J O U R N A L
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PHYSICAL CHEMISTRY Registered in U.S. Patent Office @ Copyright, 1973, by the American Chemical Society ~~
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VOLUME 77, NUMBER 13 JUNE 21, 1973
Mechanistic Structure of the Water-Gas Shift Reaction in the Vicinity of Chemical Equilibrium Shoichi Oki Department of Chemistry, Utsunomiya University, Utsunomiya, Tochigi, Japan
and Reiji Mezaki* Department of Chemicai Engineering, New Vork University, Bronx, New Vork 10453 (Received October 26, 1972)
The mechanistic study of the water-gas shift reaction over an iron oxide catalyst was made utilizing the isotopic exchange reaction of oxygen-18. Reaction temperatures ranged from 400 to 450" and the total pressure of the reaction system was 80 mm. The forward and backward rates of the rate-determining steps of the reaction, that is, CO s CO (a) (step i) and 2H (a) ~t Hz (step v) were computed and compared. The comparison indicated that the order of magnitude of the forward rate of step i is comparable with that of the forward rate of step v and that in the early stage of the reaction, step v would govern the overall rate, whereas step i becomes the governing step as the reaction progresses to approach the chemical equilibrium. The results are in good agreement with those of earlier investigations.
Introduction The mechanistic study of the water-gas shift reaction has been greatly advanced by the use of isotopic t r a c e r ~ . l - ~ In the study the stoichiometric number concept introduced by Horiuti6 has been intensively used for the determination of rate-controlling step or steps in various reaction mechanisms proposed. Recently Oki and Kanekol-5 have employeld three different isotopic tracers including deuterium, carbon-14, and oxygen-18 to obtain more definitive conclusions concerning rate-controlling steps as well as reaction mechanisms of the water-gas shift reaction over a n iron oxide catalyst. Their experimental results indicated that reaction mechanisms I and I1 are most plausible and that steps i and v of these mechanisms appear to be rate controlling. Mechanism
I
Mechanism 11
More recently Mezaki and Oki7 reanalyzed the rate data gathered in the e ~ p e r i m e n t with ~ , ~ oxygen-18 and found that for the experimental conditions employed the nature of the rate-controlling step slowly changes from step v dominance to steps i and v dominance as the experimental conditions approach chemical equilibrium. In this investigation only the ratio of the forward and backward rates of step i were computed for various experimental conditions to find the relative importance of step i to the overall reaction. It was not yet known how the forward and backward rates of steps i and v change as the reaction conditions approach chemical equilibrium. The present study thus aims to calculate the forward and backward rates of steps i and v employing experimental data obtained with oxygen-18 and to examine whether these rates decrease or increase with change in experimental conditions, in particular with decrease in the overall Y. Kaneko and S. Oki, J. Res. Inst. Catal., Hokkaido Univ., 13, 55 (1965). Y. Kaneko and S . Oki, J. Res. Inst. Catal., Hokkaido Univ., 13, 169 (1965). Y. Kaneko and S. Oki, J. Res. Inst. Catal., Hokkaido Univ., 15, 185 (1967). S. Oki, Y. Kaneko, Y . Arai, and M. Shimada, Shokubai, 11, 184 (1969). S. Oki, J. Happel, M. A. Hnatow, and Y . Kaneko, Proc. int. Congr. Catal., 5th, 7972, in press. J . Horiuti and M. Ikushima, Proc. Imp. Acad. Jap., 15, 39 (1939). R. Mezaki and S . Oki, J. Catai., in press.
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Shoichi Oki and Reiji Mezaki
rate of the water-gas shift reaction. It was hoped that the above investigation would provide a much clearer insight into the change of rate-controlling step or steps of the reaction if that change occurs when the reaction conditions pass from one extreme to another.
Mathematical Analysis In this section we developed mathematical expressions by which the forward and backward rates of oxygen paths of mechanisms I and I1 are calculated. The overall reaction of the water-gas shift reaction is given by the equation
+
* +
CO HZO CO, H2 (1) Consider a closed circulating reaction system in which a gaseous mixture consisting of carbon monoxide, water vapor, carbon dioxide, and hydrogen is circulating through a n iron oxide catalyst bed. When mechanism I is assumed, the following relationships exist for the oxygen paths i, ii, iii, and iv of mechanism I.
