Copy of Organic Chemistry Jonh Mc Murry7

Copy of Organic Chemistry Jonh Mc Murry7 - 4.6 Axial and...

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Unformatted text preview: 4.6 Axial and Equatorial Bonds in Cyclohexane 121 Figure 4.11 A ring-flip in chair cyclohexane interconverts axial and equatorial positions. What is axial (red) in the starting struc— ture becomes equatorial in the ring-flipped structure, and what is equatorial (blue) in the starting structure is axial after ringvflip. Hing-flip ‘ I Move this l carbon down M :_)'\-‘ -3 1h l Fling-flip ‘— tffiill L'Cil“. 15;) about 45 kl/rnol [10.8 kcal/mol], the process is rapid at room temperature and we see what appears to be a single structure rather than distinct axial and equa- torial isomers. Fling-flip ( Br Axial bromocyclohexane Equatorial bromocyclohexane WORKED EXAMPLE 4.2 Drawing the Chair Conformation of a Substituted Cyclohexane Draw ].1~diinethylcyclohexane in a chair conformation, indicating which methyl group in your drawing is axial and which is equatorial, Strategy Draw a chair cyclohexane ring using the procedure in Figure 4.9, and then put two methyl <groups on the same carbon. The methyl group in the rough plane of the ring is equatorial, and the other (directly above or below the ring) is axial. Solution / Axial methyl group " Equatorial methyl group 122 CHAPTER 4 Problem 4.12 Problem 4.13 Problem 4.14 4.7 Test your knowledge of Key ideas by using resources in ThomsonNOW or by answering moot-chapter problems marked with - . Figure 4.12 A plot ofthe per— centages of two isomers at equi‘ librium versus the energy difference between them. The curves are calculated using the equation AE= —RTln K. Organic Compounds: Cycloalkanes and Their Stereochemistry Draw two different chair conformations of cyclohexanol Ihydroxycyclohexane), showing all hydrogen atoms. Identify each position as axial or equatorial. Draw two different Chair conformations of [mus-l ,4—dimethylcyclohexane, and label all positions as axial or equatorial. Identity each ofthe colored positions—red, blue, and green—as axial or equatorial. Then carry out a ringtlip, and Show the new positions occupied by each color. ' . r , v: " . 1 “I Ringefllp " . H - fine mm er: .J“ Conformations of Monosubstituted Cyclohexanes Even though cyclohexane rings rapidly flip between chair conformations at room temperature, the two conformations of a monosubstituted cyclohexane aren’t equally stable. in methylcyclohexane, for instance, the equatorial confor- mation is more stable than the axial conformation by 7.6 kl/mol (1.8 kcal/mol). The same is true of other monosubstituted cyclohexanes: a substituent is almost always more stable in an equatorial position than in an axial position. You might recall from your general chemistry course that it‘s possible to cal’ culate the percentages of two isomers at equilibrium using the equation = *RT In K, where AB is the energy difference between isomers, R is the gas constant [8.315 J/(K - mob], T is the Kelvin temperature, and K is the equilibrium con- stant between isomers. For example, an energy difference of 7.6 kJ/mol means that about 95% of methylcyclohexane molecules have the methyl group equato- rial at any given instant and only 5”” have the methyl group axial. Figure 4.12 plots the relationship between energy and isomer percentages. Energy dif‘lerence lkcaI/mol) 0 i 2 3 100 «r e ' - i’__,_-’J————' ~ * _ v/fl’I ‘- // IV on: smith: innn'inr 80 ‘ ,/’ //- - / ._. 60 ‘ J// a / 33 in. 40 20 per Less stable isomer l r | I ' i t 5 10 15 Energy difference (kJ/mol) Figure 4.14 The origin of 1,3-diaxial interactions in methylcvclohexane, The steric strain between an axial methyl group and an axial hydrogen atom ih ree carbons away is iden- tical to the steric strain in gauche butane. Note that the *CH3 group in methyl» cyclohexane moves slightly away from a true axial posi- tion to minimize the strain. 