Substitution titration: a new approach to automatic titration : Determination of Acidity in Precipitation Samples

In substitution titrations, a small portion of the sample is repeatedly replaced by an exactly equal volume of titrant, by means of a rotary injection valve. The titration curves obtained in this manner can be linearized by using suitable functions, and hence equivalence volumes can be calculated. The substitution process means that there is no increase in volume during a titration. It is therefore possible to use a completely closed system, which is advantageous for samples that are sensitive to the ambient atmosphere. The principle is demonstrated for the potentiometric titration of hydrochloric acid containing varying amounts of weak acid (acetic acid or ammonium ion) with sodium hydroxide solutions. By the substitution titration, it is possible to determine the strong and weak acid in HCl/NH₄Cl mixtures with an accuracy of ca. 2%, but acetic acid is difficult to determine in the mixture because of partial protolysis at the concentration level examined. Sample concentrations are chosen in the range 125–1000 μM total acidity, to conform with the concentrations normally found in precipitation samples. The development of a procedure for determining the acidity in rain-watet and throughfall samples is described. The substitution titrations are easily automated and provide adequate sensitivity for routine work.     

Coupled chemical processes at clay/electrolyte interface: a batch titration study of Na-montmorillonites

The present work addresses the protolytic charge of montmorillonite, which occurs on the broken-bond sites at the particle edges. The purpose is to overcome the general difficulty arising in potentiometric titration due to coupled side reactions, which severely impede the titrant budget (partial dissolution of the clay and of secondary phases, hydrolysis and readsorption of dissolved species, cation exchange). Batch potentiometric titrations were carried out on the montmorillonite fractions extracted from two bentonites (MX80 and SWy2) to quantify their protolytic charge. The effects of equilibration time (24 h and 7 days), pH from 4 to 10, and ionic strength (0.1 and 0.01 mol L(-1)) were extensively studied for the MX80 sample. Quantification of dissolution was achieved by analysis of the equilibrium solutions for dissolved species and by La(3+) exchange of the readsorbed species. The results clearly show that secondary phases such as iron- or silica-rich minerals contribute to the dissolved species, according to the nature of the raw bentonite. Furthermore, readsorption affects significant amounts of dissolved species. The overconsumption of proton/hydroxide due to dissolution, readsorption, and hydrolysis of dissolved species was evaluated using a self-consistent thermodynamic calculation. The ability of such calculation to correct the raw titration curves in order to extract the titrable surface charge of montmorillonite was evaluated by comparison with the continuous titration procedure. Especially in the alkaline domain, correcting the raw batch titration curves for the measured side reactions failed to reproduce the continuous titration curves. These observations demonstrate the limitations of the batch titration method and the superiority of fast, continuous methods for quantifying the dissociable surface charge of clays.     

Theory of titration curves : Points of minimum slope on potentiometric strong acid-strong base and precipitation titration curves

Strong acid-strong base and precipitation titration curves, like other kinds of potentiometric titration curves, inherently possess an inflection point where the slope is a minimum as well as one where it is a maximum. In any kind of titration the first of the inflection points can be caused to occur earlier, and can eventually be made to disappear altogether, by adopting certain expedients. For a weak acid-strong base titration, for example, these include decreasing the concentration of the acid titrated and titrating in the presence of an excess of its conjugate base. For strong acid-strong base and precipitation titrations they include decreasing the concentration of the substance titrated and increasing the concentration of the titrant. The conditions under which a physically significant inflection point of minimum slope can exist are defined, and explicit equations are given from which its position can be calculated under various experimental conditions, for strong acid-strong base and for both isovalent and heterovalent precipitation titrations.     

Application of various electrodes in potentiometric titration of calcium

In complexometric titrations various indicator electrodes may be employed for monitoring the course of titration and for detection of the end-point. Several of them, including the silver, mercury, bivalent cation membrane, calcium membrane and manganese dioxide electrodes were investigated and compared in their usefulness. As titrant, EDTA was mostly used, but results with similar chelating titrants were also obtained. The practical utility of the electrodes in titrations depends on their selectivity, magnitude of the end-point break and precision in determination of the end-point. For the electrodes studied, in some instances there is good correlation between the theoretical and experimental titration curves, but it is not always possible to predict the electrode response in the low activity range. In other cases poor correlation does not mean that reasonably good analytical results may not be obtained.     

Potentiometric titration of hydrogen peroxide with an electropolished stainless steel electrode

The preparation and use of a stainless steel indicator electrode in the accurate potentiometric titration of aqueous hydrogen peroxide are described. The results agree excellently with those obtained by a standard colorimetric weight-titration procedure. The nature of the titration curves, potential changes and the factors affecting them are discussed. Rapid potentiometric titrations directly to the equivalence-point potential are possible, owing to the nature of the titration curve.     

