Metal-Catalysed Reactions of Hydrocarbons / 05-Introduction to the Catalysis of Hydrocarbon Reactions
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INTRODUCTION TO THE CATALYSIS OF HYDROCARBON REACTIONS
PREFACE
The impatient reader may be wondering when we are going to get around to the main subject of the book, namely the reactions of hydrocarbons catalysed by metals. The material of the earlier chapters will be found of use in what follows, and of course the first encounter with catalysis has already occurred when we considered reactions undergone by hydrogen alone (Chapter 3). It is now necessary to look at the essential nature of the catalytic process; it is a kinetic phenomenon and susceptible to quantitative description, although the application of the principles of chemical kinetics as developed for reactions in a single phase is not without its difficulties. A careful and critical evaluation of the experimental and computational procedures used for extracting mechanistic information is therefore in order, and indeed the very concept of reaction mechanism in a catalysed reaction is something demanding attention. At the heart of this discussion is the notion that for every reaction there is a characteristic active centre, the identification of which has been a kind of Holy Grail for catalysis research. Its nature and structure in a particular case may be sought by systematic variation of parameters such as crystal face and particle size, and assessing the effect on the kinetic features of the reaction; and the size of the grouping of metal atoms which the reaction needs can, it has been argued, be deduced by diluting the active metal with an inactive one in an alloy or bimetallic particle.
The purpose of this chapter is to construct a framework of concepts and procedures that will be employed repeatedly in the ensuing chapters.
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5.1. THE ESSENTIAL NATURE OF CATALYSIS1−6
5.1.1. A Brief History of Catalysis
The basic idea of catalysis can be traced to the writings of J. J. Berzelius,7 who in 1836 reviewed a number of curious occurrences in which traces of certain substances seemed to have an effect on chemical reactions disproportionate to their amounts. In a passage often quoted, but bearing repetition, he wrote:8,9
I shall therefore call it the catalytic power of substances, and the decomposition by means of this power catalysis, just as we use the word analysis to denote the separation of the component parts of bodies by means of ordinary chemical forces. Catalytic power actually means that the substance is able to awake affinities which are asleep at this temperature by their mere presence and not by their own affinity.
We should not mock this first attempt to impart scientific rigour to such an elusive concept, but rather seek to place it in its historical context, remembering how rudimentary were chemical ideas at that time; the metaphor of awaking sleeping affinities is one which sticks in the memory.
It is not absolutely clear why he selected the word catalysis, which is formed from two Greek words, namely, the prefix cata- meaning ‘down’ and lysein, meaning ‘to break’. Both of these words make frequent appearance in the English language (catastrophe, catalepsy; hydrolysis, photolysis). Most probably Berzelius thought that substance causing the effect was breaking down the normal constraints that prevent reactions occurring, and it is in this sense the Chinese language selects the same word for catalysis as for marriage broker. It is somewhat ironic however that in journalistic use the word has come to mean ‘a bringing together’, which at first sight is quite the opposite to its original meaning, but on reflection we see that the coming together is an inevitable consequence of the abolition of the inhibiting barrier.8 Although not used in archaic Greek, the term catalysis has sometimes been used before the scientific era to mean a riot or a breaking down of social constraints.
The early work of Sir Humphrey Davy,10 of Dobereiner,¨ 11 and many others, that led Berzelius to coin the word and apply it to a diverse range of phenomena, has often been described,1–4 as have the ensuing but somewhat slowly developed practical applications. These may be of interest to the historian of science, but do not greatly help our present purposes. The next significant development was a much clearer definition of what a catalyst is and does, namely, a catalyst is a substance that increases the rate at which a chemical system attains equilibrium, without being consumed in the process. This form of words follows that suggested by F. W Ostwald;2 numerous modifications of the wording have been suggested, mainly in the final phrase, to allow for physical deterioration and deactivation during use. We need not pursue these efforts, as precise definition is the task of the
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Figure 5.1. Schematic Arrhenius plots of (A) catalysed and (B) non-catalysed reactions showing how the lower activation energy increases the rate at a given temperature and lowers the temperature needed to achieve a given rate.
pedant not the scientist. As Humpty Dumpty said, When I use a word it means just what I choose it to mean – neither more nor less (a sentiment incidentally which erodes the basis of a fair part of philosophy).
The implications of this definition have also been frequently explored.8 By increasing the rate of a reaction at some fixed temperature, a catalyst can also have the effect of lowering the temperature at which a given rate is achieved (Figure 5.1), and for many practical purposes this is its chief advantage. It can only assist reactions that are thermodynamically favourable, and the position of the equilibrium has to be the same as that which would have resulted, albeit in a much longer time, without it. This also implies that rates of forward and reverse reactions must be helped by the same factor if the equilibrium constant is to remain unaltered. Just how a catalyst manages to exert its influence will be considered in the next section.
