In the Classroom
Determination of the Natural Abundances of Krypton and Xenon Isotopes Using Mass Spectrometry: A Demonstration of Isotopes and the Basis of Atomic Mass David N. Blauch,* Merlyn D. Schuh, and Felix A. Carroll Department of Chemistry, Davidson College, Davidson, NC 28035; *
[email protected] Gas chromatography–mass spectrometry (GC–MS) is an extremely powerful and versatile analytical tool, as evidenced by the numerous articles on this technique in recent issues of this Journal (1). We have sought to incorporate GC–MS into our curriculum at many levels, including introductory chemistry courses. In this article we describe a demonstration that we perform during the very first laboratory period in our general chemistry program. Its objectives are to show how mass spectrometry can be used to determine the natural abundances of the isotopes of an element and to give students a basis for understanding the relationship between the isotopic composition of an element and its atomic mass. This demonstration is scheduled to coincide with our classroom discussion of atomic properties, which occurs very early in the course. In fact, many textbooks introduce mass spectrometry at an early stage to explain how one can detect the existence of isotopes and determine their relative abundances (2). Our demonstration is unique among the many published GC–MS undergraduate experiments, including some dealing with the distribution of isotope peaks in molecular mass spectra (3), because it is directed toward students who are just beginning their first course in chemistry and because it requires no knowledge of molecular structure or fragmentation reactions. An added benefit of the demonstration is that it involves no dangerous or toxic substances. This simple demonstration consists of injecting a sample of krypton or xenon gas into a GC–MS. The noble gas is not retained on the GC column and elutes quickly, at which time its mass spectrum is recorded. Each student is given a copy of the resulting mass spectrum and asked to determine (i) the naturally occurring isotopes of the noble gas, (ii) the relative abundance of each isotope, and (iii) the average atomic mass of the noble gas. The students are also asked to locate published values for the isotopic abundances and the average atomic mass and to compare these values with those obtained from the demonstration. This exercise thus provides early experience in finding information in reference books and on the World Wide Web, and it gives students an important early lesson about the origin of the information contained in textbooks. Krypton and xenon are attractive analytes for this demonstration. As unreactive nontoxic gases, they are easy and safe to handle. The atomic masses of krypton (the most abundant isotope has mass number 84) and xenon (the most abundant isotope has mass number 132) lie in the operating range of commercial GC–MS instruments. In addition, both elements have a large number of naturally occurring isotopes, which makes the interpretation of the mass spectra of these elements interesting and challenging. Because the analysis of xenon isotopes may be employed for monitoring compliance with the Nuclear Test Ban Treaty (see below), this experiment 584
also provides students with a practical application of their studies on the first day of chemistry laboratory. The gas chromatograph is not really necessary for this demonstration, because no separation of the xenon–air or krypton–air mixture is required. However, many departments have GC–MS instruments, and a high-resolution mass spectrometer is not essential for the demonstration. In addition, it is beneficial for the students to learn about instrumental chromatographic techniques at an early stage and to see how multiple instrumental techniques (in this case, gas chromatography and mass spectrometry) can be combined. Furthermore, our system includes an auto-injector, which gives students a glimpse of how automation is utilized in modern analytical chemistry. Under the conditions we employ, unretained analytes elute approximately 1.3 minutes after injection. The short period required for injection and elution of the analyte gives the instructor time to briefly explain the principles of operation of the instrument and to show the students its components. The Demonstration
