Design the liquid-liquid extraction that transfers a dissolved solute into a second, immiscible solvent. Adjust the feed concentration, solvent volume, distribution coefficient and stage count to see the extraction yield and raffinate concentration update in real time, and compare how a cross-current multistage extraction outperforms a single contact.
Parameters
Feed solute concentration x_F
g/L
Solute concentration of the feed (aqueous phase) before extraction
Feed volume F
L
Total solvent volume S
L
Total solvent available. Split equally among stages when multistage
Distribution coefficient K
Equilibrium concentration ratio K = y/x. Larger means the solute prefers the solvent
Number of stages N (cross-current)
stages
Stages the total solvent is split into. N = 1 equals a single stage
Operating mode
Contact all solvent at once, or split it across stages
Results
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Raffinate conc. x (g/L)
—
Extraction yield (%)
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Extraction factor E
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Solute remaining (g)
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Mean extract conc. (g/L)
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Multistage gain (vs single)
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Extraction process — partition & stage-to-stage animation
In each vessel two immiscible liquid layers form; solute dots (yellow) migrate across the interface into the extract phase. In multistage mode the feed grows cleaner stage by stage as solute collects in each extract layer.
Extraction yield vs number of stages (same total solvent)
Raffinate concentration x and extraction yield for a single-stage extraction. F: feed volume, x_F: feed concentration, S: solvent volume, K: distribution coefficient. Both volumes are assumed constant in a dilute system.
Fraction of solute remaining in the raffinate after N cross-current stages, with the total solvent S split equally among them. For the same S, raising N lowers the remaining fraction — splitting the solvent extracts more than using it all at once.
$$E=\frac{K S}{F}$$
Extraction factor E. The distribution coefficient multiplied by the solvent-to-feed ratio S/F; a larger E means the extraction proceeds more favourably.
What is Liquid-Liquid Extraction?
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Liquid-liquid extraction is that thing where you shake a separating funnel and it splits into two layers, right? What is actually happening?
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Yes, exactly that. In plain terms, it is "moving house" for a target component (the solute) dissolved in one liquid — relocating it into a second, immiscible solvent. When you shake two liquids that don't mix, like water and ether, the solute distributes itself between the two layers in a fixed ratio. Pick the solvent the target prefers, and the solute keeps migrating into that solvent. That is how you separate it.
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Is that "fixed ratio" the distribution coefficient K on the left?
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Exactly. K is the equilibrium ratio of the extract-phase concentration y to the raffinate concentration x — that is, K = y/x. If K = 5, the solvent layer is five times more concentrated at equilibrium. So choosing a solvent with a large K is step one. Raise the K slider and you will see the extraction yield jump up. K is a physical property set by the solute-solvent pair, plus temperature and pH.
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Then surely adding lots of solvent extracts everything — but raising the solvent volume S never reaches 100%.
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Good catch. With a single stage — one contact — the yield saturates at K·S/(F+K·S). Infinite solvent would approach 100% in theory, but in reality solvent costs money and must be recovered, so you can't use that much. The clever move is to "split the solvent and use it several times". With the same total amount, contacting in two halves, or in a few small portions, extracts far more than dumping it in all at once.
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Wait — the same amount of solvent, but just splitting it changes the result? That seems strange.
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It seems strange, but the formula makes it click. The fraction remaining after N cross-current stages is [F/(F+K·S/N)]^N, a function that shrinks as N grows. Intuitively: the liquid is already dilute after the first contact, then you hit it again with still-clean solvent — even from a dilute liquid the solute migrates into the solvent again in the K ratio. Repeat, and the total recovered is larger. Push the stage count N from 1 to 4 on the left: with the same 10 L of solvent, the yield rises sharply. That is the heart of cross-current multistage extraction.
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Do real factories actually split the solvent like this?
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They do. In practice, mixer-settlers — a mixing tank plus a settling tank that lets the two layers separate — are chained in series. Hydrometallurgy recovering copper, cobalt and rare earths from ore leach liquor, recovering antibiotics from fermentation broth, reprocessing spent nuclear fuel — liquid-liquid extraction is the star of all of them. Real plants often use "counter-current" extraction, which is even more solvent-efficient than cross-current, but this tool is a great way to first grasp the feel that "splitting the solvent helps".
Frequently Asked Questions
For a single-stage extraction with feed volume F, feed concentration x_F, solvent volume S and distribution coefficient K, the raffinate concentration is x = F·x_F/(F + K·S) and the fraction extracted is K·S/(F + K·S). The distribution coefficient K is the equilibrium ratio of the solute concentration in the extract phase y to that in the raffinate phase x, K = y/x, and both solvent volumes are assumed unchanged in a dilute system. This tool uses these relations to report the extraction yield, the extraction factor E = K·S/F and the mass of solute remaining.
In cross-current multistage extraction the total available solvent S is split equally among N stages, with each stage receiving S/N of fresh solvent. After N stages the fraction of solute remaining in the raffinate is [F/(F + K·S/N)]^N, which decreases as N grows. So with the same total amount of solvent, dividing it among several successive contacts extracts substantially more solute than using it all at once. That is the essential advantage of multistage extraction.
The distribution coefficient K is a property of the solute: the equilibrium concentration ratio between the extract and raffinate phases, K = y/x. It depends on the solute-solvent pair, temperature and pH. The extraction factor E = K·S/F is a dimensionless operating parameter — the distribution coefficient multiplied by the solvent-to-feed ratio S/F. When E is well above 1 the extraction proceeds favourably; when E < 1 the solvent quantity is insufficient. In design, K is a given value while E is tuned through the solvent volume.
