The solute can exist partly or wholly as associated molecules in one of the phases or it may dissociate into ions in either of the liquid phases. The distribution law applies only to the concentration of the species common to both phases, namely, the monomer or simple molecules of the solute. Consider the distribution of benzoic acid between an oil phase and a water phase. When it is neither associated in the oil nor dissociated into ions in the water, equation C₁/C₂ = K can be used to compute the distribution constant. When association and dissociation occur, however, the situation becomes more complicated. The general case is where benzoic acid associates in the oil phase and dissociates in the aqueous phase. Two cases will be treated. First, according to Garrett and Woods, benzoic acid is considered to be distributed between the two phases, peanut oil and water. Although benzoic acid undergoes dimerization (association to form two molecules) in many nonpolar solvents, it does not associate in peanut oil. It ionizes in water to a degree, however, depending on the pH of the solution. For the case under consideration, Co, the total concentration of benzoic acid in the oil phase, is equal to [HA]o, the monomer concentration in the oil phase, because association does not occur in peanut oil. The species common to both the oil and water phases are the unassociated and undissociated benzoic acid molecules. The distribution is expressed as

K = [HA]₀/[HA]_w = C₀/[HA]_w                                                                                                       (1)

where K is the true distribution coefficient, [HA]o = Co is the molar concentration of the simple benzoic acid molecules in the oil phase, and [HA]w is the molar concentration of the undissociated acid in the water phase.

The total acid concentration obtained by analysis of the aqueous phase is

C_w = [HA]_w + [A^–]_w                                                                                                                       (2)

and the experimentally observed or apparent distribution coefficient is

K’ =   [HA]₀/ [HA]_w + [A^–]_w  = C₀/ C_w                                                                                          (3)

The observed distribution coefficient depends on two equilibria: the distribution of the undissociated acid between the immiscible phases as expressed in equation (1) and the species distribution of the acid in the aqueous phase, which depends on the hydrogen ion concentration [H3O+] and the dissociation constant Ka of the acid, where

K_a.[H₃O⁺][A^–]_w/  [HA]_w                                                                                                                 (4)

Association of benzoic acid in peanut oil does not occur, and Kd (the equilibrium constant for dissociation of associated benzoic acid into monomer in the oil phase) can be neglected in this case. Given these equations and the fact that the concentration, C, of the acid in the aqueous phase before distribution, assuming equal volumes of the two phases, is

C =  C₀ + C_w                                                                                                                                  (5)

One arrives at the combined result:

K_a + [H₃O⁺]/ C_w  = (K_a/ C) + (K+1/C) [H₃O⁺]                                                                              (6)

Expression (6) is a linear equation of the form y = a + bx, and therefore a plot of (Ka +[H3O+])/Cw against [H3O+] yields a straight line with a slope b = (K + 1)/C and an intercept a = Ka/C. The true distribution coefficient, K, can thus be obtained over the range of hydrogen ion concentration considered. Alternatively, the true distribution constant could be obtained according to equation (1) by analysis of the oil phase and of the water phase at a sufficiently low pH (2.0) at which the acid would exist completely in the un-ionized form. One of the advantages of equation (6), however, is that the oil phase need not be analyzed; only the hydrogen ion concentration and Cw, the total concentration remaining in the aqueous phase at equilibrium, need be determined.

Second, let us now consider the case in which the solute is associated in the organic phase and exists as simple molecules in the aqueous phase. If benzoic acid is distributed between benzene and acidified water, it exists mainly as associated molecules in the benzene layer and as undissociated molecules in the aqueous layer.

