Partition Coefficient (Kp)
Distribution between immiscible solvents
Understanding Partition Coefficients
The partition coefficient (Kp or KD) is a fundamental parameter in chemistry that quantifies how a solute distributes itself between two immiscible solvents at equilibrium. First systematically studied by Walther Nernst in 1891, this concept has become indispensable in pharmaceutical chemistry, environmental science, and analytical chemistry. The partition coefficient represents the ratio of concentrations of a compound in two immiscible phases, typically an organic solvent (like octanol or chloroform) and water. This dimensionless constant is temperature-dependent and specific to each solute-solvent system.
In pharmaceutical applications, the octanol-water partition coefficient (log P) serves as a critical predictor of drug absorption, distribution, metabolism, and excretion (ADME properties). Lipophilic drugs with high log P values readily cross lipid membranes but may have poor water solubility, while hydrophilic drugs with low log P dissolve well in blood but struggle to penetrate cell membranes. The optimal log P for oral drugs typically ranges from 0 to 3, balancing membrane permeability with aqueous solubility. Medicinal chemists manipulate log P through structural modifications—adding polar groups decreases log P (more hydrophilic), while adding nonpolar groups increases log P (more lipophilic).
Environmental chemists use partition coefficients to predict pollutant behavior in ecosystems. The octanol-water partition coefficient (Kow) correlates with bioaccumulation in fatty tissues, soil adsorption, and atmospheric partitioning. Compounds with log Kow > 4 tend to bioaccumulate in organisms, raising toxicity concerns. Understanding partition coefficients enables prediction of contaminant fate during remediation and assessment of chemical hazards in regulatory frameworks.
Partition Coefficient Formula and Definitions
Kp = [solute]organic / [solute]aqueous
Logarithmic Form (log P):
log P = logâ‚â‚€(Kp)
Commonly reported because Kp values span many orders of magnitude. log P values typically range from -3 (very hydrophilic) to +10 (extremely lipophilic).
Distribution Ratio (D):
D = [total solute in organic phase] / [total solute in aqueous phase]
Accounts for all species (ionized and unionized). For ionizable compounds, D varies with pH while true Kp (for neutral species only) remains constant.
Key Relationship:
High Kp (>1) → solute prefers organic phase (lipophilic)
Low Kp (<1) → solute prefers aqueous phase (hydrophilic)
Kp = 1 → equal distribution between phases
Detailed Step-by-Step Example
Problem: Calculate partition coefficient and extraction efficiency
Given: After equilibration, [iodine]CHCl₃ = 0.80 M and [iodine]H₂O = 0.20 M
Step 1: Apply partition coefficient formula
Kp = [solute]organic / [solute]aqueous
Kp = 0.80 M / 0.20 M = 4.0
Step 2: Calculate log P
log P = logâ‚â‚€(4.0) ≈ 0.60
This positive log P indicates iodine prefers the organic chloroform phase
Step 3: Calculate percentage extracted
Assume equal volumes (Vorg = Vaq = V)
Moles in organic = 0.80V; Moles in aqueous = 0.20V
% extraction = (0.80V)/(0.80V + 0.20V) × 100% = 80%
Step 4: Interpret the result
Kp = 4 means iodine is 4 times more concentrated in chloroform than water. A single extraction removes 80% of iodine from the aqueous phase, demonstrating efficient separation.
Answer: Kp = 4.0; log P ≈ 0.60; 80% extracted
Key Concepts in Partition Behavior
1. Multiple Extraction Strategy
Multiple small-volume extractions are more efficient than a single large-volume extraction. For n extractions with volume ratio r = Vorg/Vaq:
Fraction remaining in aqueous = [1 / (1 + Kpr)]n
Example: Three 10 mL extractions are more efficient than one 30 mL extraction with the same total organic solvent volume.
2. pH Dependence for Ionizable Compounds
For weak acids (HA ⇌ H⺠+ Aâ») and bases, distribution depends on pH because only the neutral form partitions into organic solvents:
D = Kp / (1 + 10pH-pKa) for acids
D = Kp / (1 + 10pKa-pH) for bases
Adjusting pH controls extraction selectivity for acidic and basic compounds.
3. Temperature Effects
Partition coefficients are temperature-dependent, typically following van't Hoff relationship:
ln Kp = -ΔH°/RT + ΔS°/R
Most extractions are conducted at controlled temperatures (often 25°C) for reproducibility. Higher temperatures generally increase distribution into less polar phases.
4. Solvent Selection Considerations
- Immiscibility: Organic and aqueous phases must not significantly mix
- Selectivity: Choose solvents that maximize Kp differences for target vs. impurities
- Safety: Consider toxicity, flammability, and volatility
- Recovery: Easy to evaporate or chemically remove from extracted solute
- Common solvents: Dichloromethane, ethyl acetate, hexane, diethyl ether, chloroform
Real-World Applications
Drug Design and Development
Pharmaceutical companies use log P to optimize drug candidates. Lipinski's Rule of Five states successful oral drugs typically have log P ≤ 5. Chemists modify molecular structures to achieve optimal log P: adding hydroxyl or amine groups decreases log P (better solubility), while adding alkyl chains or aromatic rings increases log P (better membrane penetration).
Environmental Fate Modeling
Kow predicts how pollutants partition between water, soil, sediment, and biota. Pesticides with log Kow > 4 bioaccumulate in fish and wildlife. The EPA uses partition coefficients in risk assessments for chemical approvals, determining safe exposure limits and cleanup standards for contaminated sites.
Liquid-Liquid Extraction
Industrial separation processes exploit partition coefficients for purification. Caffeine extraction from coffee uses dichloromethane (high Kp for caffeine). Rare earth metal separation employs selective extractants with vastly different partition coefficients for adjacent lanthanides. Petroleum refining uses liquid-liquid extraction to remove sulfur and nitrogen compounds.
Analytical Chemistry
Sample preparation for chromatography and mass spectrometry often involves extraction to concentrate analytes and remove matrix interferences. Solid phase extraction mimics liquid-liquid partitioning using bonded stationary phases. Knowing compound log P values helps predict retention times in reversed-phase HPLC where separation depends on differential partitioning between mobile and stationary phases.
Common Mistakes and Tips
Confusing Kp with Distribution Ratio (D)
Kp applies only to the neutral, un-ionized form of a compound. Distribution ratio D accounts for all species (ionized and neutral). For ionizable compounds, D varies with pH while Kp is constant. Always specify which you're reporting and under what conditions (pH, temperature).
Ignoring Volume Ratios in Extraction Calculations
When calculating extraction efficiency, you must account for phase volume ratios. The fraction extracted = KpVorg/(KpVorg + Vaq). Many students incorrectly assume equal volumes or forget this term entirely, leading to erroneous extraction efficiency predictions.
Using Partition Coefficients Outside Dilute Solution Range
Kp assumes ideal behavior and constant activity coefficients, valid only for dilute solutions. At high concentrations, solute-solute interactions, dimerization, and non-ideal mixing can cause significant deviations. Always verify concentration ranges where reported Kp values apply.
Pro Tip: Computational Prediction
Software packages (AlogP, XlogP, ClogP) predict log P from molecular structure with reasonable accuracy (±0.5 log units). These tools accelerate drug design by screening virtual libraries before synthesis. However, always validate predictions experimentally for lead compounds, as subtle structural changes can significantly affect log P.