Osmotic pressure concentration dependence

The lowering of freezing point and the generation of osmotic pressure both depend on the total concentration of solute particles. Therefore, by using the colligative property to determine the amount of solute present, and knowing its mass, we can infer its molar mass. 

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. 

A nonadsorbing polymer added to dispersions will often cause aggregation of particles. Asakura and Oosawa were the first to describe the cause of this instability as two particles approach the finite size of the polymer chains ensures their exclusion from the region between the two particles. The osmotic pressure is dependent on the concentration of macromolecule and hence it is diminished in this overlap region. The excess osmotic pressure in the main bulk fiuid causes the two particles to be pushed together. This is called the depletion potential and has been extensively studied.This is shown in Fig. 6. 

The effect of osmotic pressure in macromolecular ultraflltra-tlon has not been analyzed in detail although many similarities between this process and reverse osmosis may be drawn. An excellent review of reverse osmosis research has been given by Gill et al. (1971). It is generally found, however, that the simple linear osmotic pressure-concentration relationship used in reverse osmosis studies cannot be applied to ultrafiltration where the concentration dependency of macromolecular solutions is more complex. It is also reasonable to assume that variable viscosity effects may be more pronounced In macromolecular ultra-filtration as opposed to reverse osmosis. Similarly, because of the relatively low diffuslvlty of macromolecules conqiared to typical reverse osmosis solutes (by a factor of 100), concentration polarization effects are more severe in ultrafiltration. 

Boiling point, vapor pressure, and osmotic pressure all depend on particle concentration Therefore, these solutions also have the same boiling point, osmotic pressnre, and vapor pressure. 

The osmotic pressure tt depends upon the difference in molar concentration, i.e. the difference in the numbers of solute molecules in equal volumes of both solutions. The type of solute (sugar, salt, or a particular protein) is irrelevant. This reminds us of the ideas behind the model of ideal gases, where gas pressure is independent of the type of gas. However, the equation does assume that the solute does not dissociate or otherwise react with the solvent, since this would alter the number of particles per unit volume of solution. 

COlligative property A property of a solvent (vapor-pressure lowering freezing-point lowering boiling-point elevation osmotic pressure) that depends on the total concentration of solute particles present. (Section 13.5)... 

All solutions exhibit osmotic pressure, which is another colligative properly. Osmotic pressure is a pressure difference between the system and atmospheric pressure. The osmotic pressure of a system can be measured by applying enough pressure to stop the flow of water due to osmosis in the system. The difference between the applied pressure and atmospheric pressure is the osmotic pressure. When pressure greater than the osmotic pressure is applied to a system, the flow of water can be reversed from that of osmosis. This process can be used to obtain useful drinking water from seawater and is known as reverse osmosis. Osmotic pressure is dependent only on the concentration of the... 

Osmotic pressure is the external pressure that must be applied to stop osmosis. In the example given above, osmosis caused the level of the solution to rise until the height of the solution provided the pressure necessary to stop osmosis. Because osmotic pressure is dependent on the concentration of solute particles and not on the type of solute particles, it... 

Sodium ar chloride comprise the bulk of the electrolytes in plasma and interstitial fluid. Sodium constitutes 90 % of the total base of the plasma, the normal concentration being 140 meq. per liter. The normal concentration of chloride is 104 meq. per liter. The sodium ion plays an important role in the maintenance of acid-base equilibrium and in the maintenance of osmotic pressure, which depends largely on total base. Cations in blood, other than sodium, are calcium, potassium, and magnesium anions, other than chloride, are bicarbonate, protein, and small amounts of organic acid. The pH is usually regulated by the relative amounts of chloride and bicarbonate. Acidosis and alkalosis are encountered in many diseases of man, but these problems belong in the fleld of clinical medicine rather than nutrition and will not be discussed here. 