Hence eq 9 reduces to (11) The overall reaction rate Vof eq 11can be obtained from V = -dnCo/dt
(12)
Combination of eq 2,11, and 12 gives
For the direct use of experimental data the following equation may be more advantageously employed
where pco denotes the partial pressure of carbon monoxide in the system. The overall net reaction rate V is also given in terms of U + i and u - i , that is V = -dpco/dt
= u+i
-
u-i
(15)
Note that eq 14 and 15 may be solved simultaneously to give the values of u t i and u - i for various experimental conditions. When steps i and v are rate controlling, the chemical affinity of the water-gas shift reaction, -AG, may be expressed by the following relationships where U * i denotes the forward and backward rates of step i and ni is the number of moles of the i component in the reaction system. Note that Zi is the atomic fraction of oxygen-18 in i component and that Z i ( a ) is the atomic fraction of oxygen-18 in the i species adsorbed on the catalyst surface. Solving for ZC0ia) and Z C O ~in( eq ~ , 2 and 6, respectively, and substituting the resulting solutions in eq 3, we obtain
For a n oxygen exchange path which includes steps i, iii, and iv, we define . ... . v = V+l,lll,lV - v-i,iii,iv (8) where V denotes the overall rate of the water-gas shift reaction and V+iJiiJv and V- i,iii& are, respectively, the forward and the backward rate of the oxygen exchange path. Using Csuha's definitions8 of V+iJiiJv and V-iJiJV and combining eq 7 and 8, we get
A detailed derivation of eq 9 is presented elsewhere.5 The results of the earlier investigations425 which were obtained under exactly the same reaction conditions as those employed in this work showed that the forward and backward rates of steps ii, iii, and iv are extremely high compared to those of steps i and v. On this ground it is assumed that the following relationship also holds for our case, that is The Journalof Physical Chemistry, Vol. 77, No. 13, 7973
and
A G = R T ( In
(2)+
In
(z)}
(17)
in which K , is the thermodynamic equilibrium constant of the reaction, T is the reaction temperature, and pi is the partial pressure of gaseous component i. Thus the ~ u-" can be readily obtained if those of values of u + and u + I and u - i are available.
Experimental Section Heavy water containing 10.9% lSO was purchased from the Research and Development Ltd., Rehovoth, Israel, and was used without further purification. Carbon monoxide was prepared by dehydration of formic acid and purified by passing it through a liquid nitrogen trap. Carbon dioxide was formed by decomposition of sodium bicarbonate and purified by vacuum distillation. Hydrogen gas was supplied by Takayama Shoji Co. For purification the hydrogen gas was passed through a silica gel column, a liquid nitrogen trap, a palladium thimble which was kept at 380", and a liquid nitrogen trap. All the gases fed into the reaction system were analyzed by a mass spectrometer and the analysis indicated that the concentrations of all the gases were higher than99.9970. An iron oxide catalyst was donated by Mitsubishi Kasei Co., Ltd. The catalyst was crushed and screened to about 12 mesh. The amount of the catalyst used was 0.5 g. On pretreatment of the catalyst iron oxide in the form of Fez03 was reduced to Fe30c. Prior to the experiments, the catalyst was bathed with a gaseous mixture of carbon (8) R. S. Csuha and J. Happel, A/Ch€ J., 17, 927 (1971)
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Mechanistic Structure of the Water-Gas Shift Reaction monoxide, water vapor containing oxygen-18, hydrogen, and carbon dioxide, for approximately 100 hr a t 500". After each experiment, the reaction system was evacuated a t the temperature of that experiment. The reaction temperature ranged from 400 to 450". For all experiments the feed contained carbon monoxide, water vapor, carbon dioxide, and hydrogen. The partial pressures of these component gases were varied widely. In absence of the catalyst ? series of experiments was made by employing the same experimental conditions as those used for experiments in the presence of the catalyst. Results of these blank experiments showed that no oxygen exchange nor water-gas shift reaction occurred to any measurable extent. Thus it was established that all measurable conversions of these reactions were due to the iron oxide catalyst. A detailed description of the experimental apparatus and the procedure utilized in this study was presented elsewhere.2 A closed-recycling type reactor was used. The entire apparatus was made of Pyrex glass because our experiments showed that oxygen exchange between the wall of apparatus and