Partition Coefficients in Drug Design — log P, log D and the Distribution Law
In your practical class you shook an organic compound with ether and water, and your textbook called the ratio of concentrations the distribution coefficient. That same ratio, measured in one particular solvent pair, is the single most quoted physical number in medicinal chemistry. It is written as log P, and it is used to decide whether a molecule can cross a cell membrane at all. This article takes the formula you already have, computes it three ways, and then does the part most summaries skip — showing exactly where the simple ratio stops describing what a drug does inside a body.
The formula you already know
For an ionisable compound: log DpH = log P − log₁₀ (1 + 10(pH − pKa)) for an acid
log DpH = log P − log₁₀ (1 + 10(pKa − pH)) for a base
What each term means
| Symbol | Meaning | Unit |
|---|---|---|
| corganic, caqueous | Equilibrium concentration of the same chemical species in each phase | mol/L or g/L (any unit, provided both are the same) |
| P | Partition coefficient — strictly for the neutral, un-ionised form only | dimensionless |
| log P | Base-10 logarithm of P. log P = 0 means equal preference; log P = 3 means 1000× preference for octanol | dimensionless |
| D | Distribution coefficient — the ratio of total concentration (ionised + un-ionised) at a stated pH | dimensionless |
| pKa | Acid dissociation constant of the ionisable group, as −log₁₀ Ka | dimensionless |
The solvent pair is not arbitrary. 1-Octanol saturated with water against water saturated with 1-octanol is the agreed reference pair, because octanol has a polar hydroxyl head and a long non-polar tail, which makes it a crude but reproducible stand-in for the lipid part of a cell membrane. Change the solvent and you change the number, so "log P" without naming octanol–water is meaningless.
Worked example 1 — measuring P by the shake-flask method
100.0 mg of a neutral compound is shaken to equilibrium with 50.0 mL of 1-octanol and 50.0 mL of water at 25 °C. Analysis finds 90.0 mg in the octanol layer. Find P and log P.
Mass in water = 100.0 − 90.0 = 10.0 mg
coctanol = 90.0 mg ÷ 50.0 mL = 1.80 mg/mL
cwater = 10.0 mg ÷ 50.0 mL = 0.200 mg/mL
P = 1.80 ÷ 0.200 = 9.00
log P = log₁₀ 9.00 = 0.954
Cross-check by the mass route. Because the two volumes are equal, the volumes cancel and P must simply be the mass ratio: 90.0 ÷ 10.0 = 9.00. ✔ If the volumes had been unequal you could not take this shortcut — that is the most common slip in this calculation.
Worked example 2 — why log P alone misleads you at blood pH
A carboxylic acid drug has log P = 3.00 (so P = 1000) and pKa = 4.20. Blood plasma sits close to pH 7.40. What is log D there?
pH − pKa = 7.40 − 4.20 = 3.20
103.20 = 1584.9
1 + 1584.9 = 1585.9 · log₁₀ 1585.9 = 3.200
log D7.4 = 3.00 − 3.200 = −0.200, so D = 10−0.200 = 0.631
Cross-check the other way. The fraction present as the neutral acid is 1 ÷ (1 + 10pH − pKa) = 1 ÷ 1585.9 = 6.31 × 10⁻⁴. Only that fraction partitions, so D = P × 6.31 × 10⁻⁴ = 1000 × 6.31 × 10⁻⁴ = 0.631. ✔ The two routes agree.
Read what just happened. A compound that "prefers oil 1000 to 1" in the log P table actually prefers water at the pH of blood, because more than 99.9% of it is sitting as the charged carboxylate. This is why a medicinal chemist quotes log D at pH 7.4 for an ionisable molecule and reserves log P for neutral ones — and why the pH of the compartment matters: the stomach, the small intestine and the blood are three very different pH environments for the same molecule.
Worked example 3 — the same law explains "extract twice with small portions"
You have 100 mL of an aqueous solution of the compound from Example 1 (P = 9.00 into octanol) and 60 mL of solvent. Is one 60 mL extraction better, or three 20 mL extractions?
