# Distribution law

Distribution law

According to Nernst’s Distribution law (1891) or Partition law, “When a solute is taken up with two immiscible liquids, in both of which the solute is soluble, the solute distributes itself between the two liquids in such a way that the ratio of its concentration in the two liquid phases is constant at a given temperature provided the molecular state of the distributed solute is same in both the phases”.

I.e.

$\dfrac{C_1}{C_2} = K_D$

Where $C_1 \text{and} C_2$ are the concentrations of the solute in two phases. $K_D$ is called distribution coefficient or partition coefficient.

(A)   When solute undergoes association in one of the solvents, we have

$K_D = \dfrac{C_1}{n \sqrt{C_2}} or K_D = \dfrac{n \sqrt{C_1}}{C_2}$

Where ‘n’ =order of association.

(B)   When solute undergoes dissociation, we have

$K_D = \dfrac{C_1}{C_2 (1- \alpha)} \text{or} K_D = \dfrac{C_1 (1- \alpha)}{C_2}$

Where $\alpha$=  on degree of dissociation.

(C)   When solute is to be extracted from solution by another suitable solvent, we have.

Amount left unextracted = $W[ \dfrac{K_DV}{K_DV + v_1}]^n$

Where ‘W’ =Initial amount present in solution, ‘V’ =volume of solution, $v_1$ volume of extracting solvent, $K_D$ = Distribution coefficient, ‘n’ = Number of extraction operations.

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