Potentiometric liquid junction potentials

Electrochemical methods covered in this chapter include poten-tiometry, coulometry, and voltammetry. Potentiometric methods are based on the measurement of an electrochemical cell s potential when only a negligible current is allowed to flow, fn principle the Nernst equation can be used to calculate the concentration of species in the electrochemical cell by measuring its potential and solving the Nernst equation the presence of liquid junction potentials, however, necessitates the use of an external standardization or the use of standard additions. 

Standard potentials Ee are evaluated with full regard to activity effects and with all ions present in simple form they are really limiting or ideal values and are rarely observed in a potentiometric measurement. In practice, the solutions may be quite concentrated and frequently contain other electrolytes under these conditions the activities of the pertinent species are much smaller than the concentrations, and consequently the use of the latter may lead to unreliable conclusions. Also, the actual active species present (see example below) may differ from those to which the ideal standard potentials apply. For these reasons formal potentials have been proposed to supplement standard potentials. The formal potential is the potential observed experimentally in a solution containing one mole each of the oxidised and reduced substances together with other specified substances at specified concentrations. It is found that formal potentials vary appreciably, for example, with the nature and concentration of the acid that is present. The formal potential incorporates in one value the effects resulting from variation of activity coefficients with ionic strength, acid-base dissociation, complexation, liquid-junction potentials, etc., and thus has a real practical value. Formal potentials do not have the theoretical significance of standard potentials, but they are observed values in actual potentiometric measurements. In dilute solutions they usually obey the Nernst equation fairly closely in the form ... 

In view of the problems referred to above in connection with direct potentiometry, much attention has been directed to the procedure of potentio-metric titration as an analytical method. As the name implies, it is a titrimetric procedure in which potentiometric measurements are carried out in order to fix the end point. In this procedure we are concerned with changes in electrode potential rather than in an accurate value for the electrode potential with a given solution, and under these circumstances the effect of the liquid junction potential may be ignored. In such a titration, the change in cell e.m.f. occurs most rapidly in the neighbourhood of the end point, and as will be explained later (Section 15.18), various methods can be used to ascertain the point at which the rate of potential change is at a maximum this is at the end point of the titration. 

It would appear from Eq. (3.2.8) that the pH, i.e. the activity of a single type of ion, can be measured exactly. This is not, in reality, true even if the liquid junction potential is eliminated the value of Eref must be known. This value is always determined by assuming that the activity coefficients depend only on the overall ionic strength and not on the ionic species. Thus the mean activities and mean activity coefficients of the electrolyte must be employed. The use of this assumption in the determination of the value of Eref will, of course, also affect the pH value found from Eq. (3.2.8). Thus, the potentiometric determination of the pH is more difficult than would appear at first glance and will be considered in the special Section 3.3.2. 

The EMF across the entire potentiometric cell, shown in Fig. 18a.l, is the sum of the individual potentials that include the reference electrode potential and other sample-independent potentials (Econst), the liquid junction potential (Ej) and the membrane potential (EM) ... 

Keeping in view the above serious anomalies commonly encountered with direct potentiometry, such as an element of uncertainty triggered by liquid junction potential (E.) and high degree of sensitivity required to measure electrode potential (E), it promptly gave birth to the phenomenon of potentiometric titrations,... 

When considering potentiometric errors, it is necessary to appreciate how a liquid junction potential, Ej, arises, and appreciate how such potentials can lead to significant errors in a calculation. In addition, we saw how the IR drop can affect a potentiometric measurement (and described how to overcome this). Finally, we discussed the ways that potentiometric measurements are prone to errors caused by both current passage through the cell, and by the nature of the mathematical functions with which the Nemst equation is formulated. 

Ideal potentiometric measurements, especially in analytical chemistry, would require that the potential of the reference electrode be fixed and known, and that the composition of the studied solution affect only the potential of the indicator electrode. This would occur only if the liquid-junction potential could be completely neglected. In practice this situation can be attained only if the whole system contains an indifferent electrolyte in a much larger concentration than that of the other electrolytes, so that the concentration of a particular component in the analysed solution, which is not present in the reference electrode solution, has only a negligible effect on the liquid-junction potential Such a situation rarely occurs, so that it is necessary to know or at least fix the liquid junction potential... 

Czaban JD, Cormier AD, Legg KD. Establishing the direct potentiometric normal range for Na/K residual liquid junction potential and activity coefficient effects. Chn Chem 1982 28 1936-45. 

The presence of a liquid-junction potential limits the accuracy of potentiometric measurements. 

In potentiometric measurements, a cell of the type shown in Figure 13.5 is set up. For direct potentiometric measurements in which the activity of one ion is to be calculated from the potential of the indicating electrode, the potential of the reference electrode will have to be known or determined. The voltage of the cell is described by Equation 13.7, and when a salt bridge is employed, the liquid-junction potential must be included. Then,... 

