See image — Hydrocarbons Chemistry Question

💡 Solution & Explanation

Concept: A racemic mixture is produced when a reaction generates a chiral center (or centers) without any stereocontrol, yielding equal amounts of R and S enantiomers. This happens when a prochiral face is attacked equally from both sides. Option (b): The starting material is cyclopentylidene substituted with two methyl groups on the exocyclic carbon — specifically (cyclopentylidene)dimethyl, i.e., 2-(propan-2-ylidene)cyclopentane or more precisely cyclopentane with an exocyclic C=C bearing two methyl groups: the alkene is (CH3)2C=cyclopentane (isopropylidenecyclopentane). When Br2 in CCl4 adds across this exocyclic double bond, the two carbons of the double bond become sp3. The cyclopentane carbon (C1 of ring) becomes a new chiral center, and the exocyclic carbon bearing two identical methyl groups does NOT become chiral (it has two CH3 groups). Wait — let me reconsider the structure: it is cyclopentylidene with H3C and CH3 on the exo carbon, meaning the exo carbon has one H3C and one CH3 (two methyls, same), so it's (CH3)2C=cyclopentyl. Upon bromonium ion formation and ring opening, Br adds to both carbons. The exo carbon gets Br and two CH3 — that carbon is not chiral (two identical methyl groups). The ring carbon (C1 of cyclopentane) gets Br and is connected to four different groups, making it a new chiral center. Because the starting alkene is symmetric with respect to the two faces of the double bond (the molecule has no existing chirality and the two faces are enantiotopic), Br2 attacks from either face with equal probability, giving equal amounts of R and S at C1 — a racemic mixture. Option (a): The starting material already has a defined stereocenter (wedge CH3), and H2/Pt hydrogenation tends to proceed with facial selectivity based on existing stereocenters (substrate-controlled), giving predominantly one diastereomer, not a racemic mixture. Option (c): The trans-1,4-dimethylcyclohexane derivative with H2/Pd — the existing stereocenters (both CH3 groups defined by wedge/dash) control facial selectivity of hydrogenation, giving preferential cis addition from the less hindered face, producing a specific diastereomer predominantly rather than a racemic mixture. Option (d): The cyclopentene with defined stereocenters (H3C on dash at one carbon, CH3 on wedge at another) reacting with Br2 — the existing chirality creates diastereotopic faces, so addition is not equal from both faces, giving unequal amounts of the two possible products (diastereomers), not a racemic mixture. Therefore, option (b) produces a racemic mixture because the symmetric exocyclic alkene lacks facial differentiation, and bromine addition creates one new chiral center with equal probability from both faces. Therefore, the correct answer is B.