One 60 mL portion (n = 1):
100 ÷ (100 + 9.00 × 60) = 100 ÷ 640 = 0.1563 → 15.6% left behind
Three 20 mL portions (n = 3):
100 ÷ (100 + 9.00 × 20) = 100 ÷ 280 = 0.3571
0.3571² = 0.1276 · 0.1276 × 0.3571 = 0.04555 → 4.56% left behind
Same total solvent, but three small extractions recover 95.4% against 84.4%. The laboratory rule you were told to memorise falls straight out of the distribution law.
Where this is actually used
Getting a drug from a tablet to its target means crossing at least one lipid membrane, and a molecule can only diffuse through a membrane if it dissolves in it. The octanol–water ratio is the standard laboratory surrogate for that step, which is why it appears at nearly every stage of development:
| Where it is used | What the number is doing there |
|---|---|
| Early screening of candidate molecules | Filtering out compounds too polar to be absorbed or too greasy to dissolve, before any synthesis effort is spent |
| Oral absorption | Estimating passive diffusion across the gut wall; log D at intestinal pH is the relevant figure, not log P |
| Formulation | Choosing salts, co-solvents and dosage forms for compounds whose solubility and partitioning fight each other |
| Distribution in the body | Very lipophilic compounds accumulate in fatty tissue and leave the body slowly |
| Environmental chemistry | The identical measurement predicts whether a pollutant will build up in fatty tissue rather than wash away |
| Analytical method development | Choosing extraction solvents and predicting retention order in reversed-phase chromatography |
Widely used drug-likeness screening guidelines — the set commonly taught as the "rule of five" — include an upper limit on lipophilicity for exactly this reason. Treat such rules as rules of thumb from accumulated industrial experience, not as laws: useful for sorting a large library quickly, and routinely broken by successful medicines.
Where the simple formula stops being valid
- P describes one species, not one compound. The distribution law is derived for a species with the same chemical form in both phases. The moment the molecule ionises, dimerises, or associates with anything, the plain ratio of analytical concentrations is no longer P. That is precisely the gap log D fills — and log D is not a constant, it is a function of pH.
- Octanol is not a membrane. A real bilayer is ordered, charged at its surface and asymmetric; octanol is an isotropic liquid. The correlation between octanol partitioning and membrane permeation is empirical and works best within a family of similar molecules. Outside that comfort zone it can be badly wrong.
- Partitioning is not permeability, and neither is absorption. Permeability also depends on molecular size, hydrogen-bonding capacity, and on active transporters and efflux pumps that pull a molecule back out of the cell. A drug can have perfect log D and still fail to be absorbed.
- More lipophilic is not better. Raising log P eventually destroys aqueous solubility, raises binding to plasma proteins, speeds up metabolic clearance and increases the chance of hitting unintended targets. The useful range is a window, not a direction.
- The shake-flask method has a working range. Above roughly log P = 4–5 the aqueous concentration becomes too small to measure reliably, and octanol droplets or emulsions carry compound across as suspended material, inflating the apparent value. Very lipophilic compounds are handled by chromatographic or slow-stirring methods instead, and calculated log P values (usually written clog P) are estimates from a model, not measurements — never mix the two in one table without saying which is which.
- Temperature and ionic strength are part of the answer. P is temperature-dependent, and the aqueous phase must be buffered — if the compound itself shifts the pH, the log D you measure is not the log D at the pH you intended.
- Exam slip to avoid: log D is always less than or equal to log P, never greater. If your worked answer comes out above log P, you have used the acid formula for a base or dropped the "1 +" inside the logarithm.
Why this matters for JAM, GATE, NET and CUET-PG
| Exam area | What is typically asked |
|---|---|
| Physical chemistry — solutions | Nernst distribution law; effect of association or dissociation in one phase |
| Analytical chemistry | Extraction efficiency, why repeated small extractions beat one large one, back-extraction |
| Ionic equilibria | Fraction ionised from pH and pKa; pH-dependent extraction of acids and bases |
| Separation techniques | Reversed-phase chromatography retention and its link to lipophilicity |
| Applied / conceptual questions | Why log D and not log P is quoted for an ionisable drug at pH 7.4 |
No single tool computes a partition coefficient — so rather than send you to the wrong page, here is the whole suite. The concentration, pH and equilibrium tools inside it handle every sub-step used above: converting masses to concentrations for each phase, and finding the ionised fraction from pH and pKa.
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