JEE Challenger
More from Surface Chemistry
ChemMedAdv 2008 • Paper 2

Surfactant with Lowest Critical Micelle Concentration

Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is

Options

A

CH3(CH2)15 N+(CH3)3 Br−\text{CH}_3(\text{CH}_2)_{15}\text{ N}^+(\text{CH}_3)_3\text{ Br}^-

Correct
B

CH3(CH2)11OSO3− Na+\text{CH}_3(\text{CH}_2)_{11}\text{OSO}_3^-\text{ Na}^+

C

CH3(CH2)6COO− Na+\text{CH}_3(\text{CH}_2)_6\text{COO}^-\text{ Na}^+

D

CH3(CH2)11 N+(CH3)3Br−\text{CH}_3(\text{CH}_2)_{11}\text{ N}^+(\text{CH}_3)_3\text{Br}^-

Topics & Concepts

Surface ChemistryColloids

Step-by-Step Solution

To determine which surfactant forms micelles at the lowest molar concentration, we consider the concept of Critical Micelle Concentration (CMC). The CMC is the minimum concentration of a surfactant in a solution above which micelles spontaneously form.

Factors Affecting CMC:

  1. Hydrophobic Effect: Micelle formation is primarily driven by the hydrophobic effect, which minimizes the thermodynamically unfavorable interactions between the non-polar hydrocarbon tail of the surfactant and water.

  2. Chain Length Dependence: As the length of the non-polar hydrophobic alkyl chain increases, the hydrophobic repulsion from water increases significantly. According to Klevens' empirical relationship for homologous series of surfactants:
    log⁡10(CMC)=A−B⋅Nc\log_{10}(\text{CMC}) = A - B \cdot N_c
    where:

    • NcN_c is the number of carbon atoms in the hydrophobic alkyl chain.
    • AA and BB are constants for a specific homologous series and temperature.

    This relationship shows that an increase in the hydrophobic chain length NcN_c results in an exponential decrease in the Critical Micelle Concentration (CMC\text{CMC}).

Analysis of the Given Surfactants:

  • Option (A): CH3(CH2)15N+(CH3)3Br−\text{CH}_3(\text{CH}_2)_{15}\text{N}^+(\text{CH}_3)_3\text{Br}^-

    • Hydrophobic alkyl chain length: 1+15=161 + 15 = 16 carbon atoms (Cetyl / Hexadecyl group).

  • Option (B): CH3(CH2)11OSO3−Na+\text{CH}_3(\text{CH}_2)_{11}\text{OSO}_3^-\text{Na}^+

    • Hydrophobic alkyl chain length: 1+11=121 + 11 = 12 carbon atoms (Dodecyl group).

  • Option (C): CH3(CH2)6COO−Na+\text{CH}_3(\text{CH}_2)_6\text{COO}^-\text{Na}^+

    • Hydrophobic alkyl chain length: 1+6=71 + 6 = 7 carbon atoms in the alkyl portion (Octanoate group).

  • Option (D): CH3(CH2)11N+(CH3)3Br−\text{CH}_3(\text{CH}_2)_{11}\text{N}^+(\text{CH}_3)_3\text{Br}^-

    • Hydrophobic alkyl chain length: 1+11=121 + 11 = 12 carbon atoms (Dodecyl group).

Conclusion:

The surfactant in Option (A), cetyltrimethylammonium bromide (CTAB\text{CTAB}), has the longest hydrophobic carbon chain (1616 carbons). Consequently, it exhibits the strongest hydrophobic interaction with water and forms micelles at the lowest molar concentration.

Correct Option: (A)

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