Potentiometric titration of diprotic systems

 The approximate nature of Gran’s method of linearization of potentiometric titration curves applied to diprotic systems has been thoroughly investigated. A function involving pH and titrant volume V (which is linearly dependent on V and becomes zero at the first equivalent point of titration of a weak diprotic base with a strong monoprotic acid) has been critically examined and validated by means of widely extended simulated experiments. Accurate experimental confirmation of the theoretical expressions has been obtained by performing many real titrations of the primary standard Na₂CO₃ with HCl. This particular application, analytically significant itself, can be a prototype of analogous applications. Received: 25 March 1996/Revised: 15 November 1996/Accepted: 19 November 1996     

Potentiometric titration of diprotic systems

 The approximate nature of Gran’s method of linearization of potentiometric titration curves applied to diprotic systems has been thoroughly investigated. A function involving pH and titrant volume V (which is linearly dependent on V and becomes zero at the first equivalent point of titration of a weak diprotic base with a strong monoprotic acid) has been critically examined and validated by means of widely extended simulated experiments. Accurate experimental confirmation of the theoretical expressions has been obtained by performing many real titrations of the primary standard Na₂CO₃ with HCl. This particular application, analytically significant itself, can be a prototype of analogous applications. Received: 25 March 1996/Revised: 15 November 1996/Accepted: 19 November 1996     

Stepwise a.c. amperometric titration of cadmium and zinc with EGTA

The theory of d.c. and a.c. amperometric titrations based on complexometric reactions is presented. It is shown that when E(1 2 )(M(I)) > E(1 2 )(M(II)) and log K(M(I)L) < log K(M(II)L), M(I) and M(II) can be sequentially determined by d.c. as well as a.c. amperometric titration. If, on the other hand E(1 2 )(M(I)) > E(1 2 )(M(II)) and log K(M(II)L), a stepwise titration can be performed only by a.c. amperometry. The effect of oxygen on an a.c. amperometric titration is also discussed. The stepwise a.c. amperometric titration of cadmium and zinc with EGTA at pH 6 in the presence of oxygen and an excess of 0.05 M acetate illustrates the theory.     

Application of potentiometric stripping analysis to compleximetric titrations

Samples that are 0.1–10 mM in lead(II) or 0.025–0.25 mM in bismuth(III) can be titrated with EDTA and the titrations monitored by means of computerized potentiometric stripping analysis. The coefficients of variation are 0.12–0.40%; systematic errors are estimated from computer-calculated titration curves using conditional constants obtained from the titration curves. The conditional stability constants for calcium(II), manganese(II) and lanthanum(II) in 0.5 M sodium chloride are determined from the exchange reaction with the lead—EDTA complex.     

End-point evaluation in instrumental titrimetry-II Confidence intervals in extrapolation of linear titration curves

The random titration error has been evaluated by single linear regression analysis of both linear branches of titration curves. As a simplification the confidence interval of a titration is estimated by substituting divergent linear confidence limits for the curved confidence limits of both branches of the curve. The influence of the angle between both branches upon the confidence interval of a titration has also been evaluated. The procedure has been proved advantageous by applying it to several amperometric and photometric titrations of lead and by comparing the results with those obtained by the complementary approach of Liteanu and C?rm?s, and by the usual statistical treatment of end-points obtained by graphical extrapolation. The method allows a critical consideration of the experimental conditions with regard to the desired level of precision.     

A digital image-based method for determining of total acidity in red wines using acid-base titration without indicator

This work proposes the use of digital image-based method for determination of total acidity in red wines by means of acid-base titration without using an external indicator or any pre-treatment of the sample. Digital images present the colour of the emergent radiation which is complementary to the radiation absorbed by anthocyanines present in wines. Anthocyanines change colour depending on the pH of the medium, and from the variation of colour in the images obtained during titration, the end point can be localized with accuracy and precision. RGB-based values were employed to build titration curves, and end points were localized by second derivative curves. The official method recommends potentiometric titration with a NaOH standard solution, and sample dilution until the pH reaches 8.2-8.4. In order to illustrate the feasibility of the proposed method, titrations of ten red wines were carried out. Results were compared with the reference method, and no statistically significant difference was observed between the results by applying the paired t-test at the 95% confidence level. The proposed method yielded more precise results than the official method. This is due to the trivariate nature of the measurements (RGB), associated with digital images.     

End-point evaluation in instrumental titrimetry-I Linear extrapolation of hyperbolic titration curves

A method is described for the estimation of a systematic titration error which is introduced by linear extrapolation of hyperbolic titration curves in amperometric, photometric, and other instrumental titrations. It is assumed that the titration is based upon a single-step ion-association reaction mA + nB right harpoon over left harpoon A(m)B(n) and that the measured physical property falls within known minimum and maximum values. The procedure is suitable for end-point determination, even when the titration curves have extensive curvature, and for predicting the choice of optimum experimental conditions for a given titration.     

