Langmuir 1999, 15, 5825-5828
5825
Carbon-13 Kinetic Isotope Effects in CO Oxidation by Ag† Ivan Kobal,‡ Uwe Burghaus,§ Marjan Senegacˇnik,‡ and Nives Ogrinc*,‡ J. Stefan Institute, Jamova 39, P.O. Box 3000, 1001 Ljubljana, Slovenia, and Department of Physical Chemistry I, Ruhr-University Bochum, Universita¨ tstrasse 150, D-44801 Bochum, Germany Received September 22, 1998. In Final Form: January 21, 1999 In the catalytic oxidation of carbon monoxide over silver wool the 13C kinetic isotope effects in the 343-453 K temperature range were experimentally determined and the following temperature dependence was found: 100 ln(k12/k13) ) (3.398 - 630/T) ( 0.083. A reaction CO/O2 gas mixture of 1:2 ratio was used in a static system with initial pressures ranging from 20 to 40 kPa. Under these conditions the reaction is of order 1 with respect to CO and order 0 with respect to O2 and CO2 pressure. The apparent activation energy is 59.3 ( 1.7 kJ mol-1. In our theoretical interpretation of the experimental data various geometries of (CO2)q and (CO3)q transition states were applied, and only a (CO2)q with an interbond angle of 110° and CO stretching force constants of 1700 and 1000-1400 N m-1, respectively, with an asymmetric reaction coordinate was found to be acceptable.
Introduction For the catalytic oxidation of carbon monoxide over silver wool, carbon-13 kinetic isotope effects (KIE) were experimentally determined within a temperature range of 343453 K.1 For the simultaneously running isotopic reactions 12
k12
13
k13
C16O + 1/216O2 98 12C16O2 C16O + 1/216O2 98 13C16O2
(1) (2)
the k12/k13 ratio was obtained by isotopic analysis of the reactant before the reaction started and after reaching a known extent of reaction. The following temperature dependence was found:
(
100 ln (k12/k13) ) 3.398 -
630 ( 0.083 T
)
(3)
The experiments were carried out in a static vacuum system with the CO-O2 (1:2) gas mixture at an initial pressure of 20-40 kPa. Under these conditions the reaction was first order with respect to the carbon monoxide and zeroth order with respect to carbon dioxide and oxygen pressure. An activation energy of 59.3 ( 1.7 kJ mol-1 was found. CO oxidation is interesting from the theoretical point of view and also plays an important role in the three-way catalyst used for cleaning exhaust pollution,2-5 electric fuel cells,6,7 special laser light sources (e.g. closed-cycle CO2 lasers),8,9 gas sensors,10 and in the Martian atmo† Presented at the Third International Symposium on Effects of Surface Heterogeneity in Adsorption and Catalysis on Solids, held in Poland, August 9-16, 1998. ‡ J. Stefan Institute. § Ruhr-University Bochum.
(1) Senegacˇnik, M.; Kobal, I.; Policˇ, S. “J. Stefan” Institute Report DP-K304 1976. (2) Taylor, K. C. Catal. Rev. 1993, 35, 457 and references therein. (3) Kasˇpar, J.; de Leitenburg, C.; Fornasiero, P.; Trovarelli, A.; Graziani, M. J. Catal. 1994, 146, 136. (4) Fornasiero, P.; Di Monte, R.; Ranga Rao, G.; Kasˇpar, J.; Meriani, S.; Trovarelli, A.; Graziani, M. J. Catal. 1995, 151, 168. (5) Ranga Rao, G.; Fornasiero, P.; Di Monte, R.; Kasˇpar, J.; Vlaic, G.; Balducci, G.; Meriani, S.; Gubitosa, G.; Cremona, A.; Graziani, M. J. Catal. 1996, 162, 1.
