Liquid junction potential error

Using KOH or NaOH with pH in the range 13 to 14 as the inner electrolyte gives rise to a change in the liquid junction potential error of about 30 to 35 mV for one pH unit change in the outer test solution. Consequently, when pH in a high pH test solution gradually decreases due to carbonation, a reference electrode of this kind will drift . 

Morse (21) recently reported near-equilibrium pH-stat rates in sea water at 25°C and 10 atm CO2. His rates are all less than 8 mg cm yt . Table III compares our calculations (using equation 15 and assuming surface PCO2 is equal to the bulk fluid value) of a set of Morse s rates near equilibrium, and shows generally poor agreement. In calculation of Q and aH (s), no correction for liquid junction potential error in measured pH was necessary, as in our earlier calculations for pseudo-sea water. 

Although the Henderson formula depends on a number of simplifications and also employs ion concentrations rather than activities, it can nonetheless be used for estimation of the liquid junction potential up to moderate electrolyte concentrations, apparently as a result of compensation of errors. 

Liquid junction potentials are rarely large, so a value of E as large as 0.1 V should be regarded as exceptional. Nevertheless, junction potentials of 30 mV are common and a major cause of experimental error, in part because they are difficult to quantify, but also because they can be quite irreproducible. 

To leam about how a liquid junction potential, j, arises, and appreciate how it can lead to significant errors in a calculation which uses potentio-metric data. 

An electrode potential Eaq+.aq is measured as 0.670 V. In fact, this value is too high because the value of Eaq+.aq also incorporates a liquid junction potential of 22 mV. Calculate two values of a(Ag ), first by assuming that Eaq+.aq is accurate, and secondly by taking account of E. What is the error in a(Ag ) caused by the liquid junction potential Take E + = 0.799 V at 298 K. 

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. 

The results obtained with ISEs have been compared several times with those of other methods. When the determination of calcium using the Orion SS-20 analyser was tested, it was found that the results in heparinized whole blood and serum were sufficiently precise and subject to negligible interference from K and Mg ([82]), but that it is necessary to correct for the sodium error, as the ionic strength is adjusted with a sodium salt [82], and that a systematic error appears in the presence of colloids and cells due to complexa-tion and variations in the liquid-junction potential [76]. Determination of sodium and potassium with ISEs is comparable with flame photometric estimation [39, 113, 116] or is even more precise [165], but the values obtained with ISEs in serum are somewhat higher than those from flame photometry and most others methods [3, 25, 27, 113, 116]. This phenomenon is called pseudohyponatremia. It is caused by the fact that the samples are not diluted in ISE measurement, whereas in other methods dilution occurs before and during the measurement. On dilution, part of the water in serum is replaced by lipids and partially soluble serum proteins in samples with abnormally increased level of lipids and/or proteins. 

The experimental apparatus consists essentially of a narrow vertical glass tube down the inner surface of which one liquid is made to flow, the other liquid emerges from a fine glass tip in the form of a narrow jet down the axis of the tube. The two solutions are connected with calomel electrodes employing potassium chloride or nitrate as junction liquids. The E.M.F. of the cell is measured by means of a sensitive quadrant electrometer. The greatest source of error in the method is the elimination of or the calculation of the exact values of the liquid-liquid junction potentials in the system. For electrolytes which are not very capillary active, the possible error may amount to as much as fifty per cent, of the observed E.M.F. 

Accuracy and Interpretation of Measured pH Values. To define the pH scale and pertnil the calibration of pH measurement systems, a scries of reference buffer solutions have been certified hy the U.S. National Institute of Standards and Technology iNIST). The acidity function which is the experimental basis for the assignment of pH. is reproducible within about O.IKl.I pH unit from It) to 40T. However, errors in the standard potential of the cell, in the composition of the buffer materials, and in the preparation of the solutions may raise the uncertainty to 0 005 pH unit. The accuracy of ihe practical scale may he furthei reduced to (I.Ot)X-(l.(ll pH unit as a result of variations in the liquid-junction potential. 