oxygen-containing gases was minimized when Pyrex glass was utilized. Gas samples were drawn into gas sampling bulbs a t specified time intervals, The atomic fractions of oxygen-18 in carbon monoxide and carbon dioxide were determined by a Hitachi mass spectrometer, RMS-3B type, with a constant electron accelerating voltage of 80 V. Preliminary experiments were performed to determine the effect of gas flow rate on reaction rate. Using 0.5 g of the iron oxide catalyst, the reaction rates were measured for various flow rates of gas mixture a t temperatures between 400 and 450" and a t a total pressure of 80 mm. The mixture initially contained equal portions of carbon monoxide, carbon dioxide, hydrogen, and water vapor. The result of these preliminary experiments indicated that mass flow rates greater than 1.5 g/min g of catalyst had no appreciable effect on the reaction rate. Consequently, this flow rate was employed in the present study. By using the method of Yang and Hougeng we calculated the partial pressure drops of the reactants and the products between the gas stream and exterior surface of the catalyst particle for the highest possible reaction rate. It was determined that the drops do not exceed 0.2% of their ambient values. Concerning diffusion inside the catalyst, calculationdo showed that the value of the ,effectiveness factor was essentially unity even a t the highest reaction rate. In light of these experimental and computational results it was considered that the gaseous diffusion inside and outside the catalyst has no effect on the reaction rate for the experimental conditions of this study.
Results Table slhows the experimental data used for the computation of the forward and backward rates of step i, step v, and the rate of the overall reaction. These rates were calculated by a procedure detailed in a previous section. Figure 1 presents, as an example, the rates of run 1. Similar results were obtained for other sets of experimental data. As can be seen from the figure, the forward and backward rates of step i decrease rather monotonously and the difference of these two rates, that is, the net overall rate diminishes continuously as the reaction conditions approach the chemical equilibrium. Whereas the forward and backward rates of step v seem to increase as the
0
50
0
50
100
150
100
I50
time o f r e a c t i o n ( m i n )
Figure 1. The forward and backward ( r u n 1, reaction temperature 400').
rates of step i and step v
water-gas shift reaction proceeds. The difference of these two rates of step v is also reduced steadily, indicating that the rate of increase of the backward rate of step v is higher compared to that of the forward rate. This difference, needless to say, ultimately vanishes when the reaction reaches chemical equilibrium. It should be noted that the forward rate of step v goes through the minimum value to approach equilibrium conditions. In Figure 2 the forward reaction rates of run 1 are compared. The comparison indicates that at the beginning of the reaction the forward rate of step i is higher than that of step v. As the reaction progresses toward equilibrium, however, the magnitudes of these rates were reversed. Figure 3 shows relationships between the forward rates of step i and the partial pressure of carbon monoxide for various reaction temperatures. In Figure 4 the dependence of the forward rate of step v on the partial pressures of water vapor is presented. We examine these figures more fully in Discussion section.
Discussion It can be seen from Table I that for all the runs ZCOincreases gradually with reaction time elapsed, whereas the maximum Zco2 occurs within the first 30 min of reaction time. This experimental result may provide evidence to support the adequacy of reaction mechanisms of the K. H. Yang and 0. A. Hougen, Chem. Eng. Progr., 4 6 , 1 4 6 (1950). C. N. Satterfield, "Mass Transfer in Heterogeneous Catalysis," M.I.T. Press, Cambridge, Mass., 1970. Table I will appear following these pages in the microfilm edition of this volume of the journal. Single copies may be obtained from the Business Operations Office, Books and Journals Division, American Chemicai Society, 1155 Sixteenth St., N.W., Washington, D. C. 20036. Remit check or money order for $3.00 for photocopy or S2.00 for microfiche, referring to code number JPC-73-1601 The Journal of Physicai Chemistry. Voi. 77, No. 73, 7973
Shoichi Oki and Reiji Mezaki
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150
100
50
0
time o f r e a c t i o n ( m i n )
Figure 2. A comparison of the forward rates of step i , step v, and the overall reaction ( r u n 1, reaction temperature 400").
