Transference numbers Hittorf method

The detailed theory and mode of operation of the main experimental methods of obtaining transference numbers—Hittorf, direct and indirect moving boundary, analytical boundary, e.m.f. of cells with transference or of cells in centrifugal fields— have been published elsewhere. Only the features particularly pertinent to work with electrolytes in organic solvents will be dealt with here. 

As mentioned earlier, electrolytes used in lithium batteries are usually concentrated, binary electrolytes that exhibit nonideal behavior. In addition, polymer and gel electrolytes are opaque, highly resistive, and sticky, and therefore their transference numbers are not easily measurable using traditional techniques such as the Hittorf or moving boundary methods. Recent theoretical studies have described the substantial error involved in measuring transference numbers with techniques that assume ideal behavior [14, 15], and have described how experimental data can be interpreted rigorously using concentrated-solution theory to obtain transference numbers. One method is the galvanostatic polarization technique [120,121,122] ... 

Hittorf method phys chem A procedure for determining transference numbers in which one measures changes in the composition of the solution near the cathode and near the anode of an electrolytic cell, due to passage of a known amount of electricity. hi-dorf, meth-od ... 

The quantity [ zlLkf izfLJ is the transference number of the fcth ion as determined by the Hittorf method and, therefore, Equation (12.105) may be written as... 

Unequal velocities of ions cause changes in concentrations in the proximity of electrodes. From these changes the transference numbers can be calculated provided the quantity of electricity passed through the electrolyte is known (Hittorf s method). 

Three methods have been generally employed for the experimental determination of transference numbers the first, based on the procedure originally proposed by Hittorf (1853), involves measurement of changes of concentration in the vicinity of the electrodes in the second, known as the moving boundary method, the rate of motion of the boundary between two solutions under the influence of current is studied (cf. p. 116) the third method, which will be considered in Chap. VI, is based on electromotive force measurements of suitable cells. 

Hittorf Method Experimental Procedure.—In Hittorf s original determination of transference numbers short, wide electrolysis tubes were used in order to reduce the electrical resistance, and porous partitions were inserted to prevent mixing by diffusion and convection. These partitions are liable to affect the results and so their use has been avoided in recent work, and other precautions have been taken to minimize errors due to mixing. Many types of apparatus have been devised for the determination of transference numbers by the Hittorf method. One form, which was favored by earlier investigators and is still widely used for ordinary laboratory purposes, consists of an H-shaped tube, as shown... 

Although the Hittorf method is simple in principle, accurate results are difficult to obtain it is almost impossible to avoid a certain amount of mixing as the result of diffusion, convection and vibration. Further, the concentration changes are relatively small and any attempt to increase them, by prolonged electrolysis or large currents, results in an enhancement of the sources of error just mentioned. In recent years, therefore, the Hittorf method for the determination of transference numbers has been largely displaced by the moving boundary method, to be described later. 

True and Apparent Transference Numbers.—The fundamental assumption of the Hittorf method for evaluating transference numbers from concentration changes is that the water remains stationary. There is ample evidence, however, that ions are solvated in solution and hence they carry water molecules with them in their migration through the electrolyte this will result in concentration changes which affect the measured or apparent transference number. Suppose that each cation and anion has associated with it and w- molecules of water, respectively let T+ and be the true transference numbers, i.e., the actual fraction of current carried by cations and anions, respectively. For the passage of one faraday of electricity the cations will carry w T+ moles of water in one direction and the anions will transport W-T- moles in the opposite direction there will consequently be a resultant transfer of... 

If the net amount of water (x) transported were known, it would thus be possible to evaluate the true and apparent transference numbers from the results obtained by the Hittorf method. 

Results of Transference Number Measurements.—Provided the measurements are made with great precision, the results obtained by the Hittorf and moving boundary methods agree within the limits of experimental error this is shown by the most accurate values for various solutions of potassium chloride at 25° as recorded in Table XXVIII. 

It may be noted that the values obtained by the moving boundary method, like those given by the Hittorf method, are the so-called apparent transference numbers (p. 114), because the transport of water by the ions will affect the volume through which the boundary moves. It is the practice, however, to record observed transference numbers without applying any correction, since much uncertainty is attached to the determination of the transport of water during the passage of current. Further, in connection with the study of certain types of voltaic cell, it is the apparent" rather than the true" transference number that is involved (cf. p. 202). 

Influence of Temperature on Transference Numbers.—The extent of the variation of transference numbers with temperature will be evident from the data for the cations of a number of chlorides at a concentration of 0.01 N recorded in Table XXX these figures were obtained by the Hittorf method and, although they may be less accurate than those in Table XXIX, they are consistent among themselves. The transference... 

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. 

Much use of transference numbers has been made in the development of electrochemistry. The chief methods for their determination are (a) the Hittorf method, (6) die moving boundary method and (c) the electromotive force method. Of these the first two will be considered in this chapter. 

