大学化学 >> 2023, Vol. 38 >> Issue (2): 243-252.doi: 10.3866/PKU.DXHX202205041

师生笔谈 上一篇    下一篇

酸碱滴定曲线的数学分析及其化学意义的探讨

王旭洋1,2, 孙树喆1,2, 徐晓文1, 邹桂征1, 张斌1,*()   

  1. 1 山东大学化学与化工学院, 济南 250100
    2 山东大学泰山学堂, 济南 250100
  • 收稿日期:2022-05-11 录用日期:2022-06-05 发布日期:2022-06-21
  • 通讯作者: 张斌 E-mail:binzhang68@sdu.edu.cn
  • 基金资助:
    山东大学教育教学改革研究项目(2021Y234);山东大学教育教学改革研究项目(2022Y071);“基础学科拔尖学生培养计划”研究课题(20180212)

Mathematical and Chemical Analyses of Acid-Base Titration Curve

Xuyang Wang1,2, Shuzhe Sun1,2, Xiaowen Xu1, Guizheng Zou1, Bin Zhang1,*()   

  1. 1 School of Chemistry and Chemical Engineering, Shandong University, Jinan 250100, China
    2 Taishan College, Shandong University, Jinan 250100, China
  • Received:2022-05-11 Accepted:2022-06-05 Published:2022-06-21
  • Contact: Bin Zhang E-mail:binzhang68@sdu.edu.cn

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摘要：

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。

关键词: 分析化学, 酸碱滴定, 滴定曲线, 酸碱平衡, 数学模型

Abstract:

Acid-base titration is the most basic experiment in analytical chemistry. The titration curve reflects the whole process of neutralization reaction and is very important to understand acid-base titration. Based on three basic hypotheses, the chemical equilibrium, electroneutrality principle and mass balance, we established mathematical model between ionization degree and pH as well as titration percentage by keeping one parameter unchanged and the other two changed at the initial point. In addition, we recovered the acid-base titration curve by performing mathematical analysis and derivatization of the function. Through the analysis of two initial conditions in mathematical formula and the effects on the function, the quantitative validation on interpretations was introduced for reactions of different concentrations and strength of acids in titrations described in traditional teaching materials. With theoretical expansion of titration curves, we proposed a possible method for weak acid titration.

Key words: Analytical chemistry, Acid-base titration, Titration curve, Acid-base equilibrium, Mathematical model