sphere.11 Although a large number of studies have been conducted on single-crystal surfaces,12,13 relatively few publications14 deal with CO oxidation under measuring conditions that might be relevant for technical applications. Despite the large number of studies focusing on the kinetics and the adsorption of the participating reactants12,13 little work has been conducted with respect to identification of the geometry of a possible transitition state for CO2 formation. Carbon monoxide is probably also adsorbed upright15 on silver surfaces, and the CO2 molecule is of linear geometry. Thus, a large change of the bond angle during the formation of CO2 must take place. Geometries for the (CO2)q transition state such as flat adsorbed CO2 molecules,16 intermediates with an interbond angle of 120°,17 and upright adsorbed CO2 have been suggested rather speculatively.18 The possible geometry of the (CO2)q complex remains unclear for a number of transition metal surfaces. The aim of this work was to produce a theoretical interpretation for the 13C-kinetic isotope effects in the catalytic CO oxidation over Ag in order to provide the geometry and force constants of the transition state of this reaction. This approach has been applied for a long time19 and can still be successfully used to get additional information about the studied reaction. (6) Ianniello, R.; Schmidt, V. M.; Stimming, U.; Wallau, A. Electrochim. Acta 1994, 39, 1863. (7) Friedrich, K. A.; Geyzer, K.-G.; Linke, U.; Stimming, U.; Stumper, J. Electroanal. Chem. 1996, 402, 123. (8) Gardner, S. D.; Hoflund, G. H.; Schryer, D. R.; Schryer, J.; Upchurch, B. P.; Kielin, E. J. Langmuir 1991, 7, 2135. (9) Schreyer, D. R., Hoflund, G. B., Eds. Low-Temperature-COOxidation Catalysis for Long-Life CO2 Lasers. NASA Conference Publication 3076; NASA: VA, 1990. (10) Delabie, L.; Honore´, M.; Lenaerts, S.; Huyberechts, G.; Rpggen, J.; Maes, G. Sens. Actuators, B 1997, 44, 446. (11) Choi, W.; Leu, M.-T. Geophys. Res. Lett. 1997, 24/23, 2957. (12) Engel, T.; Ertl, G. Adv. Catal. 1979, 28, 2 and references therein. (13) Burghaus, U.; Conrad, H. Surf. Sci. 1995, 338, L869; Surf. Sci. 1997, 370, 17 and references therein. (14) E.g.: Keulks, G. W.; Chang, C. C. J. Phys. Chem. 1970, 74, 2590. (15) Burghaus, U.; Vattuone, L.; Gambardella, P.; Rocca, M. Surf. Sci. 1997, 374, 1. (16) Brown, L. S.; Sibener, S. J. J. Chem. Phys. 1989, 90 (5), 2807. (17) Campbell, C. T.; Ertl, G.; Kuipers, H.; Segner, J. J. Chem. Phys. 1980, 73 (11), 5862. (18) Allers, K. H.; Pfnu¨r, H.; Feulner, P.; Menzel, D. J. Chem. Phys. 1994, 100, 3985. (19) Johnston, H. S.; Bonner, W. A.; Wilson, D. J. J. Chem. Phys. 1957, 26, 1002.
10.1021/la981309n CCC: $18.00 © 1999 American Chemical Society Published on Web 04/03/1999
5826 Langmuir, Vol. 15, No. 18, 1999
Kobal et al. equals 1 mdyne/Å); Fd, 100-2000 N m-1 in steps of 100 N m-1; FR, 50-300 N m-1 in steps of 10 N m-1 R, 70-180° in steps of 10°. The off-diagonal elements were set at zero, with the only exception of the FDd needed to get a zero determinant of the F matrix, this resulting in one zero normal frequency belonging to the reaction coordinate. Its value was calculated from the following equation:
Figure 1. Transition states: (a) (CO2)q; (b) (CO3)q.
