Aug., 1956
THEPOWER RATELAWIN HETEROGENEOUS CATALYSIS
1033
POWER RATE LAW I N HETEROGENEOUS CATALYSIS BYTAKAO KWAN~ Frick Chemical Laboratory, Princeton University, Princeton, New Jersey Received December I Y , 1966
It is emphasized that a number of chemisorption data can suitably be represented by a power rate law and the Freundlich type of chemisorption isotherm. The formulation of heterogeneous kinetics is developed on this basis with reference to some fundamental heterogeneous reactions such as ammonia synthesis, water gas shift parahydrogen conversion, etc. The conformity with experimental kinetics is attained generally in a simple way. An added feature is that kinetic constants can be calculated from chemisorption data.
Introduction The formulation of heterogeneous kinetics has been achieved in many cases by use of the Langmuir-Hinshelwood treatment.2 This treatment is essentially based on an ideal picture as if a homogeneous reaction occurs on an energetically u n i f o r m surface. Numerous experimental data on chemisorption rates and equilibria, notably by H. S. Taylor and his school, however, indicate that surfaces are probably not uniform; the heat of chemisorption decreases and the activation energy for chemisorption increases with increasing coverage. Thus, Temkin and Pyzhev3 advanced an adsorption rate expression, given in the second line of Table I, based on the assumption that the heat of chemisorption and the activation energy are linear functions of surface coverage. If chemisorption and desorption are rate-determining steps of a surface reaction, this expression represents fairly satisfactorily the reaction kinetics as in ammonia synthesis. As pointed out by Temkin and Pyzhev and by Brunauer, et u Z . , ~ the Temkin-Pyzhev equation is valid only for a middle range of coverage. Furthermore it fails to account for certain chemisorption rate data, e.g., for the adsorption of hydrogen on zinc oxide.6 Thus, de Bruijna introduced a factor t o take into consideration the inhomogeneous nature of the surface, arriving a t the same expression as Temkin-Pyzhev’s with the exception of this factor. Boudart’ recalled that experimental kinetics in a restricted range of coverage can be fitted by both Langmuir and Freundlich functions equally well, and derived the kinetic law of ammonia synthesis on the basis of the Langmuir kinetics. On the other hand, reference should be made to the fact that a number of chemisorption rate data have been shown to obey the power rate law8 (see Table I). Moreover many experimental datag-’a have been found to be most suitably ex(1) 1954-1955 Fulbright/Smith-Mundt scholar, on leave of absence from Hokkaido Univ., Sapporo, Japan. (2) C. N. Hinshelwood, “Kinetics of Chemical Change,” Oxford Univ. Press, London, 1940, p. 218. (3) M. Temkin and V. Pyzhev, Acta Physicochim. 12, 327 (1940). (4) S. Brunauer, K. S. Love and R. G. Keenan, J . Am. Chem. Soc., 64,751 (1942). (5) H.8. Taylor and D. V. Sickman, ibid., 64,602 (1936). (6) H.de Bruijn, Faraday Soc. Disc., 8 , 69 (1950). (7)M.Boudart, Ind. Chim. BeEge, 19, 489 (1953). (8) T.Kwan, J . Res. Inal. Catalysis. 8 , 16 (1953). (9) W.G.Franksnburg, J . Am. Chem. Soc., 66,1827(9144); (b) R. T. Davis, ibid., 68, 1395 (1946). (IO) E. Crerner, 2. Eleklrochem., 5 6 , 439 (1952). (11) B. M.W. Trapnell. Proc. Roy. Soc. (London),!206A,39 (1951). (12)G.C. A. Schuit, Rec. Irau. chin., 72, 909 (1953). (13) T.ICwan, J . Res. Inst. Catalusis. 9,109 (1955),
pressed by the Freundlich equation over a very wide range of pressure. So it seems justified to develop the kinetics of heterogeneous reactions on the basis of the power rate law and the corresponding Freundlich isotherm equation. Power Rate Law.-Some basic characteristics of the power rate law will be reviewed here in order to prepare the ground for its application to reaction kinetics. This law was originally deduced to fit the rate of chemisorption of nitrogen on a promoted iron catalyst, and was expressed as
- -ddtp = kp0-u - k’$S
(1)
where k , a,k’ and 6 are constants except for a low coverage. At equilibrium, it gives the Freundlich equation in the form h e = - 1I n P-
+
n
Pa
where n = a p and pa = k’/k. It shows that when p reaches pa, 0 becomes unity. I n the case of the nitrogen-iron catalyst system, pa was found to be approximately independent of temperature; in other words, all isotherms in the log-log plot have a common intersection if extrapolated linearly to higher equilibrium pressures. A similar trend has been shown in other gas-solid system^.^-'^ The validity of the power rate law may be examined by evaluating - dp/dt graphically from the chemisorption rate curve in the plot of p vs. time, and plotting log (-l/p (dp/dt)/l - (p,/p)) vs. log 0. Here,. p , is the pressure of gas which would be in equilibriuni with chemisorbed amounts at time t, and is obtainable from the isotherm. If the reverse rate is negligible, Le., pe
