Dependence of the distribution ratio:

A detailed discussion on the extraction equilibria of this class of extractants. The extraction by chelating agents may be easier to describe by simple mass equations. The situation in case of extraction by carboxylic, suphonic and alkylphosphorus acids is likely to be more complicated due to self association of the acids in the organic phase or the solvation of the extracting species by the extractant.

A dependence of the distribution ratio of the metal chelate, formed by the metal ion Mⁿ⁺ by the chelating agent HR, on pH, is given by the following equation.

D = K * [HR ]ⁿ_o/[H ⁺ ]ⁿ

here K is a constant including some constants.

If [HR ]ⁿ_o   remains constant, then

D=K'*[H+]ⁿ_a =E/100-E, where E is percent extraction

And,

log D = log E - log (100 - E) = log K´* + n pH

The given above equation represents a family of symmetrical sigmoid curves with the position of each along the pH axes depending only upon the value of K´* and the  lope of each depending on n. Figure (a) shows a set of curves qualitatively representing the extraction of metal dithizonates in carbon tetrachloride. The above relation will not be strictly applicable where hydrolysis of metal ion occurs or intermediate chelate formation takes place. A slope of the curve alters of corresponding to n, will be significantly lower. The pH value at % E = 50 has been designated as pH ½ 

pH ½   =  - 1/n log K ′ *

You will see within the further section in which the difference in pH ½ values of the metals in a specific system is a measure of the separability of the two ions.