Problem 77 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

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) \(\mathrm{C}_{8} \mathrm{H}_{17} \mathrm{COONa}\)

Step-by-Step Solution

Answer

(c) \(\mathrm{C}_{11} \mathrm{H}_{22} \mathrm{NH}_{4} \mathrm{Cl}\) will have the least CMC value due to its longest hydrophobic chain.

Step 1: Understand the concept of Critical Micelle Concentration (CMC)

CMC is the concentration of surfactants above which micelles form and all additional surfactants added to the system go to micelles. The CMC of a surfactant is affected mainly by the hydrophobic (water-fearing) part of its molecule. The longer the hydrophobic chain, the more hydrophobic the molecule is, and typically, the lower the CMC value will be.

Step 2: Compare the hydrophobic chain length of the given substances

To predict which substance has the least CMC value, compare the length of the hydrocarbon chains in each molecule. (a) has a chain of 6 carbon atoms, (b) has 9, (c) has 11, and (d) has 8. The substance with the longest hydrocarbon chain, which is (c) \(\mathrm{C}_{11} \mathrm{H}_{22} \mathrm{NH}_{4} \mathrm{Cl}\), is likely to have the least CMC value due to increased hydrophobic interactions.

Step 3: Identify the substance with the least CMC value

Based on the understanding of hydrophobic interactions and CMC, the molecule with the longest hydrocarbon chain will form micelles at the lowest concentration. Therefore, the substance with the least CMC value from the options given is (c) \(\mathrm{C}_{11} \mathrm{H}_{22} \mathrm{NH}_{4} \mathrm{Cl}\).

Key Concepts

Surfactants

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

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

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.