118. Solving a chemistry problem

Determine the molar mass and aggregation number of micelles of sodium deoxycholate (one of the components of bile salts responsible for digestion of food, molecular weight 414.6 g/mol) using the data of equilibrium centrifugation. The data include: temperature 200C, solvent density (0.3 mol/l NaCl) 1.0104 g/cm3, specific partial volume of micelles 0.76 cm3/g, angular velocity 1318 s-1. The design of the centrifuge made it possible to measure the concentration gradient dc/dx and the concentration at a certain distance x from the rotation axis. At x=6.8712 cm c=0.07845 g/dl and dc/dx=0.1080 (g/dl)/cm were determined. (Note that the concentration unit is irrelevant for the solution).