Computer-controlled titrations: Part 1. Considerations based on systems theory

Automated titrimetric procedures are considered on the basis of systems theory, with emphasis on the dynamic behaviour of the system. In the case of continuous addition of titrant, conditions are derived for the maximum addition speed and a correction procedure is given. Control algorithms for discontinuous addition of titrant are given, including an algorithm for on-line estimation of the dynamic (overall) effects of the titration system; this is useful for determining the waiting time between two successive additions of titrant. Shannon's theorem is utilized in order to decide on the sampling of the titration curve, both for continuous and discontinuous additions of titrant. Finally, confidence intervals for the end-point determination are derived, based on zero crossing statistics, and applied on the second derivative of a sigmoidal titration curve.     

非水滴定法测定酰胺缩醛

对非水滴定酰胺缩醛的溶剂、滴定剂和指示剂进行了选择试验，用ＨＣｌ甲醇标准液进行滴定，通过电位滴定曲线或甲基橙指示剂可以准确的确定滴定终点，方法简便，结果准确。     

Simple instrument for titrimetry without visual indicators. gasometric titrations: Cerimetry,chlorometry, nitrate,nitrite, hydroxide and carbonate determination

It was shown in previous papers, that many titrimetric problems can be solved by observing the pressure change of a closed system above the solution titrated at the equivalence point. This principle was made the basis of a gasometric titration method in which the end-point is found graphically. The titrant is added to the sample solution in measured increments at fixed intervals of time and the corresponding gas pressure or volume of the system is recorded and then plotted against the volume of added titrant. Half a dozen readings are sufficient to establish the end-point of a titration, which is found at the intersection of two straight lines. This graphical method was applied to cerimetry and chlorometry, as well as to some other analytical reactions (determination of nitrite, nitrate, hydroxide and carbonate) already described in previous papers on the gas pressure end-point technique. The results are comparable in precision and accuracy to the values obtained by the conventional visual end-point titrations. A gasometric titration takes about 10 minutes. The presence of other substances in the sample capable of reacting with the titrant does not necessarily cause interference.     

Simple instrument for titrimetry without visual indicators. Gasometric titrations: Dichromatometry

Even ions which do not release gases with a certain titrant can be determined by direct gasometric titration. To achive this end, a substance which liberates a gas with the titrant, must be added to the sample solution. The end-point of the main reaction can be read from the gasometric titration curve of this indicator substance.This principle is applied in the present paper to the titration of ferrous and stannous ions by potassium dichromate. Hydrazine sulfate serves as indicator. The results are comparable in precision and accuracy to the values obtained by the conventional visual end-point titrations.     

Fitting and Analyzing pH Titration Curves on a Graphing Calculator

The pH titration curve is a well-known figure in chemistry. It is easy to plot this graph from experimental data by measuring pH as a function volume of added titrant; however, there is no simple mathematical equation of expressing pH as a function of titrant volume. The logistic function has been suggested but, as discussed in this paper, it is inadequate for modeling titration curves. Developed in this paper is a piecewise continuous function (with chemically meaningful parameters) of pH versus volume. A program has been written to display this function on a graphing calculator. This program can be used by students (1) to analyze the characteristics of pH titration curves, for example, the derivative and the presence of two inflection points, and (2) to interactively fit experimental titration data that they have collected.     

A simple method for the titration of multicomponent acid-base mixtures

A titration method has been developed to analyze acid mixtures, in which the pK values differed by 0.5 to 1 pH units. Instead of the use of equivalence points a buffer capacity curve is numerically derived from the titration curve resulting in a presentation similar to chromatograms and spectra. The consumption of the NaOH titrant is determined within pH intervals of 0.2-0.6 units around the pK values of the components. The buffer capacity measured is expressed as the consumption of NaOH over the pH interval. The amounts of compounds are found from these results using simple models of chemometrics. The method has been applied to a mixture of formic and acetic acids with concentrations of 0-3 mmol/20 ml with an error of 0-0.05 mmol. Furthermore a curve-fitting method based on a theoretical equation of buffer capacity can be applied with an error slightly larger than with the previous method. In this case, the pK values were also computed. For titrations beyond the pH range 4-10, the buffer capacity of water has to be subtracted from the titration results. The whole procedure requires including the computations about 3-6 min.     

