3482
J. Phys. Chem. 1983, 87, 3482-3486
from the well-known i W f " 2 9 8 of H202and H. They obtained AHf"2gpjHO.J = 5.0 f 2 kcal/mol when the data were corrected to 25 "C. In their analysis Foner and Hudson assumed that the fragments at the observed threshold energy of the dissociative ionization process 9 separated with zero relative velocity and that the H02+ion was not vibronically excited, i.e., zero kinetic and internal energies. The most probable source of error in their measurement is that the fragments in process 9 may possess some excess kinetic and/or excitation energy; thus, their value would be most likely too high, i.e., AHHfOzss(HOz) C 5.0 kcal/mol. The value 1.6 kcal/mol from Khachatryan et al.18 is too low with a large uncertainty of f2.5 kcal/mol. The value of 0.4 from Wagman's calculation was derived from AH0224,25 and the value AHfo(H3+)which was obtained by quantum-mechanical calculation^.^^^^^ If the value of (26)M. E.Schwartz and L. J. Schaad, J.Chem. Phys., 47,5325(1967). (27)A. J. Duben and J. P. Lowe, J . Chem. Phys., 56, 2824 (1972).
AHHfO(H3+)is off by 3 kcal/mol (which is more than likely), this would bring the value up to AHf0298(H02) = 3.4 f 2 kcal/mol, which is in good agreement with most data. A mean value AHHf0%&H02)= 3.5 kcal/mol is obtained by considering most of the data except those from Kochubei and Moin (which was ruled out) and from Khachatryan et al. (which has a large uncertainty). An upper limit of 4.5 is adopted from Foner and Hudson's measurements and Heneghan and Benson's measurements. A lower limit of 3.0 is assigned since three s t ~ d i e s ' ~ Jshow ~9~~ that the value of AHf0(H02)has to be greater than 3.0 kcal mol. Therefore, we recommend AHf02g8(H02)= 3.5G.50 kcal/mol as the best value.
Acknowledgment. This work has been supported by the
US.Army Research Office for scientific research under grant No. DAAG29-82-K-0043and the National Science Foundation under grant No. CHE-79-26623. Registry No. Hydroperoxyl radical, 3170-83-0.
Kinetics of H2 Desorption from Silica-Supported Rhodium Arthur A. Chlnt and Alexls T. Bell' Department of Chemical Englneering, University of California, Berkeley, Callfornia 94720 (Received: October 7, 1982)
Temperature programmed desorption spectroscopy has been used to characterize the kinetics of Hzdesorption from a Rh/Si02catalyst. Desorption is observed to occur from two states, designated p1and p2. By simulation of the experimentally observed spectra, it is determined that the preexponential factor for desorption from both states is 3.8 x cm2/s. The activation energy for desorption from the p1state is 14 kcal/mol and that for the Pz state is 21 kcal/mol.
Introduction Temperature programmed desorption (TPD) spectroscopy is a powerful method for characterizing the binding states of molecules adsorbed on a catalyst Theoretical methods for determining desorption kinetics and rate parameters have been established and used extensively to interpret TPD spectra obtained from unsupported metals under ultrahigh vacuum conditions. Similar methods can also be applied to interpret TPD spectra obtained from supported metal catalysts studied under conditions in which desorption occurs into a flowing carrier gas.8 Recent theoretical workgJOhas shown that readsorption of the desorbing gas must be taken into account in the analysis of such experiments. Furthermore, experimental conditions must be selected carefully to avoid mass transfer effects which can give rise to modifications in peak position and shape. In the present paper we report on a study of the kinetics of H2 desorption from a silicasupported Rh catalyst. TPD spectra were obtained by rapid desorption into a stream of flowing helium. The distribution of binding states and the rate parameters for desorption from these states were determined by simulation of the observed TPD spectra. Studies by various authors1'-" have shown that H2 adsorbs dissociatively on both supported and unsupported Present address: Mobil Research and Development Corp., Research Department, Paulsboro, N J 08066.