Sample Preparation Before performing the demonstration, the instructor purges a 2-mL sample vial with krypton or xenon gas1 and fits it with a screw-on cap equipped with an integral septum. Although the noble gas is slowly lost from the vial, an amount sufficient for performing this demonstration remains in the vial for two weeks. Mass Spectrometry At our institution the demonstration is performed using a Varian Saturn 2000 gas chromatograph–mass spectrometer (an ion-trap mass spectrometer), but we have also successfully tested the demonstration on an Agilent 6890 Series gas chromatograph with 5973 Mass Selective Detector (a quadrupole mass spectrometer). No separations are required for this demonstration. The gas chromatograph simply provides a convenient means to introduce the sample into the mass spectrometer.2 In each demonstration, 1 µL of gas from the sample vial is injected onto the GC column using a 100:1 split ratio. Even after a period of more than a week, sufficient analyte remains in the vial for a 1-µL sample volume to provide a strong signal. We use a 30-m × 0.25-mm CP-Sil 8CB column (Varian), but the choice of column is relatively unimportant owing to the negligible interactions of krypton and xenon with the stationary phase. The only relevant features of the chromatography are the size of the column and the flow rate of the carrier gas, because these factors determine the elution time for the analyte. At 40 °C and a flow rate of 1.4 mL
Journal of Chemical Education • Vol. 79 No. 5 May 2002 • JChemEd.chem.wisc.edu
In the Classroom Table 1. Stable Isotopes of Krypton
Percent Base Peak
100
Kr
Mass Number
80 60
Percent Natural Abundance Lit. (4)
This Worka
0.3535
0.3 ± 0.5
78
77.920386
40
80
79.916378
2.2809
3.2 ± 0.4
20
82
81.913485
11.5830
12.1 ± 0.9
83
82.914136
11.4953
13.2 ± 1.1
84
83.911507
56.9889
54.0 ± 1.9
86
85.910610
17.2984
17.2 ± 1.2
0 40
50
60
70
80
90
100
110
120
130
140
m /z
aUncertainties
100
Percent Base Peak
Atomic Mass/ amu (4)
are standard deviations for a set of six measurements.
Table 2. Stable Isotopes of Xenon
Xe 80 60
Mass Number
Atomic Mass/ amu (4)
Percent Natural Abundance Lit. (4)
This Worka
124
123.906120
0.0891
not detected
40
126
125.904288
0.0888
not detected
20
128
127.903540
1.9173
0
129
128.904784
26.4396
130
129.903509
4.0827
5.5 ± 0.7
131
130.905085
21.1796
22.0 ± 0.6
132
131.904161
26.8916
26.5 ± 0.6
134
133.905815
10.4423
10.1 ± 0.7
136
135.907221
8.8689
8.2 ± 0.6
40
50
60
70
80
90
100
110
120
130
140
m /z Figure 1. Mass spectra of krypton and xenon.
min᎑1, both krypton and xenon elute approximately 1.3 min after injection. The mass spectrometer is configured to employ electron impact ionization and to record mass spectra with m/z in the range of 36 to 249.3,4
Data Analysis The peak in the total ion chromatogram attributable to krypton or xenon is readily identified because it is the only significant peak. In our experience, no background peaks are observed in the mass spectrum for the noble gas (unless the concentration of noble gas is very small). A mass spectrum and data table are printed for each of the students. Interpretation and Data Analysis Identification of the Naturally Occurring Isotopes Sample mass spectra for krypton and xenon are shown in Figure 1.5 Both analytes are monatomic elements; thus no fragmentation occurs and the peaks in the mass spectrum are solely attributable to krypton or xenon ions. Most ions bear a +1 charge, so the mass-to-charge ratio (m/z) corresponds to the mass of the xenon isotope.6 Although the dominant peaks in the mass spectrum of krypton lie in the m/z range 78 to 86, one or two small peaks appear around m/z 42.7 Similarly, the mass spectrum of xenon shows a small cluster of peaks around m/z 65 to 68, while the dominant peaks lie in the m/z range of 128 to 136. Perceptive students will recognize that these small peaks at low m/z correspond to mass-to-charge ratios that are exactly one-half those of the dominant peaks and that, because fragmentation cannot occur, these peaks are attributable to ions bearing a +2 charge. The most abundant isotopes are readily identified from the positions of the peaks for the +1 ions in the mass spectrum. The absence of a peak, however, does not indicate that an isotope does not occur naturally. The natural abundances of
aUncertainties
2.69 ± 0.11 25.0 ± 0.8
are standard deviations for a set of six measurements.
124Xe
and 126Xe, for example, are 0.0891% and 0.0888%, respectively (4 ). In our experiments, we did not detect these trace isotopes,8 and thus no peaks at m/z 124 or 126 appear in the mass spectrum for xenon (Fig. 1B). However, other instructors may observe these peaks depending upon their instrument and operating conditions. The natural abundance of 78Kr is 0.3535% (4 ). Depending upon the instrument parameters and the particular injection, a peak at m/z 78 may or may not be observed.9 Thus the absence of a peak indicates either that the isotope does not occur naturally or that the natural abundance of the isotope is below the detection limits of the instrument under the operating conditions.