Because liquid-liquid extraction does not rely on a difference in boiling points, it is advantageous for (1) heat-sensitive substances such as pharmaceuticals, natural products and proteins, (2) mixtures with close boiling points that distillation cannot separate, (3) azeotropic mixtures, and (4) purifying aqueous solutions containing non-volatile solutes. Recovering antibiotics from a fermentation broth, and separating copper, cobalt and rare earths in hydrometallurgy, are standard extraction applications. Distillation can still be more economical when components are volatile with widely separated boiling points, since extraction also needs a separate solvent-recovery step.
Real-World Applications
Hydrometallurgy (metal recovery): Liquid-liquid extraction is widely used to recover metals such as copper, cobalt, nickel, rare earths and uranium from the acid leach liquor of ores. For copper, a chelating extractant dissolved in an organic solvent selectively grabs copper ions from the aqueous phase and carries them into the organic phase (extraction). The organic phase is then contacted with strong acid to strip the copper back into a concentrated aqueous phase (stripping), and electrowinning yields metallic copper. The strength of the method is that it selectively concentrates only the target metal even from low-grade ore.
Pharmaceutical and natural-product purification: Antibiotics (such as penicillin), vitamins and fragrance compounds are heat-sensitive and would decompose if distilled. To recover a target component from a fermentation broth or plant extract, the pH is adjusted so the target's distribution coefficient K becomes large, moving it into the organic solvent. Impurities stay in the aqueous phase, so purification and concentration happen together under mild conditions. Producing decaffeinated coffee — extracting caffeine from coffee beans with a solvent — is another example.
Reprocessing of spent nuclear fuel: In the process known as PUREX, spent nuclear fuel is dissolved in nitric acid, and uranium and plutonium are selectively extracted with an organic solvent containing tributyl phosphate (TBP). The fission products stay in the aqueous phase, so the useful uranium and plutonium are separated from the radioactive waste. Multistage counter-current extraction achieves high recovery and separation — a flagship large-scale application of liquid-liquid extraction.
Petroleum refining and wastewater treatment: Extraction is an important unit operation in petrochemistry too — solvent refining to remove aromatics from lubricating base oils, and recovering BTX (benzene, toluene, xylene) from reformate. Extraction is also used to remove and recover pollutants such as phenol and organic acids from industrial wastewater with a solvent, helping to reduce environmental load.
Common Misconceptions and Pitfalls
A common belief is that "adding more solvent pushes the yield toward 100%". It is true that increasing the solvent volume S raises the extraction factor E = K·S/F and the yield, but a single stage follows the saturation curve K·S/(F+K·S) and never reaches 100% no matter how much S you add. Worse, using a large amount of solvent makes downstream solvent recovery (distillation, etc.) far more energy-intensive and dilutes the extract concentration. Remember that "splitting the solvent into multiple stages" or "going counter-current" is far more solvent-efficient than simply "adding more solvent".
Next, the misconception that "the distribution coefficient K is a fixed constant". This tool treats K as a single value, but the real K varies strongly with temperature, pH, co-existing ions and solute concentration. For extracting organic acids or metal ions in particular, the effect of pH is decisive — shifting the pH by just one unit can change K by an order of magnitude. Turned around, this is the key to real processes that recycle the extractant: adjust the pH so K is large during extraction and small during stripping. This "K switching" is central to design. Also note that at high concentrations the partition departs from a straight line (constant K), so the dilute-system assumption breaks down.
Finally, the idealisation that "the two solvents are completely immiscible". This calculation assumes both volumes are unchanged and the solvents are perfectly immiscible, but real solvents dissolve slightly in each other. If solvent dissolves into the feed side, it becomes solvent loss and product contamination, and the reverse happens too. Also, mixing too violently in the mixer can form an emulsion in which the two layers will not separate, so phase separation in the settler takes a long time or the interface becomes unclear. Real equipment always balances "mix well to approach equilibrium" against "separate the two layers quickly and cleanly", and accounts for the mutual solubility of the solvents.
How to Use
Set feed concentration (g/L) and feed volume (mL) for your aqueous solution containing dissolved solute.
Specify organic solvent volume (mL) and distribution coefficient Kdist for the solute between phases at equilibrium.
Run single or multistage extraction; simulator calculates raffinate concentration, extraction yield (%), and solute mass transfer to the organic phase.
Worked Example
Feed: 500 mL of 8 g/L acetone in water. Organic solvent: 300 mL toluene with Kdist=2.5 (acetone partitions 2.5× preferentially into toluene). Single stage extraction yields raffinate concentration 2.1 g/L, extraction yield 73.8%, solute remaining 1.05 g, mean extract concentration 9.3 g/L. Two-stage crosscurrent extraction with fresh solvent per stage improves yield to 89.2%, demonstrating 1.21× multistage gain versus single contact.
Practical Notes
Higher Kdist values (e.g., Kdist=5 for phenol-toluene) require less solvent volume to achieve target extraction; lower Kdist (e.g., 0.8) demands larger volumes or multiple stages.
For pharmaceutical impurity removal, increase solvent-to-feed ratio above 1:1 stoichiometric; typical industrial practice uses 1.5–3:1 ratios to push equilibrium toward product phase.
Multistage extraction with staged solvent addition outperforms single-batch contact; three stages typically recovers 95%+ solute from dilute feeds (initial 2–5 g/L).