Conformational Analysis

Monosubstituted Cyclohexanes

As noted earlier cyclohexanes can invert between two chair conformations.  When another substituent is present on the ring the two conformations can have different free energies.  For example methylcyclohexane can exist in the following two chair conformations.  The methyl group is either in an axial (left side) or equatorial (right side) position.  The conformer with the methyl group in the axial position is destabilized by about 7.3 kj/mol.  This destabilization is due to 1,3-diaxial strain.

In general chemistry you should recall the relationship K=e^(-ΔG/RT), which relates ΔG with the equilibrium constant K.  You can calculate K as follows;

ΔG = 0 kj/mol-(-7.3 kj/mol) = 7.3 kj/mol

K = e^{(7.3/298/8.314)} = 19

This means that at equilibrium there is a 19 to 1 ratio of the left to right conformers (i.e 95% of the time the methyl group prefers to be in an equatorial position).

As the substituent gets larger the equilibrium constant would get larger.  For example t-butylcyclohexane has an equilibrium constant, K=4800.

What is 1,3-diaxial strain?

1,3-diaxial strain is really just the result of two gauche interactions.  We need to look at the Newman projection and/or 3D models of methylcyclohexane to see the gauche interactions.

The following Newman projection has the axial methyl group and the methylene group shaded blue.  They are in a gauche conformation.   

Rotate the following 3D structure of methylcyclohexane so you can see each gauche interaction.

Di-substituted Cyclohexanes