THE ACTIVATED COMPLEX IN HETEROGENEOUS CATALYSIS BY KEITH J. LAIDLER Received 16th February, 1950 The evidence that certain surface reactions proceed by interaction between an adsorbed molecule and a gas-phase molecule is reviewed briefly, with special reference to the para-ortho hydrogen conversion and the combination of atoms and free radicals. On the basis of absolute rate theory, general rate expressions are developed for reaction between two molecules A and B, of which A is more strongly adsorbed, assuming the following alternative mechanisms ; (I) inter- action between adsorbed A and adsorbed B, (2) interaction between adsorbed A and gaseous B, (3) interaction between adsorbed B and gaseous A. According to mechanism ( I ) the rate passes through a maximum and later decreases as the concentration of A is increased, but according to (2) and ( 3 ) a limiting rate is reached at high concentrations of A.It is shown that at the maximum accord- ing t o mechanism ( I ) the frequency factor is approximately the same as a t high A concentrations according to (2) and (3). The rate expressions are compared with special reference t o the reaction between ethylene and hydrogen, for which it is shown that the data appear to favour mechanism (I). The low frequency factor for the reaction ( t u 10-6) is explained quantitatively on the basis of the theory, being due to the loss of translational and rotational freedom in forming the activated complex. The close analogy between surface and enzyme reactions is discussed, and it is shown that many enzyme processes can be interpreted on the basis of mechanism ( I ) .The initial step in the dehydrogenation of lactic acid, the urease-catalyzed hydrolysis of urea and other reactions are considered briefly from this point of view. From the standpoint of the theory of absolute reaction rates the central problem in the theoretical treatment of the rates of chemical and physical processes is the determination of the configuration of the activated complex. The manner in which the activated complex is composed of the reactant molecules controls the way in which the rate depends upon the concentrations of the reactants (i.e. the order of the reaction), and the entropy and energy of the complex with respect to the reactants control the rate of the reaction. In principle the structure and energy of the activated complex can be calculated by the methods of quantum mechanics, and hence the rate obtained : in practice this cannot be done satisfactorily, and an empirical method must be used.This has usually consisted of obtaining information as to the configuration of the activated complex from the experimental order of the reaction, and deriving the energy of the complex (corrected to oo K) from the experi- mental activation energy. It is then possible to calculate frequency factors and rates €or postulated mechanisms, and to decide between various possibilities on the basis of the agreement with the experimental data. This type of treatment has been applied successfully to adsorption and desorption processes at surfaces,2 to a variety of chemical processes on surface~,~ and to the para-ortho hydrogen conver~ion.~ In the present Eyring, J .Chem. Physics, 1935, 3, 107. 2 Laidler, Glasstone and Eyring, ibid., 1940, 8, 659. Laidler, Glasstone and Eyring, ibid., 1940, 8, 667. Eley and Rideal, Proc. Roy. Soc. A , 1941, 178, 429. 4748 THE ACTIVATED COMPLEX IN CATALYSIS paper we discuss further examples, and in particular extend the treat- ment to a somewhat different type of surface activated complex, in which only one of two reacting molecules is attached t o the surface. and Hinshelwood * have formulated the theory of bimolecular surface reactions on the assumption that in order for reaction to occur it is necessary for the two reactant molecules to become adsorbed side by side, and the calculations referred to above (except for the ortho-para hydrogen conversion) were a development of this idea.There seems to be little doubt that such mechanisms are applicable to most, if not all, of the reactions to which they have been applied. However, there are a few reactions, which have been the centre of recent interest, in which it appears to be more likely that the activated complex is formed not from two adsorbed molecules but from an adsorbed molecule or atom and a mole- cule or atom in the gas phase or in a van der Waals’ layer. This type of mechanism was first propounded by Rideal,? and was applied by him and Eley to the para-ortho hydrogen conversion, the activated complex for which may be represented as being formed by the process Langmuir H H-H H H H H H H H i H H -s-u-s-s-k- r i l l [ -+ -A&+”- t l ! (activated complex) Such a mechanism seems necessary in this case, since the alternative explanation that the conversion involves an adsorption process followed by rearrangement and desorption, H-H H-H H H -s-s- I t -S-S- i I - 1 1 - -s-s- is excluded by Roberts’ result s that the observed rates of desorption are much too slow.Further support for the Eley-Rideal mechanism is pro- vided by the fact that a quantitative treatment lo gives good agreement between