See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

A center of symmetry (inversion center) is a point in a molecule such that for every atom at position (x, y, z) there is an identical atom at (-x, -y, -z). A molecule with a center of symmetry is achiral (it is a meso compound or has overall inversion symmetry). Concept: Center of inversion (i) means that inverting all coordinates through a central point maps the molecule onto itself. Analysis of each option: Option (a): The paracyclophane-like molecule has two benzene rings with Br substituents pointing in opposite directions (one up, one down) and CH2 bridges connecting them symmetrically. While it has rotational symmetry elements, the presence of Br on only one position of each ring and the geometry of the bridges must be checked. This structure does not possess a true center of inversion in its drawn form because the two rings are not related by inversion through a central point in the way required. Option (b): The diketopiperazine structure has two stereocenters. The left center has H on wedge and CH3 on dash; the right center has CH3 on wedge and H on dash. This makes the two centers have opposite configurations (one R, one S if substituents allow), which is characteristic of a meso compound. However, for a center of inversion specifically, the molecule must map onto itself through a point. In diketopiperazine (cyclic dipeptide), the inversion center would require both ring geometry and substituent geometry to be consistent. The drawn structure shows opposite wedge/dash arrangements at the two centers, suggesting a meso-like relationship, but the ring amide bonds (C=O-NH) must also be considered. This structure may have a plane of symmetry rather than a strict center of inversion. Option (c): The structure shown is meso-2,3-dichlorobutane. In meso-2,3-dichlorobutane, C2 has configuration R and C3 has configuration S (or vice versa). In the anti conformation, meso-2,3-dichlorobutane possesses a center of inversion: inverting through the midpoint of the C2-C3 bond maps C2 onto C3 and vice versa, with Cl mapping to Cl, CH3 mapping to CH3, and H mapping to H. The drawn structure with Cl on top-left carbon and Cl on bottom-right carbon, with H and CH3 in opposite positions, represents the anti conformation of meso-2,3-dichlorobutane, which has a center of inversion (Ci symmetry). This is the classic textbook example of a molecule with a center of symmetry. Why (d) is not correct: Not all three structures unambiguously possess a center of inversion. Option (c) is the definitive example of a center of symmetry (inversion center), specifically meso-2,3-dichlorobutane in anti conformation. Therefore, the correct answer is C.