Which of the following substances will have least CMC value? (a) \(\mathrm{C}_{6} \mathrm{H}_{13} \mathrm{COOK}\) (b) \(\mathrm{C}_{9} \mathrm{H}_{19} \mathrm{SO}_{3} \mathrm{Na}\) (c) \(\mathrm{C}_{11} \mathrm{H}_{22} \mathrm{NH}_{4} \mathrm{Cl}\) (d) \(\mathrm{C}_{8} \mathrm{H}_{17} \mathrm{COONa}\)

Surfactants, or surface-active agents, are unique compounds that contain both hydrophilic (water-loving) and hydrophobic (water-fearing) parts. These dual characteristics enable surfactants to reduce surface tension in liquids and allow miscibility of oil and water. An everyday example of surfactants in action would be when you use soap to wash greasy dishes; the surfactant molecules surround oil particles, with their hydrophobic tails embedding in the oil, and hydrophilic heads facing the water, effectively breaking down the grease.

When you sprinkle surfactants into water, initially, they distribute themselves along the surface. As the concentration increases, surfactants begin forming structures called micelles, which takes us to a critical point known as the Critical Micelle Concentration (CMC). This concentration is significant because it marks the threshold where additional surfactants form micelles instead of dispersing individually.

Hydrophobic interactions are a type of non-covalent bonding that occur between nonpolar molecules or parts of molecules. These parts are 'hydrophobic' or 'water-fearing', meaning they tend to avoid contact with water. Molecules with hydrophobic portions do not dissolve well in water and instead prefer to associate with each other. These interactions are fundamental for many biological processes, such as the formation of cell membranes and the folding of proteins.

In the context of surfactants and CMC, the strength of hydrophobic interactions has a direct impact on micelle formation. A longer hydrophobic chain in a surfactant molecule strengthens these interactions, leading to an easier and more stable formation of micelles, and consequently, a lower CMC. Thus, hydrophobic interactions play a crucial role in determining the CMC of a particular surfactant.

Micelle formation is a process where surfactant molecules spontaneously arrange themselves into a spherical form in an aqueous solution. The surfactants' hydrophobic tails are shielded from the water and congregate at the center of the micelle, while the hydrophilic heads point outwards toward the water. This orientation minimizes the unfavorable contact between the hydrophobic tails and water, resulting in a stable structure.

Micelles are not just a scientific curiosity; they have practical applications, including in drug delivery systems and the aforementioned soaps and detergents. The formation of micelles occurs when the concentration of surfactants in a solution reaches the CMC. Below this concentration, you have individual surfactant molecules scattered throughout the solution. Above the CMC, additional surfactants are more likely to join existing micelles than to exist on their own in solution.