In the Classroom
“Dishing Out” Stereochemical Principles Harold Hart Department of Chemistry, Michigan State University, East Lansing, MI 48824-1322;
[email protected] The chirality or achirality of molecules is part of a more general phenomenon involving symmetry properties of natural and unnatural objects, both large and small. It may help students to relate molecular symmetry to that of objects that are more familiar (1). This is why teachers often use the left and right hands (2–7) (or gloves, feet, shoes, screws, nuts, bolts) to illustrate enantiomers. Indeed, numerous articles in this Journal have dealt with this subject. Among the common (and not so common) objects used for this purpose have been stereowordimers (8), tire treads (9), knots (10), automobile wheels and hubcaps (11), toy animals (12), crackers (13), cookies with creme fillings (14), rooms with right- and lefthanded doors (15), eyeglasses, some with reversed earpieces (16), English beer glasses and coffee mugs (17), narwhal tusks (18), and paper clips (19). In this short article1 I will describe a simple, new, and as far as I am aware unique way of illustrating stereochemical principles for the undergraduate course. The objects used are inexpensive, readily available, and may be used either as a lecture aid or, in a modified nonbreakable form, in a handson experiment by students. It is especially easy to determine whether these mirror image objects are superimposable, and also to see their clockwise/counterclockwise relationship. Although the models do not possess a unique stereogenic center (just as a left or right hand, though chiral, lacks a unique stereogenic center), one can use them to accurately predict the number and kinds of stereoisomers that are possible in molecules with such stereocenters. The Model Consider a set of plain, identical dishes (plates or bowls). That they are superimposable is evident, since they can be stacked (Fig. 1); neither the order of stacking nor the rotation of one dish with respect to the other matters. The dishes are clearly achiral.2 Now suppose we place a marker on the edge of the dish, and also create its mirror image (Fig. 2). As the marker, I used a white, circular, self-sticking paper disc. Such discs are readily available in various sizes and colors; they also come in other shapes—squares, rectangles, stars, etc., and they are inexpensive.3 By rotating one plate 180° (Fig. 3) and stacking them (Fig. 4) one can see that the plates are still superimposable, but with the restriction that the dots must be aligned. They are still achiral. Here it is useful to discuss with students the central vertical axis and infinite number of vertical symmetry planes through it in the unlabeled plates, and the single symmetry plane in plates with one label. Now introduce a second label adjacent to and different from the first, say a rectangle, and create its mirror image (Fig. 5).4 If we rotate one plate 180° (Fig. 6) and try to superimpose it on the other, we see that this is not possible; the rectangle overlaps the circle and vice versa (Fig. 7). The
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plates are now chiral; one can introduce the term enantiomers (or enantiomorphs) in relation to the plates in Figure 5, and point out that the plate with a top surface, a bottom surface, and two different markers is not unlike a tetrahedral carbon with four different groups attached (a stereogenic or chiral center). The enantiomorphous plates in Figures 5 and 6 can be represented by the following 2-dimensional images: mirror 180° c r
c r
r c
where c is circle and r is rectangle. I will use this representation hereafter, to save on the number of figures. Rotation of these representations in the plane of the paper is allowed, but they may not be flipped out of the plane (because it would interconvert the top and bottom surfaces of the plate). One may call attention to the fact that to move from the circular to the rectangular label by the shortest path, one must proceed clockwise with one enantiomer and counterclockwise with the other; the analogy with the direction of rotation of plane-polarized light by enantiomers is obvious. One may also think about keeping one label fixed and moving the other label around the periphery of the plate; when it reaches the symmetry plane, the plate becomes achiral; when it continues on around until it is again adjacent to the fixed label but on its opposite side, we have the enantiomer. This is not entirely unlike racemization via an SN1 process. Finally, it is the pair of different labels that imparts chirality to the plate. A plate with only one label, or with two identical labels, say two circles or two rectangles, has a plane of symmetry that passes between the two labels and is achiral.
Two Chiral Centers By adding additional labels the model can easily be extended, provided that two simple rules are followed: 1. A new label can be added at either end of a sequence already present; it may not be inserted between labels already present. The reason is clear: such an insertion would cause a structural change. That is, the chirality that results from a particular label pair (say, c r) would be destroyed by inserting a label between its elements. 2. The standard definition of isomers applies (isos, equal, and meros, parts); that is, isomeric models must have identical numbers of each kind of label.
Let us see how these rules work by adding a third label to the circle and rectangle. If the third label is different (say a star, s) then we get two enantiomeric pairs, whose structures are determined by whether the new label is placed adjacent
Journal of Chemical Education • Vol. 78 No. 12 December 2001 • JChemEd.chem.wisc.edu
In the Classroom
to the circle or the rectangle. This is as expected for stereoisomers with two different chiral centers: mirror
mirror 180°
180°
Figure 1.
c r s
c r s
s r c
enantiomeric pair #1, chiral
Figure 2.
s c r
s c r
enantiomeric pair #2, chiral
Members of the separate sets are related as diastereomers. (Note that insertion of the star between c and r would give another enantiomeric pair, but they would be structural isomers to those shown. In that pair, c and r would no longer be connected to the same chiral center). Suppose that the third label is identical with one of those already present (say a rectangle, r); then we get one enantiomeric pair and one meso form (in exact analogy with the tartaric acids): mirror
mirror 180°
180°
Figure 3.
c r r
r r c
c r r
r c r
r c r
r c r
meso form, achiral
enantiomeric pair, chiral
Figure 4.
r c s
Notice that we must choose either the r or the c, but we cannot choose both; the model with two r’s and one c is not an isomer of the model with two c’s and one r. If the meso form above (r c r), for example, were to correspond to meso tartaric acid, the other meso form (c r c) must be different, perhaps dimethyl tartrate.
