When a solute distributes itself between two immiscible solvents, there is a definite relationship between the solute concentration in the two phases at equilibrium. To explain this relation, Nernst gave a law in 1891, known as the Nernst distribution law. According to this law, a solute can distribute itself between two immiscible solvents in contact in such a way that the ratio of its concentration in these solvents at equilibrium conditions is constant at a given temperature.
Nernst distribution law
This law can be stated as ” At constant temperature, when two solutions of a solute in two immiscible solvents are in contact with each other, then solute distributes itself to keep a fixed ratio of concentration in the two immiscible solvents at equilibrium.
If a solute S distributes itself between two immiscible solvents of phase 1( aqueous solvent) and phase 2(organic solvent) at equilibrium, the ratio of the concentration of solute in phases 1 and 2 remains the same at a constant temperature. If [S1] is the concentration of solute in phase 1 and [S2] is the concentration of solute in phase 2, then at equilibrium, distribution coefficient Kd is expressed as:
Nernst distribution law holds true under the following conditions:
- The temperature should remain constant. Otherwise, the value of the distribution coefficient changes by changing the temperature.
- The solute should not undergo association or dissociation i.e it should be present in the same molecular form in both solvents.
- Solute should not react with either solvent.
- The concentration of solute should be low.
Nernst distribution law derivation
Let a solute is soluble in solvent A and solvent B such that solvent A and solvent B are immiscible with each other.
Let, µ(A)= Chemical potential of the solute in solvent A.
µ(B)= Chemical potential of the solute in solvent B.
µo(A)= Standard chemical potential of the solute in solvent A.
µo(B)=Standard chemical potential of the solute in solvent B.
aA= Activity of the solute in solvent A.
aB=activity of the solute in solvent B.
The chemical potential of solute is solvent A can be given as
µ(A)=µo(A) + RTlnaA
Similarly, For in solvent B,
µ(B)=µo(B) + RTlnaB
Where R is the universal gas constant and T is the temperature in Kelvin.
When the solution of the solute in solvent A is mixed with a solution of the solute in solvent B then, at equilibrium the chemical potential µ(A) and µ(B) become equal.
At equilibrium, µ(A)=µ(B)
µo(A) + RTlnaA=µo(B) + RTlnaB
µo(A)–µo(B)=RT In (aA/aB)
At a particular temperature, µo(A), µo(B), and R are constant.
In (aA/aB)= Constant.
Taking antilog on both sides,
aA/aB= K …………………….(i)
This equation is the mathematical expression of the Nernst distribution law.
For dilute solution, equation(i) can be modified as,
Application of Nernst distribution law
- It can be used to determine the solubility of a substance.
- It is applicable in solvent extraction.
- This is useful in Parke’s process of desilverization of lead.
- This is used in the determination of the equilibrium constant of a chemical equilibrium involving the formation of complex ions.
- With the help of this law, we can determine the value of the molecular complexity of the solute.
Limitations of Nernst distribution law
- This law does not hold true when solutes undergo ionization or dissociation.
- If solute combines with one or both of the solvents, then this law does not hold true.
- If the mutual solubility of two solvents is affected due to the presence of solute, the law does not hold true.
- The law holds true for only ideal solutions only.
- S. M. Khopkar, Basic Concepts of Analytical Chemistry, (3rd Edition), New Age International Pvt. Ltd., New Delhi, India (2008).