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## Theoretical Explanation of the Special Temperature Dependence of Rate Constant for Oxidation of Carbon

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Abstract

For oxidation of carbon in different temperature ranges,there is different temperature dependence of rate constant.The temperature dependence can be divided into two sections.The first section is mainly determined by the chemical adsorption of oxygen on the carbon surface,forming oxygencontaining surface complexes.The effect of temperature on adsorption equilibrium of oxygen results in the first increase and then decrease of rate constant with increasing temperature.For the second section,it is mainly influenced by gasification of carbon in carbon dioxide,in which desorption of the carboxyl group is the rate-determining step (r.d.s.).In this paper,a comparison among the formerly established mechanisms for carbon oxidation at high temperature was made and a simplified mechanism was put forward.The rate equation for the second section was deduced based on this new mechanism using r.d.s.approximation and pre-equilibrium approximation treatments.The deduced rate equation is in good accordance with the main experimental facts.Therefore,a satisfactory explanation is given for the unusual behavior of carbon oxidation.

Keywords： Carbon oxidation ; Heterogeneous reaction ; Adsorption equilibrium ; Carbon dioxide ; Reaction mechanism

KONG Ling-Ran, ZHANG Shu-Yong. Theoretical Explanation of the Special Temperature Dependence of Rate Constant for Oxidation of Carbon. University Chemistry[J], 2016, 31(10): 84-88 doi:10.3866/PKU.DXHX201603015

## 1 前言

### 2.1 曲线的第一段

$C\left( s \right)\text{ }+\text{ }{{O}_{2}}\left( g \right)\to C{{O}_{2}}\left( g \right)\text{ }{{\Delta }_{r}}H_{m}^{\ominus }=-393.514\text{ }kJ.\text{mo}{{\text{l}}^{-1}}$

#### 2.2.1 反应的基本情况

$\begin{matrix} C\left( s \right)\text{ }+\text{ }C{{O}_{2}}\left( g \right)\to 2CO\left( g \right) & {{\Delta }_{r}}H_{m}^{\ominus }=172.47\text{ }kJ.mo{{l}^{-1}} \\\end{matrix}$

$\begin{matrix} 2CO\left( g \right)\text{ }+\text{ }{{O}_{2}}\left( g \right)\to 2C{{O}_{2}}\left( g \right) & {{\Delta }_{r}}H_{m}^{\ominus }=-565.99\text{ }kJ.mo{{l}^{-1}} \\\end{matrix}$

#### 2.2.2 反应的机理研究进展

$C{{O}_{2}}\underset{{{k}_{-1}}}{\overset{{{k}_{1}}}{\longleftrightarrow}}\left( C{{O}_{2}} \right)$

$\left( C{{O}_{2}} \right)+C\xrightarrow{{{k}_{2}}}CO+\left( CO \right)$

$\left( CO \right)\underset{{{k}_{-3}}}{\overset{{{k}_{3}}}{\longleftrightarrow}}CO$

1956年，Ergun[8]基于同位素示踪法研究，提出了如下机理：

$C{{O}_{2}}+{{C}_{f}}\underset{{{k}_{-1}}}{\overset{{{k}_{1}}}{\longleftrightarrow}}CO+{{C}_{O}}$

${{C}_{O}}\xrightarrow{{{k}_{2}}}CO+n{{C}_{f}}$

1993年，Chen等[5]提出该反应由4个步骤组成：

$C{{O}_{2}}+{{C}_{f}}\underset{{{k}_{-1}}}{\overset{{{k}_{1}}}{\longleftrightarrow}}CO+CO$

$C{{O}_{2}}+{{C}_{f}}\left( O \right)\underset{{{k}_{-2}}}{\overset{{{k}_{2}}}{\longleftrightarrow}}C\left( O \right){{C}_{f}}\left( O \right)+CO$

$C\left( O \right){{C}_{f}}\left( O \right)\xrightarrow{{{k}_{3}}}CO+{{C}_{f}}\left( O \right)$

${{C}_{f}}\left( O \right)\xrightarrow{{{k}_{4}}}CO+{{C}_{f}}$

#### 2.2.3 反应动力学特征讨论

$-\overset{|}{\mathop{\underset{\left( A \right)}{\mathop{C}}\,}}\,+C{{O}_{2}}\underset{{{k}_{-1}}}{\overset{{{k}_{1}}}{\longleftrightarrow}}-\overset{|}{\mathop{\underset{\left( B \right)}{\mathop{C}}\,}}\,-CO-\overset{|}{\mathop{\underset{\left( C \right)}{\mathop{C}}\,}}\,\left( O \right)$

$-\overset{|}{\mathop{\underset{\left( B \right)}{\mathop{C}}\,}}\,-CO\xrightarrow{{{k}_{2}}}-\overset{|}{\mathop{\underset{{}}{\mathop{C}}\,}}\,+CO$

$-\overset{{}}{\mathop{\underset{\left( B \right)}{\mathop{C}}\,}}\,-\overset{|}{\mathop{\underset{{}}{\mathop{C}}\,}}\,\left( O \right)\xrightarrow{{{k}_{3}}}-\overset{|}{\mathop{\underset{{}}{\mathop{C}}\,}}\,+CO$

$r\text{ }=\text{ }{{k}_{3}}\left[ \left( C \right) \right]$

$K=\frac{{{k}_{1}}}{{{k}_{-1}}}=\frac{\left[ \left( B \right) \right]\left[ \left( C \right) \right]}{\left[ \left( A \right) \right]\left[ C{{O}_{2}} \right]}$

$r=\text{ }{{k}_{3}}\frac{{{k}_{1}}}{{{k}_{-1}}}\frac{\left[ \left( A \right) \right]\left[ C{{O}_{2}} \right]}{\left[ \left( B \right) \right]}$

## 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

Chen, S. G.; Yang, R. T.; Kapteijn, F.; Moulijn, J. A. Ind. Eng. Chem. Res. 1993, 32(11), 2835.

von Fredersdorff, C. G. Ins. Gas Techn. Res. Bull. 1955, 19, 75.

Ergun, S. J. Phys. Chem. 1956, 60(4), 480.

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