Rh. Measurements of the initial sticking coefficient for H2 have been made on both polycrystalline and singlecrystal Rh Previous studies of H2 desorption have been restricted to unsupported Rh.l1-l5 The TPD spectra obtained in these investigations suggest that H2 desorbs primarily from a single state. Moreover, spectra obtained for smooth and stepped surfaces do not differ ~ignificantly.'~J~J~ In those cases where the TPD spectra (1) Redhead, P. A. Vacuum 1962,12,203. (2)Cvetanovic, R.J.;Amenomiya, Y. Ado. Catal. Related Subj. 1967, 17, 103. (3)Cvetanovic, R. J.; Amenomiya, Y. Catal. Rev. 1972,6,21. (4)Petermann, L.A. In "Adsorption-DesorptionPhenomena";Ricca, F. Ed.; Academic Press: New York, 1972. (5)Schmidt, L.D.Catal. Reu. 1974,9, 115. ( 6 ) Smutek, M.; Cemy, S.; Buzek, F. Ado. Catal. Related Subj. 1975, 24,343. (7)Madix, R. J. Catal. Reo. 1977,15, 293. (8) Falconer, J. L.; Schwartz, J. A. Catal. Reo. Sci. Eng. 1983,25,141. (9) Herz, R. K.; Kiela, J. B.; Marin, S. P. J. Catal. 1982,73,66. (10)Gorte, R. J. J . Catal. 1982, 75, 164. (11) Mimeault, V. J.; Hansen, R. S. J . Chem. Phys. 1966,45, 2240. (12)Castner, D.G.; Sexton, B. A.; Somorjai, G. A. Surface Sci. 1978, 71,519. (13)Castner, D.G.; Somorjai, G. A. Surface Sci. 1979,83,60. (14)Yates, Jr.,J. T.;Thiel, P. A.; Weinberg, W. H. Surface Sci. 1979, 84,427. (15)Gorodetakii, V. V.; Nieuwenhuys, B. E.; Sachtler, W. M.H.; Boreskov, G. K.Surface Sci. 1981,108,225. (16)Edwards, S. M.; Gasser, R. P. H.; Green, D. P.; Hawkins, D. S.; Stevens, A. H. Surface Sci. 1978, 72, 213. (17)Zakumbaeva, G. D.;Omashev, K. G.Kinet. Katal. 1977,18,450.
0022-3654/83/2087-3482$01.50/00 1983 American Chemical Society
Kinetics of H, Desorption from Si-Supported Rh
have been analyzed to determine desorption rate parameters, it has been concluded that the activation energy for desorption decreases with increasing coverage.l'J4 In contrast to these observations, calorimetric and desorption experiments conducted with alumina-supported Rh" suggest that there can be as many as three forms of adsorbed H2. The heats of adsorption for each form are distinct but decrease with increasing coverage.
Experimental Section Apparatus. The apparatus used in the present study has been described previ~usly.'~J~ The central part of this apparatus is a quartz microreactor, which can be heated at up to 1 K/s. The desorbing gas is swept from the microreactor by a continuous flow of helium. Analysis of the effluent flow is done with a quadrupole mass spectrometer. A microprocessor-based data acquisition system is used to direct the mass spectrometer to a series of preselected masses and to record the signal intensity at each mass setting together with the catalyst temperature. Typical transfer times from the microreactor to the mass spectrometer were less than 1.5 s, and the Peclet number for the transfer line was estimated to be 2 X lo4. Under such conditions, distortion of the TPD peaks due to dispersion is not expected to occur. Materials. A 5% Rh/SiOz catalyst was prepared by impregnation of Davison 70 silica with an aqueous solution of RhCl3.3Hz0. The resulting slurry was dried overnight in air at 378 K. A 30 to 60 mesh fraction was screened and reduced in flowing hydrogen for 4 h at 623 K. The concentration of Rh surface sites was determined by H2 chemisorption. The amount of H2adsorbed on the freshly reduced catalyst was 73.3 pmollg, corresponding to a dispersion of 30.2%. After several TPD experiments, the Rh dispersion declined to 16.4% (38.8 pmol of H2/g), but remained constant thereafter. It is significant to note that no changes in peaks location or shape were observed due to sintering. Helium (99.998%) was purified of oxygen down to about 200 ppb by passage through an Oxyclear (Labclear) filter. Water was removed by a trap filled with Linde 13X molecular sieve and immersed in liquid nitrogen. High-purity Hz (99.999%) was passed through a Deoxo purifier (Engelhard) to convert any oxygen to water and then passed through a liquid nitrogen cooled trap filled with Linde 13X molecular sieve to remove the water. Experimental Procedure. The procedure for all experiments was similar. A 25-mg sample of the catalyst was placed in the microreactor, and the air in the reactor was evacuated with a mechanical pump. The reactor was then backfilled with helium and reevacuated. This procedure was repeated several times to reduce the oxygen impurity level to below 1ppm. Next, the catalyst was reduced at 723 K for at least 4 h in pure H2 flowing at 200 STP cm3/min. Following reduction, the microreactor was evacuated, and the catalyst was heated to 1073 K at 0.25 K/s. The catalyst was then cooled to room temperature while still under vacuum. At this point, the reactor was repressurized with helium. To achieve essentially uniform partial coverage of the catalyst sample, H2adsorption was carried out in the following manner. The catalyst was first saturated with Hz by passing a stream of pure H2through the reactor for 15 min. Next, gaseous H2 and a portion of the adsorbed H2were removed by evacuation. The desorption of Hz was slow enough at room temperature to permit a near uniform (18)Low,G.; Bell, A. T. J. Catal. 1979, 57, 397. (19) Uchida, M.; Bell, A. T. J. Catal. 1979, 60, 204.
