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Chemical Kinetics
Published in Himadri Roy Ghatak, Reaction Engineering Principles, 2018
Referring to Section 3.2, the reaction rate depends on the probability of the reactant molecules converting into products. In an elementary reaction, the reactant molecules must pass through transition states with one or more chemical bonds at excited energy states. Consequently, the molecules with higher energy will have a higher probability of acquiring the transition state and converting into products. Since the average energy of molecules depends on temperature, it will be natural to expect the reaction rate to also depend on temperature. In Equation 3.19, the specific reaction rate constant “k– is constant only if the temperature of the reacting system does not change. The specific reaction rate constant has different values at different temperatures. The higher the temperature, the higher is the specific reaction rate constant. The dependence of a specific reaction rate constant with temperature is best represented by Arrhenius’ equation (Arrhenius, 1889; Logan, 1982). It is an empirical equation that fits the experimental observation excellently over a wide range of temperature for almost all reactions. Mathematically, by this equation the specific reaction rate constant for a reaction is expressed as
A
Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[atomic, computational, quantum] Expression of the temperature dependence of the reaction rate k of a chemical reaction developed by Svante August Arrhenius (1859–1927), in 1889, based on the work by van’t Hoff: k=Ane−(Ea/R)1/T, with Ea the reaction energy, R the universal gas constant, T the absolute temperature, and An a unit equalizer constant, with n the order of the reaction. The reaction rate constant depends on the order of the reaction in value and units, for a first order reaction the units are s−1, which can be interpreted as the number of collisions leading to a chemical reactions per second. In diffusion limited reactions the unit constant An will play a more significant role than under standard pressure and temperature kinetic reactions. In general physics and mathematics expressions, the term “Arrhenius equation” refers to an exponential decay with a straightforward exponential coefficient.
Electrochemistry of Fuel Cells
Published in Xianguo Li, Principles of Fuel Cells, 2005
where B’s are the pre-exponential factor, Δgf, r is the molar Gibbs function of activation for the oxidation (or ionization) reaction for the present simple charge transfer reaction given in Equation (3.37), and similarly Δgb, r is the molar Gibbs function of activation for the reduction reaction (or discharge of ions). In general, the temperature dependence of the reaction rate constant is primarily due to the exponential term, and the linear dependence in the pre-exponential term is very weak in comparison and hence may be neglected, then the resulting expression becomes similar to the empirical Arrhenius equation for the reaction rate constant of a homogeneous chemical reaction.
Mechanism and Kinetic Study on Elemental Mercury Oxidation in Flue Gas by Ozone Injection
Published in Ozone: Science & Engineering, 2018
Zhengcheng Wen, Zhihua Wang, Yuan Li, Kefa Cen
When the temperature is 373K and 423K, the experimental results are in good agreement with the results of the kinetic simulation. When the temperature is 473K and 523K, the oxidation efficiency of Hg0 in kinetic simulation is higher than that in experiments. The cause of this deviation may be the kinetic parameters of R1 reaction: Hg+NO3→HgO+NO2. Due to the lack of literature data, the reaction kinetic parameters of R1 were obtained from the preceding quantum chemistry calculation. But for transition metal elements Hg, high accuracy basis sets such as 6-31G(d) and 6-311G(d,p) are not suitable. And thus, SDD, which is the basis function of effective core potential (ECP) (Fuentealba et al. 1989; Wedig et al. 1986), is employed for quantum chemistry calculations. And so, the calculation results have some deviation. Furthermore, the lower limit values are selected as the results in our quantum chemistry calculations, which lead to the lower calculated activation energy. Therefore, the higher the temperature, the higher the reaction rate constant.
Statistical optimization and kinetic study on biodiesel production from a potential non-edible bio-oil of wild radish
Published in Chemical Engineering Communications, 2019
Chokkalingam Senthilkumar, Chandrasekaran Krishnaraj, Pandian Sivakumar, Anirbid Sircar
Figure 3 represents the experimental results obtained for biodiesel conversion at different temperatures (40 to 60 °C) with respect to time. The other process parameters like methanol to oil molar ratio (9:1) and catalyst concentration (1.0 wt%) were kept constant as obtained from optimization results. The ME conversion percentage reaches maximum at 50 °C which is optimum to ME yield during optimization and this ensures that the reaction attains maximum conversion. Kinetic rate constant and root mean square value (R2) are determined and tabulated in Table. 7. The reaction rate constant shows that the rate of the reaction increases with respect to temperature proving that the reaction is sensitive to temperature.
Preparation and photocatalytic kinetic study of ternary composite photocatalyst 12-phosphotungstic acid/PANI/SnO2
Published in Journal of Coordination Chemistry, 2019
50 mL of 10 mg L−1 gentian violet solution was adjusted to pH 7, adding catalysts 100 mg L−1, 200 mg L−1, 300 mg L−1, 400 mg L−1, 500 mg L−1 and 600 mg L−1. Figure 9(a) shows the amount of catalyst added will directly affect the photocatalytic degradation reaction rate; too much or too little catalyst is not conducive to the photocatalytic degradation reaction. When the catalyst is 300 mg L−1, the decolorization of gentian violet solution is the highest, reaching 96.32%. Figure 9(b) shows the first-order reaction kinetics of catalyst degradation on gentian violet. Table 4 shows the linear relationship between the amount of catalyst and the degradation of gentian violet, and the value of R is close to 1. The reaction rate constants k are 0.00563 min−1, 0.00616 min−1, 0.00875 min−1, 0.00784 min−1, 0.00705 min−1 and 0.00508 min−1. When the catalyst is added in an amount less than 300 mg L−1, the reaction rate constant increases as the amount of the composite catalyst added increases. When the amount of the catalyst added is more than 300 mg L−1, the reaction rate decreases as the amount of the composite catalyst added increases. This is mainly because the composite catalyst is added less and the photon energy is not fully utilized [12]. Within a certain range, increasing the amount of the composite catalyst can produce more activating substances, and the excessive amount of the composite catalyst leads to a light shielding effect between the catalysts and the color of the catalyst itself affects the absorption of light, which reduces its photocatalytic degradation efficiency and activity.