Potentiometric Determination of Transport Numbers of Ternary Electrolyte Systems in Charged Membranes Jose ´ A. Manzanares,* Gonzalo Vergara, and Salvador Mafe ´ Departament of Thermodynamics, UniVersity of Valencia, E-46100 Burjasot, Valencia, Spain Kyo 1 sti Kontturi and Pasi Viinikka Laboratory of Physical Chemistry and Electrochemistry, Helsinki UniVersity of Technology, P.O. Box 6100, FIN-02015 HUT, Finland ReceiVed: January 14, 1997; In Final Form: NoVember 25, 1997 The potentiometric determination of transport numbers in charged membranes for the case of ternary systems is critically analyzed, and expressions are derived to evaluate these transport numbers close to equilibrium conditions. The apparent potentiometric transport number (i.e., that obtained by assuming that the ternary system behaves as a binary system) is also studied and the conditions that make it reliable for the estimation of the membrane fixed charge concentration are given. Particular attention is paid to the case of amphoteric membranes where the pH adjustment is necessary and the bathing solutions are often ternary systems. However, our theoretical study is general, and can also be applied to estimate the effect of any impurity ion present in the bathing solution. The main conclusion is that the interpretation of ion transport data in terms of the binary system equations can be an erroneous procedure even when the third ion present has a relatively low concentration. Introduction The electric conduction process in an ionic solution is often described in terms of Hittorf’s transport numbers which represent the fraction of the total current density transported by every charged species in the absence of concentration gradients. 1,2 However, when the electric conduction takes place across a membrane system of finite conductivity, concentration gradients are always present and this can lead to errors in the transport number determination due to back diffusion. Modi- fications of Hittorf’s method that avoid the correction for back diffusion 3,4 and the use of radiotracers 5 have been suggested, though they are not easy to use in practice. Furthermore, diffusion boundary layers exert also an important effect whose influence is difficult to estimate. 6 Alternatively, the transport numbers may be found by mea- suring concentration potentials. 7 These are known as poten- tiometric transport numbers, and quite frequently do not coincide with those obtained by Hittorf’s method because these two methods characterize the membrane system as a whole and the values they yield depend on the experimental conditions. Since there is no satisfactory way at present to determine transport numbers reliably, and Hittorf’s method or its modifications are relatively laborious, the potentiometric method is often used. The determination of transport numbers through charged membranes is required to study the performance of electromem- brane proceses. The counterion transport number is then one of the characteristics provided by the manufacturers of industrial membranes. However, this information is of limited value because it has been obtained with binary electrolyte solutions, a situation that differs often from that in the electromembrane process. For instance, in the case of acid and alkali production with bipolar membranes, it is important to determine the transport numbers through the monopolar membranes in systems such as NaCl-HCl or NaCl-NaOH. 8 Even in systems where the bathing solutions are intended to be binary, 9 the minimal presence of hydrogen ions from the autoprotolysis of water makes them at least ternary systems at high dilution. 10 The incorporation of the third ion (H + ) in the calculation of the emf is then of great importance. 11-15 The measured transport numbers are also used to estimate the membrane fixed charge concentration, 9,16-18 as well as the presence of any intrinsic asymmetry present in the membrane. 19-21 Particularly interesting is the case of biological membranes such as cornea or skin. The recent interest in electro-assisted transdermal drug delivery processes has recalled the need for accurate determination methods of the transport numbers of drugs. 22 Since biological membranes are often amphoteric, a change in bathing solution pH can alter the ratio of negatively charged to positively charged groups in the membrane. 23 The transport number determination is then carried out in the presence of an acid or a base that is added to adjust the pH of the bathing electrolyte solutions. The bathing solutions become then (at least) ternary systems, e.g., KCl-HCl or KCl-KOH. However, the effect of this acid or base addition on the potentiometric determination of transport numbers has not been analyzed in detail, except for a few studies. 10-15 On the contrary, the theoretical expression of the membrane potential corresponding to a binary system is sometimes used and the comparison with the observed membrane potential yields then the apparent potentiometric transport numbers. 9 The use of this procedure is not surprising: the relations between the transport data of binary and ternary electrolyte solutions are not trivial, 24 and these relations become even more complicated in the case of charged membranes. The expression of the membrane potential in a ternary system is known, e.g., from thermodynamics of irreversible processes 1301 J. Phys. Chem. B 1998, 102, 1301-1307 S1089-5647(97)00216-2 CCC: $15.00 © 1998 American Chemical Society Published on Web 01/27/1998