Evaluation of acid-base titration curves obtained by the triangle-programmed titration technique in flowing solutions

Different evaluation techniques for triangle-programmed coulometric acid—base titration curves obtained with various detector systems are compared. In the case of potentiometric detection, hardware differentiation and linearization of the titration curves was investigated. Photometric end-point detection with single or mixed indicators was also studied. It was concluded that among the techniques studied the hardware potentiometric differentiation and the photometric detection with an indicator mixture are the most advantageous.     

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.     

Approach to accuracy assessment of the glass-electrode potentiometric determination of acid-base properties

Thermodynamic data are suitable subject for investigating strategies and concepts for the evaluation of complete measurement uncertainty budgets in situations where the measurand cannot be expressed in a mathematical formula. Some suitable approaches are the various forms of Monte Carlo simulations in combination with computer-intensive statistical methods that are directed to an evaluation of empirical distribution curves for the uncertainty budget. Basis of the analysis is a cause-and-effect diagram. Some experience is available with cause-and-effect analysis of thermodynamic data derived from spectrophotometric data. Another important technique for the evaluation of thermodynamic data is glass-electrode potentiometry. On basis of a newly derived cause-and-effect diagram, a complete measurement uncertainty budget for the determination of the acidity constants of phosphoric acid by glass-electrode potentiometry is derived. A combination of Monte Carlo and bootstrap methods is applied in conjunction with the commercially available code SUPERQUAD. The results suggest that glass-electrode potentiometry may achieve a high within-laboratory precision because major uncertainty contributions become evident via interlaboratory comparisons. This finding is further underscored by analysing available literature data.     

Theoretical study of the acid-base properties of the montmorillonite/electrolyte interface: influence of the surface heterogeneity and ionic strength on the potentiometric titration curves

The parallel shape of the potentiometric titration curves for montmorillonite suspension is explained using the surface complexation model and taking into account the surface heterogeneity. The homogeneous models give accurate predictions only if they assume unphysically large values of the equilibrium constants for the exchange process occurring on the basal plane. However, the assumption that the basal plane is energetically heterogeneous allows to fit the experimental data (reported by Avena and De Pauli [M. Avena, C.P. De Pauli, J. Colloid Interface Sci. 202 (1998) 195-204]) for reasonable values of exchange equilibrium constant equal to 1.26 (suggested by Fletcher and Sposito [P. Fletcher, G. Sposito, Clay Miner. 24 (1989) 375-391]). Moreover, we observed the typical behavior of point of zero net proton charge (pznpc) as a function of logarithm of the electrolyte concentration (log[C]). We showed that the slope of the linear dependence, pznpc=f(log[C]), is proportional to the number of isomorphic substitutions in the crystal phase, which was also observed in the experimental studies.     

The determination of molybdenum in high-nickel alloys by potentiometric titration with cerium(IV) solutions

A combination of ion-exchange separation and potentiometric titration is used in the determination of the molybdenum content of various high-nickel alloys that contain more than 4% molybdenum. The molybdenum(VI) fraction of a sample separated by ion exchange is reduced with tin(II) chloride and titrated with cerium(IV) sulfate. The method facilitates accurate, routine determinations without the extreme care that is required by the standard photometric method or the length and complexity of the gravimetric method. By suitable adjustment of the sample size or the strength of the titration solution, effective titrations can be conducted on samples containing up to 100% molybdenum.     

A desk-computer program for calculation of the parameters of acid-base titration curves and protonation or metal-complex stability constants from potentiometric data

The program MINIPOT is designed to run on a desk-computer with 16-kbyte of memory. It can calculate the optimum values of the parameters of a blank acid-base titration in any solvent, and the protonation/deprotonation or overall stability constants of a maximum of four species with compositions H(q)L(p) or M(q)L(p) from potential, titrant volume and analytical concentration data. The program, written in BASIC, is based on the least-squares principle and is capable of simultaneous refinement of a maximum of four parameters.     

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.     

A graphical method for locating the end point in potentiometric titration curves

Summary A new graphical method for locating the end point in potentiometric titration curves is described. By moving two glass rods to scan the entire curve, the end point is determined when the difference between the two refracted lines is maximum. The method is particularly useful when the end point is ill-defined.

---

Graphisches Verjahren zur Bestimmung des Endpunktes potentiometrischer Titrationskurven

Zusammenfassung Zwei gleich starke Glasstäbe werden senkrecht zur Volumenachse über die Titrationskurve geführt. Der Endpunkt ist durch den maximalen Abstand der durch die Refraktion verzerrten Titrationskurve gekennzeichnet. Das Verfahren eignet sich auch noch bei Titrationskurven mit sonst schlecht definiertem Endpunkt.

     

Approximation of potentiometric titration curves by logarithmic functions: Factors affecting the accuracy of redox titration

The influence of random errors in measuring the potential and dosing the titrant volume on the reliability of the parameters of redox titration calculated using logarithmic relationships has been studied. It is found that the propagation of measurement errors in this case mostly depends on the difference between the real potentials of the reacting redox couples, on the number and distribution of points in the titration curve, and on the stoichiometry of the reaction.     

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.     

A note on the calculation of acid-base titration curves and their equivalence points

An equation has been developed for the calculation of the titration curve of any mixture of acids and bases, and an alternative way of defining an equivalence point, suitable for computer calculations, is presented.     