-
30.
. c E
I m
E *-
E
3 at 440'C
2 20'
N
st
2 a t 420'C
,
I a t 400'C
"
io
5
20
15
Pco ( m m H g )
Figure 3. Relationships between the forward rates of step i and the partial pressures of carbon monoxide.
+
R u n 2 a t 420'C
Run I 0 1 400'C
5
io
15
20
(mmHg)
Figure 4. Relationships between the forward rates of step v and the partial pressures of water vapor. The Journal of Physical Chemistry, Vol. 77,
No. 13, 7973
water-gas shift reaction, which were proposed in an earlier section of this article. That is, water vapor containing oxygen-18 is readily transferred into carbon dioxide because the rates of steps ii, iii, and iv are quite high. During this period of reaction Zcoz increases sharply with reaction time. The accumulation of oxygen-18 in the carbon dioxide increases the reverse transfer rates of oxygen18 uia steps i-iv. In particular, a noticeable amount of oxygen-18 is transferred to carbon monoxide by way of step i, the rate of which is considered to be low in the forementioned mechanisms. This balance between the forward and reverse transfer rates of oxygen-18 seems to explain the occurrence of the maximum Zcoz during the course of the reaction. It is evident from eq 13 and 14 that experimental measurements of Z C O and ZcoZ have a profound effect on the estimates of u + i , u-,, u + ~ ,and u - ~ .It is also evident from the derivation of eq 2-14 that the relationship of eq 14 is dependent upon the reaction mechanism of the reaction. In the case where the oxygen reaction occurs through a scheme or schemes other than those included in mechanism I or 11, the results obtained here would become equivocal. For this reason, a comprehensive study was made on isotopic oxygen exchange reaction which may possess significant bearing on the present investigation. Several investigators12J3 reported that the isotopic oxygen exchange occurs between oxygen in reactant gases and the lattice oxygen of the catalyst. In order to determine the extent of the isotopic oxygen exchange reaction, about 20 mm of water vapor which contained 10.9% of oxygen-18 was allowed to contact the iron oxide catalyst at temperatures between 400 and 450" to attain equilibrium of the exchange reaction. A similar experiment was made by using carbon dioxide containing oxygen-18. Note that the amount of oxygen-18 employed was the same as that used for the rate study. These experimental studies showed that the amount of oxygen of the iron oxide catalyst which was replaced with gaseous oxygen-18 was about oxygenatoms. In the rate study approximately 2 x 18 atoms were introduced to the reaction system. Assuming that carbon dioxide, carbon monoxide, and water vapor, respectively, exchange their oxygen-18 with the lattice oxygen atoms of the catalyst in proportion to the partial pressures of oxygen-18 carrying carbon dioxide, carbon monoxide, and water vapor, it was determined that the errors in ZcoZ and ZCo due to this isotopic oxygen exchange were less than 0.1% under the present experimental conditions. Temkinl4 and Glavachekls reported that a Rideal-Eley type mechanism can best describe the rate data of the water-gas shift reaction, obtained using an ironchromium catalyst. However, the results of previous investigationsl-5.7J6 with deuterium, oxygen-18, and carbon-14 entirely ruled out this reaction mechanism. It may also be conceivable that the isotopic oxygen exchange takes place by homogeneous reactions. A case of interest COZ g HzC03 equilibrium. The is represented by H2O compound H2CO3 exists only in the liquid phase. Thus it seems improbable that the compound is formed at temperatures as high as those employed in this investigation. (12) 0. V. Krylov, Z. A. Markova, I . I . Tret'yakov, and E. A. Fokina, Kinet. Katai., 6, 128 (1965). (13) C.Wagner,Advan. Catai., 21, (1970) (14) G. G. Shchibrya, N. M. Morozov, and M. I . Temkin, Kinef. Katal., 6, 1057 (1965). (15) V. Glavachek, M. Marek, and M. Korzhinkova, Kinef. Katai., 9, 1107 (1968). (16) S. Oki and R. Mezaki, J. Phy. Chem., 77, 447 (1973).
