Distribution of acetic acid:

Problem:

Derive an expression for the distribution of acetic acid between water and benzene in terms of its dissociation and polymerization constants. Also analyze the dependence of distribution on different variables.

Answer:

1. The distribution of acetic acid in water and benzene can be described as under (CH₃COOH)_a   ↔ (CH₃COOH)_o

K_D = [CH ₃ COOH] o/ [CH ₃ COOH]_a o, and a refer to benzene and aqueous phases, respectively.

However, acetic acid dissociates in the aqueous phase

CH₃COOH    ↔ CH₃COO¯ + H⁺

K_a =    [CH₃COO - ] × [H ⁺]/ [CH ₃ COOH]

and forms a dimer in benzene.

2 CH₃COOH ↔   (CH₃COOH)₂

K_D   = [(CH₃COOH) ₂ ]_o/ [CH₃COOH]²_a

The overall distribution of acetic acid, described by Distribution ratio (D), is given by

D = Total conc. of acetic acid in its different forms in organic phase/Total conc. of acetic acid in its different forms in aqueous phase

[CH₃COOH]_o   + 2[(CH ₃ COOH) ₂ ]_o/ [CH₃COOH]_a  + [CH₃COO]_a

Incorporating the equilibrium constants given above

D = K _D[1 + 2 K _D (CH ₃ COOH)]_o/ 1 + K_a [H ⁺ ]

This shows that the distribution of acetic acid varies as a function of the pH and acid concentration in organic phase.