## Spectrophotometric Method for Kinetics of Reversible Reaction

Huang Xizhe, Liao Zengjun, He Xinyi, Xu Rongtian, Han Dongmei,

 基金资助: 广东省高等教育教学改革项目.  粤教高函（2018）179号-6中山大学教学改革研究项目.  中山大学教务[2018]294号-171

Abstract

Kinetics is an important part of physical chemistry laboratory teaching. In this article, we present a spectrophotometric method for study of the reversible kinetic reaction process of phenolphthalein-NaOH system. The ambient temperature has little influence on the experimental reaction, and the spectrophotometer is the only required instrument for carrying out this experiment. All reagents used are in small amount and low toxic, which is in accordance with the green chemistry concept.

Keywords： Spectrophotometric method ; Reversible reaction ; Dynamics ; Sodium hydroxide ; Phenolphthalein

Huang Xizhe. Spectrophotometric Method for Kinetics of Reversible Reaction. University Chemistry[J], 2021, 36(2): 2008028-0 doi:10.3866/PKU.DXHX202008028

## 1 原理讨论

### 图1

$\frac{\mathrm{d} x}{\mathrm{~d} t}=k\left(a-x_{\mathrm{B} t}\right)\left(b-x_{\mathrm{Bt}}\right)-k^{\prime} x_{\mathrm{B} t}$

ab时，可推出xBt < ab，可得：

$\frac{\mathrm{d} x}{\mathrm{~d} t}=k b\left(a-x_{\mathrm{B} t}\right)-k^{\prime} x_{\mathrm{B} t}=k a b-\left(k b+k^{\prime}\right) x_{\mathrm{B} t}$

$x_{\mathrm{B} t}=\frac{k a b}{k b+k^{\prime}}\left\{1-\exp \left[-\left(k b+k^{\prime}\right) T\right]\right\} \Longrightarrow \exp \left[-\left(k b+k^{\prime}\right) T\right]=1-\frac{k b+k^{\prime}}{k a b} x_{\mathrm{B} t}$

T = ∞时，由于xA∞= axB∞，可得：

$x_{\mathrm{B} \infty}=\frac{k a b}{k b+k^{\prime}} \Longrightarrow x_{\mathrm{A} \infty}=a-x_{\mathrm{B} \infty}=a-\frac{k a b}{k b+k^{\prime}}=\frac{k^{\prime} a}{k b+k^{\prime}}$

$\exp \left[-\left(k b+k^{\prime}\right) T\right]=1-\frac{x_{\mathrm{B} t}}{x_{\mathrm{B} \infty}}=\frac{x_{\mathrm{B} \infty}-x_{\mathrm{B} t}}{x_{\mathrm{B} \infty}}=\frac{a-x_{\mathrm{A} \infty}-\left(a-x_{\mathrm{A} t}\right)}{a-x_{A \infty}}=\frac{x_{\mathrm{A} t}-x_{\mathrm{A} \infty}}{a-x_{\mathrm{A} \infty}}$

$\exp \left[-\left(k b+k^{\prime}\right) T\right]=\frac{A_{t}-A_{\infty}}{A_{0}-A_{\infty}} \Longrightarrow A_{t}=A_{\infty}+\left(A_{0}-A_{\infty}\right) \exp \left[-\left(k b+k^{\prime}\right) T\right]$

$\ln \left(\frac{A_{0}-A_{\infty}}{A_{t}-A_{\infty}}\right)=\left(k b+k^{\prime}\right) T$

Ac结合(4)式可得：

$x_{\mathrm{B} \infty}=a-x_{\mathrm{A} \infty}=a\left(1-\frac{x_{\mathrm{A} \infty}}{a}\right)=a\left(1-\frac{A_{\infty}}{A_{0}}\right)=\frac{k a b}{k b+k^{\prime}} \Longrightarrow \frac{A_{0}-A_{\infty}}{A_{0}}=\frac{k b}{k b+k^{\prime}}$

1、将实验数据用Origin软件作Exponential拟合并结合(6)、(8)式可求得kk’。

2、将实验数据做$\ln \left(\frac{A_{0}-A_{\infty}}{A_{t}-A_{\infty}}\right)$–T图，根据斜率并结合(8)式可求得kk’。

### 2.1 试剂

0.05 mol∙L−1酚酞乙醇溶液、0.5 mol∙L−1 NaOH溶液(经邻苯二甲酸氢钾标定)、去离子水。

### 4.1 改变酚酞浓度获取各动力学曲线

 序号 酚酞乙醇溶液加入量/mL 酚酞浓度/(mmol∙L−1) Origin中Exponential拟合曲线 R2 (1) 0.05 0.05 At = 0.3264 + 1.258exp(−0.040T) 0.9999 (2) 0.10 0.1 At = 0.6252 + 2.479exp(−0.039T) 0.9998 (3) 0.15 0.15 At = 0.7391 + 2.950exp(−0.037T) 0.9974 (4) 0.20 0.20 At = 1.139 + 2.922exp(−0.38T) 0.8523 (5) 0.25 0.25 曲线平滑度不佳，未作Exponential拟合 (6) 0.50 0.5 曲线平滑度不佳，未作Exponential拟合

### 4.2 改变体系温度获取各动力学曲线

 序号 温度/℃ Origin中Exponential拟合曲线 R2 k/(L∙mol−1∙s−1) k’/ms−1 xA∞/(μmol∙L−1) xB∞/(μmol∙L−1) (1) 25 At = 0.6252 + 2.4791exp(−0.039T) 0.9998 0.623 7.85 20.14 79.86 (2) 30 At = 0.7130 + 2.400exp(−0.057T) 0.9997 0.879 13.1 22.90 77.10 (3) 35 At = 0.9470 + 2.443exp(−0.075T) 0.9993 1.08 21.0 27.94 72.06 (4) 40 At = 1.163 + 2.618exp(−0.105T) 0.9972 1.45 32.3 30.76 69.24

## 参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

Nicholson L. J. Chem. Ed. 1989, 66 (9), 725.

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