Approximation of titration curves and other sigmoidal functions by proportionally spaced cubic B-splines

Proportionally spaced cubicB-splines are an appropriate function system for the approximation of titration curves and other sigmoidal functions. They give a smooth weighted leastsquares fit without instability problems. The degree of smoothing depends only on the number of spline function which can be chosen by the user. The equivalence points of titration curves can be estimated with high accuracy from the zeros of the second derivative.The method gives good approximation curves even in the case of empty data regions, i. e. there are no artefacts in subranges where no data points exist. The routine has been tested successfully with large series of simulated and experimental data.     

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.     

Gran电位滴定法测定乳酸环丙沙星

介绍了乳酸环丙沙星测定的Gran电位滴定法。采用Gran线性函数进行电位滴定,经图解外推或线性回归处理求出计量点,可直接用于测定乳酸环丙沙星原料药的含量。该法用于多批原料药的测定,结果与药典法基本一致。     

用紫外分光光度法和电位滴定法测定几种植物激素的电离常数

分别采用紫外分光光度法和电位滴定法测定了脱落酸、3-吲哚乙酸、赤霉素、水杨酸等几种植物激素的电离常数,对比分析了两种测试方法的原理、测试步骤和数据处理方法.结果表明,采用两种方法测定的四种样品的电离常数与文献报道值一致,且测量结果的重现性较好;这表明紫外分光光度法和电位滴定法可方便地用于测定有机化合物的电离常数.     

电位滴定测定富锂锰基正极材料中锰

采用盐酸、硝酸溶解样品,加入焦磷酸钠溶液并调节溶液pH为6.0~7.0。用高锰酸钾标准溶液滴定至电位滴定仪上,根据消耗的高锰酸钾标准溶液的体积计算样品中的锰含量。探究了焦磷酸钠用量、溶液pH、共存元素等对测定锰含量的影响。在最优的实验条件下,方法的相对标准偏差在0.13%~0.22%之间,加标回收率在99.8%~100.5%之间。本方法是富锂锰基正极材料中质量分数10%~60%的锰测定的理想方法。     

火试金富集--自动电位滴定法测定粗碲中的银含量

粗碲是由铜、铅、锌冶炼带来的副产品,其中含有大量的金、银等贵金属。快速准确检测粗碲中银含量,具有十分重要的意义。样品预先采用硫酸溶解,还原沉淀金、银,过滤分离大部分的铋、硒、碲等元素,经配料、高温熔融,熔融态的金属铅捕集试料中的贵金属形成铅扣,试料的其他物质与熔剂生成易熔性熔渣。将铅扣灰吹,得金银合粒,清除合粒表面粘附的杂质,经硝酸分金,用硫氰酸钾滴定法测定银量。银的加标回收率在99.5%～101%,相对标准偏差(RSD)小于5%。方法速度快,稳定性好,适用于粗碲中银含量的测定。     

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.     

Critical comparison of evaluation methods of potentiometric titration data using a microcomputer-controlled automatic potentiometric titration system

A microcomputer-controlled automatic potentiometric titrator withP controlled intelligent auto-sampler has been built for serial analysis. Controlling and evaluating programs have also been written. In order to use the most powerful evaluating method, a comparison was made between the methods. The data of the titration curves were obtained by the implicit relation characterizing the curve. The different evaluating methods were tested by using these data. The effects of random errors stemming from measurements were also investigated. The methods used were: two point differentiating formula, differentiation of interpolating and smoothing spline functions, the Gran method, and implicit regression with the Gauss-Newton-Marquardt method. Regression is outstanding among the methods, but it needs much more computing time compared with others. The second-best method is the differentiation with smoothing spline function with end point determination based on finding the sign reversal of the second derivative. This method is much faster than regression.     

Transitions of serum albumin in patients with glomerulosclerosis 'in vivo' characterization by electrophoretic titration curves

HSA functions as a physiological transporter of solutes and small molecules that induce structural transitions 'in vitro'. Analysis of these transitions requires prior purification of HSA that could introduce bias due to conformational changes. We utilized electrophoretic titration curves to describe a neutral to acid (N-A) transition of HSA directly in sera of seven patients with active focal segmental glomerulosclerosis (FSGS). The divergent electrophoretic profile of HSA was characterized by a shift in the range of pHs between 4.5 and 7.5 with an average variation of free electrophoretic mobility corresponding to loss of 1 positive charge in the pKa protonation range of histidyl residues and should involve domain I of HSA. 'In-gel' determination by maleimide-PEO2-biotin of free SH 34 of domain I showed inaccessibility of the dye at this site in pathological HSA and alkylation with the same complex induced N-A transition in normal HSA. Potential binders of free imidazoles such as Ca++ and/or of SH 34 such as NO were excluded on the basis of direct titration and studies on binding stimulation. This is the first report describing a transition of HSA directly 'in vivo', and the utilization of electrophoretic titration curves was critical to this purpose. This transition appears to be specific to FSGS and is unrelated to the nephrotic syndrome, Ca++ and NO binding. Spectroscopic analysis will elucidate the structural implication.     

