Accuracy of pH Measurements

The accuracy of pH measurements is governed by the accuracy to which the hydrogen ion activity of the standard buffer is known. As mentioned above, this accuracy is not better than 0.01 pH unit because of limitations in calculating the activity coefficient of a single ion. 

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. 

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. 

If pH measurements are made at a temperature other than that at which the standardization is made, other factors being equal, the liquid-junction potential will change with temperature. For example, in a rise from 25° to 38°C, a change of -1-0.76 mV has been reported for blood and —0.55 mV for buffer solutions. Thus, for very accurate work, the cell should be standardized at the same temperature as the test solution. 

The residual liquid-junction potential limits the accuracy of pH measurement. Always calibrate at a pH close to that of the test solution. 

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Experimental data for a titration of the amino acid glycine are given in Figure 13-13. The initial 40.0-mL solution contained 0.190 mmol of glycine plus 0.232 mmol of HC1 to increase the fraction of fully protonated + H3NCH2C02H. Aliquots of 0.490 5 M NaOH were added and the pH was measured after each addition. Volumes and pH are listed in columns A and B beginning in row 16. pH was precise to the 0.001 decimal place, but the accuracy of pH measurement is, at best, 0.02. 

Errors 1 and 2 limit the accuracy of pH measurement with the glass electrode to 0.02 pH unit, at best. Measurement of pH differences between solutions can be accurate to about 0.002 pH unit, but knowledge of the true pH will still be at least an order of magnitude more uncertain. An uncertainty of 0.02 pH unit corresponds to an uncertainty of 5% in J4H.,... 

Considering the definition presented, the accuracy of pH measurements of the skin is questionable. There are two inconsistencies emerging from the definition of pH. First, the skin, especially the epidermis, is not a diluted aqueous solution. Moreover, various residues located on the skin surface may influence the readings, if conducted by devices not designed for existence of many different substances. 

The absolute accuracy of pH measurements is no better than 0.02 pH units. See Chapter 13. 

Commercial solid-state potential measuring devices based on the type of op-amp described are often called pH or plon meters and are designed to work with glass pH electrodes, ion selective electrodes, and other indicator electrodes described earlier. Research quality plon meters have built-in temperature measurement and compensation, autocalibration routines for a three-point (or more) calibration curve, recognition of electrodes (so you do not try measuring fluoride ion with your pH electrode ), and the ability to download data to computer data collection programs. The relative accuracy of pH measurements with such a meter is about +0.005 pH units. Meters are available as handheld... 

Because the volume contraction, usually occurred after mixing D and T, the concentrations of C and 0 (or Qi) of suitable ingredients increase when mixing the solutions in various solvents. However, the effects of the contractions were neglected in the derivation of the relationships x = x(V) specified above (Table 9.4.3), when compared with the limited accuracy of pH measurements. From simple calculations, it is pertinent that the uncertainty of ApH = 0.02 in the pH determination is associated with the uncertainty of the H ion concentration equal to ca 5%. Therefore, the simplifying assumptions C = C(x) = const and C i = Cti(x) = const are justified. 

In addition, most devices provide operator control of settings for temperature and/or response slope, isopotential point, zero or standardization, and function (pH, mV, or monovalent—bivalent cation—anion). Microprocessors are incorporated in advanced-design meters to faciHtate caHbration, calculation of measurement parameters, and automatic temperature compensation. Furthermore, pH meters are provided with output connectors for continuous readout via a strip-chart recorder and often with binary-coded decimal output for computer interconnections or connection to a printer. Although the accuracy of the measurement is not increased by the use of a recorder, the readabiHty of the displayed pH (on analogue models) can be expanded, and recording provides a permanent record and also information on response and equiHbrium times during measurement (5). 

To find the best a priori conditions of analysis, the equilibrium analysis, based on material balances and all physicochemical knowledge involved with an electrolytic system, has been done with use of iterative computer programs. The effects resulting from (a) a buffer chosen, (b) its concentration and (c) complexing properties, (d) pH value established were considered in simulated and experimental titrations. Further effects tested were tolerances in (e) volumes of titrants added in aliquots, (f) pre-assumed pH values on precision and accuracy of concentration measured from intersection of two segments obtained in such titrations. 

Accuracy is a measure of how close the result is to the true value while reproducibility or precision is a measure of how close a series of measurements on the same sample are to each other. The accuracy and reproducibility of pH measurements can be highly variable and are dependent on several factors electrode stability (drift and hysteresis), response slope/calibration curve, and accuracy of the pH meters. While some of these factors are determined by the properties of electrodes, some measures can be taken to improve measurement accuracy and reproducibility. 

Ben Yaakov and Lorch [8] identified the possible error sources encountered during an alkalinity determination in brines by a Gran-type titration and determined the possible effects of these errors on the accuracy of the measured alkalinity. Special attention was paid to errors due to possible non-ideal behaviour of the glass-reference electrode pair in brine. The conclusions of the theoretical error analysis were then used to develop a titration procedure and an associated algorithm which may simplify alkalinity determination in highly saline solutions by overcoming problems due to non-ideal behaviour and instability of commercial pH electrodes. 

The primary source of error is ground loop currents. This is caused by galvanic errors introduced by small potentials resulting from the ionic liquids and dissimilar metals that the electrode is in contact with in a bioreactor. Additional sources of error are interactions with other electrodes. We have frequently found that a pH electrode not connected to an isolation amplifier that floats the reference can show errors of 1-2 pH units. A simple test is to measure the pH of a buffered solution on-line and off-line to check the accuracy of a measurement. 

