The value of a partition coefficient can be determined experimentally by:

• adding an immiscible liquid to a solution of known concentration;
• shaking the mixture to allow equilibrium to be established;
• finding the concentration of the solute in one of the liquids.

Alternatively, the solute can be added to a mixture of immiscible liquids and the concentration of the solute found in both of them.

The following worked example takes you through the calculation of a partition coefficient.

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100 cm³ of a solution of iodine in water containing 0.090 g iodine was shaken with 10.0 cm³ of carbon disulfide. The carbon disulfide, CS₂, was found by titration with sodium thiosulfate solution to contain 0.088 g of iodine.

What can we work out from the given data?

We can work out:
- the mass of iodine remaining in the water
- the equilibrium concentration of iodine in carbon disulfide and in water in g cm^–3

What is the expression for the partition coefficient, K, for the partition of iodine between carbon disulfide and water?

K = (concentration of iodine in carbon disulfide) / (concentration of iodine in water)

What is the equilibrium concentration of iodine in carbon disulfide?

0.088/10.0 = 0.0088g cm^–3

What is the mass of iodine remaining in the water?

0.090 – 0.088 = 0.002 g

What is the equilibrium concentration of iodine in water?

0.002/100 = 0.00002 g cm^–3

What is the partition coefficient for iodine between carbon disulfide and water at this temperature?

K = 0.0088/0.00002 = 440

Suppose we had shaken the 100 cm³ of iodine solution in water containing 0.090 g of iodine with 100 cm³ of carbon disulfide at the same temperature. How can we calculate how much iodine would have been transferred to the carbon disulfide layer?

Let's call the mass of iodine in the CS₂ at equilibrium X g. What will be the mass of iodine remaining in the water?

(0.090 – X) g

What expression can we write that links X with the partition coefficient?

440 = (X/100) / ((0.090 – X)/100)

440 = X/(0.090 – X)

How can we manipulate this expression to work out the value of X?

440(0.090 – X) = X

39.6 – 440X = X

440X + X = 39.6

441X = 39.6

X = 39.6/441 = 0.0898 g