OSMOTIC PRESSURE AND DENSITY

The freezing point, temperature of maximum density, osmotic pressure and specific heat for seawater of various salinities are given in Table 21.23. 

A sample consisting of 155 mg of a purified protein is dissolved in 10.0 mL of ethanol. This solution is placed in a device for measuring osmotic pressure and rises to a final height of 32.5 cm above the level of pure ethanol. The experiment is performed at 1.00 atm and 298 K. The density of ethanol at 298 K is 0.79 g-cm "3. What is the molar mass of the protein Assume that the density of the solution is the same as that of pure ethanol. See Exercise 8.95. 

K and a in the expression, [17] = KM , are 3.7 x 10-5 m3 kg-1 and 0.62, respectively, for this polymer-solvent system. Assuming a constant density for the solutions, calculate an average relative molecular mass for the polystyrene sample. How would this relative molecular mass be expected to compare with the relative molecular mass of the same sample of polystyrene in toluene determined from a) osmotic pressure and (b) light-scattering measurements ... 

A number of experimental techniques by measurements of physical properties (interfacial tension, surface tension, osmotic pressure, conductivity, density change) applicable in aqueous systems suffer frequently from insufficient sensitivity at low CMC values in hydrocarbon solvents. Some surfactants in hydrocarbon solvents do not give an identifiable CMC the conventional properties of the hydrocarbon solvent solutions of surfactant compounds can be interpreted as a continuous aggregation from which the apparent aggregation number can be calculated. Other, quite successful, techniques (light scattering, solubilization, fluorescence indicator) were applied to a number of CMCs, e.g., alkylammonium salts, carboxylates, sulfonates and sodium bis(2-ethylhexyl)succinate (AOT) in hydrocarbon solvents, see Table 3.1 (Eicke, 1980 Kertes, 1977 Kertes and Gutman, 1976 Luisi and Straub, 1984 Preston, 1948). 

What is the interaction energy as a function of separation of a periodic array of flat plates with a fixed charge density oq and a spacing 2D Compute this explicitly from the free energy using the solution for n(z). Find the longitudinal osmotic pressure and compare with osmotic pressure derived above nt = Tn 0). 

For qualitative understanding of the origin of oscillatory fluid flow, one has to examine the role of (i) density gradient, (ii) osmotic pressure and (iii) interfacial tension, if any. 

Figure 6 shows the potential of mean force (PMF) between a sodium ion and a chloride ion in water, at infinite dilution of the two ions, obtained from classical atomistic simulations [75]. The first minimum of the potential corresponds to the contact ion pair (CIP) distance, the second minimum corresponds to the solvent-shared ion pair (SIP) distance, and the third minimum to the solvent-separated ion pair (2SIP) distance. Figure 7a shows an example of a SIP in aqueous NaCl [75]. The infinite dilute potential of mean force in Fig. 6 can be used as an effective pah-potential in implicit solvent simulations. The osmotic coefficient (j) (ps) = nilpJc- T (with n the osmotic pressure and ps the salt number density) can be obtained through the virial route. For the case of a binary mixture of components i and j and pairwise additive, density-independent pair potentials, the virial equation can be expressed as... 

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