observed and calculated rates. Another class of reactions for which it seems necessary to assume that the activated complex is formed directly from a gas-phase species and a surface species comprises the recombinations of atoms and free radicals on surfacesll These are almost always first-order processes, and one mechanism that would explain this behaviour is surface adsorp- tion of the atoms or radicals followed by recombination on the wall; however, this is again excluded by the facts with regard to the stability of the adsorbed layer.An alternative explanation, and the most probable one, is that the reaction involves interaction between a surface-adsorbed atom or radical and a gaseous one ; thus the recombination of hydrogen atoms on clean glass surfaces may be represented as H H H-€1 H H H H H H i E l H H H H ___f I I I I -LLL -s-s-s-s- lip, - -+ -s-s-./-s (ac:ivated complex) Langmuir, Trans. Faraday Soc., 1921, 17, 621. 6 Hinshelwood, Kinefzcs of Chemzcal CJzangc (Oxford University Press, 1926) p.145 ; (1940)~ p. 187. Rideal, Proc. Camb. Phil. Soc., 1939, 35, 130 ; Chew. and I n d . , 1943, 62,335. Farkas, 2. physik. Chem. B, 1931, 14, 371. Roberts, Trans. Faraday SOC., 1939, 35, 941. l o Eley, Trans. Faraduy SOC., 1948,44,216 ; K. J. Laidler and G. M‘. Castellan, l1 Shuler and Laidler, J . Chem. Physics, 1049, K7, 1212, 1356. (unpublished results).KEITH J. LAIDLEK 49 Detailed calculations on the basis of such a mechanism again give satis- factory agreement with the experimental results. In view of the importance of Rideal mechanisms in processes of this kind it is natural t o inquire whether similar mechanisms are applicable t o reactions which have conventionally been regarded as controlled by interaction between two adsorbed molecules.In the general case of a reaction between two molecules A and B we can formulate the Langmuir- Hinshelwood mechanism as follows : A**.B I I . . A B 1 1 _3 - . -+ . . -s-s- - 3 - S - + products. ( I ) With the Rideal mechanism there are two distinct possibilities : in the first, reaction occurs between a gas phase molecule of A and an adsorbed molecule of B, e.g. I I A + B + - S - S - + -S-S- (activated complex) A B -+ -S- + products; . (2) I B I A+-s- __f -s- (activated complex) in the second, A is adsorbed and B is in the gas phase ; A A B --+ I I B+-S- -S- -c- - + products. . ( 3 ) (activated complex) I n mechanism ( 2 ) it is not necessary that A is not at all adsorbed, but rather that an adsorbed A does not contribute directly t o reaction ; how- ever, it may be noted that if A is adsorbed more than very weakly it will indirectly affect the rate by influencing the concentration of adsorbed B molecules. With a view t o contributing t o the problem of distinguishing between the three mechanisms (I), ( 2 ) and ( 3 ) in any instance we will now formulate the rate laws in each case.It will be assumed throughout that A is much more strongly adsorbed than B, i.e. that there are more adsorbed A mole- cules than B ; however, no other restriction is placed on the degree of adsorption. The equations will then be applied briefly t o the kinetics of the hydrogenation of ethylene, with A = C,H, and B = H,. Beeckl, has suggested that this reaction proceeds by mechanism (z), gaseous ethylene reacting with adsorbed hydrogen ; A (ethylene) is strongly ad- sorbed but the adsorbed ethylene molecules do not interact directly with adsorbed hydrogen molecules.The data certainly exclude mechanism ( 3 ) , but it will be seen that the formulation of the rate laws leads us t o the conclusion that the data are more consistent with mechanism ( I ) than with mechanism (2). Interaction Between Two Adsorbed Molecules (Mechanism (1)) .- The concentration c, of adsorbed -4 is given by where c, is the concentration (in molecular units) of bare surface sites and 12Beeck, Rez. M o d . Physics., 1945, 17, GI. * The derivations given here and in the following two sections employ the same notation and general assumptions as in Glasstone, Laidler and Eyring, The Theory of Rate Processes (McGraw-Hill Book Company, Kew York, 1g41), Chap.VII.5 0 THE ACTIVATED COMPLEX IN CATALYSIS c , that of A in the gas phase ; K is the equilibrium constant, given by K = f,eejkT * (2) Fgfs ' - where the f are the partition functions and the energy of adsorption. Similarly, for the adsorption of B, denoting the quantities by primes, * (3) - _ "' - K'cpl, . C S where K' is now given by In addition, where L is the conzentration of sites when the surface is completely bare. Eqn. (I), ( 3 ) and ( 5 ) give rise to and LKc, I + Kc, + K'c,'' c,= -- ' L K'c ,' I + Kc, + K'c,' c,' = The condition that c , @ c,' implies that Kc, $ k'c,' ; these equations thus reduce to - ( 8 ) LKc, c, = - I + Kc,' ' and The fraction 8' of surface covered by B is clearly c,'/L, i.e. The rate can now be formulated as follows.The average number of adsorbed B's adjacent to any given adsorbed A is so', where s is the maximum possible number of near neighbours; the total number of adsoibed A-B pairs is thus c ~ d ' , which equals sLKK'c,c ,' If these react with an activation energy (at the absolute zero) of E,,, the rate