Q. how to calculate partition coefficient

Definition. The partition coefficient P of a solute between two immiscible solvents is the ratio of its equilibrium concentrations in the two phases. For a solute S distributed between an organic phase and an aqueous phase,

\[ P \;=\; \frac{[S]_{\text{organic}}}{[S]_{\text{aqueous}}} \]

Often the logarithm base ten is reported. The octanol–water partition coefficient is commonly denoted by P or \( K_{\mathrm{ow}} \). The logarithmic form is

\[ \log_{10}P \;=\; \log_{10}\!\left(\frac{[S]_{\text{organic}}}{[S]_{\text{aqueous}}}\right) . \]

Laboratory procedure to determine P from measurements. Follow these steps exactly.

Step 1. Prepare and equilibrate. Mix known volumes of the two immiscible solvents, for example n‑octanol and buffered water, containing the solute at an appropriate initial amount. Agitate until the two phases reach equilibrium and then allow them to separate completely.

Step 2. Sample and analyze. Withdraw samples from each phase and determine the solute concentration in each phase using a validated analytical method such as HPLC, GC, or UV spectroscopy. Call the measured equilibrium concentrations \( [S]_{\text{org}} \) and \( [S]_{\text{aq}} \).

Step 3. Calculate P. Compute the partition coefficient by substituting into the definition. For example,

\[ P \;=\; \frac{[S]_{\text{org}}}{[S]_{\text{aq}}} . \]

Step 4. Report the result. Give P and the logarithmic value. For example, the numerical log is

\[ \log_{10}P \;=\; \log_{10}\!\left(P\right) . \]

Worked numerical example. Suppose the measured equilibrium concentrations are \( [S]_{\text{org}} \) equals 2.50 millimolar and \( [S]_{\text{aq}} \) equals 0.500 millimolar. Then

\[ P \;=\; \frac{2.50}{0.500} \;=\; 5.00 . \]

\[ \log_{10}P \;=\; \log_{10}(5.00) \;\approx\; 0.699 . \]

Ionizable solutes and the distribution coefficient. For ionizable molecules the measured distribution between phases depends on pH because the ionized form usually partitions differently from the neutral form. The intrinsic partition coefficient P refers to the neutral species only. The pH‑dependent distribution coefficient D is the observed ratio of total concentrations in the two phases. For a monoprotic acid HA with dissociation constant \( \mathrm{p}K_a \), the fraction of HA that is unionized in the aqueous phase is \( \dfrac{1}{1+10^{\mathrm{pH}-\mathrm{p}K_a}} \). The pH dependent distribution coefficient is

\[ D_{\text{acid}} \;=\; P \times \frac{1}{1+10^{\mathrm{pH}-\mathrm{p}K_a}} \;=\; \frac{P}{1+10^{\mathrm{pH}-\mathrm{p}K_a}} . \]

For a monoprotic base B with \( \mathrm{p}K_a \) (for BH+ ⇌ B + H+), the fraction unionized in water is \( \dfrac{1}{1+10^{\mathrm{p}K_a-\mathrm{pH}}} \). The distribution coefficient is

\[ D_{\text{base}} \;=\; P \times \frac{1}{1+10^{\mathrm{p}K_a-\mathrm{pH}}} \;=\; \frac{P}{1+10^{\mathrm{p}K_a-\mathrm{pH}}} . \]

Note that when pH << pKa for an acid, the acid is mostly unionized and D approaches P. When pH >> pKa for an acid, the acid is mostly ionized and D becomes much smaller than P. Analogous statements apply for bases with the inequalities reversed.

Practical notes. Use matched solvent conditions and validated analytical methods. Correct for any solvent dilution or sampling volumes. For accurate octanol‑water P values, pre‑saturate each solvent with the other to avoid concentration shifts due to mutual solubility. Report temperature, pH, and measurement uncertainty along with P or log P.