A l-mV error results in an error in Up,g+ of 4%. This is quite significant in direct potentiometric measurements. The same percent error in activity will result for all activities of silver ion with a 1-mV error in the measurement. The error is doubled when n is doubled to 2. So, a 1-mV error for a copper/copper(II) electrode would result in an 8% error in the activity of copper(II). It is obvious, then, that the residual liquid junction potential can have an appreciable effect on the accuracy. 

Potentiometric titrations are more accurate than direct ISE measurements because the liquid-junction potential is not important. 

Potentiometric titration experiments of Zr chloride, nitrate, sulphate and perchlorate solutions were conducted at (25.00 + 0.05)°C until the onset of precipitation. Initial solutions (0.038, 0.019, 0.0095 and 0.0047 M in Zr) contained < 0.4% Hf and had an excess of 2 M of the acid of the anion studied. Titrations were performed with carbonate free 0.101 N NaOH. Glass electrodes where calibrated regularly but no correction for differences between liquid junction potential of reference and measured solutions was performed. The pH convention used was not reported and it is assumed that a NBS type convention was used. The pH at the onset of precipitation and coagulation of an uncharacterised and presumably amorphous solid were determined optically. The pH of coagulation was the pH at whieh the precipitate coagulated and the supernatant solution was clear. Reproducibility of these characteristic pH values was within 0.05 to 0.07 pH units. 

Rapson HOC and Bird AE, /. Pharm. Pharmacol, 15,222T (1963). Cited in Perrin Bases Suppl. No. 7777 ref R6. NB Potentiometric titrations used a glass electrode with an unsymmetrical cell and liquid junction potentials. 

NB Also gave 8.04 (U, potentiometric with glass electrode and liquid junction potentials H2O) 8.15 (U, spectro H2O ... 

Kolfiioff IM, The dissociation constants, solubility product and titration of alkaloids, Biochem. Z., 162,289-353 (1925). Cited in Perrin Bases 2901. NB See Aconitine for details of file spectrophotometric mefiiod. The data were not corrected for overlapping pK values. The potentiometric study used hydrogen electrodes in an asymmetric cell wifii liquid junction potentials. 

Muller F, Z. Elektrochem., 30,587 (1924). Cited in Perrin Bases 2923 ref. M60. NB The study used potentiometric titration with hydrogen electrodes in an unsymmetric cell with liquid junction potentials. 

One interesting result of this property is that the relative concentration error for direct potentiometric measurements is theoretically independent of the actual concentration. Unfortunately, the error is rather large—approximately 4n% per mV uncertainty in measurement, perhaps the most serious limitation of ISEs. Since potential measurements are seldom better than 0.1 mV total uncertainty, the best measurements for monovalent ions under near-ideal conditions are limited to about 0.5% relative concentration error. For divalent ions, this error would be doubled and in particularly bad cases where, for example, liquid-junction potentials may vary by 5 to 10 mV (as in high or variable ionic-strength solutions), the relative concentration error may be as high as 507o- This limitation may be overcome, however, by using ISEs as endpoint indicators in potentiometric titrations (Sec. 2.6). At the cost of some extra time, accuracies and precisions on the order of 0.1% or better are possible. 

Ideally, one would like to measure all potentials between the reference solution in the indicator electrode and the test solution. Unfortunately there is no way to do that. Interface potentials develop across any metal-liquid boundary, across liquid junctions, and across the ion-selective membrane. The key to making potentiometric measurements is to ensure that all the potentials are constant and do not vary with the composition of the test solution except for the potential of interest across the ion-selective membrane. By maintaining the solutions within the electrodes constant, the potential between these solutions and the metal electrodes immersed in them is constant. The liquid junction is a structure which severely limits bulk flow of the solution but allows free passage of all ions between the solutions. The reference electrode commonly is filled with saturated KCl, which produces a small, constant liquid-junction potential. Thus, any change in the measured voltage (V) is due to a change in the ion concentration in the test solution for which the membrane is selective. 

The mutual correlation of pH scales in different solvents creates more problems as a number of effects must be considered, such as electric permitivity and the solvation of ions. Potentiometric measurements of the hydrogen ion activity can be made using the hydrogen electrode in many solvents however, more difficulties are concerned with the reference electrode. When using an aqueous reference electrode the liquid junction potential on the boundary of two solvents is large. For a reference electrode in a nonaqueous solvent the interactions of various ions must be considered. Some good approximation can be reached when the reference electrode uses a... 

In a direct potentiometric measurement, we use an electrode such as a silver wire to measure [Ag ] or a pH electrode to measure [H" ] or a calcium ion-selective electrode to measure [Ca " ]. There is inherent inaccuracy in most direct potentiometric measurements because there is usually a liquid-liquid junction with an unknown voltage difference making the intended indicator electrode potential uncertain. For example. Figure 15-5 shows a 4% standard deviation among 14 measurements by direct potentiometry. Part of the variation could be attributed to differences in the indicator (ion-selective) electrodes and part could be from varying liquid junction potentials. 

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