Which compound will produce an offensive smell when heated with chloroform and alcoholic potash?

\(C_2H_5NH_2\)

The correct answer is option 3.  \(C_2H_5NH_2\).

When a primary amine is heated with chloroform and alcoholic potash, it produces a foul-smelling compound called carbylamine (also known as isocyanide). The reaction is known as the Hoffmann carbylamine test.

The other options are incorrect. Option (1) \((C_2H_5)_2NH\), is a secondary amine and will not react with chloroform and alcoholic potash to produce carbylamine. Option (2) \((CH_3)_3N\), is a tertiary amine and will not react with chloroform and alcoholic potash to produce carbylamine. Option (4)\(CH_3CN\), is acetonitrile and is not an amine, so it will not react with chloroform and alcoholic potash to produce carbylamine.

Therefore, the only compound that will produce an offensive smell when heated with chloroform and alcoholic potash is \(C_2H_5NH_2\), a primary amine.