The equilibrium between simple molecules HA and associated molecules (HA)n in

(HA)n                                                                    n(HA)

(Associated molecules)                                    (Simple molecules)

and the equilibrium constant expressing the dissociation of associated molecules into simple molecules in this solvent is

K_d = [HA]₀ⁿ/[( HA)]_n                                                                                                                     (7)

Or

Because benzoic acid exists predominantly in the form of double molecules in benzene, Co can replace [(HA)2], where Co is the total molar concentration of the solute in the organic layer. Then equation (8) can be written approximately as

In conformity with the distribution law as given in equation (1), the true distribution coefficient is always expressed in terms of simple species common to both phases, that is, in terms of [HA]w and [HA]o. In the benzene–water system, [HA]o is given by equation (9), and the modified distribution constant becomes

K’’ =   [HA]o/   [HA]w = √C₀/ [HA]w                                                                                       (10)

Distribution Coefficient:

If an excess of liquid or solid is added to a mixture of two immiscible liquids, it will distribute itself between the two phases so that each becomes saturated. If the substance is added to the immiscible solvents in an amount insufficient to saturate the solutions, it will still become distributed between the two layers in a definite concentration ratio.

If C1 and C2 are the equilibrium concentrations of the substance in Solvent1 and Solvent2, respectively, the equilibrium expression becomes

C₁/C₂ = K                                                                                                                                     (11)

The equilibrium constant, K, is known as the distribution ratio, distribution coefficient, or partition coefficient. Equation (1), which is known as the distribution law, is strictly applicable only in dilute solutions where activity coefficients can be neglected.

Multiple choice questions:

1.The solute can exist partly or wholly as associated molecules in one of the phases or it may dissociate into ions in either of the liquid phases.

a)true

b)false

2.The distribution law applies only to the concentration of the species common to both phases, namely, the _____ or simple molecules of the solute.

a)momomers

b)dimers

c)oligomers

d)none of the above

3.Association to form two molecules is known as

a)dimerization

b)epimerization

c)both of these

d)none of these

4.Benzoic acid undergoes dimerization in many nonpolar solvents, it does not associate in

a)castor oil

b)peanut oil

c)eucalyptus oil

d)all of the above

5.K = [HA]₀/[HA]_w = C₀/[HA]_w  In this equation K is

a)molar concentration

b)true distribution coefficient

c)equilibrium constant

d)all of the above

6.K = [HA]₀/[HA]_w = C₀/[HA]_w  In this equation C_{0  is}

a)molar concentration of the simple benzoic acid molecules in the oil phase

b)molar concentration of the undissociated acid in the water phase

c)true distribution coefficient

d)equilibrium constant

7.K = [HA]₀/[HA]_w = C₀/[HA]_w  In this equation [HA]w is

a)molar concentration of the simple benzoic acid molecules in the oil phase

b)molar concentration of the undissociated acid in the water phase

c)true distribution coefficient

d)equilibrium constant

8.The distribution coefficient depends on which of the following equilibria?

a)distribution of the undissociated acid between the immiscible phases

b)species distribution of the acid in the aqueous phase

c)both of these

d)none of these

9.The equilibrium constant for dissociation of associated benzoic acid into monomer in the oil phase is denoted as

a)Ka

b)Kw

c)Kd

d)K0

10.If benzoic acid is distributed between benzene and acidified water, it exists mainly as associated molecules in the benzene layer and as undissociated molecules in the aqueous layer.

a)true

b)false

11.(HA)n is

a)Associated molecules

b)Simple molecules

c)both of these

d)none of these

12.If an excess of liquid or solid is added to a mixture of two immiscible liquids, it will distribute itself between the two phases so that each becomes unsaturated.

a)true

b)false

13.If the substance is added to the immiscible solvents in an amount insufficient to saturate the solutions, it will not become distributed between the two layers in a definite concentration ratio.

a)true

b)false

14.The equilibrium constant, K, is known as

a)distribution ratio

b)distribution coefficient

c)partition coefficient

d)all of the above

15.C₁/C₂ = K  This equation is known as

a)distribution ratio

b)distribution coefficient

c)partition coefficient

d)distribution law

Solutions:

1. a)true
2. a)momomers
3. a)dimerization
4. b)peanut oil
5. b)true distribution coefficient
6. a)molar concentration of the simple benzoic acid molecules in the oil phase
7. b)molar concentration of the undissociated acid in the water phase
8. c)both of these
9. c)Kd
10. a)true
11. a)Associated molecules
12. b)false
13. b)false
14. d)all of the above
15. d)distribution law

References:

1. Martins Physical Pharmacy, 6th edition 2011, page no. 350-354.

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