Chemical Connections Arrhenius equation, reaction rate

After the introduction of rate of reaction we have seen how a chemical reaction depends of other things than stoichiometry. It is thereby reasonable to assume that the temperature also plays a significant role for the cause and velocity of reaction. This combination is described by the Arrhenius-equation named after the Swedish chemist Svante Arrhenius due to his work on reaction kinetics in the 1880 ies. The Arrhenius-equation gives the connection between temperature, reaction constant and the concentration of reactant in the following manner ... 

The phenomenon of compensation is not unique to heterogeneous catalysis it is also seen in homogeneous catalysts, in organic reactions where the solvent is varied and in numerous physical processes such as solid-state diffusion, semiconduction (where it is known as the Meyer-Neldel Rule), and thermionic emission (governed by Richardson s equation ). Indeed it appears that kinetic parameters of any activated process, physical or chemical, are quite liable to exhibit compensation it even applies to the mortality rates of bacteria, as these also obey the Arrhenius equation. It connects with parallel effects in thermodynamics, where entropy and enthalpy terms describing the temperature dependence of equilibrium constants also show compensation. This brings us the area of linear free-energy relationships (LFER), discussion of which is fully covered in the literature, but which need not detain us now. 

The Arrhenius equation predicts that the rate of reaction increases exponentially with an increase in temperature. Bretherick noted that an increase of 10 °C in reaction temperature can increase the reaction rate by a factor of 2. (See Chemical Connection 5.3.10.1 in Section 5.3.10 for more discussion of the Arrhenius equation and reaction rates.) Thus, it is critical that temperature be adequately controlled to prevent the reaction from accelerating to a dangerous rate. Be prepared to provide adequate control of the temperature—you will need to measure the temperature and have cooling means readily available. If you are unable to control the temperature, an explosion may occur. You should try to avoid systems that hold in heat—adiabatic systems. You can often control a reaction by controlling the rate of addition of a reagent. You should consider the best way to provide adequate mixing for the reaction. 

Then it was possible to collect reaction rates in form of simple functions of a single parameters with Arrhenius formulas, which are quite common in literature and databases of chemical kinetics and reaction rates. The use of electron temperature as a parameter does not prevent the capability to make comparison with other existing models, since it could be related, in a one to one correspondence, with experimental informations on the streamer electric field. Indeed electron temperature is trivially connected with the mean electron energy, which is determined by the local electric field in the Boltzmann equation (Raizer, 1991). This is sufficient to make straightforward a direct comparison between this simulation and other existing ones or experimental data. In the following we considered as reference an electron temperature value of 4 eV (Kulikovsky, 1998). 

The kinetic parameters depend on temperature as do the rates of chemical reactions. This dependence is described by the Arrhenius equation, which already has been introduced as Eq. (16) in connection with the term activation energy . 

Figure 1.3 illustrates the concept on which this book is based. It shows the relation between macroscopic kinetics, as used by the chemical engineer, and microscopic atomic information, as needed or provided by the chemist. The connection is provided by the rate equation (1.1). Rates of catalytic reactions can be predicted from the reactivity of intermediates absorbed on the surface of the catalyst, using transition-state theory to calculate the parameters in the Arrhenius expression for the reaction-rate constant. This is the philosophy behind this book. 

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