As a chemist, I cannot provide the exact critical micelle concentration CMC of surfactant X without knowing the specific surfactant and its properties. However, I can explain the methods used to determine the CMC of surfactants and the significance of CMC in surface chemistry.The critical micelle concentration CMC is the concentration of surfactants above which micelles form and all additional surfactants added to the solution will be incorporated into micelles. Below the CMC, surfactants exist as monomers in the solution. The CMC is an important parameter in surface chemistry as it helps to understand the behavior of surfactants in solutions and their applications in various industries such as detergents, emulsifiers, and dispersants.There are several methods to determine the CMC of surfactants:1. Conductivity measurements: As surfactants are amphiphilic molecules, they have both hydrophilic and hydrophobic parts. In an aqueous solution, the hydrophilic part interacts with water, and the hydrophobic part tends to avoid water. When the concentration of surfactants reaches the CMC, micelles start to form, and the conductivity of the solution changes. By measuring the conductivity of the solution at different surfactant concentrations and plotting the data, the CMC can be determined as the point where the slope of the curve changes.2. Surface tension measurements: Surfactants can reduce the surface tension of a solution. By measuring the surface tension at different surfactant concentrations and plotting the data, the CMC can be determined as the point where the slope of the curve changes. Below the CMC, the surface tension decreases rapidly with increasing surfactant concentration, while above the CMC, the surface tension remains almost constant.3. Fluorescence spectroscopy: A fluorescent probe can be added to the surfactant solution, and its fluorescence intensity can be measured at different surfactant concentrations. The probe's fluorescence intensity will change when it is incorporated into micelles. By plotting the fluorescence intensity against the surfactant concentration, the CMC can be determined as the point where the slope of the curve changes.4. Light scattering: The formation of micelles can be detected by dynamic light scattering DLS or static light scattering SLS techniques. The intensity of scattered light will change when micelles form in the solution. By measuring the scattered light intensity at different surfactant concentrations and plotting the data, the CMC can be determined as the point where the slope of the curve changes.The significance of CMC in surface chemistry lies in its ability to provide information about the behavior of surfactants in solutions. The CMC is a critical parameter for optimizing the performance of surfactants in various applications, such as detergents, emulsifiers, and dispersants. Understanding the CMC helps to control the aggregation of surfactants, which in turn affects the solubilization, wetting, foaming, and emulsification properties of the surfactant-containing solutions.