Several mixtures containing one or more of the common elements are possible for the 4 f and 5 f elements, which permit the valid normalized measurement of D as a function of pH. If the absolute error in logj3/or logK y is 30%, we can expect a relative accuracy of the measurement of about 5 %. The respective free energy values (AG° = - RT Ln 3) are accurate to within 0.05 % relative to each other. 

In Table 11-1, the volume of acid added is designated Va. pH is expressed to the 0.01 decimal place, regardless of what is justified by significant figures. We do this for the sake of consistency and also because 0.01 is near the limit of accuracy in pH measurements. 

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. 

Quality control procedures (5-7) in the field included semiannual audit visits. These procedures were employed to maximize capture of uncontaminated samples, to identify and document them, to preserve their integrity until their arrival at the laboratory, to obtain dynamic blanks and to determine each site s precision and accuracy of pH and conductivity measurement. (The field measurements were used as a quality control to determine if precipitation samples had degraded between the field and laboratory measurements.)... 

Estimation of Uncertainty in The determination of the total ion molal concentration of calcium from salinity measurement is relatively precise with a probable error of less than 0.3% under open ocean conditions. Dickson and Riley (37) have recently discussed the effect of analytical errors on the evaluation of the components of the aquatic carbon-dioxide system for seawater at 25°C and 1 atmosphere total pressure. Their conclusions Indicate that if alkalinity and total carbon dioxide are the measured parameters a probable combined uncertainty in the total carbonate ion molal concentration from 3 to 6 percent results, depending on Fco2 If pH and alkalinity are the measured parameters the uncertainty is approximately 4 percent. In addition to the probable error introduced by analytical precision, the absolute accuracy of the measurements introduces an error which is difficult to evaluate. The results of the GEOSECS intercalibration study (38) were indicative of this problem. A conservative guess is that accuracy introduces at least a one percent further uncertainty. It is also difficult to determine exactly what error is introduced through temperature and pressure corrections to situ conditions. For the deep sea this may introduce a further uncertainty of at least... 

While the above approach works very well at temperatures below 100 °C, it is difficult to apply the IUPAC recommendations at temperatures above 100 °C when a high-temperature system should be pressurized. Definitely, at temperatures below 300 °C the HECC represented by (25) can be employed for pH measurements in the solutions where the half-reaction of the Pt(H2) electrode is a reversible process. Accuracy of the measurements could be 0.01 pH units and is mainly limited from estimating the diffusion potential in Eq. (26). 

The water used throughout all experiments was deionized and purified with a Millipore Super Q system. It had a pH value of about 6 and conductivity which varied between 0.05 and 0.1 /iS cm The increase in ionic strength was effected with the salts used to buffer the system (O.IM NaBr aqueous solutions). Values of pH were determined with Tacussel electrode (France). The accuracy of the measurement was to 0.05 pH unit. When needed, the pH was adjusted by the controlled addition of O.IN HCl or O.IN NaOH solutions depending on the pH desired. All inorganic chemicals were of Analyzed Reagent grade. 

Accuracy of colorimetric measurements. An accuracy of 0.06-0.1 pH unit is possible in routine work when buffer solutions differing by 0.2 pH are employed. Estimates to 0.01 unit, as is customary when measuring the pH of blood serum, are significant only if the pH difference between comparison solutions is 0.05-0.1 pH unit. The attainment of such precision is facilitated by the colorimeter or spectrophotometer, although an experienced worker may obtain equal precision with the naked eye. In no event should the accuracy of the measurement be exaggerated, for a number of other factors influence the results (differences in ionic strengths of unknown solution and buffer). An accuracy... 

We have already stated that, in buffer solutions, indicator papers will show approximately the same transformation intervals as do the corresponding indicator solutions. The hydrogen exponent can be estimated rather closely if a sufficient number of comparison solutions are at hand. Hemple found that the use of laemoid paper was practical between pH s 3.8-6.0. A drop of the solution under investigation was placed on the paper, and the color compared with papers containing drops of a series of buffer mixtures. The accuracy of the measurement was about 0.2-0.5 pH unit. 

G. K. McMiUan, Understand some basic truths of pH measurement, Chein. Eng. Prog. 87 (10), 30-7 (1991). (Why actual accuracy of pH electrodes in most industrial applications falls far short of the level expected). 

Indeed, the E- of Fe-substituted Mn-SOD was found to be almost 0.5 V lower than that of Fe-SOD, and the E of Mn-substituted Fe-SOD appears to be at least 0.5 V higher than that of Mn-SOD, although the accuracy of E measurements for SODs is severely limited ( 100mV) by the difficulty of achieving true equilibrium. These lower (or higher)-than-native FmS can explain the inactivity of Fe-substituted Mn-SOD (or Mn-substituted Fe-SOD). Spectroscopic comparisons, the X-ray crystal structure, and the fact that Fe-substituted Mn-SOD can still reduce (but not oxidize) 02 demonstrate that the active site is not grossly disrupted and still reacts with substrate. Inactivity related to a low E for Fe-substituted Mn-SOD is also consistent with Fe-substituted Mn-SOD s increased activity at lower pH since the E should increase by 60 mV per pH unit to a closer-to-native value at lower pH. 

The approximate graphical solution is used to simplify the PBE. All terms that are seen to be less than 5% of the main components in the PBE are discarded. The choice of 5% as a cutoff criterion is based on the usual limit of 0.02 units accuracy in pH measurements. Since pH is logarithmic, the corresponding numerical difference is 10° , which is 1.05, or 5%. The difference in logarithms corresponding to 5% (or 1 part... 

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