Effect of the phase volume ratio on the potential of a liquid-membrane ion-selective electrode

Two-phase liquid system IA(w)|IX(o) comprising the interface between the aqueous solution (w) of uni-univalent electrolyte IA and an organic solvent solution (o) of a uni-univalent electrolyte IX with the common cation I(+) is considered as a simple model of a liquid-membrane ion-selective electrode (ISE). Taking into account the electroneutrality and mass balance conditions, the equilibrium Galvani potential difference (pd) between the aqueous and organic phases, phi = phi(w) - phi(o), is calculated numerically as a function of the ratio of the initial electrolyte concentrations, x = / = 10(-)(4)-10(4), for the selected values of the phase volume ratio r = V(o)/V(w) = 10(-)(3), 1, and 10(3), and the standard ion transfer potentials of the present ions ranging from -0.5 to 0.5 V. Numeric results corroborate the symbolic expressions derived for the cases when X(-) and A(-) are extremely lipophilic and hydrophilic ions, respectively, or when the concentration ratio x is extremely large or small. In contrast to the extraction system, where both electrolytes are initially present in the aqueous phase, the effect of the phase volume ratio on the equilibrium pd in the ISE model is rather weak, unless the counterions X(-) and A(-) differ little in their lipophilicity from the target ion I(+). It is shown that both the ISE and extraction model exhibit the Nernstian behavior only in a limited range of the concentration ratio x depending on the value of the standard ion transfer potentials of the counterions. When this ratio is extremely large or small, equilibrium pd approaches the limiting value given by the distribution potential of the electrolyte IA or IX, respectively. Similar conclusions can be drawn for the two-phase liquid system AI(w)|XI(o) with the common anion I(-).