For each pair of conformations shown, choose which is most stable. [If both conformations have the same number of gauche interactions, choose the one where the interactions are between smaller groups.]
(f)

Verified step by step guidance

1. Step 1: Analyze the Newman projections for conformations A and B. Both conformations represent staggered arrangements of substituents around a central carbon-carbon bond.
2. Step 2: Identify gauche interactions in each conformation. Gauche interactions occur when two substituents are 60° apart in a staggered conformation. In conformation A, the methyl group (CH₃) on the front carbon is gauche to the ethyl group on the back carbon. In conformation B, the methyl group on the front carbon is gauche to the methyl group on the back carbon.
3. Step 3: Compare the steric hindrance caused by the gauche interactions. In conformation A, the interaction is between a methyl group and an ethyl group, which is less sterically hindered compared to the interaction between two methyl groups in conformation B.
4. Step 4: Consider the rule provided in the problem: If both conformations have the same number of gauche interactions, the conformation with smaller groups involved in the interactions is more stable. Since conformation A involves a methyl-ethyl interaction and conformation B involves a methyl-methyl interaction, conformation A is more stable.
5. Step 5: Conclude that conformation A is the most stable due to fewer steric hindrance in its gauche interactions compared to conformation B.

Key Concepts

Conformational Analysis

Conformational analysis involves studying the different spatial arrangements of atoms in a molecule that can be interconverted by rotation around single bonds. In alkanes, these conformations can significantly affect the molecule's stability due to steric interactions and torsional strain. Understanding how to visualize and compare these conformations is crucial for determining which is more stable.

Gauche Interactions

Gauche interactions occur when two substituents on adjacent carbon atoms in a chain are positioned 60 degrees apart in a staggered conformation. These interactions can lead to increased steric strain, making the conformation less stable. When comparing conformations, the number and type of gauche interactions are key factors in assessing stability, with fewer gauche interactions generally indicating a more stable conformation.

Steric Hindrance

Steric hindrance refers to the repulsion between atoms that occurs when they are brought close together, often due to their size. In conformational analysis, larger groups can create more steric hindrance, leading to increased energy and decreased stability of a conformation. When evaluating the stability of conformations, it is important to consider the size of substituents and their spatial arrangement to minimize steric interactions.