Reference ID: MET-1DCA | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Liquid–liquid extraction of weak acids or bases is governed by two simultaneous equilibria: acid–base dissociation in the aqueous phase and partitioning of the neutral species into the organic solvent. The fraction of the solute that is neutral, quantified by the distribution ratio α, collapses from ≈1 at low pH to ≈0 as the pH rises above the solute pKa. Because only the neutral form partitions, the overall extraction efficiency E is a strong function of pH. This relationship is critical when designing extraction columns, mixer-settler batteries, or pH-swing purification loops in pharmaceutical, fine-chemical, and hydrometallurgical operations.
Methodology & Formulas
Acid–base speciation
For a monoprotic acid, the neutral fraction is
\[
\alpha = \frac{1}{1 + 10^{\,(\text{pH}-\text{p}K_a)}}
\]
The term 10(pH–pKa) is the concentration ratio of ionised to neutral species.
Partition equilibrium
The Nernst partition coefficient P (organic ↔ aqueous, neutral species only) is assumed constant at the temperature of interest.
Overall extraction factor
With equal phase volumes (Φ = Vorg/Vaq = 1), the fraction extracted is
\[
E = \left(1 + \frac{1}{P\,\alpha\,\Phi}\right)^{-1}
\]
E ranges from 0 (no extraction) to 1 (complete extraction).
Operating regime summary
Variable
Range
Consequence
Temperature
15–40 °C
P variation within ±10%
pH
< 1
Risk of partial miscibility (MEK/water)
pH
> 7
E < 5%, impractical
pH controls the protonation state of ionizable solutes. Only the uncharged (or correctly charged) species partitions into the organic phase; the aqueous phase retains the opposite form. Shifting pH changes the ratio of extractable to non-extractable species, directly altering the distribution coefficient and overall yield.
Measure or obtain the pKa of the target compound.
Run small-scale shake tests at 0.5–1 pH unit intervals across pKa ±2.
Plot recovery vs. pH; the plateau maximum is your operating window.
Verify that the chosen pH does not precipitate solids or corrode equipment.
Yes. Near the iso-electric point, surfactant-like molecules lose charge, reducing electrostatic repulsion and promoting stable emulsions. Maintain pH at least 0.5 units away from the iso-electric point, and if needed, add a demulsifier or increase temperature to break the rag layer.
Within ±0.1 pH units of the set-point. A drift of 0.3 units can shift the distribution coefficient by 20–30% for compounds with pKa close to the operating pH. Install inline pH probes with automated acid/base addition and cascade control to the organic-phase flow meter for tight regulation.
Select a pH where only one species is uncharged and extractable.
Extract the first component, then shift pH to make the second species extractable and perform a second extraction step.
Alternatively, use pH-swing extraction: extract at one pH, then back-extract (strip) at another pH to recover each species into separate aqueous streams.
Worked Example: pH Effect on Extraction Efficiency
A process engineer is designing a liquid–liquid extraction to recover 3-methoxybenzoic acid from an aqueous waste stream. The solvent is methyl isobutyl ketone (MIBK), and the operation is carried out at 25 °C. The engineer needs to know how much acid will be extracted if the aqueous raffinate is buffered to pH 7.0.
Calculate the fraction of the acid that is in the neutral form at pH 7.0:
\[
\alpha = \frac{1}{1 + 10^{(\text{pH}-\text{pKa})}} = \frac{1}{1 + 10^{(7.0-3.13)}} = 0.000135
\]
Determine the effective distribution coefficient D:
\[
D = P_{\text{lit}} \cdot \alpha = 2.8 \cdot 0.000135 = 0.000378
\]
Compute the extraction efficiency E for a single equilibrium stage:
\[
E = \frac{D \cdot \Phi}{1 + D \cdot \Phi} = \frac{0.000378 \cdot 1.0}{1 + 0.000378 \cdot 1.0} = 0.000378
\]
Final Answer
At pH 7.0, only 0.038% of the 3-methoxybenzoic acid is extracted into the MIBK phase under the specified conditions.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