Determination of the total acidity in soft drinks using potentiometric sequential injection titration

A potentiometric SI titration system for the determination of total acidity in soft drinks is proposed. The concept is based on the aspiration of the acid soft drink sample between two base zones into a holding coil with the volume of the first base zone twice to that of the second one and channelled by flow reversal through a reaction coil to a potentiometric sensor. A solution of 0.1 mol l⁻¹ sodium chloride is used as ionic strength adjustment buffer in the carrier stream. The system has been applied to the analysis of some South African soft drinks having a total acidity level of about 0.2–0.3% (w/v). The method has a sample frequency of 45 samples per h with a linear range of 0.1 and 0.6% (w/v). It is easy to use, fully computerised, and gives the results that are comparable to both automated batch titration and manual titration.     

Development of a method for estimating an accurate equivalence point in nickel titration of cyanide ions

In a nickel titration of cyanide ions using murexide as indicator, an accurate equivalence point was determined by a non-linear least-squares curve-fitting for a titration curve. This method was developed to establish a standard solution for cyanide ions. In a curve-fitting procedure, a theoretical titration curve was calculated, assuming that nickel ion formed only a 1:4 Ni²⁺:CN⁻ complex with cyanide ions and formed only a 1:1 complex with murexide. Results of the curve-fitting were reasonable at any pH and any indicator concentration studied. The combined standard uncertainty for a concentration of a 1000 mg kg⁻¹ cyanide solution by this method was 0.079%.     

End-point detection in potentiometric titration by continuous wavelet transform

The aim of this work was construction of the new wavelet function and verification that a continuous wavelet transform with a specially defined dedicated mother wavelet is a useful tool for precise detection of end-point in a potentiometric titration. The proposed algorithm does not require any initial information about the nature or the type of analyte and/or the shape of the titration curve. The signal imperfection, as well as random noise or spikes has no influence on the operation of the procedure.The optimization of the new algorithm was done using simulated curves and next experimental data were considered. In the case of well-shaped and noise-free titration data, the proposed method gives the same accuracy and precision as commonly used algorithms. But, in the case of noisy or badly shaped curves, the presented approach works good (relative error mainly below 2% and coefficients of variability below 5%) while traditional procedures fail. Therefore, the proposed algorithm may be useful in interpretation of the experimental data and also in automation of the typical titration analysis, specially in the case when random noise interfere with analytical signal.     

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.     

Elimination of equivalence point errors in the potentiometric titration of chloride, bromide and iodide mixtures with silver nitrate

When two or more halides are determined in solution by precipitation titration with silver nitrate as the titrant, significant errors can occur at the first equivalence point as a result of coprecipitation. Errors of up to 33% were found for the first equivalence point for solutions containing mixtures of halides at micromolar levels. The addition of a flocculating agent to the solution reduced coprecipitation by increasing the rate of exchange between the precipitated silver halide and the halide ion remaining in solution. A logarithmic relationship was observed between the charge of the flocculating agent and the logarithmic concentration of the agent needed to minimise coprecipitation. Although flocculating agents reduced coprecipitation, they do not, however, completely eliminate equivalence point errors. Here a new method is presented which effectively eliminates the problem of coprecipitation during precipitation titrations for solutions containing two halides. In order to decrease the possibility of coprecipitation, we used selective complexation of the precipitation ion Ag⁺ in order to control the AgX solubility. For example, in the case of CF⁻ plus X⁻ (X=Br⁻ or I⁻), we added sufficient NH₃ to form Ag(NH₃)⁺ so that the free Ag⁺ activity was reduced below that required for theoretical AgCl precipitation in the absence of the other halides. Once the titration of the less soluble halide was completed and the first equivalence point determined, the Ag(NH₃)⁺ complex was destroyed by acidification of the solution to a pH less than 6. The titration is then continued and the second equivalence point determined. Equivalence point errors were reduced to less than 1.5% with careful application of the method.     

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.     

Determination of total fluoride in HF/HNO3/H2SiF6 etch solutions by new potentiometric titration methods

In the photovoltaic industry the etching of silicon in HF/HNO₃ solutions is a decisive process for cleaning wafer surfaces or to produce certain surface morphologies like polishing or texturization. With regard to cost efficiency, a maximal utilisation of etch baths in combination with highest quality and accuracy is strived. To provide an etch bath control realised by a replenishment with concentrated acids the main constituents of these HF/HNO₃ etch solutions including the reaction product H₂SiF₆ have to be analysed. Two new methods for the determination of the total fluoride content in an acidic etch solution based on the precipitation titration with La(NO₃)₃ are presented within this paper. The first method bases on the proper choice of the reaction conditions, since free fluoride ions have to be liberated from HF and H₂SiF₆ at the same time to be detected by a fluoride ion-selective electrode (F-ISE). Therefore, the sample is adjusted to a pH of 8 for total cleavage of the SiF₆²⁻ anion and titrated in absence of buffers. In a second method, the titration with La(NO₃)₃ is followed by a change of the pH-value using a HF resistant glass-electrode. Both methods provide consistent values, whereas the analysis is fast and accurate, and thus, applicable for industrial process control.     

溴酸钾滴定法测定铜冶炼烟尘中的砷含量

研究了测定铜冶炼烟尘中砷含量的溴酸钾滴定方法。对测定体系中的各共存元素进行研究,探讨了测定方法的各项测定条件,方法的相对标准偏差RSD为0.13%～0.61%,样品加标回收率在99.5%～100%,方法精密度高,准确度好,适用于铜冶炼烟尘中砷含量为1.00%～50.00%的测定。