Consider the cyclohexane framework in a chair conformation

Consider the cyclohexane framework in a chair conformation, where carbon 1 has two substituents, X and Y. a. Label each position as axial or equatorial. b. On the same figure, label all positions that are gauche to the Y group on carbon 1. A bin may hold more than one label. Answer Bank x gauche quatorial 6 N 3 gauche

The correct answer and explanation is:

To understand the chair conformation of cyclohexane and its substituents, let’s analyze step by step:

Chair Conformation of Cyclohexane:

Cyclohexane adopts a chair conformation to minimize steric strain and angle strain, providing maximum stability. In this conformation:

• Each carbon atom has one axial position (pointing straight up or down) and one equatorial position (pointing slightly outward and parallel to the ring plane).

Labeling Positions (Axial or Equatorial):

1. Assume carbon 1 has substituents X and Y. Place carbon 1 at the top-right position of the chair for simplicity.
2. The substituent directly up or down at carbon 1 is axial. The other substituent (pointing outward) is equatorial.
   • Example: If X is up (axial), Y is equatorial, or vice versa.
3. Alternate axial and equatorial positions around the ring:
   • Carbons 2, 4, and 6 have axial positions pointing downward.
   • Carbons 3 and 5 have axial positions pointing upward.
   • Equatorial positions alternate similarly, pointing outward around the ring.

Identifying Gauche Interactions:

The term “gauche” refers to a dihedral angle of approximately 60° between two groups in a Newman projection. For a substituent at carbon 1:

1. The substituent gauche to Y includes groups on carbons 2 and 6 in axial or equatorial positions.
2. For instance, if Y is equatorial:
   • The axial group at carbon 2 is gauche to Y.
   • The equatorial group at carbon 6 is also gauche to Y.

Final Labels:

• Axial: Positions alternate between up and down, starting at carbon 1.
• Equatorial: Positions alternate parallel to the plane.
• Gauche: Groups on carbons 2 and 6.

Explanation:

This analysis considers the spatial relationship between substituents to minimize steric interactions. Labeling helps predict reactivity, conformation, and stability of cyclohexane derivatives.