4.7 Conformations oiMonosubstituted Cyclohexanes 123 The energy difference between axial and equatorial conformations is due to steric strain caused by 1,3—diaxial interactions. The axial methyl group on C1 is too close to the axial liydrogens three carbons away on C3 and CS, resulting in 7.6 kJ/mo] of steric strain {Figure 4.13). Siei‘ic interlerenoe Ring; iii-ii __ H\ Figure 4.13 Interconversion of axial and equatorial methylcyclohexane, as represented in several formats. The equatorial conformation is more stable than the axial conformation by 7.6 kJ/mol. The 1,3-diaxial steric strain in substituted methylcyciohexane is already familiar—we saw it previously as the steric strain between methyl groups in gauche butane. Recall from Section 3.7 that gauche butane is less stable than anti butane by 3.8 kJ/Inol (0.9 kcal/inoi) because of steric interference between hydrogen atoms on the two methyl groups. Comparing a four-carbon fragment of axial metbylcyclohexane with gauche butane shows that the steric interac- tion is the same in both cases [Figure 4.14). Because axial methylcyclohexane has two such interactions, though, it has 2 x 3.8 = 7.6 kj/moi of steric strain. Equatorial methylcyclohexane, however, has no such interactions and is there- fore more stable. CH3 ' I . H H CH» HJC .i i? r_ ,i-i , "J H H .' It I i: H ' ,V '.-i i H .9,- Gauche butane 4. Axial (3.8 kJ/mol strain) methylcyciohexane (7.6 kJ/mol straini 124 CHAPTER 4 Organic Compounds: Cycioalkanes and Their Stereochemistry Problem d.15 Problem 4.16 Problem 4.17 4.8 What is true for methylcyclohexane is also true for other rnonosubstituted cyclohexanes: a substituent is almost always more stable in an equatorial posi- tion than in an axial position. The exact amount of 1,3-diaxial steric strain in a given substituted cyclohexane depends on the nature and size of the sub- stituent, as indicated in Table 4.1. Not surprisingly, the amount of steric strain increases through the series 1-13C— < Cl-lsCl-lz— < (CH3)ZCH7 << (CH3)3C—, paralleling the increasing bulk of the alkyl groups. Note that the values in Table 41.1 refer to 1.,3-diaxia1 interactions of the substituerrt with a single hydrogen atom. These values must be doubled to arrive at the amount of strain in a mono- substituted cyclohexane. Table 4.1 Static Strain in Monosubstituted Cyclohexanes H ' Y 1,3-Diaxial straini__ ‘L‘ V lkJ/mol) (kcaI/moll Z F 0.5 (1.12 Cl, Br 1.0 [1.25 OH 3.1 0.5 CH3 3.8 0.9 CH2CH3 4.0 0.95 CH(CH3i2 4.6 1.1 ClCl—I3l3 11.4 2 7 €ng 6.3 is cogH 2.9 0.7 CN 0.4 0.1 What is the energy difference between the axial and equatorial conformations of cyclohexanol (hydroxycyclohexanei? Why do you suppose an axial cyano (—CN) substituent causes practically no 1,3—diaxiai steric strain (0.4 kl/mol)? Use molecular models to help with your answer. Look at Figure 4.12, and estimate the percentages ot axial and equatorial conformers present at equilibrium in bromocyclohexane. Conformations of Disubstituted Cyclohexanes Monosubstituted cyclohexanes are more stable with their substituent in an equatorial position, but the situation in disubstituted cyclohexanes is more complex because the steric effects of both substituents must be taken into account. All steric interactions in both possible chair confonnations must be analyzed before deciding which conformation is favored. Let’s look at 1,2-dimethylcyclohexane as an example. There are two iso- mers, cis-1,2—diinethylcyclohexane and trans-l,Z-dimethylcyclohexane. which 4,8 Cantormations otDisubstituted Cyclohexanes 125 must be considered separately. In the cis isomer, both methyl groups are on the same face of the ring, and the compound can exist in either of the two chair con- formations shOWn in Figure. 