Partition coefficients

· Partition coefficient, Kpc = ratio of the concentrations of a solute in two immiscible solvents at equilibrium.
· General expression: Kpc = [solute] in solvent 1 ÷ [solute] in solvent 2.
· The two solvents must be immiscible, e.g. water and an organic solvent.
· The solute must be in the same physical state / same molecular form in both solvents.
· Kpc has no units because it is a ratio of concentrations.
· Kpc is constant at a fixed temperature for a given solute and pair of solvents.
· Always state clearly which solvent is in the numerator and which is in the denominator.

This diagram shows a solute distributed between two immiscible liquid phases at equilibrium. It supports the idea that the solute does not move completely into one layer, but reaches a fixed concentration ratio between the two layers. Source

Writing Kpc expressions

· Use square brackets for concentration, usually in mol dm⁻³.
· Example: for iodine distributed between hexane and water: Kpc = [I₂]hexane ÷ [I₂]water.
· If Kpc > 1, the solute is more concentrated in the numerator solvent.
· If Kpc < 1, the solute is more concentrated in the denominator solvent.
· Do not include volumes directly in the Kpc expression; convert to concentrations first.
· The expression must match the wording of the question: Kpc for solute between A and B may be written either way if the question defines it.

This image is useful for remembering that Kpc is a concentration ratio. It also reinforces that the solvent named in the numerator determines how the value of Kpc is interpreted. Source

Calculating Kpc

· Step 1: Write the correct Kpc expression.
· Step 2: Calculate moles using n = cV, remembering to convert cm³ to dm³.
· Step 3: Use concentration = moles ÷ volume for each solvent layer.
· Step 4: Substitute the two concentrations into the Kpc expression.
· Step 5: Interpret the value: high concentration in the numerator solvent gives Kpc > 1.
· For titration data, use the titre to find moles of solute in one layer, then use total moles – moles in one layer = moles in the other layer.
· Common exam trap: using moles instead of concentrations when the two solvent volumes are different.

Practical use: solvent extraction

· Partition coefficients explain solvent extraction: a solute distributes between two immiscible solvents according to its Kpc.
· A separating funnel is used to shake the two solvents and allow the layers to separate.
· The less dense layer is usually on top; the denser layer is usually at the bottom.
· The solute is extracted more effectively into the solvent where it has the greater solubility.
· In practice, repeated extractions with fresh solvent can remove more solute than one single extraction.
· Allow layers to separate fully before draining to avoid contamination between phases.

This photograph shows two immiscible liquid layers in a separating funnel. It is a clear practical example of the type of apparatus used when a solute partitions between an organic phase and an aqueous phase. Source

These diagrams show how a compound partitions between aqueous and organic layers during extraction. They are useful for linking the Kpc calculation to real laboratory separation technique. Source

Factors affecting Kpc

· Polarity of the solute affects which solvent it dissolves in better.
· Polarity of the solvents affects the strength of solute–solvent interactions.
· Like dissolves like: polar solutes tend to dissolve better in polar solvents, while non-polar solutes tend to dissolve better in non-polar solvents.
· Stronger intermolecular forces between solute and solvent increase solubility in that solvent.
· Examples of important interactions: hydrogen bonding, permanent dipole–permanent dipole forces, and instantaneous dipole–induced dipole forces.
· Changing the solvent pair changes the numerical value of Kpc.
· Changing the temperature can also change Kpc, so calculations assume constant temperature unless stated otherwise.

Exam technique

· Always check whether the question defines Kpc = organic / aqueous or aqueous / organic.
· Use dm³, not cm³, when calculating concentration in mol dm⁻³.
· If given masses, convert using moles = mass ÷ Mr before finding concentration.
· If one layer is analysed by titration, scale up if only an aliquot was titrated.
· Interpret final answers in words: e.g. “The solute is more soluble in the organic solvent because Kpc > 1.”
· Do not give units for Kpc.