Osmotic pressures treatment

Id. Treatment of Data.—Typical osmotic data are shown in Figs. 38 and 39. Here the ratio ( n/c) of the osmotic pressure to the concentration is plotted against the concentration. If the solutions behaved ideally, van t Hoff s law Eq. (11) would apply and m/c should be independent of c. Owing to the large effective size of the polymer molecules in solution (Fig. 34) and the interactions between them which consequently set in at low concentrations, /c increases with c with a... 

The predominant force is that of osmotic pressure, unless both the charge density and the concentration are low. These statements may be substantiated by a simple and approximate mathematical treatment which applies for very dilute solutions. 

In physical chemistry] we were, one must confess, quite in a hurry, while our more aged sister [physics] had already this stage behind it. And so it happened that, first gradually, after we had already enjoyed some results, mathematical-physical treatments followed Max Planck, Duhem, Van der Waals, Lespieaux [sic], Lorentz, Boltzmann but we can rest assured osmotic pressure is well seen by all of them. 12... 

In all hydrodynamic methods we have the effect of both the hydrodynamic and thermodynamic interactions and these do not contribute additively but are coupled. This explains why the theoretical treatment of [77] and of the concentration dependence of has been so difficult. So far a satisfactory result could be achieved only for flexible linear chains [3, 73]. Fortunately, the thermodynamic interaction alone can be measured by static scattering techniques (or osmotic pressure measurement) when the scattering intensity is extrapolated to zero scattering angle (forward scattering). Statistical thermodynamics demonstrate that this forward scattering is given by the osmotic compressibility dc/dn as [74,75]... 

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. 

Osmotic laxatives (e.g., lactulose, sorbitol) are poorly absorbed or nonabsorbable compounds that draw additional fluid into the GI tract. Lumen osmolality increases, and fluid movement occurs secondary to osmotic pressure. Lactulose is a synthetic disaccharide that is poorly absorbed from the GI tract, since no mammalian enzyme is capable of hydrolyzing it to its monosaccharide components. It therefore reaches the colon unchanged and is metabolized by colonic bacteria to lactic acid and to small quantities of formic and acetic acids. Since lactulose does contain galactose, it is contraindicated in patients who require a galactose-free diet. Metabolism of lactulose by intestinal bacteria may result in increased formation of intraluminal gas and abdominal distention. Lactulose is also used in the treatment of hepatic encephalopathy. 

Elementary and advanced treatments of such cellular functions are available in specialized monographs and textbooks (Bergethon and Simons 1990 Levitan and Kaczmarek 1991 Nossal and Lecar 1991). One of our objectives in this chapter is to develop the concepts necessary for understanding the Donnan equilibrium and osmotic pressure effects. We define osmotic pressures of charged and uncharged solutes, develop the classical and statistical thermodynamic principles needed to quantify them, discuss some quantitative details of the Donnan equilibrium, and outline some applications. 

One can also recognize that application of sufficient pressure (above the equilibrium osmotic pressure n) to the right-hand chamber in (7.67) must cause the solvent flow to reverse, resulting in extrusion of pure solvent from solution. This is the phenomenon of reverse osmosis, an important industrial process for water desalination. Reverse osmosis is also used for other purification processes, such as removal of H20 from ethanol beyond the azeotropic limit of distillation (Section 7.3.4). Reverse osmosis also finds numerous applications in wastewater treatment, solvent recovery, and pollution control processes. 

Complete neglect of the Coulomb interaction between charges fixed on the network is also a problem. It has been argued [33] that the contribution from fixed charges to the osmotic pressure plays an important role in determining the swelling equilibrium of gels. However, we will not discuss these theoretical problems further because the main concern of the present article is to clarify experimentally the nature of the first-order transition rather than to improve theoretical treatment. 

The movement of Na+ and glucose from the lumen of the intestine across the epithelial cell to the blood sets up a difference in osmotic pressure across the cell. As a result, water flows through the cell, across the apical and basolateral membranes by simple diffusion. Hence the uptake of water requires both Na+ and glucose (or amino acids) to be present in the lumen of the intestine. The presence of water alone in the lumen of the intestine is much less effective. This is the basis of glucose rehydration therapy as a remedy for dehydration a solution of glucose and salt (NaCl) is administered to the patient. This is a simple, inexpensive but extremely important treatment which has saved the lives of many infants in developing countries who would have otherwise died of the effects of dehydration, usually associated with diarrhea. 

It should be pointed out at this juncture that strict thermodynamics treatment of the film-covered surfaces is not possible [18]. The reason is difficulty in delineation of the system. The interface, typically of the order of a 1 -2 nm thick monolayer, contains a certain amount of bound water, which is in dynamic equilibrium with the bulk water in the subphase. In a strict thermodynamic treatment, such an interface must be accounted as an open system in equilibrium with the subphase components, principally water. On the other hand, a useful conceptual framework is to regard the interface as a 2-dimensional (2D) object such as a 2D gas or 2D solution [ 19,20]. Thus, the surface pressure 77 is treated as either a 2D gas pressure or a 2D osmotic pressure. With such a perspective, an analog of either p- V isotherm of a gas or the osmotic pressure-concentration isotherm, 77-c, of a solution is adopted. It is commonly referred to as the surface pressure-area isotherm, 77-A, where A is defined as an average area per molecule on the interface, under the provision that all molecules reside in the interface without desorption into the subphase or vaporization into the air. A more direct analog of 77- c of a bulk solution is 77 - r where r is the mass per unit area, hence is the reciprocal of A, the area per unit mass. The nature of the collapsed state depends on the solubility of the surfactant. For truly insoluble films, the film collapses by forming multilayers in the upper phase. A broad illustrative sketch of a 77-r plot is given in Fig. 1. 

Fig. 7. Experimental values for the osmotic pressure as a function of separation distance from Ref. [13] (stars water, circles 1 M KC1 triangles 1 M KBr) are compared with calculations that combine the polarization model for hydration forces with the statistical treatment of the undulation, for the following values of the parameters = 9 Debyes, A = 60 A , A = 1 A, o = 0,...

As is well known, the value of A2 obtained from a set of osmotic pressure measurements is much influenced by the treatment of the third virial coefficient As in the series,... 

RTfVw) nNw because yw was set equal to 1. For an exact treatment when many interfaces are present (e.g., in the cytosol of a typical cell), we cannot set yw equal to 1 because the activity of water, and hence the osmotic pressure (n), is affected by proteins, other colloids, and other interfaces. In such a case, Equation 2.11 suggests a simple way in which a matric pressure may be related to the reduction of the activity coefficient of water caused by the interactions at interfaces. Equation 2.11 should not be viewed as a relation defining matric pressures for all situations but rather for cases for which it might be useful to represent interfacial interactions by a separate term that can be added to Fly, the effect of the solutes on FI. 

Just as in the treatment of osmotic pressure and light scattering, a power series can be used to fit the relative viscosity data, which at low concentrations can be truncated after a couple of terms (Equation 12-42) ... 

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