Osmotic Pressure Data

The activity of the solvent can be related to the osmotic pressure using the following equation. 

V1 = molar volume of solvent, cubic meters per kilomole R = gas constant = 8314.0 (Pa)(m3) / (kmol) (K) 

Then the weight fraction activity coefficient of the solvent is given by 

Shiomi et al. (1980) provide osmotic pressure poly(dimethylsiloxane) (PDMS) system at 293.15 K. 

Input data methyl ethyl ketone = 1, PDMS = 

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Figure 8.9 is a plot of osmotic pressure data for a nitrocellulose sample in three different solvents analyzed according to Eq. (8.87). As required by Eq. (8.88), all show a common intercept corresponding to a molecular weight of 1.11 X 10 the various systems show different deviations from ideality, however, as evidenced by the range of slopes in Fig. 8.9. 

Figure 8.9 Osmotic pressure data plotted as n/RTc2 versus concentration for nitrocellulose in three different solvents. [Data from A. Dobry,/. Chem. Phys. 32 50 (1935).]...

Use the method described in Problem 9 to obtain values of and p from these data. How do the values of these parameters compare with the values obtained for the same system from osmotic pressure data in Problem 8 ... 

Fig. 59. Agreement between LS data and osmotic pressure data for solutions of sucrose in water ) at...

TABLE 15.1. Osmotic Pressure Data for Polyvinyl Acetate in Methyl Ethyl Ketone at 10°C... 

Table 15.1 contains osmotic pressure data calculated from the work of Browning and Ferry [3] for solutions of polyvinyl acetate in methyl ethyl ketone at 10°C. Plot H/vv against w, fit the data to a quadratic polynomial, and calculate the number-average molar mass from the intercept with the n/w axis. 

Krigbaum, W.R. and Flory, P.J. 1952. Treatment of osmotic pressure data. J. Polym. ScL, 9 503. Kulichke, W. 2004. Viscometry of Polymers and Polyelectrolytes. Springer, New York. 

Now we compare the above osmotic pressure data with the scaled particle theory. The relevant equation is Eq. (27) for polydisperse polymers. In the isotropic state, it can be shown that Eq. (27) takes the same form as Eq. (20) for the monodisperse system though the parameters (B, C, v, and c ) have to be calculated from the number-average molecular weight M and the total polymer mass concentration c of a polydisperse system pSI in the parameters B and C is unity in the isotropic state. No information is needed for the molecular weight distribution of the sample. On the other hand, in the liquid crystal state2, Eq. (27) does not necessarily take the same form as Eq. (20), because p5I depends on the molecular weight distribution. 

We now illustrate the use of the equations developed in Section 3.2 for interpreting osmotic pressure data. Figure 3.5 shows examples of two plots of -k/RTc versus concentration. In Figure 3.5a the data all describe different molecular weight fractions of the same solute, cellulose acetate, in acetone solutions. Since the lines in this plot all have essentially the same slope, B must be the same for each. 

Discuss the reasons why it is so difficult to obtain meaningful osmotic pressure data in salt-free solutions. Consider specifically the reconciliation of the electrolyte-free aspect of the experiment with the accurate control of pH. 

The author is indebted to R. T. Guliana for the osmotic pressure data and intrinsic viscosities, to G. A. Tirpak for the infrared measurements, and to R. D. HoflFman for the melt viscosities. 

Since polymer solutions are markedly non-ideal, osmotic pressure data are taken at low concentrations and are extrapolated to infinite dilution (c — 0). In the case of membrane osmometry, the relevant equation is... 

Figure 2.3 Typical osmotic pressure data, where solvent A is a very good solvent (strong polymer-solvent interactions), B is a moderately good solvent, and C is a 0 solvent (in which polymer-solvent interactions have been adjusted to nullify the excluded volume effect).31a Reprinted with permission from J. E. Mark, Physical Chemistry of Polymers, ACS Audio Course C-89, American Chemical Society, Washington, DC, 1986. Copyright 1986, American Chemical Society.

