Cell with transference

In the concentration cells which we have just been considering, the passage of the current produces concentration changes in two separate solutions. 

There is another type of concentration cell, however, in which local changes in concentration are produced within a single Tkeorie des Bleiakhnnulators, Halle, 1901. 

At the electrodes, however, one equivalent of the cation is deposited (or dissolved), since the amount deposited at the cathode, for example, is the sum of the amount v carried by the current and the amount 1 — v set free owing to the migration of the anions. 

The concentration changes at the electrodes may be elucidated by the diagram (Fig. 35) I. represents the solution before the passage of the current, II. after the deposition of 4 cations. During the passage of the current 3 cations traverse the cross-section of the electrolyte in the positive direction of the current and 1 anion in the negative direction. In this example the transference number of the cation v has been arbitrarily chosen as J and that of the anion as J. 

At the anode the 4 free anions are neutralised by the dissolution of metal from the electrode (indicated by the crosses in brackets). 

In a concentration cell with transference two solutions of different concentration are brought into direct contact, either in a suitably designed junction, or by means of a porous diaphragm. At the interface of both solutions an electric double layer is formed the potential difference across which must be included into the total electromotive force of the cell. Before deriving, however, the relations for determining the EMF of such cells, the origin and magnitude 

A salt bridge is a liquid junction filled with a normal solution, or better, with a saturated solution of potassium chloride where the formation of a precipitate would be the result of the contact between the solution and the electrolyte containing e. g. ions Ag+, T1+, Hg4+, a saturated solution of ammonium nitrate is applied. This junction is interposed between the electrolytes surrounding both electrodes and at the same time is an intermediary of their electric connection. In this way, instead of one interface between the electrolytes, two are formed, as is evident, e. g. from the schematic representation of this system  

Ah already stated the liquid junction potential results from the different mobility of ions. Consequently no diffusion potential can result at the junction of the electrolyte solution the ions of which migrate with the same velocity. It is just this principle on which the salt bridge, filled by solutions of those salts the ions of which have approximately the same mobilities, is based (the equivalent conductivities of ions Kf and Cl- at infinite dilution at 25 °C are 73.5 and 70.3 respectively and the conductivities of ions NH+ and NOg are 73.4 and 71.4 respectively). Because ions of these salts have approximately the same tendency to transfer their charge to the more diluted solution during diffusion, practically no electric double layer is formed and thus no diffusion potential either. The effect of the salt bridge on t he suppression of the diffusion potential will be better, the more concentrated the salt solution is with which it is filled because the ions of the salt are considerably in excess at the solution boundary and carry, therefore, almost exclusively the eleotric current across this boundary. 

As already mentioned, the magnitude of the diffusion potential can be approximately calculated only in some special instances in general, this problem lias not yet been solved by electrochemistry. One of the above mentioned special cases is the combination of two different uni-univalent electrolytes, having a common ion and an identical concentration, such as. 

The liquid junction potential sr is in this case calculated according to the formula 

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As the cell is discharged, Zn2+ ions are produced at the anode while Cu2+ ions are used up at the cathode. To maintain electrical neutrality, SO4- ions must migrate through the porous membrane,dd which serves to keep the two solutions from mixing. The result of this migration is a potential difference across the membrane. This junction potential works in opposition to the cell voltage E and affects the value obtained. Junction potentials are usually small, and in some cases, corrections can be made to E if the transference numbers of the ions are known as a function of concentration.ee It is difficult to accurately make these corrections, and, if possible, cells with transference should be avoided when using cell measurements to obtain thermodynamic data. 

The broken vertical line denotes an area of contact between any two ionic conductors, particularly between liquid ionic conductors (electrolyte-electrolyte interface or liquid junction). Ions can transfer between phases by diffusion across such a boundary hence, circuits containing such an interface are often called circuits or cells with transference. 

In the case of the cell with transference (1.20), the OCV includes an additional liquid-junction potential (a potential difference between electrolytes), and... 

We can readily show that for cells without transference, the OCV value is equal to the difference in electrode potentials of the two electrodes (i.e., it can be written in terms of two parameters that are measurable, and each of them refers to just one of the electrodes). In the expression for OCV, the (P(j values for the reference electrode cancel, so that the reference electrode itself has no effect on the results (provided that all potentials refer to the same reference electrode). In the case of cells with transference, the difference in electrode potentials is equal not to the total but to the corrected OCV value, %. ... 