Potentiometric titration of metal ions in ethanol

The potentiometric titrations of Zn2+, Cu2+ and 12 Ln3+ metal ions were obtained in ethanol to determine the titration constants (defined as the at which the [-OEt]/[Mx+]t ratios are 0.5, 1.5, and 2.5) and in two cases (La3+ and Zn2+) a complete speciation diagram. Several simple monobasic acids and aminium ions were also titrated to test the validity of experimental titration measurements and to establish new constants in this medium that will be useful for the preparation of buffers and standard solutions. The dependence of the titration constants on the concentration and type of metal ion and specific counterion effects is discussed. In selected cases, the titration profiles were analyzed using a commercially available fitting program to obtain information about the species present in solution, including La3+ for which a dimer model is proposed. The fitting provides the microscopic values for deprotonation of one to four metal-bound ethanol molecules. Kinetics for the La3+-catalyzed ethanolysis of paraoxon as a function of are presented and analyzed in terms of La3+ speciation as determined by the analysis of potentiometric titration curves. The stability constants for the formation of Zn2+ and Cu2+ complexes with 1,5,9-triazacyclododecane as determined by potentiometric titration are presented.     

Liquid-liquid interfaces as potentiometric ion-sensors-I The n-butanol-water interface as indicating sensor for the potentiometric titration of some acids and bases

The property that liquid-liquid interfaces modify their electrical charge as a function of the composition of the two phases in contact has been used to detect the end-points in a series of acid-base titrations in the aqueous phase. Although the titration curves are not classical in shape, the equivalence points can be located if the solutions are not too dilute. Good results for concentrations down to 10(-3)N have been obtained. The electrode has a fast response. The influence of surface-active substances on the titration has also been investigated.     

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.     

Conductometric titration of thiosulfate using new-type conductivity cells

The conductometric titration of thiosulfate with silver ions using non-conventional conductivity cells is described. For this purpose conductivity cells with different cell constants and electrode constructions, equipped with silver, amalgamated silver, stainless-steel and polished platinum electrodes were used. Two well-resolved break-points were observed at 1:1 and 2:1 silver/thiosulfate stoichiometries. Accurate conductometric determinations can be made, using the second break-points of the titration curves as equivalence points, in the range of thiosulfate concentrations 10(-4)-10(-2) M. Reverse titrations are less accurate.     

Titrations with piezoelectric monitoring : Part 1. Fundamental theory and titration of acids and bases

The use of a piezoelectric quartz crystal detector is proposed for monitoring the course of a titration reaction by observation of the frequency shift of the oscillating crystal. Satisfactory titrations can often be obtained using the acid-base technique, which is much more sensitive than the classical conductimetric titration and oscillometric titrration, with a lowest titratable concentration that is much lower but which can still be applied in the presence of a large amount of unreacting electrolyte.     

Simplex optimization procedure for evaluating equivalence points in sigmoidal and segmented titration curves

The use of the simplex procedure as a non-linear least-squares curve-fitting method is proposed for evaluation of equivalence points in sigmoidal and segmented titration curves. The application of this procedure to theoretical curves affected by different amounts of random noise indicates its effectiveness and accuracy for locating the correct end-point in titrations characterized by very low reaction constants. The relevant results are compared with those obtained by other regression methods as well as by the first-derivative and Gran approaches.     

The automatic titration of primary aromatic amines with nitrous acid

The “dead-stop” and potentiometric systems have been compared as a basis for the automatic titration of primary aromatic amines with nitrous acid; either system can be used but the potentiometric method is more widely applicable and is less subject to interference. Titrations of sulphanilamide and o-anisidine have been made with two commercial titrimeters and with both instruments the results obtained were at least equal in precision to those which would normally be obtained in manual titrations.     

Use of pH electrode for precipitation titration analysis: Theory and practice

A theoretical model for the potentiometric analysis of precipitation titrations using a pH electrode has been developed and tested. The new analytical method is possible by introducing a mediator which must be a weak acid and must be able to form an insoluble salt with a cation (a titrant). Theoretical expressions of pH, as well as the concentrations of all other species, were derived and solved numerically using bisection method. Among the various factors that influence pH during the titration, concentrations of the mediator and initial values of pH were proved to be very critical. The experimental potentiometric titration curves agree well with those predicted from the theoretical model. Crossing point method was adopted to determine an equivalence point from the titration curves. The method is tested using a known system of chloride determination. Among the several mediators tested (bisulfite, chromate, phosphate, cyanide, arsenate and EDTA), phosphate yielded the best results with an error of 0.1%; bisulfite, chromate and arsenate yielded comparably good results with an error of 0.3∼0.5%, but cyanide and EDTA yielded unsatisfactory results. The optimum mediator concentration found to be in a range of 1–2 mM.