Chemical kinetics is a key subdiscipline of physical chemistry that studies the reaction rate in every elemental step and corresponding catalytic mechanism. It mainly concludes molecular reaction dynamics, catalytic dynamics, elemental reaction dynamics, macrodynamics, and microdynamics. Such a research field has wide applications in heterogeneous catalysis. Based on the Arrhenius plot fitted by the catalytic conversions below 15% without the mass transfer effect and heat transfer effect, the apparent activation energy echoing with the intrinsically catalytic sites and the pre-exponential factor echoing with the relative number of active sites can be, respectively, derived from the slope and intercept of the Arrhenius plots, which can be used to compare the intrinsically catalytic activity of different catalysts and the relative amount of active sites. Reaction orders of both reactants and products are derived from the reaction rate equation and also fitted by the catalytic conversions below 15% without the mass transfer effect and heat transfer effect. According to the acquired reaction orders, the reaction mechanism can be proposed and even defined in some simple reactions. Therefore, investigations of chemical kinetics are of extreme importance and meaning in heterogeneous catalysis.
- Arrhenius equation
- reaction rate equation
- apparent activation energy
- reaction order
- heterogeneous catalysis
Chemical kinetics, also known as reaction kinetics or chemical reaction kinetics, is a key branch of physical chemistry. Its main task is to investigate the rate during chemical process and to propose the catalytic mechanism of chemical process by a method of research object acting as a nonequilibrium dynamic system whose properties change with time [1, 2]. Through the study of chemical kinetics, it can reasonably guide us to know how to control the reaction conditions and improve the main reaction rate, in order to increase the production of chemical products, and also guide us to learn how to suppress or slow down the reaction rate of side reactions to reduce the consumption of raw materials, reduce the burden of separation operations, and eventually improve the product quality. Chemical kinetics can provide general knowledge on how to avoid explosion of dangerous goods, material corrosion, and aging and deterioration of products. It can also carry out optimal design and control for the industrialization of scientific research results and select the most suitable operating conditions for the existing production. Generally speaking, chemical kinetics is one of the main theoretical bases of chemical reaction engineering, accompanied by the chemical thermodynamics for the improved study of chemical reactions.
Chemical kinetics is of great antiquity with continuous improvements. Date back to the first half of the twentieth century, a great deal of research was devoted to the parameter determination, theoretical analysis, and using these parameters to study the reaction mechanism. However, investigation of the reaction mechanism was extremely difficult at that time, which was dominantly limited by the abilities of probe and analyze reaction intermediates. As time goes on, the study of free radical chain reaction kinetics was generally carried out in the late twentieth century, which brought two development trends for chemical kinetics. One was for the study of elemental reaction dynamics, and the other was to urgently establish a method for detecting active intermediates. Such researches were accompanied by the development of electronics and laser technology. Notably, Herschbach, Lee, and Polanyi, three famous scientists in this field, were awarded the Nobel Prize in chemistry in 1986, which marked the importance of chemical kinetics and indicated the current progress and the achieved level.
Nowadays, chemical kinetics has become an indispensable tool in both chemical discipline development and scientific research. The application in heterogeneous catalysis is a typical example . Heterogeneous catalysis, possessing most of the catalytic reactions in the industry, refers to the catalytic reaction that occurs at the interface of two phases. The heterogeneously catalytic reaction generally occurs on the catalyst surface on which the reactant molecular adsorbs, diffuses, activates, reacts, and desorbs to acquire the final products. Therefore, the surface compositions and structures of catalytic materials are extremely critical in determining the catalytic properties . The adsorption center on catalyst surface is often the center of catalytic activity, which is denoted as active site. The reactant molecule bonds to the active site to form surface adsorption complex, which is denoted as active intermediate species. The existence of active site on catalyst surface can affect the formation and activation of active intermediate species, thus altering the reaction path and consequently the required activation energy [5, 6].
In this chapter, two important kinetic equations, the Arrhenius equation and the reaction rate equation, were comprehensively introduced, accompanied by the applications in heterogeneous catalysis. Through the introduction of the Arrhenius equation, the apparent activation energy (
2. Applications of kinetic equations in heterogeneous catalysis
2.1 The Arrhenius equation and its applications in heterogeneous catalysis
The Arrhenius equation is an empirical formula with chemical reaction rate changing with temperature, which was established by Svante August Arrhenius, a famous scientist in Sweden. This equation can be expressed in different forms containing the differential expression (Eq. (1)), antiderivative form expression (Eq. (2)), derivative form expression (Eq. (3)), and exponential form expression (Eq. (4)), as listed below. Among them,
As shown in the above listed equations, it shows a wide applicability in catalytic reactions, including not only gas-phase reactions but also liquid-phase reactions, as well as most of complex catalytic reactions. However, the precondition of this equation in use is to assume that
This equation is of wide applications in heterogeneous catalysis. Typical in the catalytic oxidation of CO, a representative probe reaction in heterogeneous catalysis [7, 8, 9, 10, 11, 12], the Arrhenius equation is often used as an evaluation standard to compare the intrinsic activity of different catalysts and relative amount of active sites. Bao et al.  reported a crystal-plane-controlled surface restructuring and catalytic performance of Cu2O nanocrystals in CO oxidation with excess O2. As shown in Figure 1, the relationships of catalyst structure and catalytic property were deeply explored. Based on the microscopic and spectroscopic characterization results (detailed descriptions shown in Ref. ), the surface compositions and structures of the restructured CuO/Cu2O catalysts were distinctly identified. Their corresponding catalytic performance in CO oxidation with the plotted Arrhenius equation was also conducted. The derived
Similar results have been extensively reported in many other heterogeneous catalytic reactions, which were used by the calculated
The above-mentioned results are a relatively straightforward and convenient method in the use of the Arrhenius equation. For more in-depth use, the Arrhenius equation can also have been utilized to identify the role and contribution of different active sites of a catalyst nanoparticle to the catalytic reaction based on the calculated
The Arrhenius equation is also suitable for some complex reactions [16, 17, 18], such as the oxidative dehydrogenation of propane (ODHP) to selectively produce propene. You et al.  reported that the NbOx/CeO2-rod catalysts applied for such a reaction and the calculated
2.2 Reaction rate equation and its application in heterogeneous catalysis
Reaction rate equation is an equation of utilizing the concentration or partial pressure of reactants to calculate the reaction rate of chemical reaction. The general expression (Eq. (5)) and differential expression (Eq. (6)) are listed, in which
For a sample heterogeneous catalytic reaction involving a typical MvK mechanism, such as the above-mentioned CO oxidation reaction in Figure 3D , the calculated reaction orders of CO and O2 are 1 and 0, respectively, indicating that the catalytic reaction is only dependent on CO but not on O2. Such dependence suggests the adsorption of CO and O2 onto catalyst surface proceeded step by step, as well as the rate-determining step prior to the O2 adsorption process. Thereby, it can be reasonably proposed that the CO oxidation reaction catalyzed by the facet sites and edge sites of CuO/c-Cu2O catalysts is both proceeding with the MvK mechanism.
