Q50P - Organic Chemistry (Mcmurry)

Question

One of the two chair structures of cis-1-chloro-3-methylcyclohexane is more stable than the other by 15.5 kJ/mol (3.7 kcal/mol). Which is it? What is the energy cost of a 1,3-diaxial interaction between chlorine and a methyl group?

Step-by-Step Solution

Answer

Therefore, CH₃-Cl diaxial interactions cost 10.7 kJ/mol worth of strain energy. 

Step 1: Diaxial interaction

Chair cyclohexanes are conformationally mobile and can undergo a ringflip, which interconverts axial and equatorial positions. Substituents on the ring are more stable in the equatorial position because axial substituents cause 1,3-diaxial interactions.

Step 2: Energy calculation

The two chair confirmations of cis-1-chloro-3-methylcyclohexane are shown below:

There are three 1,,3 diaxial interactions, a H-Cl diaxial interaction (1.0 kJ/mol), a CH₃ - H diaxial interaction (3.8 kJ/mol), and a CH₃ - Cl diaxial interaction. In the given structure there is no diaxial interactions as both substituents are in equatorial positions. Since the energy difference between the two conformations is equal to 15.5 kJ/mol the total strain energy associated with the CH₃ - Cl  diaxial interaction can be calculated as:

Strain from 1,3-diaxial interaction between Me-Cl:

                                                = 15.5 kJ/mol – (CH₃ - H kJ/mol) –(Cl-H kJ/mol)

                                                = 15.5 kJ/mol – (3.8 kJ/mol) – (1.0 kJ/mol)

                                               = 10.7 kJ/mol

Therefore, CH₃ - Cl  diaxial interactions cost 10.7 kJ/mol worth of strain energy.