The partitioning of solute(s) between two phases is an equilibrium process and is characterized by an equilibrium constant called the partition coefficient:
The use of expensive anhydrous organic solvents is not necessary. The solubility of water in many common solvent is not zero, so upon mixing the phases water dissolves in the organic solvent. If an anhydrous organic solvent was used, it would not be anhydrous once the extraction begins. If solvated water needs to be removed (it usually does, whether to aid crystallization of the solute or to prevent damage to the GC column), the organic solvent can be passed through an anhydrous salt capable of forming a solid hydrate after separation from the the aqueous phase. Anhydrous sodium sulfate is commonly used.