For example,

Suppose the compound has a distribution coefficient K = 2 between solvent1 and solvent2.

(1) If there are 30 particles of compound , these are distributed between equal volumes of solvent1 and solvent2...

(2) If there are 300 particles of compound , the same distribution ratio is observed in solvents 1 and 2,

See? No matter how much solute there is, the distribution coefficient K remains constant, equal to 2.

Organic Web Chem University of Alberta