See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Step 1: Identify the structure of compound (A). Compound (A) is 1,1-dimethylcyclopentane-2,5-dicarboxylic acid. The cyclopentane ring has a quaternary carbon at C1 (bearing two methyl groups, so C1 is NOT a stereocenter). C2 and C5 each bear one H and one COOH group, making them stereocenters. The molecule has a local symmetry axis through C1 (the gem-dimethyl carbon) and the midpoint of C3-C4, making C2 and C5 equivalent positions. Step 2: Count stereocenters and possible stereoisomers. There are two stereocenters: C2 and C5. With 2 stereocenters, the maximum number of stereoisomers = 2^2 = 4. However, because C2 and C5 are related by the internal symmetry of the molecule (they are in symmetric positions relative to the C1 gem-dimethyl carbon and the C3-C4 bridge), a meso form is possible. Step 3: Enumerate the stereoisomers. - (2R,5R): one enantiomer - (2S,5S): the other enantiomer (these two form an enantiomeric pair) - (2R,5S): this is the meso compound (the molecule has an internal plane of symmetry making it achiral) - (2S,5R): identical to (2R,5S) by the internal symmetry, so it is the same meso compound Thus total distinct stereoisomers = 3: one pair of enantiomers [(2R,5R) and (2S,5S)] + one meso form. Step 4: Evaluate each statement in part A. (a) Total number of stereoisomers = 3. TRUE. (b) Total number of meso isomers = 1 (the cis form, where both COOH groups are on the same face, is the meso compound). TRUE. (c) Total number of pairs of enantiomers = 1 (the (2R,5R)/(2S,5S) pair). TRUE. (d) All of these — since (a), (b), and (c) are all correct, (d) is correct. Answer to A: (d). Step 5: Planes of symmetry in the cis-form for part B. The cis-form of compound (A) is the meso compound where both COOH groups are on the same side of the ring plane. In the cis-meso isomer: - There is a plane of symmetry that bisects the molecule through C1 (the gem-dimethyl carbon) and the midpoint of C3-C4 bond, passing through the ring plane or bisecting the C2-C5 axis. This mirror plane interconverts C2 and C5, confirming it is a meso compound. - The ring itself and the arrangement of substituents allow exactly 1 plane of symmetry (the plane that passes through C1, bisects the C3-C4 bond, and reflects C2 onto C5). Thus the number of planes of symmetry in the cis-form = 1. Answer to B: (b). Why other options fail for B: - (a) 0 is wrong because the meso form does have a plane of symmetry (that is precisely what makes it meso). - (c) 2 and (d) 3 are wrong because there is only one such symmetry plane; the ring is not flat in a way that provides additional planes, and the gem-dimethyl group does not add extra planes beyond the one bisecting C2 and C5. Therefore, the correct answer is (A)-(d); (B)-(b).