Rate Expressions catalytic

Equations similar to Eqs. (13)-( 15) can be derived for any other components of which the concentrations appear in the rate expression for the catalytic reaction. 

This type of isotherm is more realistic for describing chemisorption at intermediate 0a values but quickly leads to mathematically cumbersome or intractable expressions with many unknown parameters when one considers coadsorption of two gases. One needs to know how -AHa is affected both by 0A and by the coverages of all other adsorbates. Thus for all practical purposes the LHHW kinetics represent even today the only viable approach for formulating mathematically tractable, albeit usually highly inaccurate, rate expressions for catalytic kinetics. In Chapter 6 we will see a new, medium field type, approach which generalizes the LHHW kinetics by accounting also for lateral interactions. 

The oxidation of CO on Pt is one of the best studied catalytic systems. It proceeds via the reaction of chemisorbed CO and O. Despite its complexities, which include island formation, surface reconstruction and self-sustained oscillations, the reaction is a textbook example of a Langmuir-Hinshelwood mechanism the kinetics of which can be described qualitatively by a LHHW rate expression. This is shown in Figure 2.39 for the unpromoted Pt( 111) surface.112 For low Pco/po2 ratios the rate is first order in CO and negative order in 02, for high pco/po2 ratios the rate becomes negative order in CO and positive order in 02. Thus for low Pcc/po2 ratios the Pt(l 11) surface is covered predominantly by O, at high pco/po2 ratios the Pt surface is predominantly covered by CO. 

The kinetics and mechanism of this reaction have been studied for years on Pt films deposited on doped Zr02.15 It has been found that at temperatures above 280°C the open-circuit catalytic kinetics can be described quantitatively by the rate expression... 

However, the mechanisms by which the initiation and propagation reactions occur are far more complex. Dimeric association of polystyryllithium is reported by Morton, al. ( ) and it is generally accepted that the reactions are first order with respect to monomer concentration. Unfortunately, the existence of associated complexes of initiator and polystyryllithium as well as possible cross association between the two species have negated the determination of the exact polymerization mechanisms (, 10, 11, 12, 13). It is this high degree of complexity which necessitates the use of empirical rate equations. One such empirical rate expression for the auto-catalytic initiation reaction for the anionic polymerization of styrene in benzene solvent as reported by Tanlak (14) is given by ... 

Steps 1 through 9 constitute a model for heterogeneous catalysis in a fixed-bed reactor. There are many variations, particularly for Steps 4 through 6. For example, the Eley-Rideal mechanism described in Problem 10.4 envisions an adsorbed molecule reacting directly with a molecule in the gas phase. Other models contemplate a mixture of surface sites that can have different catalytic activity. For example, the platinum and the alumina used for hydrocarbon reforming may catalyze different reactions. Alternative models lead to rate expressions that differ in the details, but the functional forms for the rate expressions are usually similar. 

Suppose a gradientless reactor is used to obtain intrinsic rate data for a catalytic reaction. Gas-phase concentrations are measured, and the data are fit to a rate expression using the methods of Chapter 7. The rate expression can be arbitrary ... 

Clearly, catalytic rate constants are much slower than vibrational and rotational processes that take care of energy transfer between the reacting molecules (10 s). For this reason, transition reaction rate expressions can be used to compute the reaction rate constants of the elementary reaction steps. 

For catalytic reactions and systems that are related through Sabatier-type relations based on kinetic relationships as expressed by Eqs. (1.5) and (1.6), one can also deduce that a so-called compensation effect exists. According to the compensation effect there is a linear relation between the change in the apparent activation energy of a reaction and the logarithm of its corresponding pre-exponent in the Arrhenius reaction rate expression. 

Assuming that the catalytic reaction takes place in a flow reactor under stationary conditions, we may use the steady state approximation to eliminate the fraction of adsorbed intermediate from the rate expressions to yield ... 

An interesting catalytic effect upon the alkaline ferricyanide oxidations of ketones is shown by osmium(VIII) tetroxide, the rate expression being... 

Experimental studies of the catalytic decomposition of ozone in the presence of nitrogen pentoxide follow a rate expression of the form... 

