Chemical Kinetics Reactants

Smoluchowski theory [29, 30] and its modifications fonu the basis of most approaches used to interpret bimolecular rate constants obtained from chemical kinetics experiments in tenus of difhision effects [31]. The Smoluchowski model is based on Brownian motion theory underlying the phenomenological difhision equation in the absence of external forces. In the standard picture, one considers a dilute fluid solution of reactants A and B with [A] [B] and asks for the time evolution of [B] in the vicinity of A, i.e. of the density distribution p(r,t) = [B](rl)/[B] 2i ] r(t))l ] Q ([B] is assumed not to change appreciably during the reaction). The initial distribution and the outer and inner boundary conditions are chosen, respectively, as... 

As reactants transfonn to products in a chemical reaction, reactant bonds are broken and refomied for the products. Different theoretical models are used to describe this process ranging from time-dependent classical or quantum dynamics [1,2], in which the motions of individual atoms are propagated, to models based on the postidates of statistical mechanics [3], The validity of the latter models depends on whether statistical mechanical treatments represent the actual nature of the atomic motions during the chemical reaction. Such a statistical mechanical description has been widely used in imimolecular kinetics [4] and appears to be an accurate model for many reactions. It is particularly instructive to discuss statistical models for unimolecular reactions, since the model may be fomuilated at the elementary microcanonical level and then averaged to obtain the canonical model. 

Every chemical reaction occurs at a finite rate and, therefore, can potentially serve as the basis for a chemical kinetic method of analysis. To be effective, however, the chemical reaction must meet three conditions. First, the rate of the chemical reaction must be fast enough that the analysis can be conducted in a reasonable time, but slow enough that the reaction does not approach its equilibrium position while the reagents are mixing. As a practical limit, reactions reaching equilibrium within 1 s are not easily studied without the aid of specialized equipment allowing for the rapid mixing of reactants. 

A final requirement for a chemical kinetic method of analysis is that it must be possible to monitor the reaction s progress by following the change in concentration for one of the reactants or products as a function of time. Which species is used is not important thus, in a quantitative analysis the rate can be measured by monitoring the analyte, a reagent reacting with the analyte, or a product. For example, the concentration of phosphate can be determined by monitoring its reaction with Mo(VI) to form 12-molybdophosphoric acid (12-MPA). 

The Rate Law The goal of chemical kinetic measurements for weU-stirred mixtures is to vaUdate a particular functional form of the rate law and determine numerical values for one or more rate constants that appear in the rate law. Frequendy, reactant concentrations appear raised to some power. Equation 5 is a rate law, or rate equation, in differential form. 

When a relatively slow catalytic reaction takes place in a stirred solution, the reactants are suppHed to the catalyst from the immediately neighboring solution so readily that virtually no concentration gradients exist. The intrinsic chemical kinetics determines the rate of the reaction. However, when the intrinsic rate of the reaction is very high and/or the transport of the reactant slow, as in a viscous polymer solution, the concentration gradients become significant, and the transport of reactants to the catalyst cannot keep the catalyst suppHed sufficientiy for the rate of the reaction to be that corresponding to the intrinsic chemical kinetics. Assume that the transport of the reactant in solution is described by Fick s law of diffusion with a diffusion coefficient D, and the intrinsic chemical kinetics is of the foUowing form... 

In the former case, the rate is independent of the diffusion coefficient and is determined by the intrinsic chemical kinetics in the latter case, the rate is independent of the rate constant k and depends on the diffusion coefficient the reaction is then diffusion controlled. This is a different kind of mass transport influence than that characteristic of a reactant from a gas to ahquid phase. 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

Chemical engineering inherited the definition for the reaction rate from chemical kinetics. The definition is for closed systems, like batch reactors, in which most of the classical kinetic studies were done. Inside a batch reactor little else besides chemical reaction can change the concentration of reactant A. In a closed system, for the reaction of... 

The two main principles involved in establishing conditions for performing a reaction are chemical kinetics and thermodynamics. Chemical kinetics is the study of rate and mechanism by which one chemical species is converted to another. The rate is the mass in moles of a product produced or reactant consumed per unit time. The mechanism is the sequence of individual chemical reaction whose overall result yields the observed reaction. Thermodynamics is a fundamental of engineering having many applications to chemical reactor design. 

