Chapter 3, Problem 40P

Identify the more stable stereoisomer in each of the following pairs, and give the reason for your choice:

$\text{cis- or}\text{trans-1-Isopropyl-2-methylcyclohexane}$

$\text{cis- or}\text{trans-1-Isopropyl-3-methylcyclohexane}$

$\text{cis- ortrans--Isopropyl--methylcyclohexane}$

Interpretation Introduction

Interpretation:

The most stable stereoisomer in each of the given pairs is to be identified and the reason for it is to be explained.

Concept introduction:

The most stable conformation is the one that has the largest number of substituents in the equatorial orientation.

An axial substituent in the molecule is said to be crowded because of $\text{1,3-diaxial}$ repulsions between itself and the other two axial substituents located on the same side of the ring.

Crowding causes increase in the potential energy of an isomer, which decreases its stability.

The basic chair conformation of cyclohexane is shown below:

Stereoisomers are isomers having the same constitution but differ in the arrangement of atoms in space. Cis-trans isomers are stereoisomers.

Two substituents are cis to each other if they are on the same side of the ring.

Two substituents are trans to each other if they are on the opposite side of the ring.

Answer to Problem 40P

Solution:

a)

In the cis isomer, the methyl substituent is in the axial orientation while in the trans isomer, the methyl substituent is in the equatorial orientation. The axial methyl group experiences $\text{1,3-diaxial}$ interactions between itself and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in the trans isomer.

Thus, the trans isomer (B) is more stable than the cis isomer (A).

b)

In isomer (A), the methyl substituent is in the equatorial orientation while in isomer (B), the methyl substituent is in the axial orientation. The axial methyl group in isomer (B) experiences $\text{1,3-diaxial}$ interactions between itself and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in isomer (A).

Thus, isomer (A) is more stable than isomer (B).

c)

In isomer (A), the methyl substituent is in the axial orientation while in isomer (B), the methyl substituents is in the equatorial orientation. The axial methyl group in isomer (A) experiences $\text{1,3-diaxial}$ interactions between itself and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in isomer (B).

Thus, isomer (B) is more stable than isomer (A).

d)

In isomer (A), all three methyl substituents are in an equatorial orientation while in isomer (B), one methyl substituent $\text{C4}$ is in the axial orientation. The axial methyl group in isomer (B) experiences $\text{1,3-diaxial}$ interactions between itself and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in isomer (A).

Thus, isomer (A) is more stable than isomer (B).

e)

In isomer (A) all three methyl substituents are in an equatorial orientation while in isomer (B), one methyl substituent is in the axial orientation. The axial methyl group in isomer (B) experiences $\text{1,3-diaxial}$ interactions between itself and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in isomer (A).

Thus, isomer (A) is more stable than isomer (B).

f)

In isomer (A), the two methyl groups are on the same side as the cyclopentane ring and its hydrogen atoms. In isomer (B), the two methyl groups are on the opposite side of the cyclopentane ring and its hydrogen atoms. Isomer (A) is more crowded than isomer (B). Crowding increases the potential energy of the molecule and makes the molecule less stable.

Thus, isomer (B) is more stable than isomer (A).

Explanation of Solution

a) The given name of the compound shown below is $\text{1-isopropyl-2-methylcyclohexane}$:

For cis and trans isomers of this compound, two substituents, an isopropyl and methyl groups at $\text{C1}$ and C2 carbon atoms must be located on the same side and on the opposite side of the ring respectively. An isopropyl substituent is bulkier than a methyl substituent. The most stable conformation is the one that has the bulkier substituent in the equatorial orientation. Thus, in order to draw the most stable conformations for cis and trans $\text{1-isopropyl-2-methylcyclohexane}$, the isopropyl substituent must be in the equatorial orientation.

The most stable cis and trans isomers for this compound are shown below:

In isomer (A), the methyl substituent is in the axial orientation while in isomer (B), the methyl substituents is in the equatorial orientation. The axial methyl group experiences $\text{1,3-diaxial}$ interactions between itself and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in isomer (B).

Thus, isomer (B) is more stable than isomer (A).

b) The given name of the compound shown below is $\text{1-isopropyl-3-methylcyclohexane}$:

For cis and trans isomers of $\text{1-isopropyl-3-methylcyclohexane}$, two substituents, an isopropyl and methyl groups at $\text{C1}$ and C3 carbon atoms must be located on the same and on the opposite side of the ring respectively. An isopropyl substituent is bulkier than a methyl substituent. The most stable conformation is the one that has the bulkier substituent in equatorial orientation. Thus, in order to draw the most stable conformations for cis and trans $\text{1-isopropyl-3-methylcyclohexane}$, the isopropyl substituent must be in the equatorial orientation.

The most stable cis and trans isomers for this compound are shown below:

In isomer (A), the methyl substituent is in the equatorial orientation while in isomer (B), the methyl substituent is in the axial orientation. The axial methyl group in isomer (B) experiences $\text{1,3-diaxial}$ interactions between itself and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in isomer (A).

Thus, isomer (A) is more stable than isomer (B).

c) The given name of the compound shown below is $\text{1-isopropyl-4-methylcyclohexane}$:

For cis and trans isomers of this compound, two substituents, an isopropyl and methyl groups at $\text{C1}$ and $\text{C4}$ carbon atoms must be located on the same side and on the opposite side of the ring respectively. An isopropyl substituent is bulkier than a methyl substituent. The most stable conformation is the one that has the bulkier substituent in the equatorial orientation. Thus, in order to draw the most stable conformations for cis and trans $\text{1-isopropyl-4-methylcyclohexane}$, the isopropyl substituent must be in the equatorial orientation.

The most stable cis and trans isomers for this compound are shown below:

In isomer (A), the methyl substituent is in the axial orientation while in isomer (B), the methyl substituents is in the equatorial orientation. The axial methyl group in isomer (A) experiences $\text{1,3-diaxial}$ interactions between itself and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in isomer (B).

Thus, isomer (B) is more stable than isomer (A).

d) The given structures for two stereoisomers are as follows:

Both of the given isomers have three methyl groups attached to the cyclohexane. Their most stable conformations are shown below:

In isomer (A), all three methyl substituents are in an equatorial orientation while in isomer (B), two methyl substituenst at $\text{C3}$ and $\text{C4}$ are in the axial orientation. Axial methyl groups in isomer (B) experience $\text{1,3-diaxial}$ interactions between themselves and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in isomer (A).

Thus, isomer (A) is more stable than isomer (B).

e) The given structures for two stereoisomers are as follows:

Both of the given isomers have three methyl groups attached to the cyclohexane. Their most stable conformations are shown below:

In isomer (A), all three methyl substituents are in an equatorial orientation while in isomer (B), two methyl substituents are in axial orientation. The axial methyl group in isomer (B) experiences $\text{1,3-diaxial}$ interactions between itself and the other two axial hydrogen atoms located on the same side of the ring. These $\text{1,3-diaxial}$ interactions are absent in isomer (A).

Thus, isomer (A) is more stable than isomer (B).

f) The given structures for two stereoisomers are as follows:

Both of the conformations represent two different cis conformations of the same compound. In isomer (A), the two methyl groups and hydrogen atoms on the cyclopentane ring are on the same side. In isomer (B), the two methyl groups and hydrogen atoms on the cyclopentane rings are on the opposite side. Isomer (A) is more crowded than isomer (B). Crowding increases potential energy of the molecule and makes the molecule less stable.

Thus, isomer (B) is more stable than isomer (A).