Determination of Natural Abundances The height of a peak in the mass spectrum is directly proportional to the number of ions with that mass-to-charge ratio detected by the instrument.10 The total number of ions detected corresponds to the sum of the ion counts for all peaks in the mass spectrum attributable to analyte ions. (Ions bearing a +2 charge appear as a constant fraction of the number of Xe+ ions and so for this reason it is not necessary to include them in this analysis.) The natural abundance of an isotope is the fraction of all +1 ions of that atom attributable to that isotope. Sample data are shown in Table 1 for krypton and in Table 2 for xenon. Determination of the Average Atomic Mass In a simple format the demonstration could end with student identification of the naturally occurring isotopes for the noble gas. The mass spectrometric data, however, permit students to quantify the abundance of each isotope and then to use these results to calculate the average atomic mass of the
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In the Classroom
noble gas. When doing this, some students may be inclined (erroneously) to calculate the average atomic mass as a simple average. Using data obtained for krypton, for example, the simple average for the six isotopes would be 1
⁄6 (78 + 80 + 82 + 83 + 84 + 86) = 82.17
(1)
This approach is based upon the flawed assumption that all isotopes are equally abundant; that is, out of 600 krypton atoms collected at random, there would be 100 of each isotope. In reality, of course, one will find many more 84Kr than 78Kr atoms. (In fact, out of 600 krypton atoms only two are likely to be 78Kr, whereas 342 are likely to be 84Kr.) Thus a weighted average is required. The atomic mass of each isotope must be weighted (multiplied) by the probability, P, that an atom chosen at random is the specified isotope. In eq 1, each mass number was multiplied by the same probability (P = 1⁄6 ) on the implicit assumption that each of the six isotopes is equally likely to be found. In reality, the probability of each isotope’s being found is the natural abundance (e.g., for 82Kr P82 = 0.121, based on the demonstration data in Table 1). The weighted average for the atomic mass of krypton is therefore 78P78 + 80P80 + 82P82 + 83P83 + 84P84 + 86P86 = 78(0.003) + 80(0.032) + 82(0.121) + 83(0.132) +
(2)
84(0.540) + 86(0.172) = 83.82 An additional factor to consider is that the atomic mass of an isotope does not correspond exactly to the mass number, which is an integer.11 The correct value is obtained by using the actual atomic masses (Table 1 for krypton and Table 2 for xenon) in eq 2. This analysis produces an atomic mass of 83.74 ± 0.05, which is in good agreement with the accepted value of 83.79894 for krypton (4). In our demonstrations, we found a mean atomic mass for xenon of 131.25 ± 0.04, which compares well with the accepted value of 131.29269 (4 ). Hazards Although they are considered nontoxic, krypton and xenon are stored under high pressure; rapid release of these gases can reduce the concentration of oxygen in the air and lead to asphyxiation. Discussion This demonstration and follow-up exercise give general chemistry students direct experience with modern instrumentation (GC–MS) at the very outset of the course. This early exposure impresses upon students the capabilities and roles of modern instrumentation and provides firsthand experience in the types of measurements discussed in the textbook and in lectures. Students see direct experimental evidence for the existence of isotopes, which is a satisfying affirmation of the statements found in their textbook. The computation of natural abundances and the average atomic mass reinforces concepts and calculations discussed in the classroom. It is important that students recognize that while krypton, for example, has an atomic mass of 83.79894, there is no krypton atom that actually possesses this mass. The average atomic mass does not represent any of the isotopes; it is instead a property of a collection of many atoms. The average 586
atomic mass should not, therefore, be used to calculate the properties of a single atom but should be employed in the calculation of properties for large numbers of atoms. In addition, our students are asked to compare their values with those found in the literature, which provides early experience in using chemical handbooks (e.g., the CRC Handbook of Chemistry and Physics [4a]) and the World Wide Web (e.g., the Table of Nuclides at the Korean Atomic Energy Research Institute [5]). In the course of comparing their data with published data, some students may discover a few discrepancies. The published data will identify 124Xe and 126Xe isotopes, whereas the students’ data may, depending upon the mass spectrometer, show no evidence for these isotopes. The discussion of such discrepancies provides an opportunity for students to learn about the detection limits of an analytical method. Furthermore, the natural abundances, although similar, will not be exact. Students who participate in different demonstration sections can compare their data to determine the reproducibility of the experimental data. In this way the concepts of random and systematic errors may also be introduced. Even