You have developed a model for the formation of micelles, based on expressions f

Question

You have developed a model for the formation of micelles, based on expressions for the chemical potential mu(mono) of the free monomeric molecules in solution and the chemical potential mu(mic) of the aggregated state of the monomers in micelles as a function of the mole fraction x of monomers in solution: mu(mono) = 0.5 + 0.1x^2 and mu(mic) = 1.3 - 25 X^2. (a) What is the state of the system at low concentration? (b) What is the state of the system at high concentration? (c) What is the concentration at which the micelle transition occurs?

Explanation / Answer

a) At low concentrations system remain in mono form as enough molecules are not available

b) high concentration allows molecules to come together and aggregate to form micelle

c) for transition, chem potential mono= micelle

0.5+0.1x2=1.3-25x2

25.1 x2=0.8

x= 0..1785

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