A
8, = 0.7 I
0.59
0.53 0.42 0.3 I
0.22 0 19
300 400
500
600
700 800
900 1000 1100
T (K)
Flgure 1. TPD s ectra for H2 desorption from Rh/SiO,: j3 = 1 K/s, 0 = 50 STP cm /min.
P
reduction in Hz coverage throughout the catalyst bed. By varying the duration of evacuation from 2 to 20 min, coverages of 0.70 to 0.05 could readily be achieved. Once the desired adsorbate level had been attained, the reactor was repressurized with helium and the helium flow rate was set to 50 STP cm3/min. Heating of the catalyst was now commenced at 1K/s, and the data acquisition system was activated to initiate analysis of the desorbing gas. Following each TPD experiment, the mass spectrometer was calibrated against a helium mixture containing 492 ppm of H,. The absolute rate of desorption was determined in the following manner. To correct for mass spectrometer baseline drift, the observed intensity for H2was normalized to the intensity of helium, the carrier gas. The rate of H2 desorption, rd, was then determined from the expression
8 273R where Iobsd and lbg are the normalized intensities for H2 observed in the experiment and background, respectively; SH2 is the calibration factor for H2;NTis the total number of surface Rh sites on the sample; and Q is the flow rate of helium at STP. The total number of moles of H, desorbed was determined from the integral of each TPD spectrum.
Results Experimental Observations. The effects of initial coverage on the TPD spectra for Hz are illustrated in Figure 1. A t the lowest coverages examined, only a single peak can be seen near 580 K. The position of this peak gradually shifts to lower temperatures as the initial coverage is increased. A second peak, centered at 400 K, becomes discernable once the initial coverage is raised to 0.53. The intensity of this low-temperature feature increases rapidly with increases in the hydrogen coverage above 0.53, and
Chin and Bell
TABLE I: Parameters Used for Simulation of TPD p = 1.0 K/s Q = 0.833 cm3/s E = 0.40 V = 0.066 cm3 p b = 0.38 g/cm3 so = 0 . 5 N , = 3.88 Fmol CJ = 7.52 X cm2/Rhsite
Carrier Flow Role ( "/nl n1
A
2v
B
C
209 49 5 I05 3
.
B
C
1
-I
0
i o 0 400
500
600
700
800
900 1000 IlOO
T (K)
Flguro 2. Effects of carrier gas flow rate on TPD spectra for desorption from Rh/SIO,: p = 1 Kls; OHo = 0.33.
