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A theoretical equation of the reversible current–potential curves is derived for the competitive ion-transfer of two kinds of cations present in an aqueous (w) phase simultaneously facilitated by a macrocyclic ligand (L) present in an organic (o) phase. Especially, for the two limiting cases, i.e. case (A): c*Mj (j=1, 2)?c*L and case (B): c*L?c*Mj (where c*Mj and c*L denote the bulk concentrations of cation Mj in the w-phase and of L in the o-phase, respectively), simple explicit expressions are derived and a method analyzing the facilitated waves is presented. Furthermore, the main part of the theoretical predictions obtained is verified experimentally at 25 °C by using the ion-transfer-polarographic method with the electrolyte dropping electrode, for the following four combinations: (i) competitive cations: protonated alanine and H+, L: benzo-18-crown-6 ether; (ii) Na+ and Li+, benzo-15-crown-5 ether; (iii) K+ and Na+, dibenzo-18-crown-6 ether; and (iv) Na+ and Ba2+, dibenzo-24-crown-8 ether.  相似文献   
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