Write the mechanism of Hoffmann bromamide reaction.

Explanation

Hoffmann bromamide reaction : It is a simple way of converting an amide to an amine having one carbon atom less than the starting amide. The reaction is a rearrangement which is brought about by bromide in presence of alkali. It is believed to proceed through the steps shown below.
`RCONH_(2)+Br_(2)+3NaOH to RNH_(2)+2NaBr+NaHCO_(3)+H_(2)O`
`RCONH_(2) overset(Br_(2)) to underset("N-Bromamide")(RCONHBr) overset(OH^(-)) to R- overset(O) overset(||)C- overset(ө)N-Br`
`to underset("Isocyanate")(R-N=C=0 )overset(H_(2)O) to underset("Carbonic acid")(RNHCOOH) overset(-CO_(2)) to RNH_(2)`
Mechanism : It is believed to proceed in following via nitrene intermediate.
i) `R-CO-NH_(2)+ :O^(-)Br to underset("Bromamide")(R-CO-ddot(N)HBr+OH^(-)`
ii) `R- underset(O) underset(||)(C)- underset(H) underset(|)(N)-Br-OH^(ө) to R- underset(O) underset(||)(C)- overset(ө)(N)-Br+H_(2)O`
iii) `R- underset(O) underset(||)(C)- overset(ө)(N)-Br to R- underset(O) underset(||)(C)- overset(ddot)(N)+ :overset(ө)Br " Un stable (Nitrene)"`
iv) `R- underset(O) underset(||)(C)- N underset("rearrangement") overset("Molecular") to O=C=underset("alkyl isocyanate")(overset(ddot)(N)-R)`
v) `R-N-C-O+2:bar(OH) to underset("Primary amine")(R-NH_(2)+CO_(3)^(2-))`