Potentiometric back-titration of sulfate ion using a tetraphenylborate derivative as a titrant and a titrant-sensitive plasticized poly(vinyl chloride) membrane electrode

A potentiometric back-titration method for the determination of sulfate ions using a plasticized poly(vinyl chloride) membrane electrode without added ion-exchanger is described. A solution of a derivative of tetraphenylborate is used as titrant. The method is based on the ion association between an excess of 2-aminoperimidinium added to the sulfate containing sample and the tetraphenylborate derivative in the titrant. The titration end-point is detected as a sharp potential change due to an increase in the concentration of the free tetraphenylborate derivative at the equivalence point. The sharpness of the titration curve at the end-point is compared for two tetraphenylborate derivatives. Good results are obtained with a solution of sodium tetrakis (4-fluorophenyl) borate.     

Potentiometric titration of anionic polyelectrolytes using a cationic surfactant solution as a titrant and a titrant-sensitive plasticized poly(vinyl chloride) membrane electrode

A potentiometric titration method for the direct determination of anionic polyelectrolytes using a plasticized poly(vinyl chloride) membrane electrode is described. A cationic surfactant solution is used as titrant. The method is based on ion association between the anionic polyelectrolyte in the sample and the cationic surfactant in the titrant. The end-point is detected as a sharp potential change due to an increase in the concentration of the free cationic surfactant at the equivalence point. The sharpness of the titration curve at the end-point is compared for several cationic surfactants; a solution of stearyltrimethylammonium ion has been found to be superior. Received: 8 October 1996 / Revised: 17 December 1996 / Accepted: 18 December 1996     

Contributions to the theory of catalytic titrations-III Neutralization catalytic titrations

Neutralization catalytic titrations of weak monoprotic adds and bases with both volumetric and coulometric addition of the titrant (strong base/acid) have been simulated by taking into account the equilibrium concentration of the catalyst during the titration. The influence of several factors on the shape of the simulated catalytic titration curve has been investigated and is discussed.     

Potentiometric titration of anionic polyelectrolytes using a cationic surfactant solution as a titrant and a titrant-sensitive plasticized poly(vinyl chloride) membrane electrode

A potentiometric titration method for the direct determination of anionic polyelectrolytes using a plasticized poly(vinyl chloride) membrane electrode is described. A cationic surfactant solution is used as titrant. The method is based on ion association between the anionic polyelectrolyte in the sample and the cationic surfactant in the titrant. The end-point is detected as a sharp potential change due to an increase in the concentration of the free cationic surfactant at the equivalence point. The sharpness of the titration curve at the end-point is compared for several cationic surfactants; a solution of stearyltrimethylammonium ion has been found to be superior. Received: 8 October 1996 / Revised: 17 December 1996 / Accepted: 18 December 1996     

A chromatographic method for detection of end points in chemical reactions

Summary Gas chromatography is recognized as an analytical technique possessing desirable advantages for a wide range of applications. The purpose of this work is to demonstrate the usefulness of GC instrumentation for determining values of end-points for a variety of reactions. Gas chromatographic titrimetry may be characterized as that in which the change of peak-height ratio of the reaction during a titration is recorded as a function of titrant added. The experimental data are fitted to simple first-order interpolation equations, so that the titration curve, when extrapolated, intersects the volume axis, the point of intersection being the equivalence-point volume. The end-point values are in good agreement with those reported in the literature and with control measurements. From the results it is concluded that the method can be used with high confidence to determine end-point values in a fast and easy way.     

Potentiometric flow titration of iron(II) and chromium(VI) based on flow rate ratio of a titrant to a sample

A new potentiometric flow titration has been proposed based on the relationship of the flow rates between titrant and sample solutions. A sample solution is pumped at a constant flow rate. The flow rate of the titrant solution is gradually increased at regular time intervals and a flow rate for the titrant solution in the vicinity of the equivalence point is obtained. The concentration of the sample is calculated by C(S) (mol l(-1))=(R(T) (ml min(-1))xC(T) (mol l(-1)))/R(S) (ml min(-1)), where C(S), C(T), R(S), and R(T) denote the unknown sample concentration, titrant concentration in the reservoir, the flow rate of the sample solution which is a constant rate, and the flow rate of the titrant solution at an inflection point, respectively. The potentiometric flow titration of iron(II) with cerium(IV) and of chromium(VI) with iron(II) has been presented. The titration time of the proposed method is about 10 min per sample. An R.S.D. of the method is 0.77% for seven determinations of 1x10(-3) mol l(-1) iron(II). Similarly, the flow titration of chromium(VI) with iron(II) is carried out over the range 1x10(-4)-1x10(-3) mol l(-1) chromium(VI) and is successfully applied to the determination of chromium in high carbon ferrochromium.     

