25.2 Partition Coefficients

2026 Syllabus Objectives

By the end of these notes, you should be able to:

  1. State what is meant by the term partition coefficient, K_pc
  2. Calculate and use a partition coefficient for a system where the solute is in the same physical state in both solvents
  3. Understand the factors that affect the numerical value of a partition coefficient in terms of the polarities of the solute and the solvents used

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1. What is a Partition Coefficient?

Setting the Scene

Imagine you have a substance — let's call it a solute (this is the thing that dissolves). Now imagine you have two liquids that do not mix with each other, like oil and water. These are called immiscible solvents — "immiscible" just means they refuse to mix and instead form two separate layers.

When you add the solute to these two solvents and shake them together, something interesting happens: the solute distributes (spreads) itself between the two layers. Some of the solute ends up in one layer, and the rest ends up in the other layer. Eventually, a state of equilibrium is reached — this is the point where the solute is moving between the two layers at exactly the same rate in both directions, so the concentrations in each layer stop changing.

The Equilibrium

We can write this as a reversible reaction (using the ⇌ symbol to show equilibrium):

Solute (in Solvent A) ⇌ Solute (in Solvent B)

For example, if the two solvents are water and an organic solvent (an organic solvent is a carbon-based liquid, like hexane):

CH₃NH₂ (aq) ⇌ CH₃NH₂ (organic solvent)

Defining the Partition Coefficient

The partition coefficient (K_pc) is the ratio of the concentration of the solute in one solvent to its concentration in the other solvent, at equilibrium and at a specific temperature.

In plain English: it tells you how much the solute "prefers" one solvent over the other.

The formula is:

Kpc=[Solute in Solvent A][Solute in Solvent B]K_{pc} = \frac{[\text{Solute in Solvent A}]}{[\text{Solute in Solvent B}]}

Important: The units of concentration cancel out, so K_pc has no units.

Important: K_pc only applies when the solute is in the same physical state in both solvents. For example, if the solute is dissolved (as a liquid solution) in both layers — not reacting, not ionising differently — then the expression above applies directly.

A Concrete Example

For methylamine (CH₃NH₂) distributed between an organic solvent (on top) and water (on the bottom):

Kpc=[CH3NH2 in organic solvent][CH3NH2 in water]K_{pc} = \frac{[\text{CH}_3\text{NH}_2 \text{ in organic solvent}]}{[\text{CH}_3\text{NH}_2 \text{ in water}]}

What Does the Value of K_pc Tell You?

  • If K_pc > 1: the solute is more concentrated in the top solvent (as written in the numerator — the top of the fraction). If you write the organic solvent on top, K_pc > 1 means the solute prefers the organic solvent.
  • If K_pc < 1: the solute is more concentrated in the bottom solvent (the denominator). If water is on the bottom, K_pc < 1 means the solute prefers water.
  • If K_pc = 1: the solute is equally distributed between both solvents.

Think of it this way: K_pc is a measure of preference. A high K_pc means the solute strongly favours whichever solvent you put on top of the fraction.

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