利用滴定曲线方程和Origin精确绘制滴定曲线*

滴定曲线是滴定分析原理的重要内容。它显示了滴定过程中平衡体系性质的变化,可以获知化学计量点和滴定突跃信息,从而指导准确滴定判别或指示剂的选择。滴定曲线方程是滴定过程中体系的某种性质X(例pH)与滴定分数a(或滴定剂体积V)的关系方程,解析方程可获得函数X=f(a)的表达式。对一些较复杂的体系,推导函数X=f(a)较困难,但多数情况下反函数a=g(X)的推导更容易,表达式也更简洁。本文对酸碱、配位、氧化还原和沉淀滴定曲线方程进行了系统总结,并对不同情况下的函数X=f(a)或反函数a=g(X)进行了推导,拓展了教材内容。根据函数关系,在Origin中利用其函数绘图功能可直接绘制出滴定曲线,不用先生成数据点再绘图,方便快捷。用反函数绘图时增加数据点即可获得高精度的滴定曲线,可直接从滴定曲线上查找化学计量点和滴定突跃信息。     

滴定曲线与缓冲容量曲线、敏锐指数曲线并联讨论滴定规律

为了研究平衡的变化规律,我们曾撰文介绍滴定曲线与滴定过程型体分布图并联的方法。本文将讨论滴定曲线与滴定液的缓冲容量曲线和敏锐指数曲线并联研究平衡的方法。理论推导 1.强碱滴定酸参照文献[2]可以得出,以浓度为C的NaOH溶液滴定浓度为C_0、体积为V_0的n元酸H_nB,当加入NaOH V时滴定曲线方程为:     

一元强碱滴定混合一元弱酸的林邦滴定曲线方程及pHsp的计算

用物料平衡式MBE、质子条件式PBE、副反应系数和条件稳定常数等知识,推导出一元强碱滴定混合一元弱酸溶液的林邦滴定曲线方程并用其推导出第一、第二化学计量点pHsp1和pHsp2的计算公式.     

一元强碱滴定二元弱酸的林邦滴定曲线方程及pH_(sp)计算

用质子条件式PBE、物料平衡式MBE、副反应系数和条件稳定常数等知识,推导出一元强碱滴定二元弱酸溶液的林邦滴定曲线方程,并用其推导出第一、第二化学计量点pH_(sp1)和pH_(sp2)的计算公式。     

计算机与化学Origin在精确绘制酸碱滴定曲线中的应用

根据林邦副反应思想,分别得到一元强碱滴定一元强酸和一元强碱滴定一元弱酸的精确滴定曲线为一元二次和一元三次方程.利用Origin软件解析酸碱滴定曲线方程,并以滴定分数为横坐标,pH为纵坐标绘制滴定曲线.     

混合离子的沉淀准确滴定

用沉淀滴定的林邦滴定曲线方程推导滴定突跃的绝对值,用滴定突跃的绝对值推导混合离子准确滴定的条件。     

可逆对称的氧化还原滴定的林邦滴定曲线方程及其化学计量点E_(sp)值的计算

用物料平衡式MBE、副反应系数和条件稳定常数等知识,推导出可逆对称的氧化还原滴定的林邦滴定曲线方程并用其推导出化学计量点Esp值的计算公式。     

多元弱酸的准确滴定

用二元弱酸滴定的林邦滴定曲线方程推导第一和第二滴定突跃绝对值,用第一和第二滴定突跃绝对值推导二元弱酸第一和第二级解离的H+准确滴定的条件,并将其应用于多元弱酸的准确滴定.     

滴定分析模型的统一、MATLAB解析及曲线绘制

在将酸碱滴定、络合滴定、氧化还原滴定和沉淀滴定反应统一为M+L=N的基础上,将4种滴定曲线方程统一为两种数学模型。通过简单迭代法计算滴定过程中变化的副反应系数,利用接近数学表达式的自然化语言MATLAB解析4种滴定曲线方程,并绘制出精确的滴定曲线,方法简单易操作。     

