Approximation of potentiometric titration curves by logarithmic functions: Prediction of random errors in titration parameters

Two possible types of the propagation of random errors in measurements of potential (pH) and the volume of the titrant to titration parameters determined using logarithmic functions are considered. It is demonstrated that errors in calculated values are variously related to the errors in initial data. Expressions that provide the estimation of errors in characteristics of the titration curve from known errors in measurement are obtained.     

Calibration of titration methods

Summary A calibration method is proposed which makes it possible to use titration techniques in the presence of systematic errors, even if these errors depend on the concentrations of the analytes. The approach uses an empirical calibration model which approximates the relationship between apparent (found) and true concentrations of the analytes. Also a calibration of the physical model of the titration process is proposed, as well as a method of determination of the model parameters, which are useful when analytes are determined by fitting the model to experimental data of titration. Both approaches, empirical and based on the physical model, may be applied jointly. The example presented reveals high efficiency of the proposed approach in cases when a deficient physicochemical model of the titration process is used in the determination of an analyte concentration (simulated titration data applied). The calibration proposed may be considered as a generalization of the titrant standardization used in the conventional volumetric analysis. It may be applied to all titration techniques and for all methods of end-point detection and determination of the concentration of analytes. It opens new possibilities for the development of titration methods. Permanent address: Department of Analytical Chemistry, Jagiellonian University, Karasia 3, PL-30-060 Krakow, Poland     

Electroanalytical measurements without electrolytes: Conducting polymers as probes for redox titration in non-conductive organic media

Electroanalytical methods have been applied only in conducting media. An application of conducting polymers allows to overcome this limitation. If such material is in electrochemical equilibrium with dissolved redox active species, its electrical conductivity depends on the redox potential of these species. Therefore, conductometric measurements with conducting polymers can provide about the same information as classical redox electrodes. The approach was applied for redox titration. Equivalent points obtained by this titration in aqueous and organic electrolytes were identical. Then the approach was applied for determination of bromine number by redox titration in non-conducting organic phase.     

Redox Titrations-II Location of inflection points of titration curves for homogeneous redox reactions

The relative positions of the inflection points and equivalence point of a homogeneous redox reaction have been studied by using the redox buffer capacity to derive an equation for the titration curve. The position of the inflection point corresponding to the maximum slope of the titration curve relative to the equivalence point depends on the electron transfers of the analyte and the titrant (the stoichiometric coefficients of the reaction equation) and on the difference between the formal potentials of the redox couples in a more complicated way than has been described previously.     

Thermometric titration of uranium(iv)with potassium dichromate

A thermometric method is presented for the redox titration of uranium(IV) with dichromate. The investigation was made primarily to determine the applicability of the thermometric method to redox titrations in solutions that contain ions deleterious to electrodes used in electrometric methods. A relative standard error of ±1% attainable in the titration of quantities of uranium(lV) of the order of 5 mg. Less than l 5 min is required to complete a titration. Fluoride ion can be tolerated in the solution provided that sufficient aluminium(111) is added to complex all the fluoride.     

Zur direkten titration organischer verbindungen mit chrom(ii)sulfat

Azo-, nitro-, nitroso- and quinoid groups can be determined directly by electrometric titration with chromium(II) sulphate. In several cases isomeres have different redox potentials, consequently they give different steps in the titration curve and can be determined without separation.     

Some theoretical considerations in analytical chemistry : Part VI The precise calculation of data for redox titration curves

The dependence of the potentials during a redox titration upon the absolute concentrations of the reactants in the general case is demonstrated and an analogy is drawn between the effects of incompleteness of reaction in redox titrations and salt hydrolysis in acid-base reactions. The interpretation of the equilibrium constant of the overall redox reaction is clarified, and rigorous expressions for the calculation of reaction deficiencies are developed. Methods of calculating data for titration curves making allowance for reaction deficiency are offered together with examples of their application.     

