Final answer:
In liquid-liquid extraction, the two solvents must be immiscible, enabling separation based on solute solubility in each distinct phase, adhering to the principle that 'like dissolves like.'
Step-by-step explanation:
In liquid-liquid extraction, the two solvents used must be immiscible so that they form two distinct phases, allowing for the efficient separation of substances based on their differing solubilities in each solvent. The key concept is that like dissolves like, meaning that polar compounds generally dissolve in polar solvents, and nonpolar compounds dissolve in nonpolar solvents due to similar intermolecular forces. The idea of miscibility is crucial since if the solvents were miscible they would mix and not allow for the separation of the solute.