Detailed osmotic studies by Mandel et al. [140] on NaPSS yield an exponent of 9/8 at low concentration and 9/4 at high concentration of the osmotic pressure-concentration power law (n c ) which again was interpreted as a dilute-semidilute concentration transition. A recent literature study [66] confirmed the experimental scaling exponents but clearly demonstrated that the cross-over concentration does not depend on the molar mass of the polyions. 

Next, we consider the situation in a salt free polyelectrol5d e network. Since charge neutrality is preserved within the gel due to the strong Coulomb forces, the counter-ions carmot leave this phase and, therefore, produce their full osmotic pressure. It depends on their concentration 4>ioCm as... 

This is the so called van t Hoff equation (Jacobus van t Hoff, first Nobel prize in chemistry for his work on chemical dynamics and osmotic pressure, 1901). Note that the osmotic pressure only depends on the molar concentration of component B and temperature (under the approximations we have made in the course of the derivation). Here osmotic pressure is another example for a colligative property. 

It must be kept in mind that both pictures are modelistic and invoke extrather-modynamic concepts. Except mathematically, there is no such thing as a two-dimensional gas, and the solution whose osmotic pressure is calculated is not uniform in composition, and its average concentration depends on the depth assumed for the surface layer. 

By describing the concentration dependence of an observable property as a power series, Eq. (9.9) plays a comparable role for viscosity as Eq. (8.83) does for osmotic pressure. 

Thus we have finally established how light scattering can be used to measure the molecular weight of a solute. The concentration dependence of r enters Eq. (10.54) through an expression for osmotic pressure, and this surprising connection deserves some additional comments ... 

Salt flux across a membrane is due to effects coupled to water transport, usually negligible, and diffusion across the membrane. Eq. (22-60) describes the basic diffusion equation for solute passage. It is independent of pressure, so as AP — AH 0, rejection 0. This important factor is due to the kinetic nature of the separation. Salt passage through the membrane is concentration dependent. Water passage is dependent on P — H. Therefore, when the membrane is operating near the osmotic pressure of the feed, the salt passage is not diluted by much permeate water. 

The properties of a solution differ considerably from those of the pure solvent Those solution properties that depend primarily on the concentration of solute particles rather than their nature are called colligative properties. Such properties include vapor pressure lowering, osmotic pressure, boiling point elevation, and freezing point depression. This section considers the relations between colligative properties and solute concentration, with nonelectrolytes that exist in solution as molecules. 

The concentration (and therefore the osmotic pressure) of the solution depends on the extent of the surface. The definition ... 

In physical chemistry, we apply the term colligative to those properties that depend upon number of molecules present. The principal colligative properties are boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. All such methods require extrapolation of experimental data back to infinite dilution. This arises due to the fact that the physical properties of any solute at a reasonable concentration in a solvent are... 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

In accordance with observed data, this model shows that water flux increases linearly with applied pressure AP, decreases with higher salt concentration through its impact on osmotic pressure Jt, increases with a smaller membrane thickness I, and increases with temperature through the temperature dependence of the water permeability P . The model also demonstrates that the solute or salt flux J, increases linearly with applied pressure AP, increases with higher salt concentration c , increases with a smaller membrane thickness I, and increases with temperature through the temperature dependence of the solute permeability Pj. Polarization, as described early in this section, causes the wall concentration c to exceed the bulk concentration ci,. 

A phenomenon that is particularly important in the design of reverse osmosis units is that of concentration polarization. This occurs on the feed-side (concentrated side) of the reverse osmosis membrane. Because the solute cannot permeate through the membrane, the concentration of the solute in the liquid adjacent to the surface of the membrane is greater than that in the bulk of the fluid. This difference causes mass transfer of solute by diffusion from the membrane surface back to the bulk liquid. The rate of diffusion back into the bulk fluid depends on the mass transfer coefficient for the boundary layer on feed-side. Concentration polarization is the ratio of the solute concentration at the membrane surface to the solute concentration in the bulk stream. Concentration polarization causes the flux of solvent to decrease since the osmotic pressure increases as the boundary layer concentration increases and the overall driving force (AP - An) decreases. 

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