Chemical reaction rate constant temperature dependence

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. 

Taffanel used measurements of the chemical reaction rate at temperatures lower than the temperature of self-ignition, and measurements of the time of self-ignition at a higher temperature, in order to determine the dependence of the heat release rate on the temperature and concentration. Further, Taffanel introduced measurements of the flame propagation velocity. He compared experimental data with the theoretical calculation, carried out under the assumptions of a constant chemical reaction rate in the interval from Tb to Tb — 9 and the absence of chemical reaction at all lower temperatures, also ignoring the Arrhenius dependence of the reaction rate on the temperature and the variation of the concentration. 

The constant K in this equation, as in some other cases discussed above, denotes the initial reaction rate. Its temperature dependence is described by the standard Arrhenius equation with activation energy U. The constant co characterizing the self-acceleration does not depend on temperature but does depend on the composition of the reactive medium in particular, such factors as the chemical structure and concentration of the curing agent, and the concentration of the catalyst and other components influence the value of co. 

The numerical value of each of these constants depends on temperature due to the temperature dependence of the diffusion coefficients, chemical reaction rate constant, and equilibrium constant. 

Arrhenius law (1889) describing the dependence of a chemical reaction rate constant on temperature T is one of the most fundamental laws of chemical kinetics. The law is based on the notion that reacting particles overcome a certain potential barrier with height E , called the activation energy, under the condition that the energy distribution of the particles remains in Boltzmann equilibrium relative to the environment temperature T. When these conditions are satisfied, the Arrhenius law states that the rate constant K is proportional to exp[ —E /Kgr], where Kg is the Boltzmann constant. It follows that, for E > 0, K tends to zero as T 0. 

At present, the model of solid-state chemical reactions suggested in the literature [48-50] has won certain recognition. McKinnon and Hurd [152] and Siebrand and co-workers [153] compare the mechanism of rate constant temperature dependence by the occupation of the highest vibrational sub-levels of the tunneling particle to that of fluctuation preparation of the barrier the latter Siebrand et al. is preferred. [153] particularly emphasize the experimental proof of the linear dependence of the rate constant logarithm on the temperature predicted by this model. The importance of an account for intermolecular vibrations in the problem of heavy-particle tunneling [48-50] is also noted elsewhere [103]. 

As we have seen, in order to determine the form of the experimental rate equation for a chemical reaction it is necessary to carry out experiments at a fixed temperature. This is to avoid any complications due to the rate of reaction changing as a function of temperature. In general, it is the rate constant, / r, for a chemical reaction that is temperature-dependent and this is illustrated in Figure 6.1 for the reaction between iodomethane (CH3I) and ethoxide ion (C2H50 ) in a solution of ethanol... 

The temperature dependence of a diffusion coefficient is sometimes represented by a formula due to Arrhenius that is used for chemical reaction rate constants ... 

By the end of the nineteenth century, the young science of physical chemistry had characterized the dependence of the rate of the chemical transformation on the concentrations of the reactants. This provided the concept of a chemical reaction rate constant k and by 1889 Arrhenius showed that the temperature dependence of the rate constant often took on the simple form k = A p —E /RT), where A is referred to as the pre-exponential factor and as the activation energy. 

Generally, in an equation of a chemical reaction rate, the rate constant often does not change with temperature. There are many biochemical reactions that may be influenced by temperature and the rate constant depends on temperature as well. The effect of temperature on... 

A vital constituent of any chemical process that is going to show oscillations or other bifurcations is that of feedback . Some intermediate or product of the chemistry must be able to influence the rate of earlier steps. This may be a positive catalytic process , where the feedback species enhances the rate, or an inhibition through which the reaction is poisoned. This effect may be chemical, arising from the mechanistic involvement of species such as radicals, or thermal, arising because chemical heat released is not lost perfectly efficiently and the consequent temperature rise influences some reaction rate constants. The latter is relatively familiar most chemists are aware of the strong temperature dependence of rate constants through, e.g. the Arrhenius law,... 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

The cross-section of a fusion reaction, as well as the rate constant of a-decay, decreases exponentially with decreasing kinetic energy of the nuclei relative motion. This strong dependence of the reaction cross-section on the energy leads to an unusual (from the point of view of the classic physical and chemical kinetics) dependence of the reaction rate constant on temperature... 