4.15. (it may be easier for you to see whether a compound is cis- or trans-disubstituted by first drawing the ring as a flat repre sentation and then converting to a Chair conformation.) Both chair conforma- tions haw one axial methyl group and one equatorial methyl group The top conformation in Figure 4.15 has an axial methyl grorip at C2, which has 1,3-cliaxial interactions with hydrogens on C4 and C6. 'l'he ring-flipped con For- group at C1, which has 1,3-diaxial interactions with hydrogens on C3 and C5. in addition, both conformations have gauche butane interactions between the two metth groups. The two confirmations are equal in energy with a total steric strain of 3 X 3.8 kJ/mol = 11.4 k_l/mol (2.7 kcal/mol). I'W’I u r inn-1 A. rn/zl-th irruuurir 11LLLlin cis—1,2_-Dimethylcyclohexane i 'iI.:3r‘a-:Ci.'iI'Ji'i t Two CH3 Li: H diaxial interactions iii) kJ.-'irir.i|l Total strain: 3.8 + 7.5 I 114 kJ/mol Thomson Click Organic Interactive to learn to draw and a55355 the stability of substituted cyclohexanes. Two f3: ‘ Iv'iterecrio'is: if Total strain: 3.8 + 7.6 =11.4l<J/mol Lii l:.l.'nioli Ring-flip r\.5.-'I'i'ir all :5 iii-.H-‘e- Figure 4.15 Conformations of cis<l,2~dimethy|cyclohexane. The two chair confor- mations are equal in energy because each has one axial methyl group and one equatorial methyl group. Sign in at www.thomsonedu.com to see a simulation based on this figure and to take a short quiz. [n [runs-l,2-dimethylcyclohexane, the two methyl groups are on opposite faces of the ring and the compound can exist in either ol‘ the two chair contor- niations shown in Figure 4.16. The situation here is quite different from that of the cis isomer. The top trans conformation in Figure 4.16 has both methyl groups equatorial and therefore has only a gauche butane interaction between methyls (3.8 kj/mol) but no 1,3ediaxial interactions. The ring-flipped confor- mation, however, has both methyl groups axial. The axial methyl group at C1 interacts with axial hydrogens at C3 and CS, and the axial methyl group at C2 interacts with axial hydrogens at C4 and C6. These four 1.,3-diaxial inter- actions produce a steric strain of 4- X 3.8 kJ/mol = 15.2 kl/mol and make the diaxial conformation 15.2 7 3.8 2 11.4 kJ/mol less favorable than the diequa- torial conformation. We therel'ore predict that trans-1,2-climethylcyclohexane will exist almost exclusively in the diequatorial conformation. The same kind of conformational analysis just carried out for cis- and trams-1,2—climethylcyclohexane can be done for any substituted cyclohexane, such as (is-1-tert-butyl-zi-chlorocyclohexane (see Worked Example 4.3). As you might imagine, though, the situation becomes more complex as the number or 125 CHAPTEH4 Organic Compounds: Cycloalkanes and Their Stereochemistry trans-1,Z-Dimethylcyclohexane One gauche interaction i138 kJi‘mni) Four CH3“ H rliaxial interactions l l5.2 ltmeoil Figure 4.16 Conformations of trans~1,2-dimethylcyclohexane. The conformation with both methyl groups equatorial is favored by 11.4 I<Jlmol (2.7 kcal/moli over the conformation with both methyl groups axial. Thomson Click Organic substituents increases, For instance, compare glucose with mannose, a carbohy- ’”’9’39“V8‘° 'eam ‘0 “3009"”9 drate present in seaweed. Which do you think is more strained? in glucose, all the most stable conformations . . y . . . . of cyclohexanes following substituents on the 51x»membered ring are equatorial) while in mannose, one of ring-flips the —OH groups is axial, making mannose more strained. H CHzOH H CHQOI-l 6 £3 1. w “.9. HO ETLO HO GEO L- 6-O/ .3 HO I OH HO I OH . _ H it H OH H H H H H ® :’ i u‘ "a. Glucose Mannose Thomson-vr’u- Click Organic A summary of the various axial and equatorial relationships among sub- ”"eracm’em “59 a“ 0'1"“ stituent groups in the different possible cis and trans substitution patterns for palette to draw and interconvert cyclohexane Structures- disubstituted