Chemistry, Third edition

11 · SOLUTIONS AND SOLUBILITY

Distribution of a solute between two

solvents

Distribution ratio

If a solute is soluble in two solvents, and the solvents are immiscible, it is found that

the concentration of solute in the one layer is always bigger than the concentration

of solute in the other layer by a fixed amount. This ratio (symbolized Kdand known

as the distributionorpartition ratio) is a constant at a particular temperature:

Kd(T)

concentration of solute in solvent A

concentration of solute in solvent B

where the subscript Treminds us that the ratio is fixed only at that particular tem-

perature. This equation does not hold if the solute dissociates, associates (such as

forming pairs of hydrogen bonded molecules) or otherwise chemically reacts with

the solvents present.

Our first example is the distribution of solid iodine (the solute) between water and

tetrachloromethane (the solvents). If we add a few crystals of iodine to some water

and tetrachloromethane (CCl 4 ) in a flask and shake the mixture well, the iodine

colours the water a pale brown colour and the tetrachloromethane a purple colour.

There is more iodine in the organic layer (the tetrachloromethane layer) than in the

aqueous layer (the water layer). At 25C experiments show that

Kd(I 2 )

concentration of I 2 in CCl 4

 85

concentration of I 2 in H 2 O

Kdis unitless, because the units of concentration cancel out.

It is important to realize that the value of Kdat one temperature is the same

whether we add 0.1 g, 1 g, or 2 g (etc.) of iodine to the mixture of solvents. This is

because the partitioning of a solute between two solvents is another example of a

dynamic equilibrium in which the relative concentration of the iodine in the two

phases is constantly being maintained:

I 2 (in H 2 O)\===\I 2 (in CCl 4 )

If we add iodine to onelayer and shake, the iodine concentration in both layers alters

so as to maintain the value of Kd.

At its simplest, the distribution ratio allows us to calculate the concentration of

solute in one layer, knowing the concentration of solute in the other. For example, if

the concentration of iodine in the aqueous layer was determined by titration with

11.4

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Distribution ratio

The distribution ratio of the gas sulfur dioxide (SO 2 ) between water and trichloromethane

(chloroform) is about 0.90 at room temperature.

In an experiment, sulfur dioxide was bubbled through a mixture of chloroform and water. At

equilibrium the concentration of SO 2 in the chloroform layer was 0.10 mol dm^3. What is the

concentration of sulfur dioxide in the water layer?

Exercise 11H