The potentiometric titration of iron(II)/HCl solutions with permanganate

Summary Reagents other than the Zimmerman-Reinhardt reagent have been used to minimize the errors incurred when Fe(II)/HCl systems are titrated with MnO₄ ^–. Potentiometric studies made of the effect of these additives on the initial and equivalence point potentials show that salts whose anions stabilize the Mn(III) state affect the equivalence point potential more than those containing Mn(II). The cation also affects the result, e.g., H₂SO₄ ^– and Na₂SO₄-containing solutions show a greater equivalence potential change than do those containing (NH₄)₂SO₄ and K₂SO₄. Ce₂(SO₄)₃, reportedly an effective inhibitor, does not affect the equivalence point potential. Less titrant is required for 6 M HCl-containing Fe(II) solutions than for 1 M HCl-containing solutions-a result opposite to that expected and only partially explained by a more rapid air-oxidation of Fe(II) in 6 M HCl. The Pt electrode is not inert in this system.

---

Zusammenfassung Bei einer Untersuchung der potentiometrischen Titration salzsaurer Eisen(II)-lösungen mit Permanganat wurde die Wirkung der verschiedenen für diese Bestimmung zur Verhinderung von Störungen empfohlenen ZusÄtze geprüft. Dabei ergab sich, da\ Salze, deren Anionen das dreiwertige Mangan stabilisieren, das Potential im Äquivalenzpunkt stÄrker beinflussen als solche, die zweiwertiges Mangan enthalten. Da\ auch das Kation das Ergebnis beeinflu\t ergab sich daraus, da\ bei H₂SO₄ und Na₂SO₄ eine grö\ere PotentialÄnderung im Äquivalenzpunkt beobachtet wurde als bei (NH₄)₂SO₄ und K₂SO₄. Bei Ce₂(SO₄)₃ wurde keine Wirkung auf die PotentialÄnderung festgestellt. Für 6 M salzsaure Fe(II)-Lösungen wurde weniger Titrationsmittel verbraucht als für 1 M salzsaure, was nur zum Teil mit der schnelleren Luftoxydation des zweiwertigen Eisens im 6 M HCl-Lösung erklÄrt werden kann. Die Platinelektrode erwies sich in diesem System nicht als inert.

     

Determination of the phenolic-group capacities of humic substances by non-aqueous titration technique

The phenolic-group capacities of five humic substances, such as, the Aldrich humic acid, the humic and fulvic acids extracted from a soil, the humic and fulvic acids extracted from a peat have been precisely determined by the non-aqueous potentiometric titration technique. The titration by KOH in the mixed solvent of DMSO:2-propanol:water = 80:19.3:0.7 at [K⁺] = 0.02 M enabled to measure the potential change in a wide range of pOH (=−log [OH⁻]), and thus to determine the capacities of phenolic groups which could not be precisely determined in the aqueous titration. The results of the titration revealed that the mean protonation constants of the phenolic groups were nearly the same for all humic substances and close to that of phenol in the same medium, indicating that each phenolic-group in the humic substances is rather isolated and is not electronically affected by other affecting groups in the humic macromolecule.     

酸碱滴定法间接测定重晶石中的硫酸钡

利用偏磷酸与重晶石在400℃时的复分解反应，将硫酸钡转化为聚偏磷酸钡，同时生成的H2SO4在高温下可挥发除去。在强碱性溶液和过氧化氢的作用下，聚偏磷酸钡转化为有确定磷钡比的磷酸钡。将磷酸钡用盐酸溶解后，在CaCl2存在下，以甲基红和酚酞为指示剂，用氢氧化钠标准溶液滴定磷酸，以间接测定重晶石中硫酸钡的含量。本法所需时间6h，分析结果与标准方法（SN／T0480．5－95）吻合，RSD为0．33％－0．68％。     

Theory of titration curves. VIII. A new interpretation of acid-base titration curves for polymeric acids. The significance of the Kern-equation parameters pKa and n

The Kern equation, pH = pK_a + n logf/(1 ? f), has been widely used in interpreting the potentiometric titration curves obtained on titrating polymeric acids with bases, and various interpretations of its empirical parameters pK_a and n have been advanced. Values of n similar to those generally obtained for polymeric acids are also obtained for dibasic and other monomeric polybasic acids for which the ratios of successive dissociation constants, K_i/K_(i+1), exceed the corresponding statistical values by a constant factor. The dependences of n on this factor and on the basicity of the acid are described. It is argued that the traditional picture of a dissociation constant varying continuously with the fraction titrated cannot be correct, and that the data can be more properly interpreted in terms of a constant non-statistical free-energy contribution to the successive values of K_i/K_(i+1).     

Development of quinhydrone electrode in chloroform. Application to the determination of equilibrium constants of acid-base reactions and potentiometric titration of some amine drugs

The optimum conditions for the functioning of quinhydrone electrode as acid indicator in chloroform was determined by voltammetric and potentiometric studies. This electrode was used for the determination of equilibrium constants of acid-base reactions and the potentiometric determination of the end point of acidimetric titrations of some amine drugs such as phenothiazinic derivatives in pharmaceutical preparations, after extraction into chloroform. The relative standard deviations of 20 mg of aliphatic amines, piperidine and piperazine substituted phenothiazines were 0.5, 0.7 and 1 % respectively.