the position of the peak maximum shifts to lower temperatures. When OH = 0.71, the low-temperature peak dominates the spectrum, and the high-temperature peak now appears as a shoulder. Spectra of a pare silica sample, previously exposed to H2, were devoid of features, indicating that the peaks seen in Figure 1 are due totally to the desorption of H2 from the surface of the supported Rh. TPD spectra could not be attained for coverages above 0.71, using the procedures previously described. This is due to the fact that a significant fraction of the hydrogen adsorbed at room temperature desorbs during the period of evacuation required to remove gas-phase H2 from the reactor. An additional fraction of a monolayer may also be lost during the time that the helium flow rate is being adjusted, prior to the onset of the temperature ramp. The effects of helium flow rate were examined in an effort to establish the extent to which readsorption of the desorbing H2 occurs. The reasoning behind this experiment is as follows. In the absence of readsorption, the positions of peaks seen in the TPD spectra should be unaffected by the helium flow rate. On the other hand, if readsorption is significant then the position of the peaks should shift to lower temperatures as the flow rate increases. This trend would be expected as a consequence of the reduction in the readsorption rate due to the lower gas-phase concentration of H2 prevailing at higher helium flow rates. The influence of helium flow rate on the TPD spectra observed experimentally is shown in Figure 2. In panel a, the data are represented as the partial pressure of H2 present in the gas stream leaving the reactor. As the helium flow rate is increased from 20.9 to 105.3 cm3/min, the peak maxima shift to lower temperatures, and the intensities of the peaks diminish. The latter effect is due to the greater dilution occurring at higher flow rates. The calculated rate of desorption, based upon the data presented in panel a, is shown in panel b. Here, too, one can observe about a 30 K shift downscale in the peak positions as the flow rate is increased. The area under each spectrum, though, is nearly the same, indicating that the amount of H2 desorbed is independent of the helium flow rate. Determination of Desorption Rate Parameters. The TPD spectra shown in Figure 1can be interpreted on the
assumption that there are two distinct states for hydrogen adsorption, designated as p1and &. The adsorption and desorption of H2can then be described by reactions 1and 2. The initial rate of Hz adsorption into both states is
Hz+ 2S1 ~i 2H-S1
&-state
(1)
Hz + 2Sz ~i 2H-Sz
&state
(2)
taken to be first order in H2 concentration and second order in the fraction of vacant sites. The rate of H2 desorption from both states is taken to be second order in the fractional coverage by atomic hydrogen. Two other desorption models were also considered. In one, it was assumed that there is only one type of site but that desorption can occur via two parallel paths, differing in rate coefficients. The second alternative was similar to the model ultimately chosen with the exception that desorption from the P2-statefollows first-order kinetics. Only the model represented by reactions 1 and 2 was capable of representing the observed TPD spectra over the full range of hydrogen coverages. To model the desorption process, we treated the catalyst as a uniform bed through which the carrier gas moves in plug flow. Because the concentration of desorbing gas is small at all times, it is assumed that the average gas concentration within the voids of the bed and catalyst is given by C H z = (CHz(i) + C H 1 ( O ) ) / 2 , where CHz(i) and CH2(0) are the concentrations of H2 at the inlet and outlet of the reactor. The diffusion of gas through the pores present in the individual catalyst particles can be neglected. This simplification is based on a separate analysis, which has shown that, for the size of particles used this study (rp 10.02 cm) and the rate parameters deduced from the present analysis, desorption is not rate-limited significantly by intraparticle diffusion.20 The conservation of species in the gas phase and adsorbed on the catalyst surface are expressed by eq 3-5.
The variables 8, and r?I2 appearing here represent the average fractional coverage of SI and Sz sites, respectively, by adsorbed atomic hydrogen. The parameters a1and a2 define the fractions of all sites which occur as types 1 and 2, respectively. Definitions for the remaining parameters appearing in eq 3-5 are given in the Nomenclature section. Magnitudes for the fixed parameters and variables are given in Table I. The temperature of the catalyst bed is assumed to be uniform spatially but increases with time according to the relationship
T = To + Pt (6) where To= 295 K and P = 1 K/s. As the catalyst temperatures rise, so do the values of the rate coefficients for (20) Chin, A. A., M. S. Thesis, Department of Chemical Engineering, University of California, Berkeley, CA, 1982.
2.00
-
-Simulation
A h ,
_ - -Experimental
-
700
900
C o m e r Flow Rate (cm3/min) A 20.0 6 49.5 C 105.3
I
VI
I .50
1
m
0
I .oo
X T)
0.50 0 200
400
300
500
600
800
T (K)
Figure 9. Comparison of observed and simulated H2TPD spectra for different initial coverages: 0 = 1 K/s; 0 = 50 STP cm3/min.
