Theory of titration curves: Locations of points of maximum slope on potentiometric heterovalent (“asymmetrical”) precipitation titration curves

By a wholly rigorous general treatment of the potentiometric titration curve representing the titration of B^m+ with A^n- to give the precipitate B_nA_m, where n ≠ m, it is shown on taking into account the effect of dilution that: (1) If $\text{n}\text{m}$ > 1, the inflection point must precede the equivalence point, but there is no inflection point if the initial concentration of the ion titrated is smaller than a certain value, which is determined by the values of m, n, and the solubility product of the precipitate. (2) If $\text{n}\text{m}$ < 1, the inflection point may follow the equivalence point — though not by more than a certain definite amount — or may precede it or coincide with it. In every such case there is a concentration of A^n- that will cause the equivalence point to coincide with an inflection point; this concentration depends on the values of m, n, and the solubility product of the precipitate. (3) Unless the difference between the equivalence and inflection points is negligibly small, the traditional treatment in which dilution is neglected gives seriously erroneous estimates of the location of the inflection point.     

Oxidation of plutonium by cobalt(III) green

A stable green solution of tricarbonatocobaltate(III) has been prepared and used for the redox titrimetric determination of plutonium in HNO₃ medium. Quantitative oxidation could be achieved and excess oxidant could be destroyed by NaNO₂. Pu(VI) was deter-ined by adding known excess of Fe(II) and carrying out potentiometric titration. The precision at the level of 0.5–5.0 mg was 2% RSD.     

Mercurimetric Potentiometric Determination of Barbiturates Using a Solid-State Iodide Ion-Selective Electrode

Abstract

A simple potentiometric method is described for mercurimetric titration of barbiturates using a solid-state iodide ion-selective electrode. The optimum titration conditions involve the use of a borate buffer of pH 9–10 as a medium and mercury(II) perchlorate of pH 1.7–1.9 as a titrant. Under these conditions, titration curves with two sharp consecutive inflection breaks are obtained. The first inflection corresponds to quantitative and stoichiometric reaction of barbiturates with mercury(II) and the second break is due to the reaction of the buffer with the titrant. No interferences are caused by Cl^?, Br^?, PO₄ ^3- and many excipients and diluents commonly used in the drug formulations. Determination of barbiturates in various pharmaceutical preparations gives reproducible results with an average recovery of 99.1% of the nominal (st.dev. 0.3 %) and the method offers significant advantages over the titrimetric method of the British Pharmacopoeia.     

Theory of titration curves : The locations of inflection points on acid-base and related titration curves

Consideration of the effect of dilution on the locations of the inflection points of potentiometric titration curves for titrations of monobasic acids or bases and for precipitation titrations in which the ions of the precipitate have numerically equal valences shows that;(I) In a strong acid-strong base or isovalent precipitation titration, the inflection point always precedes the equivalence point. No physically meaningful inflection point exists, regardless of the concentration of the substance titrated, if the concentration of the reagent is smaller than a certain value or if, when the concentration of reagent exceeds this limit, the concentration of the substance titrated is smaller than another limiting value.(2) In a weak acid-strong base or weak base-strong acid titration, the inflection point at which the slope is greatest also precedes the equivalence point, and vanishes under certain conditions. Earlier calculations are shown to have given incorrect information regarding the location and existence of this inflection point. The location of the inflection point at which the slope is smallest— the “point of maximum buffer capacity”—is shown to depend on the concentrations of the reagents employed.     

Constantes de formation des complexes de stoechiometrie 1:1 et 1:2 ainsi que des complexes mixtes formes entre le plutonium(III) et divers acides amino-polyacetiques

Determination of the formation constants of 1:1, 1:2 and mixed complexes between plutonium(III) and various aminopolyacetic acids The complexation of plutonium(III) with various aminopolyacetic acids is investigated by potentiometric titration at 25°C and at a constant ionic strength of 1 (KC1). The formation constants of the 1:1 complexes are reported for NTA, HEDTA, EDTA, DCTA and DTPA. The formation constants of the 1:2 complexes with NTA, HEDTA and EDTA as well as those of the mixed complexes formed between Pu(HEDTA) or Pu(EDTA) and NTA, IMDA or glycine are also reported. Several pK values of the 1:1, 1:2 and mixed complexes have been determined. These results are discussed within the framework of those obtained previously with the lanthanides.     

Potentiometric determination of uranium in the presence of plutonium in H2SO4 medium

The potentiometric determination of uranium is widely carried out in phosphoric acid medium to suppress the interferences of plutonium by complexation. Owing to the complexity of the recycling plutonium from the phosphate based waste involving manifold stages of separation, a method has been proposed in the present paper which does not use phosphoric acid. Uranium and plutonium are reduced to U/IV/ and Pu/III/ in 1M H₂SO₄ by Ti/III/, and NaNO₂ is chosen to selectively oxidize Pu/III/ and the excess of Ti/III/. The unreacted NaNO₂ is destroyed by sulphamic acid and excess Fe/III/ is added following dilution. The equivalent amount of Fe/II/ thus liberated is titrated against standard K₂Cr₂O₇. R.S.D. obtained for the determination of uranium /1–2 mg/ is 0.3% with plutonium being present upto 4.0 mg.     