Mechanistic Structure of the Water-Gas Shift Reaction On the basis of the above discussion the experimental measurements of Zcoz and Zco shows reasonably accurate values of exchanged oxygen-18 by the operation of mechanism I or I1 during the course of the water-gas shift reaction. The foregoing results present various interesting features of the rate-determining steps of the water-gas shift reaction. First, as shown in Figure 2 , the order of magnitude of the forward rate of step i is comparable with that of the forward rate of step v. This is true even if the experimental conditions, in particular, the partial pressures of component gases, vary rather widely. The result would justify that of a n earlier mechanistic study5J6 in which Oki and coworkers proposed that both step i and step v are rate determining. Second, for the reaction conditions employed in this study (approximately equal portions of carbon monoxide, water vapor, carbon dioxide, and hydrogen were introduced in the closed reaction system) the rate of step i is higher than that of step v in the early stage of the reaction and the rate of step v increases rapidly, yielding a higher rate compared to t h e forward rate of step i as experimental conditions approach equilibrium. This implies that during the earlier stage of the reaction, in which the partial pressure of carbon monoxide is relatively high, step v would control the overall rate and that step i becomes governing as the reaction proceeds toward equilibrium. The result partially supports that of a more recent investigation,? in which Mezaki and Oki found that the rate-determining step of the water-gas shift reaction gradually changes from dominance of step v to dominance of step v and step i. In these earlier studies537 the rate-determining step or steps of the reaction were pinpointed from the free energy change associated with the individual elementary step or from the apparent stoichiometric number observed by the experiments. In the present study we computed the forward and backward rates of step i and step v to examine the relative contribution of each step to the overall rate. The calculation of the forward and backwards rates, obviously, provides a much clearer view for the change of rate-determining step, if it occurs. It must be pointed out that the infor>mation which has been accumulated so far concerning the rate-determining step of the water-gas shift reaction is quite consistent. For example, as can be seen from Figure 2 , there exists a set of experimental conditions wherein the forward rates of step i and step v coincide. For these particular conditions the free energy changes of step i and step v are equal (see ref 5 and 7 ) and, moreover, the apparent stoichiometric number observed should be 2 (see ref 5 and 7). At this point one may wonder in what manner the for-
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ward and backward rates attain equilibrium. Unfortunately the data gathered in the present study may not be sufficient to precisely predict the behavior of these rates in the immediate vicinity of equilibrium. However, the forward rate of step i would continuously decrease up to equilibrium, whereas the forward rate of step v would level off somewhere to reach the equilibrium point. As will be discussed below, the forward and backward rates of step i and step v depend strongly on the partial pressures of the gaseous components. Thus the above pattern of the forward and backward rates would completely change when different experimental conditions are used. From the reaction scheme presented in a preceding section, the forward and backward rates of step i and step v may be written as u + , = h+iPco(1
-
0)
(18)
where k + , and k - , are, respectively, the rate constants of the forward and backward rates of step s, O is the fraction of total active site occupied by gaseous species, and Oi is the fraction of active site occupied by species i. As shown in Figures 3 and 4 the linear relationships are not obtained for the forward rates of step i and step v. Furthermore, the calculated backward rate of step i decreases with increase in the partial pressure of carbon dioxide. In the light of these experimental findings, apparently the forward and backward rates of step i and step v cannot be described by simple Langmuir-type adsorption models. More elaborate models should be used for adequate representation of experimental data. Presumably the concentration of adsorbed gaseous species as well as the total concentration of empty adsorption sites undergo some change in the course of the reaction. It may be conceivable that the fraction of adsorption sites occupied by atomic hydrogen, OH, increases with increase in the hydrogen partial pressure to produce a more reduced state of the catalyst surface. Because of this state of the surface carbon monoxide molecules adsorbed on the surface may be competitively desorbed from the surface to decrease the backward rate of step i (see eq 19). Further experimentation is vitally needed to expore the true conditions of the catalyst surface and to analyze more rigorously the results obtained in this investigation. However, the above assumption about the surface would be sufficient to provide a qualitative explanation of our experimental results.
The Journal of Physical Chemistry, Vol. 77, No. 73, 1973
