Concentration cells without transference

One can arrange two cells of the previous type in opposition to one another so that a composite cell is formed. If the concentration of the hydrochloric acid in each cell is different, a resultant e.m.f. will be obtained. Such a composite cell may be represented as follows  

It is seen that the left-hand portion of the composite cell is made to function in the non-spontaneous direction while the right-hand portion is identical with the cell of the previous section. 

for the general case with an electrolyte comprising v+ cations and anions (1 + + =v) Equation (5.28) becomes 

---

Note that there is no direct transference of the electrolyte (HC1) from one side to the other. HCI is removed from the left-hand side by the left-hand electrode reaction and it is added to the right-hand side by the right-hand electrode reaction. This cell is an example of a electrolyte concentration cell without transference. 

Tho general formula for calculating the EMF of an electrolyte concentration cell without transference is ... 

The influence of the relative values of the transference numbers, affecting the resultant value of the EMF of the concentration cell without transference, is clearly to be seen from the equation (VI-29) should t.. > <+ then eK is positive and in a concentration cell reversible with respect to cations the liquid junction potential is added to the sum of the electrode potentials should, however, < t+, then the liquid junction potential will lower the resultant EMF. In a concentration cell reversible with respect to anions (e. g. in a cell with chlorine electrodes) the EMF is decreased when ( >(+, and increased when t. < t+. 

If reversible electrodes for both the cations and anions are available concentration cells without transference... 

A cell of the type described above is called a concentiation cell without transference, for the e.m.f. depend.s on the relative concentrations, or molalities, of the two solutions concerned, and the operation of the cell is not accompanied by the direct transfer of electrolyte from one solution to the other. The transfer occurs indirectly, as shown above, as the result of chemical reactions. In general, a concentration cell without transference results whenever two simple cells whose electrodes are reversible with respect to each of the ions constituting the electrolyte are combined in opposition in the case considered above, the electrolyte is hydrochloric acid, and one electrode is reversible with respect to hydrogen ions and the other with respect to chloride ions. 

Amalgam Cells.—If the electrolyte in the concentration cell without transference is a salt of an alkali metal, e.g., potassium chloride, it is necessary to set up some form of reversible alkali metal electrode. This is achieved by dissolving the metal in mercury, thus forming a dilute alkali metal amalgam which is attacked much less vigorously by water than is the metal in the pure state." The amalgam nevertheless reactia with water to some extent, and also with traces of oxygen that may be... 

Determination of Activity Coefficients.—The e.m.f. of a concentration cell without transference is equal to Ei — Ez, where Ei and Ez are determined by the concentrations Ci and C2, respectively, of the electrolyte then for a cell to which equation (8) is applicable,... 

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... 

If the cell metal concentrated solution dilute solution metal is capable of yielding a current, the direction of the current must be such that the concentrated solution becomes more dilute and the dilute solution more concentrated. The positive current must therefore fiow from the dilute to the concentrated solution inside the cell, so that the electrode dipping into the concentrated solution becomes the cathode. As 1 —i/ equivalents of the electrolyte = 2(l —j/) equivalents of the ions are transferred by unit quantity of electricity from the more concentrated (cathode) solution to the more dilute (anode) solution, the E.M.F. of this concentration cell can be calculated by the same two methods (p. 354) which Helmholtz and Nemst employed in the calculation of the e.m.f. of concentration cells without transference. Thus, for dilute solutions of an w-valent metallic salt, we have the equation... 

Amalgam Cells. F6r the determination of activity coefficients of electrolytes the method depending upon the measurement of the potentials of concentration cells without transference has already been discussed in Chapter 6. Two examples of such cells were mentioned. These were the following ... 

The computation of activity coefficients from A log j values will be illustrated for hydrochloric acid since in that case direct comparison can be made with the results of measurements on concentration cells without transference of the type described in Chapter 6. The relevant data are given in Table II and are from the work of Shedlovsky and Maclnnes.18 The emf data in the second column were obtained from a cell of the type illustrated in Fig. 4. The transference numbers in the third column were interpolated from the measurements of Longs-worth given in Table IV of Chapter 4. The A log f values in the fourth column were computed as described in the last paragraph. 

