95
CATALYSIS OVER SUPPORTED METALS
rather poor fit of the calculated and experimental chemical shift-concentration curves for the (CH3)20-BC13 and (CH3)2-0-BF3systems could also be explained on this basis. An additional experimental difficulty arising from the high volatillty of (CH3)20.BF3 in dichloro-
Catalysis over Supported Metals.
111.
methane would also affect the accuracy of the d-concentration plot. Acknowledgments. The financial assistance of the National Research Council and the Sational Cancer Institute of Canada are gratefully acknowledged.
Comparison of
Metals of Known Surface Area for Ethane Hydrogenolysis
by J. H. Sinfelt, W. F. Taylor, and D. J. C. Yates Process Research Division, Esso Research and Engineering Co., Linden, New Jersey
(Received J u n e 3, 1964)
The kinetics of hydrogenolysis of ethane to methane have been investigated over a series of silica-supported metal catalysts containing 10 wt. % metal. The metals studied were nickel, cobalt, platinum, and copper, the surface areas of the metals being determined by hydrogen chemisorption. Over the range of temperatures studied (175-385"), the specific catalytic activities of the nickel, cobalt, and platinum for ethane hydrogenolysis vary in the order: Ni > Co > Pt. The position of copper in this sequence is far below that of nickel or cobalt, but its position relative to platinum changes over the range 173-385'. The rate of hydrogenolysis was found to be essentially first order in ethane pressure and to decrease with increasing hydrogen pressure over all the metals. However, the magnitude of the hydrogen pressure effect varied markedly for the different metals, the effect being greatest for nickel and platinum and least for copper. Apparent activation energies ranged from a maximum of 54 kcal./mole for platinum to a minimum of 21 kcal./mole for copper.
I. Introduction Much of the fundamental work on catalysis over nietals has been done using evaporated metal films as catalysts. I n the classical work of Beeck and coworkers,' the catalytic activities of various metal films were determined for ethylene hydrogenation, and it was shown how the activities could be related to the lattice spacings. Boudart,2 and subsequently also Beeck,' showed how the activities could be equally well explained in terms of an electronic picture. I n any case, the activities of various metal films for ethylene hydrogenation were clearly established by the work of Beeck and co-workers. The activities of supported metals for ethylene
hydrogenation were studied by Schuit and van Reijen3 in an effort to determine whether the earlier findings of Beeck and co-workers with metal filins applied to supported metals. These workers reported data on a series of silica-supported metals arid concluded that the results were generally in agreement with the results obtained over metal films. In this work the authors used hydrogen chemisorption measurements to enable them to account for differences in the surface areas of the various metals. This type of study is extremely (1) 0. Beeck, Discussions Faraday SOC.,8 , 118 (1950) (2) M.Boudart, J . Am. Chem. SOC, 72, 1040 (1950) (3) G. C. A. Schuit and L. L. van Reijen, AdLan Catalysis, 10, 242 (1950).
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important to progress in understanding the catalytic properties of supported metals. In general, however, data on specific catalytic activity (rate per unit metal surface area) are nonexistent for supported metal catalysts. Consequently, comparisons of the catalytic activities of supported metals are very likely to be confused by differences in the metal surface areas. Investigations in which kinetic studies are combined with measurements of metal surface area are therefore highly desirable in elucidating the factors involved in catalysis over supported metals. Recently, we have been interested in the catalytic hydrogenolysis of ethane over supported metals of known surface area. The kinetics of the reaction have been studied previously by Taylor and co-workers4-6 over commercial iron and nickel catalysts. These studies esf ablished the main features of the kinetics, but were not intended to give a quantitative comparison of the specific activities of the metals. The nickel and