cyclohexanes is given in Table 4.2. Table 4.2 Axial and Equatorial Relationships in Cis- and Trails-Disubstituted Cycinhexanes Cis/irans substitulion pattern Axial/equatorial relationships LII-(jig (iiitliJSi'il’UiL’d 41,0 or on l,2-’l tans disubblilulul an or c,c 1,37Cis‘ disubstitutml 3.3 or ex l,_i-'l‘rrins disubstitutocl rim or em 1,4-Cis (“substituted 2i_.t' or 0,3 i,4-'l‘i'niis disubstitutunl am or me woaxea'exmraptg 4.3 Strategy Solution Problem 4.18 Problem 4.19 ‘ (c) cis-1-Bromo-4-ethylcyclohexane 4,8 Contormations of Disubstituted Dyclohexanes 127 Drawing the Most Stable Conformation ofa Substituted Cyclohexane Draw the most stable conformation of (is—i-rm-t-butyl-4—chIorocyclohexane. By how much is it favored? Draw the possible conformations, and calculate the strain energy in each. Remem- ber that equatorial substittlents cause less strain than axial substituents. First draw the two chair conformations of the molecule: H30. , Hiicric . “H __. .Hl Ringeflip 7C. HBC‘ I !_! HgC H 2 X10 = 2.0 kJ/mol steric strain 2 X114 = 22.8 kJ/mol steric strain in the left-hand conformatiom the terr—butyl group is equatorial and the chlo- rine is axial. In the right-hand conformation, the ter'tebutyl group is axial and the chlorine is equatorial. ’l'hese conformations aren’t of equal energy because an axial tert-butyl substituent and an axial chloro substituent produce different amounts of steric strain. Table 4.1 shows that the 1‘3-diaxial interaction between a hydrogen and a tart-bitty] group costs 11.4 kJ/moi (2.7 kcal/mol), whereas the interaction between a hydrogen and a chlorine costs only 1.0 kJ/rnol (0.25 kcal/mol). An axial tert—bntyl group therefore produces (2 X 11.4 kJ/mol) ~ (2 X 1.0 kj/mol) : 20.8 itj/inol {4.9 ltcal/niol) more steric strain than does an axial chlorine, and the compound preferentially adopts the conformation with the chlorine axial and the tert—butyl equatorial. Draw the most stable chair conformation of the following molecules, and estimate the amount of strain in each: (a) rrans-l-Chloro-3-methylcyclohexane (b) (is-1-Ethyl—2-methylcyclohexane (d) cis-l-tmt— Bu ty]-¢l-ethylcyclohexan e identify each substituent in the follorving compound as axial or equatorial, and tell whether the conformation shown is the more stable or less stable chair form (ye110w- green : Cl): 128 CHAPTER 4 4.9 Figure 4.17 Representations of cis- and transedecalin. The red hydrogen atoms at the bridge— head carbons are on the same face of the rings in the cis isomer but on opposite faces in the trans isomer. Organic Compounds: Cycloalkanes and Their Stereochemistry Conformations of Polycyclic Molecules The last point we‘ll consider about cycloalkane stereochemistry is to see what happens when two or more cycloalkane rings are fused together along a com- mon bond to construct a polycyclic molecule—for example, decalin. iaHa 1 9/\l/\l3 I Decalin—two fused cvclohexane rings 23\ r 4 ‘7 H' is Decalin consists of two cyclohexane rings foined to share two carbon atoms (the bridgeth carbons, C1 and C6) and a common bond. Decalin can exist in either of two isomeric forms, depending on whether the rings are transfused or cis fused. [n cis-decalin, the hydrogen atoms at the bridgehead carbons are on the same face of the rings; in trans-decalin, the bridgehead hydrogens are on opposite laces. Figure 4.17 shows how both compounds can be represented using chair cyclohexane conformations. Note that cis- and trans—decalin are not interconvertible by ring-flips or other rotations. They are cis—trans stereoisomers and have the same relationship to each other that cis- and trans-1,Z-dimethyl- cyclohexane have. cis-Decalin trans—Decalin Polycyclic compounds are common in nature, and many valuable sub- stances have t'usedering structures. For example, steroids. such as the male hor- mone testosterone, have 3 six-membered rings and l five-membered ring fused together. Although steroids look complicated compared with cyclohexane or decalin, the same principles that apply to the conformational analysis or simple cyclohexane rings apply equally well (and often better) to steroids. 