Determination of plutonium and uranium in the same aliquot by potentiometric titration

A potentiometric titration method was developed for the determination of plutonium and uranium in the same aliquot in nitric acid medium. Plutonium was first determined by oxidation to Pu/VI/ by fuming with conc. HClO₄. Pu/VI/ formed was reduced to Pu/IV/ with known excess of Fe/II/ and the excess Fe/II/ was titrated with standard K₂Cr₂O₇ to a potentiometric end point. Uranium in the same solution was determined by reduction to U/IV/ with Fe/II/ in conc. H₃PO₄ medium and titrating U/IV/ formed with standard K₂Cr₂O₇ using the potentiometric end point detection technique. For the quantity of plutonium and uranium each in the range of 3–5 mg per aliquot a precision of ±0.2% and ±0.4%, respectively, was obtained.     

A new numerical method of finding potentiometric titration end-points by use of rational spline functions

A new numerical method of determining the position of the inflection point of a potentiometric titration curve is presented. It consists of describing the experimental data (emf, volume data-points) by means of a rational spline function. The co-ordinates of the titration end-point are determined by analysis of the first and second derivatives of the spline function formed. The method also allows analysis of distorted titration curves which cannot be interpreted by Gran's or other computational methods.     

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.     

Determination of Point of Zero Charge of Tunisian Kaolinites by Potentiometric and Mass Titration Methods

This paper deals with determining points of zero charge of natural and Na⁺‐saturated mineral kaolinites using two methods: (1) acid‐base potentiometric titration was employed to obtain the adsorption of H⁺ and OH^? on amphoteric surfaces in solutions of varying ionic strengths in order to determinate graphically the point of zero net proton charge (PZNPC) defined equally as point of zero salt effect (PZSE); (2) mass titration curve at different electrolyte concentrations in order to estimate PZNPCs by interpolation and to compare with those determined by potentiometric titrations. The two methods involved points of zero charge approximately similar for the two kaolinites between 6.5‐7.8, comparable to those reported previously and were in the range expected for these clay minerals. The comparison of potentiometric surface titration curves obtained at 25 °C and those published in the literature reveals significant discrepancies both in the shape and in the pH of PZNPCs values.     

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.     

Titrimetric determination of uranium in the presence of plutonium in sulphuric acid medium

Present work summairzes a method for the estimation of uranium in the presence of plutonium involving the reduction of uranium to U/IV/ and plutonium to Pu/III/ by Zn/Hg/ followed by the selective oxidation of Pu/III/to Pu/IV/with HNO₃ catalyzed by molybdate in the presence of large sulphate concenration [5M H₂SO₄+1.5M /NH₄/₂SO₄]. The oxidation of U/IV/ by K₂Cr₂O₇ is then carried out in the presence of excess of Fe/III/ and Al/NO₃/₃ to a sharp potentiometric end point. R.S.D. obtained for 20 determinations of uranium /3–6 mg/ was 0.3% in the presence of 0.35 mg of plutonium. Larger quantity for plutonium was found to interfere.     

Determination of equivalence points of sigmoidal potentiometric titration curves

The equivalence point of potentiometric titration curves coinciding with the point of inflection is calculated from the maximum of the first derivative or the zero of the second derivative. The approximation of the curve is carried out by means of cubicB-splines. The quality of the fitted curve depends on the number and position (proportionally spaced or equidistant) of knots. Series of simulated and measured titration curves were evaluated. Optimum fits were obtained with knot numbers about 20–35% of the number of data points. Only proportionally spaced splines are applicable for all types of curves and produce results of high accuracy.     

Determination of Fe(II)-Fe(III) and Fe(III)-Ni(II) by the two-component potentiometric complexometric titration

Summary The two-component complexometric potentiometric titration has been applied to the simultaneous determination of Fe(III) and Fe(II), and of Fe(III) and Ni(II) in solution. In each case the two analytes were determined by reading the end-points directly from the titration curve. The end-points are determined in a sense arbitrarily, but they are repeatable and easy to be detected precisely. However, the apparent (found) analytical results are biased. They are effectively corrected with the use of a set of two calibration equations (uncomplete second degree polynomials), which approximate the relationship between found endpoints and true concentrations of analytes in solution. The regression coefficients in the equations are determined on the basis of titration data obtained for standard solutions whose compositions correspond to a 2² factorial. Permanent address: Department of Analytical Chemistry, Jagiellonian University, Krakow     

Development and analytical applications of a new liquid-membrane 3,5-dinitrosalicylate-selective electrode

A 3,5-dinitrosalicylate (DNS)-selective electrode with a liquid membrane of either tetraphenyIphosphonium-DNSH dissolved in p-nitrocumene or dimethyldioctadecylammonium-DNSH dissolved in 1-decanol is described. The liquid membrane electrode exhibits rapid and near-Nemstian response to DNSH- activity from 10^-2 to 10^-5 M. The response is unaffected by pH in the range 2.5–6.5. The electrode has been successfully applied in the direct potentiometric titration of iron(III) and copper(II) with EDTA and in the indirect titrimetric determination of aluminium(III) and nickel(II). It is also useful in titrations of bulky quaternary cations such as cetyltrimethylammonium, cetylpyridinium and didodecyldimethylamnionium ions with DNSHNa.     

