Potentiometric measurement accuracy

Potentiometric measurements give log(3/ values which are correct to within 10% but the relative accuracy is difficult to assess due to the successive, repetitive nature of the experiments. Probably the most significant source of error, as we have stated, is the variation of pH with time. At tracer concentrations the enthalpy AH0 can be determined only by the temperature differential method. However, the temperature differential method is not as precise as the calorimetric one. The enthalpy of formation for each complex is computed with the assumption that ACp is constant over the temperature range and that the range of error corresponds to 10%. 

Whenever dissimilar electrolyte solutions are in contact, a voltage difference called the junction potential develops at their interface. This small voltage (usually a few millivolts) is found at each end of a salt bridge connecting two half-cells. The junction potential puts a fundamental limitation on the accuracy of direct potentiometric measurements, because we usually do not know the contribution of the junction to the measured voltage. 

In potentiometric measurements, the indicator electrode responds to changes in the activity of analyte, and the reference electrode is a self-contained half-cell with a constant potential. The most common reference electrodes are calomel and silver-silver chloride. Common indicator electrodes include (1) the inert Pt electrode, (2) a silver electrode responsive to Ag+, halides, and other ions that react with Ag+, and (3) ion-selective electrodes. Unknown junction potentials at liquid-liquid interfaces limit the accuracy of most potentiometric measurements. 

NaCl solution. In one set of experiments, the slurry was titrated with 0.1 normal NaOH solution in one cm increments to a pH of about 10. The samples of this set are referred to as the "slurry" samples (titration of the calcined zeolite - NaCl solution slurry). In another set of experiments, the calcined zeolite - NaCl solution slurry was filtered, the filter cake washed with about 100 cnP distilled water, and the combined filtrates were titrated with 0.1 N NaOH solution, again to a pH of about 10. The samples of this latter set are referred to as the "filtrate" samples (the zeolite being removed by filtration prior to titration of the filtrate). In addition to the manual titrations, automated potentiometric titration curves were obtained with a Metrohm E636 Titroprocessor, which has an estimated pH measurement accuracy of 0.001 pH unit and an estimated volumetric addition accuracy of 0.001 cm ... 

For assessing the viability and accuracy of high-temperature potentiometric measurements, the reference systems should be used. If Pt(H2) or YSZ(Hg/HgO) electrodes are used as the indicator electrodes, an aqueous solution with well-known activity of H+ (aq) should be used as the reference systems. At temperatures below 250 °C, the dilute aqueous solutions of strong acids and bases, such as HCl(aq) or NaOH(aq), can be employed to precisely calculate the activity of H+ (aq) so that the measured potential can be compared with the calculated one within a few millivolts or less. If HCl(aq) or NaOH(aq) is to be used at temperatures above 250 °C, the association constants of the electrolytes should be taken into account. Furthermore, at these temperatures, the precision of the calculated activities of H+ (aq) can be decreased. However, even in the low-density, supercritical aqueous solution, a reference system, which consists of a couple of three-component aqueous solutions, can be found to test the accuracy of the Pt(H2) or YSZ(Hg/HgO) electrodes within about 3 mV. Each of the three-component aqueous solutions consists of NaCl and either HC1 or NaOH... 

Although somewhat dependent on the method of electrode construction, the Rs of a potentiometric probe depends on the active tip area (24,25). One limiting factor for the ultimate size of the probe used in potentiometric measurements is the electrical characteristics. As Rs approaches 1013 fl, the noise level of the measurement will not allow greater than 1% accuracy, assuming very naively that the only noise source is the resistor Johnson noise. The noise level of small tips suggests that potentiometric tips of 0.05 /xm diameter are close to the smallest useful size. 

On the basis of the observed results there is no question that the fundamental interpretation of the left-hand side of Equation 1 is expressed correctly in Equation 19. The discrepancy between our results and those of Merle has to be a consequence of the greater accuracy of the ge volume and potentiometric measurements performed in this research. Merle did not correct for the volume of solution contained between gel beads nor did he calibrate his glass electrode in the presence of the fully dissociated sodium polyvinyl sulfate medium that he used. 

