(a) (i) Acetone shows a weak absorption at 280 nm and a strong absorption at 190 nm in the UV spectrum. Account for the…

Part (a)

(i) UV Spectrum of Acetone Acetone exhibits two distinct absorptions due to different electronic transitions. The strong band at 190 nm corresponds to the π → π^* transition of the carbonyl group. This transition is symmetry-allowed, resulting in a high molar absorptivity (ε ≈ 10⁴ L mol⁻¹ cm⁻¹). The weak band at 280 nm arises from the n → π^* transition, where a non-bonding lone pair on oxygen is excited to the antibonding π^* orbital. This transition is symmetry-forbidden (or weakly allowed via vibronic coupling), leading to low intensity (ε ≈ 10-100 L mol⁻¹ cm⁻¹).

(ii) Woodward-Fieser Calculations Using the Woodward-Fieser rules for α,β-unsaturated ketones:

• Compound A (3-methylbut-3-en-2-one): This is a methyl vinyl ketone derivative. Base value for acyclic enone = 215 nm. β-alkyl substituent = +12 nm. λₘₐₓ = 215 + 12 = 227 nm.
• Compound B (2-(cyclohex-1-en-1-yl)cyclohexan-1-one): This is a cyclic enone. Base value for 6-membered ring enone = 215 nm. The double bond is exocyclic to the carbonyl ring? No, it is endocyclic to the enone ring but exocyclic to the other ring if considered fused, but here it is a spiro or fused system? The structure is 2-(cyclohex-1-en-1-yl)cyclohexan-1-one. This is a spiro compound? No, it's a fused system if drawn as decalin-like, but the name implies a bond between C2 of one ring and C1 of another. Let's assume it is a cyclic enone with an exocyclic double bond relative to the carbonyl ring? Actually, standard W-F for cyclic enones: Base 215. If the double bond is exocyclic to the ring containing the carbonyl, add +5. If endocyclic, no extra. In this specific structure, the C=C is part of the ring attached to the carbonyl. It is an endocyclic double bond in a 6-membered ring. λₘₐₓ = 215 nm. (Note: If interpreted as having an exocyclic double bond to the carbonyl ring, add +5. Standard interpretation for this specific isomer often treats it as a simple cyclic enone). Let's refine: Base 215. No alkyl substituents on the double bond beyond the ring carbons. λₘₐₓ = 215 nm.
• Compound C (2-methylcyclopent-2-en-1-one): Cyclic enone (5-membered ring). Base value = 202 nm. β-alkyl substituent (methyl) = +12 nm. λₘₐₓ = 202 + 12 = 214 nm.
• Compound D (3,4-dihydronaphthalen-1(2H)-one): This is a bicyclic enone. The double bond is endocyclic to the enone ring and exocyclic to the benzene ring? No, it is a dihydronaphthalenone. The C=C is in the non-aromatic ring. Base value for 6-membered ring enone = 215 nm. The double bond is exocyclic to the benzene ring? No, it is endocyclic to the enone ring. However, it is part of a fused system. Standard rule: Base 215. Exocyclic double bond (to the other ring) = +5 nm. λₘₐₓ = 215 + 5 = 220 nm. (Correction: If the double bond is exocyclic to the carbonyl ring, add 5. In dihydronaphthalenone, the C=C is endocyclic to the enone ring. Thus, no exocyclic increment for the enone ring itself. However, some interpretations add for the fused system. Let's stick to standard: Base 215. No alkyl substituents. λₘₐₓ = 215 nm. Wait, re-evaluating D: 3,4-dihydronaphthalen-1(2H)-one has the double bond at C3-C4. The carbonyl is at C1. This is an α,β-unsaturated ketone? No, C1=O, C2 is CH2, C3=C4. This is a β,γ-unsaturated ketone? No, numbering: 1-one, 2H. Double bond at 3,4. This is not conjugated with the carbonyl. Correction: The question likely implies a conjugated enone. If it is 3,4-dihydronaphthalen-1(2H)-one, the double bond is at 3,4. Carbonyl at 1. C2 is sp3. This is NOT an enone. It is a saturated ketone with a remote double bond. It would not show strong enone absorption. Re-reading prompt: "bicyclic enone". This implies conjugation. Perhaps it is 1,2-dihydronaphthalen-1-one? Or the prompt implies the double bond is conjugated. Let's assume the standard "enone" classification for W-F applies, meaning the double bond is conjugated. If it is a fused enone like in 1-tetralone derivatives where the double bond is conjugated: Base 215. Exocyclic double bond (to benzene) = +5. λₘₐₓ = 220 nm.

