Errors in titrations

Two important sources of error in titrations involving iodine are (a) loss of iodine owing to its appreciable volatility and (b) acid solutions of iodide are oxidised by oxygen from the air ... 

For a mixture of 10" Af iodide and 10" Af bromide, calculate the theoretical percentage error in titration of the iodide and the bromide with AgNOa, neglecting dilution and solid-solution formation. TakeATsp Agi = 10" , A ,p.AgBr = 4 X 10- 3... 

A chief source of error in titrations involving silver is photodecomposition of AgX, which is catalyzed by the adsorption indicator. By proper standardization, however, accuracies of one part per thousand can be achieved. 

Systematic Titration Errors in Titrations of Acids with... 

Avdeef A, Kearney DL, Brown JA, Chemotti Jr AR (1982) Bjerrum plots for the determination of systematic concentration error in titration data. Anal Chem 54 2322-2326... 

One of the commonest errors in titrating with alkali is for the values, in the set of pKg values, to show an upward trend as the titration progresses. This is usually caused by an impurity in the substance undergoing determination, so that not so much of it is present as had been supposed. By far the commonest and most troublesome impurity is water. To avoid this trouble, every substance submitted for determination of pKg should be of analytical purity and dried,under the same conditions that preceded its analysis. Another possible cause of an upward pH trend is that the stream of nitrogen is too fast and is expelling some of the solution as spray. Another cause of an upward trend is that the correct amount of material is present throughout the titration but not all of it is in solution. In the... 

The determinate error in a titration due to the difference between the end point and the equivalence point. 

From a human factors perspective, the chemistry of the process can be made inherently safer by selecting materials that can better tolerate human error in handling, mixing, and charging. If a concentrated reagent is used in a titration, precision in reading the burette is important. If a dilute reagent is used, less precision is needed. 

Only a small amount of potassium iodate is needed so that the error in weighing 0.14-0.15 g may be appreciable. In this case it is better to weigh out accurately 4.28 g of the salt (if a slightly different weight is used, the exact molarity is calculated), dissolve it in water, and make up to 1 L in a graduated flask. Twenty-five millilitres of this solution are treated with excess of pure potassium iodide (I g of the solid or 10 mL of 10 per cent solution), followed by 3 mL of IM sulphuric acid, and the liberated iodine is titrated as detailed above. 

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

You may wonder why we did not use the titration curve to determine the pH at the stoichiometric point of the ephedrine titration, as we did to find the pH at the midpoint. Notice from Figure 18-6 that near the stoichiometric point, the pH changes very rapidly with added H3 O. At the stoichiometric point, the curve is nearly vertical. Thus, there Is much uncertainty in reading a graph to determine the pH at the stoichiometric point. In contrast, a titration curve is nearly fiat in the vicinity of the midpoint, minimizing uncertainty caused by errors in graph reading. 

If reaction (92) occurred during the cerimetric (or permanganometric) titration of arsenic(III) in the presence of peroxydisulphate negative errors in concentration determinations should also appear contrary to experience. Therefore step (92) is presumably replaced by a reaction in which the As(IV) radical is oxidized by the oxidant according to... 

Although Eq. (25) has no physical meaning and although its simplification is not valid thermodynamically, since the condition of electroneutrality in both phases is not fulfilled if the proton cannot partition, it agrees very well with experimental data, which justifies its use. In fact, computerized fitting procedures correct for this error in commercial two-phase titrators, so that the experimental value of p K can directly be introduced in Eq. (25). 

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). 

An important source of error in nonaqueous conductance measurements is the presence of water in the system. As little as 1 X 10 "4 M water (2mg/l) may cause errors in many solvents. The difficulties faced in maintaining anhydrous conditions are formidable. Closed cell systems for handling solvents and salts have been described earlier. The most widely used method for measuring the water content of a solvent at low levels is still the Karl Fischer titration. 

Estimated error in 15%.In CDCls/nitrobenzene 1 1 (v/v). Determined from an UV-titration in CHCI3, estimated error in K, 10%. 

The median of the titrations in the example above is 10.15 mL, which is a much more representative value. If the result 11.02 mL is replaced by 10.02 mL (this would require evidence that there had been an error in transcribing results), then the mean becomes the reasonable 10.12 mL and the standard deviation is 0.06 mL. 

