Uncertainties in pH measurements

Because they are weak acids or bases, the iadicators may affect the pH of the sample, especially ia the case of a poorly buffered solution. Variations in the ionic strength or solvent composition, or both, also can produce large uncertainties in pH measurements, presumably caused by changes in the equihbria of the indicator species. Specific chemical reactions also may occur between solutes in the sample and the indicator species to produce appreciable pH errors. Examples of such interferences include binding of the indicator forms by proteins and colloidal substances and direct reaction with sample components, eg, oxidising agents and heavy-metal ions. 

We are homing in on an estimate of [H+] in which the precision is already less than 1%. The fourth approximation gives pH = 4.36, compared with pH = 4.34 from the first approximation and pH = 4.28 from the formula pH = (pK, + pK2). Considering the uncertainty in pH measurements, all this calculation was hardly worth the effort. However, the concentration [HM ]5 is... 

List several sources of uncertainty in pH measurements with a glass/calomel electrode system. 

FIGURE 1.8 Even with very low error in XYZ (error bars not shown), the error in pH measurements (represented by error bars) makes pH, uncertain in unbuffered systems. In microelectrophoresis, errors in pH measurements are the main source of uncertainty. 

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 usefulness of equation 10 is limited for several reasons. The assumption of insignificant trace ion contribution to the conductivity is a poor one. There is no cancellation of trace cation and anion contributions as in the charge balance. Since the measured specific conductance is not a conservative quantity, mean values cannot be used. Major ion concentrations and measured specific conductance must be available for each sample. Random uncertainty in the measured values and the problem of small differences in relatively large numbers leads to large uncertainties in calculated pH values around 6.1 where... 

The non-linearity in accumulation of errors can clearly be seen from Table 8-2. The measurement combinations At, Ct and pH, /(COz) are obviously unsuitable for calculation of other CO2 system parameters since the uncertainties in the measurements are magnified during the calculation. The results suggest, however, that with the right choice of measured parameters. At and Cj can be calculated with precision similar to that achieved in direct measurement (this also applies to pH measured by potentiometry). In contrast, /(CO2) cannot be calculated with the precision which can be achieved in direct measurement. 

Variation in junction potential. We reemphasize that variation in the junction potential between standard and sample leads to a fundamental uncertainty in the measurement of pH that is not correctable. Absolute measurements more reliable than 0.01 pH unit are generally unobtainable. Even reliability to 0.03 pH unit requires tremendous care. On the other hand, it is often possible to delect pH differences between similar solutions or pH changes in a single solution that are as small as 0.001 unit. For this reason, many pH meters are designed to produce readings to less than 0.01 pH unit. The free diffusion junction described in Section 23H-5 and illustrated in Figure 23-18 can minimize the variation in the junction potential. 

In potentiometric analysis, the indicator electrode is intrinsically responsive to single ion activities. It is the potential at the reference electrode that introduces a non-thermodynamic assumption (liquid junction potential) to the measurements. This term can be kept small and corrected by calculation if needed. In pH measurements, one uses the practical determination of pH, which uses the output of a calibrated combination pH electrode (normally with the bridge electrol34 e at the reference electrode containing 3 M KCl) as the accepted pH value of the solution. In essence, any uncertainty in potential arising at the reference electrode is ascribed to... 

A second complication in measuring pH results from uncertainties in the relationship between potential and activity. For a glass membrane electrode, the cell potential, Ex, for a solution of unknown pH is given as... 

The second question concerns the quality of the chemical control, directed more at the chemical analysis proper and its procedure. Important factors here are sufficient specificity and accuracy together with a short analysis time. In connection with accuracy, we can possible consider the quantization of the analytical information obtainable. For instance, from the above example of titration, if we assume for the pH measurement an accuracy of 0.02, an uncertainty remains of 0.04 over a total range of 14.0, which means a gain in information of n1 = 14.0/0.04 = 350 (at least 8 bits) with an accuracy of 5% as a mean for the titration end-point establishment of both acids, the remaining uncertainty of 1% over a range of 2 x 100% means a gain in information of n2 = 200 (at least 7 bits), so that the two-dimensional presentation of this titration represents a quantity of information I = 2log nx n2 = 15 bits at least. 

The uncertainty in the estimate of Pi is smaller (s, = s x5.04), and the uncertainty in the estimate of Pn is smaller still (Sj, = s x0.04). The geometric interpretation of the parameters Pi and Ph in this model is not straightforward, but Pi essentially moves the apex of the parabola away from Xi = 0, and pn is a measure of the steepness of curvature. The geometric interpretation of the associated uncertainties in the parameter estimates is also not straightforward (for example, P, Pi, and p,i are expressed in different units). We will simply note that such uncertainties do exist, and note also that there is covariance between bg and hi, between and b,i, and between hi and hn. 

Now consider a primary standard buffer containing 0.025 0 m KH2P04 and 0.025 0 m Na2HP04. Its pH at 25°C is 6.865 0.006.4 The concentration unit, m, is molality, which means moles of solute per kilogram of solvent. For precise chemical measurements, concentrations are often expressed in molality, rather than molarity, because molality is independent of temperature. Tabulated equilibrium constants usually apply to molality, not molarity. Uncertainties in equilibrium constants are usually sufficiently great so that the 0.3% difference between molality and molarity of dilute solutions is unimportant. 

Moral A small uncertainty in voltage (1.3 mV) or pH (0.02 unit) corresponds to a large uncertainty (5%) in analyte concentration. Similar uncertainties arise in other potentiometric measurements. 

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.,... 

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. 

Fig. 3 Traceability system for pH measurements in Germany. This traceability chain is basically similar to those for clinical chemistry and gas analysis, as DKD-accredited calibration laboratories act as multipliers in dissemination. It is a special feature of this structure that traceability of pH measurements does not extend to the SI but to a conventional reference frame recognized worldwide. Traceability to the SI is possible but would imply a considerable increase in uncertainty...

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