Kinetics of Heterogeneous Catalytic Reactions

by Michel Boudart, G. Djega-Mariadassou

Overview

This book is a critical account of the principles of the kinetics of heterogeneous catalytic reactions in the light of recent developments in surface science and catalysis science.

Originally published in 1984.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Product Details

ISBN-13:	9780691612560
Publisher:	Princeton University Press
Publication date:	07/14/2014
Series:	Physical Chemistry: Science and Engineering , #767
Pages:	242
Sales rank:	866,254
Product dimensions:	7.00(w) x 9.80(h) x 0.60(d)

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Kinetics of Heterogeneous Catalytic Reactions

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By Michel Boudart, G. Djéga-Mariadassou

PRINCETON UNIVERSITY PRESS

Copyright © 1984 Princeton University Press
All rights reserved.
ISBN: 978-0-691-08347-6

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CHAPTER 1

CONCEPTS AND DEFINITIONS

1.1 Introduction

Heterogeneous catalysis is much more than a subfield of chemical dynamics and chemical kinetics. It is related to other disciplines, as shown in the triangular representation below.

In particular, thanks to the recent development of the chemical physics of metallic surfaces, kineticists have reconsidered earlier views and theories concerning catalysis by metals and alloys. New techniques had yielded new results, and new concepts had to be incorporated in the kinetic framework of heterogeneous catalysis.

Catalyst preparation is responsible for the composition, structure and texture of catalytic materials. Today, the synthesis of new metallic catalysts is achieved in a more rational manner than heretofore, by means of solution theory, colloidal chemistry, solid state chemistry, and organometallic chemistry. At any rate, the most striking recent advance in catalysis by metals is the control of catalyst preparation and characterization, so that reproducible surfaces yield reproducible reactivity in different laboratories.

Besides helping in the characterization of catalytic solids, new physical tools (spectroscopy, diffraction) also contribute to the identification of reaction intermediates responsible for the elementary steps that constitute the catalytic cycle.

Ultimately, the indispensable quantity for the elaboration of theories in catalysis is the correct and reproducible measurement of the true reactivity of molecules at the solid-fluid interface. This measurement is the difficult art of the chemical kineticist. The measurement must be checked so that it can be shown to be exempt from all artifacts: adventitious poisoning, improper contacting between solid and fluid, and all physical processes of heat and mass transfer. But if the kinetic data are correct, and if the catalyst characterization is adequate, the available information can lead to the progressive transformation of catalysis from an art to a science.

In fact, in the case of metals, surface science and catalysis science have progressed side by side in the past ten years. There now exist several examples where kinetic data on clean, well-defined macroscopic single crystals agree very well with those obtained on reproducible and characterized supported metallic clusters between 1 and 10 nm.

This remarkable agreement justifies the limitation of this book to metallic catalysts. Nevertheless, our attempt will be to develop the general kinetic principles involved in heterogeneous catalysis, with metals selected as an example.

The theories underlying these principles are relatively few. In spite of the post-Langmuirian era of surface science starting twenty years ago, the Langmuir (1916) isotherm remains one of the pillars that support surface catalytic kinetics. Nevertheless, it is now necessary to take into account corrosive chemisorption in which the adsorbate forms with the atoms of the metal surface a new coincidence lattice over the metal lattice itself (Bénard, 1970; Ponec and Sachtler, 1972; Hanson and Boudart, 1978). The theoretical developments of Horiuti (1957, 1967) are of wide applicability. But the two most essential theories of almost universal applicability remain that of the transition state or activated complex, elaborated by Eyring and his school (Glasstone et al., 1941) and the quasi-stationary state approximation popularized and defended by Bodenstein. Bodenstein's powerful method was further systematized by Christiansen (1953) for both catalytic and chain reactions.

In the first chapters of this book, the metal surface will be considered as made up of sites that are identical thermodynamically and kinetically without any interaction between adsorbed species. This Langmuirian view will be amended later as the early recognition by Taylor (1925) of the importance of active centers will be embodied in the theory of non-uniform surfaces following Temkin (1957, 1965, 1979) and Wagner (1970). Temkin's formalism, which rests on the Brønsted relation between rate constants and equilibrium constants (see Boudart, 1968), is very general. Since a collection of sites on a non-uniform surface can be assimilated to an array of different catalysts, Temkin's theory helps in understanding what determines the optimum catalyst for a given reaction. The finding of an optimum catalyst is the most common goal of applied catalysis.

1.2 Definitions

1.21 Stoichiometric Equation and Stoichiometric Coefficients

Generally, for any chemical reaction, whether it be an overall reaction or an elementary step, we can write:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2.1)

where vi is the stoichiometric coefficient of component Bi taken as positive if Bi is a product, or negative if Bi is a reactant.

