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。     

一种准确滴定判别的统一方法

提出一种基于滴定突跃的准确滴定判别方法,以统一方式完成不同滴定类型的判别。该方法具有原理明确、步骤简单、记忆负担轻和计算效率高的优点;当目测不确定性或者允许误差等参数发生改变时,计算效率不受影响。对于多组分复杂滴定体系,该方法同样高效,只是涉及的数值计算稍显繁复,然而通过软件也能够快速完成。该方法为准确滴定判别提供了一种不同于传统判别式的解决途径。     

基于Python的沉淀滴定学习软件设计与教学应用

在滴定分析教学中,将现代信息化Python编程语言与沉淀滴定分析法深度融合,设计开发了沉淀滴定学习软件。该软件无需安装和建立复杂的函数或计算方程,用户只需选择和输入相应参数,即可实现沉淀滴定曲线的可视化绘制、滴定可行性判断、化学计量点和滴定突跃范围以及滴定误差的计算等。软件以图形界面形式呈现,设计简洁、操作方便、内容丰富,可选择内置或自定义滴定实例,基本涵盖了沉淀滴定法教学大纲中重要知识点内容,便于教师教学和学生自主学习应用,协同提升教学效果。     

复杂氧化还原滴定曲线方程的Origin解析和曲线绘制

本文首先利用物料平衡和林邦副反应思想分别推导出n1=n2和n1≠n2两种情况时的氧化还原滴定曲线方程,然后应用Origin软件对所推导的不同曲线方程进行解析,建立起以溶液电势E为因变量,滴定分数a为自变量的函数关系,并绘制其滴定曲线。     

酸碱滴定终点误差的快速估算法——基于CurTiPot酸碱滴定曲线的快速绘制

利用CurTiPot软件快速绘制酸碱滴定曲线,并在相对误差概念的基础上,实现了酸碱滴定终点误差的快速计算。     

GUI氧化还原滴定学习软件的设计与应用

在滴定分析教学中,为推进现代信息技术与教育教学深度融合,利用Python语言设计开发了图形用户界面(GUI)氧化还原滴定学习软件。软件将氧化还原滴定体系分为对称型和不对称型滴定反应2种类型,通过自定义或选择内置的氧化还原滴定体系后,仅需设置滴定参数和选择滴定介质,即可实现滴定反应程度的自动判断和滴定曲线的静态显示或动态可视化绘制。此外,依据曲线图像还可实现化学计量点、滴定突跃范围和滴定误差的计算,具有较强的开放性、灵活性和普适性,便于教师教学和学生自主探究学习。软件界面设计简洁,操作方便,用户无需安装和专业编程知识,可直接在Windows平台上运行。     

滴定分析终点误差的通用高效计算策略

终点误差是滴定分析的核心内容之一,现行教材中众多导出公式致使终点误差的计算过于复杂。本文提出了一种通用高效的计算策略,统一了酸碱滴定、配位滴定以及氧化-还原滴定的终点误差计算;此外,还将准确滴定判别统一到终点误差的计算中。各种实例显示,这种策略不要求记忆任何导出公式即可完成计算,而且运算强度低。公式的统一性以及运算的便捷性极大地简化了终点误差的计算,在教学中能够显著减轻学生的记忆和运算负担,提升学习兴趣,从而能够将学习重点放在滴定体系的分析和处理上。本研究作为当前形势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。     

对络合返滴定过程的理论探讨

推导了络合返滴定曲线方程 ,绘制了络合返滴定曲线和计算了pN突跃。并利用双曲正弦函数的性质 ,提出了内含最大敏锐指数的络合返滴定误差计算公式 ,从而获得了计算络合返滴定pN突跃范围的公式。     

混合酸、多元酸滴定的教学探讨

为解决混合酸(碱)、多元酸(碱)滴定教学中出现的问题,提出一些思路:(1)应在搞清滴定反应及其优先次序前提下,充分利用滴定曲线这一有力工具解决各种问题。(2)教学中,应遵循由易到难、步步深入的原则。在充分讲授单种一元酸滴定的基础上,可按强碱滴混合一元酸、强碱滴多元酸、强碱滴复杂混合酸的顺序安排教学内容。由于规律相似,所以在学生学完强碱滴定酸之后,只需对强酸滴定碱略作介绍即可。另外,提出一种无需复杂计算,仅利用单种一元酸(碱)滴定曲线拼合出复杂酸(碱)体系的近似滴定曲线的新方法,获得的曲线虽不十分精确,但足以给滴定分析可能性判断以及指示剂选择等问题提供有力的支持。     