FDd ) ( xFDFd
Calculation Background Theoretical 13C-kinetic isotope effects were calculated applying Bigeleisen’s equation based on the absolute rate theory:20
k12 k13
)
q q 3n-6 u 3nq-7 uq νL,12 13,i sinh(u12,i/2) 12,i sinh(u13,i/2) q νL,13
∏u i)1
12,i
sinh(u13,i/2)
∏u i)1
q 13,i
(4)
q sinh(u12,i /2)
Here, symbols with q belong to the transition state (in our case (CO2)q or (CO3)q; see below) and those without it to the reactant molecule (in our case CO). Thus the first product runs over all the isotopic frequencies of the reactant and the second one over all the real frequencies of the transition state. u ) hcω/kBT (ω, wavenumber in cm-1; h, Planck’s constant; kB, Boltzmann’s constant; c, speed of light; T, temperature). νL is the zero (or imaginary) frequency belonging to the reaction coordinate and q q /νL,13 ratio was calculated via the following relation:21 the νL,12 q νL,12 q νL,13
)
( ) |G12|
|G13|
1/2 3nq-7
q ν13,i
∏ν i)1
(5)
q 12,i
The isotopic normal frequencies for the reactant CO molecule were obtained from the literature,22 while those for the transition state were found by solving Wilson’s FG matrix equation:21,23,24
GFL ) LΛ
(6)
where G is the Wilson matrix comprising masses of atoms and geometric parameters, F is the force-constant matrix, L is the eigenvector matrix, and Λ is a diagonal matrix of eigenvalues λii ) 4π2νi2 with νi equal to the frequency of the ith normal vibration. One of zero (imaginary was not taken into account) frequency was obtained by fulfilling the condition |F| ) 0. In the reaction between an adsorbed CO molecule and an adsorbed O atom a (CO2)q transition state may be expected. However, we also took into account a (CO3)q transition state, thus hypothetically also allowing the simultaneous interaction of an adsorbed CO molecule with two adsorbed O atoms. For the transition states, (CO2)q and (CO3)q of different geometries and force constants were checked. The definitions of the internal coordinates are based on the relations in Figure 1. (CO2)q Transition State. The symmetric F matrix had the following form: ∆D ∆D ∆d ∆R
FD FDd 0
∆d Fd 0
∆R
FR
The interaction of the transition state with the surface was neglected, as is the common practice in this field.20 In our calculations, the values of parameters were varied in the following ranges: FD, 1000-2000 N m-1 in steps of 100 N m-1 (100 N m-1 (20) Van Hook, W. A. Isotope Effects in Chemical Reaction; Van Nostrand-Reinhold: New York, 1970. (21) Guns, P. Vibrating Molecule; Chapman & Hall: London, 1971. (22) Nakamoto, K. Infrared Spectra of Inorganic and Coordination Compounds; Wiley: New York, 1963. (23) Wilson, E. B.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York, 1965. (24) Barlicˇ, B. M.S. Thesis, University of Ljubljana, 1973.
