## Discrimination of the Rationality of Data Calculation in Literature by Basic Principles of Physical Chemistry

Na Liyan, Zhang Liying, Zhi Defu, Zhang Shubiao,

 基金资助: 辽宁省普通高等教育本科教学改革研究项目大连民族大学教育教学改革研究与实践重点项目.  ZD201915

Abstract

This in-class teaching design will facilitate students' understanding of how the basic principles and methods of physical chemistry thermodynamics are used to analyze and correct the literature data calculation process in the field of adsorption. Similarly, it will enhance the accuracy and systematicness of students' knowledge of thermodynamics, as well as promote students' interest and self-confidence in learning by employing such a creative and dynamic classroom teaching model of physical chemistry.

Keywords： Chemical thermodynamics ; Standard equilibrium constant ; Empirical equilibrium constant ; Adsorption ; Langmuir equation

Na Liyan. Discrimination of the Rationality of Data Calculation in Literature by Basic Principles of Physical Chemistry. University Chemistry[J], 2020, 35(9): 159-163 doi:10.3866/PKU.DXHX201908028

### 1.2 明确各热力学函数之间的关系和计算方法

$\Delta_{\mathrm{r}} G_{\mathrm{m}}^{\ominus}=-R T \ln K^{\ominus}$

${{\Delta _{\text{r}}}G_{\text{m}}^ \ominus = {\Delta _{\text{r}}}H_{\text{m}}^ \ominus - T \cdot {\Delta _{\text{r}}}S_{\text{m}}^ \ominus }$

${\ln {K^ \ominus } = - \frac{{{\Delta _{\text{r}}}H_{\text{m}}^ \ominus }}{R} \cdot \frac{1}{T} + \frac{{{\Delta _{\text{r}}}S_{\text{m}}^ \ominus }}{R}}$

### 1.3 吸附热力学知识储备

θ来表示吸附发生时吸附剂B表面被吸附质A覆盖的分数，相应吸附剂表面空白位置的分数为(1 − θ)，平衡时吸附质浓度用cA表示，则吸附平衡时吸附过程可描述为：

$\begin{gathered} {\rm{ A(l) + B(s)}} \Leftrightarrow {\rm{A}} - {\rm{B(s) }} \\ \ \ \ \ \ \ \ \ c{}_{\rm{A}}\ \ \ \ \ \ \ \ 1 - \theta \ \ \ \ \ \ \ \ \theta \ \ \ \ \ \ \ \ \\ \end{gathered}$

${K_{\rm{L}}} = \frac{\theta }{{(1 - \theta ){c_{\rm{A}}}}}$

KL作为经验平衡常数通常是一个有单位的物理量，结合公式(4)可知，由于θ为无量纲， KL单位为[c]−1，即KL数值和单位取决于溶液浓度的表达，当溶液组成标度不同时，KL的数值也不相同。

Langmuir等温吸附方程的常用表达式为：

$\frac{{{c_{\rm{e}}}}}{{{q_{\rm{e}}}}} = \frac{{{c_{\rm{e}}}}}{{{q_{\rm{m}}}}} + \frac{1}{{{K_{\rm{L}}} \cdot {q_{\rm{m}}}}}$

### 2.1 问题描述

Journal of Porous Materials期刊在2016年报道了金属有机配位聚合物MIL-101对苯甲酸(BA)的吸附[11]，吸附过程可用Langmuir等温模型来描述，对Langmuir等温模型的拟合结果及热力学函数计算见表1

 T/K 10−3KL/(L·mg−1) ΔGϴ/(kJ·mol−1) ΔHϴ/(kJ·mol−1) ΔSϴ/(J·mol−1·K−1) 298 6.29 −4.55 −11.27 −22.65 308 5.19 −4.22 318 4.73 −4.11

ΔrGmϴ = −RTlnKL = −298 × 8.314ln6.29 = −4.556 kJ·mol−1

### 2.2 错误原因分析

${K^ \ominus } = \prod {a_B^{{\nu _{\text{B}}}}}$

${K^ \ominus } = \prod {a_B^{{\nu _{\text{B}}}}} = \frac{{{a_{{\text{A - B}}}}}}{{{a_{\text{A}}} \cdot {a_{\text{B}}}}}$

${a_{\rm{B}}} = 1 - \theta$

${a_{{\rm{A - B}}}} = \theta$

$a = \gamma \frac{b}{{{b^ \ominus }}}$

$a = \frac{c}{{{c^ \ominus }}}$

${K^ \ominus } = \frac{\theta }{{(1 - \theta )}} \cdot \frac{{{c^ \ominus }}}{{{c_{\text{A}}}}}$

${K^ \ominus } = {K_{\rm{L}}}{c^ \ominus }$

### 2.3 利用物理化学知识对文献数据进行更正

KL正确转化为Kϴ后，结合公式(1)可获得各个温度下的ΔrGmϴ，以ln Kϴ对1/T作图(见图1)，通过所得直线的斜率及截距可获得ΔrHmϴ及ΔrSmϴ，计算的结果见表2

### 图1

 T/K 10−3KL/(L·mg−1) KL/(L·mol−1) Kϴ ΔGϴ/(kJ·mol−1) ΔHϴ/(kJ·mol−1) ΔSϴ/(J·mol−1·K−1) 298 6.29 768.6 768.6 ‒16.46 ‒11.58 16.29 308 5.19 634.4 634.4 ‒16.52 318 4.73 573.4 573.4 ‒16.81

## 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

Saha, P.; Chowdhury, S. Insight into Adsorption Thermodynamics. INTECH Open Access Publisher: London, 2011, p 349.

Langmuir I. J. Am. Chem. Soc. 1916, 38 (11), 2221.

Lima E. C. ; Hosseini-Bandegharaei A. ; Moreno-Piraján J. C. ; Anastopoulos I. J. Mol. Liq. 2019, 273, 425.

Liu Y. J. Chem. Eng. Data 2009, 54 (7), 1981.

Ghosal P. S. ; Gupta A. K. J. Mol. Liq. 2017, 225, 137.

Behvandi A. ; Safekordi A. A. ; Khorasheh F. J. Porous Mat. 2016, 24 (1), 165.

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