Experience shows that the activity coefficients on this scale stay near unity (usually within experimental error) as long as the concentrations of the reactants are kept low, say less than 10% of the concentrations of the medium ions. The activity ( concentration) of several ions, notably H+, can be determined conveniently and accurately by means of e.m.f. methods, either with or without a liquid junction. In the latter case the liquid junction potential is small (mainly a function of [H+] ) and easily corrected for (3). The equilibrium constant for any reaction, on the ionic medium scale, may then be defined as the limiting value for the concentration quotient ... 

The list of error sources continues, just to mention a few the ionic strength of the sample, the liquid-junction and residual liquid-junction potentials, temperature effects, instabilities in the galvanic cell, carryover effects, improper use of available corrections (e.g., for pH-adjusted ionized calcium or magnesium). An error analysis goes beyond the limited scope of this paper more details are presented elsewhere [10]. 

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 ... 

In recent years care has been taken to eliminate, or reduce, as far as possible the sources of error in the evaluation of standard oxidation-reduction potentials highly dissociated salts, such as perchlorates, are employed wherever possible, and corrections are applied for hydrolysis if it occurs. The cells are made up so as to have liquid junction potentials whose values are small and which can be determined if necessary, and the results are extrapolated to infinite dilution to avoid activity corrections. One type of procedure adopted is illustrated by the case described below. ... 

The pH scale has been defined operationally, and standard reference solutions based on a conventional scale of hydrogen ion activity have been selected (i, 2). Measurements of the pH of seawater made with different electrodes and instruments are satisfactorily reproducible when standardized in the same way (3). The results obtained, however, do not always have a clear interpretation. Formally, this diflSculty can be attributed to the residual liquid junction potential involved in the measurement. The primary standards are necessarily dilute buffer solutions (ionic strength, I 0.1) whereas seawater normally has an ionic strength exceeding 0.6. This difference in the concentrations and mobilities of the ions coming in contact with the concentrated solution of potassium chloride of which the salt bridge-liquid junction is composed gives rise to a potential difference that is indeterminate. Consequently, the meas-m ed pH is in error by an unknown amount and does not fall exactly on the scale fixed by the primary standards. 

The presence of erythrocytes in the sample may also affect the magnitude of the residual liquid junction potential in a less predictable manner. For example, erythrocytes in blood of normal hematocrit are estimated to produce approximately 1.8mmol/L positive error in the measurement of sodium by ISEs when an open, unrestricted liquid-liquid junction is used. This bias may be minimized if a restrictive membrane or frit is used to modify the liquid-liquid junction. 

Table 1. Calculated error due to liquid junction potential in water/ethanol solutions (Frant, 1995).

First, the glass electrode may be off by as much as a pH unit due to the liquid junction potential (Table 1) (Frant, 1995). For example, a 52% solution of ethanol (EtOH) has a liquidjunction potential error of—0.46 pH units (Frant, 1995). 

Where a pH meter is standardized by use of an aqueous buffer and then used to measure the "pH" of a nonaqueous solution or suspension, the ionization constant of the acid or base, the dielectric constant of the medium, the liquid-junction potential (which may give rise to errors of approximately 1 pH unit), and the hydrogen ion response of the glass electrode are all changed. For these reasons, the values so obtained with solutions that are only partially aqueous in character can be regarded only as apparent pH values. 

As will be seen in Chapter 13, it is also difficult to measure the pH of a solution having a negative pH or pOH because high concentrations of acids or bases tend to introduce an error in the measurement by adding a significant and unknown liquid-junction potential in the measurements. 

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. 

A second limitation in the accuracy is the residual liquid-junction potential. The cell is standardized in one solution, and then the unknown pH is measured in a solution of a different composition. We have mentioned that this residual liquid-junction potential is minimized by keeping the pH and compositions of the solutions as near as possible. Because of this, the cell should be standardized at a pH close to that of the unknown. The error in standardizing at a pH far removed from that of the test solution is generally within 0.01 to 0.02 pH unit but can be as large as 0.05 pH unit for very alkaline solutions. 

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. 

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