MONOSUBSTITUTED CYCLOHEXANES. …

1 MONOSUBSTITUTED ANALYSIS277 Keq= ![[CT]]!= 10_DG , [T]= ( 10_3)[C]. Thus, in one mole of cyclohexane , we have1= [C]+ [T]= [C]+ ( X10_3)[C]= [C]Solving for [C], [C]= , by difference,[T]= [C]= , cyclohexane contains chair form and twist-boat form at 25 ANALYSISA substituent group in a substituted cyclohexane , such as the methyl group in methyl cyclo-hexane, can be in either an equatorial or an axial two compounds are not identical, yet they have the same connectivity, so they arestereoisomers. Because they are not enantiomers, they must be diastereomers. Like cyclohexaneitself, substituted cyclohexanes such as methylcyclohexane also undergo the chair interconver-sion.

2 As Fig. (p. 278) shows, axial methylcyclohexane and equatorial methylcyclohexane areinterconverted by this process. Note in this interconversion that a down methyl remains downand an up methyl remains up. (Demonstrate this to yourself with models!) Because this processis rapid at room temperature, methylcyclohexane is a mixture of two conformational diastere-omers(Sec. ). Because diastereomers have different energies, one form is more stable thanthe methylcyclohexane is more stable than axial methylcyclohexane. In fact, it isusually the case that the equatorial conformation of a substituted cyclohexane is more stablethan the axial conformation.

3 Why should this be so?Examination of a space-filling model of axial methylcyclohexane (Fig. , p. 278) showsthat van der Waals repulsions occur between one of the methyl hydrogens and the two axial hy-drogens on the same face of the ring. Such unfavorable interactions between axial groups arecalled 1,3-diaxial van der Waals repulsions destabilize the axial conforma-tion relative to the equatorial conformation, in which such van der Waals repulsions are a model of chair cyclohexane corresponding to the leftmost model in Fig. Raise car-bon-4 so that carbons 2 6 lie in a common plane. This is the half-chairconformation of cyclo-hexane, and it is the transition state for the interconversion of the chair and twist-boat confor-mations.

4 (Notice the position of this conformation on the energy diagram of Fig. ) Givetwo reasons why this conformation is less stable than the chair or twist-boat 12/8/08 12:13 PM Page 277278 CHAPTER 7 CYCLIC COMPOUNDS. STEREOCHEMISTRY OF REACTIONSHCH3 HCH3 HCH3 HCH3 Figure chair interconversion results in an equilibrium between equatorial (left) and axial (right) confor-mations of methylcyclohexane. The conversion is shown with two different ring perspectives. Notice in this inter-conversion that a down methyl remains down and an up methyl remains "CHHHHH"CHHH(a)(b)(c)van der WaalsrepulsionsFigure equilibrium between axial and equatorial conformations of methylcyclohexane is shown with (a)Lewis structures, (b) ball-and-stick models, and (c) space-filling models.

5 The hydrogens involved in 1,3-diaxial in-teractions in the axial conformation are shown in color, and the interactions themselves are indicated with 12/8/08 12:13 PM Page MONOSUBSTITUTED ANALYSIS279As Fig. shows, the energy (enthalpy) difference between axial and equatorial conforma-tions of methylcyclohexanes is kJ mol_1( kcal mol_1). Because there are two1,3-diax-ial interactions in methylcyclohexane, each interaction is responsible for one-half of the en-thalpy difference, or kJ mol_1( kcal mol_1). We ll find that we can use this value inpredicting the relative energies of other methyl-substituted cyclohexanes.

6 In other words, eachmethyl hydrogen 1,3-diaxial interaction in a cyclohexane derivative raises the enthalpy kJ mol_1( kcal mol_1).As shown in Fig. , the 1,3-diaxial interaction of a methyl group and a hydrogen in axial-methylcyclohexane looks a lot like the van der Waals interaction between methyl hydrogens ingauche-butane. The energy cost of this interaction in gauche-butane is kJ mol_1(Fig. ,p. 54). Because there are twosuch 1,3-diaxial interactions in axial-methylcyclohexane, thegauche-butane analogy would predict an energy cost of 2 = kJ mol_1. The actualvalue, kJ mol_1, is in fair agreement with this prediction.

7 For this reason, 1,3-diaxialmethyl hydrogen interactions in cyclohexane derivatives are sometimes called energy cost of placing a methyl group in the axial position of a cyclohexane ring is re-flected in the relative amounts of axial and equatorial methylcyclohexanes present at equilib-"HCH3L""HCH3 H kJ mol 1( kcal mol 1)Figure enthalpies of axial and equatorial (axial conformation)gauche-butaneFigure relationship between the axial conformation of methylcyclohexane and gauche-butane. Onegauche-butane part of methylcyclohexane is highlighted, and the corresponding van der Waals repulsion isshown with a colored bracket.

8 The second gauche-butane interaction in methylcyclohexane is shown with thegray 12/8/08 12:13 PM Page 279280 CHAPTER 7 CYCLIC COMPOUNDS. STEREOCHEMISTRY OF REACTIONS rium. As you will see when you work Problem , methylcyclohexane contains very little ofthe axial conformation at investigation of molecular conformations and their relative energies is called confor-mational h ave j u s t c a r r i e d o u t a c o n f o r m a t i o n a l a n a l y s i s o f m e t h y l cy c l o h ex a n e .The conformational analyses of many different substituted cyclohexanes have been per-formed.

9 As might be expected, the 1,3-diaxial interactions of large substituent groups aregreater than the interactions in methylcyclohexane. For example, the equatorial conformationof tert-butylcyclohexane is favored over the axial conformation by about 20 kJ mol_1(about5 kcal mol_1).This means that a sample of tert-butylcyclohexane contains a truly minuscule amount of theaxial conformation. (See Problem )Separation of Chair ConformationsThe two chair conformations of a MONOSUBSTITUTED cyclohexane are diastereomers. If these confor-mations could be separated, they would have different physical properties.

10 In the late 1960s, C. Hack-ett Bushweller, then a graduate student in the laboratory of Prof. Frederick Jensen at the Universityof California, Berkeley, cooled a solution of chlorocyclohexane in an inert solvent to -150 C. Crys-tals suddenly appeared in the solution. He filtered the crystals at low temperature; subsequent in-vestigations showed that he had selectively crystallized the equatorial form of chlorocyclohexane!When the equatorial form was heated to -120 C, the rate of the chair interconversion increased,and a mixture of conformations again resulted. Similar experiments have been carried out withother MONOSUBSTITUTED DG difference between the axial and equatorial conformations of methylcyclohexane( kJ mol_1, kcal mol_1; see Fig.)