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

We can get an idea of the accuracy required in potentiometric measurements from the percent error caused by a 1-mV error in the reading at 25 °C. For an electrode responsive to a monovalent ion such as silver,... 

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. 

The problems and accuracy hmitations discussed under pH and other direct potentiometric measurements apply to ion-selective electrodes. 

Resistivity measurements are done on meander shaped samples by the standard potentiometric method in a stirred bath of liquid nitrogen relative to a dummy specimen For this procedure of residual re istometry the ultra-high measuring accuracy of 3.10 results below 300°C and of 3.10 for annealing treatments at higher temperatures. 

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. 

Water-soluble potassium (expressed as K2O) can be determined by manual or automated flame photometric and tetraphenylboron titration methods for all types of fertilizer samples. Atomic absorption can be used for samples below 5% K2O to maintain the highest degree of precision and accuracy. (Note Tetraphenylboron method for potassium is being used less often because of safety issues associated with formaldehyde.) Methods using ICP-OES for high concentration of potassium are currently being developed. Note Potentiometric measurements can be used to determine potassium in fertilizers but are not official approved methods and do not meet the accuracy and precision requirements as current methods. 

Potentiometric measurements can be done with a precision of 0.001 pX unit. The problem lies then in the conversion of the etnf or pX values to concentrations with the same level of accuracy. One of the difficulties in this conversion is the single ion activity problem explained in Sec. 1. The lack of sufficient selectivity of some pX electrodes can be another source of error (note that the glass electrode is an extremely selective sensor). The emf response of an ion-selective electrode (ISE) for X in the presence of an interfering species can be expressed as... 

Monitoring a titration by means of an ISE has the advantage over direct potentiometric measurement that the accuracy is determined largely by the titration reaction and not simply by the calibration function of the electrode. This is especially important for ISEs with changing or unknown slopes. For this reason the determination of a surfactant should always be carried out as a titration and not as a direct measurement. 

Measuring surfactant concentration by using surface tension suffers from the same drawback as the potentiometric measurements, i.e. the change in surface tension varies with the logarithm of the surfactant concentration, rendering a low accuracy in the calculated adsorbed amount. Another drawback is due to the fact that the method is very sensitive to the most surface-active species in the measured sample. In the adsorption of a polydispersed surfactant sample on a hydrophobic surface, the most hydrophobic surfactant species will adsorb and the more hydrophilic species will remain in the solution. In the calibration, however, the original sample is used and hence the calibration curve reflects a more hydrophobic system than is used... 

Samples were deformed by rolling at room temperature after disordering and quenching (40% and 80% reduction in thickness) and after ordering by a 19h annealing at 300°C (30% reduction). Completely recrystallized samples were prepared by annealing 48h at 600°C. Resistivity measurement was done by the potentiometric method in liquid N2 relative to a dummy specimen (accuracy 3x10" ). 

C. Potentiometric methods. This is a procedure which depends upon measurement of the e.m.f. between a reference electrode and an indicator (redox) electrode at suitable intervals during the titration, i.e. a potentiometric titration is carried out. The procedure is discussed fully in Chapter 15 let it suffice at this stage to point out that the procedure is applicable not only to those cases where suitable indicators are available, but also to those cases, e.g. coloured or very dilute solutions, where the indicator method is inapplicable, or of limited accuracy. 

However, there is still a strong need to develop new methods that will be able to quantitatively or at least qualitatively estimate the prediction accuracy of log D models. Such models will allow the computational chemist to distinguish reliable versus nonreliable predictions and to decide whether the available model is sufficiently accurate or whether experimental measurements should be provided. For example, when applying ALOGPS in the LIB RARY model it was possible to predict more than 50% and 30% compounds with an accuracy of MAE <0.35 for Pfizer and AstraZeneca collections, respectively [117]. This precision approximately corresponds to the experimental accuracy, s=0.4, of potentiometric lipophilicity determinations [15], Thus, depending on the required precision, one could skip experimental measurements for some of the accurately predicted compounds. 

Potentiometric titration with a sulfide ion-selective electrode as an indicator has been used to measure hydrogen sulfide in the air at ppb levels (Ehman 1976). The method has been shown to have very good accuracy and precision. No interference could be found from nitrogen dioxide, sulfur dioxide, or ozone. 

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