Powerful surfactants like commercial soaps associate to form distinct micelles specifically above th — Surface Chemistry Chemistry Question
Question
Powerful surfactants like commercial soaps associate to form distinct micelles specifically above their Critical Micelle Concentration (CMC). For typical soap solutions, the CMC drastically alters solution properties and falls precisely in the range of $10^{-x}\text{ to }10^{-y}\text{ mol L}^{-1}$, where $x$ and $y$ are positive integers and $x > y$. Calculate the numerical product $x \times y$.
💡 Solution & Explanation
The critical micelle concentration (CMC) is an important thermodynamic threshold. For standard soaps, this vital concentration range is established to be exactly $10^{-4}\text{ to }10^{-3}\text{ mol L}^{-1}$. By mapping this to the expression $10^{-x}\text{ to }10^{-y}$, we strictly identify $x = 4$ and $y = 3$. Their mathematical product is $4 \times 3 = 12$.