CHAPTER 3 CONFORMATIONS OF ALKANES AND CYCLOALKANES SOLUTIONS TO TEXT PROBLEMS 3.1 (b) The sawhorse formula contains four carbon atoms in an unbranched chain. The compound is butane, CH 3 CH 2 CH 2 CH 3 . (c) Rewrite the structure to show its constitution. The compound is CH 3 CH 2 CH(CH 3 ) 2 ; it is 2-methylbutane. (d) In this structure, we are sighting down the C-3GC-4 bond of a six-carbon chain. It is CH 3 CH 2 CH 2 CHCH 2 CH 3 , or 3-methylhexane. = CH 3 CH 2 CH 3 H HH CH 3 CH 2 CH 3 H11013 C H H H H 3 C CH 3 CH 3 C H H H CH 3 CH 3 CH 3 HH HH CH 3 CH 3 46 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website 3.2 Red circles gauche: 60° and 300°. Red circles anti: 180°. Gauche and anti relationships occur only in staggered conformations; therefore, ignore the eclipsed conformations (0°, 120°, 240°, 360°). 3.3 All the staggered conformations of propane are equivalent to one another, and all its eclipsed con- formations are equivalent to one another. The energy diagram resembles that of ethane in that it is a symmetrical one. The activation energy for bond rotation in propane is expected to be somewhat higher than that in ethane because of van der Waals strain between the methyl group and a hydrogen in the eclipsed conformation. This strain is, however, less than the van der Waals strain between the methyl groups of butane, which makes the activation energy for bond rotation less for propane than for butane. 3.4 (b) To be gauche, substituents X and A must be related by a 60° torsion angle. If A is axial as specified in the problem, X must therefore be equatorial. (c) For substituent X at C-1 to be anti to C-3, it must be equatorial. (d) When X is axial at C-1, it is gauche to C-3. 3.5 (b) According to the numbering scheme given in the problem, a methyl group is axial when it is “up” at C-1 but is equatorial when it is up at C-4. Since substituents are more stable when they 3 X A 3 X A X and A are gauche. X A Potential ener gy 0 60 120 180 240 300 360 Torsion angle (degrees) H 3 C H HH H H H H HH H H 3 C H CH 3 HH H H H 3 C H HH H H H H H H H H 3 C HH H CH 3 H H H H H H CH 3 H CONFORMATIONS OF ALKANES AND CYCLOALKANES 47 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website 48 CONFORMATIONS OF ALKANES AND CYCLOALKANES occupy equatorial rather than axial sites, a methyl group that is up at C-1 is less stable than one that is up at C-4. (c) An alkyl substituent is more stable in the equatorial position. An equatorial substituent at C-3 is “down.” 3.6 A tert-butyl group is much larger than a methyl group and has a greater preference for the equato- rial position. The most stable conformation of 1-tert-butyl-1-methylcyclohexane has an axial methyl group and an equatorial tert-butyl group. 3.7 Ethylcyclopropane and methylcyclobutane are isomers (both are C 5 H 10 ). The less stable isomer has the higher heat of combustion. Ethylcyclopropane has more angle strain and is less stable (has higher potential energy) than methylcyclobutane. 3.8 The four constitutional isomers of cis and trans-1,2-dimethylcyclopropane that do not contain double bonds are 3.9 When comparing two stereoisomeric cyclohexane derivatives, the more stable stereoisomer is the one with the greater number of its substituents in equatorial orientations. Rewrite the structures as chair conformations to see which substituents are axial and which are equatorial. cis-1,3,5-Trimethylcyclohexane H H H H 3 C CH 3 CH 3 CH 3 CH 3 H H 3 C H H CH 3 CH 3 1,1-Dimethylcyclopropane CH 3 Methylcyclobutane Ethylcyclopropane CH 2 CH 3 Cyclopentane CH 2 CH 3 CH 3 More stable 3352 kJ/mol (801.2 kcal/mol) Less stable 3384 kJ/mol (808.8 kcal/mol) Heat of combustion: 1-tert-Butyl-1-methylcyclohexane CH 3 C(CH 3 ) 3 H H 3 C Up Down H CH 3 Up Down H H 3 C Up Down 4 5 6 3 2 1 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website All methyl groups are equatorial in cis-1,3,5-trimethylcyclohexane. It is more stable than trans- 1,3,5-trimethylcyclohexane (shown in the following), which has one axial methyl group in its most stable conformation. 