Converting Reactants to Products

Step 1. Reactants enter a packed catalytic tubular reactor, and they must diffuse from the bulk fluid phase to the external surface of the solid catalyst. If external mass transfer limitations provide the dominant resistance in this sequence of diffusion, adsorption, and chemical reaction, then diffusion from the bulk fluid phase to the external surface of the catalyst is the slowest step in the overall process. Since rates of interphase mass transfer are expressed as a product of a mass transfer coefficient and a concentration driving force, the apparent rate at which reactants are converted to products follows a first-order process even though the true kinetics may not be described by a first-order rate expression. Hence, diffusion acts as an intruder and falsifies the true kinetics. The chemical kineticist seeks to minimize external and internal diffusional limitations in catalytic pellets and to extract kinetic information that is not camouflaged by rates of mass transfer. The reactor design engineer must identify the rate-limiting step that governs the reactant product conversion rate. 

Step 2. Reactants must diffuse into the central core of the porous catalyst. A quantitative description of this diffusion process requires knowledge of the tortuosity factor of the pellet, which accounts for the tortuous pathway that strongly influences diffusion. The reactor design engineer seeks numerical values for the inflapellet Damkohler number and the effectiveness factor to characterize intrapellet diffusion in an isolated catalytic pellet. 

Step 3. Reactant gas molecules within the internal pores of the pellet adsorb on catalytically active surface sites. This chemical adsorption process is called chemisorption because the interatomic forces of attraction between adsorbed gas molecules and the active sites are similar to the strength of chemical bonds. 

Step 4. Adsorbed gas molecules or fragments form an intermediate complex on active surface sites. This short-lived intermediate, called the transition state, represents the point of no return for reactants along the reaction pathway. 

Step 5. The intermediate complex forms adsorbed products on catalytically active sites. 

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Either of the mechanisms of recrossing leads to inefficiency in converting reactant to product. How does this affect the reaction rate constant Eewer activated reactants fonn... 

Also, the rates of the propagation steps are equal to one another (see Problem 8-4). This observation is no surprise The rates of all the steps are the same in any ordinary reaction sequence to which the steady-state approximation applies, since each is governed by the same rate-controlling step. The form of the rate law for chain reactions is greatly influenced by the initiation and termination reactions. But the chemistry that converts reactant to product, and is presumably the matter of greatest importance, resides in the propagation reactions. Sensitivity to trace impurities, deliberate or adventitious, is one signal that a chain mechanism is operative. 

A mathematical statement of the dependence of the rate on the concentration of reactants is called the rate equation, for example, rate = k (A)(B), where k = the rate constant and (A) and (B) represent the concentrations of reactants. From the rate equation one can frequently extract information on the mechanism (i.e., the exact path followed to convert reactants to products). 

Chain reactions may be considered to involve three phases. First, chain initiation must occur, which for methane chlorination is activation and conversion of chlorine molecules to chlorine atoms by light. Second, chain-propagation steps convert reactants to products with no net consumption of atoms or radicals. The propagation reactions occur in competition with chainterminating steps, which result in destruction of atoms or radicals. Putting everything together, we can write ... 

Thus, only 7 collisions in 100 trillion are sufficiently energetic to convert reactants to products. 

The reaction quotient Qc is useful because it lets us predict the direction of reaction by comparing the values of Qc and Kc. If Qc is less than Kc, movement toward equilibrium increases Qc by converting reactants to products (that is, net reaction proceeds from left to right). If Qc is greater than Kc, movement toward equilibrium decreases Qc by converting products to reactants (that is, net reaction proceeds from right to left). If Qc equals Kc, the reaction mixture is already at equilibrium, and no net reaction occurs. 

Chemical reactions convert reactants to products, whose properties differ from those of the reactants. Chemical equations are a compact and convenient way to represent chemical reactions. They have the general form... 

Chain reactions rely on highly reactive free radicals that convert reactants to products while cycling through a step sequence like a DO loop in FORTRAN, in which they are consumed and produced anew. The step sequence, called propagation, is initiated by a reaction or event that generates free radicals, and is terminated by reaction of free radicals with one another to form a stable product or products or, more rarely, their deactivation by some other mechanism. With few exceptions, termination is by reaction of the most plentiful free radical with itself. Termination usually is second-order in free radicals, and this leads to rate equations with exponents of one half or integer multiples of one half. 

EFFECTS OF CHANGING THE CONCENTRATION OF A REACTANT OR PRODUCT As a simple example, consider what happens when a small quantity of a reactant is added to an equilibrium mixture. The addition of reactant lowers the reaction quotient Q below K and a net reaction takes place in the forward direction, partially converting reactants to products, until Q again equals K. The system partially counteracts the stress (the increase in the quantity of one of the reactants) and attains a new equilibrium state. If one of the products is added to an equilibrium mixture, Q temporarily becomes greater than K and a net back reaction occurs, partially counteracting the imposed stress by reducing the concentration of products (Fig. 14.7). 