TABLE 11: Desorption Rate Parameters a , = 0.74
200
0.26 k d t = 3.8 X Cm2/S Edl = 21.0 kcal/mol
a 2=
kd: = 3.8 X Cm2/S E d , = 14.0 kcal/mol
(7)
= kd: eXp(-Edi/RT)
(8)
The initial sticking coefficient for H2on a clean Rh surface, so, is taken to be the same for both types of sites. This parameter is set equal to 0.5 based on experimental measurements of H2 chemisorption on unsupported Rh surface~.'"'~ The preexponential factors, kd;, and the activation energies, Ed,for desorption from S1 and S2sites are left as adjustable parameters. The initial conditions for eq 3-5 are given by CH2=0
a2 = 8H(4/a2 82
= 1.0
81
=
(8H'"'
(9)
att = O
O1 = O
if
- a2)/a1
if
BH(~)< a2 (loa) 2
C X ~
400
500 600 T (K)
700
800
900
Figure 4. Predicted effect of carrier gas flow rate on the position of the TPD spectrum for H2 desorption: 0 = 1.0 K l s ; OHo = 0.33.
adsorption and desorption. The explicit temperature dependence of these parameters is given by
kdi
300
(lob)
where is the total initial coverage of the Rh surface by atomically adsorbed hydrogen. These initial conditions are based on the assumption that all of the higher binding energy S2sites are covered before the lower binding energy S1sites are occupied. Equations 3-5, together with the boundary conditions given by eq 9 and 10 (or lob), were solved numerically with a Gear-Hindmarsh algorithm.21 The computed value of CH?) was then used to determine the net rate of desorption for each temperature. A comparison between the theoretically predicted and experimentally observed TPD spectra is shown in Figure 3, for five different initial hydrogen coverages. The good agreement between the two sets of spectra seen here was achieved by trial and error adjustment of ai,kd?, and Ea (i = 1,2). The set of values for these parameters providing the closest fit between predicted and observed TPD spectra is given in Table 11. It is seen that the S1sites comprise 74% of the total sites chemisorbing H2. The frequency factor for H2 desorption is the same for S1 and S2 sites, 3.8 X lo9 cm2/s, but the activation energy for desorption is 14.0 kcal/mol for S1sites and 21.0 kcal/mol for S2sites. The proposed model of H2 desorption can also be used to predict the effects of helium flow rate on the TPD (21)Hindmarsh, A. "Gear: Ordinary Differential Equation Solver", UDID-3001, Rev. 1, Aug 20, 1972 (1978).
spectrum. Figure 4 shows that as the carrier gas flow rate increases, the maximum of the spectrum shifts to lower temperatures. This shift is due to the fact that the gasphase concentration of H2 is lower at a given temperature the higher the helium flow rate and, as a consequence, readsorption of the desorbing H2 does not retard the net rate of H2 desorption to as great a degree. The 40 K peak temperature difference between the highest and lowest flow rate, predicted by the model, agrees reasonably well with that observed experimentally (see Figure 2).
Discussion The experimental results presented in this paper indicate that the desorption of H2 from silica-supported Rh occurs from two states, and p2. The observed TPD spectra are well represented by an equilibrium desorption model in which it is assumed that the adsorption and desorption rate parameters are independent of surface coverage. The initial sticking coefficient and the preexponential factor for desorption are taken to be the same for both states, but the activation energies for desorption are different. In the discussion presented below, the model for H2 desorption from silica-supported Rh proposed here is compared and contrasted with models for H2 desorption from unsupported Rh, reported in the literature. Mimeault and Hansenll observed only a single peak for H2 desorption from a Rh filament. At very low coverages (8, N 0.02), the experimental data could be represented by second-order kinetics with an activation energy of 18.5 cm2/s. kcal/mol and a frequency factor of 1.3 X Analysis of the data taken at coverages up to 0.10 suggested that the activation energy decreases linearly with increasing coverage at the rate of 24 kcal/mol for every 1015 molecules adsorbed per square centimeter. In their studies of H2desorption from a Rh(ll1) surface, Yates et d.'*reported that at OH N 0.03 a single desorption peak was observed at 390 K. With increasing coverage, the peak shifted to lower temperature, broadened, and became asymmetric. For coverages above 0.5, a small desorption peak appeared near 150 K. Rate parameters for H2desorption were determined from the main peak. In the limit of zero coverage, the preexponential factor and activation energy for second-order desorption were determined to be 1.2 X cm2/s and 18.6 kcal/mol, respectively. From an analysis of the change in peak position and width with increasing coverage, it was concluded that the activation energy for desorption decreases from 18.6 to 4.5 kcal/mol, as OH increases from 0 to 1.0. Over the same range of coverages, the preexponential factor de-