酸碱滴定曲线的数学分析及其化学意义的探讨

酸碱滴定是化学专业教师及学生最为熟悉的基本实验，滴定曲线反映了整个中和反应的过程，对理解和掌握酸碱滴定十分重要。本文从三个基本假设出发，基于化学平衡思想，应用滴定过程中的电荷守恒与物料守恒关系，在一个参数不变与两个参数变动的初始条件下分别建立了电离度和pH与滴定分数之间的函数关系。通过对函数本身及其导函数进行数学分析，还原了酸碱滴定曲线；尝试利用两个初始条件在数学表达式中的位置及对函数的影响，定量验证了现有教材中对不同数量级初始浓度与不同强度的酸在滴定过程中所表现出差异的定性解释，进而对滴定曲线进行延拓，提出了一种滴定弱酸的可能方式。     

The Art of Titration. From Classical End Points to Modern Differential and Dynamic Analysis

Titration represents the quantitative determination of a chemical change in response to the variation in concentration of a standrad. Information on reaction parameters is usually obtained from an analysis of the shape of the titration curve. In this paper the derivatives of titration functions with respect to concentration variables and with respect to equilibrium parameters are compared with one another. The latter can be determined directly from amplitudes and time constants of the dynamic responses to equilibrium perturbations, brought about by fast alterations of temperature, pressure or electirc field. Three general situations have to be distinguished: 1. If the interaction is very strong (i.e. the complex stability is high: K → ∞), the (average) number of sample praticles can be counted directly by means of their reaction with a calibrated number of standard particles.—2. If, on the contrary, the interaction is weak (i.e. the complex stability is low), the sample will react quantitatively only in the presence of a large excess of standard; the half-way point of which provides a direct measure of the binding constant.—3. Only for moderate interactions can individual curves characteristic of the binding strength be observed. The limiting cases 1 and 2 yield titration curves which reflect only the general class to which the system belongs. The dynamical procedures are fairly insensitive in case 1, which represents the classical end-point situation and is most suitable for quantitative anlaysis, i.e. for a determination of sample concentrations. For case 2, the classical and dynamical techniques yield comparable information: mass-action parameters are obtained from the extrema of the curves, which occur only in the presence of an excess of the standard. In case 3 the dynamical treatment provides a more direct access to the equilibrium constants, and also to the enthalpies or volumes of reaction as well as to the rate constants. The advantage of the dynamic method is due to the fact that in the two derivatives of the titration function d T_i/d ln q and d T_i/d ln p (where q is the titration variable, i.e. the ratio of standard and sample concentration, and p the mass-action parameter, i.e. a reduced binding constant) the terms resulting from a differentiation with respect to p are more closely related to the reaction parameters than those following from a variation of q. The dynamic analysis is generalized for applications to multiple-step titration processes, where it allows for the measurement fo equilibrium and rate parameters of individual steps. A uniform representation utilizing trigonometric functions was chosen which expresses clearly the singualr character of the end-point. The relations are summarized intabular form. They provide in conjunction with the illustrations the basis for a comparative discussion.     

交流示波极谱法连续滴定LaNi4.5Sn0.5合金的分量

研究了用交流示波极谱法连续快速滴定ＬａＮｉ４．５Ｓｎ０．５合金分量的新方法。方法不用指示剂，用色溶液及沉淀不干扰，应用于该合金分量测定获得满意结果。     

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。     

再论滴定分析终点误差的统一计算

终点误差是高等分析化学课程的重要内容。当前分析化学教材多采用浓度定义式,并在此基础上推导出各种计算式。这种"公式化"的策略简单方便,但是没有实现统一计算,记忆负担重,而且难以解决复杂问题。本文从理论上证明了体积定义式完全等价于浓度定义式,从而为通过体积定义式统一计算终点误差提供支持,同时消除对体积定义式的误解。结果表明,体积定义式具有适用范围广、记忆负担轻、以及运算强度低的优点,能够统一四大滴定的终点误差计算。此外,对现行教材中的终点误差计算策略进行了梳理和归纳,剖析了现状,讨论了林邦公式在终点误差统一计算方面的缺陷,为相关研究提供参考。     