Three Different Chiral Centers Consider adding a fourth label x. Since the label is different, we now obtain four enantiomeric pairs as expected for a molecule with three different chiral centers (23 = 8, isomers): mirror
Figure 5.
c x
r s
c r s x
mirror 180°
x s r c
enantiomeric pair #1, chiral mirror s c r x
Figure 6.
Figure 7.
s c r x
x c r s
x c r s
180°
s x
r c
enantiomeric pair #2, chiral mirror
180°
x
r c s
enantiomeric pair #3, chiral
x s c r
x s c r
180°
r x
c s
enantiomeric pair #4, chiral
Similarly, with 5 different labels (4 chiral centers) we will obtain 24 = 16 isomers.5 The labeled plates described here are not intended to replace the usual molecular models. They may, however, encourage students to think about the generality of stereochemical principles; that an ordinary teacup or coffee mug can be used equally well by a left- or right-handed person because the interaction is between a chiral object (left or right
JChemEd.chem.wisc.edu • Vol. 78 No. 12 December 2001 • Journal of Chemical Education
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In the Classroom
hand) and an achiral object (with a plane of symmetry through the handle). And that a chambered nautilus shell split down the middle (Fig. 8) is not only a thing of beauty, but a pair of enantiomorphs (20). Acknowledgments I thank Leslie and Timothy Craine for the invitation to join them in presenting this material at their symmetry workshop1 and for their probing discussions beforehand. I thank Kurt Mislow for his patience in helping me to bring earlier versions of these ideas to the more precise one presented here. I thank Ernest Eliel and Jack Roberts for commenting on the manuscript. I am indebted to Bill Draper, of this department, for taking the photographs. Finally, I thank my secretary, Nancy Lavrik, without whom the preparation of the manuscript would have been impossible. Notes 1. Presented during a workshop (W50) at the 16th Biennial Conference on Chemical Education, Ann Arbor, Michigan, August 1, 2000. 2. Inexpensive, nonbreakable paper plates may be used instead of the ceramic plates shown here, in a student hands-on experiment. 3. At our local supermarket 500 can be purchased for about $1.49. 4. In principle, the two labels could be placed anywhere on the plate, as long as they are not both aligned along a symmetry plane. However it is best that they be placed near the edge of the plate and adjacent to one another so that the mirror image is most easily constructed. Also, the text offers a second reason why they should be adjacent. 5. It is not useful to explore here situations with four or more labels of which two or more are identical; their meaning will depend on the label locations. For these complex situations, unlikely to be important in an introductory course, real molecular models are no doubt more useful than labeled plates.
Literature Cited 1. For exquisite discussions of symmetry in natural and unnatural objects, see Heilbronner, E.; Dunitz, J. D. Reflections on Symmetry, in Chemistry and Elsewhere; VCH: New York, 1993. Hargittai, I.; Hargittai, M. Symmetry: A Unifying Concept. Shelter Publications: Bolinas, CA, 1994. Gardner, M. The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings, 3rd ed.; Freeman: New York, 1990. 2. Fessenden, R. J.; Fessenden, J. S. Organic Chemistry, 5th ed.; Brooks/Cole: Pacific Grove, CA, 1993; p 143.
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Figure 8. A chambered nautilus shell, split approximately in half. The author purchased this shell in a shop on the boardwalk in Atlantic City, NJ, to celebrate the LeBel–van’t Hoff Centennial Symposium held at the National ACS meeting in Atlantic City, September 11– 12, 1974.
3. Fox, M. A.; Whitesell, J. K. Organic Chemistry, 2nd ed.; Jones and Bartlett: Sudbury, MA, 1997; p 250. 4. Hart, H.; Craine, L. E.; Hart, D. J. Organic Chemistry: A Short Course, 10th ed.; Houghton Mifflin: Boston, 1999; p 146. 5. McMurry, J. Organic Chemistry, 5th ed.; Brooks/Cole: Pacific Grove, CA, 2000; p 307. 6. Solomons, T. W. G. Organic Chemistry, 6th ed.; Wiley: New York, 1996; p 181. 7. Vollhardt, K. P. C.; Shore, N. E. Organic Chemistry, 2nd ed.; Freeman: New York, 1994; p 139. 8. Neeland, E. G. J. Chem. Educ. 1998, 75, 1573. 9. Jackson, W. G. J. Chem. Educ. 1992, 69, 624. 10. Tavernier, D. J. Chem. Educ. 1992, 69, 627. 11. Gallian, J. A. J. Chem. Educ. 1990, 67, 549. 12. Nave, P. M. J. Chem. Educ. 1991, 68, 1028. 13. Griffin, S. F. J. Chem. Educ. 1991, 68, 1029. 14. Feldman, M. R. J. Chem. Educ. 1988, 65, 580. 15. Bell, W. J. Chem. Educ. 1984, 61, 901. 16. Feldman, M. R. J. Chem. Educ. 1984, 61, 1050. 17. Sanders, J. K. M. J. Chem. Educ. 1979, 56, 594. 18. Stirling, C. J. J. Chem. Educ. 1978, 55, 32. 19. Stirling, C. J. J. Chem. Educ. 1974, 51, 50. 20. For the distinction between the terms enantiomer and enantiomorph, see Eliel, E. L.; Wilen, S. H. Stereochemistry of Organic Compounds; Wiley: New York, 1994; pp 1197, 1198.
Journal of Chemical Education • Vol. 78 No. 12 December 2001 • JChemEd.chem.wisc.edu
