50-100 range and is in excellent agreement with the electrochemical selectivity ratio.A particularly interesting finding is the excellent agreement for the divalent ions Ba2+ and Sr2+. Unfortunately, these are the only multivalent cations for which useful formation constant values have been reported to date.On the basis of our studies on the valinomycin electrode (9) and the present results we propose, for neutral carrier liquid membrane electrodes in general, the useful approximation where ,2 is the potentiometric selectivity coefficient for the electrode's response to ion 1 over 2 while K,J and K,,z are the equilibrium formation constants for complexes between the carrier entity and ions l and 2, respectively. In the usual case, where the formation rate constants are independent of the cation, the right hand side of this expression is equivalent to the inverse quotient of the specific dissociation rates and shows that the electrode is selective ,for the ion held longest in the cavity of the carrier molecule. We expect that this relationship would give an approximate prediction of selectivity coefficients for those electrode systems having no special spatial arrangement of the carrier in the membrane and where the system kinetics are not potential determining. It should, thus, be possible to predict the selectivity properties of suitable neutral carrier electrodes on the basis of homogeneous complex formation data as a first approximation. Similarly, formation constants should be predictable from electrochemical data. We hope that these guidelines will facilitate the selection or synthesis of suitable membrane phase materials and will assist in the practical development of new liquid membrane electrodes.
ACKNOWLEDGMENTWe thank H. K. Frensdorff for his gift of the crown compounds and G. Eisenman for some unpublished data.
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