Free Energy Considerations

Sterics play a major role in the assignment of configurations in cyclohexanes. One can use steric hindrances to determine the propensity of a substituent to reside in the axial or equatorial plane. It is known that axial bonds are more hindered than the corresponding equatorial bonds. This is because substituents in the axial position are relatively close to two other axial substituents. This makes it very crowded when you have bulky substituents in the axial position, these types of steric interactions are commonly known as 1,3 diaxial interactions.^[1] These types of interactions are not present with substituents at the equatorial position. There are generally considered three principle contributions to the conformational free energy: ^[2] 1.Bayer Strain, defined as the strain arising from deformation of bond angles. 2. Pitzer Strain, defined as the torsional strain arising from 1,2 interactions between groups attached to contiguous carbons, 3. Van der Waals interactions, which are similar to 1,3 diaxial interactions.

Enthalpic Components

When comparing relative stability, 6- and 7-atom interactions can be used to approximate differences in enthalpy between conformations. Each 6-atom interaction is worth 0.9 kcal/mol and each 7-atom interaction is worth 4 kcal/mol. ^[3]

Entropic Components

Entropy also plays a role in a substituent’s preference for the equatorial position. The entropic component is determined by the following formula:

\Delta S=Rln\sigma

Where σ is equal to the number of micro states available for each conformation.

Due to the larger number of possible conformations of ethyl cyclohexane, the A value is reduced from what would be predicted based purely on ethalpic terms. Due to these favorable entropic conditions, the steric relevance of an ethyl group is similar to that of a methyl substituent.

References

^ Hoffman, Robert V. (2004). Organic Chemistry (second ed.). New Jersey: John Wiley and Sons, Inc. p. 167. {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)
^ Anderson, J. Edgar (1974). Dynamic Chemistry. Springer-Verlag. p. 139. doi:10.1007/3-540-06471-0. {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)
^ Anslyn, Eric V.; Dougherty, Dennis A. (2006). Modern Physical Organic Chemistry. Sausalito, CA: University Science Books. pp. 104–105.

[Hoffmanbook-1] Hoffman, Robert V. (2004). Organic Chemistry (second ed.). New Jersey: John Wiley and Sons, Inc. p. 167. {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

[dyanchem-2] Anderson, J. Edgar (1974). Dynamic Chemistry. Springer-Verlag. p. 139. doi:10.1007/3-540-06471-0. {{cite book}}: Unknown parameter |trans_title= ignored (|trans-title= suggested) (help)

[AnslynDougherty-3] Anslyn, Eric V.; Dougherty, Dennis A. (2006). Modern Physical Organic Chemistry. Sausalito, CA: University Science Books. pp. 104–105.

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