Donnan Equilibrium

Donnan Equilibrium (Donnan), or membrane equilibrium, is the equilibrium that is established between ions diffusing through a membrane when there is an ion that cannot penetrate the membrane. Let an electrolyte NaR, which dissociates into Na+ and R- ions, be present inside the membrane, with the latter being impermeable to the membrane. If the second electrolyte is NaCl, both ions of which pass through the membrane, then the following ions will be present on both sides of the membrane: (1) (2) Na+ and R- In the internal solution (1), there is an excess of Na+ ions resulting from the dissociation of both NaCl and NaR. They cannot distribute uniformly, because their migration to the external solution (2) would disrupt the electroneutrality of both solutions (leaving an excess of negatively charged anions in solution 1). Based purely on thermodynamic considerations, Donnan showed that some Na+ ions will still diffuse into solution 2, carrying with them an equal amount of chloride ions. Thus, the presence of a non-diffusing anion R' causes an uneven distribution of ions that can freely diffuse through the membrane. This effect affects not only the second ion of the given electrolyte (NaR), but even a completely foreign ion (Cl-). In this case, ions having the same name as the non-diffusing ion (in this case anions) are displaced from the solution. A more precise analysis makes it possible to establish the quantitative relationships between the diffusing ions. They are expressed by the following equation: [Na+] [Cl-] / [Na+] [Cl-]! (1). Let us denote by x the concentration of Na and Cl ions in the external solution, by y the concentration of anions Cl, and by z the concentration of anions R in the internal solution; the concentration of cations Na in the latter is equal to the sum of the anions of the corresponding electrolytes (NaCl and NaR) y+z. The D.r. will then be expressed by the following formula: x² = y(y+z) (2). This equation clearly shows that the concentration of the diffusing electrolyte in the external solution is higher than in the internal one (x > y). It is as if it displaces through the membrane the electrolyte having a non-diffusing ion. The following table, calculated by Donnan, shows the distribution of NaCl between the internal and external solutions at various molar concentrations of both electrolytes. NaCl Total Concentration Concentration Ratio [NaR] quantity internal external solution solution z x + y y 0.497 0.503 0.01 0.1 0.478 1.1 0.333 0.666 0.1 0.0083 0.0917 0.01 0.0001 0.0099 If the concentration of NaCl is large compared to NaR, the influence of the latter is insignificant; but in those cases where the diffusing salt is present in relatively small quantities, it can be almost completely displaced into the external solution. It should be noted that almost simultaneously with Donnan's theoretical derivation, the phenomenon described was experimentally discovered by Bayliss. The latter found that the sodium salt of Congo red (congo red), the anion of which does not pass through parchment membrane, changes the diffusion equilibrium of other electrolytes present in the solution. Such colloidal electrolytes as Congo red are sodium proteinate and other salt-like compounds of proteins. For their purification from crystalloids since the time of Graham, the latter are passed through membranes impermeable to colloidal particles. In this case, it seemed obvious that freely diffusing crystalloid substances should, at equilibrium, be present in the same concentration on both sides of the membrane. Their concentration in the external fluid is used to determine their content in the colloidal solution. In reality, however, due to D.r., when protein anions are present in the internal solution, like-named ions (anions) of salts will be present in the dialysate in higher, and unlike-named (cations) in lower concentration than in the colloidal solution itself. In the dialysate of blood serum, for example, Cl is present in higher, and Ca in lower concentration than in the serum itself. Since serum proteins belong to amphoteric colloids, at acidic reaction they form protein cations, as a result of which the reverse ratio of Cl and Ca is observed in serum and dialysate. At a certain intermediate reaction at the isoelectric point, proteins form as few anions as cations, and do not affect the distribution of diffusing electrolytes. The effect of reaction described is shown in the following table according to data by Rona and Petow. pH Cl content (mEq per 100 cm³) Blood serum Dialysate 7.16 6.10 4.70 3.50 134.0 149.2 159.6 150.0 152.4 157.0 147.5 126.9 Ca content (mg per 100 cm³) pH Blood serum Dialysate 7.3 6.4 5.0 3.2 8.2 8.0 7.2 7.0 6.5 7.5 8.2 8.9 The same distribution of ions as in the experiments just cited also takes place in the living organism. Many biological fluids are dialysate of blood, deprived of most of its colloids. The differences in their ionic