Rates overall reaction rate

In the reaction kinetics context, the tenn nonlinearity refers to the dependence of the (overall) reaction rate on the concentrations of the reacting species. Quite generally, the rate of a (simple or complex) reaction can be defined in temis of the rate of change of concentration of a reactant or product species. The variation of this rate with the extent of reaction then gives a rate-extent plot. Examples are shown in figure A3.14.1. In... 

The simplest manifestation of nonlinear kinetics is the clock reaction—a reaction exliibiting an identifiable mduction period , during which the overall reaction rate (the rate of removal of reactants or production of final products) may be practically indistinguishable from zero, followed by a comparatively sharp reaction event during which reactants are converted more or less directly to the final products. A schematic evolution of the reactant, product and intenuediate species concentrations and of the reaction rate is represented in figure A3.14.2. Two typical mechanisms may operate to produce clock behaviour. 

Figure A3.14.2. Characteristic features of a clock reaction, illustrated for the Landolt reaction, showing (a) variation of product concentration witii induction period followed by sharp reaction event (b) variation of overall reaction rate witli course of reaction.

In these early reactions the reactivities of the individual phases are important in determining the overall reaction rate. However, as the cement particles become more densely coated with reaction products, diffusion of water and ions in solution becomes increasingly impeded. The reactions then become diffusion-controUed at some time depending on various factors such as temperature and water—cement ratio. After about 1 or 2 days, ie, at ca 40% of complete reaction, the remaining unhydrated cement phases react more nearly uniformly. 

Cracking temperatures are somewhat less than those observed with thermal pyrolysis. Most of these catalysts affect the initiation of pyrolysis reactions and increase the overall reaction rate of feed decomposition (85). AppHcabiUty of this process to ethane cracking is questionable since equiUbrium of ethane to ethylene and hydrogen is not altered by a catalyst, and hence selectivity to olefins at lower catalyst temperatures may be inferior to that of conventional thermal cracking. SuitabiUty of this process for heavy feeds like condensates and gas oils has yet to be demonstrated. 

Similar expressions have been found to be applicable to the steam reforming of higher hydrocarbons. For example, it has been shown that if it is assumed that ethane, CaHg is adsorbed on two neighbouring sites, the overall reaction rate can be expressed by the equation... 

The order of reactivity of the hydrogen halides is HI > HBr > HCl, and reactions of simple alkenes with HCl are quite slow. The studies that have been applied to determining mechanistic details of hydrogen halide addition to alkenes have focused on the kinetics and stereochemistry of the reaction and on the effect of added nucleophiles. The kinetic studies often reveal complex rate expressions which demonstrate that more than one process contributes to the overall reaction rate. For addition of hydrogen bromide or Itydrogen... 

All catalytic reactions involve chemical combination of reacting species with the catalyst to form some type of inteniiediate complex, the nature of which is the subject of abundant research in catalysis. The overall reaction rate is often determined by the rate at which these complexes are formed and decomposed. The most widely-used nonlinear kinetic equation that describes... 

Overall reaction rates for dual substrates are the sum of the rates of dissociation of two substrates. 

Measurements of overall reaction rates (of product formation or of reactant consumption) do not necessarily provide sufficient information to describe completely and unambiguously the kinetics of the constituent steps of a composite rate process. A nucleation and growth reaction, for example, is composed of the interlinked but distinct and different changes which lead to the initial generation and to the subsequent advance of the reaction interface. Quantitative kinetic analysis of yield—time data does not always lead to a unique reaction model but, in favourable systems, the rate parameters, considered with reference to quantitative microscopic measurements, can be identified with specific nucleation and growth steps. Microscopic examinations provide positive evidence for interpretation of shapes of fractional decomposition (a)—time curves. In reactions of solids, it is often convenient to consider separately the geometry of interface development and the chemical changes which occur within that zone of locally enhanced reactivity. 