Aqueous solutions of the salts KCl and NH4NO3 are of interest inasmuch as here the mobilities (and also the diffusion coefficients) of the anion and cation are very similar. The higher the concentration of these salts, the larger is the contribution of their ions to transition-layer composition and, as can be seen from Table 5.1, the lower the diffusion potentials will be at interfaces with other solutions. This situation is often used for a drastic reduction of diffusion potentials in cells with transference. To this end one interposes between the two solutions a third solution, usually saturated KCl solution (which is about 4.2mol/L) ... 

The diffusion-potential reduction thus attained is entirely satisfactory for many measurements not demanding high accuracy. However, this approach is not feasible for the determination of the accurate corrected OCV values of cells with transference that are required for thermodynamic calculations. 

Galvanic cells that include at least one electrolyte-electrolyte interface (which may be an interface with a membrane) across which ions can be transported by diffusion are called cells with transference. For the electrolyte-electrolyte interfaces considered in earlier sections, cells with transference can be formulated, for example, as... 

Fill the cell with transfer buffer and place a stirring bar inside the transfer cell, so that the buffer is stirred during electrotransfer and temperature and conductivity are uniform during electrotransfer. 

In the previous chapters the condition of electroneutrality was applied to all systems that contained charged species. In this chapter we study the results when this condition is relaxed. This leads to studies of electrochemical systems, especially those involving galvanic cells. Cells without transference are emphasized, although simple cells with transference are discussed. At the end of the chapter the conditions of equilibrium across membranes in electrochemical systems are outlined. 

The emf of a cell with transference of the type discussed but with different electrodes is readily obtained. Consider the cell... 

The pH reference materials were selected also to cause small liquid junction potential < 0.01 in pH if the pH of the buffer solution prepared from this material is measured in cells with transference [12]. The molality of the primary buffer solutions are kept at < 0.1 mol kg-1 for the same reason [13]. Furthermore, the primary buffers have a long-time stability of stored solid material (>3 years), except solid borax buffer material. Borax buffer (0.1 mol kg-1) has a restricted stability of about 2 years only [14]. 

If these two solutions are different, transport of ions across the junction will cause irreversible changes in the two electrolytes, and we have a cell with transference. 

We distinguish between concentration cells without and with transference. In the first type the solutions surrounding both electrodes arc not brought into direct contact, while in concentration cells with transference two solutions arc in direct contact. The name cell with transference originates from the fact that during flow of the current a simultaneous transfer of the electrolyte takes place owing to the different ionic mobility. In the case of cells without transference the direct transfer of the electrolyte from one solution to the other is prevented in this instance the transport of the electromotive active substance proceeds exclusively as a result of reactions taking place at the electrodes. 

The EMF of a cell with transference is increased or decreased, as compared with the EMF of a cell without transference, by the value of the liquid junction potential existing at the interface of both solutions according to the sign of this and to the sign of the electrode potentials. 

A second instance, where the value of the diffusion potential can be under certain conditions ascertained by calculation, is the system in which two solutions of the same electrolyte, but of different concentration, are in contact. The method of such calculation will be illustrated by an example of a concentration cell with transference composed of two hydrogen electrodes, dipped into hydrochloric acid solutions with different concentrations which are in direct contact ... 

It has already been mentioned that the electromotive force of concentration cells with transference is the sum of the both electrode potentials and the liquid junction potential which arises, when two solutions of the same substance but of different concentrations are brought into contact the value of the mentioned potential is finally given by the equations (VI-28) and (VI-29). 

When dipping two identical chlorine electrodes into two hydrochloric acid solutions of different concentrations [(a+)a > (a+)jJ instead of the hydrogen electrodes, a concentration cell with transference will be obtained, reversible with respect to the anions ... 

For practical pH measurements, more convenient secondary standard - buffer solutions (SS) are recommended. Their secondary pH(SS) values are obtained by comparison with primary buffers in recommended cells with transference and have thus slightly larger uncertainties than pH(PS). pH(SS) can be traced back, again with stated uncertainties, to pH(PS) values and consequently to the definition of pH. 