But for complex reactions, the reaction mechanism is hardly proposed by the reaction orders [19, 20, 21]. However, the reaction orders are still useful to speculate the important catalytic process, especially in determining the rate-determining step of catalytic reaction [22, 23, 24, 25]. A typical example is in the preparation of formic acid, an important chemical in the H2 storage and other industrial applications, from CO2 hydrogenation. The support plays a key role in determining the catalytic mechanism of CO2 hydrogenation into formic acid, which has been confirmed in our previous report by using two common metal oxide (CeO2 and ZnO) supported Pd catalysts dominantly based on the apparent kinetic analysis and in situ DRIFTS results . The calculated
This conclusion is further proved by Pd/ZrO2 catalyzed CO2 hydrogenation into formate (Figure 6) . Experimental observation results in CO2-TPD profiles (detailed description shown in Ref. ) showed the basicity densities following an order of 2%Pd/ZrO2-T (Tetragonal ZrO2) > 2%Pd/ZrO2-M&T (Mixed ZrO2) ≈ 2%Pd/ZrO2-M (Monoclinic ZrO2), in consistent with the intrinsic activity order. Comparing the reaction orders of H2 and CO2 on 2%Pd/ZrO2-T and 2%Pd/ZrO2-M catalysts, similar H2 reaction orders were observed, while the CO2 reaction orders were higher on 2%Pd/ZrO2-M catalyst than that on 2%Pd/ZrO2-T catalyst. These results clearly demonstrate that the catalytic performance of Pd/ZrO2 catalyst in CO2 hydrogenation into formate is strongly dependent on the surface basicity densities, 2%Pd/ZrO2-T support holds the higher surface basicity densities, and thus, Pd/ZrO2-T catalyst is more active in catalyzing the formate production.
Reaction rate equation is the real reflection of chemical reaction rate. It has been widely used as an important method in investigating the catalytic mechanism. However, several factors, including temperature, chemical reaction, concentration, pressure, order, solvent, light, and catalyst, strongly affect the rate of a chemical reaction. Among them, temperature usually plays a key factor. Generally, the rate of a chemical reaction increases with an increase in reaction temperature because higher kinetic energy can result in more collisions between the reactant molecules. The increase of collision chance will cause the catalytic reaction more likely to happen. The temperature effect on reaction rate can be quantified by the Arrhenius equation. Notably, some reaction rates are negatively affected by the temperature, while some others are independent of temperature. The chemical reaction, concentration, pressure, and order directly determine the reaction rate. In chemical reaction, the complexity of the reaction and the state of the reactants are important. Such as, the reaction of a powder in a solution always proceeds faster than the reaction of a large chunk of a solid. Concentration, pressure, and order are the important parameters of reaction rate equation and thus directly affect the reaction rate. Solvent, light, and catalyst are the external factors that generally do not participate in a reaction but affect the reaction rate. In familiar with these influence factors, it can guide us to better understand and apply the reaction rate equation.
3. Summary and outlook
In summary, this chapter introduced the Arrhenius equation and reaction rate equation, two important equations in chemical kinetics, and their applications in heterogeneous catalysis in detail. By the analysis of some specific reactions in the documents, the Arrhenius equation could be used to calculate the
Nowadays, the development of chemical kinetics is very rapid and the contained fields gradually enlarged with the research mode from basement state turning to excitation state, from small molecule turning to big molecule, and from gas phase turning to condensed phase. Benefiting from the improvement of advanced characterization skills, especially in the development of surface analysis and intermediate tracking skills, the catalytic science has become the frontier field of chemical kinetics. Furthermore, the progress of basic theory method also accelerates the application and development of chemical kinetics in catalytic science. The combination of theory and experiment can help to gain a deep insight into how various elementary reactions occur. The combination of more precise experimental results with more precise theoretical research is a powerful driving force for the continued development of this research field. Practice once again proves that the close combination of theory and experiment is the only way for the development of science.
Thanks to Li-Ping Fan and Yue-Juan Wang who provided the partial writing materials and also commented on the manuscript. This work was financially supported by Shuang-long Scholars Program, Special Foundation of Youth Scholars of Zhejiang Normal University, and Natural Science Foundation of Zhejiang Province (LQ20B030007).
Conflict of interest
The authors declare no conflict of interest.