Freezing point depression, delta T/k, and pNa are measured and analyzed for aqueous solutions of trihydroxy (NaTC) and dihydroxy (NaDC and NaTDC) bile salts. The results show the existence of break points in the plot of delta T/k vs molality at 0.018, 0.013, and 0.007 m, respectively, in good agreement with previous published critical micelle concentration values. Above the break point bile salts form aggregates with average aggregation numbers of 2.59 +/- 0.12 (NaTC), 5.82 +/- 0.04 (NaDC), and 5.42 +/- 0.47 (NaTDC). Fractions of bound counterions are also deduced, being close to 0.3 for the three bile salts studied. This indicates that only one counterion is bound for every three monomers in the aggregate. The different structural models published for the bile salt aggregates are discussed.

No abstract

The determination of the molecular weight is one of the most i m~o r t a n t laboraton, methods for characterizing anv -.chemical compound. I t is not therefore surprising that a wide variety of methods are described in the educational literature. This area is particularly important for polymer characterization a s recoenized in a recent monomaoh (1) and papers hy Mathias 'i2) and Hardgrove et a c (3j who include one molecular weight determination for polymer and physical chemistry laboratory courses. Table 1 lists molecular weight determinations of polymers published hv -. . this Journal. Light-scattering techniques are very important in polymer characterization (1, 4, 5 ) in providing information about molecular weight, polydispersity, polymer size and shape, intermolecular interactions, and diffusion coefflcient-hydrodynamic radius. However, only two papers (6, 7) and one general physical chemistry laboratory textbook (8) describe the technique and propose systems to he studied. Such a low numher of descriptions may be related to the relatively high cost of commercial equipment. In his textbook, White (8) describes the construction of a light--scattering apparatus and proposes the measurement of oolv(vinvl acetate) in acetone solution. The e a u i~m e n t cite"d by Mathias (6) and Matthews (7) are commLrEia~ instruments.More common than light-scattering equipment in chemistry laboratories are fluorescence spectrometers. In the present paper we suggest the use of the Rayleigh scattering band for an introduction to the light-scattering technique. The use of the same apparatus for obtainingdifferent physicochemical parameters is economical and has an important educational impact. Polyethylene glycols (PEG'S) of different molecular weights were chosen for study because they are readily available, inexpensive, easily soluble in water (avoiding the use of organic solvents), and innocuous. Theoretical BackgroundBecause a simple analysis of the interaction of the incident light with the sample was given by White (8) and Atkins (9). we will only summarize the eauations and their physicochemical meanings. Experimental results are usuallv exoressed in terms of the inverse of the increase of the . .Rayleigh scattering ratio of the solution with respect to the solvent, AR,, according to where C is the solute concentration in dmL: M... is its molecular weight;A2 is the second virial cGfficikn<~(q) is the particle-scattering factor; and $ is the scattering angle. K is given by '~uthor to whom correspondence should be addressed. 284Journal of Chemical Education Figure 1. Concentrati0n:intensity ratio vs. concentration of 12-TSA in 0.3 M NaCI.where NA is Avogadro's numher; n, is the refractive index of the solvent; h, is the wavelength of the incident light;and dn1dC is the variation of the refractive index with solute concentration. Finally, q is the magnitude of the scattering-wave vector given by (9) In the limit of small q(R$W, where (R$l" is the radius of gyration of the scattering particle, and independently of its shap...

Experimental procedure using light-scattering intensity measured with a spectrofluoroimeter to determine micellar molecular weight, shape, and dimensions; includes data and analysis.

No abstract