# Partition Coefficient: Definition and Calculation

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• 0:03 What Is Partitioning?
• 1:00 Solute, Solvent, and Solution
• 1:40 Nernst's Distribution Law
• 3:52 Parition Coefficent Examples
• 5:58 Lesson Summary
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Lesson Transcript
Instructor: Hemnath (Vikash) Seeboo

Taught Science (mainly Chemistry, Physics and Math) at high school level and has a Master's Degree in Education.

This lesson will walk you through to the meaning of the partition coefficient. You will also learn how the partition coefficient can be calculated for different systems.

## What Is Partitioning?

Let's say that you are suffering from a headache, and you decide to take an acetaminophen tablet. Have you ever wondered what happens after you have swallowed a drug like acetaminophen? You probably know that the acetaminophen will move into your stomach, where it will be digested and fully absorbed through the membrane of the gastrointestinal tract into the bloodstream. Technically, the membrane is made of a lipid material that is hydrophobic or lipophilic in nature.

For the acetaminophen to cross the membrane barrier, it must be able to dissolve in the lipid material of the membrane to get through the membrane. It also has to be soluble in the aqueous phase in order to get out of the membrane into the blood. The acetaminophen has thus moved from a lipid setting to an aqueous environment. Generally speaking, partitioning occurs whenever there is movement of a solute (acetaminophen in this case) between two immiscible layers (the lipid, or oil, and water for example).

## Solute, Solvent, and Solution

How is syrup made? In order to make syrup, you add an amount of sugar to water and stir the mixture until all the sugar has dissolved. The sugar used is known as a solute, which is a substance that dissolves to form a solution. The water used is a solvent, which is a substance in which a solute dissolves. The resulting syrup is a solution, which is a mixture of one or more solutes dissolved in a solvent.

Water is a substance that can easily exist as solid, liquid, or gas. These different states are called phases. A phase is a physically distinctive form of matter, such as a solid, liquid, gas, or plasma.

## Nernst's Distribution law

Let us consider two immiscible liquids X and Y in a separating funnel.

Solute Z is then added to the separating funnel containing X and Y. The separating funnel is then shaken so that the solute Z dissolves in both X and Y. The resulting two immiscible solutions are then allowed to settle until dynamic equilibrium is reached. The next question that comes to mind is this: how much of Z has dissolved in liquid X, and how much of Z has dissolved in liquid Y?

In 1891, Walther Hermann Nernst developed an equation known as the partition law or Nernst's distribution law, which states the following:

'When a solute that is soluble in each of two immiscible liquids distributes between the two immiscible liquids, the solute distributes itself between the two liquids in such a way that the ratio of its concentration or solubility in the two liquid phases is equal to a constant known as the partition coefficient, Kpc, or distribution coefficient, Kd.

This partition law holds as long as the following conditions are met:

1. The temperature needs to be constant
2. The two solutions are dilute
3. The solute does not react with the solvents or liquids
4. The solute exists in the same molecular state in both of the two solvents; that is, the solute does not dissociate or associate

Let's look again at the system involving solute Z in liquids X and Y, where a dynamic equilibrium has been established.

The general equation of the partition law is:

The partition coefficient is a simple ratio between two concentrations, and it doesn't matter what concentration units you are using as long as they are the same for both solutions.

The partition law can also be applied to chromatography. Chromatography involves a sample being dissolved in a mobile phase (which may be a gas or a liquid). The mobile phase is then passed through an immobile, immiscible stationary phase. An equilibrium is then established by the solute between the mobile and stationary phase.

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