composition are in full accordance with the principle of D.r. As an example, the data obtained by Lehmann and Meesmann for cerebrospinal fluid and for the fluid of the eye chamber can serve. Proteins . . Cl .... Na . . . . pH ... Blood | Liquor Fluid of chamber 7-9% 0.36% 0.344% 7.3-7.5 0.01-0.03% 0.44% 0.29% 7.8 0.01-0.03% 0.43% 0.288% 7.7-7.8 The content of the anion (Cl) in this case is found to be higher, and that of cations (Na and H) lower than in the blood. In the examples considered, the ion not passing through the membrane was the colloidal ion. As Donnan already showed, the same equilibrium occurs if the membrane is impermeable to a group of crystalloid ions. In particular, the cell membrane has such properties, which in many cases is much more permeable to K ions than, for example, to Na and Ca. Since crystalloid ions are contained in the living cell and in the surrounding medium in incomparably higher ionic concentration than colloidal ones, D.r., caused by the unequal permeability of the cell membrane for them, must exert a very significant influence on the distribution of electrolytes and on the osmotic properties of the cell. The principle of membrane equilibrium thus acquires paramount importance also for resolving the still very obscure question of the distribution of electrolytes between the cell and the fluid bathing it (Butkevich). In recent years, the application of the Donnan principle in the theory of colloids has received particularly great development. The first generalization in this field belongs to Procter and Wilson, who showed that the principle of D. is applicable not only to solutions separated by a membrane, but also to gels consisting of colloidal electrolytes. Such a gel, for example, gelatin jelly, on the alkaline or acid side of the isoelectric point represents a salt-like compound of a colloidal ion with a crystalloid cation in the first case, with an anion in the second. Between this ion bound to the colloid and the ions of any other electrolyte in contact with the gel, D.r. must be established. The uneven distribution of ions between the gel and the solution (see equation 2) and the associated osmotic distribution of water make it possible to explain (in many cases even quantitatively) the phenomena described as swelling of the gel. The same explanation is directly applicable to the osmotic pressure of colloidal solutions, on which electrolytes, as is known, exert a very strong influence. In a series of investigations, Loeb developed a coherent theory of colloidal phenomena, reducing almost the entire theory of colloids to the principle of Donnan. Other authors dispute such a monopoly dominance of this principle in colloid chemistry.

In the examples considered, the ion not passing through the membrane was the colloidal ion. As Donnan already showed, the same equilibrium occurs if the membrane is impermeable to a group of crystalloid ions. In particular, the cell membrane has such properties, which in many cases is much more permeable to K ions than, for example, to Na and Ca. Since crystalloid ions are contained in the living cell and in the surrounding medium in incomparably higher ionic concentration than colloidal ones, D.r., caused by the unequal permeability of the cell membrane for them, must exert a very significant influence on the distribution of electrolytes and on the osmotic properties of the cell. The principle of membrane equilibrium thus acquires paramount importance also for resolving the still very obscure question of the distribution of electrolytes between the cell and the fluid bathing it (Butkevich). In recent years, the application of the Donnan principle in the theory of colloids has received particularly great development. The first generalization in this field belongs to Procter and Wilson, who showed that the principle of D. is applicable not only to solutions separated by a membrane, but also to gels consisting of colloidal electrolytes. Such a gel, for example, gelatin jelly, on the alkaline or acid side of the isoelectric point represents a salt-like compound of a colloidal ion with a crystalloid cation in the first case, with an anion in the second. Between this ion bound to the colloid and the ions of any other electrolyte in contact with the gel, D.r. must be established. The uneven distribution of ions between the gel and the solution (see equation 2) and the associated osmotic distribution of water make it possible to explain (in many cases even quantitatively) the phenomena described as swelling of the gel. The same explanation is directly applicable to the osmotic pressure of colloidal solutions, on which electrolytes, as is known, exert a very strong influence. In a series of investigations, Loeb developed a coherent theory of colloidal phenomena, reducing almost the entire theory of colloids to the principle of Donnan. Other authors dispute such a monopoly dominance of this principle in colloid chemistry.