(a) (i) In the presence of sodium ethoxide, the following transformation occurs. Explain : (ii) Propose a suitable mechanism for…

(a)(i) The NaOEt/HCl step is a Favorskii-type base-catalysed rearrangement. Ethoxide removes the acidic α′-proton to give an enolate; this E1cB-type deprotonation precedes C–O cleavage. The enolate carbon attacks the α-ethoxy/ethoxycarbonyl-bearing carbon intramolecularly and expels ethoxide, forming a strained cyclopropanone/cyclopropanolate. Ethoxide then opens the three-membered ring at the more substituted carbon, and acid work-up protonates the alkoxide to the β-keto ester shown. The driving forces are relief of cyclopropanone strain and formation of a stabilised β-keto ester; the methyl-bearing carbon migrates with the ring framework, giving the observed ring-contracted/expanded product.

(a)(ii) In H₂SO₄/H₂O the epoxide oxygen is first protonated. The C–O bond to the more substituted epoxide carbon becomes labile, and the pendant alkene attacks that carbon intramolecularly as the C–O bond breaks; this is an SN2-like backside opening when the cation is not fully developed, or an SN1-like capture when a tertiary cation forms. The result is a chair-like cyclic carbocation/oxonium. Water traps the cation and deprotonation gives the trans-fused decalin diol. The epoxide-derived OH is at the more substituted carbon, the alkene-derived OH is at the new cationic centre, and trans stereochemistry follows from anti opening of the protonated epoxide and a chair-like cyclisation. The decalin fusion is trans because a cis-fused chair-like cation would place the two ring-junction hydrogens on the same face and is higher in strain.

(b)(i) The crossed-out 3,3-dimethyl-2-butanol is not obtained by acid hydration because protonation of 3,3-dimethyl-1-butene gives a secondary carbocation next to a quaternary carbon. A 1,2-methyl shift from the tert-butyl carbon gives a more stable tertiary carbocation; water attack and deprotonation give 2,3-dimethyl-2-butanol as the major product. The same steric/electronic logic explains the Grignard variant: t-BuMgBr is too bulky to add cleanly to the hindered carbonyl, so competing proton abstraction/elimination or reduction, and formation of a rearranged tertiary alkoxide, dominate. For the non-rearranged target 3,3-dimethyl-2-butanol, use oxymercuration-demercuration, Hg(OAc)₂/H₂O then NaBH₄, which gives Markovnikov hydration without carbocation rearrangement, or a less hindered Grignard route: pivaldehyde + MeMgBr, then H₃O⁺. The acetone + i-PrMgBr combination is the clean Grignard route only to the isomeric 2,3-dimethyl-2-butanol.

(b)(ii) Photolysis of BrCCl₃ gives CCl₃• and Br•. CCl₃• adds to the terminal carbon of styrene to generate the more stable benzylic radical, which abstracts bromine from another CCl₃Br molecule; the major product is PhCHBrCH₂CCl₃. The benzylic radical is planar, so the product is racemic. Where the drawn substrate is a chiral carbonyl, the analogous stereochemical prediction is Felkin-Anh/Cram: the largest substituent is placed perpendicular to the C=O, and nucleophilic attack occurs from the least hindered face anti to the largest group, fixing the major R/S diastereomer.

(c) (i) KOH enolises the 1,5-diketone; intramolecular aldol addition followed by acid-catalysed dehydration gives the bicyclic conjugated enone, the Robinson annulation product. The corresponding Diels–Alder system gives the endo cyclohexene adduct, formed suprafacially with alkene geometry retained. (ii) Acid protonates the bridgehead tertiary alcohol; loss of water and semipinacol migration of the adjacent C–C bond gives the rearranged amine, while in the photochemical [2+2] case the product is the suprafacial cyclobutane with cis substituents retained. (iii) NH₂OH forms the 1-tetralone oxime; Al₂O₃ promotes Beckmann rearrangement, a concerted sigmatropic [1,2]-migration of the anti alkyl group to nitrogen, giving 3,4-dihydroisoquinolin-1(2H)-one. (iv) EtO⁻ effects Dieckmann cyclisation of the diester to the cyclic β-keto ester; for an electrocyclic substrate the thermal 4π closure is conrotatory and 6π closure disrotatory, fixing the observed E/Z stereochemistry. Thus, in every sub-part the product follows from the most stable ionic or radical intermediate, or from the symmetry-allowed pericyclic pathway.