Question

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. Using this information, determine the ratio of the concentrations of the equatorial and axial forms at thermal equilibrium using the Boltzmann distribution.

Answer 1

Answer:

Explanation:

According to Boltzmann, $N_o$ is number of mlecules in ground state, then the number of molecules N in excited state at a given temperature T is given by:

$N=N_0e^{\frac{-\delta E}{RT}}$

where $\delta E$ is activation energy

$\frac{N}{N_0}=e^{\frac{-\delta E}{RT}}----(1)$

Given, $\delta E=10.5kcalmol^1$

$R=1.987\times 10^{-3}kcalmol^1k^{-1}$

T= room temperature, 25°c=298k

Therefore,

$\frac{N}{N_0}=e^{\frac{-10.5}{1.987\times 10^{-3}}\times 298}\\\\\frac{N}{N_0}=17.7$

Hence, the ratio between concentration of equatorial and axial forms is 17.7:1