The Chlorine Rule: An Analysis of
Isotope Patterns of Compounds
Containing Multiple Bromine and
Chlorine Atoms
With an Introduction to the Isotope-Pattern Analyzer
Ray A. Gross, Jr.
1

My Reasons for this Presentation
•
Present results obtained at
PGCC
•
Show that content found in textbooks can be improved
•
Motivate students
2

Isotopes of Br and Cl a
Low mass b
High mass
Ratio
( a / b )
Rounde d ratio
Variable
# atoms
Br 79
(50.69)
81 (49.31)
1.028
1:1
Cl 35 (75.78) 37
(24.22)
3.129
3:1 m n
3

Mass Spectrometer
4

77
Br
79
77
Br
81
100 61 59
Bromobenzene
M = 156 158 = M + 2
Schematic diagram of a mass spectrometer 5

77
Br
79
77
Br
81
100 61 59
Bromobenzene
M = 156 158 = M + 2
6

77
Cl
35
77
Cl
35
52
Chlorobenzene
100 32
3:1
112 114
7

Br
1
Cl
1
Br
2
Cl
1
Br
3
Cl
1
M +2 +4 M +2 +4 +6
M +2 +4 +6 +8
Molecular-ion peaks of C
10
H
20
Br
1
Cl
1
, C
10
H
19
Br
2
Cl
1
C
10
H
18
Br
3
Cl
1
.
and
8

Premise
In lieu of pattern matching, it should be possible to determine the number of Br and Cl atoms in a molecular formula of a compound by analyzing the molecularion cluster (i.e., by cluster analysis).
9

Herbert C. Brown
Nobel Laureate
Hydroboration-oxidation with BH
3
(CHM 201)
Reduction with NaBH
4
(CHM 202/204)
10

Lillian Berg
NVCC-Annandale
11

77
Br
79 or 81
ArBr m
Cl n
100 61 59
m = 1, n = 0
A = m + n = 1
T = A + 1 = 2
100 98
1:1
M = 156 158 = M + 2
12

Br
Br
ArBr m
Cl n
51:100:49
m = 2
n = 0
A = 2
T = 3
1:2:1
234 238
13

Br
Br Br
ArBr m
Cl n
34:100:97:32
m = 3
n = 0
A = 3
T = 4
1:3:3:1
312 318
14

Br
Br
Br
Br
ArBr m
Cl n
m = 4
n = 0
A = 4
T = 5
18:68:100:66:16
1:4:6:4:1
390 398
15

Cl
ArBr m
Cl n
52
m = 0
n = 1
A = 1
T = 2
100 32
3:1
112 114
16

Cl
Cl
ArBr m
Cl n
m = 0
n = 2
A = 2
T = 3
100:66:11
9:6:1
146 150
17

Cl
Cl Cl
ArBr m
Cl n
m = 0
n = 3
A = 3
T = 4
27:27:9:1
180 186
18

Cl
Cl
Cl
Cl
ArBr m
Cl n
81:108:54:12:1
m = 0
n = 4
A = 4
T = 5
214 222
19

3 1
3 1
Br
0
Cl
1
3 4 1
3 4 1
Br
1
Cl
1
3 7 5 1
3 7 5 1
Br
2
Cl
1
3 10 12 6 1
3 11 13 6 1
Br
3
Cl
1
M +2 M +2 +4 M +2 +4 +6 M +2 +4 +6 +8
20

1 1
1 1
3 4 1
3 4 1
Br
1
Cl
0
Br
1
Cl
1
9 15 7 1
10 16 7 1
Br
1
Cl
2
27 54 36 10 1
30 59 38 10 1
Br
1
Cl
3
M +2 M +2 +4 M +2 +4 +6 M +2 +4 +6 +8
I
M
= 3 n
21

190
114 = Br + Cl
76 = benzene ring a disubstituted benzene
T = 3
78 100
A = 2
*L
190
/R
194
= 78/24 = 3
n = 1
m = 1
24
ArBr
1
Cl
1
190 194
22

T = 4
A = 3
*L
224
/R
230
= 63/7 = 9
L
Br = 79
2Cl = 70
149
n = 2
m = 1
Ar = 75
224
ArBr
1 a bromodichlorobenzene
Cl
2
L
R R
224 230
23

Theoretical Considerations
Ideal Compounds
Br ( a : b ) = 1:1
Cl ( a : b ) = 3:1
13 C and 2 H negligible
24

•
Ratio ( a : b ) = 1:1
•
(1 a + 1 b ) m for Br m
•
(1 a + 1 b ) 1 = 1 a + 1 b = 1:1
•
(1 a + 1 b ) 2 = 1 a 2 + 2 a b + 1 b 2 = 1:2:1
25

•
Ratio ( a : b ) = 3:1
•
(3 a + 1 b ) n for Cl n
•
(3 a + 1 b ) 1 = 3 a + 1 b = 3:1
•
(3 a + b ) 2 = 9 a 2 + 6 a b + 1 b 2 = 9:6:1
26

Ideal Model = Binomial Pair
( 1a + 1b ) m ( 3a + 1b ) n
Br
1
Cl
1
3a 2 + 4 a b + 1b 2 = 3 :4: 1
27

