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What is the critical micelle concentration (CMC) of sodium dodecyl sulfate (SDS) in water at 25°C, given that the molar mass of SDS is 288.4 g/mol and its molecular formula is C12H25NaO4S? Also, explain the mechanism of micelle formation in this process.

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The critical micelle concentration  CMC  of sodium dodecyl sulfate  SDS  in water at 25C is approximately 8.2 x 10^-3 mol/L or 8.2 mM. This value can vary slightly depending on the source, but it is generally accepted to be around this concentration.Micelle formation is a process in which amphiphilic molecules, like SDS, spontaneously aggregate in an aqueous solution to minimize the contact between their hydrophobic parts and water. SDS has a polar sulfate head group  hydrophilic  and a long hydrocarbon tail  hydrophobic . When the concentration of SDS in water reaches the CMC, the amphiphilic molecules begin to aggregate into spherical structures called micelles.In a micelle, the hydrophobic tails are sequestered in the interior, while the hydrophilic head groups face the surrounding water. This arrangement minimizes the contact between the hydrophobic tails and water, thus reducing the overall free energy of the system. Micelles can solubilize hydrophobic molecules in their core, which is one of the reasons they are used in various applications, such as detergents and drug delivery systems.The CMC is an important parameter because it indicates the concentration at which micelles begin to form. Below the CMC, the amphiphilic molecules exist primarily as monomers in the solution. Above the CMC, micelles are formed, and the concentration of monomers remains relatively constant.
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