Liquid junction potential uncertainty

An element of uncertainty is introduced into the e.m.f. measurement by the liquid junction potential which is established at the interface between the two solutions, one pertaining to the reference electrode and the other to the indicator electrode. This liquid junction potential can be largely eliminated, however, if one solution contains a high concentration of potassium chloride or of ammonium nitrate, electrolytes in which the ionic conductivities of the cation and the anion have very similar values. 

A typical set of experimental data290a,290b is shown in Fig. 11. All measurements converge to the value measured by Grahame.286 At present, the of Hg in water can be confidently indicated5 as -0.433 0.001 V (SCE), i.e., -0.192 0.001 V (SHE). The residual uncertainty is related to the unknown liquid junction potential at the boundary with the SCE, which is customarily used as a reference electrode. The temperature coefficient of of the Hg/H20 interface has been measured and its significance discussed.7,106,1 8,291... 

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,... 

Undoubtedly, the mercury/aqueous solution interface, was in the past, the most intensively studied interface, which was reflected in a large number of original and review papers devoted to its description, for example. Ref. 1, and in the more recent work by Trasatti and Lust [2] on the potentials of zero charge. It is noteworthy that in view of numerous measurements of the double-layer capacitance at mercury brought in contact with NaF and Na2S04 solutions, the classical theory of Grahame [3] stiU holds [2]. According to Trasatti [4], the most reliable PZC value for Hg/H20 interface in the absence of specific adsorption equals to —0.433 0.001 V versus saturated calomel electrode, (SCE) residual uncertainty arises mainly from the unknown liquid junction potential at the electrolyte solution/SCE reference electrode boundary. 

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. 

With this definition a reproducible number will always result. On the other hand the pHx so obtained does not correspond exactly to the second definition since it contains the uncertainty in the definition of yH and in addition an unknown difference in the liquid junction potential which may be important, especially if the solution is not very dilute. If similar solutions are compared, however, differences in pH may give accurate ratios between H+ activities or concentrations. 

Deviating from the primary method for pH, measurements for deriving SSs are carried out in cells, separating the solutions by a diffusion-limiting or liquid junction device. Liquid junction potentials forming as a result cannot be determined directly and vary with the composition of the solution forming the junction and the geometry of the junction device. The uncertainty due to the liquid junction potential can be estimated from independent measurements or from theoretical assumptions. 

The primary and the secondary buffers are separated by a liquid junction device, preferably a glass disk of fine porosity. Under these conditions, the contribution of the liquid junction potential to the cell voltage is very small. The increase in uncertainty is also very small. 

Cells with Liquid Junctions and Elimination of Junction Potentials. When electrochemical cells are employed to obtain thermodynamic data, high accuracy ( 0.05 mV) requires the use of cells that are free from liquid junction (in the sense that the construction of the cell does not involve bringing into contact two or more distinctly different electrolyte solutions). Otherwise, the previously discussed uncertainties in the calculation of liquid-junction potentials will limit the accuracy of the data. 

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 ... 

When liquid junctions exist, liquid junction potentials (LJPs) can arise due to differing ion mobilities across the interface, leading to charge separation and the development of a potential difference across the liquid junction. These can amount to some tens of millivolts and add a corresponding uncertainty in any voltammetric measurement. It follows that systems that avoid LJPs are generally preferable otherwise some consideration of their likely magnitude is desirable (see below). 

In practice, the value of k is never obtained as such, because the meter is adjusted so that the standard reads the correct value for its pX, the scale being Nernstian. As k contains in addition to the reference electrode potentials, a liquid-junction potential and an asymmetry potential, frequent standardization of the system is necessary. The uncertainty in the value of the junction potential, even when a salt bridge is used, is of the order of 0.5 mV. Consequently the absolute uncertainty in the measurement of pX is always at least 0.001/(0.059// ) or 0.02 if n = I, i.e. a relative precision of about 2% at best. For the most precise work a standard addition technique (p. 32) and close temperature control are desirable. All measurements should be made at constant ionic strength because of its effect on activities. Likewise,... 

The uncertainty in the pHj values for the seven primary standards in Table 3-1 (not including tetroxalate or calcium hydroxide) is judged to be about 0.006 pH unit at 25°C. At pH values much less than 3 or more than 11, or at temperatures other than 25°C, the uncertainties become greater. As to the significance of measured pH values, it may be concluded that, at best, pH may be regarded as an estimate of —log flH+ or lo.g [H ]yH+- The validity of the estimate depends on how constant the liquid-junction potential remains during measurement of standard and unknown... 

The problem of activity coefficient scale is more important when the measured pH is introduced in geochemical calculations. The measured pH is not likely to be on the same activity coefficient scale as the aqueous model because the buffers used to define pH are conventional (28). Even if the pH is on the same scale as the aqueous model, uncertainties in its measurement in brines, such as due to liquid-junction potentials (28.38). will always introduce inconsistencies. Consequently, it is unlikely that the measured pH will be consistent with the particular scale used for the individual ions. 

