CHM-27

Partition coefficient K

K = c_org / c_aq. Distribution of a solute between two immiscible solvents.

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SolutionsNernst partition

Governing equation

K=\dfrac{c_{\mathrm{org}}}{c_{\mathrm{aq}}}

$c_{org} \in \left[1\times 10^{-6}, 5\right]$

where

c_{org}: Organic concentration (mol/L)
c_{aq}: Aqueous concentration (mol/L)
K: Partition K (—)

The figure, part by part

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①

Governing law — red

K=\dfrac{c_{\mathrm{org}}}{c_{\mathrm{aq}}}

$c_{org} \in \left[1\times 10^{-6}, 5\right]$

$c_{org} = 1\times 10^{-6}$ $K = 5\times 10^{-5}$

Along the curve

②

Domain of the variable — blue

c_{org}_{\min} = 1\times 10^{-6},\quad c_{org}_{\max} = 5

$c_{org} \in \left[1\times 10^{-6}, 5\right]$

$c_{org} = 1\times 10^{-6}$ $c_{org} = 1\times 10^{-6}$

Along the curve

③

Response curve — green

K=\dfrac{c_{\mathrm{org}}}{c_{\mathrm{aq}}}

$c_{org} \in \left[1\times 10^{-6}, 5\right]$

$c_{org} = 1\times 10^{-6}$ $K = 5\times 10^{-5}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}K}{\mathrm{d}c_{org}}

$c_{org} \in \left[1\times 10^{-6}, 5\right]$

$c_{org} = 0.031$ $K^{\prime} = 50$

Along the curve

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-27 — Partition coefficient K) is the form associated with Nernst partition. Working symbols: $c_{org}$ , $c_{aq}$ $\rightarrow$ $K$ . From equality of chemical potentials. log P is the octanol–water special case.

Purpose

Purpose: compute

K

from

c_{org}

c_{aq}

in Physical chemistry via

K=\dfrac{c_{\mathrm{org}}}{c_{\mathrm{aq}}}

K = c_org / c_aq. Distribution of a solute between two immiscible solvents. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

c_{org} = 0.080\,\mathrm{mol/L}

c_{aq} = 0.020\,\mathrm{mol/L}

, the governing relation

K=\dfrac{c_{\mathrm{org}}}{c_{\mathrm{aq}}}

yields

K = 4.000\,\mathrm{—}

. Dilute, isothermal, two phases. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Organic concentration c_{org}0.08 mol/LAqueous concentration c_{aq}0.02 mol/L

Outputs

Partition K K4.000 —

Reading speed

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Narration of this film

Dilute, isothermal, two phases.

From equality of chemical potentials. log P is the octanol–water special case.

Reading speed

Watch on YouTube