1. The thermal interconversion of the axial and equatorial substitutents of the chair conformation of cyclohexane is extremely slow because the two forms are separated by a relatively high activation energy barrier, 10.5 kcal/mol (3672 cm−1). With CN substituents, the equatorial form is only 0.24 kcal/mol (84 cm−1) lower in energy than the axial form. Show how you would determine the ratio between the concentrations of the equatorial and axial forms using the Boltzmann distribution.

The ratio is  

Explanation:

From the question we are told that

 The activation energy separating the equatorial and the axial form is

 Generally according to the Boltzmann distribution , the relationship between  concentration(in terms of number of molecule) of the equatorial form and  the concentration of the axial form is mathematically represented as

Here is the number of molecule in equatorial form and  N is the number of the molecules in the axial form.

   R is the gas constant with value  

     T is the temperature of the room with value  

So

=>

So the ratio of the concentration of equatorial form to the axial form is