Determination of Equilibrium Constant from Distribution Coefficient

Determination of Equilibrium Constant from Distribution Coefficient

Distribution law helps in the determination of equilibrium constant of a reaction when one of the reactants is soluble in two immiscible solvents.
Example: When KI reacts with I₂ to form KI₃
KI + I₂ ⇌ KI₃
This reaction can be carried out in water, while I₂ is soluble in both water and benzene.
Procedure
To find Distribution Coefficient of I₂
I₂ is shaken with water and benzene in a bottol. The concentration of I₂ in the two layers is then determined by titration against standard thiosulphate solution.
So, (Conc. I₂ in water/Conc. I₂ in benzene) = K
To find Equilibrium Constant using the value of K

A solution of KI of concentration 'a' is shaken with I₂ in a bottol, some benzene is also added and shaken. On standing, the mixture seperates into two layers.
The concentration of I₂ is determined in the two layers by titration against standard thiosulphate solution.
Let 'b' the concentration of I₂ in benzene layer, 'c' be the concentration of I₂ in water layer which is really the total of the concentration of free I₂ and KI₃.
K is the value of Distribution coefficient of I₂ between water and I₂.
So, (Conc. I₂ in water/Conc. I₂ in benzene) = K
∴ Concentration of free I₂ in water layer = K X b
Hence, Concentration of KI₃ in water layer = c-Kb
∴ Concentration of KI in water layer = a-(c-Kb) = a-(c+Kb)
Now, we can write the equilibrium constant of the reaction-
KI + I₂ ⇌ KI₃
so, K_c = [KI₃]/[KI ] [I₂]
or, K_c = (c-Kb)/(a-(c+Kb))Kb
The square brackets denote concentrations in water layer.
Since all the quantities on RHS are known, the equilibrium constant may be determined.

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