Donnan Membrane Equilibrium: Assumptions, Application and Factors | Soil Colloids

After reading this article you will learn about:- 1. Introduction to Donnan Membrane Equilibrium 2. Assumptions of Donnan Membrane Equilibrium 3. Applications 4. Factors.

Introduction to Donnan Membrane Equilibrium:

If a solution of an electrolyte consisting of two diffusible ions is separated by a membrane from another solution containing a salt with a non-diffusible ion (protein ion), then at equilibrium the distribution of the diffusible ions will be unequal on the two sides of the membrane. This state of equilibrium of such a system was formulated by F.G. Donnan in 1911.

Suppose a solution of sodium chloride (NaCl), concentration C₁, is separated by a diffusion membrane from a solution of a salt NaR, concentration C₂, R^– being a non-diffusible ion species.

At equilibrium a certain amount of (x) of sodium (Na⁺) and chloride (CI^–) ions will have passed through the membrane and that can be represented as follows:

At equilibrium (total concentration of positive ions is equal to that of negative ions in each solution).

At equilibrium, the chemical potentials (m) of all ions present on both the solutions must be equal i.e.

µNaCl (1) = µNaCl (2)

The chemical potential of an electrolyte may be taken as the sum of the potentials of its ions hence,

µ°Na⁺ + RT ln^aNa⁺(1) + µ°Cl^– + RT ln^aCl^–

= µ°Na⁺ + RT ln^aNa⁺ (2) + µ°Cl^– + RT ln^aCl^{– a}Na⁺ (1) ×^aCl^– (1)

= ^aNa⁺ (2) ×^aCl^– (2)

where ‘a’ denotes activities of ions.

If these are dilute, the activities may be replaced by concentrations,

^CNa⁺ (1) ×^CCl^– (1) = ^CNa⁺ (2) ×^CCl^– (2)

(C₁ – x)(C₁– x) = (C₂ + x) x

x/C₁ = C₁/C₂ + 2C₁

The fraction x/C₁ gives the proportion of sodium chloride initially present which has diffused through and it is found to be smaller when the concentration of non-diffusible ion is higher. Donnan membrane equilibrium belongs to the mass-action equations.

A colloid particle, for example, a clay particle with its surrounding diffuse double layer may be looked upon as a micro-Donnan system, where the attractive electric forces between particle surface and counter ions act as a restraint, causing a non-uniform distribution of the counter ions in the inner solution or micellar solution.

For a system with more than one diffusible electrolyte, the activity of each must be constant throughout the aqueous phase. For an aqueous system containing the ions K⁺, H⁺, Ca²⁺, CI^–, OH^– and SO₄^2-, the equilibrium is expressed by

(K⁺)_i/(K⁺)_o = (H⁺)_i/(OH⁺)_o = (Ca²⁺)_i/(Ca²⁺)_o = (Cl^–)_o/(Cl^–)_i= (OH^–)_o/(OH^–)_i = (SO₄^2-)_o(SO₄^2-)_i

Assumptions of Donnan Membrane Equilibrium:

(i) The charge distribution is uniform throughout the colloidal system.

(ii) Dissociation of the colloid is complete and

(iii) The total volume of the system (colloidal clay system) remains constant.

The Donnan law defines the volume distribution of ions on either side of a semi­permeable membrane that permits all but one ionic species to diffuse across it. If the non- diffusible ion is anionic, the Donnan model become analogous to a soil-water system where the net negative charge is confined to the soil surface and all other ions freely move from the surface to bulk solution, provided the condition of a volume distribution of charge is fulfilled on the surface-adsorbed phase as well.

Applications of Donnan Membrane Equilibrium:

Donnan principles can be applied in various important processes in soil science which in turn influence the nutrient uptake by the plant viz. cation exchange equilibria, moisture changes, the ratio law, mobility of ions in the soil etc.

i. Cationequilibria and moisture changes:

The dynamic nature of the monovalent divalent cationequilibria in relation to moisture cycles, originally predicted on the basis of Donnan theory, is at present seen as a thermodynamic necessity independent of mechanisms. In the drying process the thinning of water films involves an increase in salt concentration.

But this increase is a change in the proportions of the cations caused by the thermodynamic condition that the activity ratio—|monovalent]/[divalent] in the solution phase should tend to remain constant. A change in the proportion of cations in the solution phase involves a complementary change for the exchange complex, since the total cations remain fixed.

The actual relationship between moisture tensions and K/Ca ratio are possible and would be of considerable interest in soil profile. The effects of drought on the mineral nutrition of plants can also be looked at from this point of view, especially where different layers of the profile differ in their calcium potassium relationship. It can also be applied in cation exchange phenomenon of soils.

ii. Ratio Law:

For individual soil colloid particles, typified by the layer aluminosilicates, if a sufficiently large average potential drop exists at the colloid solution boundary, and solutions are dilute, anions, have a vanishingly small concentrations compared to that of the cations associated with the colloid surface.

In order to meet Donnan theory requirements, soil particles surfaces had to be predominantly and highly negatively charged and that solution concentrations should not be too high with the upper limit varying principally with the charge on the cation and with the nature of the anion. The higher the charge on the cation the lower the concentration at which the surface potential becomes too low and the ratio law fails to hold.

iii. Donnan Hydrolysis:

Donnan hydrolysis systems generally affect the internal environment for rocks weathering. In considering Donnan hydrolysis, two factors are important:

(a) a separate aqueous phase must exist (the outer solution),

(b) hydrogen and aluminium ions must replace the calcium, leading to an acidic exchange complex. It is a common that many non-calcareous soils produce localized deposits of calcium carbonate upon drying. This arises through the operation of Donnan type hydrolysis as applied to the colloidal exchange complex.

As Donnan principles are applied for proper understanding of the activity of the exchangeable ions in soils, the physico-chemical behaviour of soils and the interaction between plant roots and soil can also be well understood.

Nutrient uptake by plants, loss of nutrients by leaching, fixation of ions in non-exchangeable form, weathering, formation or genesis of clay minerals, soil profile development etc. are intimately related with the ionic activity in soils and hence these are related with the Donnan membrane equilibrium.

Factors Affecting Donnan Membrane Equilibrium:

(i) Dilution Effect:

Dilution of a soil-water system containing monovalent and divalent cations displaces the equilibrium in such a direction that the adsorption of divalent ions increases whereas the adsorption of monovalent ions decreases i.e., the ratio of divalent to monovalent on the exchanger increases.

Raising the solution concentration, the ratio of divalent to monovalent ions on the exchanger decreases. In systems with monovalent ions, dilution has proved to have a very slight effect or none at all depending on the kind of ions.

(ii) Effect of Exchange Capacity:

The higher the exchange capacity of soils the higher will be the adsorption of divalent ions as compared to monovalent ions and vice-versa.

(iii) Valency Effects:

It affects Donnan distribution: (a) Anion effects-Assuming homogeneous charge distribution the system (IA) is being compared with the system (2A).

Thus in the simplified cases of small salt concentration it will be written as, Y₂/Y₁ = X/2Z since X < Z, Y₂< Y, which implies that the negative adsorption (X-Y) is greater in the sulphate system than in the chloride system.

(iv) Cation Effects:

Assuming homogeneous charge distribution the system (1B) is being compared with the system (2B).

Since 4 X< Z for small salt concentrations, then Y₃> Y₁. Negative adsorption is thus less, other things being equal, for the divalent cation as compared with the monovalent.