Question

Which of the following statements most accurately describes the stereochemistry between the various cyclohexanes? a)Cis-1,2-dichlorocyclohexane and trans-1,2-dichlorocyclohexane rotate plane-polarized light in opposite directions, and together in equal proportions form a racemic mixture b)The diaxial and diequatorial forms of trans-1,3-dichlorohexane can be separated by their differing physical properties c)The conformational isomers of trans-1,2-dichlorocyclohexane are enantiomers, which are not interconvertible, but resolvable d)Only cis-1,4-dichlorocyclohexane is achiral due to a plane of symmetry, and cis-1,4-dichlorocyclohexane is diastereomeric to trans-1,4-dichlorocyclohexane

Answer 1

Cis-trans isomerism in cyclohexanes refers to the spatial arrangement of substituents around the ring structure, which can lead to differing physical and chemical properties between the cis and trans isomers. Cis-1,4-dichlorocyclohexane is achiral and is considered a diastereomer to trans-1,4-dichlorocyclohexane.

Step-by-step explanation:

Stereochemistry of Cyclohexanes

The stereochemistry of cyclohexanes involves cis-trans isomerism, where the spatial arrangement of substituents differs around the ring structure. In the context of cyclohexanes with two substituents, the isomers are classed as cis if the substituents are on the same side and trans if on opposite sides of the cyclic molecule. These differences can lead to variations in physical and chemical properties.

Cis-1,2-dichlorocyclohexane and trans-1,2-dichlorocyclohexane are stereoisomers where the chlorines are on the same or opposite sides of the ring, respectively. In trans-1,3-dichlorohexane, the axial and equatorial positions of the substituents affect the compound's physical properties, but they are not considered diastereomers or enantiomers because they are simply conformers of the same molecule and can interconvert. Unlike enantiomers, which are non-superimposable mirror images of each other and rotate plane-polarized light differently, conformers are just different spatial orientations of the same molecule.

The statement about cis-1,4-dichlorocyclohexane being achiral due to a plane of symmetry is correct, and it being diastereomeric to trans-1,4-dichlorocyclohexane is also true because these two compounds are not mirror images of one another and they have the same molecular formula but different configurations in space.