Although time as a physical or philosophical concept is an extremely subtle quantity, in chemical kinetics we adopt a fairly primitive notion of time as a linear fourth dimension (the first three being spatial dimensions) whose initial value (t = 0) can be set by the experimenter (for example, by mixing two reactant solutions) and whose extent is accurately measurable in standard units. The time dimension persists as a variable until the experimenter stops observing the reaction, or until... 

What happens in a chemical reaction during the period between the initial (reactant) state and the final (product) state An answer to this question constitutes a description of the mechanism of the reaction. The study of reaction mechanisms is a major application of chemical kinetics, and most of this book is devoted to this application an introduction is given in Section 1.2. 

NMR spectroscopy finds a number of applications in chemical kinetics. One of these is its application as an analytical tool for slow reactions. In this method the integrated area of a reactant, intermediate, or product is determined intermittently as the reaction progresses. Such determinations are straightforward and will not concern us further, except to note that the use of an internal standard improves the accuracy. With flow mixing, one may examine even more rapid reactions. This is simply overflow application of the stopped-flow method. 

Because reactants are used up in a reaction, the concentration of R decreases as time passes thus, A[R] is negative. The minus sign in Eq. la is included to ensure that the rate is positive, which is the normal convention in chemical kinetics. If we follow the concentration of a product P, we express the rate as... 

In chemical kinetics an empirical relationship is used to relate the overall rate of a process to the concentrations of various reactants. A common form for this expression is... 

Mass transfer and chemical kinetic factors in CVD include the flow of initial substances and gaseous products through the system, the transport of reactants from the gas phase to the substrate surface, the transport of the gaseous products from the substrate surface to the bulk gas, as well as the reactions taking place at the substrate surface . ... 

A reaction at steady state is not in equilibrium. Nor is it a closed system, as it is continuously fed by fresh reactants, which keep the entropy lower than it would be at equilibrium. In this case the deviation from equilibrium is described by the rate of entropy increase, dS/dt, also referred to as entropy production. It can be shown that a reaction at steady state possesses a minimum rate of entropy production, and, when perturbed, it will return to this state, which is dictated by the rate at which reactants are fed to the system [R.A. van Santen and J.W. Niemantsverdriet, Chemical Kinetics and Catalysis (1995), Plenum, New York]. Hence, steady states settle for the smallest deviation from equilibrium possible under the given conditions. Steady state reactions in industry satisfy these conditions and are operated in a regime where linear non-equilibrium thermodynamics holds. Nonlinear non-equilibrium thermodynamics, however, represents a regime where explosions and uncontrolled oscillations may arise. Obviously, industry wants to avoid such situations ... 

As for all chemical kinetic studies, to relate this measured correlation function to the diffusion coefficients and chemical rate constants that characterize the system, it is necessary to specify a specific chemical reaction mechanism. The rate of change of they th chemical reactant can be derived from an equation that couples diffusion and chemical reaction of the form (Elson and Magde, 1974) ... 

Fractional and Other Order Reactions in Constant Volume Systems. In chemical kinetics, one frequently encounters reactions whose orders are not integers. Consider a reaction involving only a single reactant A whose rate expression is of the form... 

A useful tool for dealing with reaction stoichiometry in chemical kinetics is a stoichiometric table. This is a spreadsheet device to account for changes in the amounts of species reacted for a basis amount of a closed system. It is also a systematic method of expressing the moles, or molar concentrations, or (in some cases) partial pressures of reactants and products, for a given reaction (or set of reactions) at any time or position, in terms of initial concentrations and fractional conversion. Its use is illustrated for a simple system in the following example. 

In chemical equilibria, the energy relations between the reactants and the products are governed by thermodynamics without concerning the intermediate states or time. In chemical kinetics, the time variable is introduced and rate of change of concentration of reactants or products with respect to time is followed. The chemical kinetics is thus, concerned with the quantitative determination of rate of chemical reactions and of the factors upon which the rates depend. With the knowledge of effect of various factors, such as concentration, pressure, temperature, medium, effect of catalyst etc., on reaction rate, one can consider an interpretation of the empirical laws in terms of reaction mechanism. Let us first define the terms such as rate, rate constant, order, molecularity etc. before going into detail. 

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