Equilibrium:

The equilibrium among an aqueous metal ion solution and chloroform solution of aliphatic monocarboxylic acid and that of amine can be represented as

Mⁿ⁺_a+p(BHA)_o +n-p+x/2(H₂A₂)_o↔(MB_pA_n.xHA)_o +nH⁺_a                              

where Mⁿ⁺ = metal ion

n = valency of metal ion

p = number of amine molecules coordinated

HA = monomeric acid molecule

B = amine

x = number of acid molecules required for solvation

(H₂A₂)_o  = dimeric acid molecules in organic phase

Hence, the equilibrium constant is given by

K= [M.B_pA_n .xHA]_o [H⁺]ⁿ_o/[Mⁿ⁺]_a[BHA]^p_o[H2A2]_o^n-p+x/2                 

Supposing that the metal ion does not form any other complex in the organic phase and exists only as Mⁿ⁺ in the aqueous phase

D = [M.B _p .A _n .xHA]_o/       [Mn +]_a                                                                              

Substituting the value of D within Eq. 3.63, rearranging it and expressing in the logarithmic form, we found

log D = log K_ex + n pH+ (n - p + x/2) log [H₂A₂]_o + p log[BHA]

Eq. 3.65 on differentiation with respect to pH at constant acid concentration gives

[δ log D]/ [δpH] = n

Thus, the slope of log D vs. pH at constant acid and amine concentration in the organic phase will give the number of protons liberated due to consumption of acid molecules in the complex creation. Same, a plot of distribution ratio vs dimeric acid concentration at constant pH and amine concentration will give the slope equal to n - p + x/2 from which the number of acid molecules required for the solvation of extracted species can be calculated. To search out the number of amine molecules coordinated along with the extracted species, log - log plots of distribution ratio vs amine concentration at constant pH and acid concentration will have to be drawn.