Specific reaction rate temperature dependence

The oxidation of nitric oxide, NO, is a reaction involved in smog production. It is moderately rapid at normal temperatures. The oxidation of methane, CHt (household gas), however, occurs so slowly at room temperature that we may say that, for all practical purposes it doesn t react at all. Again, the difference in the reaction rates must depend upon specific characteristics of the reactants, NO and CH,. 

FromEqs. (2.60), (2.61), one can deduce an approximate power-law dependence of specific reaction rates on temperature, Tv, since... 

Temperature is a direct measure of the heat energy available at release (Edwards and Lawrence, 1993). Temperature is the most important factor influencing reaction rate as shown in the Arrhenius equation. In practice an increase in temperature of 10°C will increase a specific reaction rate by two to four times depending on the energy of activation (CCPS, 1995a). 

Thus, the important conclusion is that the specific reaction rate constant k is dependent on temperature alone and is independent of concentration. Actually, when complex molecules are reacting, not every collision has the proper steric orientation for the specific reaction to take place. To include the steric probability, one writes k as... 

A. ARRHENIUS TEMPERATURE DEPENDENCE. The effect of temperature on the specific reaction rate f is usually found to be exponential ... 

There may also be an optimum temperature profile. If the temperature-dependences of the specific reaction rates ki and kj are the same (if their activation energies are equal), the reaction should be run at the highest possible temperature to minimize the batch time. This maximum temperature would be a limit imposed by some constraint maximum working temperature or pressure of the equipment, further undesirable degradation or polymierization of products or reactants at very high temperatures, etc. 

Example 6.2. The Arrhenius temperature dependence of the specific reaction rate fe is a highly nonlinear function that is linearized as follows ... 

The overall reaction rate has a temperature dependence governed by the specific reaction rate k(T) and a concentration dependence that is expressed in terms of several concentration-based properties depending on the suitability for the particular reaction type mole or mass concentration, component vapor partial pressure, component activity, and mole or mass fraction. For example, if the dependence is expressed in terms of molar concentrations for components A(Ca) and B(Cb), the overall reaction rate can be written as... 

The temperature-dependent specific reaction rate k(T) is represented by the Arrhenius equation... 

In general, the temperature of the reactor is established in a number of different ways that depend very strongly on the chemistry and the kinetics. For the simple irreversible reaction studied in this section, in which the only issue is to achieve the desired conversion, it would appear that the reactor temperature should be made as high as possible. This would give the largest specific reaction rate and therefore the smallest reactor size, thus minimizing capital investment. However, as we show below, there are dynamic controllability considerations that must be factored in when selecting reactor temperature. For the more complex reactions considered in later sections (such as reversible, consecutive, or simultaneous reactions), in which issues of both conversion and yield are important, the selection of reactor temperature must consider the production of undesirable products as well as reactant conversion. 

The results shown in Figure 2.18 reveal some interesting effects of reactor temperature. Because the second reaction has a higher activation energy, its specific reaction rate increases more rapidly with temperature than the first reaction. Therefore the production of the undesirable product D is small at temperatures below 320 K, but increases at higher temperatures. The concentration of the desired component C reaches a maximum at about 332 K. This may or may not be the best temperature at which to operate the reactor. It depends on the economic value or the difficulty of disposing of... 

If the desired product is C, reactor temperature should be selected so that the specific reaction rate k of the desired reaction is large compared to the specific reaction rate k2 of the undesired reaction. If the orders of reactions are different in terms of their dependence on the two reactants, the concentrations can also be adjusted to favor the desired reaction ... 

The Swedish chemist Arrhenius first suggested that the temperature dependence of the specific reaction rate k could be correlated by an equation of the type k(T) = k0e E/RT. Therefore,... 

