A Source of lsomer-Drawing Assignments Richard A. Kjonaas Indiana State University, Terre Haute, IN 47809 Drawing all of the possible isomers for a particular molecular formula is a valuable learning experience. There is, however, no corhprehensive source gomwhich instructors can choose a wide variety of good isomer drawing examples to use a s homework assignments and exam questions.' I n a n effort to remedy this, the accompanying table has been generated.' Each entry i n t h e table consists of a series of three numbers:
Chem 251
Name
SIZiLPIurf
m a w a l l of the compounds that have the molecular formula ClHloO
I
1.
cH~C@H,C~@H
&-
0- C H I
H
the number of isomers that can be drawn if all stereoisomerism is ienored the n-ber of isome& that can be drawn if cis-trans isomerism is acknowledged but all other stereoisomerism is ignored the total number of isomers including all stereoisomers The number of isomers that can be drawn for a given molecular formula depends on the mles used by the one who is doing the drawing. The rules that were used for generating this table are as follows. 1. Evev atom has exactly the following number of bonds.
carbon nitrogen omen hydrogen and halogen
As a result of this, earhenes, nitrenes, and so on, are excluded from the table. 2. Trans cycloalkenes and trans-bridged compounds, including trans-fused ring compounds, are excluded from the table if they are too strained to exisL3 3. All other possible isomers are included even when their existenee is doubtful because of angle strain, steric strain, or other reasons.
'isomer enumeration is an active and important area of research. Two recent articles in this Journaleach serve as an informative introduction to thesubject, and both of them mntain numerous references to the primary and secondary literature in the area: Balaban, A. T.; Kennedy, J. W.; Quintas, L. V. J. Chern. Educ. 1988, 65, 304-313, and Hansen, P. J.; Jurs, P. C. J. Chern. Educ. 1988, 65, 661464. Neither of these two articles, nor any others that we can find,present a tabulated isomer count of the type presented herein. 'This table was generated by the "draw and count" method followed bv extensive cross-checkina. 3The imaliest known trans cvcioalkens is trans-cvcioactene: ~,~ ~,~~~~ ~. the smal esl rrans-fuse0cycfoDutaneis trans-bcyc0[3.2.0]heptaneand the smallesl irans-f~sw cycopropane 1s trans-bcyc0[5.1.0]0nane. See Marcn, J. AdvancedOrganrc Chern~stry,3rd ed.; Jonn W ley and Sons: New York, 1985;pp tl t and 114 and references therein. ~~~~~
~
~
Determining which isomers are missing and which are drawn more than once by using a vertical key and placing check marks on the student's paper ratherthan on the key itself.
452
Journal of Chemical Education
four three two one
~
~~
~
~
~
~
~
~
The Numbe? of Isomers Per Molecular Formula Entry
~orrnula~
3 4 5 6 7 8 9 9a 9b 9c 10 10a lob 10c 10d 11 Ila Ilb Ilc Ild 12 12a 12b 12c 12d
bm2nr.2 CnH2nXY CnH2o-1x3 CnHzn-iXzY CoHzn-n-~xYZ CoHzneN CnH2m20 alcohols ethers total cnH2nt1ox alcohols ethers hypohalltes total cnH2nOxz alcohols ethers hypohalites total CnH2nOXY alcohols ethers hypohalites total
13 13a 13b 1X 13d 13e 13f 14 14a 14b 14c 15 15a 15b 1%
CnHzn+202 peroxides hydroperoxides diols etherlalcohole diethersf total CnHzn alkenes cycloalkanes total C~HZRIX haloalkenes halocycloalkanes total
16 16a 16b 16c 17 17a 17b 17c
C~HZRZXZ dihaloaikenes dihalocycloalkanes total CO~ZRZXY dihaloalkenes dihalocycloalkanes total
18a 18b 18c
trihaloalkenes trihalocycloalkanes total
n=I
NO. of UnsaturationsC
U
1-1-1
n=2
L-L-L
n=3
n=4
3-3IJ
4-4-5
n=5
L I-L 1-3,
!3 22
n=6
n=7
5L-5L- IUO
31-31-69 39-39.