Results
( 1a + 1b ) m ( 3a + 1b ) n = 1 m 3 n a (m + n) + …. +
1 m 1 n b (m + n)
I
( L / R )
= 1 m 3 n / 1 m 1 n
I
M
= 3 n
Chlorine Rule: When I equals 1, 3, 9,
27 or 81; n is 0, 1, 2, 3, or 4, respectively, where n = number of chlorine atoms.
The number of bromine atoms m equals A – n.
J.Chem.Educ. 2004, 81, 1161-1168 (article available at front desk)
28

Roald Hoffmann-Nobel Laureate
Conservation of orbital symmetry
“Oxygen” Priestley vs Sheele
Hoffmann
Djerassi
Woodward
29

Gross giving lecture with Hoffmann, Djerassi and
Woodward looking on.
30

Structure Begets Properties
• Let’s examine structures.
•
Assume 3:1 and 1:1 isotopic abundances of chlorine and bromine.
•
Consider Br m
, Cl n compounds.
and Br m
Cl n
31

Br
=
m = 1, N = 2
Br
Br
=
m = 2, N = 4
*
Br
*
Br
1
(156)
Br *
Br
Br
1
(234)
2
(236)
*
Br
1
(158)
*
Br
Br *
Br
Br
1
(238)
Br
Br
Br
m = 3, N = 8
=
*
Br
Br
Br
*
Br
Br
Br
*
Br
Br
Br
*
Br
Br
Br
*
Br
Br *
Br
Br *
Br
Br
Br
1
(312)
Br
3
(314)
3
(316)
1
(318)
Br
*
Br
Br
Br
32

Cl
*
Cl
*
Cl
*
Cl
*
Cl
=
n = 1, N = 4
Cl
Cl
=
n = 2, N = 16
*
Cl
Cl
3
(112)
1
(114)
*
Cl
Cl *
Cl
Cl *
Cl
Cl
*
Cl
Cl *
Cl
Cl *
Cl
Cl *
Cl
Cl
*
Cl
Cl *
Cl
Cl *
Cl
Cl *
Cl
Cl
*
Cl
Cl *
Cl
Cl *
Cl
Cl *
Cl
Cl
9
(146)
6
(148)
1
(150) 33

m = 1, n = 0
N = 2
m = 1, n = 1
N = 8
m = 2, n = 1
N = 16
m = 2, n = 2
N = 64
Br Br
1:1
BrCl BrCl BrCl Br Cl
Br Cl Br Cl Br Cl BrCl
3:4:1
BrClBr BrClBr BrClBr Br Cl Br
Br ClBr Br ClBr Br ClBr BrCl Br
BrCl Br BrCl Br BrCl Br Br ClBr
Br Cl Br Br Cl Br Br Cl Br BrClBr
3:7:5:1
BrClBrCl BrClBrCl BrClBrCl BrClBr Cl
BrClBrCl
BrClBrCl
BrClBrCl BrClBrCl BrClBr Cl
BrClBrCl BrClBrCl BrClBr Cl
Br Cl BrCl Br Cl BrCl Br Cl BrCl Br Cl Br C l
Br ClBrCl Br ClBrCl Br ClBrCl Br ClBr Cl
Br ClBrCl Br ClBrCl Br ClBrCl Br ClBr Cl
Br ClBrCl Br ClBrCl Br ClBrCl Br ClBr Cl
BrCl BrCl BrCl BrCl BrCl BrCl BrCl Br C l
BrCl Br Cl BrCl Br Cl BrCl Br Cl BrCl BrCl
BrCl Br Cl BrCl Br Cl BrCl Br Cl BrCl BrCl
BrCl Br Cl BrCl Br Cl BrCl Br Cl BrCl BrCl
Br ClBr Cl Br ClBr Cl Br ClBr Cl Br ClBrCl
Br Cl Br Cl Br Cl Br Cl Br Cl Br Cl Br Cl BrCl
Br Cl Br Cl Br Cl Br Cl Br Cl Br Cl Br Cl BrCl
Br Cl Br Cl Br Cl Br Cl Br Cl Br Cl Br Cl BrCl
BrClBr Cl BrClBr Cl BrClBr Cl BrClBrCl
9:24:22:8:1
34

Results
N = 2 m 4 n
N = 2 m 2 n 2 n
N = 2 A 2 n
Chem. Educ. 2003, 8, 182-186
35

Summary Part I for Br m
Cl n
Compounds
• Derived a chlorine-rule equation, I
M
= 3 n
• Applied it to find gross structures of unknowns
• Derived a unit-sample equation, N = 2 A 2 n
36

Follow-on to the Chlorine Rule
•
An automated A + 2 isotope-pattern analyzer (IPA)
•
IPA is on my website
J. Chem. Educ., in press
37

Example of a Print Out of a Mass
Spectrum in the Molecular-Ion Region
Mass
224
225
226
227
228
229
230
Percent
64.4
4.3
100.0
6.9
45.6
3.2
6.4
38

Molecular-Ion Data is Entered into the IPA
The Excel program returns the A
+ 2 (Cl, Br, S) composition of the molecular formula
39

Homework Assignment for
Selected Students
• Pick up slip from front desk
• Enter data from your slip into IPA
• Obtain the Cl, Br, S composition (e.g.,
Br
1
Cl
2
) and record it on your slip
• Write your name on the slip and turn it in next Tuesday.
40

Acknowledgement: Mass
Spectra from the Spectral
Data Base System (SDBS)
41

Ende
42

Lecture attended by hordes of students eager to learn.
43

Gross and Friends
44