(7)
In the case when an asymmetric stretching vibrational normal mode of the transition state describes the movement along the reaction coordinate (“+” in the above equation), one of the bonds is weakened from its value in CO (2000 N m-1)25 to a value in CO2 (1600 N m-1)26-28 while the other bond is formed, thus having a stretching force constant between zero and a value in CO2. If, on the other side, a symmetric vibration is taken as the reaction coordinate (“-” in the above equation), both the C-O bonds in the transition state are weaker than in a CO2 molecule. For the calculation, a value for the force constant of a C-O bond was chosen and then length for that bond was obtained from the formula29
Fr ) 35.5/r5.79
r ) D, d
(8)
(CO3)q Transition State. The symmetric F matrix had the following elements:
∆D ∆d ∆d ∆R ∆R ∆τ
∆D
∆d
∆d
∆R
∆R
∆τ
FD FDd FDd 0 0 0
Fd Fdd 0 0 0
Fd 0 0 0
FR 0 0
FR 0
Fτ
Also here the interaction of the complex with the metal surface was neglected.20 The values of parameters were varied in the following ranges: FD, 200-2000 N m-1 in steps of 100 N m-1; Fd, 200-2000 N m-1 in steps of 100 N m-1; Fdd, 0-300 N m-1 in steps of 10 N m-1; FR, 20-200 N m-1 in steps of 10 N m-1; Fτ, 20-200 N m-1 in steps of 10 N m-1; R, 100-140° in steps of 10°; τ, 0-10° on steps of 2°. As seen above, only the FDd and Fdd off-diagonal elements were different from zero in the F matrix. The following relation was used in order to achieve one zero frequency:
FDd ) (
1 xFD(Fd + Fdd) x2
(9)
Only an asymmetric motion of the (CO3)q transition state may lead to a CO2 molecule; thus, the “+” sign was used in the above equation. The same correlation for the bond length and force constant was used as for the (CO2)q complex.20
Results and Discussion (CO2)q Transition State. Figure 2 shows the dependence of the calculated KIE on FD for selected values of Fd, FR, and R. Results for the lowest and higest experimental temperatures are drawn. For our purposes, those FD values are interesting for which the calculated curve passes the experimental KIE region. From such diagrams we may obtain regions of FD and Fd for selected values of (25) Politzer, P.; Kasten, S. D. Surf. Sci. 1973, 36, 186. (26) Herzberg, G. Molecular Spectra and Molecular Structure II, Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand: New York, 1949. (27) Biegeleisen, J.; Ishida, T. J. Chem. Phys. 1975, 62, 80. (28) Bilkadi, Z.; Lee, M. W.; Biegeleisen, J. J. Chem. Phys. 1975, 62, 2087. (29) Ladd, I. A.; Orville-Thomas, W. J.; Coc, B. C. Spectrochim. Acta 1964, 20, 1977.
13C
Kinetic Isotope Effects in CO Oxidation by Ag
Langmuir, Vol. 15, No. 18, 1999 5827
Figure 2. Calculated 13C-kinetic isotope effects at 343 (dashed line) and 453 K (full line) for (CO2)q TS with an asymmetric reaction coordinate (FDd ) + xFDFd) versus FD for selected Fd (values as numbers in N m-1/100 in circles attached to the curves) and FR ) 150 N m-1 and R ) 110°. The experimental ranges of KIE for these two limiting temperatures are indicated.
Figure 4. Ranges of acceptable values of FD and Fd for selected values of FR (numbers attached to curves, N m-1) and of 100 and 110°.
Figure 5. Agreement with the experiment for two successful examples of the (CO2)q transition state with an asymmetric reaction coordinate (FDd ) + xFDFd) and with parameter values listed under (1) and (2) in Table 1. Figure 3. Examples of ranges of FD-Fd values giving agreement with the experiment at 343 and 453 K for (CO2)q TS with an asymmetric reaction coordinate (FDd ) + xFDFd) for FR ) 280 N m-1, and R ) 110°.
FR and R which agree with the experiment. Some of the examples of the asymmetric reaction coordinate are shown
in Figure 3. Only those regions are acceptable which overlap at the two temperatures, thus providing agreement with the experiment throughout the whole temperature range studied. These regions are summarized in Figure 4 for interbond angles of 100 and 110°. Values of interbond angles below 100° and above 110° are not in agreement with experiment. Because of the asymmetric
Table 1. Average Values of the Experimental Data of the 13C-Kinetic Isotope Determination Together with Calculated Results of Two Successful Examples of the (CO2)q Transition Statea temp, K k
323
373
413
453
(k12/k13)exp. (k12/k13)cal. (R ) 100°) (k12/k13)cal. (R ) 110°)
1.0157 ( 0.0005 1.0172
1.0173 ( 0.0010 1.0177
1.0188 ( 0.0021 1.0181
1.0203 ( 0.0009 1.0185
1.0166
1.0175
1.0184
1.0192
FD, N m-1
Fd, N m-1
FR, N m-1
D, nm
d, nm
ω12, cm-1
ω13, cm-1
(1) R ) 100°
1600
450
120
0.115
0.143
(2) R ) 110°
1600
1100
200
0.115
0.122
2185.3 540.2 0 2383.3 753.0 0
2138.2 534.3 0 2335.2 746.3 0
a Also listed are geometries, force constants, and isotopic frequencies of normal vibrations of two successful examples of the (CO )q 2 transition state with an asymmetric reaction coordinate (FDd ) + xFDFd); the first frequency corresponds to the symmetric stretching vibration, the second frequency corresponds to the bending vibration, and the third, zero frequency corresponds to the asymmetric stretching vibration-decomposition mode.