For the various reaction mechanisms used in determining both instantaneous and the overall selectivities, selectivity depends on the energy of activation obtained from the Arrhenius equation [(k = k0exp(-E/RT)], the temperature, initial concentration, and the time of reaction. From the Arrhenius equation, the specific reaction rate k is an integral part of the selectivity expressions. Furthermore, analyzing selectivity expressions may indicate an enhanced effect of the temperature on selectivity. Maximizing the expressions for both instantaneous and overall selectivities may depend on the following ... 

Simultaneous measurements of the rate of change, temperature and composition of the reacting fluid can be reliably carried out only in a reactor where gradients of temperature and/or composition of the fluid phase are absent or vanish in the limit of suitable operating conditions. The determination of specific quantities such as catalytic activity from observations on a reactor system where composition and temperature depend on position in the reactor requires that the distribution of reaction rate, temperature and compositions in the reactor are measured or obtained from a mathematical model, representing the interaction of chemical reaction, mass-transfer and heat-transfer in the reactor. The model and its underlying assumptions should be specified when specific rate parameters are obtained in this way. 

Now let us consider what is the more common situation where both reactants are present in the reactor effluent. The reaction rate in the reactor 1Z depends upon the holdup in the reactor Vj>, the temperature (through the specific reaction rate k), and the concentrations of both reactants (zA and zs) ... 

Results from this study confirms the experimental findings that the reaction of n-bromopropane with OH radicals should be slower than the reaction with Cl atoms. The present results show that pre- and post-reaction complexes are important in the hydrogen abstraction reactions. A detailed study of these rate constants that incorporates the contribution of pre-reactive complexes, the multi-chaimel nature of these reactions, and temperature dependence is necessary. The results also find that there are subtle reaction preferences for the abstraction of site specific hydrogen on n-bromopropane. While knowledge of the dominant products of the... 

Fig. IV.3. Graphical methods of representing the temperature dependence of specific reaction rate constants, (a) For the Arrhenius equation in the form In A = In A — E/RT,...

In discussing reaction-rate constants, we shall focus our attention on a single reaction step, equation (1). For any such process, the temperature T dependence of the specific reaction-rate constant k that appears in equation (4) is given empirically by the Arrhenius expression... 

The reaction rate constant k is not truly a constant, but is merely independent of the concentrations of the sp ies involved in the reaction. The quantity k is also referred to as the specific reaction rate (constant). It is almost always strongly dependent on temperature. In gas-phase reactions, it depends on the catalyst and may be a function of total pressure. In liquid systems it can also be a fiinction of total pressure, and in addition can depend on other parameters, such as ionic strengfli and choice of solvent. These other variables normally exhibit much less effect on the specific reaction rate than does temperature, so for the purposes of the material presented here it will be assumed that kf depends only on ten erature. This assumption is valid in most laboratory and industrial reactions and seems to work quite well. 

The temperature dependence of a specific reaction rate is given by the Arrhenius equation. 

The specific reaction rate, k, will usually follow an Arrhenius temperature dependence and increase exponentially with temperature. However, the adsorption of all species on the smface is exothermic. Consequently, the higher the temperature, the smaller the adsorption equilibrium constant. Therefore, at high temperatures, the denominator of catalytic rate laws approaches 1. For example, for a smface-reaction-limited irreversible isomerization... 

The catalyst consisted of an alumina plate coated with V205/Ti02 mixtures on both sides. The mass specific reaction rate decreased with increasing thickness of the catalyst layer. Intrinsic kinetics was obtained for catalyst layers with a thickness lower than 20 mm. A power law dependence of the main reaction rate on the concentration of NO was found in the absence of water in the feed. Water reduces the activity slightly at temperatures lower than 663 K however, it increases the selectivity with respect to nitrogen. 

Here, k is the specific reaction rate and is a function only of temperature, and Cao is the entering concentration. We note in Equations (2-13) and (2-16) the reactor volume in a function of the reciprocal of For this first-order dependence. a plot of the reciprocal rate of reaction IZ-r ) as a function of conversion yields a curve similar to the one shown in Figure 2-1, where... 

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