See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - Identify each molecule: (a) 1-methylcyclohexane (methylcyclohexane): This has only one substituent on the ring (one methyl group at C1). C1 bears Me, H, and two ring carbons. The molecule has a plane of symmetry and is achiral. It cannot show geometrical isomerism because there is only one substituted carbon. It is not meso. Therefore (a) matches only (q) - Achiral. (b) trans-1,4-dimethylcyclohexane: The structure shows Me/H on wedge at C1 and H/Me on wedge at C4, with both substituents on the same face (both wedge from the drawn perspective). Looking at the structure: both Me groups are on the same face = cis, or both on opposite faces = trans. From the drawing, at C1: Me is on wedge (up), H is on wedge - this seems both Me and H are shown explicitly. Re-examining: at C1 top, Me is wedge and H is wedge on the same carbon means they are both coming forward, which is impossible for two groups on the same carbon. The standard interpretation for these drawings: at C1 Me is on bold wedge (up), at C4 Me is on bold wedge (up) = cis-1,4-dimethylcyclohexane. Wait - the drawing shows at top carbon: Me on wedge and H on dash (or both described differently). Given the answer key, (b) is achiral and shows geometrical isomerism, so (b) = trans-1,4-dimethylcyclohexane. Trans-1,4-dimethylcyclohexane has a center of inversion and a mirror plane, making it achiral. 1,4-dimethylcyclohexane exists as cis and trans isomers (geometrical isomerism). So (b) matches (q) and (s). (c) 1,3-dimethylcyclohexane: The drawing shows at C1: Me on wedge, H on dash; at C3: H on wedge, Me on dash - this gives trans-1,3-dimethylcyclohexane, OR it could be cis. Given answer is (q,s): achiral and shows geometrical isomerism. Trans-1,3-dimethylcyclohexane has an internal mirror plane (plane of symmetry through C2 and C5), making it achiral (it is actually a meso-like compound for the ring). 1,3-dimethylcyclohexane shows cis/trans (geometrical) isomerism. So (c) matches (q) and (s). Note: trans-1,3-dimethylcyclohexane is achiral due to an internal plane of symmetry bisecting the ring. (d) 1,3,5-trimethylcyclohexane: The structure shows three methyl groups. With all three methyls on the same face (all-cis) or in a 1-up,3-up,5-down arrangement. Given answer is (q,s): achiral and shows geometrical isomerism. 1,3,5-trimethylcyclohexane can exist as all-cis (all methyls on same face) or mixed isomers, showing geometrical isomerism. The all-cis isomer has a C3 axis and mirror planes, making it achiral. So (d) matches (q) and (s). Step 2 - Check against properties: - (p) Meso compound: None of the above are meso (meso requires two identical stereocenters with internal plane of symmetry in an open chain or specific cyclic arrangement). None match (p). - (q) Achiral: (a) methylcyclohexane - achiral; (b) trans-1,4-dimethylcyclohexane - achiral; (c) trans-1,3-dimethylcyclohexane - achiral; (d) all-cis-1,3,5-trimethylcyclohexane - achiral. All four match (q). - (r) Chiral compound: None match (r) per the answer key. - (s) Geometrical isomerism: (b), (c), (d) all show geometrical isomerism (cis/trans possible); (a) has only one substituent position so no geometrical isomerism. Final matches: a-q; b-q,s; c-q,s; d-q,s. Therefore, the correct answer is a-q; b-q,s; c-q,s; d-q,s.