Ch 2 · Partition coefficients · AS & A Level Chemistry 9701
Topic 2 of 2 in Equilibria — AS & A Level Chemistry 9701 — 48 lessons.
Introduction
When a solute is shaken with two immiscible solvents, it distributes itself between them until equilibrium is reached. The ratio of its concentrations in the two solvents at equilibrium, the partition coefficient, is constant at a given temperature and underlies solvent extraction, a technique used to separate and purify organic compounds.
Key ideas — Defining the partition coefficient
When a solute dissolves in two immiscible solvents in contact with each other, it establishes a dynamic equilibrium between the two solvents, for example a solute X distributed between water and an organic solvent:
🧑🏫 Teacher's explanation
Imagine you have a handful of colorful marbles and two separate bowls: one filled with water and one filled with oil. If you shake them together, some marbles will end up in the water and some in the oil. Even though they are in different liquids, they are constantly moving back and forth between the bowls. Eventually, they reach a 'balance' where the number of marbles moving from water to oil is the same as the number moving from oil to water.
📖 Definitions
🔍 Worked example — Easy
A solute X is distributed between water and benzene. At equilibrium, [X]_aq = 0.02 mol dm^-3 and [X]_benzene = 0.10 mol dm^-3. Calculate the partition coefficient K_pc using the formula K_pc = frac[X]_organic[X]_aq.
🔍 Worked example — Standard
A sample containing 0.50 g of a drug is dissolved in 100 cm^3 of water. After shaking with 100 cm^3 of ether, 0.40 g of the drug is found in the ether layer. Calculate K_pc (assume volumes are constant and no drug is lost).
🔍 Worked example — Exam-style
A solute A has K_pc = 10 (where K_pc = frac[A]_org[A]_aq). If 2.0 g of A is dissolved in 100 cm^3 of water and extracted with 100 cm^3 of organic solvent, what mass of A remains in the water layer at equilibrium?
⚠️ Common errors
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🎯 Exam question
Key ideas — Calculating and using Kpc
K_pc is calculated directly from measured equilibrium concentrations in the two solvents. Once known for a given solute–solvent pair at a given temperature, it can be used the other way: given the total amount of solute and the volumes of the two solvents, K_pc predicts how the solute will distribute between them, since K_pc remains constant regardless of the total quantity of solute present or the volumes used, provided the temperature is unchanged.
🧑🏫 Teacher's explanation
Imagine you have a room divided by a thin curtain. You throw a handful of colorful marbles into the room. Some marbles are 'sticky' and prefer to stay on the left side, while others are 'slippery' and prefer the right side. Even if you add more marbles or change the size of the room, the ratio of sticky marbles to slippery marbles in each section will always stay the same at equilibrium.
📖 Definitions
🔍 Worked example — Easy
A solute is distributed between water and hexane at 25^°C. The equilibrium concentration in water is 0.02 mol dm^-3 and in hexane is 0.10 mol dm^-3. Calculate K_pc (expressed as [solute]_organic / [solute]_aqueous).
🔍 Worked example — Standard
A solute has a K_pc = 4.0 (where K_pc = [organic] / [aqueous]). If 100 cm^3 of water contains 0.2 g of solute at equilibrium, calculate the concentration of the solute in the organic layer in g dm^-3.
🔍 Worked example — Exam-style
A sample containing 1.0 g of a drug is extracted using 50 cm^3 of water and 50 cm^3 of ether. The K_pc (ether/water) is 3.0. Calculate the mass of the drug remaining in the water layer after one extraction.
⚠️ Common errors
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🎯 Exam question
Key ideas — Factors affecting the value of Kpc
The numerical value of K_pc depends on the relative polarity of the solute compared with each solvent, following the general principle that "like dissolves like". A solute with polarity similar to the organic solvent (e.g. a non-polar or weakly polar organic molecule with a non-polar solvent such as hexane) is more strongly attracted into that solvent's layer than into water, giving a large K_pc. A solute that is more polar, or capable of hydrogen bonding with water, remains more concentrated in the aqueous layer, giving a small K_pc. Increasing the structural similarity or the strength of intermolecular forces between the solute and one solvent therefore increases the proportion of solute partitioning into that solvent.