iron catalysts used were different in form (supported us. unsupported), and data on metal surface areas were not available. More recently, studies on the hydrogenolysis of saturated hydrocarbons over evaporated metal films have been reported by Anderson and Baker.7 These investigators compared the specific activities of several different metal films (nickel, rhodium, tungsten, and platinum) and suggested that the rate-controlling step in the hydrogenolysis varied with the metal. However, the kinetics were not investigated in detail; e.g., data on reaction orders with respect to hydrogen and hydrocarbon were not reported. E'urt herniore, evaporated metal films are far less typical of real catalyst systems than a series of carefully prepared supported metals. Consequently, we have carried out an investigation of the kinetics of ethane hydrogenolysis over a series of supported metals, including nickel, cobalt, platinum, and copper. The catalysts were all prepared in the same way and contained 10 wt. % metal. Surface areas of the metals mere determined by hydrogen chemisorption. Extensive kinetic data, including orders of reaction with respect to ethane and hydrogen as well as apparent activation energies, were obtained over all the metals. 11. Experimental
Apparatus and Procedure. The apparatus used for the hydrogen chemisorption work was a conventional glass vacuum system with an 80 l./sec. oil diffusion pump. Using a trap cooled in liquid nitrogen, ultimate dyrianiic vacua of about torr were obtained. The sample cells were made of Pyrex glass and had two stopcocks to permit hydrogen to flow through the bed of material. T h e Journal of Physical Chemistry
Samples of each of the catalysts, weighing about 2 g., were put in a vacuum apparatus. After evacuation a t 100' for a short time, hydrogen was passed through the bed of the sample at a flow rate of 500 ~ n i . ~ / m i n The . temperature of the sample was then increased, in the flowing hydrogen, to 370'. This temperature was maintained overnight, and then the sample was evacuated for 1 hr. at the same temperature. After cooling to 1 8 O , a hydrogen isotherm was measured; usually three points up to a pressure of about 30 cm. were obtained. The amount adsorbed at a pressure of 10 cm. was taken as the monolayer point, and the metal surface areas were calculated 011 the basis that each nickel atom in the surface adsorbs one hydrogen atom and that each hydrogen atom occupies 6.5 .k.zof the surface.8 In the measurement of the hydrogen adsorption isotherms, the procedure adopted was to admit a known quantity of hydrogen to the adsorption cell and then wait for a period of about 1 hr. before reading the equilibrium pressure. The hydrogen adsorption isotherms for the various catalysts studied are plotted in Figure 1. The isotherms indicate that saturation is approached at hydrogen pressures above about 3 cm. and hence that the arbitrary choice of 10 cm. as the monolayer point is not unreasonable. lletal surface areas calculated from the isotherms are listed in Table
I. Table I : Summary of Metal Surface Areas of Catalysts as Determined by Ht Chemisorption Catalyst
Metal area, m.l/g.'
Xi-Si02 Co-Si02 Pt-Si02 Cu-Si02
13.6 5.6
4.4 3.3
Metal surface area per gram of catalyst after reduction with H? overnight at 370".
An idea of the rate of adsorption of hydrogen on the nickel catalyst can be obtained from Figure 2, which shows the decline in hydrogen pressure in the adsorption cell as a function of time. The data are plotted (4) K. Morikawa, W.
S.Benedict,
and H. S. Taylor, J . Am. Chem.
Soc., 58, 1795 (1936).
(5) C. Kemball and H. S. Taylor, ibid., 70, 345 (1948). (6) A. Cimino, 11.Boudart, and H. S. Taylor, J . P h y s . Chem., 58, 796 (1954). (7) J. R . Anderson and B. G. Baker, Proc. R o y . Soc. (London), A271, 402 (1963). (8) D. F. Klemperer and F. S. Stone, ibid., A243, 375 (1958)
CATALYSIS OVER SUPPORTED METALS
0
5
10
15
20
97
25
Pressure, cm.
Figure 1. Adsorption isotherms for Ht on the various silicasupported metals at 18”: 0 , Ni; ,. Co; A, Pt; 0, Cu.
0
20
40
60
80
100
120
1ime, min.
Figure 2. Pressure-time curve illustrating the rate of HI adsorption on the Ni on SiOncatalyst at room temperature: p = pressure a t any given time; p i = initial pressure.