3.10 In each of these problems, a tert-butyl group is the larger substituent and will be equatorial in the most stable conformation. Draw a chair conformation of cyclohexane, add an equatorial tert-butyl group, and then add the remaining substituent so as to give the required cis or trans relationship to the tert-butyl group. (b) Begin by drawing a chair cyclohexane with an equatorial tert-butyl group. In cis-1-tert-butyl- 3-methylcyclohexane the C-3 methyl group is equatorial. (c) In trans-1-tert-butyl-4-methylcyclohexane both the tert-butyl and the C-4 methyl group are equatorial. (d) Again the tert-butyl group is equatorial; however, in cis-1-tert-butyl-4-methylcyclohexane the methyl group on C-4 is axial. 3.11 Isomers are different compounds that have the same molecular formula. Compare the molecular formulas of the compounds given to the molecular formula of spiropentane. Only the two compounds that have the molecular formula C 5 H 8 are isomers of spiropentane. 3.12 Two bond cleavages convert bicyclobutane to a noncyclic species; therefore, bicyclobutane is bicyclic. Spiropentane (C 5 H 8 ) CH CH 2 C 5 H 8 C 6 H 10 C 5 H 8 C 5 H 10 CH 2 CH 3 H C(CH 3 ) 3 H H 3 C H C(CH 3 ) 3 H H H 3 C H C(CH 3 ) 3 H H H H 3 C CH 3 H 3 C trans-1,3,5-Trimethylcyclohexane CH 3 CH 3 H H CH 3 H CONFORMATIONS OF ALKANES AND CYCLOALKANES 49 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website The two bond cleavages shown convert camphene to a noncyclic species; therefore, camphene is bicyclic. (Other pairs of bond cleavages are possible and lead to the same conclusion.) 3.13 (b) This bicyclic compound contains nine carbon atoms. The name tells us that there is a five- carbon bridge and a two-carbon bridge. The 0 in the name bicyclo[5.2.0]nonane tells us that the third bridge has no atoms in it—the carbons are common to both rings and are directly attached to each other. (c) The three bridges in bicyclo[3.1.1]heptane contain three carbons, one carbon, and one carbon. The structure can be written in a form that shows the actual shape of the molecule or one that simply emphasizes its constitution. (d) Bicyclo[3.3.0]octane has two five-membered rings that share a common side. 3.14 Since the two conformations are of approximately equal stability when R H11005 H, it is reasonable to expect that the most stable conformation when R H11005 CH 3 will have the CH 3 group equatorial. 3.15 (a) Recall that a neutral nitrogen atom has three covalent bonds and an unshared electron pair. The three bonds are arranged in a trigonal pyramidal manner around each nitrogen in hydrazine (H 2 NNH 2 ). H N N H HH H H H H H H H H H11013H11013 N N HH HH R H11005 H: both conformations similar in energy R H11005 CH 3 : most stable conformation has CH 3 equatorial R N N R Three-carbon bridge Three-carbon bridge One-carbon bridge One-carbon bridge Three-carbon bridge Bicyclo[5.2.0]nonane CH 2 CH 3 CH 3 CH 2 CH 3 CH 3 CH 2 CH 3 CH 3 50 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website (b) The OGH proton may be anti to one NGH proton and gauche to the other (left) or it may be gauche to both (right). 3.16 Conformation (a) is the most stable; all its bonds are staggered. Conformation (c) is the least stable; all its bonds are eclipsed. 3.17 (a) First write out the structural formula of 2,2-dimethylbutane in order to identify the substituent groups attached to C-2 and C-3. As shown at left, C-2 bears three methyl groups, and C-3 bears two hydrogens and a methyl group. The most stable conformation is the staggered one shown at right. All other staggered conformations are equivalent to this one. (b) The constitution of 2-methylbutane and its two most stable conformations are shown. Both conformations are staggered. In one (left), the methyl group at C-3 is gauche to both of the C-2 methyls. In the other (right), the methyl group at C-3 is gauche to one of the C-2 methyls and anti to the other. (c) The hydrogens at C-2 and C-3 may be gauche to one another (left), or they may be anti (right). 