🧑🏫 Teacher's explanation
Imagine you have a handful of colorful marbles being poured into a container that has two layers of liquid: oil on top and water on the bottom. If the marbles are made of wood (like the oil), they will mostly float and stay in the oil layer. If the marbles are made of heavy metal (like the water), they will sink and stay in the water layer. The 'partition coefficient' is just a mathematical way of saying how much the marbles prefer one layer over the other.
📖 Definitions
🔍 Worked example — Easy
A solute is distributed between benzene and water. The concentration in benzene is 0.05 mol dm^-3 and the concentration in water is 0.01 mol dm^-3. Calculate K_pc (assuming K_pc = [solute]_organic / [solute]_aqueous).
🔍 Worked example — Standard
A sample containing 0.10 g of a drug is extracted using 50 cm^3 of water and 50 cm^3 of ether. If the K_pc (ether/water) is 4.0, calculate the mass of the drug remaining in the water layer after one extraction.
🔍 Worked example — Exam-style
A solute has a K_pc (octanol/water) of 0.001. If 1.0 g of solute is added to 100 cm^3 of water and 100 cm^3 of octanol, calculate the mass of solute in the octanol layer at equilibrium.
⚠️ Common errors
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🎯 Exam question
Key ideas — Significance in solvent extraction
Solvent extraction uses two immiscible solvents to separate a solute from a mixture, for example removing an organic product from an aqueous reaction mixture by shaking with an organic solvent in a separating funnel. A large value of K_pc for the desired solute (favouring the organic layer) and a very different value for impurities (favouring the aqueous layer) allows efficient separation and purification, since most of the desired solute transfers into the organic layer while most impurities remain in the aqueous layer. This principle underlies extraction and purification processes in both laboratory synthesis and industry, including recovering organic products from aqueous reaction mixtures and extracting natural products from plant material.
🧑🏫 Teacher's explanation
Imagine you have a crowd of people in a room divided by a glass wall. On one side is a swimming pool (the aqueous solvent) and on the other is a dry lounge (the organic solvent). If the people are 'party animals', they will spend most of their time in the pool. If they are 'bookworms', they will stay in the lounge. The partition coefficient is simply a mathematical way of describing how much the 'people' (the solute molecules) prefer one room over the other.
📖 Definitions
🔍 Worked example — Easy
A solute is distributed between water and benzene. At equilibrium, the concentration in benzene is 0.05 mol dm^-3 and the concentration in water is 0.01 mol dm^-3. Calculate the partition coefficient K_pc (assuming benzene is the organic solvent).
🔍 Worked example — Standard
A mixture contains 0.20 g of a compound. This compound is extracted using 50 cm^3 of water and 50 cm^3 of ether. The partition coefficient K_pc (ether/water) is 4.0. Calculate the mass of the compound remaining in the water layer after one extraction.
🔍 Worked example — Exam-style
An organic acid is extracted from 100 cm^3 of water using 100 cm^3 of ether. The initial mass of the acid is 1.00 g. The K_pc (ether/water) is 9.0. Calculate the mass of the acid extracted into the ether layer after a single extraction.
⚠️ Common errors
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🎯 Exam question
Worked example
Question. An organic acid, X, is shaken with water and an immiscible organic solvent until equilibrium is reached. At equilibrium, [X]_aq = 0.0400\ mathrmmol\ dm^-3 and [X]_organic = 0.360\ mathrmmol\ dm^-3. (a) Calculate K_pc for X between the organic solvent and water. [2] (b) A fresh mixture is prepared in which [X]_aq = 0.0250\ mathrmmol\ dm^-3 at equilibrium. Calculate [X]_organic in this mixture. [2]
🔍 Worked example — Easy
A solute has a concentration of 0.050 mol dm^-3 in water and 0.25 mol dm^-3 in hexane at equilibrium. Calculate the partition coefficient K_pc for the solute between hexane and water.
🔍 Worked example — Standard
A drug has a K_pc of 4.5 between octanol (organic) and water (aqueous). If the concentration in the water layer is 0.020 mol dm^-3, calculate the concentration in the octanol layer.
🔍 Worked example — Exam-style
An organic acid X is extracted using water and ether. At equilibrium, [X]_aq = 0.0400 mol dm^-3 and [X]_org = 0.360 mol dm^-3. A new sample is prepared where [X]_aq = 0.0250 mol dm^-3. Calculate the new [X]_org assuming K_pc remains constant.
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