Question

Draw the possible chair forms of cis- and trans-1-isopropyl-3-methylcyclohexane. Are the two forms identical, enantiomeric, or diastereomeric? In each case, indicate which chair form will be more stable and explain why. Is either of these molecules chiral?

Short answer

Cis and trans-1-isopropyl-3-methylcyclohexane are diastereomers. The more stable forms have isopropyl equatorial. Neither molecule is chiral.

Step-by-step solution

Draw the cyclohexane chair forms

Draw the two possible chair conformations for cyclohexane. Remember that each carbon in the chair form has two positions for substituents: axial (perpendicular to the ring) and equatorial (around the plane of the ring).

Place substituents for cis-1-isopropyl-3-methylcyclohexane

For the cis-isomer, place the isopropyl and methyl groups on carbons 1 and 3 such that both are either axial or both are equatorial. Draw the two chair conformations to show both substituents in these positions.

Determine the more stable chair form for cis-isomer

Identify which chair conformation places the bulkier isopropyl group in the equatorial position as this reduces steric hindrance. The chair form with the isopropyl group equatorial and methyl group axial (or both equatorial) will be more stable.

Place substituents for trans-1-isopropyl-3-methylcyclohexane

For the trans-isomer, place the isopropyl and methyl groups on carbons 1 and 3 such that one is axial and the other is equatorial. Draw the two chair conformations to show these positions.

Determine the more stable chair form for trans-isomer

Again, identify which conformation places the bulkier isopropyl group in the equatorial position. The more stable chair form will have the isopropyl group equatorial and the methyl group axial.

Analyze the forms (cis and trans)

Compare the chair conformations of cis- and trans-1-isopropyl-3-methylcyclohexane. Determine if they are identical, enantiomeric, or diastereomeric. Cis and trans isomers are typically diastereomers, as they are not mirror images but have different spatial positions.

Determine chirality

Examine both the cis and trans forms for a plane of symmetry. If a molecule has a plane of symmetry, it is achiral. Otherwise, it is chiral. Check if either or both of these isomers lack a plane of symmetry.

Key concepts

cis and trans isomers

In cyclohexane derivatives, 'cis' and 'trans' isomers describe the relative positions of two substituents attached to different carbons of the ring. For the cis-1-isopropyl-3-methylcyclohexane, both the isopropyl and methyl groups can be either axial or equatorial, but they must be on the same side of the ring plane. In contrast, for trans-1-isopropyl-3-methylcyclohexane, one group will be axial, and the other equatorial, positioned on opposite sides of the ring. These spatial positions greatly influence the molecule's structural properties and stability. Therefore, cis and trans isomers are not identical or mirror images; they are diastereomers as they have different spatial arrangements and physical properties.

steric hindrance

Steric hindrance occurs when atoms or groups of atoms within a molecule are so close to each other that they cause a repulsive force, impacting the molecule's stability. In chair conformations of cyclohexane, positions around the ring can cause different levels of steric hindrance. The axial position is more crowded since it lies perpendicular to the ring, directly aligning substituents above or below the ring. Larger groups like isopropyl in the axial position suffer more steric hindrance, making this conformation less stable. Therefore, placing bulkier groups like isopropyl in the less crowded equatorial position reduces steric hindrance and increases stability.

chirality

Chirality in molecules refers to their ability to exist as non-superimposable mirror images. A molecule is chiral if it lacks a plane of symmetry, meaning there is no way to divide the molecule into mirror-image halves. In cyclohexane derivatives like cis- and trans-1-isopropyl-3-methylcyclohexane, the presence of substituents can introduce or remove chiral centers. For instance, the cis isomer usually ends up achiral due to its symmetric arrangement, while the trans isomer’s asymmetry can introduce chirality, provided the molecule lacks a plane of symmetry.

axial and equatorial positions

In cyclohexane chair conformations, each carbon atom has two types of hydrogen positions: axial and equatorial. Axial positions are aligned perpendicular to the ring, alternating up and down around the ring. Equatorial positions are approximately horizontal around the ring plane, more staggered and spread out. For substituents larger than hydrogen, equatorial positions are energetically favored due to reduced steric hindrance compared to axial positions. Thus, in chair conformations, larger groups like isopropyl should be placed in equatorial positions whenever possible, to minimize steric interactions and achieve greater stability.

stability of chair conformations

The stability of chair conformations in cyclohexane predominantly depends on the steric interactions between substituents. Substituents in the equatorial position face less steric hindrance, contributing to overall molecular stability. For cis-1-isopropyl-3-methylcyclohexane, the more stable form will have both substituents in equatorial positions or the larger isopropyl group in the equatorial position, reducing steric clashes. For trans-1-isopropyl-3-methylcyclohexane, the stable form will have the bulkier isopropyl group equatorial and the smaller methyl group axial. Optimizing the placement of groups in chair conformations is a key strategy for achieving the most stable structure.