R. J. Robinson, C. G. Warner, and R. 5. Gohlkel
Spectroscopy Laboratory DOW Corninq Corporation Midland, Michigan 48640
II I
The Caldation of Relative Abundance of lsoto~eClusters in Mass Spectrometry
W i t h the advent of mass spectrometry as a widely available tool, the problem of calculation of the relative abundance of isotope peaks in a mass spectrum is becoming of wider interest. Several articles are available describing these calculation^.^ The mathematical principles involved in the calculations are set out in references a and e, but as far as we are able to determine, none of the methods described in the literature explicitly indicate which of the isotope peaks represents the molecular ion. If the elements involved do not have isotopes lower in mass than the most abundant isotope, there is no problem; but for elements that exhibit this characteristic, such as boron, tin, iron, and mercury, this recognition of which peak in the mass spectrum represents the molecular ion is not always obvious and can lead to misinterpretation. For example, from Table 1 we can see that boron has isotopes occurring as masses 10 and 11 with relative abnndances of 0.25 and 1.00, respectively, and bromine has isotopes of 79 and 80 with abundances of 1.00 and 'Present Address: Finnigan Instrument Corporation, Palo Alto, California 94304. (a) BEYNON, J. H., "Mass Spectrometry and Its Application to Organic Chemistry," Elsevier Publishing Co., Amsterdam, 1960, p. 71-83. ( b ) KISER,R. W., "Introduction toMassSpectrometry and Its Applications," Prentice-Hall, Englewood Cliffs, New Jersey, 1965, p. 229-231. (c) MARGRAVE, J.. L., AND POLANSKY, R. B., J. CHBM.EDUC.,39, 335 (1962) ( d ) REED, R. I., "Applications of Mass Spectrometry to Organic Chemistry," Academic Press, London, 1966, p. 23.
0.98. The compound RBra would show the isotope cluster given in Table 2 if its molecular ion appeared in a mass spectrum. Since the molecular ion is defined to Table 1. Relative Isotopic Abundances for Common Elementsa Element name
Mass number
Relative abundance
Hydrogen
1 2 10 11 12 13 14
1.00 (0.0001) 0.25 1.00 1.00 0.011 1.00 0.004 1.00 (0.0004) 0.002 1.00 0.32 1.00 0.98 0.029 0.020 0.010 0.432 0.230 0.728 0.260 1.00 0.143 0.181
Boron Carbon Nitrogen
15 -.
Oxygen Chlorine Bromine Tin
16 17 18 35 37 79 80 112 114 115 116 117 118 119 120 122 124
Indexb 0 +1 -1 0 0 +1 0 +I '0 +1 +2 0 +2 0
T-6 i -5 -4 -3 -2 -1 0 +2 +4
Excerpted from reference ( 5 ) and normslized to 1.00 for the most abundant isotope. 6 Index = Difference in mass between isotope under consider* tion and most abundant isotope for the element concerned.
Volume 47, Number 6, June 1970
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467
Table 2. Calculated Relative Abundonces of Isotope Peoks for BBrs Relative intensitv
Mass
0.08 0.34 (Molecular ion)
n zi;
be the sum of the product of the mass of the most abundant isotope times the number of occurrences of that element ii the compound, the parent or molecular ion of RRr? would occur at mass 248. but the relative intensityys only 0.34, and the peak aimass 247 is part of the isotope cluster but not the parent ion as is the peak of intensity 1.00 at mass 250. The following "mechanical" method for obtaining the relative abundances and relative positions of isotopic peaks, known to practicing mass spectrometrists hut apparently not known in general, is easy to use and, we feel, less tedious than execution of the combinatorial equations that describe the phenomena. The student is cautioned that an understanding of the calculations cannot be obtained from the following but rather from articles cited in the references. The key to the method is the layout of the numbers of the work sheet. This is explained in an example where the isotope ratios for BC1;Br are calculated (see Table 3). Line 1 is the index numbers of the peak position relative to the narent ion (index number = 0). The numbers in this line cover art nrbitrsry mngr itnd are ~ W e ! ~ d rn.3d the i w ~ d divl~1es. I.>w 2 I> the istrtupe mtiw for the firit d h r i w aligned urnler their index numbers. Line 3 is the isotope ratios for the first bromine again aligned under the proper index. Line 4 is the first partial product formed from thejirst element of line 3 multidied by each element of line 2 in turn and Dlaced in the position corresponding to the algebraic sum of t h e index numbers. Line 5 is the second partial product formed from the second element of line 3 mult,iplied by each element of line 2 in turn and placed in the position corresponding to the algebraic sum of the index numbers (0.32, index = +2; 0.98, index = +2; 0.31, index = +2 +2 = +4). Additional lines of partial products
.~
~
Tabie 3.
would appear for each element of line 3 if there were more than two elements in the line. Line 6 is the sum of the partial products in lines 4 and 5. These sums represent the isotope ratios for ClBr. Line 7 enters the isotope ratios for the second chlorine, again in the positions corresponding to the indices for each isotope. Lines 8 and 9 are the partial products taken as before. Line 10 is the sum of 8 and 9 and represents the isotope ratios for ClnBr. Line 11 is the isotope ratios for boron. Note the positions again corresponding to the index number. Lines 12 and 13 are the partial products. Note that each element of the partial product is placed in the column corresponding to the algebraic sum of the index numbers of the elements being multiplied (0.25, index = -1, X 1.0, index = 0, = 0.25, 0 = -1 ; 0.25, index = -1, X 1.62, index = index = -1 +2, = 0.405, index = -1 2 = +I). Line 14 is the sum of the partial products in lines 12 and 13 and is the desired result. Line 15 is the result normalized to 100% for the largest peak and line 16 shows the masses of each peak obtained by calculating the mass far index = 0 and then algebraically adding each index number to this m m . Note that the parent ion (index = 0) is unequivocally identified. The order in which each atom of each element is entered is immaterial. Since the totals of the partial products (see discussion on line 6 above) at each step represents the isotope ratio for the elements introduced up to that step, a judicious choice of the order in which elements are mtered into the calculation allows the result of a eiven s t e ~ in
+
+
ratios of groups of atoms and merely udd new or additional atoms.
The foregoing approach reduces the calculations to a svstemntir method xith rniuimum opportur~ityfor error and allow rhc oos~tiveidentifitvirion of the ourent ion. Since the meihod can be very tedious for ling calculations, it has been programmed in the BASIC language for time-sharing computers and a listing of the program is nrailable upon request. The output of this progr:irn for the comoo~indSnBr.CI. . .is eiven in Table4. L~
-
~
Table 4. Relative Dosition
Computer Output for SnClzBrn Relative intensity
Relative Dosition
Relative intensity
Somple Colculotion of Isotope Ratios for BClzBr
Linea no. Index Isotope ratios atom 1 Isotope ratios atom 2 1st partial product 2nd ~ a r t i aproduct l
1 2 3 4 5
Sum of line 4 and 5 Isotope ratios atom 3 1st partial product 2nd partial product Sum of lines 8 and 9 Isotope ratios of atom 4 1st partial product 2nd partial product Sum of 12 and 13 Normalized to 1W% Mass a
Contents of each line explained in text.
468
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Journal of Chemical Education
-1
0 1.0 1.0 1.0
+1
+2 0.32 0.98 0.32 0.98
+3
+4
0.31
f 5
+6