Part (b)

(i) Diels-Alder Reactivity Ranking Reactivity depends on the ability to adopt the s-cis conformation and electronic activation.

1. Least Reactive (1): Dienes locked in s-trans conformation (e.g., trans,trans-2,4-hexadiene) or those with steric hindrance preventing s-cis.
2. Moderate (2): Dienes that can rotate to s-cis but lack electronic activation (e.g., 1,3-butadiene).
3. High (3): Dienes with electron-donating groups (EDG) that stabilize the transition state (e.g., 1-methoxybutadiene).
4. Most Reactive (4): Dienes locked in s-cis conformation (e.g., cyclopentadiene) or those with strong EDG and favorable geometry. Ranking: A (s-trans locked) < B (flexible, no EDG) < C (flexible, EDG) < D (s-cis locked).

(ii) Product Prediction Reaction: 2-methoxybuta-1,3-diene + acrylonitrile (CN-CH=CH2). The diene is electron-rich due to the methoxy group. The dienophile is electron-poor. Regioselectivity: The "ortho" or "para" rule applies. For 1-substituted dienes (OMe at C1), the product is the "ortho" adduct (1,2-disubstituted cyclohexene). For 2-substituted dienes (OMe at C2), the product is the "para" adduct (1,4-disubstituted). Here, the diene is 2-methoxybuta-1,3-diene (OMe at C2). The major product is the para-adduct: 4-methoxycyclohex-3-enecarbonitrile. Structure: A cyclohexene ring with a methoxy group at C4 and a cyano group at C1 (relative to the double bond at C3-C4? No, double bond is between C3 and C4 in the product if diene is 1,3-diene. Let's number the product: Double bond at 3,4. CN at 1. OMe at 4. Hydrolysis: The nitrile group hydrolyzes to a carboxylic acid or amide depending on conditions, but the prompt says H+, H2O. Usually, nitriles hydrolyze to carboxylic acids. However, if the prompt implies the enol ether hydrolysis, the OMe group might be labile. But typically, Diels-Alder adducts are stable. The question asks for the product of the sequence: 1) Heat (DA reaction) 2) H+, H2O. The DA product is 4-methoxycyclohex-3-enenitrile. Hydrolysis of the nitrile yields 4-methoxycyclohex-3-ene-1-carboxylic acid.

Part (c)

(i) Sigmatropic Rearrangement The reaction is a [3,3]-sigmatropic rearrangement (Cope rearrangement) of a 1,5-diene system. Starting material: A bicyclic system with a vinyl group and a butyl group. The rearrangement breaks the C-C bond between the two allylic fragments and forms a new C-C bond. Product Structure: The product is an acyclic or differently bridged diene. Specifically, the bond between the bridgehead carbons breaks, and a new bond forms between the terminal carbons of the allyl systems. The product is (E)-1-butyl-5-vinyl-1,4-pentadiene (or similar open-chain diene depending on the exact starting bicyclic structure). Correction: If the starting material is a bicyclic [3,3] system, the product is often an acyclic diene. Orbital Feasibility: Thermal [3,3] shifts are suprafacial-suprafacial. The HOMO of one allyl fragment interacts with the LUMO of the other. The phase match allows bonding interaction at the termini, making the thermal process allowed.

(ii) Electrocyclic Reactions

1. Mode of Ring Closure:

• Reaction A: Cyclooctatriene (6 π electrons) to bicyclic product. 6 π electrons follow the 4n+2 rule. Thermal closure is disrotatory.
• Reaction B: Bicyclic diene to cyclooctatriene. Reverse of A. Thermal opening is disrotatory.

2. Stereochemistry:

• In Reaction A, the starting triene has specific stereochemistry. Disrotatory motion of the terminal carbons determines the cis/trans relationship of the bridgehead hydrogens.
• If the terminal hydrogens rotate inwards (disrotatory), they become cis to each other in the product.
• If the prompt indicates the product has trans hydrogens, the starting material must have had the appropriate geometry (e.g., (E,E) or (Z,Z) depending on the specific isomer) to allow disrotatory closure to give trans.
• For Reaction B, the trans hydrogens in the bicyclic starting material undergo disrotatory opening to form the triene. The hydrogens in the resulting triene will be trans (E,E or Z,Z depending on rotation direction) relative to the chain.

Conclusion The UV data confirms the electronic nature of the carbonyl, W-F rules quantify the conjugation effects, and pericyclic reactions follow orbital symmetry rules (Woodward-Hoffmann), with thermal 6π electrocyclic reactions proceeding via disrotatory pathways and [3,3] shifts via suprafacial interactions.