Step 1: Detergent Functionality
Detergents, functioning as surfactants, facilitate the emulsification of grease and oils, rendering them water-soluble.
Anionic detergents, exemplified by sodium lauryl sulphate (\( {CH}_3 ({CH}_2)_{10} {CH}_2 - {OSO}_3^-{Na}^+ \)), are prevalent.
Step 2: Rationale for Sodium Lauryl Sulphate Use
Sodium stearate is an ingredient in soaps, not detergents.
Calcium stearate exhibits insolubility and is unsuitable for detergent applications.
Sodium lauryl sulphate's widespread adoption in detergents stems from its superior cleansing capabilities.
Consequently, the accurate selection is (D).