Percentage Extraction:

Distribution ratio (D) is merely a concentration ratio and the extent of extraction will, therefore, depend upon the volume ratio of organic to water phases. Since we are mainly interested in the extent of extraction, we go for another practical term which is known as percent extraction (% E) or E.

Let f be the fraction of the total metal in the organic solvent at equilibrium, then (1-f) is its fraction in the aqueous phase. Let V_o and V_a be the volumes of the organic and aqueous phases, respectively. Then

D = Total metal in organic phase/Total metal in aqueous phase

=   [M]_o/[M]_a                                                                                                                             

D =      (f/V_o)/1 - f/V_a =     fV_a/ (1 - f) V_o =        fV_a/V_o  - fV_o

DV_o - DfV_o = fV_a

DV_o= DfV_o + fV_a

DV_o= f(DV_o  + V_a)

f =       DV_o/V_a + DV_o                                                                                                              

Percentage of metal extracted = 100 f = 100D/D + (V_a /V_o  )

If the volumes of the two phases are equal, then the denominator simplifies to D + 1.

i.e.,

% E or E = 100D/ D + 1