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Which of the following represents a synthetic detergent ?
A.${C_{15}}{H_{31}}COOK$
B.$C{H_3}{(C{H_2})_6}COONa$
C.${C_{12}}{H_{25}} - ({C_6}{H_4}) - S{O_3}Na$
D.None of the above

Answer
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Hint: Synthetic detergents are the ammonium , sulphonate or sulphate salts of long-chain hydrocarbon containing twelve to eighteen carbon atoms but the more common detergents are the sodium salt of long-chain sulphonic acids

Complete step by step answer:
We have been given four options and asked to check whether any of them is a synthetic detergent or not .
-${C_{15}}{H_{31}}COOK$ is potassium palmitate . It is a potassium salt of higher fatty acid . Hence it is a soap .
-$C{H_3}{(C{H_2})_6}COONa$ contains only eight carbon atoms hence it is neither a soap nor a synthetic detergent .
-${C_{12}}{H_{25}} - ({C_6}{H_4}) - S{O_3}Na$ is n- dodecyl benzene sulphonate , it represents a synthetic detergent . The anionic part of synthetic detergents is involved in the cleansing action . It is used for cleaning purposes like in household cleaning and it is also used in toothpaste .
Hence , option C is correct .

Additional Information:
Dodecyl benzene is a colorless waxy solid which consists of a dodecyl group which is attached to a benzene ring. It is a precursor to sodium dodecylbenzenesulfonate. n- dodecyl benzene sulphonate is one of the most commonly used detergents . It is prepared by Friedel - Crafts alkylation of benzene with a long chain alkyl halide or an alkene or an alcohol followed by sulphonation and neutralization with sodium hydroxide .

Note:
The basic criteria to check whether the compound is a soap or synthetic detergent is by looking at its functional group . AS soaps are sodium and potassium salts of higher fatty acids whereas synthetic detergents are ammonium , sulfate or sulphate salts of long chain hydrocarbon .