SOLID CATALYSTS and
REACTION RATES
General Principles
Based on the theory of activated adsorption, general rate equations are developed for chemical reactions ~ataly5edby solids. Cbnsideration is given to the differences in equation forms resulting from control of the rate by different types of activated s t e p . Quantitative expressions are proposed for the effects of adsorption, catulyst activity, particle &e, porosity, j b w conditions,poisons, anddiluents as well as temperature, pressure, and concentration. Experimental procedures for the evaluation of the constants of the equations are discussed. A general method is outlined for integration of rate equations in the design of commercial reactors.
0. A. Hougen and K . M . Watson UNNERSITY OF VISCONSLN, MADISON, VIS.
5 A BASIS for the development of rata equations, it is poetulated that when catalyzed by a solid, a liquidor gasphase chemical reaction actnaUy occurs on the
A
surface of the catalyst and involves the reaction of moleculea or atoms wbich are adsorbed by activation on the active centern of the surface. From this viewpoint the catalyst incthe rate of reaction through ita ability to adsorb the reedsnts in such a form that the activation energy necesssry for reaction is reduced far below ita value in the uncatalyd reaction. Theee principles are extensively diseuaeed in the periodical literature and in theoretical treatises on catalytic rate phenomena (4, 7). The purpose of this paper is to d e velop from theae principles equations which may be applied to the interpretation and extension of rate data and to point out expebental procedures best adapted to the complete evaluation of such equations from a minimum of data. Methods am slso developed for the u8e of such equations in the d& of industrial reactors. In order that a reactant in the main fluid phase may be converted catalytically to 8 prcduct in the main fluid phase, it is nBee8BBIy that the reactant be trsn%ferreerredfmm its psition in the fluid to the catalytic interface, be activatdy adsorbed on the surface, and undergo reaction to form the adsorbed prcduct. The prcduct must then be desorbed and transferred from the interface to a psition in the fluid phase. The rate at wbich each of these Bteps occm Muencea the &bution of concentrations in the system and plays a part in determining the over-all rate. Because of the differencea in the mechanisms involved, it is convenient to claasify these steps 88 follows when dealing with cstalynb in the form of prow particlea: 1. "he mssa transfsr of reactsnts and products to and from the gross m o r d a c e of the catalyst particle and the main hodv of the ttuid. 2: The di5u8iond and tiOw transfer of rsaotants and, pmducta in and out of the pore structnre of the aataljat partide when reaction tat- place at interior interfaces.
MSY. 1943
3. The d v a t e d adsorption of reactants and activated d e
wrption of pmducta at tb catslyti0 interface. 4. The nvface reaotion of adsoresotants to
vation-adsorbed products.
form acti-
It is evident that the rate of these four types of operations are d-dent on widely different factors in addition to the concentrations or concentration gradients involved. Type 1 is determined by the flow characteristics of the system, such
w the m m velocity of the fluid stream, the size of the particles, and the diiTwiona1 charactmktics of the fluid., Type 2 is determined by degree of porcaity of the catalyst, the dimensions of the pores, the extent to which they are interconnected, the size of the particlea, the diffusional chsrsct8riatics of the system, and the rate at which the reaction 00. curs at the interface. Type 3 is detmnined by the charscter and extent of the catalytic swfaca, and by the p i 6 c activation energiea required for the adsorption and dmrption of each of the components of the fluid. Tspe 4 is determind by the nature and extent of the catalytic surface and by the activation energies required for the resotion on the surface. The relative importance cf these four operations in determining the over-all rate variea widely. Type 1 is important only when dealing with rapid reactions or where flow conditions are unfavorable. Since the rate of this operation is little dected by temperature, its relative imprtance tends to vary for a particular system; it is frequently negligible at low and highly important at bigb temperatures. Type 2 is frequently negligible for catsl@a of low activity in small particles with large interconnected pores, and ceaeea to be a faator for nonpmus catalysts having no internal surface. However, in the general ease of an active catalyst in mcderably large particles having large internal surfaces with restricted capillarity it may be of major importance. Operations of types 3 and 4 are chemical phenomena generaUy involving relatively large activation energies and a~ therefom highly d t i v e to tamperatnm. The actual chemical transformations frequently p m d by m r a l mi-
INDUSTRIAL A N D ENQINIIERINQ CHEMISTRY
&ve stspas, each with ita own characteristic rate. This is particularly true where aeveral molecules are involved. Gince chemical rates vary over wide ranges,it is improbable that the rates of any two step of typea 3 and 4 w i l l be of equal order in any given system. For this m m n in msny CBBBB it is permissible to consider only the Slowest single Btep of types 3 and 4 and wume that equilibrium is maintained in dl other steps of these types. Under such conditions the eloweat activated step may be termed the “rat4eontmllinp step”, and the o d rata is determined by consideration of it in combination witb the physical steps of types 1and 2.
(3)
If component A is in admixture with other components B, R,S, and I which are aka adsorbed on active centera of the name type, rate and equilibrium equations similar to 1,2,and 3 may he mitten for each component. Then, 01 L - (CA + CB + CB + C8 G I . . .) (4)
+
At equilibrium conditions each of the adsorbate concentration terms in Ekption 4 may be replaced by an e x p e o n similar to that obtained by solving Equation 3 for or:
ACTIVATED A D S O P m O N
Activated adsorption, 88 differentiated from ordinary van der Wade adsorption and capillary condensation, ia a highly speoisc reaction betwean the adsorbate and the surface, and the aharacteristica of a reversible chemical reaction. Bince this concept wan introduced by Taylor in 1930, much attention has been devoted to it in the Literature, recently BummsriBed by Taylor (71, Emmatt (71, and Ghatone, Laidk,and Eyring (4). It may be m e d that a unit area of catalytic surface contains L‘ active centers on which activated adsorption can take place and that all of these centera behave similsrly. Frequently the active centers are not uniform, and 88 adsorp tion proceeds, the remaining centem are pmgreaaivfy active; the rmulta rn an increase in energy of &vatton and a decrease in heat of adsorption. In the p m n t dip d o n the energy of activated adsorption will be aesumed the m e for all spate,or an average value will be aesumed to represent the entire d a c e . The rate of h r p t i o n of a component, A, from a fluid in contact with the surface is then proportional to ita activiityc.g in the fluid at the inkdace and to the conmtration 4 of vacant active centera per unit area of surface. A surface concentration of e: adsorbed A molecules per unit area will result. In the development of rate equationsfor application to i n d w trial pmcesees, it ie convenient to expm rates r in moles per unit time per unit msaa of catalyst at uniform conditions. The total volume occupied by the catalyst particles, including intemticeu between particles; is dated to the maen of the catalyst by the bulk density, f i , 88 contrasted to the deasity of the individual peUeta, p,, and the true density of the catalytic =Lid pc. Similarly, it is convenient to expm surface concentrations in moles per unit mass of aatalpt. Thus, if A is the catalytic area per unit m m ,
+
L = AL’IN.
-
marimum molal sdso on capedts per nnun of c a ~ v s tsiZ?om m o M e r m
Expmsing the rate of adsorptton, r, in moles per wit time per unit msaa of catalyat: I
-
kAclArCl
.
(1)
Since activated adsorption is a reversible phenomenon, Oomponent A is slso deeorbed from the Burface at a rate proportionst to the concentration of adsorted moleculea,on the surface. Thus the rate of desorption is e x p d by: r
-
kioA
(a)
When adsorption equilibrium is reached, the rates of adSorption and deeorption become equal. Equating (1) and (21, kAaA