Another viable method to compare experiments and theories are simulations of either the cell model with one or more infinite rods present or to take a solution of finite semi-flexible polyelectrolytes. These will of course capture all correlations and ionic finite size effects on the basis of the RPM, and are therefore a good method to check how far simple potentials will suffice to reproduce experimental results. In Sect. 4.2, we shall in particular compare simulations and results obtained with the DHHC local density functional theory to osmotic pressure data. This comparison will demonstrate to what extent the PB cell model, and furthermore the whole coarse grained RPM approach can be expected to hold, and on which level one starts to see solvation effects and other molecular details present under experimental conditions. 

Add the appropriate boxes and connectors to Figure 12.10 to illustrate the calculation of mole-related quantities from (a) vapor-pressure depression data, (b) freezing-point lowering data, (c) boiling-point elevation data, and (d) osmotic pressure data. 

FIGURE 12-7 Plot of osmotic pressure data for solutions of polyisobutylene in chlorobenzene [replotted from J. Leonard and H. Doust, J. Pofym. Sci., 57,53 (1962)1. 

FIGURE 12-8 Plot of osmotic pressure data [replotted from the data of Leonard and Doust, J. Polym. Set., 57,53(1962)]. 

Kalyuzhnyi, Yu.V., Rescic, J., and Vlachy, V. Analysis of osmotic pressure data for aqueous protein solutions via a one-component model. Acta Chimica Slovenica, 1998, 45, No. 2, p. 194-208. 

Figure 5.7(b) demonstrates that the functional form of Eq. (5.43) reduces osmotic pressure data at various M and 6 (or c) to a universal curve. The limiting scaling laws of II (/> or II are only valid sufficiently far from the overlap concentration. Near (f> (and more generally near any crossover point), a more complicated functional form than a simple power law is needed. For osmotic pressure in a good solvent (and many other examples) the full functional form of Eq. (5.43) is well described by a Simple sum of the two limiting behaviours ... 

Concentration dependence of osmotic pressure data for five poly(a methyl styrene)s in the good solvent toluene at 25 °C. (a) Raw data—the data below c for the lowest three molar masses are... 

For experiments with proteins, this theory, together with data for osmotic pressure, also aids in explaining the rather unusual response of ultrafiltration rate to pressure and the virtual Independence of this response from fiber length and axial flow velocity. Osmotic pressure data are available in the literature for bovine serum albumin at pH 7.4 ( ), and osmotic pressure measurements of moderate accuracy were made by the authors on bovine calf serum. 

Our own osmotic pressure data for calf serum at 37°C can be expressed by a 2-parameter power series (14). 

Osmotic pressure limited ultrafiltration data were analyzed by using Eq. (92) and the osmotic pressure data of Vllker (1975) for 0.15M Saline BSA solutions at pH 7.4. Vilker s data are reproduced in Fig. 5 for BSA in both 7.4 and 4.5 pH 0.15M saline solution. The comparison between theory and experiment is quite good as shown in Table I where the value of D was taken as 6.91 x 10 cm /sec. 

Problem 3.6 The osmotic pressure data for polystyrene of molecular weight 1.6x10 yielded, according to Eq. (3.72), the following values for the second virial coefficient (a) 2.88x10 mol cm in dichloroethane and (b) —0.37x10 mol cm in cyclohexane, both at 22°C. Determine x for the polymer-solvent systems. Which is a better solvent ... 

The linearity of the osmotic pressure data above O.lg/dl (see figure 1) may indicate that above this critical concentration, the "monomeric" pectin concentration is practically constant whereas it changes with total polysaccharide concentration below the critical concentration. Ionic detergents behave in this fashion. 

For low values of flux, c, can be predicted from Eq. (30.53) using standard correlations for K, and then using osmotic pressure data to get An, Ap can be calculated from Eq. (30.50). If Ap is specified, a trial-and-error calculation is needed to get V. Either approach shows that v should be nearly proportional to Ap for... 

Because of concentration polarization, the permeate flux is a nonlinear function of AP, and a trial-and-eror solution is needed to calculate v for a given AP. However, when there is complete rejection of the solute and no gel resistance, for a specified volume flux of the solvent, equation (9-87) can be used to determine c, osmotic pressure data to get Ajc, and equation (9-83) to calculate the required AP. 

Osmotic Pressure Data for Some Aqueous Solutions at Standard Temperature... 

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