Chelating Reaction:

The chelating anion, (R^-), reacts with metal ion (Mⁿ⁺) to form the chelate as shown below:

Mⁿ⁺ + n R ↔ MR _n

The creation constant of the complex Kf is provided as follows: [MRn] _a

Kf = [MR_n]_a /[Mⁿ⁺]a[R-]ⁿ_a

A metal chelate created on equilibration with the organic phase distributes itself between the aqueous and organic phases till equilibrium is attained.

(MR_n)_a  ↔      (MR_n)_o

The distribution constant of the complex, KDX, is given by

K_DX =   [MR_n]_o  /[MR _n ]_{a                                                                   (1)}

We assume that the metal in the aqueous phase predominantly exists as Mn⁺ only and in the organic phase as MR_n only. Alternatively, these assumptions could be elaborated as under:

i)          The metal ion forms no hydrolysis or anionic complexes in appreciable amounts.

ii)        The chelate concentration in the aqueous phase is negligible.

iii)       The concentration of the intermediate chelate species is negligible. If these assumptions are taken as valid, then

D = [M ]_o /[M]_a = [MR n ]_o/[Mⁿ⁺]_{a                                                (2)}

By combining the Eqs. 3.1 Through Eq.2, the final Eq. 1 becomes as follows:

D= [MR_n]_o/[Mⁿ⁺]_a = K_fKⁿ_aK_DX/Kⁿ_DR. [HR]ⁿ_o/[H+]ⁿ_a                                        

This equation has been experimentally verified for various metal chelate extraction systems. From the equation, it is evident that

D ∝ K_f, Kⁿ_a , K_DX and [HR]ⁿ_o

Also, D ∝ K ^{- n}_DR and [H⁺] ^{- n}_a