Abstract: The mathematical expressions about separation factor were derived from the extraction reactions.The establishment conditions for the second basic hypothesis in fractional extraction system were investigated on the mathematical expressions in cation exchange extraction,neutral molecule association complex extraction,ion-association complex extraction and synergistic extraction mechanism.The research results indicate that the establishment conditions are the equal metal ions loaded charge in cation exchange extraction,and the establishment conditions are both the equal metal ions loaded charge and the equal extraction reaction coefficients of extraction reactions in neutral molecule association complex extraction,ion-association complex extraction and synergistic extraction.Separation factor dissatisfies the second basic hypothesis when separating the metal ions of unequal loaded charge.