Axial strain energies

The two conformations of methylcyclohexane are rapidly interconverting— they are in equilibrium. The conformer with the methyl equatorial is more stable than the conformer with the methyl axial, so the equatorial conformer is present in a larger amount in the equilibrium mixture. The axial strain energy is actually the free energy difference between the conformations and can be used to calculate the equilibrium constant for the process by using the equation A G° = —RT In K. Using the value of —1.7 kcal/mol (—7.1 kJ/mol) for AG°, the equilibrium constant is calculated to be 18 at room temperature. Therefore, at any instant, 95% of methylcyclohexane molecules have the methyl group equatorial, and only 5% have the methyl axial. 

In contrast, neomenthyl chloride, with the opposite configuration at the carbon bearing the chlorine, has both the isopropyl and the methyl groups equatorial in the reactive conformation, with the chlorine axial (see Figure 9.5). Because both of these groups have larger axial strain energies than chlorine (see Table 6.2), the reactive conformation is the more stable one. There is less steric strain in the transition state for elimination,... 

Axial strain energy (Section 6.7) The amount of destabilization caused by a group in the axial position in the chair conformation of cyclohexane. 

Substituents larger than H prefer to be equatorial on a cyclohexane ring. Larger substituents have a smaller amount of the conformation with the substituent axial present at equilibrium than smaller substituents. Therefore, compare the axial strain energies (see Table 6.2) of the substituents. The one with the smaller axial destabilization energy will have a larger amount of the conformation with the substituent in the axial position present at equilibrium. 

Both enantiomers of the c/s-diastereomer are of equal stability as are both enantiomers of the frans-diastereomer. The frans-diastereomer is more stable than the c/s-diastereomer because it has the conformation with both substituents equatorial. The methyl group is axial in the more stable conformer of the less stable diastereomer (cis) because the axial strain energy of the phenyl group is larger than that of the methyl group. 

Draw the possible conformations, and calculate the strain energy in each.. Remember that equatorial substituents cause less strain than axial substituents. 

Diaxial interaction (Section 4.8) The strain energy caused by a steric interaction between axial groups three carbon atoms apart in chair cyclohexane. 

For /rani,-l,3-dimethylcyclohexane, one methyl is axial and one methyl is equatorial in either conformation. Both conformations have 1.7 kcal/mol (7.1 kJ/mol) of strain energy, and the equilibrium constant for their interconversion is 1.0. The /rans-isomer is less stable than the civ-isomer by 1.7 kcal/mol (7.1 kJ/mol) because of this axial methyl group. 

The methyl on C-1 is closer to the top of the page, and the methyl on C-2 is closer to the bottom of the page. Both methyl groups are axial in this conformation. The strain energy due to an axial methyl is 1.7 kcal/mol (7.1 kj/mol), so the total strain energy of this conformer is twice this value, or 3.4 kcal/mol (14.2 kj/mol). 

As mentioned before, the AHg, value for the polymerization of 6,8-dioxabicyclo [3.2.1] octane is less negative than that for l,3-dioxolanes. Bicyclo [3.2.1] octane, in which a five-membered ring is fused to a cyclohexane ring at two axial positions, has 51 kJ/mol strain energy. However, from the fact that 7-oxabicyclo [2.2.1] heptane has less strain energy than bicyclo [2.2.1] heptane can be deduced that the strain energy of 6,8-dioxabicydo [3.2.1] octane may also be less than that of bicyclo [3.2.1] octane. 

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