In addition to the above sources that should be assessed, for burettes used in titration there is the end point error. There is the repeatability of the end point determination, which is in addition to the repeatability of reading the burette scale, but is part of the repeatability calculated from a number of replicate, independent analyses. There is also uncertainty about the coincidence of the end point, when the color of the solution changes, and the equivalence point of the titration, when a stoichiometric amount of titrant has been added. 

Atmospheric moisture is a major cause of error in Karl Fischer titrations. Moisture can enter the sample, titrant, and titration vessel. The apparatus and titrant must... 

Starch is readily biodegraded, so it should be freshly dissolved or the solution should contain a preservative, such as Hgl2 ( I mg/lOOmL) or thymol. A hydrolysis product of starch is glucose, which is a reducing agent. Therefore, partially hydrolyzed starch solution can be a source of error in a redox titration. 

The direct Ripper iodometric titration is still used, but it is subject to error. In its place, direct iodate-iodide titration is used (44). This is followed by fixing the sulfur dioxide with glyoxal in a second sample and retitrating. The difference represents the free sulfur dioxide. The second titration roughly represents the amount of reduction and the amount of ascorbic acid present. Formulas for calculating the amount of sulfur dioxide to add in order to produce a predetermined level of free sulfur dioxide have been given by Stanescu (45). 

Active site burst titrations of the Zn(II) enzyme and the Co(II) enzyme at acidic pH and low substrate concentrations [(70-1) X 10 6 M] indicated one active site (96, 98, 99, 110, 135), while similar experiments (186) at high substrate concentration (2 X 10-3 M) yielded a value of 2.7 sites per dimer. In the latter experiment, error in the number of active sites might arise from the fact that the results were obtained by extrapolation from steady state measurements without direct observa-ion of the pre-steady-state phase. In the low substrate experiments, the pre-steady-state phase was observed directly. A burst was obtained at intermediate substrate concentrations (4 X 10"4 M), but the size was not reported (137). 

It is desirable to avoid errors in pH measurement, which limit the accuracy of the above NMR pH titration. If an NMR titration is applied to a mixture of two acids, HA and HA, each of whose chemical shifts, 6 and S, follows Equation (13), it is possible to eliminate pH from the two equations and replace it with n, the number of equivalents of titrant added. Thus Ellison and Robinson obtained Equation (14), where A = 6-6, A = 6 -6, A° = <5° -S °, and R = KJK1 20 Moreover, it is not necessary to prepare solutions of exact molarity, because n can be evaluated more readily as (6-6 )/(6° -6 ), from the variation of the chemical shift of HA during the titration. When R is near 1, this is approximately a parabolic dependence of A on n. The titration of a mixture of formic acid and 1802-formic acid permitted the evaluation of the lsO IE on acidity from the 13C NMR chemical shifts 6 and S of the carboxyl carbons. In practice, this involved fitting to the three parameters A-, A°, and R. This same equation was used with 31P chemical shifts to evaluate the lsO IE on the acidity of phosphoric acid and alkyl phosphates.21... 

Often, greater accuracy may be obtained, as in Volhard type titration, by performing a back titration of the excess silver ions. In such a case, a measured amount of standard silver nitrate solution is added in excess to a measured amount of sample. The excess Ag+ that remains after it reacts with the analyte is then measured by back titration with standard potassium thiocyanate (KSCN). If the silver salt of the analyte ion is more soluble than silver thiocyanate (AgSCN), the former should be filtered off from the solution. Otherwise, a low value error can occur due to overconsumption of thiocyanate ion. Thus, for the determination of ions (such as cyanide, carbonate, chromate, chloride, oxalate, phosphate, and sulfide, the silver salts of which are all more soluble than AgSCN), remove the silver salts before the back titration of excess Ag.+ On the other hand, such removal of silver salt is not necesary in the Volhard titration for ions such as bromide, iodide, cyanate, thiocyanate, and arsenate, because the silver salts of these ions are less soluble than AgSCN, and will not cause ary error. In the determination of chloride by Volhard titration, the solution should be made strongly acidic to prevent interference from carbonate, oxalate, and arsenate, while for bromide and iodide analysis titration is carried out in neutral media. 

Fish, W. and Morel, F.M.M. (1985) Propagation of error in fulvic acid titration data a comparison of three analytical methods. Can.J. Chem., 63, 1185-1193. 

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