When a solute is added to a system containing two immiscible liquids (such as water and an organic solvent), it distributes itself between the two layers.
The principle that governs this distribution is called the Nernst Distribution Law, which is quantitatively expressed through the distribution coefficient (or partition coefficient).
The distribution coefficient, $K_D$, is defined as:
\[
K_D = \frac{[C]_{\text{organic}}}{[C]_{\text{aqueous}}}
\]
where $[C]_{\text{organic}}$ is the concentration of solute in the organic phase and $[C]_{\text{aqueous}}$ is the concentration in the aqueous phase.
This law assumes that the solute is in the same molecular form in both liquids and that temperature remains constant.
This principle is extensively used in solvent extraction techniques, where a compound is preferentially extracted into one solvent based on its distribution coefficient.
Other options like Henry's Law (related to gases dissolving in liquids), Le Chatelier's Principle (related to equilibrium shifts), and Dalton’s Law (related to partial pressures) do not apply to liquid-liquid solute distribution.
Hence, the correct answer is: Distribution coefficient.