CHL721 Adv Chem Engg ThermodynamicsHW #8 Due date: 27th April, 2015 (in lecture)(* all equation numbers below are w.r.t Ch-2 of Barret & Hansen)Q1: Thermodynamics of micelle formationa. Assuming ideal gas statistics, derive the entropic contribution to surface free energy in eq. 2.101b. Starting with eq. 2.106, show that chemical potential can be expressed in form given in eq. 2.107.

Q2: Spherical MicellesEach sodium dodecyl sulfate surfactant (SDS) molecule in a spherical micelle can be visualized as a cone of fixed volume and variable head-group area . In the micellar form, the internal interaction free energy per molecule can the be written as

where, * signifies values corresponding to the minimum of free energy.a. Show that aggregation number for a spherical micelle of radius R can be written as .b. Now use a Taylor series expansion up to 2nd order in aggregation number to express internal free energy as , where C is a constant. Also find C in terms of known parameters (, , ).c. Now starting at eq. 2.108 and using the result derived in part (b) above, derive an expression for distribution of surfactant mole fraction about . Determine the corresponding standard deviation.d. Determine numerical value of standard deviation and make a plot of versus given following data for SDS: , , .