-
1-1-1
5-3-4
J-3-10
1-1-2 1-1-1
44-8 2-2-2
13-13-32 4-4-4
LI-LI-60 42-42-120 6-89
17-17-21
39-39-55
1-1-1 0-0-0 1-1-1
1-1-1 1-1-1 2-2-2
2-2-2 1-1-1 3-3-3
4-45 3-3-3 7-7-8
8-8-11 6-6-7 14-14-18
17-17-28 15-15-19 32-32-47
39-39-74 33-33-49 72-72-123
1-1-1 0-0-0 1-1-1 2-2-2
2-2-3 1-1-1 1-1-1 4-4-5
5-5-8 3-3-4 2-2-2 10-10-14
12-12-23 9-9-13 4-45 25-25-41
31-31-69 25-25-42 8-8-11 64-64-122
17-17-28
39-39-74
1-1-1 0-0-0 1-1-1 2-2-2
3-3-4 2-2-2 2-2-3 7-7-9
9-9-16 6-6-8 5-5-8 20-2032
27-27-60 22-22-36 12-12-23 61-61-119
1-1-2 0-0-0 22-2 3-34
4-4-8 13-13-32 2-2-3 9-416 4-4-6 10-10-16 10-10-17 32-32-64
42-42-120 33-33-69 24-24-46 99-99-235
0-0-0 1-1-1 1-1-1 0-0-0 0-0-0 P2-2
1-1-1 1-1-1 2-2-2 1-1-1 0-0-0 5-5-5
1-1-1 2-2-2 4-4-5 3-54 1-1-1 11-H-I3
3-3-3 4-4-5 9-9-13 9-9-13 3-3-3 28-28-37
6-6-7 15-15-19 8-8-H 17-17-28 52-52-108 21-21-37 25-25-42 8-8-10 25-25-35 68-68-107
33-33-49 39-39-74
0-0-0 0-0-0 0-0-0
1-1-1 0-0-0 1-1-1
1-1~1 1-1-1 2-2-2
3-44 2-2-2 5-6-6
5-6-6 5-6-7 10-12-13
27-36-42 29-42-59 56-78-101
0-0-0 0-0-0 0-0-0
1-1-1 0-0-0 1-1-1
3-4-4 1-1-1 4-54
8-11-12 4-5-7 12-16-19
21-30-36 14-21-32 35-51-68
0-0-0 0-0-0 0-0-0
2-3-3 0-0-0 2-3-3
5-7-7 2-3-4 7-10-11
18-27-31 9-15-22 27-42-53
52-78-106 36-66-112 88-144-218
1 1 1
0-0-0 0-0-0 0-0-0
2-3-3 0-0-0 2-3-3
8-13-14 2-3-5 10-16-19
27-43-56 12-22-39 39-65-95
1 1 1
0-0-0 0-0-0 0-0-0
1-1-1 0-0-0 1-1-1
6-8-8 2-3-4 8-11-12
u
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1
n=8
31-31-69
62-62-138
13-17-18 12-16-20 25-33-38
1
~~~
'Tne t mt number n earn tnree-n~moerentry gnores a1 slereosomensm The semno nLmoer acknowsdges cs-lrans samersm. but gnorss all otner stereo samer sm The lnm n~mberac*no*leaoes al slereosomensm. b ~ Y,, and Z are halogens.
'The sum of all rings plus n bonds. ~n =~9, the r entry is 35-3M5. 'induding hemiacetalsand hemiketals. 'including acetals and ketals. d
Volume 69 Number 6 June 1992
453
The Numbea of Isomers Per Molecular Formula Entry
19 19a 19b 19c 20 20a 20b 20c 21 21a 21b 21c 21d 22 22a 22b 22c 22d 22e 23 2% 23b 23c 23d 23e 23f 239 24 24a 24b 24c 243 25 25a 25b 25c 25d 26 26a 26b 26c 26d 2% 26f 27 27a 2% 27c 27d 27e 27f ~
~orinula~
CnH2~3X2Y trihaloalkenes trihalocycloalkanes total cnH2~3XYz trihaloalkenes trihalocycloalkanes total CnHzwiN heterocycles imines all others total CnHnnO aldehydes ketones ethersg alcohols and enols total C~H~RIOX aldehydes ketones acyl halides ethersg hypohalites alcohols and enols total CnH2nOz carboxylic acids esters all others total CnHzrriOzX carboxvlic acidsh esters' all others total CoHvrr? .. dienes alkynes two rings 1 ring, 1 n bond allenes total CnH2mX dienes alkynes two rings 1 ring, 1 n bond allenes total ~
No. of UnsaturationsC
n=1
n=3
n=4
n=5
n=6
n=7
n=8
17-17-28 15-15-19
39-39-74 33-33-49
31-31-69 25-25-42 8-8-14
17-17-28
39-39-74
4-4-5 9-9-10
8-8-11 20-20-25
17-17-28 45-45-64
39-39-74
1 1 1 I
0-0-0 0-0-0 0-0-0
2-3-3 0-0-0 2-3-3
12-19-22 3-6-10 15-25-32
53-86-124 24-52-97 77-138-221
1 1 1 1
0-0-0 0-0-0 0-0-0
3-6-6 0-0-0 3-6-6
19-34-44 4-10-20 23-44-64
87-151-248 37-94-194 124-245-442
0-0-0 1-1-1 0-0-0 1-1-1
1-1-1 2-2-2 1-1-1 4-4-4
3-3-4 4-5-5 5-6-6 12-14-1 5
9-10-14 8-10-10 17-22-25 34-42-49
24-28-44 18-24-28 58-80-100 100-132-172
1-1-1 0-0-0 0-0-0 0-0-0 1-1-1
1-1-1 0-0-0 1-1-1 1-1-1 3-3-3
1-1-1 1-1-1 3-3-4 4-5-5 9-10-11
2-2-2 1-1-1 11-13-16 12-16-19 26-32-38
4-4-5 8-8-11 3-3-3 6-6-7 31-39-54 35-51-68 73-97-130
0-0-0 0-0-0 1-1-1 0-0-0 0-0-0 0-0-0 1-1-1
1-1-1 0-0-0 1-1-1 1-1-2 1-1-1 2-3-3 6-7-8
2-2-3 1-1-1 1-1-1 8-10-15 4-5-5 10-16-19 26-35-44
5-5-8 3-3-4 2-2-2 35-49-76 12-16-19 39-65-95 96-140-204
12-12-23 9-9-13 4-4-5
1-1-1 0-0-0 1-1-1 2-2-2
1-1-1 1-1-1 1-1-1 2-2-2 8-9-10 31-37-46 10.1 1-12 34-40-49
