Membrane equilibrium Donnan

A Donnan potential can be measured electrically, with some uncertainty due to unknown liquid junction potentials, by connecting silver-silver chloride electrodes (described in Sec. 14.1) to both phases through salt bridges. 

Consider solution phases a and separated by a semipermeable membrane. Both phases contain a dissolved salt, designated solute B, that has v+ cations and v anions in each formula unit. The membrane is permeable to these ions. Phase P also contains a protein or other polyelectrolyte with a net positive or negative charge, together with counterions of the opposite charge that are the same species as the cation or anion of the salt. The presence of the counterions in phase prevents the cation and anion of the salt from being present in stoichiometric amounts in this phase. The membrane is impermeable to the polyelectrolyte, perhaps because the membrane pores are too small to allow the polyelectrolyte to pass through. 

To find an expression for the Donnan potential, we can equate the single-ion chemical potentials of the salt cation (0 ) = When we use the expression of Eq. 

T/7 rmodynam/cs andC/Tsm/sfry, second edition, version 3 2011 by Howard DeVoe. Latest version www.chem.umd.edu/themobook 

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

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Donnan membrane equilibrium This concerns the distribution of ions on each side of a membrane separating two portions of a solution of... 

One of the earliest, and reasonably successful, approaches to quantitatively predicting selectivity behaviour was through the thermodynamic treatment of ion exchange systems as a Gibbs-Donnan membrane equilibrium. Such a description is given by equation 5.29 which for the sake of simplicity is shown in terms of single ion activity coefficients ... 

Neale J. Text. Inst., 1929, 373 1930, 225 1931, 349) attributes the attraction of cellulose towards sodium ions to the formation of non-diffus-ible anions of the type (CeHioOj)- or (CgH 9O5.H2O)-. This, it has been suggested, causes a distribution of sodium and hydroxyl ions on each side of the fibre boundary in accordance with the Donnan membrane equilibrium theory. The Donnan theory provides thermodynamic proof that if a solution of an electrolyte containing two diffusible ions is separated by a membrane from another solution containing a salt with a non-diffusible ion, then the equilibrium distribution of the former will not be equal on the two sides of the membrane . This state is illustrated diagrammatically in Fig. 3.12 where, on the side marked A of the membrane (which in this case is the... 

Figure 6.7. Donnan membrane equilibrium shown diagrammatically at initial and at equilibrium state. Note that inside the bead that K > CL. [after Khym (1974), published with permission of Prentice-Hall, Inc.]...

R. M. Wallace. Concentration and Sepemtion of Ions by Donnan Membrane Equilibrium, btd-... 

D.G. Donnan, The theory of membrane equilibria, Chem. Rev., 1924, 1, 73-90 R.M. Wallace, Concentration and separation of ions by Donnan membrane equilibrium, Ind. Eng. Chem. Process Design Dev. 1967, 6, 423. 

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. 

In order to explain this transmembrane potential, a number of authors have proposed membrane potential theories. Historically, the first membrane potential theory for biological systems was the use of the concept of the Donnan membrane equilibrium. 

Hill TL (1956) A fundamental studies. On the theory of the donnan membrane equilibrium. Discussions of the Faraday Society 21 31-45. doi 10.1039/ DF9562100031... 

Hill TL (1957) Electrolyte theory and the donnan membrane equilibrium. J Phys Chem 61 548-553... 

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 above examples have made us understand the usefulness of Donnan membrane equilibrium in biology. However, there are cases where the same effect becomes a bane to the system. An example that can be cited is that of oedema in tissues. When the plasma albumin content falls below the normal value, salt and water retention takes place in the tissues. The movement of the concerned electrolytes In and out of the cell membranes occurs mainly due to tlie Donnan effect. Other developments like Increased secretion of aldosterone and vasopressin follow soon to result in a full-fledged oedema state. 

This statement regarding the uniform chemical potential of a species applies to both a substance and an ion, as the following argument explains. The derivation in this section begins with Eq. 9.2.37, an expression for the total differential ofU. Because it is a total differential, the expression requires the amount , of each species i in each phase to be an independent variable. Suppose one of the phases is the aqueous solution of KCl used as an example at the end of the preceding section. In principle (but not in practice), the amounts of the species H2O, K+, and Cl can be varied independently, so that it is vahd to include these three species in the sums over i in Eq. 9.2.37. The derivation then leads to the conclusion that K+ has the same chemical potential in phases that are in transfer equilibrium with respect to K+, and likewise for Cl . This kind of situation arises when we consider a Donnan membrane equilibrium (Sec. 12.7.3) in which transfer equilibrium of ions exists between solutions of electrolytes separated by a semipermeable membrane. 

Ref. [120]. Ref. [158]. Donnan was an Irish physical chemist after whom the Donnan membrane equilibrium and Donnan potential (Sec. 12.7.3) are named. Ref [45]. 

As a specific example of a Donnan membrane equilibrium, consider a system in which an aqueous solution of a polyelectrolyte with a net negative charge, together with a counterion M+ and a salt MX of the counterion, is equilibrated with an aqueous solution of the salt across a semipermeable membrane. The membrane is permeable to the H2O solvent and to the ions M+ and X , but is impermeable to the polyelectrolyte. The species in phase a are H2O, M" ", and X those in phase P are H2O, M+, X , and the polyelectrol5he. In a equilibrium state, the two phases have the same temperature but different compositions, electric potentials, and pressures. 

Figure 12.9 Process for attainment of a Donnan membrane equilibrium (schematic). The dashed ellipse represents a semipermeable membrane.

It should be clear that the existence of a Donnan membrane equilibrium introduces complications that would make it difficult to use a measured pressure difference to estimate the molar mass of the polyelectrolyte by the method of Sec. 12.4, or to study the binding of a charged ligand by equilibrium dialysis. 

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