Precise coulometric titration of sodium thiosulfate and development of potassium iodate as a redox standard

In this paper, we determine the effective purity of potassium iodate as a redox standard with a certified value linked to the international system of units (SI units). Concentration measurement of sodium thiosulfate solution was performed by precise coulometric titration with electrogenerated iodine, and an assay of potassium iodate was carried out by gravimetric titration based on the reductometric factor of sodium thiosulfate assigned by coulometry. The accuracy of the coulometric titration method was evaluated by examining the current efficiency of iodine electrogeneration, stability of sodium thiosulfate solutions and dependence on the amount of sodium thiosulfate solution used. The measurement procedure for gravimetric titration of potassium iodate with sodium thiosulfate was validated based on determination of a reference material of known purity (potassium dichromate determined by coulometry with electrogenerated ferrous ions) using the same gravimetric method. Solutions of 0.2 and 0.5 mol/L sodium thiosulfate were stable over 17 days without stabilizer. Investigation of the dependency of titration results on the amount of sodium thiosulfate solution used showed no significant effects, no evidence of diffusion of the sample, and no effect of contamination appearing during the experiment. Precise coulometric titration of sodium thiosulfate achieved a relative standard deviation of less than 0.005% under repeating conditions (six measurements). For gravimetric titration, the results obtained for the effective purity of potassium dichromate were sufficiently close to its certified value to allow confirmation of the validity of the gravimetric titration was confirmed. The relative standard deviation of gravimetric titration for potassium iodate was less than 0.011% (nine measurements), and a redox standard with a certified value linked to SI units was developed.     

Effect of excess AgO and EDTA on the redox titration involved in potentiometric determination of plutonium

Attempts to carry out potentiometric determination of plutonium (by AgO-oxidation method) following the determination of thorium (by complexometric EDTA titration) gave positively biased irreproducible values of plutonium. In order to understand the factors leading to the erroneous values of plutonium, the effect of varying amounts of AgO and EDTA on redox [Fe(II)/K₂Cr₂O₇] titration in the medium consisting of 1M H₂SO₄ and 0,4M HNO₃ was studied. When AgO (up to 200 mg) was added in the titration medium and destroyed by sulfamic acid prior to the redox titration, the dichromate tittre value (amount of standard K₂Cr₂O₇ solution equivalent to 1 g of Fe(II) solution) showed negative bias. The bias was found to decrease with increase in time interval between AgO destruction and the redox titration. The presence of EDTA (up to 15 mg) gave positive bias in the titre value. Results on the titre values obtained under different conditions of the aqueous medium indicated the possibility of formation of unstable Ag(II)-sulfamic acid compled, which is probably responsible for the irreproducible values of plutonium.     

Thermometric titration of cadmium with sodium diethyldithiocarbamate, with oxidation by hydrogen peroxide as indicator reaction

A new method of end-point indication is described for thermometric titration of cadmium with sodium diethyldithiocarbamate (DDTC). It is based on the redox reaction between hydrogen peroxide added to the system before titration, and the first excess of DDTC. Amounts of cadmium in the range 10-50 mumoles are titrated within 1% error.     

Improved linear titration plots for weak-acid titrations

Linear titration plot functions are derived for the following types of titration: weak monobasic acid-strong base, weak dibasic acid-strong base weak acid-weak base. These functions are compared with the corresponding Gran functions, where possible, and the effects of the following sources of error are discussed: the neglect of activity coefficients, errors in equilibrium constants and the presence of a hydrolysable salt.     

Evaluation of certified reference materials for oxidation-reduction titration by precise coulometric titration and volumetric analysis

The accuracy and uncertainty of coulometric titration of Japanese certified reference materials (CRMs) for oxidation-reduction titration were examined in this study. The results for potassium dichromate, sodium oxalate, and potassium iodate are presented. Potassium dichromate was directly determined by coulometric titration, and sodium oxalate and potassium iodate were determined by volumetric analysis using potassium dichromate assigned by coulometry.The uncertainty of the method was investigated by examining the dependency on the sample size and on the electrolysis current. Changes in the titration parameters did not result in any significant effects on the titration results. The coulometric system used primarily consists of a constant current source, timer, switching circuit, indicator unit, and voltmeter. They were controlled using the coulometry software by a PC/AT compatible computer. A highly automated coulometric system achieves repeatabilities of less than one part in 30,000 (k = 2) and uncertainties of less than one part in 15,000 (k = 2). In addition, using volumetric method, SI units traceable sodium oxalate and potassium iodate (purity standards for redox reaction) CRMs were developed.Reference materials for volumetric analysis are the most basic substances used in analytical chemistry. These materials are analyzed by several analytical methods and are produced globally; however, their purities have not been compared at the international level. Therefore, the relationship between the purity and reliability of these materials has not yet been established. In this paper, we determine the relationship between these parameters by titrating each material obtained from different laboratories.     

