Transference numbers, liquid junction potentials

In fact, at the pzc, the membrane should show the liquid junction potential [88] based on the transference numbers of the ions in the bulk solution. 

Although the detailed mechanism of electron transport and transfer involving PVF electrodes may be complex, they show remarkable stability and rapidly reversible redox behaviour in non-aqueous solvents such as acetonitrile. This has led to the suggestion69 that they might function as standard electrodes for non-aqueous solvents. Such standards are required since the SCE is unsatisfactory in a number of respects. Particularly, the liquid junction potential between aqueous and non-aqueous solutions is unknown and irreprodudble also there is a danger that the test solution will become contaminated with water and with potassium and sodium ions. 

The logarithmic response of ISEs can cause major accuracy problems. Very small uncertainties in the measured cell potential can thus cause large errors. (Recall that an uncertainty of 1 mV corresponds to a relative error of 4% in the concentration of a monovalent ion.) Since potential measurements are seldom better than 0.1 mV uncertainty, best measurements of monovalent ions are limited to about 0.4% relative concentration error. In many practical situations, the error is significantly larger. The main source of error in potentio-metric measurements is actually not the ISE, but rather changes in the reference electrode junction potential, namely, the potential difference generated between the reference electrolyte and sample solution. The junction potential is caused by an unequal distribution of anions and cations across the boundary between two dissimilar electrolyte solutions (which results in ion movement at different rates). When the two solutions differ only in the electrolyte concentration, such liquid junction potential is proportional to the difference in transference numbers of the positive and negative ions and to the log of the ratio of the ions on both sides of the junction ... 

The formula (VI-29) is valid for any uni-univalent electrolyte. It is evident from this formula that the sign of the liquid junction potential and also the orientation of the diffusion double layer, in respect to the double layer at the electrodes, depends on the relative magnitude of the anion and cation transference numbers. Should the anion transference number exceed that of cation... 

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 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. 

Type of Boundary and Liquid Junction Potential.—When the two solutions forming the junction contain different electrolytes, the structure of the boundary, and hence the concentrations of the ions at different points, will depend on the method used for bringing the solutions together. It is evident that the transference number of each ionic species, and to some extent its activity, will be greatly dependent on the nature of the boundary hence the liquid junction potential may vary with the type of junction employed. If the electrolyte is the same in both solutions, however, the potential should be independent of the manner in which the junction is formed. In these circumstances the solution at any point in the boundary layer will consist of only one electrolyte at a definite concentration hence each ionic species should have a definite transference number and activity. When carrying out the integration... 

The theoretical basis of the use of a bridge containing a concentrated salt solution to eliminate liquid junction potentials is that the ions of this salt are present in large excess at the junction, and they consequently carry almost the whole of the current across the boundary. The conditions will be somewhat similar to those existing when the electrolyte is the same on both sides of the junction. When the two ions have approximately equal conductances, i.e., when their transference numbers are both about 0.5 in the given solution, the liquid junction potential will then be small [cf. equation (36a)]. The equivalent conductances at infinite dilution of the potassium and chloride ions are 73.5 and 76.3 ohins cm. at 25, and those of the ammonium and nitrate ions are 73.4 and 71.4 ohms cm. respectively the approximate equality of the values for the cation and anion in each case accounts for the efficacy of potassium chloride and of ammonium nitrate in reducing liquid junction potentials. 

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... 

It is however possible to evaluate the liquid junction potential using all the data available for the transference numbers and the ionic activities and any assumed distribution of electrolytes in the boundary with the aid of graphical methods. In the discussion below the procedure followed so far in this chapter will be reversed. The potential for a complete cell will be computed, after which the liquid junction will be obtained by subtracting a computed value of the electrode potentials. 

Another factor which may influence the liquid junction potential is termed the "suspension effect" in which the presence of colloids or suspended particles, e.g., red blood cells, produce an anomalous liquid junction potential. It has been suggested that this phenomenon is caused by the effect of colloidal particles on the relative rates of diffusion, i.e., transference numbers, of the salt bridge electrolyte. Another possibility is that colloids with ion-exchange properties give rise to a Donnan potential across the suspension/supernatant liquid interface. Whatever the cause, the effect may be significant and must be avoided in accurate studies with electrodes. 

It is important to emphasize here the difference between cells without transfer and the cell with transfer. A cell with transfer has two additional potential differences between the salt bridge and the electrolytes at each end of the bridge. These potentials can be minimized and almost eliminated in a number of ways. The additional potentials are referred to as the diffusion or liquid junction potentials, which will be discussed in Chapter 3. 

Of these three issues, the first two are the most serious, with the first severely limiting the systems that can be studied to those that are stable in the presence of hydrogen, and the second hmiting the upper temperature. The third constraint is not a major issue in high subcritical systems, because the transference numbers of the ions of most, if not all, binary electrolytes tend toward 0.5 with increasing temperature however, at temperatures above the critical temperature the solubility of a salt is severely restricted and it may not be possible to attain a sufficiently high concentration to suppress the liquid junction potential. Note that the isothermal liquid junction is most effectively suppressed if the transference numbers of the cation and the anion of the background electrolyte are equal, a condition that is fulfilled by KCl at ambient temperature (and hence the reason for the choice of KCl in ambient temperature studies). 

The arrows above and the symbols below the interfaces indicate the transfer of the charge at each interface when the concentration of NaF in the sample is abruptly increased. It is possible to estimate the actual number of ions that are required to establish the potential difference at the interfaces. A typical value for the doublelayer capacitor is 10 5 F cm 2. If a potential difference of n = 100 mV is established at this interface, the double-layer capacitor must be charged by the charge Q = nCdi = 10 6 coulombs. From Faraday s law (6.3), we see that it corresponds to approximately 10 11 mol cm 2 or 1012 ions cm 2 of the electrode surface area. Thus, a finite amount of the potential determining ions is removed from the sample but this charge is replenished through the liquid junction, in order to maintain electroneutrality. 

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