is given by (I + Kc,)a' sLKK'c,~,' kT ff -ro/kT 3 - - (11) - (I + KC,)^ * h ' fTe v = where f* a.nd fa,' are the partition €unctions for the activated complex and for the adsorbed pair of molecules. Expressing the K and K' in the numerator using eqn. ( 2 ) and (4) gives I t is seen that the rate is always proportional to c,' (provided that the condition Kc, ,> K'c,' holds), but that when c , is increased the rate at first increases linearly, later goes through a maximum, and finally decreases.The maximum rate corresponds to c , = I / K , and is equal toKEITH J. LAIDLER 5 1 The activation energy of the reaction increases with increasing con- centration of A owing to the positive heat of adsorption of A, i.e. to the fact that K varies with temperature as eelkT, where E is positive. At low concentrations of A, when I 9 Kc,, it is seen from eqn. (12) that the activation energy at the absolute zero * is - E - E' ; at the maximum eqn. (14) shows it to be e0 - E', while at high concentrations it is eo+ E - E'. Eqn. (12) also predicts that the activation energy will decrease with increasing temperature, owing to the decrease in the importance of Kc, compared with unity in the denominator. In view of these variations the importance of measuring activation energies under well-defined conditions is obvious ; unfortunately this has not always been done.Interaction Between an Adsorbed Molecule A and a Gaseous Molecule B (Mechanism (2)) .-The concentration of adsorbed A is given by eqn. (I), and the rate of reaction with a gaseous B molecule is therefore given by kT f+ e--rAlkT v = cg'ca . - - h . F v Y a The rate now varies with thq concentration of A in a different manner, increasing linearly at first and finally reaching a constant value. The activation energy is ci - E at low concentrations of A and EI, at high ones. Interaction Between an Adsorbed Molecule of B and a Gaseous Molecule of A (Mechanism (3)).-The rate is now given by This mechanism predicts the same type of variation of the rate and activation energy with the concentration of A as does mechanism ( 2 ) .Comparison of the Mechanisms .-An interesting feature of the treatments given above is that a t low concentrations of A all three mechanisms correspond t o approximately the same frequency factor. Moreover, in the region of the maximum rate mechanism ( I ) predicts the same frequency factor as is given by mechanisms ( 2 ) and ( 3 ) at high concentrations of A, when the rate is no longer dependent upon the pressure of A. This conclusion could hardly have been reached without the detailed treatment, and indeed other conclusions have been arrived at on intuitive grounds. Thus Beeck l2 implies that the low experimental frequency factor for the ethylene-hydrogen reaction is in favour of mechanism (3), the argument being that since the surface is sparsely covered with hydrogen only a small fraction of the sufficiently energetic collisions of -ethylene molecules will be effective.The reason that this argument is not valid is that the concentration of adsorbed hydrogen varies with the temperature, so that the effect appears in the activation energy and not in the frequency factor. We shall see later that the low frequency factor is due to the loss of translational and rotational freedom in forming the adsorbed activated complex. The same assumption as * This differs slightly from the value a t experimental temperatures owing t o the temperature dependence of kT/h and the partition functions.5 2 THE ACTIVATED COMPLEX IN CATALYSIS Beeck’s is also implicit in Eley’s discussion l3 of the factors determining whether a reaction will proceed by a Langmuir-Hinshelwood or by a Rideal mechanism.Since the frequency factors are the same the question must be deter- mined by the relative activation energies for the three possible mechanisms. In general this factor will favour mechanism (I), since adsorbed mole- cules are more reactive than gaseous ones. Mechanisms ( 2 ) and ( 3 ) may, however, involve lower activation energies than mechanism (I) if the product of the reaction is strongly adsorbed on the surface, so that a considerable energy of activation is required for its removal. This would seem to be the only factor which will cause a reaction to proceed by mechanism ( 2 ) or ( 3 ) . This situation particularly arises when the product of reaction is a hydrogen molecule.Our general conclusion is therefore that the Langmuir-Hinshelwood mechanism is probably the general rule, and that the Rideal mechanism would seem to apply only when the reaction product is strongly adsorbed on the surface. The Reaction Between Hydrogen and Ethylene .