1. 1 Factoring Isotope Patterns Chlorine and Bromine with nitrogen Ray A. Gross, Jr. Prince George’s Community College

2. 2 Outline Develop an equation for the isotope patterns of Br m Cl n compounds Show the isotope-patterns equal two independent factors: Br and Cl factors Show that the chlorine factor and n are evident by the first term in the isotope pattern.

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6. 6 Bromine Binomial Ratio of Br-79 to Br-81 = 1:1 (a + b) m for Br m (a + b) 1 = a + b = 1:1 (a + b) 2 = a 2 + 2ab + b 2 = 1:2:1

7. 7 Chlorine Binomial Ratio of Cl-35 to Cl-37 = 3:1 (3a + b) n for Cl n (3a + b) 1 = 3a + b = 3:1 (3a + b) 2 = 9a 2 + 6ab + b 2 = 9:6:1

8. 8 Ideal Model (1a + 1b) m (3a + 1b) n Br 1 Cl 1 3a 2 + 4ab + 1b 2 = 3:4:1

9. 9 Isotope Pattern (I.P.) equals a product of Br and Cl factors I.P. = (1a + 1b) m (3a + 1b) n 3:4:1 = (1:1) 1 (3:1) 1

10. 10 Premise Because an isotope pattern for a Br m Cl n compound is composed of the product of a bromine factor and a chlorine factor, the pattern should be divisible by either factor to give the other factor.

11. 11 Question For 27: 81: 90: 46: 11: 1 What factor do we divide by?

12. 12 Bromine and Chlorine Factors m or nBromine (1:1) m Chlorine (3:1) n Terms T 11:13:12 21:2:19:6:13 31:3:3:127:27:9:14 41:4:6:4:181:108:54:12:15

13. 13 Results The lead term in a normalized pattern equals 3 n. The value of n determines the chlorine factor. T = m + n + 1, or m = T – (n + 1)

14. 14 9:15:7:1 = (9:6:1) (1:1) m 1: 1 9: 6 : 1 9: 6 :1) 9: 15: 7: 1 1:1) 9: 15: 7 : 1 9: 6: 1 9 : 9 9: 6: 1 6 : 7 9: 6: 1 6 : 6 1 : 1

15. 15 T = m + n + 1 _ _ _ 1: 2: 1 27: 81: 90: 46: 11: 1 27: 27: 9: 1 _ _

16. 16 Br 2 Cl 3 27 Cl Cl Cl Br Br 27: 81: 90: 46: 11: 1

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21. 21 Summary The lead number in a normalized isotope pattern of an unknown Br m Cl n compound uniquely defines n and the corresponding chlorine factor within the pattern. Given n, the number of bromine atoms can be found from the number of terms T in the pattern.

22. 22 Acknowledgements Junhua Yan’s Isotope Pattern Calculator http://www.geocities.com/junhuayan/pattern.htm (accessed May 2003). Institute of Advanced Industrial Science and Technology; Tsukuba, Ibaraki, Japan SDBSWeb: http://www.aist.go.jp/RIODB/SDBS/ (accessed May 2003). NSF Grant: DUE-0202431 Submitted to The Chemical Educator