See image — GOC and Organic Chemistry Basics Chemistry Question

💡 Solution & Explanation

Concept: The barrier to rotation about a C-C single bond depends on the steric strain (from eclipsing interactions) and any electronic/conjugative effects. Higher steric bulk around the bond and conjugation increase the rotational barrier. Step 1 - Analyze option (a): Cyclopentane ring. The indicated bond is part of the ring, meaning rotation about it is constrained by the ring structure itself. The bond cannot rotate freely; it is locked in the ring. The ring introduces angle strain and torsional strain, and true free rotation is not possible. This is not a freely rotating bond in the conventional sense. Step 2 - Analyze option (b): 1,3-butadiene, central C-C single bond between two sp2 carbons. This bond has partial double-bond character due to conjugation (p-orbital overlap between the two double bonds). The barrier to rotation is elevated (~4-5 kcal/mol) compared to a simple C-C single bond (~3 kcal/mol for ethane) because rotating out of the planar conformation disrupts conjugation. Step 3 - Analyze option (c): Butane, central C-C single bond between two sp3 CH2 groups (each bearing two hydrogens and one methyl). This is a simple C-C single bond with modest steric interactions. The barrier is approximately 3-4 kcal/mol (the gauche-anti interconversion barrier), which is relatively low and typical for a simple alkane C-C bond. Step 4 - Analyze option (d): 2,3-dimethylbutane, central C-C single bond between two CH(CH3)2 (isopropyl) groups. Each carbon bearing the bond has two methyl substituents, creating significant steric bulk. The eclipsed conformations involve severe steric clashing between methyl groups, raising the rotational barrier substantially higher than simple butane. Step 5 - Compare: (a) is ring-constrained, not freely rotating. (b) has conjugation raising its barrier. (d) has high steric bulk raising its barrier significantly. (c) butane has only modest substituents (CH3 and H on each side of the central bond) and represents the lowest steric demand among the freely rotating single bonds, giving it the lowest barrier to rotation. Therefore, the correct answer is C.