-The hydrogen- ation of ethylene has been very thoroughly investigated, on a variety of surfaces, l4 and will now be discussed briefly in the light of the conclusions derived above. Ethylene is more strongly adsorbed than hydrogen on the surfaces employed, so that A = C,H, and B = H,. The product, ethane, is very weakly adsorbed, so that we should expect the reaction to proceed by the Langmuir-Hinshelwood mechanism (I).Support for this conclusion is provided by the fact that the rate decreases at high ethylene concentrations, a result that is predicted by mechanism (I) but not by mechanisms (2) and (3). That the reaction is frequently stated to be of zero order with respect to ethylene is probably due to the fact that the measurements were made in the neighbourhood of the maximum. ’ We may now consider whether the frequency factor predicted by mechanism ( I ) at the maximum rate is consistent with the experimental data. Beeck l 2 has found on nickel a steric factor of - I O - ~ , - this is the ratio of the rate to the number of ethylene molecules striking the surface with the required energy of activation. According to eqn. (14) the frequency factor at the maximum is where w is the mass of the ethylene molecule and b , is the rotational and vibrational contribution to the partition function.The frequency factor for striking the surface is l5 kT I B - -h (2nrnkT)lle a h The steric iactor for the reaction is therefore l3 Eley, Advamxs in Catalysis (Academic Press, New York, 1948), Vol. I, l4 For full references see Eley.13 l5 Laidler, J . Physic. Chem., 1949, 53, 712. p. 157 : Quart. Rev., 1949, 3, 209.KEITH J. LAIDLER 53 For ethylene at 300' K, (zrmkT)/h2 is 2.6 x 10" and b , is 2.2 x 1 0 3 ; with s = 4 and L = 5 x 1014 the steric factor is found to be BJB, = 0.9 x 10-6, . - (25) in excellent agreement with the experimental value of - 10-6. This low steric factor is seen to be due to the loss of translational and rotational freedom in forming the activated complex, and there is no need to assume that only a fraction of the surface is active.Certain arguments have been invoked by Beeck l 2 in favour of mechan- ism (3). His thermochemical objection to mechanism ( I ) , the main argu- ment, has been answered by Eley,13 while the point with regard to the frequency factor is covered above. Our conclusion is therefore that mechanism (I) is entirely consistent with all the data that have been recorded, and that the evidence favours it strongly in comparison with mechanisms (2) and (3). Reactions Catalyzed by Enzymes.-The above considerations have direct application to the kinetics of enzyme-catalyzed reactions, which may now be considered very briefly. Enzymes are in some ways easier to treat than inorganic surfaces, since the sites at which adsorption can occur are more clearly defined, a fact that can be inferred from the very high specificity. Enzymes can be divided into two classes, according to whether they have one or two different types of surface sites which are concerned in reaction.The former comprises many of the protolytic enzymes, the latter all of the hydrogenases, in which one site interacts with the substrate and the other with the coenzyme. We have else- where l 6 formulated the kinetic laws applicable to the two-site systems, and will here only indicate the analogies between them and the surface reactions considered above. One example is the reaction : lactic acid + coenzyme I --f pyruvic acid + reduced coenzyme I, which is catalyzed by the apoenzyme of lactic dehydrogenase ; we have recently studied this reaction experimentally from the present stand- p0int.l' The rate is found to increase at first linearly with increasing concentrations of lactic acid and of coenzyme. At higher concentrations of lactic acid the rate reaches a constant limiting value, while at higher concentrations of coenzyme the rate passes through a minimum and then diminishes.This may be interpreted by a mechanism which is similar to mechanism ( I ) for the hydrogenation of ethylene. For reaction to occur it is supposed that a lactic acid molecule must be adsorbed on a site of type I, and a coenzyme molecule on a site of type 2 . The in- hibition at high coenzyme concentrations must be due to the fact that a coenzyme molecule can also be attached to a site of type I, replacing a lactic acid molecule. However, lactic acid presumably cannot displace a coenzyme molecule on site 2 , since there is no inhibition at high lactic acid concentrations. A somewhat similar situation appears to exist in the urease-catalyzed hydrolysis of urea, the rate of which passes through a maximum as the urea concentration is increased. Here it is supposed that for reaction to occur a urea molecule must be adsorbed on one type of site and a water molecule on the second type ; urea may, however, exclude the water by becoming adsorbed on a site of type 2 . A similar situation exists in the decomposition of hydrogen peroxide catalyzed by catalase, a reaction that is also inhibited at high substrate concentrations ; presumably two sites are again involved, although a detailed mechanism has not been worked out. When there is no such inhibition, as with the majority of 16 Laidler and Socquet, J . Physic. Chem. (in press). 17 Socquet and Laidler, Arch. Bzochem. 1g50,25, 171. 18 Laidler and Hoare, J . Amer. Chern. Soc., 1949, 71, 2699.54 THE ROLE OF HETEROGENEITY protolytic enzymes, it may be supposed that it is not necessary for the water t o be attached to a site on the enzyme, so that here the situation resembles mechanisms ( 2 ) and (3). Department of Chemistry, The Catholic University of America, Washington, D.C., U.S.A.