5828 Langmuir, Vol. 15, No. 18, 1999
Figure 6. Examples of ranges of FD-Fd values giving agreement with the experiment at 343 and 453 K (numbers attached) for (CO2)q TS with a symmetric reaction coordinate (FDd ) xFDFd) for R ) 90°: FR ) 50 N m-1 (full line) and FR ) 150 N m-1 (dashed line).
Kobal et al.
Figure 8. Examples of ranges of FD-Fd values giving agreement with the experiment at 343 and 453 K (numbers attached) for (CO3)q TS with an asymmetric reaction coordinate (FDd ) + xFDFd).
N m-1, respectively. Among the ranges for 110°, we selected only FD ) 1800 N m-1, Fd ) 1000-1050 N m-1, FR ) 150 N m-1, and FD ) 1600 N m-1, Fd ) 1100 N m-1, FR ) 200 N m-1; the remaining values do not fit our requirements. In Figure 5 agreement with the experiment is shown for two transition states for which the parameters are listed in Table 1. Figure 6 shows the FD-Fd ranges for the (CO2)q transition state with a symmetric reaction coordinate. The regions for both temperatures do not overlap; the calculated KIE are close to the experimental values but do not have a correct temperature dependence and as such are not acceptable. (CO3)q Transition States. It is evident from Figures 7 and 8, showing only several examples of FD-Fd regions, that this complex does not provide a correct temperature dependence of KIE because the regions at the two temperatures are far from overlapping.
Figure 7. Examples of ranges of FD-Fd values giving agreement with the experiment at 343 and 453 K (numbers attached) for (CO3)q TS with an asymmetric reaction coordinate (FDd ) + xFDFd).
motion within the reaction coordinate, for our purposes only cases with one stretching force constant between 1600 and 1800 N m-1 (weakening the bond in the CO molecule) and the other between 0 and 1600 N m-1 (forming a new C-O bond between CO2) are really acceptable. For R ) 100° the following ranges of values attract our attention: if FD ) 1600 N m-1, then Fd may take values in the range of 350-450 and 300-450 N m-1 for FR ) 100 and FR ) 150
Conclusions As expected, the interpretation of the kinetic isotope effects has given us additional insight into the reaction studied.30-33 The fact that the (CO3)q transition state does not reproduce the temperature dependence of the experimental KIE confirms that an adsorbed CO molecule interacts simultaneously only with one adsorbed O atom at the Ag surface. Moreover, with the (CO2)q transition state only an asymmetric reaction coordinate gives a satisfactory agreement with the experiment. Its interbond angle is in the region of 100-110°; the values of other parameters are collected in Table 1. LA981309N (30) Zielinski, M.; Zielinska, A.; Bernasconi S.; Papiernik-Zielinska, H. J. Radioanal. Nucl. Chem. 1997, 220, 263. (31) Lesar, A.; Senegacˇnik, M. J. Chem. Phys. 1993, 99, 187. (32) Ogrinc, N.; Kobal, I.; Senegacˇnik, M. J. Phys. Chem. 1997, 101, 7236. (33) Wang, H.-Y.; Au, C.-T. Catal. Lett. 1996, 38, 77.
