Let  be the concentration-scale standard equilibrium constant for the equilibrium  between...

Let  be the concentration-scale standard equilibrium constant for the equilibrium  between monomers and micelles in solution, where L is an uncharged species (for example, a polyoxyethylene). (a) Let c be the stoichiometric concentration of the solute (that is, the number of moles of monomer used to prepare a liter of solution) and let x be the concentration of micelles at equilibrium: x = [Ln], where the brackets denote concentration. Show that  Assume all activity coefficients are 1. (b) Let fbe the fraction of L present as monomer. Show that f = 1 ‒ nx/c. (c) For n = 50 and  = 10200, calculate and graph [L], n[Ln], and f as functions of c. (Hint: Calculate c for various assumed values of x, rather than the reverse.) (d) If the cmc is taken as the value of c for which f = 0.5, give the value of the cmc.