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

Answer:

The ratio is  $0.67 : 1$

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

       $N = N_o e^{-\frac{\Delta E }{RT} }$

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

    $\frac{N}{N_o} = e^{-\frac{0.24 }{1.987*10^{-3} * 298} }$

=> $\frac{N}{N_o} = 0.67$

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

      $0.67 : 1$