Contributions to the theory of catalytic titrations--I: Complexometric catalytic titrations

Complexometric catalytic titrations with both volumetric and coulometric addition of the titrant have been simulated. By taking into consideration the equilibrium concentration of the catalyst during the titration, general mathematical equations have been set up. The influence of several factors on the shape of the simulated catalytic titration curve has been investigated and is discussed. The work also deals with the conditions under which the approximate mathematical expressions (equilibrium concentration of the catalyst being neglected) can be applied to simulate the catalytic titration curves with a satisfactory accuracy.     

Macro and semimicro determination of inorganic bromide by cerium(IV) oxidimetry

Aqueous solutions containing 1-200 mg of inorganic bromide in 25-100 ml of solution are quantitatively analysed at room temperature by direct titration with ammonium hexanitratocerate(IV) in 2M perchloric acid. The titration medium is perchloric acid at a concentration of at least 4M. End-points are determined from potentiometric (Pt vs. S.C.E. electrodes) titration plots, the potential break at the end-point being 300 mV. Iodide up to at least 0.02N and sulphate up to 0.01N do not interfere. Chloride depresses the end-point potential break but a satisfactory titration curve is still obtained in the presence of 0.04N chloride. Standard deviations are +/- 0.068 mg of bromide in the 1- to 20-mg range [0.02M cerium(IV) titrant] and +/- 0.45 mg of bromide in the 20- to 200-mg range [0.1M cerium(IV) titrant].     

Potentiometric back-titration of sulfate ion using a tetraphenylborate derivative as a titrant and a titrant-sensitive plasticized poly(vinyl chloride) membrane electrode

A potentiometric back-titration method for the determination of sulfate ions using a plasticized poly(vinyl chloride) membrane electrode without added ion-exchanger is described. A solution of a derivative of tetraphenylborate is used as titrant. The method is based on the ion association between an excess of 2-aminoperimidinium added to the sulfate containing sample and the tetraphenylborate derivative in the titrant. The titration end-point is detected as a sharp potential change due to an increase in the concentration of the free tetraphenylborate derivative at the equivalence point. The sharpness of the titration curve at the end-point is compared for two tetraphenylborate derivatives. Good results are obtained with a solution of sodium tetrakis (4-fluorophenyl) borate. Received: 9 March 1998 / Revised: 21 April 1998 / Accepted: 25 April 1998     

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.     

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.     

Tracer-monitored flow titrations

The feasibility of implementing tracer-monitored titrations in a flow system is demonstrated. A dye tracer is used to estimate the instant sample and titrant volumetric fractions without the need for volume, mass or peak width measurements. The approach was applied to spectrophotometric flow titrations involving variations of sample and titrant flow-rates (i.e. triangle programmed technique) or concentration gradients established along the sample zone (i.e. flow injection system). Both strategies required simultaneous monitoring of two absorbing species, namely the titration indicator and the dye tracer. Mixing conditions were improved by placing a chamber with mechanical stirring in the analytical path aiming at to minimize diffusional effects. Unlike most of flow-based titrations, the innovation is considered as a true titration, as it does not require a calibration curve thus complying with IUPAC definition. As an application, acidity evaluation in vinegars involving titration with sodium hydroxide was selected. Phenolphthalein and brilliant blue FCF were used as indicator and dye tracer, respectively. Effects of sample volume, titrand/titrant concentrations and flow rates were investigated aiming at improved accuracy and precision. Results were reliable and in agreement with those obtained by a reference titration procedure.     

控制电位滴定法的误差分析

研究了影响控制电位滴定法测定结果准确度的因素,得到的结论是:第一,电位的控制误差及滴定剂体积的测定误差是影响控制电位滴定法测定结果准确度的主要因素.计算模型中的比例系数越大,滴定曲线的变化率越大,这种影响越小.第二,多组分体系的测定误差,与组分在计算模型中比例系数的相对大小有关.比例系数越大,测定误差越小.第三,不同浓度(或不同浓度比)待测溶液滴定曲线的差异越大,对控制电位滴定法的测定越有利.