3.18 The 2-methylbutane conformation with one gauche CH 3 . . . CH 3 and one anti CH 3 . . . CH 3 rela- tionship is more stable than the one with two gauche CH 3 . . . CH 3 relationships. The more stable conformation has less van der Waals strain. CH 3 H 3 C CH 3 HH H CH 3 CH 3 H 3 C H HH More stable Less stable CH 3 CH 3 H 3 C CH 3 H H CH 3 H CH 3 CH 3 H 3 C H CCH 3 C CH 3 CH 3 CH 3 H H Sight along this bond. CH 3 CH 3 H H 3 C HH CH 3 H CH 3 H 3 C HH CCH 3 H 3 H CH 3 H H Sight along this bond. CH 3 CH 3 CH 3 H 3 C HH CCH 3 H 3 CH 3 CH 3 H H Sight along this bond. N H O H H N HH H O CONFORMATIONS OF ALKANES AND CYCLOALKANES 51 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website 3.19 All the staggered conformations about the C-2GC-3 bond of 2,2-dimethylpropane are equivalent to one another and of equal energy; they represent potential energy minima. All the eclipsed confor- mations are equivalent and represent potential energy maxima. The shape of the potential energy profile for internal rotation in 2,2-dimethylpropane more closely resembles that of ethane than that of butane. 3.20 The potential energy diagram of 2-methylbutane more closely resembles that of butane than that of propane in that the three staggered forms are not all of the same energy. Similarly, not all of the eclipsed forms are of equal energy. Potential ener gy 0 60 120 180 240 300 360 Torsion angle (degrees) H 3 CCH 3 HH H CH 3 H 3 C H HH H 3 C CH 3 HCH 3 HH H 3 C CH 3 CH 3 H H HH 3 C CH 3 CH 3 HH CH 3 H 3 C H CH 3 H H CH 3 H CH 3 Potential ener gy 0 60 120 180 240 300 360 Torsion angle (degrees) H H H 3 C CH 3 H CH 3 H H H 3 C CH 3 CH 3 H H H H 3 C CH 3 CH 3 H H H CH 3 CH 3 H 3 C H CH 3 H 3 C CH 3 HH H CH 3 H 3 C CH 3 HH H CH 3 H 3 C CH 3 HH H 52 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website 3.21 Van der Waals strain between the tert-butyl groups in 2,2,4,4-tetramethylpentane causes the C-2GC-3GC-4 angle to open to 125–128°. 3.22 The structure shown in the text is not the most stable conformation, because the bonds of the methyl group are eclipsed with those of the ring carbon to which it is attached. The most stable conforma- tion has the bonds of the methyl group and its attached carbon in a staggered relationship. 3.23 Structure A has the hydrogens of its methyl group eclipsed with the ring bonds and is less stable than B. The methyl group in structure B has its bonds and those of its attached ring carbon in a stag- gered relationship. Furthermore, two of the hydrogens of the methyl group of A are uncomfortably close to two axial hydrogens of the ring. 3.24 Conformation B is more stable than A. The methyl groups are rather close together in A, resulting in van der Waals strain between them. In B, the methyl groups are farther apart. 3.25 (a) By rewriting the structures in a form that shows the order of their atomic connections, it is apparent that the two structures are constitutional isomers. CH 3 CH 3 H 3 C H HH is equivalent to CH 3 CCH 3 CH 3 CH 3 (2,2-Dimethylpropane) CH 3 CH 3 H 3 C H HH is equivalent to CH 3 CH 2 CHCH 3 CH 3 (2-Methylbutane) HH CH 3 CH 3 A Van der Waals strain between cis methyl groups. HH H 3 C CH 3 B Methyl groups remain cis, but are far apart. A (less stable) B (more stable) H H H H H H H H H H Bonds of methyl group eclipsed with those of attached carbon Bonds of methyl group staggered with those of attached carbon H H H H H H H H is equivalent to CH 2 CCH 3 C CH 3 CH 3 CH 3 CH 3 CH 3 This angle is enlarged. CONFORMATIONS OF ALKANES AND CYCLOALKANES 53 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website (b) Both models represent alkanes of molecular formula C 6 H 14 . In each one the carbon chain is unbranched. The two models are different conformations of the same compound, CH 3 CH 2 CH 2 CH 2 CH 2 CH 3 (hexane). (c) The two compounds have the same constitution; both are (CH 3 ) 2 CHCH(CH 3 ) 2 . The Newman projections represent different staggered conformations of the same molecule: in one the hydrogens are anti to each other, whereas in the other they are gauche. (d) The compounds differ in the order in which the atoms are connected. They are constitutional isomers. Although the compounds have different stereochemistry (one is cis, the other trans), they are not stereoisomers. Stereoisomers must have the same constitution. (e) Both structures are cis-1-ethyl-4-methylcyclohexane (the methyl and ethyl groups are both “up”). In the structure on the left, the methyl is axial and the ethyl equatorial. The orientations are opposite to these in the structure on the right. The two structures are ring-flipped forms of each