Question

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.

Answer 1

The ratio is
`0.67 : 1`

Step-by-step explanation:

From the question we are told that

The activation energy separating the equatorial and the axial form is
`\Delta E = 0.24\ kcal/mol`

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

`N = N_o e^{-(\Delta E )/(RT) }`

Here
`N_o` 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
`R = 1.987 *10^(-3) \ kcal\cdot mol^(-1) \cdot k^(-1)`

T is the temperature of the room with value
`T = 25^oC = 298 \ K`

So

`(N)/(N_o) = e^{-(0.24 )/(1.987*10^(-3) * 298) }`

=>
`(N)/(N_o) = 0.67`

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

`0.67 : 1`