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What is the mechanism of the Hofmann degradation reaction for primary amides, and how does it differ from the mechanism of Gabriele reaction?

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The Hofmann degradation reaction is a chemical reaction that involves the conversion of primary amides to primary amines with the loss of one carbon atom. The reaction is named after its discoverer, August Wilhelm von Hofmann. The mechanism of the Hofmann degradation reaction involves the following steps:1. Formation of an intermediate: The primary amide reacts with a halogen  usually chlorine or bromine  in the presence of a strong base  such as NaOH or KOH  to form an N-haloamide intermediate. The base deprotonates the amide, and the resulting anion attacks the halogen to form the intermediate.RCONH2 + Br2 + 4NaOH  RCONHBr + 2NaBr + 2H2O2. Rearrangement: The N-haloamide undergoes a rearrangement, with the migration of the R group  alkyl or aryl  from the carbonyl carbon to the nitrogen atom. This migration is accompanied by the elimination of a halide ion.RCONHBr  RNH2 + CO2 + Br-3. Formation of the primary amine: The resulting primary amine is then protonated by water to give the final product.RNH2 + H2O  RNH3+ + OH-The Gabriele reaction, on the other hand, is a method for the synthesis of N-acyl--amino esters from -amino esters and acyl chlorides. The mechanism of the Gabriele reaction involves the following steps:1. Formation of an iminium ion: The -amino ester reacts with an acyl chloride to form an iminium ion intermediate.R1NHCH R2 COOR3 + R4COCl  R1N=CH R2 COOR3 + R4COOH + HCl2. Nucleophilic attack: The iminium ion is attacked by a nucleophile  usually an amine or an alcohol , leading to the formation of the N-acyl--amino ester.R1N=CH R2 COOR3 + NuH  R1NHCH R2 COOR3 + NuH2+The key difference between the mechanisms of the Hofmann degradation reaction and the Gabriele reaction is that the former involves the conversion of primary amides to primary amines with the loss of one carbon atom, while the latter involves the synthesis of N-acyl--amino esters from -amino esters and acyl chlorides. The Hofmann degradation involves the formation of an N-haloamide intermediate and a rearrangement step, whereas the Gabriele reaction involves the formation of an iminium ion intermediate and a nucleophilic attack step.
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