Study notes

Qwestrum Engineering360 · Chemical Engineering · Separation Processes

Liquid Liquid Extraction

Liquid-liquid extraction transfers a solute from feed to an immiscible solvent according to a distribution coefficient; multistage design is done on a ternary equilibrium diagram using tie lines and the lever rule, with counter-current contacting giving the best recovery.

Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

$Selectivity \beta = \frac{m_{solute}}{m_{carrier}} governs solvent choice$
Counter-current multistage beats single-stage extraction
The plait point limits the two-phase region on the ternary diagram

Topic details

Introduction

This Treybal topic separates components by preferential solubility rather than volatility, useful for heat-sensitive or close-boiling mixtures. You read equilibrium from a ternary (triangular) diagram, apply the lever rule to split feed into extract and raffinate, and step off stages for counter-current cascades much as in distillation, guided by the distribution coefficient and selectivity.

Key relations & formulas

E = m \frac{V}{L}

(extraction factor, m = distribution coefficient)

y*/x = m

(distribution / partition relation)

Formulas (Indian textbook notation)

$Lever rule on the ternary diagram fixes raffinate and extract amounts$

Notation and sign conventions

Relation 1 —

E = m \frac{V}{L}

E = m \frac{V}{L}

(extraction factor, m = distribution coefficient)

Write this relation with symbols exactly as in Separation Process Principles — Seader & Henley before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

y*/x = m

y*/x = m

(distribution / partition relation)

Relation 3 —

Lever rule on the ternary diagram fixes raffinate and extract amounts

Formulas (Indian textbook notation)

$Lever rule on the ternary diagram fixes raffinate and extract amounts$

Concept in depth

When a solute distributes between two immiscible liquids it reaches equilibrium set by the distribution coefficient m; a good solvent has both a high m (loads a lot of solute) and high selectivity (rejects the carrier). The ternary diagram is essential because the three components are partially miscible, so tie lines connect equilibrium extract and raffinate compositions and the lever rule apportions the amounts. A single stage is limited by equilibrium, so counter-current cascades are used to push recovery high while keeping solvent use low — the same driving-force logic as gas absorption, transplanted to two liquid phases.

Assumptions and validity limits

State assumptions explicitly before using any relation for liquid liquid extraction — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Separation Processes viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Separation Processes papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to liquid liquid extraction.
4. Use equation 1:

E = m \frac{V}{L}

.
5. Use equation 2:

y*/x = m

.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Liquid Liquid Extraction appears in refineries and specialty chemicals. In Indian chemical curricula this topic is tested because it connects theory to distillation, extraction, and membranes.

GATE and semester exams often combine liquid liquid extraction with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use liquid liquid extraction?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Students treat the phases as fully immiscible when the solvent and carrier partly dissolve each other, misapply the lever rule direction, and confuse distribution coefficient with selectivity. Reading tie lines off the wrong side of the binodal curve is a frequent diagram error.

Quick revision checklist

Before attempting liquid liquid extraction problems, confirm you can:

Selectivity \beta = \frac{m_{solute}}{m_{carrier}} governs solvent choice

2. Counter-current multistage beats single-stage extraction
3. The plait point limits the two-phase region on the ternary diagram

Revise the solved examples in Separation Process Principles — Seader & Henley and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Single-stage extraction split

Problem

A distribution coefficient m = 3 relates y* = 3x. With equal solvent and feed rates (V = L), find the extraction factor E.

Solution

E = mV/L = 3×1 = 3. Since E > 1, a single stage removes most solute; fraction remaining in raffinate ≈ 1/(1 + E) = 0.25, so 75% is extracted.

Conceptual check — Liquid Liquid Extraction

Problem

In a Separation Processes semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of liquid liquid extraction." What should a complete answer include?

Exams & GATE

Treybal Ch. 10 — use the equilateral ternary diagram and the lever-arm rule.

📖 Standard books (India)

Separation Process Principles — Seader & Henley
Read: Syllabus unit
Distillation, extraction, and membranes

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📚Key formulas & points