Chemical engineering transport & equilibrium foundations of Liquid–Liquid Extraction Equilibrium.
Liquid–liquid extraction (solvent extraction) is a key chemical engineering separation technology used when distillation is economically or thermodynamically impractical—such as separating close-boiling mixtures, recovering heat-sensitive bioproducts, breaking azeotropes, or purifying dilute specialty chemicals. In extraction, an immiscible or partially miscible liquid solvent (ethyl acetate) is mixed with a liquid feed mixture (water and acetic acid). Solute (acetic acid) distributes between the two liquid phases based on chemical potential and activity coefficient differences until thermodynamic phase equilibrium is achieved. The solute-rich solvent phase is termed the extract, and the remaining solute-depleted feed phase is termed the raffinate. Phase equilibria for ternary liquid systems are represented on equilateral or right-triangular coordinates featuring a binodal solubility curve that separates the single-phase homogeneous region from the two-phase immiscible envelope. Within the two-phase region, straight tie lines connect conjugate liquid phases in mutual thermodynamic equilibrium. According to Nernst's distribution law for dilute-to-moderate concentrations, the equilibrium distribution coefficient K_D = y_A / x_A (ratio of solute mass fraction in extract to raffinate) remains constant: y_A = K_D · x_A. In this laboratory investigation, ternary mixtures of water, acetic acid, and ethyl acetate are equilibrated in a jacketed separatory cell across raffinate concentrations from 5.0 to 30.0 wt% to construct tie lines, determine distribution coefficient K_D, and evaluate extraction selectivity β.
1. Thermodynamic Foundations of Liquid–Liquid Extraction
Liquid–liquid extraction separates chemical components based on their relative solubilities in two immiscible or partially miscible liquid phases. Extraction is preferred when distillation is energy-intensive (e.g., dilute recovery of high-boiling acids from water) or hindered by close boiling points or azeotrope formation.
2. Phase Equilibrium & The Nernst Distribution Law
At thermodynamic equilibrium, the chemical potential $\mu_i$ of each component $i$ is identical in both extract ($E$) and raffinate ($R$) phases:
\[ \mu_{i,E} = \mu_{i,R} \implies \gamma_{i,E} y_i = \gamma_{i,R} x_i \]where $\gamma$ represents the liquid-phase activity coefficient. The distribution coefficient $K_D$ is defined as the ratio of solute mass fractions:
\[ K_D = \frac{y_A}{x_A} = \frac{\gamma_{A,R}}{\gamma_{A,E}} \]In dilute-to-moderate concentration regimes where activity coefficients remain relatively stable, Nernst's distribution law dictates a linear partition equilibrium:
\[ y_A = K_D \cdot x_A \]where $K_D$ is the slope of the equilibrium distribution curve.
3. Ternary Phase Diagrams & Selectivity
On a ternary phase diagram, the binodal curve bounds the two-phase immiscible zone. Straight tie lines connect conjugate extract ($y_A, y_B, y_S$) and raffinate ($x_A, x_B, x_S$) compositions. The separation effectiveness is quantified by the dimensionless selectivity (separation factor) $\beta$:
\[ \beta = \frac{y_A / x_A}{y_B / x_B} = \frac{K_{D,A}}{K_{D,B}} \]where $B$ is the carrier solvent (water). A viable extraction solvent requires $\beta \gg 1.0$.
Viva voce questions & analytical theory
What is the physical significance of the distribution coefficient K_D in liquid extraction?
The distribution coefficient K_D = y_A / x_A measures the affinity of the solute for the extract solvent relative to the raffinate carrier; K_D > 1 indicates favorable extraction requiring less solvent, while K_D < 1 requires higher solvent-to-feed ratios.
How is extraction selectivity (separation factor) β defined and why must β > 1?
Selectivity is β = (y_A / x_A) / (y_B / x_B) = K_D,A / K_D,B, where B is the carrier solvent; if β = 1, solute and carrier distribute equally with zero separation, meaning an effective solvent must have β substantially greater than 1.
What is the plait point on a ternary liquid-liquid binodal solubility curve?
The plait point is the unique point on the binodal curve where the tie line length shrinks to zero, meaning the compositions of the conjugate extract and raffinate phases become identical and two-phase separation ceases.
Why does acetic acid dimerize in non-polar organic solvents and how does it affect distribution?
Acetic acid molecules form cyclic hydrogen-bonded dimers in non-polar solvents (e.g., benzene); dimerization causes K_D to vary with concentration (y_A ∝ x_A^2), whereas in polar solvents like ethyl acetate, hydrogen bonding with solvent maintains monomer distribution.
What are the key criteria for selecting an industrial extraction solvent?
High distribution coefficient K_D, high selectivity β, low miscibility with carrier, sufficient density difference (Δρ > 100 kg/m^3) for rapid settling, ease of solvent recovery (boiling point difference for distillation), low toxicity, and low cost.
How does temperature affect the two-phase binodal envelope?
Increasing temperature generally increases mutual solubility between carrier and solvent, shrinking the two-phase immiscible region and shifting the binodal curve until the Upper Critical Solution Temperature (UCST) is reached, where miscible single-phase behavior occurs.
Experimental precautions and process safety
- Ethyl acetate is volatile and flammable; perform all mixing and sampling inside an active fume hood.
- Ensure sufficient settling time (at least 30 minutes) to eliminate microscopic haze droplets before sampling.
- Maintain cell temperature strictly at 25.00 ± 0.05 °C, as liquid-liquid phase equilibria are sensitive to temperature.
- Pipette sample aliquots carefully without disturbing the liquid-liquid meniscus interface.
Theoretical assumptions & boundary condition limits
- The transport and thermodynamic models apply within the specified calibrated operating window (5.0 to 30.0 wt%).
- Assumes ideal continuum flow and homogeneous phase mixing without unmodeled parasitic wall losses.
- Continuous sensor readings reflect ordinary least-squares regression across successive observations.
- High-temperature or extreme concentration excursions require non-ideal equation-of-state corrections.