though krypton and xenon are known for being remarkably unreactive, they do find practical application in society. One example is the Automated Radioxenon Sampler/ Analyzer (ARSA) developed at Pacific Northwest National Laboratory to detect nuclear detonations as a monitoring technique for the Nuclear Test Ban Treaty (6 ). Radioactive isotopes of xenon are formed by decay of the fission products from a nuclear explosion. ARSA samples the atmosphere, traps and purifies xenon gas from the air sample, and quantifies the 133Xe and 135Xe isotopes using a scintillation counter. The halflives of 133Xe and 135Xe are 5.24 days and 9.10 hours, respectively. The measurement of the 135Xe/133Xe ratio can be used to detect and characterize a recent nuclear explosion. Conclusions In summary, this simple, fast, safe demonstration provides introductory chemistry students with direct evidence for the existence of isotopes and allows them to understand the origins of the atomic masses of elements presented in their textbooks. In addition, data from the demonstration can be used as the basis for a discussion of exact atomic mass and stable and unstable isotopes. Acknowledgments The Saturn 2000 GC–MS instrument employed in this demonstration was purchased through an Undergraduate Instrumentation and Laboratory Improvement grant from the National Science Foundation, award number 9750603. We are also indebted to Owen Moe for his assistance in testing this demonstration on the Agilent 6890 Series GC/5973 Mass Selective Detector at Lebanon Valley College. We thank the reviewers for their helpful comments. Notes 1. Our samples of krypton and xenon were obtained as compressed gases from Air Products. One-liter ampules of these gases can be obtained from Alfa Aesar. 2. The sample injected into the gas chromatograph will include
Journal of Chemical Education • Vol. 79 No. 5 May 2002 • JChemEd.chem.wisc.edu
In the Classroom air in addition to the noble gas. The major components of air have masses below the minimum m/z setting of 36 employed in the mass spectrometry and thus do not appear in the mass spectrum. By lowering the minimum m/z setting, however, students may be shown the mass spectrum of air. 3. The target ion count (TIC) for the ion trap should be set to a sufficiently low value to avoid space–charge effects and to minimize background signals. We found a TIC of 1000 to 5000 to work well, although this setting may differ for other instruments. The mass spectrum of perfluorotributylamine was used to calibrate m/z positions immediately prior to performing the demonstration. 4. The chromatographic peak for the noble gas is very narrow (one to two seconds in width), and the mass spectrometer must be able to acquire a mass spectrum in less than a second. For instruments with slower scanning rates, it may be necessary to reduce the mass range to permit faster scanning. It is only necessary, though, to have one or two points on the peak for the noble gas. With the Saturn 2000 a single mass spectrum over the m/z range 36 to 249 was acquired in 0.16 s; typically three spectra were acquired and the average was recorded every 0.50 s. With the Saturn 2000 a single mass spectrum in the m/z range 36 to 650 may be acquired in 0.32 s. 5. All sample data were acquired on a Varian Saturn 2000 GC–MS. 6. The Saturn 2000 GC–MS provides unit mass resolution, and at this level of precision the atomic mass and mass number are the same. If the mass spectrometer employed provides higher resolution, students can read the atomic mass directly and round that value to the nearest integer to obtain the mass number. 7. Figure 1A displays a mass spectrum with unit resolution for m/z. For this reason the six-peak cluster around m/z 84 for Kr+ ions appears as two small peaks around m/z 42 for Kr+2 ions. 8. The detection limit is clearly dependent upon the choice of instrument and upon instrumental parameters. A low ion-trap TIC setting (e.g., 1000) produces too few ions for trace isotopes to be ionized and detected. As an approximation, it is necessary that the product of the TIC and the natural abundance be greater than unity for an isotope to be detected. In our experience, raising the TIC above ca. 5000 produced background signals substantially larger than the signals expected for xenon-124 and xenon-126, preventing reliable detection and quantification of these trace isotopes. In testing this demonstration on an Agilent 5973 Mass Selective Detector, however, peaks for xenon-124 and xenon-126 were detected. 9. In our experience, the m/z 78 peak is frequently missing when the ion-trap TIC is below 1000 because there are insufficient ions in the trap for a significant number of krypton-78 ions to be formed. At higher TIC settings, the krypton-78 may be reliably detected. 10. We have not attempted to measure a calibration curve (signal versus concentration) or to test whether the response varies from
one isotope to another. We have found the results obtained assuming a linear response to be sufficiently accurate for the purposes of this demonstration. 11. If the mass spectrometer provides m/z resolution of ±0.1 or better, the isotopic mass obtained directly from the mass spectrum is sufficiently precise for the calculation of the average atomic mass.
