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T > 1000 K)
Published in J. F. Griffiths, J. A. Barnard, Flame and Combustion, 2019
J. F. Griffiths, J. A. Barnard
This calculation illustrates how, at high temperatures, reactions with a high activation energy and high pre-exponential factor tend to be more important than those with a lower activation energy but lower pre-exponential term. Many of the simpler bimolecular reactions have similar pre-exponential factors and differ only in their activation energies. Since the exponential term approaches unity at high temperatures, many of these reactions have similar rate constants at flame temperatures and so are of comparable importance. For this reason, the reactions associated with flames should be represented as reversible processes since, at T > 1500 K say, there may be a sufficiently high reaction rate for both the forward and reverse processes that an equilibrium is established.
Chemically Reacting Flows
Published in Greg F. Naterer, Advanced Heat Transfer, 2018
The reaction rate coefficient, k, normally has a strong dependence on temperature. This dependence is described by the Arrhenius equation, k=Aexp(−EaRT) where Ea and R refer to the activation energy and gas constant, respectively. Also, the pre-exponential factor, A, is a constant that is unique for each chemical reaction and characterizes the frequency of collisions of reactant molecules. The Arrhenius equation indicates that the number of collisions resulting in a reaction per second is equal to the number of collisions (both leading to a reaction and not leading to a reaction) per second, multiplied by the probability that any given collision results in a reaction.
Heat and Mass Transfer and Reaction Kinetics Under Microwaves
Published in Veera Gnaneswar Gude, Microwave-Mediated Biofuel Production, 2017
Activation energy Ea and pre-exponential factor A were determined by using Arrhenius equation [29] analytically for the two temperatures and reaction rate constants at each temperature investigated. The reaction rate constant was calculated from equation [29] as presented in Table 3. A higher value of pre-exponential factor, A indicates a higher reaction rate, as its value is largely associated with the frequency of the vibrating molecules in the reaction mixture. Microwaves increase molecular vibrations due to the oscillatory electric field, resulting in an increased value of A and subsequently the reaction rate. The activation energy of soybean oil is higher than that of the rice bran oil at 50°C because rice bran oil had a higher conversion rate. At a higher temperature (73°C) the conversions were almost the same, with the activation energy playing less of a role as nearly complete conversion was observed for both the oils.
A comprehensive thermo-kinetics devolatilization analysis of waste motor oil: Thermal degradation kinetics, kinetic model, thermodynamic analysis, and ANN
Published in International Journal of Green Energy, 2023
Asmita Mishra, Mayuri Sonowal, Venkata Yasaswy Turlapati, Payal Maiti, B.C. Meikap
The minimal energy essential to commence a chemical reaction is termed as activation energy. The molecules demand a certain amount of kinetic energy or velocity for molecular collision with other molecules for the reaction to proceed. Thus, without collision and sufficient kinetic energy, no reaction will occur. The pre-exponential factor, well known as the frequency factor, depicts the reactant molecules’ collision frequency. The molecular collision is a function of temperature. And the frequency factor is associated with the molecular collision, hence temperature-dependent. The activation energy (Eα, kJ mol−1) and pre-exponential factor (A, s−1) increase with the increase in conversion (α) (Table 4, Figure 3). This increase in Eα and A is a general trend observed in the thermal decomposition of polymers and fossil fuels mainly because of the secondary cracking reaction of intermediate compounds (Vyazovkin et al. 2011). The dependence of E α with α depicts a complex reaction of WMO pyrolysis. Similar trends are observed for algal pyrolysis (Sharara et al. 2014) and chili straw waste (Hu et al. 2021).
Kinetic and thermodynamic analysis of pyrolysis of oily cold rolling mill sludge of steel industry under non-isothermal conditions
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2022
Hailu Wang, Enhui Liu, Rongxuan Zhao, Aimin Ji, Xin Yao, Jinghua Guan, Xuda Wu
The pre-exponential factor (A) refers to the number of collisions per unit time when the reaction occurs in the correct direction, and its physical mean is interpreted by the collision theory. The reaction mechanism function at different heating rates determined above was substituted into Equation (S11) presented in appendix. According to Equation (S11), the relationships G(α) versus were plotted by linear least square fitting method and displayed in Figure 4. The kinetic three factors (Eα, A, f(α)) of OCRMS at all heating rates were presented in Table 3. The A value was acquired based on the average Eα and usually used to explain changes in chemical reactions. If A value less than 109 s−1, the reaction was considered as a simple surface reaction, and otherwise the reaction was a relatively complex reaction (Turmanova et al. 2008). From Table 3, it can be seen that A value was 265.6–871 s−1 at conversion of 0.2–0.9, which denoted decomposition of OCRMS was simple and helpful for the formation of pyrolysis products (Asghar et al. 2021).
The Novel Lixiviants for Maximizing Antimony Extraction from Tetrahedrite-Rich Concentrate: Mechanism and Kinetic Studies
Published in Mineral Processing and Extractive Metallurgy Review, 2022
Sajjad Aghazadeh, Hadi Abdollahi, Mahdi Gharabaghi, Mirsaleh Mirmohammadi
As discussed above, the activation energy of diffusion-controlled process is ranged between 5 and 20 kJ.mol−1, and for chemically controlled process, this values is mostly greater than 40 kJ.mol−1. Therefore, these values of activation energies approve that the reaction rates of glycine-Na2S-NaOH and EDTA-Na2S-NaOH follow diffusion and chemical reaction models, respectively. This implies the fact that antimony dissolution via glycine-Na2S-NaOH solutions will be strongly affected with the change of stirring speed; however, temperature plays a key and essential role during antimony leaching via EDTA-Na2S-NaOH solutions. Pre-exponential factor is also known as the frequency factor, and is associated with the frequency of collisions between reactant molecules at a specified concentration. It is usually defined as temperature independent; however, it is actually dependent on temperature because it is related to molecular collision, which is a function of temperature. As obtained above, for glycine-Na2S-NaOH experiment, pre-exponential factor was obtained 0.0108 min−1 which is relatively low compared to the value of 868.35 min−1 for EDTA-Na2S-NaOH experiment. In other words, the collision possibility of molecules and therefore product formation for EDTA-Na2S-NaOH solution is greater than glycine-Na2S-NaOH solution leading to the higher dissolution of antimony from tetrahedrite mineral.