factoring isotope patterns chlorine and bromine with nitrogen

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Factoring Isotope Patterns Chlorine and Bromine

withnitrogen

Ray A. Gross, Jr.Prince George’s Community College

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Outline

• Develop an equation for the isotope patterns of BrmCln 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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156

Br m = 1T = 2

1:1

100 61 59

100 98

Brm

4

Cl

Cln

n = 1T = 2

52 100 31

100 32

3:1

112

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Br

Cl

BrmCln

m = 1 n = 1 T = 3

77 100 24

78 100 24

3:4:1

190

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Bromine Binomial

• Ratio of Br-79 to Br-81 = 1:1

• (a + b)m for Brm

• (a + b)1 = a + b = 1:1

• (a + b)2 = a2 + 2ab + b2 = 1:2:1

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Chlorine Binomial

• Ratio of Cl-35 to Cl-37 = 3:1

• (3a + b)n for Cln

• (3a + b)1 = 3a + b = 3:1

• (3a + b)2 = 9a2 + 6ab + b2 = 9:6:1

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Ideal Model

(1a + 1b)m(3a + 1b)n

Br1Cl1

3a2 + 4ab + 1b2 = 3:4:1

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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

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Premise

• Because an isotope pattern for a BrmCln

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.

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Question

• For 27: 81: 90: 46: 11: 1

• What factor do we divide by?

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Bromine and Chlorine Factors

m or n Bromine

(1:1)m

Chlorine

(3:1)n

Terms

T

1 1:1 3:1 2

2 1:2:1 9:6:1 3

3 1:3:3:1 27:27:9:1 4

4 1:4:6:4:1 81:108:54:12:1 5

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Results

• The lead term in a normalized pattern equals 3n.

• The value of n determines the chlorine factor.

• T = m + n + 1, or m = T – (n + 1)

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

1: 1 9: 6 : 19: 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 1 : 1

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T = m + n + 1

_ _ _ 1: 2: 1

27: 81: 90: 46: 11: 1

27: 27: 9: 1 _ _

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Br2Cl3

27 Cl Cl Cl Br Br

27: 81: 90: 46: 11: 1

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224

10:17:7:1

62 100 45 6Unknown

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224

10:17:7:1

62 100 45 6

UnknownBr

10:17: 7 : 1 9:Cl:Cl:Br

224149 = Br1Cl2 75 = benzene residue

Cl

Cl

Mass spectrum of 1-bromo-2,4-dichlorobenzene

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M = 283

85 190 132 26

3:7: 5:1

Unknown

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NH2

M = 283 = N1

Figure 4. Mass spectrum of 2,6-dibromo-4-chloroaniline.

BrBr

Cl

283207 = Br2Cl1N1 76 = benzene residue

85 190 132 26

3:7: 5:13 : 7 : 5 : 13 Cl Br BrUnknown

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Summary

• The lead number in a normalized isotope pattern of an unknown BrmCln

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.

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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