as the ratio of the pressure, p , a t any given time to the initial pressure, pi. The rate of decline is negligible after about 1 hr. , indicating attainment of equilibrium. Complete pressure-tinie curves were not obtained for the other catalysts, but in the case of the cobalt and platinum catalysts, a t least, it was observed that the amount of adsorption after 1 hr. was negligible. Hence for nickel, cobalt, and platinum, the method of obtaining the hydrogen adsorption isotherms and the estimation of nietaI areas from the isotherms is reasonable. In the case of the copper catalyst, however, the use of hydrogen chemisorption to determine the metal surface area may be less reliable. A considerable amount of work on copper catalysts reported in the literature indicates that the adsorption of hydrogen is slow and not completed in times comparable to the 1 hr. used in obtaining the isotherms in the present work.9
Our experiments on the copper catalyst also gave an indication of this. Because of this complication, data obtained on the room temperature chemisorption of carbon monoxide over the copper catalyst are of interest. The adsorption in this case was found to be fast and essentially complete in about 15 min., and approached saturation at pressures below 10 cm. The ratio of the amount of carbon monoxide adsorbed a t 10 cm. to the amount of hydrogen adsorbed was found to be 1.4. However, determination of metal surface area from carbon monoxide adsorption involves the complication that carbon monoxide may be chemisorbed in two forms, the bridge form occupying two sites and the linear form occupying one site. If the carbon monoxide is assumed to be adsorbed entirely in the linear form, with a cross-sectional area of 9.3 A.z per molecule of carbon monoxide,lo the copper surface area agrees with that determined from the hydrogen adsorption data. If some of the carbon monoxide were adsorbed in the bridge form, the true copper surface area would be somewhat higher. In view of the fact that the hydrogen chemisorption method for estimating the surface area of the copper is not entirely free from objection, it could simply be fortuitous that the area obtained in this manner agrees even roughly with the carbon monoxide data. Nevertheless, the carbon monoxide adsorption data suggest that the surface area value reported in Table I is reasonable, although it is considered to be less reliable than the surface area values reported for the other supported metals in Table I. This is not a critical point, however, as the differences in the catalytic activities of the various nietals are such that the uncertainty in the copper area has little bearing on the comparison of the catalysts. The ethane hydrogenolysis data were obtained in a flow reactor system at atmospheric pressure, using a vertically mounted stainless steel reactor tube 1.0 cm. in diameter and 8.0 cni. in length. Details of the reactor assembly, flow rate measurements, and the gas chromatographic analysis of the reaction products have been reported previously. l 1 The ethane and hydrogen were mixed with helium and passed downflow through a bed containing 0.20 g. of catalyst diluted uniformly with 0.50 g. of ground Vycor glass. By appropriate adjustment of the helium flow rate, it was possible to vary the partial pressures of ethane and hydrogen individually. The total gas 00w was niain~~
~
(9) T. Kwan, Adean. Catalysis, 6 , 67 (1954). (10) B. M . W. Trapnell, ‘Chemisorption,” Butterworth and Co., Ltd., London, 1955,p . 183. (11) J. H.Sinfelt. J. Phys. Chem., 6 8 , 344 (1964)
Volume 69, .l‘limber 1
January 1965
98
J. H. SINFELT, W. F. TAYLOR, AND D. J. C. YATES
tained a t 1 l./min. throughout. In a typical run the The rate measurements on the hydrogenolysis of reactant gases were passed over the catalyst for 3 min. ethane to methane were made at low conversion levels prior to sampling products for analysis. The ethane (0.04 to 7.0%). Rates were calculated from the relawas then cut out and the hydrogen flow continued tion for 10 min. prior to another reaction period. As an 7J 1' insurance against possible complications due to r = @ x changing catalyst activity, most of the ieaction periods were bracketed by periods a t a standard set of where F represents the feed rate of ethane to the reconditions, so that the kinetic data could be expressed actor in moles per hour, W represents the weight in as rates relative to the rate a t the standard conditions. grams of the catalyst, and x represents the fraction of Detailed data illustrating the utility of this technique ethane converted to methane. The reaction rate r have been published previously.12 Prior to any reis thus expressed as moles of ethane converted to action rate measurements, the catalysts were reduced methane per hour per gram of catalyst. overnight in flowing hydrogen (50 cc./min.) a t 370' In a run to measure reaction rates the catalyst was in the reactor. first prereduced with hydrogen using the identical Materials. The supported metal catalysts investischedule of temperatures used in