Question

Under ambient conditions, which among the following surfactants will form a micelle in aqueous solution at lowest molar concentration?
(A) $C{{H}_{3}}{{\left( C{{H}_{2}} \right)}_{11}}\overset{\oplus }{\mathop{N}}\,{{\left( {{\left( CH \right)}_{3}} \right)}_{3}}B{{r}^{-}}$
(B) $C{{H}_{3}}-{{\left( C{{H}_{2}} \right)}_{13}}-OSO_{3}^{\ominus }N{{a}^{+}}$
(C) $C{{H}_{3}}-{{\left( C{{H}_{2}} \right)}_{15}}\overset{\oplus }{\mathop{N}}\,{{\left( {{\left( CH \right)}_{3}} \right)}_{3}}\overset{\ominus }{\mathop{Br}}\,$
(D) $C{{H}_{3}}-{{\left( C{{H}_{2}} \right)}_{8}}-CO{{O}^{\ominus }}N{{a}^{+}}$

Answer 1

For attending the question a basic knowledge about action of surfactants is required. Keep in mind that, the larger the molecular chain, the more easily it will form micelles at lowest molar concentrations. Thus the compound with larger number of carbon atoms will form micelles at lowest molar concentrations.

Complete step by step solution:
- As we know surfactants surface active agents. They are the compounds which can reduce surface tension. They can reduce the surface tension between a solid and a liquid, between two liquids or between a liquid and a gas.
- Surfactants are generally organic compounds and salts of long chains of fatty acids. The compound will have two ends; one is hydrophobic and the other is hydrophilic. The hydrophobic end is water repellent or water insoluble whereas the hydrophilic end is water soluble or water loving.
- The above mentioned surfactants form aggregate molecules called micelles. They can be defined as ions formed spontaneously in their solutions at a definite concentration or aggregates of long-chain diphilic surfactant molecules.
- Micelles are formed as a result of the cooperative binding of monomers to one another at the concentrations which usually surpasses a narrow region called the critical micellization concentration (CMC). Also, the hydrophobic ends of surfactants make micelles.
- Hence, larger the size of the hydrophobic chain, lower will be its solubility in water and it increases the chances to form micelle. Or in other words, larger the hydrophobic portion of the surfactant, easier will be the micellization and smaller will be the critical micelle concentration.
- Among the given options $C{{H}_{3}}-{{\left( C{{H}_{2}} \right)}_{15}}\overset{\oplus }{\mathop{N}}\,{{\left( {{\left( CH \right)}_{3}} \right)}_{3}}\overset{\ominus }{\mathop{Br}}\,$ has the highest number of carbon atoms or it has the longest hydrophobic chain. Thus it will form a micelle in aqueous solution at lowest molar concentration.

Therefore the answer is option (C). $C{{H}_{3}}-{{\left( C{{H}_{2}} \right)}_{15}}\overset{\oplus }{\mathop{N}}\,{{\left( {{\left( CH \right)}_{3}} \right)}_{3}}\overset{\ominus }{\mathop{Br}}\,$.

Note: As we mentioned, longer the hydrophobic chain, lesser will be the CMC .The reason is that ,as the molecular weight of hydrocarbon chain of surfactant or micelle grows, the true solubility will diminish and the tendency of surfactant molecule to associate increases and as a result the critical concentration for micelle formation decreases.