Transference numbers, of ions

If the boundary conditions are well-defined—which is not always the case here—the transient behavior of the Coulometric titration, i.e., emf(/) allows one to determine D5 directly. Appendix 5 details the time behavior of the voltage depending on the transference numbers of ions and electrons in the central phase as given by Preis und Sitte267 (Appendix 5). 

Platikanov et al. [108-111] have developed a measuring cell which can be used not only in the measurement of the electrical conductivity but also in the calculation of transference numbers of ions in black films. Two cylindrical hollow electrodes made of silver 1 (Fig. 2.17) are situated coaxially one over the other. The lower electrode is placed in a Teflon vessel 3 in which the solution is poured. The upper electrode can move vertically by a precise micrometric system. Ring 2 made of a porous glass is placed on each electrode. 

Analogous results have been reported from the systematic measurements of electrical conductivity and transference numbers of ions (// and tf) in black foam films [336] and parallel measurements of these quantities in highly concentrated surfactant/water system [337], Furthermore, it has been found that while the electrical conductivity of CBF depends on the electrolyte concentration in the initial solution, that of NBF does not. The transference numbers of the ions measured for films and a gel obtained from NaDoS-NaCl-HCl system are given below... 

Transference Numbers in Mixtures.—Relatively little work has been done on the transference numbers of ions in mixtures, although both Hittorf and moving boundary methods have been employed. In the former case, it follows from equation (3) that the transference number of any ion in a mixture is equal to the number of equivalents of that ion migrating from the appropriate compartment divided by the total number of equivalents deposited in a coulometer. It is possible, therefore, to derive the required transference numbers by analysis of the anode and cathode compartments before and after electrolysis. 

The Transference Numbers of Ion Constituents in Mixtures of Electrolytes. The moving boundary method can in certain cases be used to determine the transference numbers of the ion constituents in mixtures of electrolytes. The method used by Longsworth 32 for determining the transference numbers in mixtures of hydrochloric acid and potassium chloride is as follows. 

Table VI. Transference Numbers of Ions in Aqueous Hydrochloric Acid-Potassium Chloride Mixtures at 25°...

Because the specific conductivity k (S/m) of an electrolyte is determined readily and easy, this property is widely used for optimizing the battery performance. In contrast, other parameters which are more difficult to obtain, e.g., diffusion coefficients of ions near to or in the electrode materials or transference numbers of ions, are seldom studied and not yet included in optimization. We expect that automated measurement systems will be used in the future to optimize this and other critical parameters of solutions as long as no valid theoretical approach is available. These systems should be able to measure selected quantities automatically as a function of temperature and composition of solutions according to proposals made by optimization methods such as simplex. First steps on this way were undertaken by Schweiger et al., who presented an equipment that is able to measure K(T(t)) and T(t) automatically in up to 32 cells [34-38]. 

The ionic transference number of SPE and NCPE thin films has been estimated by Wagner s polarization techniqne (Wagner et al., 1957) for which the likely mobile species are protonic. In the polarization technique, a potentiostatic current is recorded as a function of time domain across the cell configuration electrode/sample/electrode and shown in Figure 3. The transference number of ions (f has been calculated using the relation... 

Experiments under the restrictions of classical thermoelectrochemistry in open cells with moderate temperature variation addressed, to some extent, also the conditions in the bulk electrolyte solution and the properties of ions. Potentiometric measurements in aqueous solutions of hydrogen and potassium bromides yielded the temperature dependence of activity coefficients of important ions [58]. As mentioned in Chap. 2, all electrolyte solutions tend to approach the ideal state with increasing temperature. The conductance of various electrolytes has been studied in dependence on temperature [59-66]. Solvents studied were propanol [59], propylene carbonate [60, 64], dimethoxyethane [65], primary alcohols and acetonitrile [62]. Conductance values were used to determine transference numbers of ions in non-aqueous solution [62]. Salt melts of sodium and caesium halides also have been studied [66]. Theoretical considerations were subject of [63]. 

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