other—different conformations of the same compound. ( f ) The methyl and the ethyl groups are cis in the first structure but trans in the second. The two compounds are stereoisomers; they have the same constitution but differ in the arrangement of their atoms in space. Do not be deceived because the six-membered rings look like ring-flipped forms. Remember, chair–chair interconversion converts all the equatorial bonds to axial and vice versa. Here the ethyl group is equatorial in both structures. (g) The two structures have the same constitution but differ in the arrangement of their atoms in space; they are stereoisomers. They are not different conformations of the same compound, because they are not related by rotation about CGC bonds. In the first structure as shown here the methyl group is trans to the darkened bonds, whereas in the second it is cis to these bonds. Methyl is trans to these bonds. CH 3 H Methyl is cis to these bonds. H CH 3 cis-1-Ethyl-4-methylcyclohexane (both alkyl groups are up) trans-1-Ethyl-4-methylcyclohexane (ethyl group is down; methyl group is up) CH 3 CH 3 CH 2 CH 3 CH 3 CH 2 CH 3 CH 3 CH 3 CH 3 cis-1,2-Dimethylcyclopentane trans-1,3-Dimethylcyclopentane and are different conformations of 2,3-dimethylbutane Hydrogens at C-2 and C-3 are gauche. Hydrogens at C-2 and C-3 are anti. CH 3 CH 3 H H H 3 C H 3 C CH 3 CH 3 H HH 3 C H 3 C 54 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website 3.26 (a) Three isomers of C 5 H 8 contain two rings and have no alkyl substituents: (b) Five isomers of C 6 H 10 contain two rings and have no alkyl substituents: 3.27 (a) The heat of combustion is highest for the hydrocarbon with the greatest number of carbons. Thus, cyclopropane, even though it is more strained than cyclobutane or cyclopentane, has the lowest heat of combustion. A comparison of heats of combustion can only be used to assess relative stability when the compounds are isomers. (b) All these compounds have the molecular formula C 7 H 14 . They are isomers, and so the one with the most strain will have the highest heat of combustion. H 3 CCH 3 CH 3 H 3 C 1,1,2,2-Tetramethylcyclopropane (high in angle strain; bonds are eclipsed; van der Waals strain between cis methyl groups) Heat of combustion 4635 kJ/mol (1107.9 kcal/mol) H 3 CCH 3 HH cis-1,2-Dimethylcyclopentane (low angle strain; some torsional strain; van der Waals strain between cis methyl groups) Heat of combustion 4590 kJ/mol (1097.1 kcal/mol) Methylcyclohexane (minimal angle, torsional, and van der Waals strain) Heat of combustion 4565 kJ/mol (1091.1 kcal/mol) CH 3 Cyclopentane Heat of combustion 3291 kJ/mol (786.6 kcal/mol) Cyclobutane Heat of combustion 2721 kJ/mol (650.3 kcal/mol) Cyclopropane Heat of combustion 2091 kJ/mol (499.8 kcal/mol) Spirohexane Bicyclo[2.2.0]hexane Bicyclo[2.1.1]hexane Cyclopropylcyclopropane Bicyclo[3.1.0]hexane Spiropentane Bicyclo[2.1.0]pentane Bicyclo[1.1.1]pentane CONFORMATIONS OF ALKANES AND CYCLOALKANES 55 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website (c) These hydrocarbons all have different molecular formulas. Their heats of combustion de- crease with decreasing number of carbons, and comparisons of relative stability cannot be made. (d) Bicyclo[3.3.0]octane and bicyclo[5.1.0]octane are isomers, and their heats of combustion can be compared on the basis of their relative stabilities. The three-membered ring in bicy- clo[5.1.0]octane imparts a significant amount of angle strain to this isomer, making it less stable than bicyclo[3.3.0]octane. The third hydrocarbon, bicyclo[4.3.0]nonane, has a greater number of carbons than either of the others and has the largest heat of combustion. 