3.5 Conformations of Cyclohexane Furthermore, the heats of combustion per methylene group of the very large rings are all about the same and similar to that of cyclohexane. Rather than rising because of increasing angle strain in large rings, the heat of combustion per methylene group remains constant at approximately 653 kJ/mol (156 kcal/mol), the value cited in Section 2.15 as the difference between successive members of a homologous series of alkanes We conclude, therefore, that the bond angles of large cycloalkanes are not much differ- ent from the bond angles of alkanes themselves. The prediction of the Baeyer strain the ory that angle strain increases steadily with ring size is contradicted by experimental fact. The Baeyer strain theory is useful to us in identifying angle strain as a destabilize- ing effect. Its fundamental flaw is its assumption that the rings of cycloalkanes are pla- nar. With the exception of cyclopropane, cycloalkanes are nonplanar. Sections 3.5-3.11 describe the shapes of cycloalkanes. Six-membered rings rank as the most important ring size among organic compounds; thus let us begin with cyclohexane to examine the forces that determine the shapes of cycloalkanes 3.5 CONFORMATIONS OF CYCLOHEXANE Experimental evidence indicating that six-membered rings are nonplanar began to accu- Hassel shared the 1969 Nobel mulate in the 1920s. Eventually, Odd Hassel of the University of Oslo established that Prize in chemistry with Si is called the chair conformation. With C-C-C bond angles of 111, the chair con- Collegellondog'mperial the most stable conformation of cyclohexane has the shape shown in Figure 3. 10. This Derek barton of A&M University. Bar- formation is nearly free of angle strain. All its bonds are staggered, making it free of ton demonstrated how Has- torsional strain as well. The staggered arrangement of bonds in the chair conformation of cyclohexane is apparent in a Newman-style projection be extended to an analysis of informational effects o H chemical reactivity Staggered arrangement of bonds in chair conformation cyclohexane of the chair H H A second, but much less stable, nonplanar conformation called the boat is shown C-C bonds in Figure 3. 11. Like the chair, the boat conformation has bond angles that are approxi mately tetrahedral and is relatively free of angle strain. As noted in Figure 3.11, how- Recall from Section 3.2 that ever, the boat is destabilized by van der Waals strain involving its two "flagpole"hydro- the sum of the van der Waals gens, which are within 180 pm of each other. An even greater contribution to the radii of two hydrogen atoms is 240 pm. FIGURE 3.10(a)A ball-and-spoke model and ( b)a space-filling model of the chair conformation of cyclohexane Back Forward Main MenuToc Study Guide ToC Student o MHHE Website
Furthermore, the heats of combustion per methylene group of the very large rings are all about the same and similar to that of cyclohexane. Rather than rising because of increasing angle strain in large rings, the heat of combustion per methylene group remains constant at approximately 653 kJ/mol (156 kcal/mol), the value cited in Section 2.15 as the difference between successive members of a homologous series of alkanes. We conclude, therefore, that the bond angles of large cycloalkanes are not much different from the bond angles of alkanes themselves. The prediction of the Baeyer strain theory that angle strain increases steadily with ring size is contradicted by experimental fact. The Baeyer strain theory is useful to us in identifying angle strain as a destabilizing effect. Its fundamental flaw is its assumption that the rings of cycloalkanes are planar. With the exception of cyclopropane, cycloalkanes are nonplanar. Sections 3.5–3.11 describe the shapes of cycloalkanes. Six-membered rings rank as the most important ring size among organic compounds; thus let us begin with cyclohexane to examine the forces that determine the shapes of cycloalkanes. 