Synthetic detergents are cleansing agents that have a soap-like action but are not soaps (salts of fatty acids).
They typically have a long hydrophobic hydrocarbon tail and a hydrophilic head group.
They are classified as anionic, cationic, or non-ionic.
A) \( \text{C}_9\text{H}_{19} - \text{Ph} - \text{O}(\text{CH}_2\text{CH}_2\text{O})_6\text{CH}_2\text{CH}_2\text{OH} \)
This is a non-ionic detergent.
The long hydrocarbon chain (\(\text{C}_9\text{H}_{19}\)-Ph-) provides the hydrophobic part.
The polyoxyethylene chain (-\text{O}(\text{CH}_2\text{CH}_2\text{O})_6\text{CH}_2\text{CH}_2\text{OH}\)) provides the hydrophilic part due to ether linkages and the terminal -OH group capable of hydrogen bonding.
Example: detergents formed by reaction of polyethylene glycol with alkylphenols.
This is a synthetic detergent.
B) \( \text{CH}_3(\text{CH}_2)_{10}\text{CH}_2\text{OSO}_3\text{Na} \) (Sodium lauryl sulfate or sodium dodecyl sulfate, SDS)
This is an anionic detergent.
The \( \text{CH}_3(\text{CH}_2)_{10}\text{CH}_2- \) is the hydrophobic tail.
The \( -\text{OSO}_3^-\text{Na}^+ \) is the hydrophilic head group (sulfate group).
This is a common synthetic detergent.
C) \( \text{CH}_3(\text{CH}_2)_{15}\text{N(CH}_3\text{)}_3\text{Br} \) (Cetyltrimethylammonium bromide, CTAB)
This is a cationic detergent.
The \( \text{CH}_3(\text{CH}_2)_{15}- \) is the hydrophobic tail.
The \( -\text{N}^+\text{(CH}_3\text{)}_3\text{Br}^- \) is the quaternary ammonium hydrophilic head group.
This is a synthetic detergent.
D) \( (\text{C}_{15}\text{H}_{31}\text{COO})_3\text{C}_3\text{H}_5 \) (Glyceryl tripalmitate, a triglyceride)
This is a fat or oil (specifically, tripalmitin).
Fats and oils are triglycerides, which are esters of glycerol and fatty acids.
Soaps are made by saponification (hydrolysis with alkali) of fats/oils.
This compound itself is a fat, not a detergent.
Therefore, A, B, and C are synthetic detergents.
This matches option (1).