For reversible reactions the principle of microscopic reversibility (Section 4.1.5.4) indicates that a material that accelerates the forward reaction will also catalyze the reverse reaction. In several cases where the catalytic reaction has been studied from both sides of the equilibrium position, the observed rate expressions are consistent with this statement. 

The Langmuir adsorption isotherm provides a simple mechanistic picture of the adsorption process and gives rise to a relatively simple mathematical expression. It can also be used to obtain a crude estimate of specific surface areas. More important, from the viewpoint of the chemical engineer, it serves as a point of departure for formulating rate expressions for heterogeneous catalytic reactions. 

REACTION RATE EXPRESSIONS FOR HETEROGENEOUS CATALYTIC REACTIONS... 

Reaction Rate Expressions for Heterogeneous Catalytic Reactions... 

In the treatment of rate expressions for heterogeneous catalytic reactions the definition of local reaction rates in terms of interfacial areas (3.0.10) is appropriate. 

ILLUSTRATION 6.1 DEVELOPMENT OF A HOUGEN-WATSON RATE EXPRESSION FOR A HETEROGENEOUS CATALYTIC REACTION... 

Equation 8.3.4 may also be used in the analysis of kinetic data taken in laboratory scale stirred tank reactors. One may directly determine the reaction rate from a knowledge of the reactor volume, flow rate through the reactor, and stream compositions. The fact that one may determine the rate directly and without integration makes stirred tank reactors particularly attractive for use in studies of reactions with complex rate expressions (e.g., enzymatic or heterogeneous catalytic reactions) or of systems in which multiple reactions take place. 

Effectiveness Factors for Hougen-Watson Rate Expressions. The discussion thus far and the vast majority of the literature dealing with effectiveness factors for porous catalysts are based on the assumption of an integer-power reaction rate expression (i.e., zero-, first-, or second-order kinetics). In Chapter 6, however, we stressed the fact that heterogeneous catalytic reactions are more often characterized by more complex rate expressions of the Hougen-Watson type. Over a narrow range of... 

The rates at which chemical transformations take place are in some circumstances strongly influenced by mass and heat transfer processes (see Sections 12.3 to 12.5). In the design of heterogeneous catalytic reactors, it is essential to utilize a rate expression that takes into account the influence of physical transport processes on the rate at which reactants are converted to products. Smith (93) has popularized the use of the term global reaction rate to characterize the overall rate of transformation of reactants to... 

Through the years, several catalyst formulations have been employed, but one of the traditional catalytic agents has been vanadium pentoxide. Calderbank (114) has indicated that for a catalyst consisting of V205 supported on silica gel, the kinetic data are represented by a rate expression of the form... 

In terms of the fraction conversion, the catalytic reaction rate expression then becomes... 

These assumptions are the basis of the simplest rational explanation of surface catalytic kinetics and models for it. The preeminent of these, formulated by Langmuir and Hinshelwood, makes the further assumption that for an overall (gas-phase) reaction, for example, A(g) +...- product(s), the rate-determining step is a surface reaction involving adsorbed species, such as A s. Despite the fact that reality is known to be more complex, the resulting rate expressions find wide use in the chemical industry, because they exhibit many of the commonly observed features of surface-catalyzed reactions. 

When the best catalyst has been chosen and found to fulfil the requirements with respect to activity, strength, pressure drop, production and profitability, a procedure must be developed for calculation of the catalyst volume required to obtain a given SO2 conversion in an industrial reactor. In its simplest form, the calculation basis can be a table or an expression for space velocity (NHSV) as a function of feed gas properties and final conversion. A more detailed approach is used for design of catalytic reactors at Haldor Topsoe, where a rate expression of the form... 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Depressed catalytic activity occurring when an inhibitor binds more than once to a single enzyme form (or forms). While standard double-reciprocal plots are usually linear, secondary replots of the data (i.e., plots of slopes and/or intercepts vx. [I], the concentration of the inhibitor) will be nonlinear depending on the relative magnitude of the [I], [If,. .., and [If terms in the rate expression. 

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