Literature Cited 1. See, for example (all in J. Chem. Educ.): Schildcrout, S. M. 2000, 77, 501–502. Nahir, T. M. 1999, 76, 1695–1696. O’Malley, R. M.; Lin, H. C. 1999, 76, 1547–1551. Burden, S. L.; Petzold, C. J. 1999, 76, 1544–1547. Fleurat-Lessard, P.; Pointet, K.; Renou-Gonnord, M.-F. 1999, 76, 962–965. Pelter, M. W.; Macudzinski, R. M. 1999, 76, 826–828. Galipo, R. C.; Canhoto, A. J.; Walla, M. D.; Morgan, S. L. 1999, 76, 245– 248. McGowin, A. E.; Hess, G. G. 1999, 76, 23–24. 2. See for example: Zumdahl, S. S. Chemical Principles, 3rd ed.; Houghton Mifflin: New York, 1998. Brown, T. L.; LeMay, H. E. Jr.; Bursten, B. E. Chemistry: The Central Science, 8th ed.; Prentice Hall: Upper Saddle River, NJ, 2000. Olmsted, J. III; Williams, G. M. Chemistry: The Molecular Science, 2nd ed.; William C. Brown: Chicago, 1997. 3. All in J. Chem. Educ.: Schildcrout, S. M. 2000, 77, 1433–1434. Amenta, D. S.; DeVore, T. C.; Gallaher, T. N.; Zook, C. M.; Mosbo, J. A. 1996, 73, 572-575. Eichstadt, K. E. 1992, 69, 48–51. O’Malley, R. M. 1982, 59, 1073–1076. O’Malley, R. M.; Lin, H. C. 1999, 76, 1547–1551. 4. (a) CRC Handbook of Chemistry and Physics, 80th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1999; this handbook provides natural abundances (precise to 0.1–0.2%) and atomic masses for the isotopes of krypton and xenon. (b) Valkiers, S.; De Bièvre, P. In Separation Technology; Vansant, E. F., Ed.; Process Technol. Proc. 1994, 11, 965–968. (c) Audi, G.; Wapstra, A. H. Nucl. Phys. A 1995, 595, 409–480; this information is available electronically: Atomic Mass Data Center. The 1995 Update to the Atomic Mass Evaluation; http://www-csnsm.in2p3.fr/AMDC/ web/masseval.html (accessed Mar 2002). 5. Nuclear Data Evaluation Lab, Korean Atomic Energy Research Institute; Table of Nuclides; http://atom.kaeri.re.kr/; this information is mirrored at the Brookhaven National Laboratory Web site: http://www2.bnl.gov/CoN/ (both accessed Mar 2002). 6. Johnson, J. Chem. Eng. News 2000, 78 (Jun 12), 29. Bowyer, T. W.; Abel, K. H.; Hubbard, C. W.; Panisko, M. E.; Reeder, P. L.; Thompson, R. C.; Warner, R. A. J. Radioanal. Nucl. Chem. 1999, 240, 109–122. Bowyer, T. W.; Abel, K. H.; Hubbard, C. W.; McKinnon, A. D.; Panisko, M. E.; Perkins, R. W.; Reeder, P. L.; Thompson, R. C.; Warner, R. A. J. Radioanal. Nucl. Chem. 1998, 235, 77–81.
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