Osmotic membrane equilibrium

A semi-permeable membrane, which is unequally permeable to different components and thus may show a potential difference across the membrane. In case (1), a diffusion potential occurs only if there is a difference in mobility between cation and anion. In case (2), we have to deal with the biologically important Donnan equilibrium e.g., a cell membrane may be permeable to small inorganic ions but impermeable to ions derived from high-molecular-weight proteins, so that across the membrane an osmotic pressure occurs in addition to a Donnan potential. The values concerned can be approximately calculated from the equations derived by Donnan35. In case (3), an intermediate situation, there is a combined effect of diffusion and the Donnan potential, so that its calculation becomes uncertain. 

As we discussed in Section 3.2, samples of solution and solvent separated by a semipermeable membrane will be at equilibrium only when the solution is at a greater pressure than the solvent. This is the osmotic pressure. If the solution is under less pressure than the equilibrium osmotic pressure, solvent will flow from the pure phase into the solution. If, on the other hand, the solution is under a pressure greater than the equilibrium osmotic pressure, the pure solvent will flow in the reverse direction, from the solution to the solvent phase. In the last case, the semipermeable membrane functions like a filter that separates solvent from solute molecules. In fact, the process is referred to in the literature by the terms hyperfiltration and ultrafiltration, as well as reverse osmosis (Sourirajan 1970) however, the last term is enjoying common use these days. 

If a solution is placed on one side of a semipermeable membrane and water is placed on the other side, then there is a natural tendency (oj/nwi.t) for waler to diffuse through the membrane lo the solute side until an equilibrium osmotic pressure is reached. 

Let the equilibrium pressures in the left and right chambers be P and P + n, respectively. We call II the osmotic pressure. It is the extra pressure that must be applied to make p,A in the solution equal to i% so as to achieve membrane equilibrium for species A between the solution and pure A. If the solution in the right chamber is dilute enough to be considered... 

These basic quantities are derived from the results of two fundamental experiments the measure of the osmotic pressure II of the solution, at membrane equilibrium with the solvent, and the measure of the intensity scattered by the solution at constant pressure. 

In the dilute case, the osmotic pressure was measured at membrane equilibrium, with the help of an osmometer (Chapter 5, Section 1.9). 

Polyelectrolyte molecules in highly dilute aqueous solutions exert strong electrical repulsions on each other. These repulsive forces are long range (proportional to l/r ) by comparison with normal dispersion forces (proportional to 1/r ), and as a consequence the intermolecular interactions persist down to the lowest measured concentrations. In osmotic-pressure measurements on polyelectrolytes, the Donnan membrane equilibrium must be satisfied and experimental results indicate that the second virial coefficient in the osmotic-pressure equation (p. 915) becomes very large. 

At the beginning of an osmotic experiment, the difference in heights A/z observed after filling both chambers of the osmometer does not correspond to the osmotic pressure at equilibrium. The equilibrium pressure is only observed after solvent molecules permeate the membrane. If A/z is greater than the equilibrium osmotic pressure, the solvent molecules permeate from the solution chamber into the solvent chamber, and in the reverse direction if A/z is smaller than the equilibrium osmotic pressure. The time taken to reach equilibrium increases with the amount of solvent that must be displaced, i.e., increases with the diameter of the capillaries. Since, experimentally, problems such as dirt in the capillaries, etc., limit the size of capillary that one can go down to, and since the membranes must be tight (semipermeability), the establishment of osmotic equilibrium can take days or weeks. Other problems such as poor solvent drainage in the capillaries, adsorption of solute on the membrane, partial permeation of solute through the membrane, etc., can interfere with the attainment of a true osmotic equilibrium. The absence or presence and allowance for these complications must be individually established. 

Osmotic pressure is a thermodynamic property of the solution. Thus, n is a state variable that depends upon temperature, pressure, and concentration but does not depend upon the membrane as long as the membrane is semipermeable. Osmotic equilibrium requires that the chemical potentials of the solvent on the two sides of the membrane be equal. Note that the solutes are not in equilibrium since they cannot pass through the membrane. Although osmotic pressure can be measured directly, it is usually estimated from other measurements (e.g., Reid, 1966). For an incompressible liquid osmotic pressure can be estimated from vapor pressure measurements. 

Two cases should be considered (i) nonosmotic membrane equilibrium (ii) osmotic membrane equilibrium. In the latter case, where solvent molecules can enter the surface layer or the membrane, the situation is more complicated since mechanical equilibria are also involved. We will start by considering nonosmotic equilibrium. 

Osmotic Membrane Equilibrium and Electrochemical and Mechanical Equilibria... 

Osmotic Membrane Equilibrium and Incorporation of Solvent Molecules... 

Osmotic equilibrium is a most important special case of membrane equilibrium. Let 7 be 2 one phase (/) is the solvent (component 1) and the other (//) is the solution of component 2 in 1 (mixture 1 + 2). The membrane is impermeable to the molecules of solute 2. 

In a colloidal dispersion, if the particle is a macromolecule of polyelectrolyte nature, additional properties to the general physicochemical properties may arise. The British physicist Donnan, in 1911, showed that when two solutions of electrolytes arc separated by a semlpermeable membrane, potentials arise at the junction. This happens v icn movement of atleast one of the ions through the semlpermeable membrane is hindered. Th<- hindrance may be due to the colloidal nature of the ion or the electroMe may be chcndcimmobile matrix of macromolecular nature like an ion-exchange resin on oiie side. In addition, an osmotic pressure difference between the two compartments is observed at equilibrium. Tlie explanation for these apparent anomalies was provided by Donnan and therefore the phenomenon, Donnan membrane equilibrium bears his name to this day. 

The condition needed for an osmotic membrane equilibrium related to the solvent can be written... 

Just as equilibrium with a semipermeable membrane produced a difference in pressure (the osmotic pressure) between the two sides of the membrane, equilibrium of ions across a membrane that is permeable to one ion but not another results in an electric potential difference. As an example, consider a membrane separating two solutions of KCl of unequal concentrations (Fig. 10.4). We assume that the membrane is permeable to K" " ions but is impermeable to the larger Cl ions. Since the concentrations of the K" " ions on the two sides of the membrane are unequal, K+ ions will begin to flow to the... 

There are two aspects to liquid-membrane equilibrium. The first one is concerned with the osmotic equilibrium between two solutions on two sides of a semipermeable membrane permeable to the solvent and impermeable to the solute the second one covers partitioning of the solute between the solution and the membrane. Both porous and nonporous membranes are of interest. The second aspect is also useful for porous sorbent/gel particles. 

When a solution is separated from the pure solvent by a semi-permeable membrane i.e. a membrane that permits the passage of solvent molecules but not of solute molecules, the solvent molecules always tend to pass through the membrane into the solution. This general phenomenon is known as osmosis, and the flow of solvent molecules leads to the development of an osmotic pressure which at equilibrium just prevents further flow. The equilibrium osmotic pressure, n, can be measured using a capillary osmometer such as that shown schematically in Fig. 3.9. 

Fig. 3.9 Schematic representation of an osmotic pressure cell consisting of a polymer solution in equilibrium with pure solvent across a semi-permeable membrane. The osmotic pressure fl can be determined from the difference of the height of the liquids in the capillaries.

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