Which of the following is NOT an example of synthetic detergent?

We need to identify which compound is NOT a synthetic detergent.

Understanding synthetic detergents and soaps, we note that soaps are sodium or potassium salts of long-chain fatty acids (carboxylates), while synthetic detergents are non-soap cleaning agents that may be anionic, cationic, or non-ionic surfactants.

Option A: Sodium lauryl sulphonate ($$CH_3(CH_2)_{11}C_6H_4SO_3^-Na^+$$) — This is sodium dodecylbenzenesulphonate, an anionic synthetic detergent. It contains a sulphonate group, not a carboxylate group.

Option B: $$CH_3(CH_2)_{16}COO^-Na^+$$ — This is sodium stearate, which is a sodium salt of stearic acid (a long-chain fatty acid with 18 carbon atoms). This is a soap, not a synthetic detergent.

Option C: Cetyltrimethylammonium bromide (CTAB) — This is a quaternary ammonium salt, which is a cationic synthetic detergent.

Option D: $$CH_3(CH_2)_{16}COO(CH_2CH_2O)_nCH_2CH_2OH$$ — This is a polyethylene glycol ester of stearic acid, which is a non-ionic synthetic detergent.

$$CH_3(CH_2)_{16}COO^-Na^+$$ (sodium stearate) is a soap, not a synthetic detergent, because soaps are derived from natural fats and oils, while synthetic detergents are manufactured chemically.

Therefore, the correct answer is Option B.