1.22 Extent of Reaction

This quantity, introduced by the Brussels school of thermodynamics, is defined by:

[xi] (mol) = [ni - n0i]/vi (1.2.2)

where n0i and ni are the quantity of substance of Bi, expressed in mole, at time zero or at any time respectively.

1.23 Reaction Rate

Following the recommendations of IUPAC (1976, 1979), reaction rate is defined in the most general way by:

[xi] = d[xi]/dt mol s-1 (1.2.3)

But in practice, the rate is referred to unit volume, mass or area of the catalyst. Thus we can have a volumic rate:

1/V d[xi]/dt mol cm-3 s-1 (1.2.4)

where V is the volume of the solid catalyst, or a specific rate:

1/m d[xi]/dt mol g-1s-1 (1.2.5)

where m is the mass of the catalyst, or an areal rate:

1/A d[xi]/dt mol cm-2 s-1 (1.2.6)

where A is the area of the catalyst. These expressions for the rate of reaction will be designated by v, the meaning of which will be made clear by the context.

It is clear that the areal rate (1.2.6) is the best one of the three. Yet, two catalysts can have the same surface area but different concentrations of active sites. A definition of the rate in terms of the number of active sites would seem to be preferred.

1.24 Number of Turnovers

This is the number n of times that the overall reaction takes place through the catalytic cycle. The rate is then:

rate = dn/dt s-1 (1.2.7)

where n = [xi] × NA with NA = 6.0225 × 1023 mol-1. The areal rate can also be expressed as:

areal rate = 1/A dn/dt cm-2 s-1 (1.28)

1.25 Turnover Frequency or Rate of Turnover (Formerly Called Turnover Number, Boudart 1972)

This is the number of turnovers per catalytic site and per unit time, for a reaction at a given temperature, pressure, reactant ratio, and extent of reaction. The latter may be so small that the rate may be considered as initial rate.

The turnover frequency is thus:

vt [equivalent to] N(s-1) = 1/S dn/dt (1.2.9)

where S is the number of active sites used in the experiment. Also:

s = [L] × A (1.2.10)

where [L] is the number density (cm-2) of sites, i.e., the number of sites per unit area. The definition (1.2.9) will be used whenever possible. Not the least of its merit is that its dimension is one over time so that it is simply expressed in reciprocal seconds. This permits an easy comparison between the work of different investigators.

But there remain problems in the use of vt. Indeed, we still do not know how to count the number of active sites. With metals, all we can do is count the number of exposed surface atoms. How many of the latter are grouped in an active site? Besides, different types of active sites probably always exist, and a molecule may be adsorbed differently on each type and react at a different rate. Thus vt is likely to be an average value of the catalytic activity and a lower bound to the true activity, as only a fraction of the surface atoms may contribute to the activity. Besides, vt is a rate, not a rate constant, so that it is always necessary to specify all conditions of reaction as spelled out above.

Yet, the systematic use of the turnover frequency is an immense progress made possible by techniques that count the number of surface metallic atoms. It is likely that the progress made in the case of metals will also be made with oxides (Djéga-Mariadassou et al., 1982), in particular, the comparison between the activity of large single crystals and of powders with large specific surface areas.

The number of turnovers of a catalyst before it dies is clearly the best definition of the life of the catalyst. In practice, this turnover can be very large, say 106 or more. As to the turnover frequency, it is frequently of the order of one per second. With much smaller values, the rate is too small to be measured, or to be practical. With much higher values, the rate is too large and becomes influenced by transport phenomena in catalyst pores (see Chapter 6). In fact, reaction temperature is frequently adjusted so as to obtain this commonly encountered value of the activity, vt = 1 s-1 (Burwell and Boudart, 1974).

1.26 Selectivity

With more than one reaction taking place, catalyst selectivity is defined, for two reactions, as the ratio of their rates:

S = v1/v2 (1.2.11)

Selectivity is frequently easier to measure correctly than individual rates. This is particularly so if the catalyst is readily poisoned in a way in which it is very difficult to control. Besides, selectivity is of intrinsic interest for considerations of mechanisms, as shall be seen later (Maurel et al., 1975).

1.27 Quantities Related to Reaction Rate

In flow reactors, a number of quantities are related to the reaction rate. The first one is defined in terms of the volumetric flow rate and the catalyst volume:

space velocity = F/V s-1

Frequently this quantity is expressed in h-1 and is of the order of 1 h-1 in large-scale processing. The inverse of the space velocity is the space time:

τ = V/F s

As to the space time yield, it is the quantity of a product produced per quantity of catalyst per unit time. A similar useful quantity can be defined as the site time yield: it is the number of molecules of a product made per site in the reactor per second. If the reactor is well-stirred (CSTR, continuous-stirred-tank-reactor), the site time yield is proportional to the turnover frequency as defined above.