Finally, the measurement of pH(X) of unknown solutions, the actual subject of pH measurement, is carried out in practical cells with transference containing -> glass electrodes. Calibration procedures for such practical cells are recommended so that the unknown pH(X) is traced back to pH(SS), pH(PS) and to the defined pH. 

Thus, emf measurements of cells with transference yield transference numbers. 

Feakins et al used concentration cells with transference to get Washburn... 

Concentration Cells with Transference.—When two solutions of the same electrolyte are brought into actual contact and if identical electrodes, reversible with respect to one or other of the ions of the electrolyte, arc placed in each solution, the result is a concentration cell with transference for example, the removal of the AgCl(s) Ag AgCl(s) system from the cell on page 196 gives... 

ACTIVITY COEFFICIENTS FROM CELLS WITH TRANSFERENCE... 

Activity Coefficients from Cells With Transference.—In order to set up a cell without transference it is necessary to have electrodes reversible with respect to each of the ions of the electrolyte this is not always possible or convenient, and hence the use of cells with transference, which require electrodes reversible with respect to one ion only, has obvious advantages. In order that such cells may be employed for the purpose of determining activity coefficients, however, it is necessary to have accurate transference number data for the electrolyte being studied. Such data have become available in recent years, and in the method described below it will be assumed that the transference numbers are known over a range of concentrations. ... 

For solutions dilute enough for equation (29) to be applicable, the plot of log (///o) + -4 Vc against [a — log (///o)]Vc should be a straight line with intercept equal to a. The value of a, which is required for the purpose of this plot, is obtained by a short series of approximations. Once a, which is equal to — log /o, is known, it is possible to derive log / for any solution from the values of log ///o obtained previously. The activity coefficient of the electrolyte can thus be evaluated from the e.m.f. s of cells with transference, provided the required transference number information is available. 

Determination of Transference Numbers.—Since activity coefficients can be derived from e.m.f. measurements if transference numbers are known, it is apparent that the procedure could be reversed so as to make it possible to calculate transference numbers from e.m.f. data. The method employed is based on measurements of cells containing the same electrolyte, with and without transference. The e.m.f. of a concentration cell without transference E) is given by equation (11), and if the intermediate electrodes are removed so as to form a concentration cell with transference, the e.m.f., represented by Et, is now determined by equation (25), provided the transference numbers may be taken as constant within the range of concentrations in the cells. It follows, therefore, on dividing equation (25) by (11), that... 

The use of equation (30) gives a mean transference number of the electrolyte within the range of concentrations from Ci to C2, but this is of little value because of the variation of transference numbers with concentration a modified treatment, to give the results at a series of definite concentrations, may, however, be employed. If the concentrations of the solutions are c and c + dc, the e.m.f. of the cell with transference is given by the general form of equation (22) as... 

This approximate relationship can be tested by suitable measurements on concentration cells with transference. 

As indicated above, the e.m.f. of a cell with transference can be regarded as made up of the potential differences at the two electrodes and the liquid junction potential. It will be seen shortly (p. 229) that each of the former may be regarded as determined by the activity of the reversible ion in the solution contained in the particular electrode. In the cell depicted above, for example, the potential difference at the left-hand electrode is dependent on the activity of the chloride ions in the potassium chloride solution of concentration Ci similarly the potential difference at the right-hand electrode depends on the chloride ion activity in the solution of concentration Cz. For sufficiently dilute solutions the activity of a given ion, according to the simple Debyc-Huckel theory, is determined by the ionic strength of the solution and is independent of the nature of the other ions present. It follows, therefore, that the electrode potentials should be the same in all cells of the type... 

If the right-hand side is constant, for cells with transference containing different chlorides at definite concentrations, it may be concluded that the approximate equation (36) gives a satisfactory measure of the liquid junction potential between two solutions of the same electrolyte. The results in Table XLV provide support for the reliability of this equation, within certain limits the transference numbers employed are the mean values for the two solutions, the individual figures not differing greatly in the range of concentrations involved. 

The same point can be brought out in another manner. The e.m.f. of the cell with transference... 

Nernst showed also that the e.m.f. of a concentration cell with transference such as... 

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