic Compositions. National Institute of Standards and Technology, Gaithersburg, MD.

Outside Links

• http://en.wikipedia.org/wiki/Mass_spectrometer
  • This wikipedia page is about the Mass Spectrometer instrument.
• http://en.wikipedia.org/wiki/Mass_spectrum_analysis
  • This wikipedia page is more directly related to isotope effects, as it focuses on reading mass spectra.
• http://www.chem.uoa.gr/applets/AppletMS/Appl_Ms2.html
  • This applett is fun to play with. It generates isotope peaks in a specified mass fragment.

Problems

1. Predict the (M+1)⁺ relative peak heights for meta-nitrobenzene.
2. Why would this method of looking at isotope ratios relating to peak heights make distinguishing molecules with Chlorine and Bromine from other molecules very easy?
3. Predict the (M+4)⁺ relative peak heights for C₃H₂SCl₂
4. Predict the (M+1)⁺ and (M+2)⁺ relative peak heights for 1,1,1-tribromo-2-propene

Contributors

• Morgan Kelley (UCD)