Solubility part 8

Distribution of solutes between immiscible solvents
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 solution, 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:
The equilibrium constant, K, is known as the distribution ratio, distribution coefficient, or partition coefficient. Equation (9-13), which is known as the distribution law, is strictly applicable only in dilute solutions where activity coefficients can be neglected.
Example: When boric acid is distributed between water and amyl alcohol at 25°C, the concentration in water is found to be 0.0510 mole/liter and in amyl alcohol it is found to be 0.0155 mole/liter. What is the distribution coefficient?
No convention has been established with regard to whether the concentration in the water phase or that in the organic phase should be placed in the numerator. Therefore, the result can also be expressed as:
One should always specify, which of these two ways the distribution constant is being expressed.
Knowledge of partition is important to the pharmacist because the principle is involved in several areas of current pharmaceutical interest. These include preservation of oil-water systems, drug action at nonspecific sites, and the absorption and distribution of drugs throughout the body. Certain aspects of these topics are discussed in the follow sections.
Effect of ionic dissociation and molecular association on partition
 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 simple molecules of the solute.
Consider the distribution of benoic acid between an oil phase and a water phase. When it is neither associated in the oil nor dissociated into ions in the water, then equation 913 can be used to compute the distribution constant. When association and dissociation occur, the situation becomes more complicated. Two cases will be treated. First, 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 non polar solvents, it does not associate in peanut oil. It ionizes in water to a degree, however, depending on the pH of the solution. Therefore, for this case,  , which is the total concentration of benzoic acid in the oil phase, is equal to  , 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:
Where K is the true distribution coefficient,   is the molar concentration of yhe simple benzoic acid molecules in the oil phase, and   is the molar concentration of the undissociated acid in water phase.
The total acid concentration obtained by analysis of the aqueous phase is:
and the experimentally observed or apparent distribution coefficient is:
The observed distribution coefficient depends on two equilibria: the distribution of the undissociated acid between the immiscible phases as expressed in equation (9-14) and the species distribution of the acid in the aqueous phase, which depends on the hydrogen ion concen¬tration [H3O+] and the dissociation constant Ka of the acid, where:
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: