Arrhenius expressions

Temperature Dependence of Rate Constants a. Arrhenius Expression 

The temperature dependence of many rate constants can be fit over a relatively narrow temperature range by the exponential Arrhenius equation 

To a first approximation over the relatively small temperature range encountered in the troposphere, A is found to be independent of temperature for many reactions, so that a plot of In k versus T l gives a straight line of slope —E.d/R and intercept equal to In A. However, the Arrhenius expression for the temperature dependence of the rate constant is empirically based. As the temperature range over which experiments could be carried out was extended, nonlinear Arrhenius plots of In k against T 1 were observed for 

For many reactions, the temperature dependence of A is small (e.g., varies with Tl/2) compared to the exponential term so that Eq. (F) is a good approximation, at least over a limited temperature range. For some reactions encountered in tropospheric chemistry, however, this is not the case. For example, for reactions in which the activation energy is small or zero, the temperature dependence of A can become significant. As a result, the Arrhenius expression (F) is not appropriate to describe the temperature dependence, and the form 

While most reactions with which we deal in atmospheric chemistry increase in rate as the temperature increases, there are several notable exceptions. The first is the case of termolecular reactions, which generally slow down as the temperature increases. This can be rationalized qualitatively on the basis that the lifetime of the excited bimolecular complex formed by two of the reactants with respect to decomposition back to reactants decreases as the temperature increases, so that the probability of the excited complex being stabilized by a collision with a third body falls with increasing temperature. 

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Fast transient studies are largely focused on elementary kinetic processes in atoms and molecules, i.e., on unimolecular and bimolecular reactions with first and second order kinetics, respectively (although confonnational heterogeneity in macromolecules may lead to the observation of more complicated unimolecular kinetics). Examples of fast thennally activated unimolecular processes include dissociation reactions in molecules as simple as diatomics, and isomerization and tautomerization reactions in polyatomic molecules. A very rough estimate of the minimum time scale required for an elementary unimolecular reaction may be obtained from the Arrhenius expression for the reaction rate constant, k = A. The quantity /cg T//i from transition state theory provides... 

Each k is given by an Arrhenius expression, k = A exp(—F/i T), and the fraction of the tightly bound component is a parameter. For the high temperature results in Figure 6, some charring of toluene was observed at the highest wall temperature (790°C). The fraction of toluene remaining in the bed was deterrnined from gas-phase total hydrocarbon, O2, and CO2 measurements. 

The classical experiment tracks the off-gas composition as a function of temperature at fixed residence time and oxidant level. Treating feed disappearance as first order, the pre-exponential factor and activation energy, E, in the Arrhenius expression (eq. 35) can be obtained. These studies tend to confirm large activation energies typical of the bond mpture mechanism assumed earlier. However, an accelerating effect of the oxidant is also evident in some results, so that the thermal mpture mechanism probably overestimates the time requirement by as much as several orders of magnitude (39). Measurements at several levels of oxidant concentration are useful for determining how important it is to maintain spatial uniformity of oxidant concentration in the incinerator. 

AH the models described above indicate the importance of system temperature on growth rate. Dependencies of growth kinetics on temperature are often expressed in terms of an Arrhenius expression ... 

The model that best describes the mechanism is usually very complicated. For dynamic studies that require much more computation (and on a more limited domain) a simplified model may give enough information as long as the formalities of the Arrhenius expression and power law kinetics are incorporated. To study the dynamic behavior of the ethylene oxide reactor. 

Temperature of the system has a pronouneed effeet on the growth rate. The relation between growth kineties and temperature is often given by Arrhenius expression... 

Experimentalists often analyse their data in terms of an Arrhenius expression instead of the TST expression eq. (12.2) by plotting ln(k) against 7 ... 

Expression (109) appears to be similar to the Arrhenius expression, but there is an important difference. In the Arrhenius equation the temperature dependence is in the exponential only, whereas in collision theory we find a dependence in the pre-exponential factor. We shall see later that transition state theory predicts even stronger dependences on T. 

The temperature coefficient of the rate of a polymerization induced by a thermally decomposing initiator must depend according to Eq. (12) both on the temperature coefficient of kp/k] and on that of kd. Upon substituting Arrhenius expressions for each of the rate constants... 

The rate model contains four adjustable parameters, as the rate constant k and a term in the denominator, Xad, are written using the Arrhenius expression and so require a preexponential term and an activation energy. The equilibrium constant can be calculated from thermodynamic data. The constants depend on the catalyst employed, but some, such as the activation energy, are about the same for many commercial catalysts. Equation (57) is a steady-state model the low velocity of temperature fronts moving through catalyst beds often justifies its use for periodic flow reversal. 

The magnitude of Eacl for a reaction may be calculated from values of k, the rate constant (cf p. 39), determined experimentally at two different temperatures, Tj and T2, using the Arrhenius expression which relates k to T, the absolute temperature ... 

Oxidation rate constant k, for gas-phase second order rate constants, koH for reaction with OH radical, kN03 with N03 radical and ko3 with 03 or as indicated, data at other temperatures and/or the Arrhenius expression see reference ... 

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