3486
The Journal of Physical Chemistry, Vol. 87, No. 18, 1983
creased by nine orders of magnitude. In the present work it was concluded that, for OH < 0.25, desorption occurs only from the p2 state. The kinetics of desorption are second order in atomic hydrogen and are characterized by a preexponential fador of 3.8 X cm2/s and an activation energy of 21 kcal/mol. While the values of these rate parameters are somewhat larger than those reported by Mimeault and Hansen'l and Yates et al.14for zero coverage, the degree of agreement is sufficient to conclude that at low coverages the kinetics of H2desorption are similar for supported and unsupported Rh. Desorption of H2from two states was observed for silica-supported Rh, whereas desorption of H2from unsupported Rh has been reported to occur from only a single state. Yates et al.14indicated that, with the exception of a small low-temperature peak ( T , = 150 K), the majority of H2 adsorbed on a Rh(ll1) surface desorbs in a single, broad peak. They proposed that the sharp decrease in the values of the activation energy and preexponential factor with increasing hydrogen coverage, deduced from the analysis of this peak, could be ascribed to the desorption of H2from a mobile precursor and/or repulsive interactions between adsorbed H atoms. Both of these factors would help to explain why the observed shift in the maximum temperature TPD peak is much greater than that predicted for second-order desorption assuming coverage-independent rate parameters. In view of the results presented here, one may develop yet another interpretation. If it is assumed that desorption occurs from two distinct types of sites, then the broad asymmetric nature of the TPD peak observed by Yates et al. at high coverages could readily be attributed to the occurrence of two overlapping TPD peaks. Such behavior has been observed, for example, in TPD studies of Hzdesorption from Pt(lll), -(llO), -(loo), and 4210) surface^.^^-^^ Thus, it would appear that the observation of two peaks for Hzdesorption from silica-supported Rh, while not previously observed for unsupported Rh, is consistent with H2desorption from Pt single crystal surfaces. Finally, it should be noted that the observation of two binding states for dissociative adsorption of Hzon Rh/Si02 is consistent with the observations reported by Zakumbaeva and Omashe@ in their studies of Hzadsorption on Rh/A1203. Based upon calorimetric and desorption measurements, these authors concluded that H2is adsorbed in three forms with heata of adsorption of 50-14,14-7, and (22) McCabe, R. W.; Schmidt, L. D. Surface Sci. 1976, 60, 85. (23) McCabe, R. W.; Schmidt, L. D. Surface Sci. 1977, 65,89. (24) McCabe, R. W.; Schmidt, L. D. R o c . Int. Vac. Congr., 7th 1977, 2, 1201.
Chin and Bell
7-3 kcal/mol. The two higher binding-energy states are ascribed to dissociatively adsorbed Hz, and the lowest binding-energy state is ascribed to molecularly adsorbed
H2. Conclusions TPD spectra of H2 adsorbed on silica-supported Rh indicate the presence of two adsorption states, p1and pz. Desorption from both states follows second-order kinetics. The activation energy for the &state is 14 kcal/mol and that for the P2-state is 21 kcal/mol. The preexponential cm2/s, The rate pafactor for both states is 3.8 X rameters for desorption from the &-state are close t~ those observed for H2 desorption from polycrystalline Rh and Rh(ll1) surfaces, at zero coverage. TPD spectra for H2 desorption from silica-supported Rh are well-represented by a model of the desorption process which takes into account free readsorption of the desorbing gas.
Acknowledgment. This work was supported by the National Science Foundation through Grant CPE-7826352. Nomenclature gas-phase concentration of H2, mol/cm3 activation energy for desorption from state i, kcal/mol intensity of mass spectrometer signal for mass H2, A rate coefficient for adsorption into state i, cm3mol-' S-1
rate coefficient for desorption from state i, s-' preexponential factor for desorption from state i, S-1
mass of H2, g total number of Rh surface sites volumetric flow rate of helium carrier gas, STP cm3/s gas constant, atm mol K-' experimentally observed rate of desorption, s-l initial sticking coefficient calibration factor for Hz,A/atm temperature, K time, s catalyst bed volume, cm3 fraction of all Rh surface sites on which adsorption can occur into state i heating rate, K/s catalyst bed void fraction catalyst bed density, g/cm3 area per Rh site, cm2 fractional coverage of type i sites by atomic hydrogen Registry No. Rh, 7440-16-6; H,, 1333-74-0.
