Temperature dependence of chemical reactions

At home, you take advantage of the temperature dependence of chemical reactions all the time. For example, to keep your food fresh, you store it in a refrigerator. If you have ever left milk or vegetables in the refrigerator for several weeks, however, you have probably observed that refrigeration does not stop food from spoiling. Instead, it decreases the rate of the reactions that cause spoilage. When you want to cook your food quickly, you increase the temperature of the stove. This increases the rate of the reactions that take place as the food cooks. 

To achieve a homogeneous temperature distribution across the library is a challenging problem. Homogeneity is essential due to the temperature dependence of chemical reactions (Arrhenius law). With increasing reactor diameters, temperature gradients increase. Fig. 7.2 (see page 180) shows the temperature distribution... 

It has already been mentioned that the properties of a dielectric sample are a function of many experimentally controlled parameters. In this regard, the main issue is the temperature dependence of the characteristic relaxation times—that is, relaxation kinetics. Historically, the term kinetics was introduced in the field of Chemistry for the temperature dependence of chemical reaction rates. The simplest model, which describes the dependence of reaction rate k on temperature T, is the so-called Arrhenius law [48] ... 

Arrhenius is mainly known for his eqnation describing the temperature dependence of chemical reaction rates ... 

The temperature dependence of chemical reactions can be evaluated by considering the thermodynamic significance of Eq. 4.4, which gives... 

The temperature dependency of the reaction rate of microbial processes and chemical or physicochemical reactions can be described based on the Arrhenius equation ... 

SURFTHERM Coltrin, M. E. and Moffat, H. K. Sandia National Laboratories. SURFTHERM is a Fortran program (surftherm.f) that is used in combination with CHEMKIN (and SURFACE CHEMKIN) to aid in the development and analysis of chemical mechanisms by presenting in tabular form detailed information about the temperature and pressure dependence of chemical reaction rate constants and their reverse rate constants, reaction equilibrium constants, reaction thermochemistry, chemical species thermochemistry, and transport properties. 

This exponential temperature dependenee represents one of the most severe non-linearities in chemical engineering systems. Keep in mind that the apparent temperature dependence of a reaction may not be exponential if the reaction is mass-transfer limited, not chemical-rate limited. If both zones are eneountered in the operation of the reactor, the mathematical model must obviously include both reaction-rate and mass-transfer effeets. 

In computations of very fine spatial and temporal resolution, local chemical equilibrium cannot be assumed and the chemical reactions are described as finite-rate reactions. The temperature dependence of the reaction rate is presented as an Arrhenius reaction ... 

Correlations of the kind that appear in Fig. 3.4 must be tempered, however, with the reminder that Eqs. 3.1 and 3.7 always represent hypotheses about dissolution and precipitation processes. If the rates of these processes are controlled by how quickly aqueous-solution species can approach the surface of the solid phase transport control), then a rate law based solely on an assumed chemical reaction at the surface reaction control) is quite irrelevant. This issue cannot be decided simply by fitting rate data to models like that in Eq. 3.7, but instead must be resolved through direct experimentation (e.g., by comparing the temperature dependence of the reaction with that for aqueous species transport,... 

The key problem in making a small fitted ode model is not the determination of the values of the parameters, but finding a small set of odes with optimal structure. So far, the main approach has been to set up a skeleton mechanism that corresponds to chemical kinetic knowledge about the system. Arrhenius-type expressions are used for the description of the temperature dependence of the reaction rates, and the powers of concentrations in the rate expressions are parameters to be fitted. This way of setting up the small systems of odes is heuristic, but the fitting of parameters has been an automatic process based on the least-squares method. 

Temperature Dependence of Fast Reactions It is to be noted that rate constants for fast (diffusion-controlled) steps are also temperature dependent, since the diffusion coefficient depends on temperature. The usual experimental procedure, suggested by the Arrhenius equation, of plotting In k versus /T will indicate apparent activation energies for diffusion control of approximately 12-15 kJ moP. For fast heterogeneous chemical reactions in which intrinsic chemical and mass transfer rates are of comparable magnitude, care needs to be taken in interpretation of apparent activation energies for the overall process. 

In general, it is concluded that ash/bed material interaction processes are very important and often determine the bed agglomeration and defluidisation tendency. Therefore, the properties of both materials and the nature of their interaction should be considered when predicting these tendencies. This conclusion appeared clearly from the static heating experiments with sand/ash mixtures, which showed dissolution and reaction processes between both materials determining the melt composition. These interaction processes are temperature dependent, resulting in a temperature dependence of chemical and physical properties (e.g. viscosity, wetting ability) of the melt phase. 

We conclude this section on chemical transformations of organic pollutants involving inorganic nucleophiles by a few remarks on the temperature dependence of such reactions, particularly hydrolysis. As can be easily deduced from the Arrhenius equation (see Chapter 1, this volume), for a given chemical reaction, the ratio of the rate constants (and thus of the reaction rates) at two different temperatures 7 [in kelvins (K)] and T2 (K) is given by... 

The relative importance of vibrational and translational energy in promoting chemical reactions is of both theoretical and practical interest. In reactions of diatomic molecules with atoms it has been substantiated both experimentally and theoretically that for endothermic reactions vibrational energy is more important, while for exothermic reactions the opposite is true. For polyatomic molecules, however, there is insufficient experimental and theoretical evidence to draw conclusions. The major work on laser-excited polyatomic reactions has involved the vibrational excitation of ozone in its exothermic reaction with nitric oxide. Although the vibrational energy increased the reaction rate, comparison with statistical models and the temperature dependence of the thermal reaction indicate about equal importance for vibrational and translational energy. On the other hand, a molecular beam study of the temperature dependence of the reaction of potassium with sulfur hexafluoride" has shown a definite preference for vibrational energy of the SF. ... 

Activation energy - In general, the energy that must be added to a system in order for a process to occur, even though the process may already be thermodynamically possible. In chemical kinetics, the activation energy is the height of the potential barrier separating the products and reactants. It determines the temperature dependence of the reaction rate. 

It provides a direct measure of the hazard potential related to the process. It combines thermodynamics and reaction kinetics by being directly proportional to the temperature dependence of the reaction rate represented by the activation temperature E/R and the adiabatic temperature increase. Reactions with a small to moderate hazard potential are characterized by thermal reaction number values around 2, and processes with an extremely high potential have values up to 50 and more. To illustrate the meaning especially of this number, which, if applied correctly, has a similar significance to the adiabatic temperature increase for chemical hazard assessment, the relationship between activation temperature, adiabatic temperature increase and the thermal reaction number B is presented in Fig. 4-4. As a typical process temperature 25°C is assumed. 

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