the hydrogen chemigated in this work all contained 10% by weight of metal sorption measurements. This was done to ensure that based on the combined weight of metal and support. the metal surface area of the freshly reduced catalysts The catalysts were prepared by impregnating silica would correspond exactly to that determined in the with solutions of salts of the metals in deionized water. hydrogen chemisorption measurements. Then the Aqueous solutions of Ni(N03)2.6H20,C O ( N O ~ ) ~ . ~ H ~temperature O, was lowered and at a standard set of hyand C U ( N O ~ 6Hz0 )~ were used for impregnating the drogen and ethane partial pressures ( p a = 0.20 atm., nickel , cobalt, and copper catalysts, respectively. The pE = 0.030 atm.), the rates were measured at a series platinum catalyst was prepared by impregnating the of temperatures in a rising temperature sequence. The silica with Pt(NH3)2(NOz)z, obtained from the Baker data for the four catalysts are shown in the Arrhenius Division of Englehard Industries, Newark, N. J. plots in Figure 3. The silica used as a support was Cabosil HS 5 (300 After determining the effect of temperature on rates, mS2/g.surface area), obtained from the Cabot Corp., the temperature was lowered to an intermediate value Boston, Mass. After impregnation, the catalysts were in the range studied, and a series of measurements was all dried overnight a t 105'. The dried catalysts were made to determine the effects of the partial pressures of pressed at 8000 p.s.i. into wafers which were subhydrogen, pH,and ethane, p E , on rates. As preliminary sequently crushed and screened to a size between 45 experiments had indicated that some variation of cataand 50 mesh. lyst activity could occur in an extended set of rate The ethane used in this work was obtained from measurements of this type, each reaction period was the Rlatheson Co. A chromatographic analysis showed bracketed by periods a t a standard set of conditions. no detectable impurities. It is estimated that an The rate r at any given set of conditions, relative to impurity, e.g., methane, would have been detected by the rate ro a t the standard conditions ( p H = 0.20 atm., the chromatographic analysis if it were present a t a pE = 0.030 atm.), is then given by the ratio r/ro. concentration above 0.01 wt. %. High purity hyThis procedure serves to minimize the effects of variadrogen was obtained from the Linde Co., Linden, tions in catalyst activity. Data on the effects of hyN. J. I t was further purified in a Deoxo unit condrogen and ethane partial pressures on r / r o are given in taining palladium catalyst to remove trace amounts Table 11. of oxygen. The water formed was then removed by a For all four catalysts the data in Table I1 show that trap cooled in Dry Ice or by a molecular sieve drier, the rate of ethane hydrogenolysis increases with inthe latter having been employed for the hydrogen used creasing ethane partial pressure, but decreases with in the kinetic measurements. increasing hydrogen partial pressure. The dependence of the rate on the partial pressures of ethane and hy111. Results drogen can be expressed in the form of a simple power The metal surface areas of the various catalysts, law, r = kpEnpHm. Approximate values of the expoas determined from the hydrogen chemisorption nents n and mas derived from the experimental data are measurements, are listed in Table I. There was approxiinately a fourfold variation in the surface areas (12) D.J. C. I'ates, W. F. Taylor, and J. H. Sinfelt. J . A m . Chem. of the different metals. Soc., 8 6 , 2996 (1964). The Journal of Phgsical Chemistry
CATALYSIS OVER SUPPORTED METALS
1
99
I
Table 11: Effect of C2Heand H2 Pressures on Rates of C2H6 Hydrogenolysis
'" Catalyst
Ni-Si02 (177')
Co-Si02 (219')
Pt-SiOa (357')
Cu-SiOa ( 330 O )
10-4
I
1.5
I
I
I
1.6
1.7
1.8
I
1.9 1/T ("K.)X 108.
I
1
I
2.0
2.1
2.2
Figure 3. Effect of temperature on the rate of ethane hydrogenolysis over silica-supported metal catalysts a t p~ = 0.030 atm. and p~ = 0.20 atm.: 0, Ni; . , Co; A, Pt; 0, Cu.
summarized in Table 111. Values of the apparent activation energy E and the pre-exponential factor r' in the equation, r = r' exp(-E/RT), expressing the temperature dependence of the rate r a t the standard conditions ( p H = 0.20 atm., p~ = 0.03 atm.) are also given in Table 111. The pre-exponential factors were calculated per cm.2 of the supported metal, using the measured values of the metal surface areas given in Table I. The general features of the kinetics of ethane hydrogenolysis over the catalysts employed in this study are in accord with the earlier studies of Taylor and cow o r k e r ~ , ~in- ~ which the kinetics were investigated over nickel and iron catalysts of unknown metal surface area. These workers showed that the kinetics could be explained satisfactorily in terms of a mechanism involving a preliminary dehydrogenation of the ethane to an unsaturated radical CzH, on the surface, followed by attack of the surface radical by hydrogen CZH6
Hz
CZH,
+ HZ
+ C2H, +CH, + CH, 5 CH,
(2)
(3)
PH, atm.