1-1-1 0-0-0 2-2-2 3-3-3
1-1-1 2-2-2 18-22-28 21 -25-31
2-2-3 5-5-8 5-5-6 13-13-18 103-145-205 110-152-214
12-12-23 34-34-54
31-31-69
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
0-0-0 1-1-1 0-0-0 0-0-0 0-0-0 1-1-1
0-0-0 1-1-1 0-0-0 1-1-1 1-1-1 3-34
1-1-1 2-2-2 1-1-1 4-4-4 1-1-1 9-9:9
3-4-4 3-3-3 5-6-6 12-12-15 3-3-4
11-17-17 7-7-8 17-23-29 37-42-56 5-5-6
26-28-32
77-94-116
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
0-0-0 1-1-1 0-0-0 0-0-0 0-0-0 1-1-1
0-0-0 2-2-2 0-0-0 2-2-2 1-1-1 5-5-5
2-3-3 4-5-5 2-3-3 10-10-14 3-3-4 21-24-29
12-22-22 10-10-14 25-25-41 13-22-30 42-48-76 8-8-12 21-21-36 85-110-154
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I
1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
eincludingepaxides and other cyclic ethers. "ncluding X-COzH.
'including X 4 0 2 R .
454
n=2
Journal of Chemical Education
2-2-2 4-4-4
35-51-68
31-53-57 14-14-18
32-32-47
13-13-18
27-27-42
64-64-122
of Isomers Per Molecular Formula
The Numb& Entw
28 28a 28b 28c 28d 28e 28f 29 29a 29b 29c 29d 29e 29f 30 30a 30b 30c 30d 30e 30f 31
orm mu la^ CnH2~4X2
dienes alkynes two rings I ring, IE bond allenes total CnHzm4XY dienes aikynes two rings Iring, 1 E bond allenes total CnH2n4X3
dienes alkynes two rings 1 ring. 1 n bond allenes total CoH2nsX2Y
dienes alkynes two rings 1 ring, 1 E bond allenes total coH2*5X/z
321 33 33a 33b 33c 33d 33e 33f 34 34a 34b 34c 34d 34e 34f 349 34h 35 35a 35b 35c 35d
dienes alkynes two rings 1 ring, 1 E bond allenes total CnH2*20
aldehydes ketones ethersg alcohols and enols ketenes total coH2mox
aldehydes ketones acid halides alcohols and enols hypohalites ethersg ketenes total CoH2*202
carboxylic acids esters and lactones all others total
No.of UnsaturationsC 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
n=l
n=2
n=3
n=4
n=5
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
0-0-0 1-1-1 0-0-0 0-0-0 0-0-0 1-1-1
0-0-0 2-2-2 0-0-0 3-3-4 2-2-3 7-7-9
5-9-9 7-7-9 4-7-9 19-22-32 5-5-7 40-50-66
29-61-64 20-20-32 30-62-93
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
0-0-0 1-1-1 0-0-0 0-0-0 0-0-0 1-1-1
0-0-0 3-3-4 0-0-0 4-4-6 2-2-3 9-9-13
7-15-15 10.1 0-17 5-11-15 28-32-58 8-8-14 56-76-119
49-116-125 32-32-64 44-105-176
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
0-0-0 2-2-2 0-0-0 2-2-2 1-1-1 5-5-5
5-10-10 8-8-10 4-6-10 21-24-36 6-68 44-56-74
45-100-106 30-30-50 43-100-158
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
o-o-o
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
o-o-o 4-4-8
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
n=6
n=7
n=8
14-14-18
32-32-47
18-18-31
27-27-56
20-20-38
3-3-4
o-o-o 4-4-6 2-2-3 9-9-13
o-o-o 6-6-12 3-3-6 13-13-26
146-236-424
0-0-0 0-0-0 1-1-1 1-1-1 1-1-1 3-3-3
1-1-1 1-1-1 5-5-5 5-5-5 1-1-1 13-13-13
4-5-5 3-3-4 23-25-30 21-24-29 2-2-2 53-59-70
0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0 0-0-0
0-0-0 0-0-0 0-0-0 1-1-1 1-1-1 1-1-1 I t 4-4-4
2-3-3 1-1-2 1-1-1 9-9-13 5-5-5 11-13-16 2-2-2 31-34-42
10-16-19 39-65-95 8-10-15 35-49-76 4-5-5 12-16-19 35-51-68 58-76-119 21-24-29 85-110-154 66-81-126 44-5 10-10-14 25-2541 171-216-318
0-0-0 0-0-0 1-1-1 1-1-1
0-0-0 1-1-1 8-8-8 9-9-9
1-1-1 3-34 48-51-59 52-55-64
4-5-5 11-12-15
12-16-19 11-13-16
35-51-68' 31-39-54
85-110-154 3-3-3 7-7-8
12-16-19 34-41-54
64-64-122
35-51-68
Volume 69
Number 6
June 1992
455
Grading the Assignment
