Calculate and use a partition coefficient
Use Kpc, phase volumes and total solute amount to calculate how much solute is present in each immiscible solvent.
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 25. Use the equilibrium expressions and data stated in the question; written practice is self-checked and human subject-teacher review remains pending.
Before you begin
- Use AS equilibrium expressions, mole calculations, logarithms, and Brønsted–Lowry acid–base ideas.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
If Kpc = [org]/[aq], which two equations usually determine phase amounts?
What you will learn
- Use equilibrium concentration ratio with a stated solvent convention
- Combine the ratio with conservation of solute
- Calculate equilibrium amounts or concentrations in both phases
Concentration ratio and conservation determine the distribution
With Kpc = [solute]organic/[solute]aqueous, write the ratio using n/V for each phase. A second equation comes from conservation: total solute amount equals the amount in the organic phase plus the amount in the aqueous phase.
Use both equations to solve for the unknown amounts. The solute is the same species in the same physical state in each solvent, as required by the syllabus outcome.
Repeated extraction can be compared carefully
For an extraction calculation, the partition ratio relates equilibrium concentrations after contact and settling. If solvent volumes and total amount are known, calculate each phase concentration and amount explicitly.
Do not assume that an amount ratio equals Kpc unless the phase volumes are equal. Keep the solvent order, units and total amount balance visible.
Pause and explain
When the solvent volumes differ, what must be used in Kpc?
Worked example
A total of 0.50 mol solute is distributed between 0.20 dm³ water and 0.10 dm³ organic solvent. Kpc=[org]/[aq]=4.0. Find the amounts in each phase.
Show the worked solution
- Let x mol be in the organic phase; then 0.50−x is aqueous.
- Use (x/0.10)/((0.50−x)/0.20)=4.0.
- Solve and check the amounts sum to 0.50 mol.
Answer 2x/(0.50−x)=4, so x=0.333 mol is organic and 0.167 mol is aqueous.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A total of 0.30 mol solute is shared between 0.10 dm³ organic solvent and 0.20 dm³ water. Kpc=[org]/[aq]=2.0. Find the amount in each phase.
Give me a hint
Let x be organic; form the concentration ratio and mass balance.
Compare my reasoning
- Organic amount is x; aqueous amount is 0.30−x.
- Set (x/0.10)/((0.30−x)/0.20)=2.0.
- Solve and check the total.
2x/(0.30−x)=2, giving x=0.15 mol organic and 0.15 mol aqueous.
Look for these in your work
- Amounts assigned
- Concentration ratio used
- Mass balance checked
At equilibrium, 0.24 mol solute is in 0.08 dm³ organic solvent and 0.06 mol is in 0.12 dm³ water. Calculate Kpc.
Give me a hint
Calculate both phase concentrations before taking the ratio.
Compare my reasoning
- [org]=0.24/0.08.
- [aq]=0.06/0.12.
- Divide organic concentration by aqueous concentration.
[org]=3.0 mol dm⁻³ and [aq]=0.50 mol dm⁻³, so Kpc=6.0.
Look for these in your work
- Volumes included
- Concentrations calculated
- Convention followed
A learner reports Kpc=3 from 0.30 mol organic and 0.10 mol aqueous, ignoring that the volumes are 0.15 dm³ and 0.20 dm³. Correct the calculation.
Give me a hint
Convert amounts to concentrations first.
Compare my reasoning
- [org]=0.30/0.15=2.0 mol dm⁻³.
- [aq]=0.10/0.20=0.50 mol dm⁻³.
- Use organic over aqueous.
Kpc = 2.0/0.50 = 4.0. The amount ratio is not the partition coefficient because phase volumes differ.
Look for these in your work
- Both volumes used
- Concentration ratio recalculated
- Amount-ratio error explained
Common mistakes
- Equating Kpc to the ratio of amounts when phase volumes differ
- Using the wrong phase in the numerator
- Losing solute during the mass balance
- Mixing dm³ and cm³ without conversion
What can you explain now?
If Kpc = [org]/[aq], which two equations usually determine phase amounts?
Compare with the explanation
The concentration ratio and total-solute balance
The ratio describes distribution and conservation supplies total amount.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do the concentration ratio and conservation of total solute combine to solve a partition problem?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.