Propanoic acid to Ethanoic acid/ acetic acid

Explanation: The structure of propanoic acid is CH₃CH₂COOH and the structure of ethanoic acid is CH₃COOH. To convert propanoic acid to ethanoic acid (the number of carbon atoms are decreasing), we need propionamide (amide group-RCONH₂). Then propionamide undergoes Hoffman Bromamide reaction to form methylamine. Then methylamine formed can be converted to ethanol to form ethanoic acid by oxidation.

Step 1: Convert propanoic acid to propionamide

Propanoic acid (CH₃CH₂COOH) reacts with ammonia (in excess) to form propionamide (CH₃CH₂CONH₂)

Step 2: Convert propionamide to ethyl amine by Hoffman Bromamide reaction

Propionamide (CH₃CH₂CONH₂) reacts with potassium hydroxide and bromine to form ethylamine (CH₃CH₂NH₂) which has one carbon atom less than the propionamide (Hoffman Bromamide reaction)

Step 3: Convert ethyl amine to methanol by forming diazonium salt

Ethyl amine (CH₃CH₂NH₂) reacts with NaNO₂ and HCl to form diazonium salt (R--N₂⁺Cl^-) then diazonium salt undergoes hydrolysis to from ethanol (CH₃CH₂OH)

Step 4: Convert ethanol to ethanoic acid by oxidation

Ethanol (CH₃CH₂OH) undergoes oxidation in the presence of strong oxidizing agent KMNO₄ to form ethanoic acid (CH₃COOH-final product)