Which of the following is the correct range of critical micelle concentrations (CMC) for soaps?

$10^{-4}$ to $10^{-3}$ mol/L

The correct answer is Option 4. $10^{-4}$ to $10^{-3}$ mol/L.

CMC is the concentration at which surfactant molecules in a solution begin to aggregate into micelles. Before reaching this concentration, surfactant molecules exist primarily as individual molecules in solution.

Micelles: These are spherical structures formed when the hydrophobic (water-repelling) tails of surfactant molecules cluster together to minimize their exposure to water, while the hydrophilic (water-attracting) heads face outward, interacting with the water.

Factors Affecting CMC

Nature of the Surfactant: Different surfactants have different hydrophilic-lipophilic balance (HLB) values, which influence their CMC. For example, soaps, which are fatty acid salts, tend to have a CMC in a specific range due to their molecular structure.

Temperature: CMC generally decreases with increasing temperature because higher temperatures provide more energy for the surfactant molecules to overcome the energy barrier for micelle formation.

Ionic Strength: The presence of electrolytes in solution can affect the CMC. For ionic surfactants like soaps, increased ionic strength usually lowers the CMC, as the ions screen the electrostatic repulsion between charged heads.

CMC Range for Soaps

Typical Range: For most soaps, the CMC falls within 10⁻⁴ to 10⁻³ mol/L. This range is typical for ionic surfactants, where the long hydrophobic tails and the polar head groups contribute to the micellization process.

Why the Other Ranges are Not Suitable:

1. 10² to 10⁴ mol/L: This range is too high. Such concentrations would be unusual for any surfactant to reach micelle formation. Typically, concentrations this high may lead to saturation rather than micelle formation.

2. 10⁻⁵ to 10⁻⁸ mol/L:

This range is too low for soaps. While some highly soluble surfactants might have lower CMCs, soaps generally require a higher concentration to reach micelle formation due to their larger molecular size and structure.

3. 10⁻¹ to 10⁻³ mol/L:

While this range may encompass some surfactants, it does not specifically reflect the common CMC values for soaps, which are better captured in the 10⁻⁴ to 10⁻³ mol/L range.

Conclusion

The CMC is an essential parameter in understanding the behavior of surfactants, particularly in applications such as cleaning, emulsification, and stabilization of colloidal systems. For soaps, their typical CMC range of 10⁻⁴ to 10⁻³ mol/L reflects the balance between their hydrophilic and hydrophobic properties, allowing them to effectively form micelles in aqueous solutions.