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Design a multi-step synthesis of 2-phenylbutanoic acid starting from benzene and any other necessary reagents, using retrosynthesis to plan the reaction steps. Include reaction mechanisms, reagents, and conditions for each step.

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To synthesize 2-phenylbutanoic acid from benzene, we can use the following retrosynthetic analysis:2-phenylbutanoic acid -> Friedel-Crafts alkylation -> benzyl bromide + 1,3-butadiene -> bromination -> benzeneHere's the step-by-step synthesis:1. Bromination of benzene:   Reaction: Electrophilic Aromatic Substitution  EAS    Reagents: Br2, FeBr3  Lewis acid catalyst    Conditions: Room temperature, anhydrous conditions   Mechanism:   - Formation of the electrophile: FeBr3 coordinates with Br2 to form a complex, which generates the electrophile Br+.   - Electrophilic attack: The benzene ring attacks the Br+ electrophile, forming a carbocation intermediate.   - Deprotonation: A base  Br-  deprotonates the carbocation intermediate, regenerating the aromatic ring and yielding bromobenzene.2. Conversion of bromobenzene to benzyl bromide:   Reaction: Radical Chain Reaction   Reagents: NBS  N-bromosuccinimide , AIBN  azobisisobutyronitrile, radical initiator , CCl4  solvent    Conditions: Heating under reflux   Mechanism:   - Initiation: AIBN undergoes homolytic cleavage upon heating, generating two alkyl radicals.   - Propagation  step 1 : The alkyl radical abstracts a bromine atom from NBS, forming a new radical species and HBr.   - Propagation  step 2 : The bromine radical reacts with bromobenzene, abstracting a hydrogen atom from the benzylic position and forming benzyl bromide and a new bromine radical.3. Friedel-Crafts alkylation of benzyl bromide with 1,3-butadiene:   Reaction: Friedel-Crafts Alkylation   Reagents: 1,3-butadiene, AlCl3  Lewis acid catalyst    Conditions: Room temperature, anhydrous conditions   Mechanism:   - Formation of the electrophile: AlCl3 coordinates with the benzyl bromide, generating a carbocation at the benzylic position.   - Electrophilic attack: The 1,3-butadiene attacks the carbocation, forming a new carbocation intermediate.   - Deprotonation: A chloride ion  from AlCl4-  deprotonates the carbocation intermediate, yielding 1-phenylbut-1-ene.4. Oxidation of 1-phenylbut-1-ene to 2-phenylbutanoic acid:   Reaction: Oxidation   Reagents: KMnO4, H2O  solvent , H2SO4  acidic conditions    Conditions: Heating under reflux   Mechanism:   - Formation of the diol: The alkene reacts with the permanganate ion  MnO4-  under acidic conditions, forming a cyclic intermediate which then hydrolyzes to form a vicinal diol.   - Oxidative cleavage: The diol undergoes oxidative cleavage by another equivalent of permanganate ion, yielding 2-phenylbutanoic acid and a carboxylic acid byproduct  formic acid .The final product, 2-phenylbutanoic acid, is obtained through this multi-step synthesis starting from benzene.

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