5.1.2. How Catalysts Act
It would be useful to know by exactly how much a catalyst speeds up a given reaction, but a comparison of rates obtained with and without its help depends upon the chosen conditions. If we consider a gas-phase reaction, the rate will be proportional to the volume, and will be some function of reactant pressures and temperature; the rate of the catalysed reaction will depend on the surface area of the catalyst, i.e. on the number of points at which the reaction occurs, and on the surface coverages by the reactants, and also on temperature. A precise comparison is therefore clearly impossible, but if it is attempted on the basis of the number of potentially effective collisions between reactants, this will be very much larger (perhaps12 by as much as 106) in the homogeneous case than in the catalysed case.
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The rate at each reacting centre must therefore be very much faster with the latter, so that if we now adopt the Arrhenius equation
k = A exp (−E/RT ) |
(5.1) |
as a framework for the discussion, Acat will be very much smaller than Ahom, and therefore the exponential term must be correspondingly larger, i.e. Ecat must be much smaller than Ehom. Remembering that in elementary kinetic theory
A = PZ |
(5.2) |
where Z is a collision number and P a ‘steric factor’, there may be some relief in that Pcat may exceed Phom by 102 or 103: but the conclusion is that (Ehom − Ecat) must be at least 65 kJ mol−1 at a typical temperature just to compensate for the difference in the A terms, and should exceed 100 kJ mol−1 for efficient catalysis. There is much experimental evidence to show that this is indeed the case,12 and it has become an article of faith that the principal way in which a catalyst acts is by lowering the activation energy of a reaction. However as we shall see (Section 5.6) it does not automatically follow that the member of a set of catalysts showing the lowest activation energy is necessarily the most active.
To lower the activation energy, the reactants must have found an easier pathway across the potential barrier separating them from the product state (Figure 5.2) The nature of this new route depends upon the reaction and the catalyst, and perhaps also on the experimental conditions, but certainly it is the act of chemisorption that prepares molecules for reaction and it evades the sometimes large energy input needed to secure this preparation in the gas phase. In case of hydrogen-deuterium
Figure 5.2. Potential energy profile for (A) catalysed and (B) non-catalysed reactions.
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equilibration (Section 3.4.2) dissociative chemisorption removes the necessity to find the 434 kJ mol−1 of energy required for breaking the molecule in the gas phase. The reaction can then proceed at a measurable rate well below room temperature, compared to the 800 K or more that the homogeneous reaction needs. There are of course other ways of speeding up this reaction, e.g. by photolysis, but the energy resident in the free valencies of the metal surface is the most convenient way of activating hydrogen molecules. This concept is readily extended to all reactions in which hydrogen is a reactant so that for example a similar comparison can be drawn for hydrogenation of ethene, which defies study as a homogeneous reaction because other parasitic reactions intervene at the necessary high temperature. Catalysed hydrogenation was widely use to measure heats of reaction at about ambient temperature, safe in the knowledge that, following the accepted definition of catalysis, the answer would be the same as that which would have resulted without a catalyst had that experiment been possible. Chemisorption of the hydrocarbon reactant will also help the progress of reaction by its partial conversion towards the configuration of the product: this is a matter that will command out attention in later chapters.
5.1.3. The Catalytic Cycle13
The total requirements for a successful and sustained catalysed reaction can be summarised in the catalytic cycle (Figure 5.3) which provides a kind of checklist of points to which we shall return for closer examination. There must exist an active centre (Section 5.5) at which reactants can chemisorb in the appropriate for with an optimum energy for conversion to the desired products. Particularly with hydrocarbons there may be inappropriate chemisorbed forms, such as we have met in the last chapter; the optimum adsorption energy is that which just secures
Figure 5.3. The Catalytic Cycle (see text for explanation).
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full surface coverage, because stronger adsorption implies a lower reactivity and weaker adsorption means incomplete surface coverage, and inefficient use of the catalyst. These important considerations are enshrined in catalytic science as the
Sabatier Principle or the Volcano Plot.
