Methylcyclohexanes, conformational equilibria

By the study of 12 isotopomers of protoadamantane, the stereochemical dependence of isotope effects was also observed. A Karplus-type relationship similar to that for spin-spin coupling constants was proposed Recently, the first quantitative stereochemical dependence between isotope effects and dihedral angle was reported for a series of deuteriated norbornanes, as shown in Figure Observations of the influence of substitution with deuterium on conformational equilibria led to a new method in physical organic chemistry called isotopic perturbation of equilibrium. Details can be found in a recent review The effect was first observed for the chair-tO"Chair interconversion of deuteriated 1,3-dimethylcyclohexane 43 and later in 4-ethyl-l-methylcyclohexane " as well as in 1,1,4,4-tetramethylcyclohexane. In contrast, the isotope effect on conformational equilibrium in related systems turned out to be too small to be observable... 

Figure 6.15 NBO analysis of hyperconjugative interactions of the main hyperconjugative interactions that influence the conformational equilibrium of methylcyclohexane. ...

At 202 K, the conformational equilibrium of ds-l-benzyl-4-methylcyclohexane favors the chair conformation having the benzyl group axial by 0.08 kcal/mol. However, at room temperature or higher, the equilibrium favors the chair conformation with the benzyl group equatorial by 0.04 kcal/mol. Explain this result. 

The more stable diastereomer in each case is the one having both methyl groups equatorial. The free-energy difference favoring the diequatorial isomer is about the same for each equilibrium (about 1.9 kcal/mol), and is close to that for the conformational equilibrium between equatorial and axial methylcyclohexane (1.8 kcal/mol). This near agreement is reasonable, since the equilibria are, in all cases, established between an isomer having no axial substituents and an isomer with one axial methyl substituent. 

Conformational equilibrium between the axial (left) and equatorial (right) Isomers of methylcyclohexane. The steric Interactions between the axial methyl and the 1,3-dlaxlal hydrogens are evident In the left ball-and-stick structure. 

When cyclohexane is substituted by an ethynyl group, —C=CH, the energy difference between axial and equatorial conformations is only 1.7 kj (0.41 kcal)/mol. Compare the conformational equilibrium for methylcyclohexane with that for ethynylcyclohexane and... 

When two conformations of a molecule are m equilibrium with each other the one with the lower free energy predominates Why is equatorial methylcyclohexane more sta ble than axial methylcyclohexane ... 

Substitution on a cyclohexane ring does not greatly affect the rate of conformational inversion but does change the equilibrium distribution between alternative chair forms. All substituents that are axial in one chair conformation become equatorial on ring inversion, and vice versa. For methylcyclohexane, AG for the equilibrium... 

In the equilibrium mixture, the conformation of methylcyclohexane with an equatorial methyl group is the predominant one (-95%). 

The low temperature H-NMR spectra of 2-methyl-3,6-dihydro-2H-1,2-oxazine (239) gives a AG° favoring the /V-Meeq of 0.9 kcal mol", which is significantly less than that for the tetrahydro-l,2-oxazine (>1.9 kcal mol"1).246 This is similar to the decrease in conformational free energy of a methyl substituent on going from methylcyclohexane (1.7 kcal mol"1) to 4-methylcyclohexene (1.0 kcal mol 1),247 and the equilibrium 240 241 may represent a balance between lone-pair-Ti-bond repulsion in 240 and lone-pair-lone-pair repulsions in 241.246... 

Other substituted cyclohexanes are similar to methylcyclohexane. Two chair conformations exist in rapid equilibrium, and the one in which the substituent is equatorial is more stable. The relative amounts of the two conformations depend on the effective size of the substituent. The size of a substituent, in the context of cyclohexane conformations, is related to the degree of branching at the atom connected to the ring. A single... 

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. 

Given that the equilibrium constant for the interconversion of the axial and equatorial conformations of methylcyclohexane is 18, show how to calculate the percentage of each that is present at equilibrium. 

A substituent on a cyclohexane ring (in the chair conformation) can occupy either an axial or an equatorial position. In many cases, the reactivity of the substituent depends on whether its position is axial or equatorial. The two possible chair conformations for methylcyclohexane are shown in Figure 3-23. These conformations are in equilibrium because they interconvert at room temperature. The boat (actually the twist boat) serves... 

The equilibrium constant does not depend on the actual size of the substituent, but rather its interaction with the neighbouring axial hydrogens. In the axial conformer of methylcyclohexane there is a direct interaction between the methyl group and the axial hydrogen atoms. 

Given the difference in strain energy between the axial and equatorial conformations of methylcyclohexane, we can calculate the ratio of the two conformations at equilibrium using the equation that relates the change in Gibbs free energy (AG°) for an equilibrium, the equilibrium constant (Al q), and the temperature (T) in kelvins. R, the universal gas constant, has the value 8.314 J (1.987 cal)-il -moD. ... 

The two forms of chair methylcyclohexane are in equilibrium. The equatorial conformer is more stable by 1.7 kcal moF (7.1 kJ moF ) and is favored by a ratio of 95 5 at 25°C (Section 2-1). The activation energy for chair-chair interconversion is similar to that in cyclohexane itself [about 11 kcal moF (46 kJ moF )], and equilibrium between the two conformers is established rapidly at room temperature. 

Calculate AG° for the equilibrium between the two chair conformers of (a) 1-ethyl-l-methylcyclohexane (b) cis-l-ethyl-4-methylcyclohexane (c) irons-l-ethyl-4-methylcyclohexane. 

Let s consider methylcyclohexane in a chair conformation with an equatorial methyl group. When the ring flips, the equatorial methyl group moves into an axial position (Figure 4.14). These two structures are different conformations, not structural isomers. A methyl group in an axial position is 8.1 kj mole less stable than a methyl group in an equatorial position. At equilibrium, about 95% of the mixture has an equatorial methyl group. 

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