微机模拟计算各种类型酸的滴定曲线以及滴定误差

本文对三元酸滴定曲线的精确计算公式加以改进,设计出适合各种类型酸的滴定曲线和滴定误差的模拟计算程序,通过在Rainbow-100机上运行,计算结果与文献报道相符。此法简单、快速,对选择滴定条件,优化实验方法具有很重要的应用价值。     

结合图像讨论酸碱滴定曲线与酸碱平衡曲线的关系

The two distribution fraction curves of a weak acid and its conjugated base are integrated to the pH-δ_A, δ_HA coordinate system. The two curves coincide with each other to form a conjugate distribution fraction curve, which is also an acid-base equilibrium curve. The titration process is discussed with images to understand how a specific equilibrium curve to a titration.     

Numerische Endpunktsbestimmung bei unsymmetrischen potentiometrischen Titrationskurven

Zusammenfassung Die üblichen Interpolationsverfahren zur Endpunktsbestimmung bei potentiometrischen Titrationen geben falsche Resultate bei unsymmetrischen Titrationskurven und versagen vielfach auch bei symmetrischen, wenn der Endpunkt an den Grenzen eines Volumeninkrements liegt. In der vorliegenden Arbeit wird eine einfache Formel abgeleitet, mit deren Hilfe es möglich ist, bei symmetrischen und unsymmetrischen Titrationskurven den Äquivalenzpunkt exakt zu ermitteln. Die Formel enthält zwei, den Grad der Unsymmetrie berücksichtigende Faktoren, deren Zahlenwert sich entweder aus theoretischen Überlegungen ergibt oder einmalig für jeden Titrationstyp zu ermitteln ist. Die Tauglichkeit des Verfahrens wird an mathematisch simulierten Titrationskurven und durch statistische Prüfung an realistischen Titrationsdaten bewiesen.

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Numerical endpoint determination of unsymmetrical potentiometric titration curves

Summary The usual interpolation methods for the calculation of potentiometric endpoints give wrong results for unsymmetrical titration curves and often fail for symmetrical ones, if the endpoint is near the boundaries of a volume increment. In the present paper a simple formula is deduced which permits the calculation of the endpoint exactly for both symmetrical and unsymmetrical titration curves. The formula contains two factors relating to the degree of asymmetry, the numerical values of which are to be determined either theoretically or empirically for each kind of titration. The validity of the method is tested with mathematically simulated titration curves and with statistically evaluated experimental titration data.

     

硼酰化钴中硼的快速测定

硼酰化钴中硼的测定采用EDTA作为钴的络合掩蔽剂,消除了钴对测定硼的影响。同时改用溴甲酚绿-甲基红-酚酞三元混合指示剂作为测定硼的指示剂,使滴定终点灵敏、准确。建立了一种测定硼酰化钴中硼含量的简便、快速的分析方法。     

Ion-selective electrodes in potentiometric titrations; a new method for processing and evaluating titration data

A new method to convert the potential of an ion-selective electrode to concentration or activity in potentiometric titration is proposed. The advantage of this method is that the electrode standard potential and the slope of the calibration curve do not have to be known. Instead two activities on the titration curve have to be estimated e.g. the starting activity before the titration begins and the activity at the end of the titration in the presence of large excess of titrant. This new method is beneficial when the analyte is in a complexed matrix or in a harsh environment which affects the properties of the electrode and the traditional calibration procedure with standard solutions cannot be used. The new method was implemented both in a method of linearization based on the Grans's plot and in determination of the stability constant of a complex and the concentration of the complexing ligand in the sample. The new method gave accurate results when using titrations data from experiments with samples of known composition and with real industrial harsh black liquor sample. A complexometric titration model was also developed.