The (en) compound developed nuclei which advanced rapidly across all surfaces of the reactant crystals and thereafter penetrated the bulk more slowly. Kinetic data fitted the contracting volume equation [eqn. (7), n = 3] and values of E (67—84 kJ mole"1) varied somewhat with the particle size of the reactant and the prevailing atmosphere. Nucleus formation in the (pn) compound was largely confined to the (100) surfaces of reactant crystallites and interface advance proceeded as a contracting area process [eqn. (7), n = 2], It was concluded that layers of packed propene groups within the structure were not penetrated by water molecules and the overall reaction rate was controlled by the diffusion of H20 to (100) surfaces. 

Obviously, if the step in which T reacts is rate-controlling, then the overall reaction rate depends in some way upon the concentration and identity of T. This dependence may take the form of a direct proportionality to [T], but more complex forms have been given in the preceding paragraphs. If the reaction of an intermediate with a trap is faster than the step generating the intermediate, on the other hand, then the rate may not depend on either the concentration or the identity of the trap. If, for example, an organometal (RM) undergoes a slow, homolytic decomposition,... 

LAB of outstanding stable quality. The overall reaction rate will be gas phase-controlled. 

When an irreversible chemical reaction is carried out in a packed or fluidised bed composed of catalyst particles, the overall reaction rate, is influenced by ... 

This is a transitional region in which reaction kinetics and mass transfer resistance both affect the overall reaction rate. 

On the basis of the examples given above, it is reasonable to suggest that the underlying principles for optimization of the overall reaction rate with respect to the choice of metal ion are similar. That is, there are basically three states along the reaction pathway which determine the most suitable choice of metal ion. These are (1) the reactant state with bound metal and substrate before the proton transfer step, (2) the intermediately created free OH nucleophile and, (3) the subsequent transition state associated with... 

The diffusion of the condensate in the polymer does not seem to be the Imitating process but it does play a part in the overall reaction rate. 

Changing the equilibrium conditions by having condensate in the sample due to water in the carrier gas or the diffusion limitation of the condensate in larger particles changes the reaction speed. Although the kinetics of the reaction and the diffusion of the condensate are not the process Imitating steps they have an effect on the overall reaction rate as described above. 

Example 2.1 Determine the overall reaction rate for each component in the following set of reactions ... 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

Solution Assume the reverse reaction has the form =kr c Setting the overall reaction rate equal to zero at the equilibrium point gives a second... 

All these steps can influence the overall reaction rate. The reactor models of Chapter 9 are used to predict the bulk, gas-phase concentrations of reactants and products at point (r, z) in the reactor. They directly model only Steps 1 and 9, and the effects of Steps 2 through 8 are lumped into the pseudohomoge-neous rate expression, a, b,. ..), where a,b,. .. are the bulk, gas-phase concentrations. The overall reaction mechanism is complex, and the rate expression is necessarily empirical. Heterogeneous catalysis remains an experimental science. The techniques of this chapter are useful to interpret experimental results. Their predictive value is limited. 

The concentration of gas over the active catalyst surface at location / in a pore is ai [). The pore diffusion model of Section 10.4.1 linked concentrations within the pore to the concentration at the pore mouth, a. The film resistance between the external surface of the catalyst (i.e., at the mouths of the pore) and the concentration in the bulk gas phase is frequently small. Thus, a, and the effectiveness factor depends only on diffusion within the particle. However, situations exist where the film resistance also makes a contribution to rj so that Steps 2 and 8 must be considered. This contribution can be determined using the principle of equal rates i.e., the overall reaction rate equals the rate of mass transfer across the stagnant film at the external surface of the particle. Assume A is consumed by a first-order reaction. The results of the previous section give the overall reaction rate as a function of the concentration at the external surface, a. ... 

The theory of radiation-induced grafting has received extensive treatment [21,131,132]. The typical steps involved in free-radical polymerization are also applicable to graft polymerization including initiation, propagation, and chain transfer [133]. However, the complicating role of diffusion prevents any simple correlation of individual rate constants to the overall reaction rates. Changes in temperamre, for example, increase the rate of monomer diffusion and monomer... 

---