Natural pyrite as an electrochemical sensor for potentiometric titrations with EDTA, mercury(II) and silver(I)

The results obtained in potentiometric titrations of copper(II), mercury(II) and iron(III) with standard EDTA solutions are presented. The titration of copper(II) at pH values in the range from 8.11 to 10.99 (ammonia buffer) and the titration of mercury(II) and iron(III) at pH values from 3.59 to 5.65 (acetate buffer) were performed. The titration end-point (TEP) was detected with an indicator electrode made from natural crystalline pyrite as an electrochemical sensor. The results obtained in potentiometric titration with the pyrite electrode were compared with those obtained using a platinum electrode (Fe³⁺), a Cu ion selective electrode (Cu²⁺) and a Hg electrode (Hg²⁺). Accurate and reproducible results with good agreement were obtained, but higher potential changes at the TEP were obtained using the pyrite electrode. In the course of the titration the potential was established within less than 1 min, whereas at the TEP it was within about 2–3 min. The potential changes at the TEP were in the range from 60 to 200 mV per 0.1 ml EDTA, according to the stability constant of the complex formed. The highest potential changes, ranging from 160 to 200 mV, were obtained in the titration of iron(III) at pH 3.59. Reverse titration was also performed and accurate and reproducible results were obtained. Moreover, titration of halogenide and thiocyanate with standard mercury(II) solutions, as well as cyanide with silver(I) solution, were performed and accurate and reproducible results were again obtained. Received: 20 February 1998 / Accepted: 19 November 1999     

Titrimetric applications of multiparametric curve-fitting : Part 1. Potentiometric titrations of weak bases with strong acids at extreme dilutions

A multiparametric curve-fitting procedure is described for locating the equivalence point of a potentiometric titration and is applied to data obtained in titrations of acetate ion with hydrochloric acid over a wide range of concentrations (down to 6.5 · 10^-5M acetate). It does not depend on the existence of a point of inflection on the titration curve, and therefore yields useful results in titrations of this very weak base at concentrations well below that at which the point of maximal slope disappears. Three parameters are involved: the concentration of the base being titrated, the concentration dissociation constant K_a of its conjugate acid in the medium employed, and the apparent activity coefficient y_H⁺ of hydrogen ion in that medium, and all three of these must be evaluated when a new supporting electrolyte is employed. In 3.0 M potassium chloride at 24°, the apparent activity coefficient of hydrogen ion is 1.746₀, and this value permits data obtained in titrations of other or unknown bases in this medium to be interpreted by two-parameter fits. The value of K_a for acetic acid in this medium is 1.313₄ · 10^-5M; by means of these two numerical values routine titrations of acetate in this medium can be interpreted by one-parameter fits. It is possible to locate the equivalence point with an accuracy and a precision that cannot be approached by other techniques and even to obtain useful and reliable results under conditions so unfavorable that other techniques fail completely.     

Chromium(III) Potentiometric Sensor Based on Para‐Tertiary‐Butyl Calix[4]arene

A new chromium(III) PVC membrane sensor incorporating p‐tertiary‐butyl calix[4]arene as ionophore, potassium tetrakis as additive and dibutyl phthalate (DBP) as plasticizer was constructed. The electrode exhibited an excellent potentiometric response over a wide concentration range of 1.0×10^?7–1.0×10^?1 M with a Nernstian slope of 20±0.5 mV per decade. The detection limit was 5.0×10^?8 M. The electrode showed a better performance over a pH range of 3.0–8.0, and had a short response time of about <15 s.The electrode was successfully applied to potentiometric titration of Cr (III) with EDTA and for direct determination of chromium(III) in waste water.     

Four points function fitted and first derivative procedure for determining the end points in potentiometric titration curves: statistical analysis and method comparison.

A new method that belongs to the differential category for determining the end points from potentiometric titration curves is presented. It uses a preprocess to find first derivative values by fitting four data points in and around the region of inflection to a non-linear function, and then locate the end point, usually as a maximum or minimum, using an inverse parabolic interpolation procedure that has an analytical solution. The behavior and accuracy of the sigmoid and cumulative non-linear functions used are investigated against three factors. A statistical evaluation of the new method using linear least-squares method validation and multifactor data analysis are covered. The new method is generally applied to symmetrical and unsymmetrical potentiometric titration curves, and the end point is calculated using numerical procedures only. It outperforms the "parent" regular differential method in almost all factors levels and gives accurate results comparable to the true or estimated true end points. Calculated end points from selected experimental titration curves compatible with the equivalence point category of methods, such as Gran or Fortuin, are also compared with the new method.