P E , atm.
rho0
0.10 0.20 0.40 0.20 0.20 0.20 0.10 0.20 0.40 0.20 0.20 0.20 0.10 0.20 0.40 0.20 0.20 0.20 0.10 0.20 0.40 0.20 0.20 0.20
0.030 0.030 0.030 0.010 0.030 0.100 0.030 0.030 0.030 0.010 0.030 0.100 0.030 0.030 0.030 0.010 0.030 0.100 0.030 0.030 0.030 0.010 0.030 0.100
4.03 1.00 0.14 0.37 1.00 3.91 1.69 1.00 0.52 0.35 1.00 3.51 4.25 1.00 0.13 0.31 1.00 2.39 1.46 1.00 0.79 0.38 1.00 3.42
Rate relative to the rate at standard conditions ( p =~ 0.20 atm., p~ = 0.030 atm.) for the particular catalyst and temperature in question.
where u is equal to (6 - 2)/2. On the assumption that the first step was an equilibrated one, and that the rate was limited by the rate of rupture of carboncarbon bonds by reaction of the surface species CzH, with Hz, a rate law was derived which could be put in the form
(4) From the experimental value of the exponent on ethane Table I11 : Summary of Kinetic Parameters for Ethane Hydrogenolysis over the Various Supported Metals Cats-
Temp range,
lyst
OC.
n"
mb
E'
177-219 219-259 344-385 283-330
1.0 1.0 0.9 1.0
-2.4 -0.8 -2.5 -0.4
40.6 29.9 54.1 21.4
Ni CO Pt CU
4 4.9 X 3.0 X 5 9 X 4.5 X
loa1 10" lo3' 10''
a Exponent on ethane pressure. Exponent on hydrogen pressure. Apparent activation energy, kcal./mole. Preexponential factor, molecules/sec./cm.2, in the equation, r = r' exp( - E / R T ) , expressing the temperature dependence of the rate r at the standard conditions ( p a = 0.20 atm., PE = 0.030 atm.).
Volunze 69,Number 1
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J. H. SINFELT,W. F. TAYLOR, AND D. J. C. YATES
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partial pressure n, the exponent (1 - na) on hydrogen pressure can be calculated for a given value of a and compared with the experimental value m. A simple and reasonable assumption is that a can have values of 1, 2, or 3 , corresponding to ethylene, acetylene, or acetylenic residues on the surface.6 A comparison of observed and calculated values of the exponent on hydrogen pressure, in which a values are chosen to give the best fit to the data, is given in Table IV.
Table IV: Comparison of Observed and Calculated Values of the Exponent on Hydrogen Pressure -Exponent
on pa-
Catalyst
a
Calcd.
Obsd.
Ni-Si02 Co-Si02 Pt-Si02 Cu-Si02
3 2 3
-2.0 -1.0
-2.4
-1.7
-0.8 -2 5
1
0
-0.4
It is clear that the value of a which gives best agreement between observed and calculated values of the exponent on hydrogen pressure varies when the ethane hydrogenolysis reaction is carried out over the different metals. Part of this could be an effect of temperature, since the catalysts were studied over different temperature ranges due to their wide variations in activity. I n considering the results over platinum and nickel, the value of 3 for a indicates that the initial dehydrogenation step proceeds all the way to a completely hydrogen deficient dicarbon surface residue. Cimino, Boudart, and Taylor6 arrived a t a similar conclusion from a study of the kinetics over a nickel catalyst. In the case of the cobalt catalyst, a value of a = 2 accounts best for the observed kinetics, indicating that the surface residue is less hydrogen deficient. Finally, the data on the copper catalyst appear to be described best when a is taken equal to 1, indicating that the initial ethane chemisorption step involved in the hydrogenolysis over copper involves the least extensive rupture of carbon-hydrogen bonds in the molecule. IV. Discussion The results of this work show substantial differences in the catalytic activities per unit area of metal of various silica-supported metals for ethane hydrogenolysis. The order of activities of the three group VI11 metals studied is: Ni > Co > Pt. The other metal studied (copper) is much less active than nickel or cobalt, but more active than platinum. However, a slight extrapolation of the data in Figure 1 on the copper The Journal of Physical Chemistry
