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GATE 2024 CY – Question 18

Physical Chemistry · Surfaces and Interfaces: Physisorption and chemisorption. Langmuir, Freundlich and Brunauer-Emmett-Teller (BET) isotherms. Surface catalysis: Langmuir-Hinshelwood mechanism. Surface tension, viscosity, Self- assembly/ physical chemistry of colloids, micelles and macromolecules. · 1 mark · Multiple choice

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

  1. 0.010
  2. 0.001
  3. 0.008
  4. 0.088

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Correct answer: (B) 0.001

Explanation

Below the **critical micelle concentration (CMC)** the surfactant exists as free molecules (monomers). Above it, the extra surfactant forms micelles while the monomer concentration stays at about the CMC.

**Step 1: surfactant in micelles.**
$$[S]_{micelle}=0.088-0.008=0.080\text{ M}.$$

**Step 2: concentration of micelles.** Each micelle contains 80 surfactant molecules (the aggregation number):
$$[\text{micelles}]=\frac{0.080}{80}=\mathbf{0.001\ M}.$$