Titration, potentiometric errors

Dilute solutions of nominally 0.001 M NaOH and HGl are used to demonstrate the effect of an indicator s color transition range on titration error. Potentiometric titration curves are measured, and the indicator s color transition range is noted. Titration errors are calculated using the volume of titrant needed to effect the first color change and for a complete color change. 

For the primary stage (phosphoric) V) acid as a monoprotic acid), methyl orange, bromocresol green, or Congo red may be used as indicators. The secondary stage of phosphoric) V) acid is very weak (see acid Ka = 1 x 10 7 in Fig. 10.4) and the only suitable simple indicator is thymolphthalein (see Section 10.14) with phenolphthalein the error may be several per cent. A mixed indicator composed of phenolphthalein (3 parts) and 1-naphtholphthalein (1 part) is very satisfactory for the determination of the end point of phosphoric(V) acid as a diprotic acid (see Section 10.9). The experimental neutralisation curve of 50 mL of 0.1M phosphoric(V) acid with 0.1M potassium hydroxide, determined by potentiometric titration, is shown in Fig. 10.6. 

In such reactions, even though the indicator electrode functions reversibly, the maximum value of AE/AV will not occur exactly at the stoichiometric equivalence point. The resulting titration error (difference between end point and equivalence point) can be calculated or can be determined by experiment and a correction applied. The titration error is small when the potential change at the equivalence point is large. With most of the reactions used in potentiometric analysis, the titration error is usually small enough to be neglected. It is assumed that sufficient time is allowed for the electrodes to reach equilibrium before a reading is recorded. 

Active matter (anionic surfactant) in AOS consists of alkene- and hydroxy-alkanemonosulfonates, as well as small amounts of disulfonates. Active matter (AM) content is usually expressed as milliequivalents per 100 grams, or as weight percent. Three methods are available for the determination of AM in AOS calculation by difference, the two-phase titration such as methylene blue-active substances (MBAS) and by potentiometric titration with cationic. The calculation method has a number of inherent error factors. The two-phase titration methods may not be completely quantitative and can yield values differing by several percent from those obtained from the total sulfur content. These methods employ trichloromethane, the effects from which the analyst must be protected. The best method for routine use is probably the potentiometric titration method but this requires the availability of more expensive equipment. 

For an example of curve fitting involving classical propagation of errors in a potentiometric titration setting, see Ref. 142. 

Even if we make the stringent assumption that errors in the measurement of each variable ( >,. , M.2,...,N, j=l,2,...,R) are independently and identically distributed (i.i.d.) normally with zero mean and constant variance, it is rather difficult to establish the exact distribution of the error term e, in Equation 2.35. This is particularly true when the expression is highly nonlinear. For example, this situation arises in the estimation of parameters for nonlinear thermodynamic models and in the treatment of potentiometric titration data (Sutton and MacGregor. 1977 Sachs. 1976 Englezos et al., 1990a, 1990b). 

The titration of nalidixic acid in DMF with lithium methoxide has been reported(1)(2) with thymolphthalein as the indicator. It has also been titrated with sodium methoxide in ethylene-diamine or DMF methanol 1 2 with thymol blue indicator.(31) An error for this titration was reported as + 0.7%. A titration with sodium borohydride followed potentiometrically or with thymol blue indicator has also been reported by Bachrata and co-workers. The standard deviation was reported as + 0.60%.(32)... 

The titration error (i.e., difference between end-point and equivalence point) is found to be small when the potential change at the equivalence point is large. Invariably, in most of the reactions employed in potentiometric analysis, the titration error is normally quite small and hence may be neglected. 

This agreement is considered to be quite good when allowance is made for the fact that these are independently measured runs at concentrations varying by a ratio of 5000 to 1 The 10 ppm run at 120°C is probably in error due to a trace contaminant in the vapor samples observed in the potentiometric titration curve. This problem was not observed at 80°C. 

While the redox titration method is potentiometric, the spectroelectrochemistry method is potentiostatic [99]. In this method, the protein solution is introduced into an optically transparent thin layer electrochemical cell. The potential of the transparent electrode is held constant until the ratio of the oxidized to reduced forms of the protein attains equilibrium, according to the Nemst equation. The oxidation-reduction state of the protein is determined by directly measuring the spectra through the tranparent electrode. In this method, as in the redox titration method, the spectral characterization of redox species is required. A series of potentials are sequentially potentiostated so that different oxidized/reduced ratios are obtained. The data is then adjusted to the Nemst equation in order to calculate the standard redox potential of the proteic species. Errors in redox potentials estimated with this method may be in the order of 3 mV. 

By differentiating the titration curve twice and then equating the second derivative to zero, it can be shown that for a symmetrical titration curve ( i = the point of maximum slope theoretically coincides with the equivalence point. This conclusion is the basis for potentiometric end-point detection methods. On the other hand, if 2> the titration curve is asymmetrical in the vicinity of the equivalence point, and there is a small titration error if the end point is taken as the inflection point In practice the error from this source is usually insignificant compared with such errors as inexact stoichiometry, slowness of titration reaction, and slowness of attainment of electrode equilibria. 

The result obtained by a titration is usually more precise than that obtained in a direct potentiometric measurement. It is usually not too difficult to create an end point with a precision of better than 5 %. In the direct potentiometric determination the relative error Frei is given by... 

Standard titration techniques, using indicators [4,5,13] with 2-butanol as the titrant, have greater error (3 standard deviations = 1-5% of value), but usually this is still acceptable. The real advantage of these indicator methods is that virtually no capital investment is required for the equipment. The equipment for the more accurate potentiometric titration method can cost upward of 15,000 dollars. This is why titrations using 2,2 -bipyridyl or 1,10-phenanthroline are more prevalent in the literature. 

Sulfa drug sensitive electrodes have been used for the potentiometric titration of sulfonamides using standard sulfuric acid solution as titrant with distinct potential jump at the equivalence point and a maximum error of 0.7%. No significant interference is caused by the common inorganic anions (69). Ion-pair complexes of sulfa drugs and quaternary ammonium agents such as cetyltrioctylammonium have been employed as membrane electrodes for the potentiometric determination of sulfonamides (70). 

The course of add-base titrations conducted in the presence of specifically adsorbing species is different from that observed at pristine conditions. The experimental limitations and difficulties encountered by potentiometric titration have been discussed in Section 3.I.B.1 and 3.LB.2. Cancellation of some errors simplifies the assessment of the effect of spedfic adsorption on surface charging (comparison of titrations in the presence and absence of specific adsoiption), but the compensation of errors is not complete, e.g. the solubility of materials (adsorbents) is strongly affected by specific adsorption. 

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