It is then necessary to bring the reactant molecules to the active centre by a process of mass transport which can sometimes be rate limiting (Section 5.2.1). Having been chemisorbed they must then react at the reacting centre, and how they do this will occupy us for much of the rest of the book. The product molecules remain on the surface or may be ejected from the surface as it is formed; in the former case it its desorption may be the slow step, and if it does not desorb quickly its further reaction may lead to undesired products. Speedy removal of the product from the neighbourhood of the surface by another mass transport step is often important if it is an intermediate product that is wanted. Conversion of reactants or products into strongly held residues, or adventitious poisons in the feedstock, can block the active centre and lead to deactivation. In their absence the reaction should continue indefinitely.
5.2. THE FORMULATION OF KINETIC EXPRESSIONS14 –16
5.2.1. Mass Transport versus Kinetic Control1,2,8
If it is intended to study the reaction kinetics, that is, the dependence rate upon variables such as reaction pressures or temperature, it is important to be sure that the surface reaction is the slowest of all those forming the catalytic cycle, and that therefore mass transport to and from the surface are not rate limiting. Symptoms of mass transport limitation include the following.
1.The rate is proportional to the catalyst weight W or surface area As to a power less than unity.
2.The conversion is not accurately proportional to the inverse of the reactant flow rate F .
3.Thus for kinetic control the rate r should be proportional to the contact time τ so that
r = kW/F = kτ |
(5.3) |
4.The temperature coefficient is low, corresponding to an apparent activation energy of 10–15 kJ mol−1; gaseous diffusion processes do not in fact obey the Arrhenius equation, their rates being proportional to T 1/2.
If the rate is thought to be governed diffusion of reactants or products within the body of a porous catalyst, it will be increased by diminishing the particle size,
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i.e., the average length of pore that has to be traversed. Mass transport limitation will arise when the rate of the surface reaction is very fast, for example, at high temperature; a decrease in the apparent activation energy therefore betokens its onset. It will also tend to occur at large contact times and high conversions, where reactant concentrations are low.
Although under conditions of mass transport control the catalyst is inefficiently used, it is sometimes beneficial to operate under these conditions, as for example when in a sequential reaction such as
A → B → C |
(5.A) |
it is desired to optimise the yield of the intermediate product B. In what follows it will be assumed that kinetic control is operative, to which region the term microkinetics is applied; mass transport control is described in greater detail in textbooks having a chemical engineering flavour.1,15,17
5.2.2. The Purpose of Kinetic Measurements18
The manner in which the rates of reactant consumption and of formation of each individual product varies with reactant concentrations and temperature affords information that is useful in two ways: first, as providing the basis for the reactor design if the reaction is to be operated on a significant scale, and second, and more to the immediate point, to give a framework within which a reaction mechanism can be formulated. Whatever the practical difficulties of obtaining this information, and they can be considerable with microporous catalysts and those undergoing rapid deactivation, it is essential for mechanistic analysis. It cannot be stressed to strongly that no formulation of a reaction mechanism can be accepted as plausible until shown to be consistent with experimentally determined kinetics. The corollary is however equally important: the mechanism cannot be deduced from kinetic measurements alone, because many different mechanisms can lead to the same kinetic expression.
Kinetic analysis therefore proceeds into two convergent directions. Experimental results are often first fitted to an empirical rate expression in which rate is proportional to the product of the pressure P of each component raised to the power of its order of reaction: thus for the process
A + B → C |
(5.B) |
The rate expression will be
r = k PAa PBb PCc |
(5.4) |
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where a, b and c are the orders of reaction, and may be positive, negative or fractional. Such a rate expression is termed a Power Rate Law and although results are often quoted in this form it is of limited value, as the exponents may apply only over a limited pressure range, and give only the vaguest idea as to what the mechanism might be.
The second approach starts with an idea of possible mechanism, leading to a theoretical kinetic equation formulated in terms of concentrations of adsorbed reactants and intermediate species; use of the steady-state principle then leads to an expression for the rate of product formation. Concentrations of adsorbed reactants are related to the gas-phase pressures by adsorption equations of the Langmuir type, in a way to be developed shortly: the final equation, the form of which depends on the location of the slowest step, is then compared to the Power Rate Law expression, which if a possibly correct mechanism has been selected, will be an approximation to it. A further test is to try to fit the results to the theoretical equation by adjusting the variable parameters, mainly the adsorption coefficients (see below). If this does not work another mechanism has to be tried.
5.2.3. Measurement and Expression of Rates of Reaction16,19
Straightforward laboratory reactors are of two kinds: (i) the dynamic or flow reactor, in which the reactants are forced through a catalyst, and (ii) the static, constant-volume reactor, in which however the reactants can be made to circulate around a closed-loop or ‘race-track’ and so through the catalyst bed. Where the reactants move, fewer problems with mass transport and with keeping a constant catalyst temperature are met. With the static reactor, the rate follows directly from the changes of pressure or concentration with time and the orders of reaction from the dependence of initial rate on reactant pressure, or the variation of rate with time, according to the traditional precepts of chemical kinetics. For the dynamic reactor, constant conversion is obtained (in the absence of deactivation) by maintaining a fixed flow-rate, and the time dimension is only accessed by changes in this rate.13 The rate of reaction is then obtained as follows.