3.5 CONFORMATIONS OF CYCLOHEXANE Experimental evidence indicating that six-membered rings are nonplanar began to accumulate in the 1920s. Eventually, Odd Hassel of the University of Oslo established that the most stable conformation of cyclohexane has the shape shown in Figure 3.10. This is called the chair conformation. With C±C±C bond angles of 111°, the chair conformation is nearly free of angle strain. All its bonds are staggered, making it free of torsional strain as well. The staggered arrangement of bonds in the chair conformation of cyclohexane is apparent in a Newman-style projection. A second, but much less stable, nonplanar conformation called the boat is shown in Figure 3.11. Like the chair, the boat conformation has bond angles that are approximately tetrahedral and is relatively free of angle strain. As noted in Figure 3.11, however, the boat is destabilized by van der Waals strain involving its two “flagpole” hydrogens, which are within 180 pm of each other. An even greater contribution to the H H CH2 H CH2 H H H H H Staggered arrangement of bonds in chair conformation of cyclohexane 3.5 Conformations of Cyclohexane 99 Hassel shared the 1969 Nobel Prize in chemistry with Sir Derek Barton of Imperial College (London), now at Texas A&M University. Barton demonstrated how Hassel’s structural results could be extended to an analysis of conformational effects on chemical reactivity. (a) (b) FIGURE 3.10 (a) A ball-and-spoke model and (b) a space-filling model of the chair conformation of cyclohexane. Make a molecular model of the chair conformation of cyclohexane, and turn it so that you can look down one of the C±C bonds. Recall from Section 3.2 that the sum of the van der Waals radii of two hydrogen atoms is 240 pm. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website
CHAPTER THREE Conformations of Alkanes and Cycloalkanes FIGURE 3.11(a)a ball-and-spoke model and (b)a space-filling model of the boat conformation of cyclohexane. The close ap proach of the two upper ly evident in the ng model estimated 27 kJ/mol (6.4 kcal/mol)energy difference between the chair and the boat the torsional strain associated with eclipsed bonds on four of the carbons in the boat Figure 3. 12 depicts the eclipsed bonds and demonstrates how the associated torsional strain may be reduced by rotation about the carbon-carbon bonds to give the slightly more stable twist boat, or skew boat, conformation The same bond rotations that reduce the torsional strain also reduce the van der Waals strain by increasing the distance between the two flagpole hydrogens The various conformations of cyclohexane are in rapid equilibrium with one another, but at any moment almost all of the molecules exist in the chair conformation Not more than one or two molecules per thousand are present in the higher energy skew boat and boat conformations. Thus, the discussion of cyclohexane conformational analy sis that follows focuses exclusively on the chair conformation 3.6 AXIAL AND EQUATORIAL BONDS IN CYCLOHEXANE One of the most important findings to come from conformational studies of cyclohexane is that its 12 hydrogen atoms are not all identical but are divided into two groups, as shown in Figure 3. 13. Six of the hydrogens, called axial hydrogens, have their bonds parallel to a vertical axis that passes through the rings center. These axial bonds alter FIGURE 3. 12 (a)The boat and(b)skew boat conformations of cyclohexane. A the torsional strain in the boat is relieved by rotation about c-C bonds in the at Bond rotation is accompanied by movement of flagpole hydrogens away from each duces the van der waals strain between them Back Forward Main MenuToc Study Guide ToC Student o MHHE Website
estimated 27 kJ/mol (6.4 kcal/mol) energy difference between the chair and the boat is the torsional strain associated with eclipsed bonds on four of the carbons in the boat. Figure 3.12 depicts the eclipsed bonds and demonstrates how the associated torsional strain may be reduced by rotation about the carbon–carbon bonds to give the slightly more stable twist boat, or skew boat, conformation. The same bond rotations that reduce the torsional strain also reduce the van der Waals strain by increasing the distance between the two flagpole hydrogens. The various conformations of cyclohexane are in rapid equilibrium with one another, but at any moment almost all of the molecules exist in the chair conformation. Not more than one or two molecules per thousand are present in the higher energy skew boat and boat conformations. Thus, the discussion of cyclohexane conformational analysis that follows focuses exclusively on the chair conformation. 