The residual liquid-junction potential, combined with the uncertainty in the standard buffers, limits the absolute accuracy of measurement of pH of an unknown solution to about 0.02 pH unit. It may be possible, however, to discriminate between the pH of two similar solutions with differences as small as 0.004 or even 0.002 pH units, although their accuracy is no better than 0.02 pH units. Such discrimination is possible because the hquid-junction potentials of the two solutions will be virtually identical in terms of true a. For example, if the pH values of two blood solutions are close, we can measure the difference between them accurately to 0.004 pH. If the pH difference is fairly large, however, then the residual hquid-junction potential will increase and the difference cannot be measured as accurately. For discrimination of 0.02 pH unit, large changes in the ionic strength may not be serious, but they are important for smaller changes than this. 

The required attributes listed above effectively limit the range of primary buffers available to between pH 3 and 10 (at 25 °C). Calcium hydroxide and potassium tetraoxalate tire excluded because the contribution of hydroxide or hydrogen ions to the ionic strength is significant. Also excluded are the nitrogen bases of the type BH+ (such as tris(hydroxymethyl)aminomethane and piperazine phosphate) and the zwitterionic buffers (e.g. HEPES and MOPS (10)). These do not comply because either the Bates-Gu enheim convention is not applicable, or the liquid junction potentials are high. This means the choice of primary standards is restricted to buffers derived from oxy-carbon, -phosphorus, -boron and mono, di- and tri-protic carboxylic acids. The uncertainties (11) associated with Harned cell measurements are calculated (1) to be 0.004 in pH at NMIs, with typical variation between batches of primary standard buffers of 0.003. 

Liquid-junction potentials introduce uncertainties in the results of certain physical measurements in which great accuracy is desired, for example, pH membrane potentials. Thus, it is desirable to find methods for reducing the magnitude of liquid-junction potentials in various systems. Salt bridges containing saturated solutions of KCl are utilized... 

The imprecision of 0.02 in the definition of pH is made up of approximately equal contributions from two quite different sources. One source of imcertainty is the variability in the liquid jimction potential [45, 59, 61] under different conditions of solution composition and dynamics. This is an intrinsic feature of the glass electrode-reference electrode combination used for pH measurements. This uncertainty does not arise in conductance measurements, and can be neglected in measurements of hydronium ion activity only by the use of reversible electrochemical (electrometric) cells that are constructed without liquid junction potentials. These approaches require considerable technical expertise and attention to detail in order to obtain results with maximal accuracy and precision. 

With regard to the significance of pH values, it can be said that they are at best an estimate of — logUH+, depending on how accurately the liquid-junction potential remains constant for the measurement of standard and unknown. For many dilute solutions (less than 0.1 M) between pH 2 and 12, the pH may be considered to correspond to the true hydrogen-ion activity to within about + 0.02 pH. This is equivalent to 1.2 mV in the potential reading, and about a 5% uncertainty in Oa. ... 

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. 

Some uncertainties still remain, however, because of ill-defined liquid junction potentials. Moreover, the method can be applied only in the case when the free energy of solvation is not much smaller than the free energy of hydration. Otherwise, the ion remains hydrated up to very low mole fractions of water in the solvent and the extrapolation becomes dubious. 

In polarographic practice the most important reference electrodes are separated calomel electrodes, a mercurous sulphate electrode, or, especially for small volumes, a silver chloride electrode immersed into an electrolysed solution containing OT M chlorides. This electrode proved satisfactory over the pH-range 1-13 when sodium or potassium chloride was added to the buffer solutions. Measurements in solutions forming complexes with silver e.g. glycine, veronal or ammonia buffers are precluded. The use of this electrode eliminates the uncertainty concerning the liquid junction potential. 

A Donnan potential can be measured electrically, with some uncertainty due to unknown liquid junction potentials, by connecting silver-silver chloride electrodes (described in Sec. 14.1) to both phases through salt bridges. 

One possible way to avoid some of the problems described above would be to use an electrode pair without a liquid junction, i.e., a cell without transference. In this way, uncertainties due to the liquid junction, such as alteration of the sample solution by electrolyte diffusion, streaming potentials, suspension effect, and the liquid junction potential itself, may be eliminated by using a pH or other ion-selective electrode as the reference electrode. The difficulty in this approach arises because, in order to assign an accurate emf value to the reference electrode, the activity of the reference ion in the sample solution must be accurately known and remain constant. Once again we are confronted by the necessity of a bootstrap operation. There is no way, at the present state-of-the-art, to accurately calculate the activity of an ion in such a complex mixture as a biologic fluid. If an activity is arbitrarily assigned to the reference ion and if it remains constant, then such an electrode system can be used for precise measurements of relative ion activities, but little can be said about the absolute activities. 

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