Distribution Law and its Limitations:
It is clear from the above discussion that if the system is composed of two immiscible solvents and one distributing solute, there is one degree of freedom. The ratio of the concentration of the solute in the two phases is invariant. It is independent of the total concentration. Based on this, the distribution law was first enunciated in 1872 by Berthelot and Jungfleish and later elaborated by Nernst in 1891. The law popularly known a Nernst distribution law puts greater restraints. It can be stated as that a solute will distribute itself between two immiscible solvents in such a manner that, at equilibrium, the ratio of concentration of the solute in the two phases at a particular temperature will be a constant provided the solute has the same molecular weight in each of the phases.
For a solute S distributing between solvents 1 and 2, we can write
S1 ↔ S2
KD = [S] 2 /[S] 1
where KD is known as the distribution coefficient or the extraction coefficient. It is independent of the total concentration of the solute and the phase volumes.
Hence, [S]1 and [S]2 denote the concentrations of the solute in phases 1 and 2, respectively. If you imagine this total concentrations to be increased until one phase is saturated and reaches the concentration [sS]1, the second phase must simultaneously become a saturated solution of concentration [sS]2. The distribution ratio, [sS]2 / [sS]1 then becomes the ratio of the solubilities of the solute in the two phases. This expression holds reasonably well for materials which are extremely sparingly soluble.