Discussion
Critical micellar concentration of a surfactant is 0.008 M in water at 25 °C. If the aggregation number of the micelles is 80, the concentration of the micelles (in M) present in 0.088 M aqueous solution of the surfactant at 25 °C is
Answer: B
The micelle concentration is 0.001 M.
Above the critical micelle concentration, surfactant in excess of the CMC goes into micelles, while the CMC amount stays as free monomer:
\[ \begin{aligned} [\text{surfactant in micelles}] &= 0.088 - 0.008 = 0.080\ \text{M} \\ [\text{micelles}] &= \frac{0.080}{80} = 0.001\ \text{M} \end{aligned} \]
Dividing the full 0.088 M by 80 gives 0.0011 M, close but not the intended value; 0.008 M is the CMC itself and 0.088 M the total concentration, neither of which is a micelle concentration.
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