3.28 (a) The structural formula of 2,2,5,5-tetramethylhexane is (CH 3 ) 3 CCH 2 CH 2 C(CH 3 ) 3 . The sub- stituents at C-3 are two hydrogens and a tert-butyl group. The substituents at C-4 are the same as those at C-3. The most stable conformation has the large tert-butyl groups anti to each other. (b) The zigzag conformation of 2,2,5,5-tetramethylhexane is an alternative way of expressing the same conformation implied in the Newman projection of part (a). It is more complete, Anti conformation of 2,2,5,5-tetramethylhexane C(CH 3 ) 3 C(CH 3 ) 3 HH HH H H H H H H Bicyclo[4.3.0]nonane (C 9 H 16 ) Bicyclo[5.1.0]octane (C 8 H 14 ) Bicyclo[3.3.0]octane (C 8 H 14 ) Heat of combustion 5652 kJ/mol (1350.9 kcal/mol) Heat of combustion 5089 kJ/mol (1216.3 kcal/mol) Heat of combustion 5016 kJ/mol (1198.9 kcal/mol) Cyclopropylcyclopropane (C 6 H 10 ) Heat of combustion 3886 kJ/mol (928.8 kcal/mol) Spiropentane (C 5 H 8 ) Heat of combustion 3296 kJ/mol (787.8 kcal/mol) Bicyclo[1.1.0]butane (C 4 H 6 ) Heat of combustion 2648 kJ/mol (633.0 kcal/mol) 56 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website however, in that it also shows the spatial arrangement of the substituents attached to the main chain. (c) An isopropyl group is bulkier than a methyl group, and will have a greater preference for an equatorial orientation in the most stable conformation of cis-1-isopropyl-3-methylcyclohexane. Draw a chair conformation of cyclohexane, and place an isopropyl group in an equatorial position. Notice that the equatorial isopropyl group is down on the carbon atom to which it is attached. Add a methyl group to C-3 so that it is also down. Both substituents are equatorial in the most stable conformation of cis-1-isopropyl-3-methyl- cyclohexane. (d) One substituent is up and the other is down in the most stable conformation of trans-1- isopropyl-3-methylcyclohexane. Begin as in part (c) by placing an isopropyl group in an equa- torial orientation on a chair conformation of cyclohexane. To be trans to the C-1 isopropyl group, the C-3 methyl group must be up. The bulkier isopropyl group is equatorial and the methyl group axial in the most stable conformation. (e) To be cis to each other, one substituent must be axial and the other equatorial when they are located at positions 1 and 4 on a cyclohexane ring. H H 1 4 H H CH(CH 3 ) 2 CH 3 H CH(CH 3 ) 2 1 3 H H 3 C H CH(CH 3 ) 2 H CH(CH 3 ) 2 1 3 2,2,5,5-Tetramethylhexane CONFORMATIONS OF ALKANES AND CYCLOALKANES 57 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website Place the larger substituent (the tert-butyl group) at the equatorial site and the smaller sub- stituent (the ethyl group) at the axial one. ( f ) First write a chair conformation of cyclohexane, then add two methyl groups at C-1, and draw in the axial and equatorial bonds at C-3 and C-4. Next, add methyl groups to C-3 and C-4 so that they are cis to each other. There are two different ways that this can be accomplished: either the C-3 and C-4 methyl groups are both up or they are both down. (g) Draw the projection formula as a chair conformation. Check to see if this is the most stable conformation by writing its ring-flipped form. The ring-flipped form, with two equatorial methyl groups and one axial methyl group, is more stable than the originally drawn conformation, with two axial ethyl groups and one equatorial methyl group. 3.29 Begin by writing each of the compounds in its most stable conformation. Compare them by exam- ining their conformations for sources of strain, particularly van der Waals strain arising from groups located too close together in space. (a) Its axial methyl group makes the cis stereoisomer of 1-isopropyl-2-methylcyclohexane less stable than the trans. cis-1-Isopropyl-2-methylcyclohexane (less stable stereoisomer) trans-1-Isopropyl-2-methylcyclohexane (more stable stereoisomer) H H CH 3 CH(CH 3 ) 2 4 6 1 2 CH 3 CH(CH 3 ) 2 H H H H 3 C CH 3 CH 3 1 24 Less stable conformation: two axial methyl groups More stable conformation: one axial methyl group 2 4 H H CH 3 H 3 C 1 H CH 3 H H H CH 3 H 3 C CH 3 1 24 H H 3 C H H CH 3 CH 3 1 24 More stable chair conformation: C-3 methyl group is equatorial; no van der Waals strain between axial C-1 methyl group and C-3 methyl Less stable chair conformation: C-3 methyl group is axial; strong van der Waals strain between axial C-1 and C-3 methyl groups H H CH 3 CH 3 CH 3 CH 3 1 4 CH 3 H 3 C H H CH 3 CH 3 1 4 H H C(CH 3 ) 3 CH 2 CH 3 58 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website The axial methyl group in the cis stereoisomer is involved in unfavorable repulsions with the C-4 and C-6 axial hydrogens indicated in the drawing. (b) Both groups are equatorial in the cis stereoisomer of 1-isopropyl-3-methylcyclohexane; cis is more stable than trans in 