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 CH,CH,CH CH3 (c) Rewrite the structure to show its constitution. The compound is CH,CH,CH(CH,)2; it is 2-methylbutane H3 (d) In this structure, we are sighting down the C-3--C-4 bond of a six-carbon chain. It is CH CH, CH,CHCH, CH3, or 3-methy lhexane CH3 H1CH_ CH, 46 Back Forward Main Menu TOC Study Guide Toc Student OLC MHHE Website
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, CH3CH2CH2CH3. (c) Rewrite the structure to show its constitution. The compound is CH3CH2CH(CH3)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 CH3CH2CH2CHCH2CH3, or 3-methylhexane. = CH3 H CH2CH3 H H CH3 CH2CH3 C H H H H3C CH3 CH3 C H H H CH3 CH3 CH3 H H H H CH3 CH3 46 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website
CONFORMATIONS OF ALKANES AND CYCLOALKANES 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%, 1200, 2400, 3600) 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. H H H D H H, C H H H 240 300 Torsion angle(degrees) 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 nformation. 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 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. gauche (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 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 conformations 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 energy 0 60 120 180 240 300 360 Torsion angle (degrees) H3C H H H H H H H H H H H3C H CH3 H H H H H3C H H H H H H H H H H H3C H H H CH3 H H H H H H CH3 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 →H2C (c) An alkyl substituent is more stable in the equatorial position. An equatorial substituent at C-3 C 3.6 A tert-butyl group is much larger than a methyl group and has a greater preference for the equator- rial position. The most stable conformation of l-tert-butyl-1-methylcyclohexane has an axial methyl group and an equatorial tert-butyl group CH3 C(CHi) I-ferr-Butyl-1-methylcyclohexane 3.7 Ethylcyclopropane and methylcyclobutane are isomers(both are CsHo) 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 CHCH Less stable More stable Heat of combustion: 3384 kI/m (808.8 kcal/mol) (801.2 kcal/mol) 3. 8 The four constitutional isomers of cis and trans-1, 2-dimethylcyclopropane that do not contain double bond CH,CH3 I, l-Dimethylcyclopropane Ethy cyclopropane CH Methylcyclobutane Cyclopentane 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. H3C H3 H,C cis-1, 3. 5-Trimethy lcycloher 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 equatorial 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 C5H10). 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 H3C CH3 CH3 CH3 CH3 H H3C H H CH3 CH3 1,1-Dimethylcyclopropane CH3 Methylcyclobutane Ethylcyclopropane CH2CH3 Cyclopentane CH2CH3 CH3 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 CH3 C(CH3)3 H H3C Up Down H CH3 Up Down H H3C Up Down 4 5 6 3 2 1 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website
CONFORMATIONS OF ALKANES AND CYCLOALKANES 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 H3C CH H CH H,C H CH 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-l-tert-butyl 3-methylcyclohexane the C-3 methyl group is equatorial (c) In trans-l-tert-butyl-4-methylcyclohexane both the tert-butyl and the C-4 methyl group are equatorial H3C H (d) Again the tert-butyl group is equatorial; however, in cis-l-tert-butyl-4-methylcyclohexane the methyl group on C-4 is axial. H 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 H=CH, CH Spiropentane(CsHg) CsHs CHIO CsH& Only the two compounds that have the molecular formula Cs Hg are isomers of spiropentane 3. 12 Two bond cleavages convert bicyclobutane to a noncyclic species; therefore, bicyclobutane is bicycl A一一不个 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 C5H8 are isomers of spiropentane. 3.12 Two bond cleavages convert bicyclobutane to a noncyclic species; therefore, bicyclobutane is bicyclic. Spiropentane (C5H8) CH CH2 C5H8 C6H10 C5H8 C5H10 CH2 CH3 H C(CH3)3 H H3C H C(CH3)3 H H H3C H C(CH3)3 H H H H3C CH3 H3C trans-1,3,5-Trimethylcyclohexane CH3 CH3 H H CH3 H CONFORMATIONS OF ALKANES AND CYCLOALKANES 49 Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website
CONFORMATIONS OF ALKANES AND CYCLOALKANES 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 directl Bicyclo[5.2.0]nonane (c) The three bridges in bicyclo[3. 1. I ]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 Three- carbol One-carbon (d) Bicyclo[3.3. 0]octane has two five-membered rings that share a common side. Three-carbon Three-carbon 3. 14 Since the two conformations are of approximately equal stability when r= H, it is reasonable to expect that the most stable conformation when R= CH3 will have the CH3 group equa R =H: both conformations similar in energy R=CH3: most stable conformation has CH, equ 3.15(a) Recall that a neutral nitrogen atom has three covalent bonds and an unshared electron pair he three bonds are arranged in a trigonal pyramidal manner around each nitrogen in hydrazine(H,NNH,) H H H 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 fivecarbon 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 H, it is reasonable to expect that the most stable conformation when R CH3 will have the CH3 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 (H2NNH2). H N N H H H H H H H H H H H N H N H H H R H: both conformations similar in energy R CH3: most stable conformation has CH3 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 CH2 CH3 CH3 CH2 CH3 CH3 CH2 CH3 CH3 50 CONFORMATIONS OF ALKANES AND CYCLOALKANES Back Forward Main Menu TOC Study Guide TOC Student OLC MHHE Website