A concentration cell without transference (that is, without a liquid junction) is shown in Fig. 17.8. The cell consists of two cells in series, which can be symbolized by... 

Other cells without transference such as redox cells follow the same general principles as discussed above and further details are given else-where. Some description of concentration cells with and without transference is necessary, however, since measurements of this type are often made in organic solvents. A concentration cell without transference is illustrated by cell (II) which is a combination of two cells of type I... 

Yt is obtained directly from the e.m.f. measurements (3,14-16), say, of concentration cells without transference, from the deficit free energy, A-G(non-id), attributed to non-ideality. 

Electrochemical Cell Without Transference Assume that we want to determine the activities of HCl solutions of various concentrations. We assemble a galvanic cell with hydrogen and calomel electrode ... 

As a liquid junction potential is avoided, the cell potential consists merely of the electrode potentials of the hydrogen and the silver/silver chloride reference electrode. Chloride at known concentrations, mcl, must be added to the (chloride-free) buffer solution to use the silver-silver chloride electrode in cells without transference as a reference. This is different from silver/silver chloride reference systems with fixed potentials used for example as standard references in single-rod glass electrodes. 

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. 

Concentration Cells Cells without Transference.—In the operation of the cell... 

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. ... 

Instead of transferring the mole of HC1 via the vapour we may transfer it by the passage of one faraday of electricity through a concentration cell (without transport) of the type—... 

This chapter is concerned with the determination of activity coefficients with the aid of various types of concentration cells, and with the comparison of such activity coefficients with the predictions of the Debye-Hiickel theory, developed in the previous chapter. The types of cells discussed are (a) cells without transference, including those containing amalgam electrodes, (b) cells with transference, and (c) cells without transference containing mixtures of electrolytes. 

Two test series have to be done, including measurements in two nearly identical cells, an emf cell with transference and a cell without transference the ceU without transference includes a salt bridge. Both cells have different molal concentrations in their half cells that is the... 

Let us consider the Harned cell, which is a cell without transfer ( jff = 0), to show how a standard electrode potential can be obtained by measuring the concentration dependence of the cell potential and, then, making an extrapolation to the infinitely dilute solution. The electrochemical diagram and the corresponding Nernst equation (4.22) for the Harned cell were considered in Chapter 4. Equation 4.22, which can, first, be simplified if the activity of H2(g) equals 1 (pni = 1 bar and fugacity coefficient is very close to 1) and, second, is rearranged as follows ... 

Concentration cells are a useful example demonstrating the difference between galvanic cells with and without transfer. These cells consist of chemically identical electrodes, each in a solution with a different activity of potential-determining ions, and are discussed on page 171. 

Mean activity coefficients can be measured potentiometrically, mostly in a concentration cell with or without transfer. Consider, for example, the cell (with a non-aqueous electrolyte solution)... 

Concentration cells with/without transference - concentration cells... 

If the E.M.p. s of the cells, with and without transference, in which the concentration of one of the solutions is varied while the other is kept at a constant low value, e.g., 0.001 molar, are plotted against log a of the variable solution, the slopes of the curves a e dEtjd log a and dEjd log a, respectively. The transference number of the appropriate ion may thus be determined at any concentration by taking the ratio of the slopes at the value of log a corresponding to this concentration. The activities at the different concentrations, from which the log a data are obtained, must be determined independently by e.m.f. or other methods. 

The third type of concentration cell involves two electrolyte solutions of different concentrations. Such a cell can be set up with or without transference. The simpler system is one without transference and it is considered first. It can be constructed by placing two cells of identical format but different electrolyte concentrations in opposition to one another. An example based on cell (9.5.8) is... 

It will be observed that the process which actually takes place m a concentration cell, either with or without transport, and which gives rise to the e m f, is the tendency of the two solutions to become equal in concentration. If instead of transferring solute from one solution to the other we were to transfer solvent by isothermal distillation from, weak to strong, the same equalisation of concentration could be obviously brought about If we could evaluate the expression for this isothermal distillation work, we could equate it to the electrical work, for if We pass from one equilibnum stage to another by any reversible... 

The Determination of Transference Numbers from the Potentials of Concentration Cells. Another use of concentration cells, which involves the principles already discussed in this chapter, is that of the determination of transference numbers. Since a cell without liquid junctions of the type... 

---