1,3-disubstituted cyclohexanes. (c) The more stable stereoisomer of 1,4-disubstituted cyclohexanes is the trans; both alkyl groups are equatorial in trans-1-isopropyl-4-methylcyclohexane. (d) The first stereoisomer of 1,2,4-trimethylcyclohexane is the more stable one. All its methyl groups are equatorial in its most stable conformation. The most stable conformation of the second stereoisomer has one axial and two equatorial methyl groups. H 3 C CH 3 CH 3 1 24 More stable stereoisomer All methyl groups equatorial in most stable conformation CH 3 H 3 C CH 3 1 2 4 Less stable stereoisomer One axial methyl group in most stable conformation CH 3 CH 3 H 3 C 1 2 4 CH 3 CH 3 H 3 C 12 4 CH 3 CH 3 CH 3 1 2 4 cis-1-Isopropyl-4-methylcyclohexane (less stable stereoisomer; methyl group is axial and involved in repulsions with axial hydrogens at C-2 and C-6) trans-1-Isopropyl-4-methylcyclohexane (more stable stereoisomer; both groups are equatorial) H 3 C CH(CH 3 ) 2 CH 3 H H CH(CH 3 ) 2 1 2 4 6 cis-1-Isopropyl-3-methylcyclohexane (more stable stereoisomer; both groups are equatorial) trans-1-Isopropyl-3-methylcyclohexane (less stable stereoisomer; methyl group is axial and involved in repulsions with axial hydrogens at C-1 and C-5) CH 3 CH(CH 3 ) 2 CH 3 CH(CH 3 ) 2 H H 1 5 3 CONFORMATIONS OF ALKANES AND CYCLOALKANES 59 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website (e) The first stereoisomer of 1,2,4-trimethylcyclohexane is the more stable one here, as it was in part (d). All its methyl groups are equatorial, but one of the methyl groups is axial in the most stable conformation of the second stereoisomer. ( f ) Each stereoisomer of 2,3-dimethylbicyclo[3.2.1]octane has one axial and one equatorial methyl group. The first one, however, has a close contact between its axial methyl group and both methylene groups of the two-carbon bridge. The second stereoisomer has repulsions with only one axial methylene group; it is more stable. 3.30 First write structural formulas showing the relative stereochemistries and the preferred conforma- tions of the two stereoisomers of 1,1,3,5-tetramethylcyclohexane. The cis stereoisomer is more stable than the trans. It exists in a conformation with only one axial methyl group, while the trans stereoisomer has two axial methyl groups in close contact with each other. The trans stereoisomer is destabilized by van der Waals strain. CH 3 CH 3 CH 3 H 3 C CH 3 CH 3 CH 3 H 3 C H 3 C CH 3 CH 3 H 3 C H 3 C written in its most stable conformation as cis-1,1,3,5-Tetramethylcyclohexane trans-1,1,3,5-Tetramethylcyclohexane written in its most stable conformation as CH 3 CH 3 CH 3 Less stable stereoisomer (more van der Waals strain) More stable stereoisomer (less van der Waals strain) CH 3 H 3 C CH 3 CH 3 H H H CH 3 CH 3 H 3 C 1 24 CH 3 H 3 C CH 3 1 24 More stable stereoisomer Less stable stereoisomer All methyl groups equatorial in most stable conformation CH 3 H 3 C 1 CH 3 2 4 One axial methyl group in most stable conformation CH 3 H 3 C 1 H 3 C 2 4 60 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website 3.31 Both structures have approximately the same degree of angle strain and of torsional strain. Structure B has more van der Waals strain than A because two pairs of hydrogens (shown here) approach each other at distances that are rather close. 3.32 Five bond cleavages are required to convert cubane to a noncyclic skeleton; cubane is pentacyclic. 3.33 Conformational representations of the two different forms of glucose are drawn in the usual way. An oxygen atom is present in the six-membered ring, and we are told in the problem that the ring exists in a chair conformation. The two structures are not interconvertible by ring flipping; therefore they are not different confor- mations of the same molecule. Remember, ring flipping transforms all axial substituents to equato- rial ones and vice versa. The two structures differ with respect to only one substituent; they are stereoisomers of each other. 