In spite of its simplicity accurate results are very difficult to get with the Hittorf method. The main difficulties are, first, the necessity for avoiding mixing of the electrode and middle portions during an electrolysis, which may take from sixteen to twenty-four hours, and secondly, the need for extremely accurate analyses of the solutions, since the method depends essentially on small differences between large quantities. For these reasons the more recent accurate data on transference numbers have been obtained, in greatest part, by means of the more complicated, but more speedily and accurately carried out, method of moving boundaries, which will be next described. 

The Moving Boundary Method for Determining Transference Humbers. A means of obtaining transference numbers which has proved, in recent years, to be of greater precision than the Hittorf procedure is the method of moving boundaries. The phenomenon which makes the measurements possible is as follows. If a potassium chloride solution is placed in a tube above a cadmium chloride solution, as is shown in Fig. 4a, and electric current is passed in the direction indi-... 

The Hittorf transference number may be defined as the number of equivalents of a given ion constituent which, on passage of one faraday of electricity, cross a plane fixed with respect to the solvent, usually, of course, water. In a determination by the moving boundary method the position of a boundary is fixed with respect to the graduations of the tube. Hence, in order to obtain a value of a transference number comparable with that found by the Hittorf method, the motion of the water with respect to the tube must be computed. 

Although we have assumed that the moving boundary and the Hittorf methods, when correctly used, yield the same values of transference numbers, there has been no adequate test of this assumption until recently. The only measurements of transference numbers by the Hittorf method available for this comparison, in which modern technique has... 

Table V. Cation Transference Numbers at 25° of Aqueous Solutions of Electrolytes Determined by the Hittorf Method, Compared with the Results of Moving Boundary Determinations...

Transference numbers obtained by a method which is uninfluenced by the movement of water of hydration have been called true 41 transference numbers. The first attempt to obtain such numbers was made by Nernst and associates.42 Successful measurements in this field have been carried out by Buchbock43 and much more extensively by Washburn.44 The procedure employed was essentially that of a Hittorf measurement. However, a second solute (usually a carbohydrate, such as sucrose or raffinose) is added to the aqueous solution, and, instead of referring the changes of salt concentration to the water, as in the computations for Hittorf transference numbers, the changes, both of salt and of water, are referred to the added solute. The apparatus used by Washburn has already been described. It is evident that if the added "reference substance is uninfluenced by the passage of the... 

Here NaCl (ft) represents a solution of sodium chloride, the chemical potential of the solute of which is and fan is the number of equivalents per faraday transferred from the higher to the lower concentration during the reversible operation of the cell. It will be noted that the operation of cell (12) is, differentially and reversibly, the opposite of the Hittorf method for determining the Hittorf transference number fan as described in Chapter 4. If now a second cell is made as follows... 

Solution Molality of solution m Emf, volts per centimeter height, X10 ——Cation Transference Number. Gravity Hittorf method method Reference... 

Transference numbers are often measured by the Hittorf method as illustrated in this problem. Consider the three-compartment cell ... 

Wilhelm Hittorf Transference number determination first method of studying complexes in solution... 

The moving-boundary method yields more accurate data on transference numbers than does the Hittorf method. Experimentally it is easier to handle. The difficulties lie in the establishment of a sharp boundary, the necessity of avoiding convection currents, and excessive heating by the current. However, once the boundary is established, the flow of current sharpens the boundary, making this a minor difficulty. The relative concentrations of the two solutes are important in maintaining a sharp boundary. The faster moving ion, M in this example, does not lead by more than a few atomic diameters, since a potential difference develops in such a sense as to slow it down in the steady state the two ions move with the same velocity, but M is always a little bit ahead of M. 

The classical method of determining transference number is, apart from the e.m.f method described previously, long time electrolysis with electrodes reversible to only one of the conducting species. Subsequent chemical analysis of the electrolyte at the vicinity of the anode and cathode is then performed. The method was extensively used by Hittorf on liquid electrolytes and some solids and later on by Tubant in numerous studies of pure salts and mixtures of salts (Tubant (1914, 1920, 1921)1 - ). 

Around the turn of the century discrepancies were noted between transference numbers obtained by the Hittorf method and those obtained by the moving boundary (m.b.) method. Explanations proposed in terms of complex ions were clearly unsatisfactory. 

The Hittorf and m.b. methods both involve the passage of current and observation of the resulting changes in the system. No current flow takes place in the third major method of determining transference numbers, the measurement of the emf of concentration cells with transference such as... 

If Equation 9 is true then the transference number measured by the Hittorf or the m.b. method should be identical to that obtained from the emfs of cells with transport (111). Moreover, the sensitivity of this test increases with increasing electrolyte concentration. During the 1970s three transference studies with concentrated solutions were undertaken to test the equation ... 

Some empirical assumptions have been made to avoid the difficult and time-consuming experiments (Hittorf or moving boundary method) to determine transference numbers. 

In useful variant of Hittorf s method, the solvent that is containing a small amount of (ideally) noninteracting molecules is analyzed as weU. This experiment suggested by Nemst yields specific solvation numbers for anions and cations and can also contribute to a better precision of transference numbers determined by Hittorf s method as cations and anions generally transport different number of solvent molecules. 

---