Problem 19 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Under ambient conditions, which among the following surfactants will form micelles in aqueous solution at lowest molar concentration?(a) \(\mathrm{CH}_{3}-\left(\mathrm{CH}_{2}\right)_{8}-\mathrm{COO}^{-} \mathrm{Na}^{+}\) (b) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{11} \oplus{\mathrm{N}}{\oplus}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Br}^{-}\) (c) \(\mathrm{CH}_{3}-\left(\mathrm{CH}_{2}\right)_{13}-\mathrm{OSO}_{3} \mathrm{Na}^{+}\) (d) \(\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{15} \oplus{\mathrm{N}}{\oplus}\left(\mathrm{CH}_{3}\right)_{3} \mathrm{Br}^{-}\)

Step-by-Step Solution

Answer

Surfactant (d) forms micelles at the lowest concentration.

Step 1: Understanding CMC

The critical micelle concentration (CMC) is the concentration of surfactants in a solution at which micelles start to form. It is influenced by the hydrophobic tail length and the nature of the hydrophilic head group of the surfactant. Generally, longer hydrophobic tails result in a lower CMC because they require less saturation to aggregate into micelles.

Step 2: Evaluating Hydrophobic Tail Length

We examine the hydrophobic tails of the given surfactants: - (a) has a 9-carbon tail - (b) has a 12-carbon tail - (c) has a 14-carbon tail - (d) has a 16-carbon tail Since longer tail length corresponds to a lower CMC, surfactant (d) has the longest tail and thus the potential for the lowest CMC.

Step 3: Analyzing Head Groups

We consider the head groups: - (a) Carboxylate (COO⁻) - (b) Ammonium (N⁺(CH₃)₃) - (c) Sulfate (OSO₃⁻) - (d) Ammonium (N⁺(CH₃)₃) as well Both (b) and (d) have the same type of head group, with a likelihood of forming micelles efficiently, not affected by specific functional differences in CMC compared to tails.

Step 4: Conclusion to Select Surfactant

Considering both tail lengths and similar head group effects across (b) and (d), surfactant (d) with the longest hydrophobic tail and consistent ammonium head group will form micelles at the lowest molar concentration.

Key Concepts

Critical Micelle Concentration

In the world of surfactants, understanding the critical micelle concentration (CMC) is crucial. This term refers to the specific concentration where surfactant molecules in a solution start to organize themselves into structures called micelles. Before reaching the CMC, surfactant molecules are mostly dispersed as individual entities in the solution. However, once the CMC is reached, these molecules can cluster together to form micelles.
The CMC is significant because it provides insight into how much surfactant is necessary to achieve effective micelle formation. In practical applications, reducing the CMC means using less surfactant to achieve the desired effect, such as cleaning or emulsifying.
Key factors influencing the CMC include the chemical makeup of the surfactant, specifically the hydrophobic tail and the hydrophilic head group.

• Longer hydrophobic tails tend to lower the CMC.
• Different head groups exhibit varying degrees of solubility, affecting micelle formation.

A surfactant with a low CMC is efficient in forming micelles even in dilute solutions, making it particularly useful in industrial and household applications.

Hydrophobic Tail

The hydrophobic tail of a surfactant is an essential component that greatly affects its behavior in solutions. These tails are typically long stretches of carbon chains, which naturally repel water, preferring instead to congregate with other hydrophobic entities.
The length of this tail is directly proportional to its hydrophobic strength. The longer the tail, the stronger its tendency to avoid water and the more powerful its aggregation force. This leads to a lower CMC because fewer surfactant molecules are needed to start forming micelles as they readily gather into these structures due to their strong hydrophobic interactions.
Considering various examples, such as those in typical exercises, you might observe how surfactants with longer carbon chains in their tails tend to achieve micelle status at lower concentrations. Thus, when selecting surfactants for specific purposes, understanding the tail's length can be a determining factor.

• Tails with 9 carbons show a higher CMC.
• Tails with 16 carbons tend to have the lowest CMC.

This understanding of the tail's role helps in choosing the right surfactant for the task, ensuring efficiency and effectiveness.

Micelle Formation

When surfactants reach their critical micelle concentration, the fascinating process of micelle formation begins. This process involves surfactant molecules spontaneously assembling into spherical structures called micelles once the concentration threshold is surpassed.
In a micelle, the hydrophobic tails of the surfactant molecules congregate together in the center, away from the surrounding water. Meanwhile, their hydrophilic heads face outward, interacting with the water. This unique arrangement is energetically favorable, as it allows the surfactant to exist comfortably in an aqueous solution.
The formation of these structures is not only a crucial principle in chemistry but also underlies many practical applications such as cleaning products, drug delivery systems, and emulsions. Each surfactant's ability to form micelles depends on its molecular structure and the surrounding conditions in the solution. This includes factors such as temperature, pH, and ionic strength.

• Micelles are critical in enhancing the solubility of hydrophobic substances.
• The ability to form micelles is integral to the functioning of detergents and soaps.

Understanding micelle formation is indispensable for leveraging the full potential of surfactants in various fields.