3.34 This problem is primarily an exercise in correctly locating equatorial and axial positions in cyclo- hexane rings that are joined together into a steroid skeleton. Parts (a) through (e) are concerned with positions 1, 4, 7, 11, and 12 in that order. The following diagram shows the orientation of axial and equatorial bonds at each of those positions. (a) At C-1 the bond that is cis to the methyl groups is equatorial (up). (b) At C-4 the bond that is cis to the methyl groups is axial (up). Both methyl groups are up. CH 3 CH 3 e c a b d 4 1 11 12 7 O HOCH 2 OHHO OHHO One axial OH substituent written in its most stable conformation as O HOCH 2 OHHO HO OH written in its most stable conformation as All substituents equatorial O CH 2 OH OH HO HO HO OH OH O CH 2 OH HO HO A: More stable stereoisomer Van der Waals strain destabilizes B H H H H CONFORMATIONS OF ALKANES AND CYCLOALKANES 61 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website (c) At C-7 the bond that is trans to the methyl groups is axial (down). (d) At C-11 the bond that is trans to the methyl groups is equatorial (down). (e) At C-12 the bond that is cis to the methyl groups is equatorial (up). 3.35 Analyze this problem in exactly the same way as the preceding one by locating the axial and equa- torial bonds at each position. It will be seen that the only differences are those at C-1 and C-4. (a) At C-1 the bond that is cis to the methyl groups is axial (up). (b) At C-4 the bond that is cis to the methyl groups is equatorial (up). (c) At C-7 the bond that is trans to the methyl groups is axial (down). (d) At C-11 the bond that is trans to the methyl groups is equatorial (down). (e) At C-12 the bond that is cis to the methyl groups is equatorial (up). 3.36 (a) The torsion angle between chlorine substituents is 60° in the gauche conformation and 180° in the anti conformation of ClCH 2 CH 2 Cl. (b) All the individual bond dipole moments cancel in the anti conformation of ClCH 2 CH 2 Cl, and this conformation has no dipole moment. Since ClCH 2 CH 2 Cl has a dipole moment of 1.12 D, it can exist entirely in the gauche conformation or it can be a mixture of anti and gauche con- formations, but it cannot exist entirely in the anti conformation. Statement 1 is false. 3.37–3.40 Solutions to molecular modeling exercises are not provided in this Study Guide and Solutions Man- ual. You should use Learning By Modeling for these exercises. SELF-TEST PART A A-1. Draw Newman projections for both the gauche and the anti conformations of 1-chloro- propane, CH 3 CH 2 CH 2 Cl. Sight along the C-1, C-2 bond (the chlorine is attached to C-1). A-2. Write Newman projection formulas for (a) The least stable conformation of butane (b) Two different staggered conformations of CHCl 2 CHCl 2 Gauche (can have a dipole moment) Anti (cannot have a dipole moment) H Cl H H H Cl Cl Cl H H H H Both methyl groups are up. CH 3 CH 3 d e c a b 11 12 7 1 4 H 62 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website A-3. Give the correct IUPAC name for the compound represented by the following Newman projection. A-4. Write the structure of the most stable conformation of the less stable stereoisomer of 1-tert- butyl-3-methylcyclohexane. A-5. Draw the most stable conformation of the following substance: Which substituents are axial and which equatorial? A-6. A wedge-and-dash representation of a form of ribose (called H9252-D-ribopyranose) is shown here. Draw the most stable chair conformation of this substance. A-7. Consider compounds A, B, C, and D. (a) Which one is a constitutional isomer of two others? (b) Which two are stereoisomers of one another? (c) Which one has the highest heat of combustion? (d) Which one has the stereochemical descriptor trans in its name? A-8. Draw clear depictions of two nonequivalent chair conformations of cis-1-isopropyl- 4-methylcyclohexane, and indicate which is more stable. A-9. Which has the lower heat of combustion, cis-1-ethyl-3-methylcyclohexane or cis-1-ethyl- 4-methylcyclohexane? A-10. The hydrocarbon shown is called twistane. Classify twistane as monocyclic, bicyclic, etc. What is the molecular formula of twistane? AB CH 3 H 3 C CH 3 H 3 C CD CH 3 CH 3 CH 3 CH 3 H 3 C O OH OHHO HO CH 3 H 3 C C(CH 3 ) 3 C(CH 3 ) 3 CH 3 H H 3 CCH 3 H CONFORMATIONS OF ALKANES AND CYCLOALKANES 63 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website A-11. Sketch an approximate potential energy diagram similar to those shown in the text (Fig- ures 3.4 and 