3.6 AXIAL AND EQUATORIAL BONDS IN CYCLOHEXANE One of the most important findings to come from conformational studies of cyclohexane is that its 12 hydrogen atoms are not all identical but are divided into two groups, as shown in Figure 3.13. Six of the hydrogens, called axial hydrogens, have their bonds parallel to a vertical axis that passes through the ring’s center. These axial bonds alter- 100 CHAPTER THREE Conformations of Alkanes and Cycloalkanes (a) (b) (a) (b) FIGURE 3.12 (a) The boat and (b) skew boat conformations of cyclohexane. A portion of the torsional strain in the boat is relieved by rotation about C±C bonds in the skew boat. Bond rotation is accompanied by movement of flagpole hydrogens away from each other, which reduces the van der Waals strain between them. FIGURE 3.11 (a) A ball-and-spoke model and (b) a space-filling model of the boat conformation of cyclohexane. The close approach of the two uppermost hydrogen substituents is clearly evident in the space-filling model. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website
3.6 Axial and Equatorial Bonds in Cyclohexane H H H Axial C-H bonds Equatorial C-H bonds Axial and equatorial FIGURE 3. 13 Axial and equatorial bonds in cyclohexane. nately are directed up and down on adjacent carbons. The second set of six hydrogens, called equatorial hydrogens, are located approximately along the equator of the mole- cule. Notice that the four bonds to each carbon are arranged tetrahedrally, consistent with an sp hybridization of carbon The conformational features of six-membered rings are fundamental to organic hemistry, so it is essential that you have a clear understanding of the directional prop. erties of axial and equatorial bonds and be able to represent them accurately. Figure 3.14 offers some guidance on the drawing of chair cyclohexane rings It is no accident that sections of our chair cyclohexane drawings resemble sawhors projections of staggered conformations of alkanes. The same spatial relationships se in alkanes carry over to substituents on a six-membered ring. In the structure x (The substituted carbons X have the spatial ubstituents A and B are anti to each other, and the other relationships-A and Y, X and Y, and X and B-are gauche PROBLEM 3.4 Given the following partial structure, add a substituent x to C-1 so that it satisfies the indicated stereochemical requirement. You may find it help- ful to build a molecular model for reference (a) Anti to A (c) Anti to C-3 d)Gauche to c-3 SAMPLE SOLUTIoN(a) In order to be anti to a, substituent x must be axia The blue lines in the drawing show the a-C-C-X torsion angle to be 180 Back Forward Main MenuToc Study Guide ToC Student o MHHE Website
3.6 Axial and Equatorial Bonds in Cyclohexane 101 H H H H H H Axial C±H bonds H H H H H H Equatorial C±H bonds Axial and equatorial bonds together H H H H H H H H H H H H nately are directed up and down on adjacent carbons. The second set of six hydrogens, called equatorial hydrogens, are located approximately along the equator of the molecule. Notice that the four bonds to each carbon are arranged tetrahedrally, consistent with an sp3 hybridization of carbon. The conformational features of six-membered rings are fundamental to organic chemistry, so it is essential that you have a clear understanding of the directional properties of axial and equatorial bonds and be able to represent them accurately. Figure 3.14 offers some guidance on the drawing of chair cyclohexane rings. It is no accident that sections of our chair cyclohexane drawings resemble sawhorse projections of staggered conformations of alkanes. The same spatial relationships seen in alkanes carry over to substituents on a six-membered ring. In the structure substituents A and B are anti to each other, and the other relationships—A and Y, X and Y, and X and B—are gauche. PROBLEM 3.4 Given the following partial structure, add a substituent X to C-1 so that it satisfies the indicated stereochemical requirement. You may find it helpful to build a molecular model for reference. (a) Anti to A (c) Anti to C-3 (b) Gauche to A (d) Gauche to C-3 SAMPLE SOLUTION (a) In order to be anti to A, substituent X must be axial. The blue lines in the drawing show the A±C±C±X torsion angle to be 180°. A 1 X A 3 1 A X Y B A X Y B (The substituted carbons have the spatial arrangement shown) FIGURE 3.13 Axial and equatorial bonds in cyclohexane. Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website