For nonylglucoside, NG, thermodynamic data for demicellization in water are presented in problem 17.26. Model the micelle reaction as n_S ⇆ M_n where S is free surfactant and M_n is a micelle. Treat the solution as an ideal solution. Vary the total concentration of NG from 0 up to 20 mmol/L. Water is 55.5 mol/L. Calculate mole fractions and molar concentrations (mmol/L) of the free surfactant (in mM) and the micelles (in μM) of NG at T=285 K, where n = 58. Plot curves for the concentrations. Identify the approximate CMC in mmol/L. Hint to simplify calculations: The mol/L added is very small relative water molarity (55.5 mol/L). The density can be assumed to be constant.

Data from problem 17.26:

Surfactants clump together to form organized structures called micelles that can be spheres, rods, and so forth. The formation of the clump can be modeled as a “chemical” reaction, though there are no chemical bonds formed or broken. When surfactants are in solution below the critical micelle concentration, CMC, the surfactant molecules are almost all “free” in solution. At the CMC, micelles start to form. Above the CMC, the amount of free surfactant is almost constant in solution and as more surfactant is added to the solution, more micelles form. It is conventional to provide the property changes of surfactants per mol of surfactant molecules, not per mole of micelle.

Given the data below for nonylglucoside (NG) demicellization in water, calculate the micellization value, ΔCP_mic, as a function of temperature. Is the heat capacity of a micelle greater than or less than the heat capacity of the molecules that make up the micelle?

Calculate ΔS_mic and for the surfactant as a function of temperature. Is the overall solution (including water) more ordered or less ordered after micellization?

NG data:

Transcribed Image Text:

T (K) 285 293 303 313 AH demic (kJ/mol) AG demic (kJ/mol) AC Pic (kJ/mol-K) -13.53 20.03 -9.00 20.78 -3.50 21.60 0.07 22.37