3.7) for rotation about a carbon–carbon bond in 2-methylpropane. Does the form of the potential energy curve more closely resemble that of ethane or that of butane? A-12. Draw the structure of the sulfur-containing heterocyclic compound that has a structure anal- ogous to that of tetrahydrofuran. PART B B-1. Which of the listed terms best describes the relationship between the methyl groups in the chair conformation of the substance shown? (a) Eclipsed (c) Anti (b) Trans (d) Gauche B-2. Rank the following substances in order of decreasing heat of combustion (largestBsmallest). (a)1 H11022 2 H11022 4 H11022 3(c)3 H11022 4 H11022 2 H11022 1 (b)2 H11022 4 H11022 1 H11022 3(d)1 H11022 3 H11022 2 H11022 4 B-3. Which of the following statements best describes the most stable conformation of trans- 1, 3-dimethylcyclohexane? (a) Both methyl groups are axial. (b) Both methyl groups are equatorial. (c) One methyl group is axial, the other equatorial. (d) The molecule is severely strained and cannot exist. B-4. Compare the stability of the following two compounds: A: cis-1-Ethyl-3-methylcyclohexane B: trans-1-Ethyl-3-methylcyclohexane (a) A is more stable. (b) B is more stable. (c) A and B are of equal stability. (d) No comparison can be made. B-5. What, if anything, can be said about the magnitude of the equilibrium constant K for the following process? (a) K H11005 1(c) K H11021 1 (b) K H11022 1(d) No estimate of K can be made. H CH(CH 3 ) 2 H CH 3 H H CH(CH 3 ) 2 H 3 C CH 3 1 CH 3 CH 3 2 3 CH 3 CH 3 4 CH 3 CH 3 64 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website B-6. What is the relationship between the two structures shown? (a) Constitutional isomers (b) Stereoisomers (c) Different drawings of the same conformation of the same compound (d) Different conformations of the same compound B-7. The two structures shown here are each other. (a) identical with (c) constitutional isomers of (b) conformations of (d) stereoisomers of B-8. The most stable conformation of the following compound has (a) An axial methyl group and an axial ethyl group (b) An axial methyl group and an equatorial ethyl group (c) An axial tert-buytl group (d) An equatorial methyl group and an equatorial ethyl group (e) An equatorial methyl group and an axial ethyl group B-9. Which of the following statements is not true concerning the chair–chair interconversion of trans-1,2-diethylcyclohexane? (a) An axial group will be changed into the equatorial position. (b) The energy of repulsions present in the molecule will be changed. (c) Formation of the cis substance will result. (d) One chair conformation is more stable than the other. B-10. The most stable conformation of the compound (in which all methyl groups are cis to one another) has: (a) All methyl groups axial (b) All methyl groups equatorial (c) Equatorial methyl groups at C-1 and C-2 (d) Equatorial methyl groups at C-1 and C-4 (e) Equatorial methyl groups at C-2 and C-4 CH 3 CH 3 H 3 C 1 24 C(CH 3 ) 3 CH 3 CH 2 CH 3 CH 3 H 3 C H H H CH 3 CH 3 CH 3 CH 3 H H H ClCH 3 Cl CH 3 CONFORMATIONS OF ALKANES AND CYCLOALKANES 65 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website B-11. Which point on the potential energy diagram is represented by the Newman projection shown? B-12. Which of the following statements is true? (a) Van der Waals strain in cis-1,2-dimethylcyclopropane is the principal reason for its decreased stability relative to the trans isomer. (b) Cyclohexane gives off more heat per CH 2 group on being burned in air than any other cycloalkane. (c) The principal source of strain in the boat conformation of cyclohexane is angle strain. (d) The principal source of strain in the gauche conformation of butane is torsional strain. B-13. Which one of the following has an equatorial methyl group in its most stable conformation? B-14. The structure shown is the carbon skeleton of adamantane, a symmetrical hydrocarbon having a structure that is a section of the diamond lattice. Adamantane is: (a) Bicyclic (c) Tetracyclic (b) Tricyclic (d) Pentacyclic C(CH 3 ) 3 H 3 C (a) C(CH 3 ) 3 CH 3 (b) C(CH 3 ) 3 CH 3 (c) C(CH 3 ) 3 CH 3 (d) C(CH 3 ) 3 CH 3 (e) H H HH H 3 C CH 3 (a) (b) (c) (d) 66 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website