The use of isomer-drawing assignments and exam questions is as much of a challenee for the instructor as it is for the students; grading the &dentss work is often dimcult and time-consumine. This is due in part to the fact that students tend to draw the same isomer more than once thinkine that thev have drawn different isomers. By placing a vekical key alongside the student's paper, and then by placing a check mark by each isomer that the student has drawn (as shown in the figure below), the instructor can quickly and easily see which structures have been omitted and which ones have been drawn more than once. To avoid having to get a new copy of the key for each student. the check marks can be made on the student's DaDer rather than on the key. Another way of shortening the madim time is to have the students use the "RIS" method. which was recently reported in this Journal? The inabilitv of students to decide which structures are the same and bhich are different certainly underscores the importance of using isomer-drawing assignments. Unless there is some pen&y for including an isomer more than once, students will make little or no effort to learn how to avoid doing so. The following policy has been found to be helpful: a compound drawn more than once is graded as though it were not drawn at all. For example, if there are five possible isomers and a student draws three of them once and a fourth one twice (for a total of five structural formulas), credit is given only for the three isomers that were each drawn once. Of wurse such a policy must be disclosed to the students before they begin drawing. Another problem is that the last few isomers are often much more difficult to generate than were all of the rest of them. As a result of this, many students do not bother to find all ofthe isomers; they would be "wasting"a lot oftime for just one or two more points. Even a student who has
.~
~
~
~
'Thall, E. J. Chem. Educ. 1991, 68,190-1 91.
456
Journal of Chemical Education
invested verv little time on the assienment or exam auestion might earn almost as much credit as a student-who invested a meat deal of time. Due to this. the instructor might choose to give most of the credit for the last few isomers. For example. if there are six possible isomers, ten points wuld he'gi;en for drawing ail six isomers, seven points for drawing any five isomers, and one point each for drawing any four or-fewer isomers. ~ ~ a i n , h o w e v ethe r, grading scheme must be disclosed to the students before they begin drawing. Flexibility of the Assignments
A nice feature of isomer-drawing assignments is that they are highly versatile. That is, they are not necessarily limited to one specific part of the wurse, and assignments of any desired level of dfliculty can be given in one spoken sentence. For example, suppose that at the end of the first lecture on aldehvdes and ketones the instructor realizes that the amount i f material that has been covered is insufficient to "iustifv eiving the darned homework assienment. The instructor can agandin the planned assi-int and verballv. or on the chalkboard. eive an isomer assienmen&erhaps involving all of thealdehydes and ketones of a particular molecular formula. The assignment is even more worthwhile when the students are asked to not only draw the isomers but also to name them, especiallv if stereoisomerism is included. Many entries in the table are much too difficult to be used as routine assignments for a sophomore organic chemistry class. Theseentries might serve as extra &edit pmiects. At the verv least, these entries might help an in&&tor to know whichm6lecular formulas not to assign to the students. It might also be best to avoid assigning the "cis-trans isomerism only" type of problems (the middle number of each three-number entry in the table) whenever ring compounds are possible, since much confusion and ambiguity can arise in those cases.
.-