通过反函数或者隐函数快速准确地绘制滴定曲线

滴定曲线是定量化学分析的重点之一,包含了大量有用信息。本文提出通过反函数或者隐函数的方式绘制滴定曲线。与传统绘制方式相比,反函数或者隐函数不仅容易推导,而且易于编程实现,因此能够快速获得大量数据点,从而显著提高滴定曲线的准确性。这种绘制方法适用于各种滴定体系,尤其是传统方法难以解决的一些复杂体系。此外,借助一些高级数据处理软件,非计算机专业人员能够快速掌握相关编程。得益于高效的绘制方案和简洁的编程,高精度滴定曲线得以发挥其应有功能,包括指示剂选择、准确滴定判别、终点误差计算以及直观地研究滴定体系的各种影响因素。本研究作为计算机技术高度发展背景下分析化学教学改革的一个尝试,对传统课程内容进行优化,去冗存精,使其简明凝练,重点突出,定量分析的主旨更加明晰。     

对氧化还原滴定过程的理论探讨

提出了氧化还原的分布系数、滴定分数、缓冲容量和敏锐指数的新概念 ,并推导和讨论了它们的函数表达式 ,建立了氧化还原滴定过程的曲线方程。它有助于进一步对氧化还原滴定过程研究的计算机化和自动化。     

Electroanalytical measurements without electrolytes: Conducting polymers as probes for redox titration in non-conductive organic media

Electroanalytical methods have been applied only in conducting media. An application of conducting polymers allows to overcome this limitation. If such material is in electrochemical equilibrium with dissolved redox active species, its electrical conductivity depends on the redox potential of these species. Therefore, conductometric measurements with conducting polymers can provide about the same information as classical redox electrodes. The approach was applied for redox titration. Equivalent points obtained by this titration in aqueous and organic electrolytes were identical. Then the approach was applied for determination of bromine number by redox titration in non-conducting organic phase.     

The formulation of the electron and proton balance equations for solving complicated equilibrium problems in redox titrations

 A plain, didactically convenient formulation of the electron balance and of the proton balance equations, suitable for complicated redox titration systems with redox, acid-base, precipitation and complexation side-reactions is discussed. Two typical examples, the standardisation of a permanganate solution by titration of iron(II), and the standardisation of a iodine solution by titration of sodium arsenite, are presented. Received: 30 January 1996/Accepted: 9 February 1996     

The formulation of the electron and proton balance equations for solving complicated equilibrium problems in redox titrations

 A plain, didactically convenient formulation of the electron balance and of the proton balance equations, suitable for complicated redox titration systems with redox, acid-base, precipitation and complexation side-reactions is discussed. Two typical examples, the standardisation of a permanganate solution by titration of iron(II), and the standardisation of a iodine solution by titration of sodium arsenite, are presented. Received: 30 January 1996/Accepted: 9 February 1996     

Some theoretical considerations in analytical chemistry : Part VI The precise calculation of data for redox titration curves

The dependence of the potentials during a redox titration upon the absolute concentrations of the reactants in the general case is demonstrated and an analogy is drawn between the effects of incompleteness of reaction in redox titrations and salt hydrolysis in acid-base reactions. The interpretation of the equilibrium constant of the overall redox reaction is clarified, and rigorous expressions for the calculation of reaction deficiencies are developed. Methods of calculating data for titration curves making allowance for reaction deficiency are offered together with examples of their application.     

Redox Titrations-II Location of inflection points of titration curves for homogeneous redox reactions

The relative positions of the inflection points and equivalence point of a homogeneous redox reaction have been studied by using the redox buffer capacity to derive an equation for the titration curve. The position of the inflection point corresponding to the maximum slope of the titration curve relative to the equivalence point depends on the electron transfers of the analyte and the titrant (the stoichiometric coefficients of the reaction equation) and on the difference between the formal potentials of the redox couples in a more complicated way than has been described previously.     

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.     

Thermometric titration of uranium(iv)with potassium dichromate

A thermometric method is presented for the redox titration of uranium(IV) with dichromate. The investigation was made primarily to determine the applicability of the thermometric method to redox titrations in solutions that contain ions deleterious to electrodes used in electrometric methods. A relative standard error of ±1% attainable in the titration of quantities of uranium(lV) of the order of 5 mg. Less than l 5 min is required to complete a titration. Fluoride ion can be tolerated in the solution provided that sufficient aluminium(111) is added to complex all the fluoride.     

An Interfacial Voltaic Cell for End Point Detection in Complexometric Titration of Metal Ions

An interfacial voltaic cell was firstly described by B. Waligra et al for the potentiometric titration of alkaloids in non-conducting solution.Our group had developed an improved one for the potentiometric titration of various alkaloids and their salts as well as pharmaceutical preparations,organic acids inorganic acids and bases. It had also been used as an end-point indicator for the potentiometric redox titration, and precipimetric titration.