Problem 6.40 As we learned in Chapter 4, mono... [FREE SOLUTION]

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Chapter 6: Problem 6.40 (page 242)

As we learned in Chapter 4, monosubstituted cyclohexanes exist as an equilibrium mixture of two conformations having either an axial or equatorial substituent. When $R = {CH}_{2} {CH}_{3}$ , $K_{eq}$ for this process is 23. When $R = C {({CH}_{3})}_{3}$ , $K_{eq}$ for this process is 4000.
a. When , which conformation is present in higher concentration?
b. Which R shows the higher percentage of equatorial conformation at equilibrium?
c. Which R shows the higher percentage of axial conformation at equilibrium?
d. For which R is more negative?
e. How is the size of R related to the amount of axial and equatorial conformations at equilibrium?

Short Answer

Expert verified

Answer

The conformer with $R = {CH}_{2} {CH}_{3}$ group on the equatorial position is present in higher concentration.
$R = C ({CH}_{3})$ shows a higher concentration for equatorial conformation at equilibrium.
$R = {CH}_{3}$ group has the higher percentage of axial conformation at the equilibrium.
$R = C {({CH}_{3})}_{3}$ group has the most negative value of $鈭� G 掳$ .
The larger the R group, the more favored is the equatorial conformation.

Step by step solution

Step-by-Step SolutionStep 1: Equilibrium Constant Keq

The value of $K_{eq}$ favoring the products should be greater than one and vice-versa.

Axial and Equatorial alignment of groups

Groups lying on the axial positions lie above and below the plane of the molecule. Groups lying in the equatorial position, remain in the plane of the molecule.

Explanation

a. The value of $K_{eq}$ in the given direction of reaction is 23 which is greater than 1. This implies that the equilibrium favors the products over reactants. Hence, the conformer with $R = {CH}_{2} {CH}_{3}$ group on the equatorial position is present in higher concentration.

b. The R group with a maximum value of $K_{eq}$ is $R = C {({CH}_{3})}_{3}$ . higher the value of $K_{eq}$ , higher is the concentration of products. Hence, $R = C {({CH}_{3})}_{3}$ shows a maximum concentration for equatorial conformation at equilibrium.

c. The lowest value of $K_{eq}$ is for $R = {CH}_{3}$ group i.e. 18. So, this group has the maximum concentration of axial conformation at the equilibrium.

d. The more the value of $K_{eq}$ greater than 1, the more negative is the value of $鈭� G 掳$ . Hence, the group with the maximum value of $K_{eq}$ has the most negative value of $鈭� G 掳$ .

e. The larger the R group, the more favored is the equatorial conformation.