Many chemical reactions do not completely convert reactants to products. A mixture of products and reactants exists, and its composition will remain constant until the experimental conditions are changed. This mixture is in a state of chemical equiiihrium. The reaction continues indefinitely (dynamic), but the concentrations of products and reactants are fixed (equilibrium) because the rates of the forward and reverse reactions are equal. This is a dynamic equilibrium. 

The Arrhenius equation was developed empirically from the observations of many reactions. The two major models that explain the observed effects of concentration and temperature on reaction rate highlight different aspects of the reaction process but are completely compatible. Collision theory views the reaction rate as the result of particles colliding with a certain frequency and minimum energy. Transition state theory offers a close-up view of how the energy of a collision converts reactant to product. 

Given the two continuous reactors in this chapter, the CSTR and the PFR, it is natural to compare their steady-state efficiencies in converting reactants to products. For simplicity, consider a constant-density, liquid-phase reaction with nth-order, irreversible reaction rate... 

Four CSTR design strategies are summarized below when simple third-order irreversible chemical kinetics convert reactants to products. 

In other words, reactants exist everywhere within the pores of the catalyst when the chemical reaction rate is slow enough relative to intrapellet diffusion, and the intrapellet Damkohler number is less than, or equal to, its critical value. These conditions lead to an effectiveness factor of unity for zerofli-order kinetics. When the intrapellet Damkohler number is greater than Acnticai, the central core of the catalyst is reactant starved because criticai is between 0 and 1, and the effectiveness factor decreases below unity because only the outer shell of the pellet is used to convert reactants to products. In fact, the dimensionless correlation between the effectiveness factor and the intrapeUet Damkohler number for zeroth-order kinetics exhibits an abrupt change in slope when A = Acriticai- Critical spatial coordinates and critical intrapeUet Damkohler numbers are not required to analyze homogeneous diffusion and chemical reaction problems in catalytic pellets when the reaction order is different from zeroth-order. When the molar density appears explicitly in the rate law for nth-order chemical kinetics (i.e., n > 0), the rate of reaction antomaticaUy becomes extremely small when the reactants vanish. Furthermore, the dimensionless correlation between the effectiveness factor and the intrapeUet Damkohler nnmber does not exhibit an abrupt change in slope when the rate of reaction is different from zeroth-order. 

Typically, the pore volume is 40 to 60% of the total volume bounded by the external surface of the catalyst, and Sp 0.50 is a reasonably good number. The range of pore radii varies from a lower limit of approximately 10 A to an upper limit slightly above 1 tim (i.e., 10" A). As illustrated below in eqnation (21-16), smaller pores correspond to a larger internal surface area per volume of catalyst, which is advantageous for converting reactants to products. However, Knudsen diffusion is restricted when the pores are too small because the mean free path of the gas, which varies inversely with gas density, is much larger than the pore diameter. 

Based on their abihty to convert reactants to products via first-order irreversible chemical kinetics, in rectangular channels with various aspect ratios at large Damkohler numbers (i.e., p = 1000) in the diffusion-limited regime. Reactant molar density vs. channel length follows a single exponential decay for those deposition profiles that are not underlined. 

True or False An endothermic heterogeneous catalytic reaction, which converts reactants to products irreversibly, occurs on the inner wall of a well-insulated tube. At any particular axial position within the tubular reactor, the maximum temperature exists at the centerline of the tube. 

It is important to remember that the X s are not normal molecules, and the 2f s not normal equilibrium constants. The species X has one less vibrational mode than a normal molecule (3n-7 instead of 3n-6). The missing mode is the motion along the reaction coordinate. This consists of that set of atomic motions which, if the restoring force is removed, will convert reactants to products. An example, given in Section I,B, is the asymmetric stretch of B—H—A in a proton transfer from A to B. Since there is no restoring force, the frequency of this motion will be zero or imaginary. The ratio of these two frequencies for two isotopic transition states can, however, still have physical meaning, as we shall see later. 

The main objective of reaction path analysis (RPA) is to determine which reactions exhibit the highest rates in converting reactants to products, and thus obtain an overall reaction map of the reaction network. The idea is to calculate which reactions are responsible for the production or consumption of species i through the following ... 

A reversible reaction is one in which a forward reaction converts reactants to products, whereas a reverse reaction converts products to reactants. 

The free-radical mechanism involves several reaction types (1) Initiation - the introduction of free radicals into the reaction system. In pyrolysis, the reaction is initiated thermally with a probable homolytic cleavage of a carbon-carbon bond. (2) Propagation - a series of reactions that converts reactants to products while leaving the radical concentrations unchanged (radical decomposition and isomerization, hydrogen transfer and radical addition). (3) Termination - the combination or disproportionation of radicals to give stable products (Rebick, 1983). 

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