JEE Main · ChemistryHard
In the context of micelle formation, the critical micelle concentration (CMC) is influenced by the length of the hydrocarbon chain. Which of the following statements correctly describes the relationship between the chain length and the CMC?
- A.CMC increases linearly with the number of carbon atoms in the chain.
- B.CMC decreases exponentially with the number of carbon atoms in the chain.
- C.CMC remains constant regardless of the chain length.
- D.CMC increases exponentially with the number of carbon atoms in the chain.
Show correct answer & step-by-step solution
Correct answer: B — CMC decreases exponentially with the number of carbon atoms in the chain.
Solution
- Micelle formation is driven by the hydrophobic effect of the hydrocarbon chains.
- The free energy of micellization is related to the chain length by .
- The CMC is related to the free energy by .
- Substituting the expression for shows that decreases linearly with .
- Therefore, the CMC decreases exponentially as the number of carbon atoms increases.
- Hence the answer is (B).
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