See image — Hydrocarbons Chemistry Question

💡 Solution & Explanation

Step 1 - Identify the compound: The structure shown is 1,1-dimethylcyclohexane fused with another cyclohexane - actually, looking more carefully, it is a bicyclo compound (bicyclo[4.4.0]decane / decalin framework is not shown; rather it appears to be two cyclohexane rings sharing a bond, i.e., bicyclohexyl or a spiro compound). Re-examining: two cyclohexane rings are drawn side by side sharing one carbon (spiro junction) or one bond. The two CH3 groups are both on the same carbon (the junction carbon) shown with two bold wedge bonds. This makes it a gem-dimethyl substituted carbon (two methyl groups on the same carbon, i.e., 1,1-dimethyl substitution at the junction). Step 2 - Determine the relationship: Both methyl groups are attached to the SAME carbon. When two substituents are on the same carbon of a ring, their spatial relationship in the chair conformation is described by the dihedral angle between them as seen in a Newman projection along the C-C bonds. Since both methyls are on the same sp3 carbon, we consider the Newman projection looking down one of the ring C-C bonds from that carbon. The two methyl groups on the same carbon are separated by approximately 60° dihedral angle relative to the ring substituents, placing them in a gauche relationship with respect to the adjacent ring carbons and each other in the context of the chair conformation. Step 3 - Why other options fail: - (a) Trans: Trans refers to substituents on different carbons being on opposite faces of the ring. Not applicable here since both methyls are on the same carbon. - (b) Anti: Anti describes a 180° dihedral relationship, which would require substituents on adjacent carbons. Two groups on the same carbon cannot be anti to each other. - (d) Eclipsed: Eclipsed describes a 0° dihedral angle. In a tetrahedral carbon with two methyls, the bond angle is ~109.5°, not 0°. Step 4 - Confirm gauche: With both methyl groups geminal (on the same carbon) in the chair conformation, when viewed via Newman projection along a C-C bond of the ring, the two methyl groups are gauche (60° dihedral) to the neighboring ring carbons. The relationship between the two gem-methyl groups themselves and the ring in the chair places them in a gauche arrangement. Therefore, the correct answer is C.