catalyst indicates that at temperatures above 365' the position of copper relative to platinum would reverse, the platinum becoming more active. I t should be noted that any comparison of the catalytic activities of these metals for ethane hydrogenolysis depends markedly on the hydrogen pressure, since the dependence of the rate on hydrogen pressure varies for the different metals. I n the analysis of the catalytic activities of the various metals, it is clear that the rate equations for ethane hydrogenolysis show considerable variation with respect to their dependence on hydrogen pressure. However, for the platinum and nickel, the rate equations are essentially the same with respect to the dependence on hydrogen as well as ethane pressure, suggesting that the intermediate surface residues formed in the initial ethane chemisorption step are similar. For these metals it is of interest to consider the difference in catalytic activities in terms of apparent activation energies and pre-exponential factors. From the data in Table 11, it is clear that the large difference in catalytic activity between the nickel and platinum (about lo5 to 106-fold in the temperature range studied) arises primarily from the difference in apparent activation energies, since the pre-exponential factors are the same within about 20%. From the data on the effect of hydrogen pressure on the rate of ethane hydrogenolysis, we have concluded that the degree of unsaturation of the surface intermediate C2H, formed in the initial ethane chemisorption step increases in the order Cu < Co < Ni = Pt. I t is interesting that the apparent activation energy also increases in a similar manner, except that the apparent activation energy for platinum is higher than that for nickel although the inferred degree of unsaturation of C2H, is the same for the latter two. If the degree of coverage of the surface by the intermediate C2H, is low, the apparent activation energy E is given by the equation E = Et A H , where Et is the true activation energy and A H is the heat of reaction associated with the over-all reaction indicated in eq. 2. The observation that the apparent activation energy increases as the degree of unsaturation of C2H, increases suggests that reaction 2 is endothermic, despite the fact that C2H, is an adsorbed species. The endothermic heat of dehydrogenation then more than counterbalances the exothermic energy of binding of CZH, to the surface. For two metals such as platinum and nickel, where the degree of unsaturation of the species CZH, is thought to be the same, the difference in apparent activation energies could be due to a difference in the binding energy of C2H, to the surface. Note that AH is given by the equation AH = AH' -
+
CATALYSIS OVER SUPPORTED METALS
101
q, where AH’ is the endothermic heat of dehydrogena-
+
aHz, tion of the gas phase reaction, CzHs = C2H, and q is the binding energy of CzH, to the surface. The higher apparent activation energy over platinum may then be due to a lower value of q for platinum. It is interesting that the supported copper catalyst shows hydrogenolysis activity comparable to or higher than that of platinum. I t is generally accepted that the chemisorption of saturated hydrocarbons takes place readily only on transition metals,13 and hence hydrogenolysis activity might be expected to be limited to the transition metals. The activity of the transition metals is attributed to the existence of partly filled d-bands which are available for bonding. In the case of copper, which has no partly filled dband but which immediately follows a transition metal series in the periodic table, it may be that electrons can be promoted from 3d to 4s states readily, since the energy required for d-s promotion is small.14 It is possible that such a promotion could occur during the chemisorption process and hence create d-band vacancies which lead to formation of covalent bonds with the hydrocarbon. Although it appears necessary for a metal to have an
unfilled d-band to possess activity for chemisorption, it is clear that the activities of the various metals for ethane hydrogenolysis do not correlate with a parameter such as the yo d-band character of the metal. Thus, platinum, with a significantly higher yo d-band character than nickel, has a much lower activity. This is not unreasonable, however, if the chemisorption step is not the limiting factor in the reaction. As already discussed, it appears that the rupture of carboncarbon bonds is probably rate limiting. To summarize, the present work has combined hydrogen chemisorption measurements of the surface areas of supported metals with kinetic data to compare the specific catalytic activities of the metals for the hydrogenolysis of ethane. The use of such a procedure has m a d i i t possible to compare activities on a more fundamental basis than is usual for supported catalyst systems, since differences in the degree of dispersion of the metals are taken into account.
(13) G.C . Bond, “Catalysis by Metals,” Academic Press, Inc., New York, N. Y., and London, 1962,p. 68. (14) B. M . W. Trapnell, “Chemisorption,” Butterworth and Co., Ltd., London, 1955,p. 174.
Volume 69, Number 1 January 1965