1.3 Elementary Step, Reaction Path, and Overall Reaction

1.3 Elementary Step

The stoichiometric equation (1.2.1) does not tell us how the chemical transformation takes place at the molecular level, unless it stands for an elementary step. But if this is indeed the case, the arbitrary choice of a set of stoichiometric coefficients or of a multiple thereof is not permitted, as the elementary step must be written as it takes place at the molecular level.

Consider as an example the dissociative adsorption of dioxygen on two adjacent free sites, each being denoted by the symbol * :

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

By contrast, one may not write:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

as this has no mechanistic meaning. The identification of the active site * is the central problem of heterogeneous catalysis.

The net rate of the elementary step is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The step may be reversible when [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], in which case the equation for the step will be written with a double arrow:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Or the step may be irreversible, if [??] >> [??]. Then the equation is written with a single arrow:

Reactants -> Products

Finally the step may be equilibrated, or quasi-equilibrated, if [??] = [??] (or nearly so), in which case a symbol denoting zero net rate (personal communication from Professor K. Tamaru) is used in the equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

For an overall reaction, the equal sign is used:

Reactants [??] Products

with [??] if the reaction is equilibrated and -> if it is far from equilibrium.

1.32 Reaction Path and Stoichiometric Number

A catalytic cycle is defined by a closed sequence of elementary steps. In the first one an active site is converted to an active intermediate. In each subsequent step, the active intermediate is converted into another one. In the last step, the last active intermediate regenerates the free active site.

If we sum up, side by side, the stoichiometric equations for each step, we obtain the stoichiometric equation for the overall equation, provided we take each step σ times, σ being the stoichiometric number of that step.

1.33 Single Path Reaction (Temkin, 1971)

As an example, consider the oxidation of SO2 on a platinum catalyst. The catalytic sequence may consist of two elementary steps: a dissociative adsorption of dioxygen followed by an Eley-Rideal step in which gaseous SO2 reacts with adsorbed oxygen:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

If we sum up side by side the equations for both steps, we obtain the stoichiometric equation for the overall reaction if we multiply each step by its stoichiometric number, in this case the couple (1, 2) corresponding to a single path N(1). Another couple (1/2, 1) would correspond to the choice of the stoichiometric equation for the overall reaction:

1/2O2 + SO2 = SO3

Both couples are of course equivalent: there exists only one single path for the reaction. The proper choice of values of σ eliminates the reaction intermediates. The turnover frequency is the number of turnovers per second and per site, along the single reaction path:

N = 1/S dn/dt(s-1)

The stoichoimetric numbers were first introduced by Horiuti (1957, 1967).

1.34 Multiple-Path Reaction

There is only one overall reaction, but it may proceed by different paths. An old example is the reaction between H2 and O2 on platinum to produce water as first studied by Faraday (1844), and then by a very large number of investigators (Hanson and Boudart, 1978). The next example shows two reaction paths N(1) and N(2) leading to the same overall reaction. The first path N(1) goes through Langmuir-Hinshelwood elementary steps where two adsorbed species react together. The second path N(2) involves an Eley-Rideal step, i.e., a reaction between a surface species and a gaseous species.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

1.35 Reaction Networks

In this case, different reaction paths lead to different overall reactions, but the paths N(i) are coupled. As an example, consider the manufacture of water gas, an old process which is attracting attention again for the production of "syngas," CO and H2:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

A rate of reaction is defined along each reaction path. In each step, we recognize stable species like C, i.e., reactants and products and Bodenstein reactive intermediates, like C*. The difference between C and C* from a mechanistic standpoint is that the former is bound to more carbon atoms than the latter (Holstein and Boudart, 1981).

Besides the material balance between reactants and products expressed by the stoichiometric equations, it is necessary to write a material balance for the reaction intermediates.

(Continues...)

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Excerpted from Kinetics of Heterogeneous Catalytic Reactions by Michel Boudart, G. Djéga-Mariadassou. Copyright © 1984 Princeton University Press. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
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Table of Contents

• FrontMatter, pg. i
• Table of contents, pg. vii
• Figures, pg. ix
• Tables, pg. xiii
• Preface To The French Edition, pg. xv
• Introduction, pg. xvii
• Chapter 1. Concepts and Definitions, pg. 1
• Chapter 2. Kinetics of Elementary Steps: Adsorption, Desorption, and Surface Reaction, pg. 38
• Chapter 3. Kinetics of Overall Reactions, pg. 77
• Chapter 4. Kinetics of Two-Step Reactions on Non-Uniform Surfaces, pg. 118
• Chapter 5. Structure-Insensitive and Structure-Sensitive Reactions on Metals, pg. 155
• Chapter 6. Parasitic Phenomena, pg. 194
• Author Index, pg. 215
• Subject Index, pg. 218