A single reactant enters a cylindrical bed of catalyst of length x and crosssectional area A at a flow-rate of F 0 and emerges at a flow-rate F : the conversion α is then given by
F/F 0 = 1 − α |
(5.5) |
In a differential slice of the bed of volume dV = ( Ad x ), the change of flowrate due to reaction is αF, and the rate r is given by
r = −d F/d V |
(5.6) |
= dα/d(V/F 0) |
(5.7) |
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or if the rate is to be expressed per unit weight of catalysts |
|
r = dα/d(W/F 0) |
(5.8) |
The average time a molecule spends in the bed is the apparent contact time τ , which is proportional to F /W . Thus
r = dα/dτ |
(5.9) |
The conversion equates to the fractional change in concentration |
|
α = (c0 − c)/c0 |
(5.10) |
and for a first-order reaction |
|
r = k1c = k1c0(1 − α) |
(5.11) |
and |
|
τ = dα/k1c0(1− α) |
(5.12) |
Similar equations may be derived for reactions of other orders.
Information relevant to determining reaction mechanism is obtained by working at low conversion, preferably less than 10%, i.e. by operating the reactor in the differential mode. The use of high conversion (>90%) gives information of more practical usefulness; the reactor is then in the integral mode.
We thus arrive at a rate per unit weight of catalyst, but for a supported metal we need the rate per unit weight of metal, although we cannot assume its metal content is what we think it to be; accurate chemical analysis is essential. This gives the specific rate, but if the metal dispersion or average particle size is known (as it should be) we may then get the rate per unit area of metal (the areal rate).20 So far, so fairly good, but difficulties may arise in studying the effect of rate on particle size (a popular pastime, see Section 5.4) if the size distribution is binodal, as it often is. The catalyst may contain both large and small particles, in amounts that vary with total loading19 (Section 2.5.6); small particles may escape detection (e.g. by XRD and TEM), and the H/Ms stoichiometry may therefore change with loading. Great care must therefore be exercised in looking for particle size effects on rate or product formation. For a time it was usual to express the rate per unit atom of exposed metal, as determined for example by hydrogen chemisorption; this is termed the turnover frequency,21–23 the units of which are mol (mol surface atom)−1s−1. It is however now appreciated that for many reactions the size of the ensemble of atoms needed for reaction is quite large, and that therefore the turnover
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frequency is not a good basis of comparison.21,24 It does however represent a way of normalising the performance of a given metal if its dispersion changes from one preparation to another. It must be understood that a TOF is simply a rate, and that it only has the units of t −1 because the mass units have been cancelled. Its value therefore depends on all operating variables (reactant pressure, temperature etc.), and these must be cited if its value is to have any meaning. This discussion is continued in Section 5.4.
5.2.4. The Langmuir-Hinshelwood Formalism25
The essential problem in formulating a theoretical rate expression for a catalysed reaction is that we do not in general have direct access to concentrations of the adsorbed reactants: we have to assume a relationship between them and their pressures in the gas phase. The simplest and most widely used way of doing this is to suppose that the Langmuir adsorption equation (Section 3.2.4) adequately describes the connection: we must however remember that the basic postulates underlying this type of equation should always apply, and much of the discussion concerning the proper derivation of rate equations concerns the definition of site (or sites) involved (see Section 5.5). Whatever the uncertainties and ambiguities associated with this approach, the resulting rate expressions first applied by C. N. Hinshelwood26 in the 1920s, have proved extraordinarily useful in understanding and interpreting the kinetics of catalysed reactions.
For the simplest possible reaction, namely A → X, the mechanism can be formulated as follows
A + → A → X + |
(5.C) |
where A is chemisorbed at an active centre designated by *, and is changed into X which is simultaneously returned to the gas phase. Thus
r = k1θA |
(5.13) |
and by introducing the Langmuir adsorption equation for θA
r = k1bA PA /(1 + bA PA) |
(5.14) |
The dependence rate on PA will thus follow the dependence of θA upon PA (Figure 5.4). The form of this curve is consistent with the conclusion that when the PA is slow and/or bA is small, the rate in simply proportional to PA , but when either or both is large it is independent of PA , i.e. the reaction is of zero order. In