4.9 Conformations of Polycyclic Molecules 129 Testosterone (a steroid) Problem 4.20 Another common ring system is the norbornane, or bicyclo[2.2.l]heptane, structure. Like decalin, norbornane is a bicyclaalkczne, so called because two rings would have to be broken open to generate an acyclic structure [ts systematic name, bicyclol2.2.1Iheptane, reflects the fact that the molecule has seven car: bons, is bicyclic, and has three "bridges" of 2, 2, and 1 carbon atoms connect- ing the two bridgehead carbons. A lrrrarbon bridge ii 2-2:.ari1im: EJrirlgr- fr / ltll'l'Igj-ili"li-' ' =_'J c: ‘ ‘ - Writ: . ——*" Norbornane (bicyc|o[2.2.1]heptane) Norbomane has a conformationally locked boat cyclohexane ring (Sec- tion 4.5) in which carbons 1 and 4 are joined by an additional CH2 group. Note how, in drawing this structure, a break in the rear bond indicates that the vertical bond crosses in front of it. Making a molecular model is particu- larly helpful when trying to see the three—dimensionality of norbornane. Substituted norhornanes, such as camphor, are found widely in nature, and many have been important historically in developing organic structural theories. Camphor Which isomer is more stable, cis-decalin or tmns-decalin? Explain. 130 CHAPTER 4 Organic Compounds: Cycloalkanes and Their Stereochemistry Computer programs make it possible to portray accurate representations of molecular geometry. Figure 4.18 The structure of Tamiflu (oseltamivir phos— phate), an antiviral agent active against type A influenza, and a molecular model of its minimum-energy conforma— tionl as calculated by molecu- lar mechanics. Molecular Mechanics All the structural models in this book are computer-drawn. To make sure they accurately portray bond angles, bond lengths, torsional interactions, and steric interactions, the most stable geometry of each molecule has been calculated on a desktop computer using a commercially available molecular mechanics program based on work by N. L. Allinger of the University of Georgia. The idea behind molecular mechanics is to begin with a rough geometry for a molecule and then calculate a total strain energy for that starting geometry, using mathematical equa— tions that assign values to specific kinds of molecular interac- tions. Bond angles that are too large or too small cause angle strain; bond lengths that are too short or too long cause stretching or com— pressing strain; unfavorable eClipsing interactions around Single bonds Cause torsional strain; and nonbonded atoms that approach each other too closely cause steric, or van der Waals, strain. :ueyer/CDRBIS let Huger Hue-s. Etotal : Ebonclslretcbing + Bangle strain + Etorsionalstrain + Evnntler Warrls After calculating a total Strain energy for the starting geometry, the pro- gram automatically changes the geometry slightly in an attempt to lower strainiperha ps by lengthening a bond that is too short or decreasing an angle that is too large. Strain is recalculated for the new geometry, more changes are made, and more calculations are done. After dozens or hundreds of iterations, the calculation ultimately converges on a minimum energy that corresponds to the most favorable, least strained conformation of the molecule. Molecular mechanics calculations have proved to be enormously useful in pharmaceutical reSearch, where the complementary fit between a drug mole- cule and a receptor molecule in the body is often a key to designing new phar- maceutical agents (Figure 4.18). H3C—C\ I \ . o "' NH3 H Tamiflu loseltamivir phosphate) ...
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