Which of the following has an achiral stereoisomer?
i. 1,2-dimethylcyclopentane
j, 1,2-dimethylcyclobutane

Verified step by step guidance

1. Step 1: Understand the concept of chirality. A molecule is chiral if it cannot be superimposed on its mirror image. Achiral molecules, on the other hand, have a plane of symmetry or a center of symmetry, making them superimposable on their mirror image.
2. Step 2: Analyze the structure of 1,2-dimethylcyclopentane. Draw the molecule and consider the positions of the two methyl groups on the cyclopentane ring. Determine if there is a stereoisomer that has a plane of symmetry, which would make it achiral.
3. Step 3: Analyze the structure of 1,2-dimethylcyclobutane. Draw the molecule and consider the positions of the two methyl groups on the cyclobutane ring. Check if there is a stereoisomer with a plane of symmetry, indicating achirality.
4. Step 4: Compare the symmetry of the stereoisomers for both compounds. For 1,2-dimethylcyclopentane, assess whether the ring and substituents can adopt a conformation that results in a plane of symmetry. For 1,2-dimethylcyclobutane, evaluate the same criteria.
5. Step 5: Conclude which compound has an achiral stereoisomer based on the analysis of symmetry in their stereoisomers. Remember that achirality arises from the presence of symmetry in the molecule.

Key Concepts

Stereoisomerism

Stereoisomerism refers to the phenomenon where compounds have the same molecular formula and connectivity of atoms but differ in the spatial arrangement of those atoms. This can lead to different properties and reactivities. Stereoisomers can be further classified into enantiomers and diastereomers, depending on their symmetry and chirality.

Chirality

Chirality is a property of a molecule that makes it non-superimposable on its mirror image, much like left and right hands. A chiral molecule typically has at least one carbon atom bonded to four different substituents, creating two distinct enantiomers. In contrast, achiral molecules possess a plane of symmetry and can be superimposed on their mirror images.

Cycloalkanes

Cycloalkanes are saturated hydrocarbons that contain carbon atoms arranged in a ring structure. The presence of substituents on the ring can lead to different stereoisomers. In the case of 1,2-dimethylcyclopentane and 1,2-dimethylcyclobutane, the arrangement of the methyl groups can influence whether the compound is chiral or achiral, depending on the symmetry of the molecule.