Automatic catalytic titration of silver

An automatic method is described for the catalytic titrimetric determination of microgram amounts of silver. The method is simple and accurate, and is based on the inhibitory effect of silver ions on the iodide-catalysed Ce(IV)-As(III) reaction. The end-point of titration with iodide is determined either automatically by the second- derivative technique or from the recorded potentiometric or spectrophotometric curves. Microamounts of silver in the range 1–2000 μg were determined with relative errors of about 0.7%.     

Determination of some dithiocarbamates by catalytic thermometric titration

The determination of dithiocarbamates by catalytic thermometric titration is described. The dithiocarbamates can be determined in the range 0.5-20 mumole with relative errors of about 5%.     

On the accuracy of acid-base determinations from potentiometric titrations using only a few points from the titration curve

There are several procedures which use only a few points on the titration curve for the calculation of equivalence volumes in acid-base titrations. The accuracy of such determinations will depend on the positions of the points on the titration curve. The effects of errors in the stability constants and in the pH measurements on the accuracy of the analysis have been considered, and the results are used to establish the conditions under which these errors are minimized.     

End-point construction and systematic titration error in linear titration curves-precipitation reactions

The systematic titration error which is introduced by the intersection of tangents to hyperbolic titration curves is discussed for precipitation reactions. A simple expression for the systematic titration error is derived, and S/C_x² is proposed as a measure of the sharpness of the titration curve. The effects of the conditional solubility product (S), the concentration of the unknown component (C_x), and the ranges used for the construction of the end-point, are considered. A graphical method is presented for the selection of pairs of ranges which result in small systematic titration errors. For equal values of S/C_x² and 1/KC_x, the optimum combinations of ranges are different for precipitation and complexation titrations. The differences are not large for values smaller than about 0.002. For titration curves with a reversed L-shape, the error is calculated when the end-point is constructed by the intersection of the tangent to the second branch of the curve with volume axis; in this case equal ranges result in the same titration error for equal values of S/C_x² and 1/KC_x. The systematic titration error is equal to -S/C_x² when the tangent to the curve is taken at f_a = 3.0.     

Linear titration plots for the potentiometric determination of mixtures of strong and weak acids

A linear titration plot method is derived for determining the components in a mixture of a strong acid and a weak acid, which may be polybasic with overlapping dissociation steps, from pH titration data. A FORTRAN program for the calculations is described and the effects of errors in the parameters of the linear function on the accuracy of the method are discussed.     

Estimation of the role of side reactions in the simulation of complexometric titration

A mathematical model was selected to describe the titration of metal ions with an arbitrary reagent in the presence of masking agents. The model takes into account the stepwise character of the complexation reaction and side reactions of protonation, hydrolysis and masking. The computed titration curves were in good agreement with the data of potentiometric titration. The corresponding program was used to optimize the titration conditions, to select promising titrants (other than complexones), and to predict systematic errors due to the shift of the titration jump in the presence of masking agents. Because of the last-named effect, the results of analysis may be underestimated several times     

Radiometric redox titration of antimony(III) with potassium iodate

The redox titration of antimony(III), labeled with¹²⁵Sb(III), by potassium iodate was radiometrically investigated using the burette method and the standard series method. The stoichiometry of the redox process was determined. The redox valence (the number of equivalents per mol) of potassium iodate for the oxidation of antimony(III) to antimony(V) was found to be 6, differing from the results obtained using the usual visual indicator method, where the value was shown to be 4. This disagreement in the equivalents of potassium iodate for the oxidation of antimony(III) is discussed.     

Dichromate titration of thallium(I)

The formal redox potentials of the thallium(III)-thallium(I) couple in different acids of varying strengths are reported. The minimum concentration of hydrochloric acid required for a direct titration of thallium(I) with potassium dichromate is 5M. Thallium(I) can be titrated directly with the primary standard oxidant, potassium dichromate, at room temperature, with ferroin as indicator, in 6M hydrochloric acid. Atmospheric oxygen must be excluded.