An organic compound ' X ' with the molecular formula ${\mathrm{C}}_4{\mathrm{H}}_{11} \mathrm{N}$ reacts with ${\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{SO}}_2\mathrm{Cl}$ and form the compound ' Y '. If ' Y ' is soluble in alkali, ' $\mathrm{X}$ ' maybe;

Hinsberg method is used for separation of amines mixtures. It involves the treatment of the mixture with benzene sulphonyl chloride. Hinsberg's reagent reacts with a primary amine and also with a secondary amine but it doesn't react with a tertiary amine. Tertiary butylamine reacts with one mole of methyl iodide to form a salt. So, the structure of compound X is the structure of sec-butyl amine.

Hence, the correct answer is option D) Sec–butyl amine.