Question

a. Calculate the percentage of isopropylcyclohexane molecules that have the isopropyl substituent in an equatorial position at equilibrium. (Its ∆G° value at 25 °C is -2.1 kcal/mol.)

b. Why is the percentage of molecules with the substituent in an equatorial position greater for isopropylcyclohexane than for fluorocyclohexane?

Short answer

1. 97%
2. Because isopropyl substituent is larger than fluoro substituent.

Step-by-step solution

 a) Given quantities -

∆G°=-2.1 kcal/mol

T= 25 °C

 Calculation of the percentage of isopropylcyclohexane molecules that have the isopropyl substituent in an equatorial position at equilibrium -

G^o = ^_RT ln K_eq

-2.1 = -1.986× 10^-3× 298× ln K_eq

ln K_eq = 3.56

K_eq= 35

K_eq= $\frac{\left[isopropylcyclohexane\right]equatorial}{\left[isopropylcyclohexane\right]axial}=\frac{35}{1}$

% of equatorial isopropylcyclohexane

$$\begin{gathered} =\frac{\left[isopropylcyclohexane\right]equatorial}{\left[isopropylcyclohexane\right]equatorial+\left[isopropylcyclohexane\right]axial}\times 100 \\ =\frac{35}{35+1}\times 100 \\ =\frac{35}{36}\times 100 \\ =97\% \end{gathered}$$

b) Because the isopropyl substituent is larger than the fluoro substituent, isopropylcyclohexane has a higher percentage of the conformer with the substituent in the equatorial position.

Because of the 1,3-diaxial interactions, the conformer with the substituent in the axial position becomes less stable as the substituent grows larger.