The units of the rate constants (e.g., seconds, days) will depend on the units of concentration as well as the exponents. Temperature is another important factor that is critical in affecting rate constants. It is well established that temperature increases chemical reaction rates and biological processes—particularly important in estuarine biogeochemical cycles... 

This problem was addressed by Van Deemter [1], who assumed a constant burning rate to obtain a solution in closed form. Later, Johnson et. al. [2] and Olson et al. [3] treated high-temperature, diffusion controlled burning, where the reaction rate depends only weakly on temperature. Both predicted the propagation of a sharply defined burn front, but neither gave any indication of what might happen at lower temperatures, where chemical reaction rate controls. This case was discussed by Ozawa [4], who showed that oxidation is slow and there is no clear burn front. 

The above calculation is quite tedious and gets complicated by the fact that the properties which ultimately control the magnitude of these fourteen unknown quantities further depend on the physical and chemical parameters of the system such as reaction rate constants, initial size distribution of the feed, bed temperature, elutriation constants, heat and mass transfer coefficients, particle growth factors for char and limestone particles, flow rates of solid and gaseous reactants. In a complete analysis of a fluidized bed combustor with sulfur absorption by limestone, the influence of all the above parameters must be evaluated to enable us to optimize the system. In the present report we have limited the scope of our calculations by considering only the initial size of the limestone particles and the reaction rate constant for the sulfation reaction. 

The reaction temperature profile is of particular importance because the reaction rate responds vigorously to temperature changes. Figure 82 plots lines of constant reaction rate illustrating its dependence on temperature and ammonia concentration in the reacting synthesis gas. The line for zero reaction rate corresponds to the temperature-concentration dependence of the chemical equilibrium. From Figure 82 it is apparent that there is a definite temperature at which the rate of reaction reaches a maximum for any given ammonia concentration. Curve (a) represents the temperature-concentration locus of maximum reaction rates. To maintain maximum reaction rate, the temperature must decrease as ammonia concentration increases. 

In order to understand how the constant k depends on temperature, it was assumed that the chemical reactions may take place only when the molecules collide. Following this collision, an intermediate state called an activated complex is formed. The reaction rate will depend on the difference between the energy of the reactants and the energy of the activated complex. This energy E is called activation energy (other notation E ). The reaction rate will also depend on the frequency of collisions. Based on these assumptions it was shown (e.g. [3]) that k has the following expression (Arrhenius reaction rate equation) ... 

Like equilibrium constants, rate constants also depend on environmental factors such as pressure and, especially, temperature. An increase in temperature usually gives rise to an increase in the chemical reaction rate, because molecules are moving faster and colliding more frequently with greater energy. If rate constants are known for two different temperatures, the rate constant for any other temperature can be calculated using the Arrhenius rate law,... 

The rate of an electrochemical reaction p, r (mole/cm catalyst surface area/s), as that of a chemical reaction, depends upon the temperature and activities of reacting species. In addition, in the case of the electrochemical reaction, the electric energy at the electrode-electrolyte interface also strongly influences the rate of the reaction. Thus, the rate of an electrochemical reaction is commonly written as the product of a reaction rate constant and a function of activities of various species, u, ..., involved in the reaction... 

In the chemical reactions considered in the following paragraphs, we take as the basis of calculation a species A. which is one of the reactants that is disappearing as a result of the reaction. The limiting reactant is u.sually chosen as our basis for calculation. The rate of disappearance of A, depends on temperature and composition. For many reactions, it can be written as the product of a reaction rate constant and a function of the concentrations (activities of the various species involved in the reaction ... 

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