Investigations of Surface Reactions by Kinetic Isotope Effects
Raziskave reakcij na površinah s študijem kinetičnih izotopskih efektov
N. Ogrinc1, P. Vidmar, I. Kobal, M. Senegačnik, IJS Ljubljana
Prejem rokopisa - received: 1996-10-04; sprejem za objavo - accepted for publication: 1997-01-17
The kinetic isotope effect is the phenomenon that in a chemical reaction in which two isotopic species of the same reacting molecule are involved, the rate constants of these two isotopic reactions differ, the value for the isotopically heavier reaction generally being smaller. Kinetic isotope effects can be obtained experimentally by analysing isotopic ratios in either the reactants or products at a given extent of the reaction. Applying Bigeleisen's formalism within the framework of absolute rate theory, kinetic isotope effects can be calculated if the geometry and force field of the transition state in the rate determining step of the reaction mechanism is postulated on the basis of chemical intuition and data are availabie on the chemical kinetics and the reaction mechanism. In this contribution, investigations of the kinetic isotope effects in the reduction of carbon monoxide and dioxide over Mg, and in its catalytic oxidation with oxygen over Pd, NiO and ZnO are presented. The resuits obtained give additional information about the reaction mechanisms of these reactions.
Key words: kinetic isotope effects, CO, Mg, Pd, NiO. ZnO
Izotopski efekt imenujemo pojav; da se konstanti hitrosti dveh izotopskih reakcij razlikujeta. V večini primerov poteka izotopsko težja reakcija počasneje. Kinetične jzotopske efekte ekperimentalno določimo z izotopsko analizo bodisi preostalega reaktanta ali nastalega produkta reakcije. Če predpostavimo geometrijo in konstante sile aktiviranega kompleksa najpočasnejše stopnje v reakcijskem mehanizmu, lahko po metodologiji Bigeieisena, ki je osnovana na teoriji absolutnih reakcijskih hitrosti, izračunamo kinetične izotopske efekte. Če se ekperimentalne in teoretično izračunane vrednosti ujemajo, razumemo, da je bila predpostavka za aktivirani kompleks prava. V tem prispevku podajamo rezultate raziskav kinetičnih izotopskih efektov v redukcijo ogljikovega monoksida in dioksida na magneziju in v kataiitični oksidaciji s kisikom na Pd, NiO in ZnO. Rezultati dajejo dodatne informacije o mehanizmih teh reakcij.
Ključne besede: kinetični izotopski efekti, CO, Mg, Pd, NiO, ZnO
1 Introduction
According to Bigeleisen1,2, based on the Absolute Rate Theory of chemical reactions3, kinetic isotope effects, i.e. the ratio of the rate constants of two simultane-ously running isotopic reactions, may be calculated ap-plying the following equations:
3n-6	3n"-7
k I Vli 1-t u2i smh(un/2) -p, uf; sinh(u^/2)
k, " v£2 H u„ sinh(u2/2) * * u* sinh(u?/2)
i=l i=l
/ v 1/2 3n*-7
n- (d
VL2 |G£| Ll<
v / 1=1
The meaning of the symbols is as follows: 1, 2 refer to the lighter and heavier isotope, respectively; denotes the transition state of the rate determining step of the reaction mechanism; n, n" - number of atoms in reactant molecule and transition state, respectively; T - temperature; kb - Boltzmann's constant; h - Planck's constant; v - frequency; u = hv/kbT; Vl - reaction-coordinate fre-quency.
The frequencies of the reactant molecules are usually taken from the literature, while those for the transition state are obtained by solving Wilson's matrix equation4:
Mag. Nives OGRINC
Inšliiui Jožef SLelan. Ljubljana
Jamova 39. I (XX) Ljubljana. Slovenija
GFL = LA
in which G is the Wilson's matrix comprising geometric parameters; F is the force constants matrix; L is the eigenvector matrix; A is a diagonal matrix of eigenval-ues = 4I1V with Vi equal to the frequency of the /th normal vibration.
For the transition state the above equation is to be solved under the condition5:
|F| = 0
in order to obtaine for a 3n* non-liner transition state 3n* -7 real frequencies, the remaining frequency (refer-ring to the reaction coordinate) being zero or imaginary (mainly the first čase is used). When an agreement of the calculated kinetic isotope effects with the experi-mental values is achieved, the proposed transition state is accepted.
In our laboratory, kinetic isotope effects of carbon and oxygen in the reduction of CO and CO2 over Mg, and in catalytic oxidation of CO over Pd, NiO and ZnO were investigated vvith the aim of obtaining additional understanding of the reaction mechanisms of these reactions. The experiments were carried out under steady state conditions in a reaction vessel connected to a vacuum system6. The reaction, run at a selected temperature, was stopped at the desired extent of reaction. The kinetic isotope effects were obtained from the extent of reaction, and the isotope enrichment factors6 measured by a mass
spectrometer for the stable isotopes C-13, 0-18, and by an ionisation chamber for C-14 in the residual reactant or the product formed. Due to isotopic exchange on the surface, we were not always able to determine oxygen effects experimentally. For the slowest step of the mecha-nism of the reactions studied, several geometries of the transition state, guessed by the chemical intuition and on the basis of information available for the reaction sys-tem, were considered in Wilson's analysis. In ali the cases presented here the reactant molecule is CO for vvhich the isotopic frequencies were taken from the literature7. Kinetic isotope effects (ki2/ki3, ki2/ki4, kie/kis, k being the rate constants) were calculated using Bigeleisen's equation as written above8 and an agree-ment with the experimental data was sought9.
2 Discussion
1.040
10
1.030
""(NI
1.020
1.010
_L
600
700 800 T/K
900
A. Reduction of CO over Mg
Carbon kinetic isotope effects determined in the temperature range of 723-823 K were found to be practically temperature independent and amounted to 1.017 ± 0.001 and 1.035 ± 0.002 for C-13 (ki2/kis) and C-14 (kn/ku), respectively. For the slowest step of the reaction mecha-nism the reaction of adsorbed CO with either one or two surface Mg atoms was assumed. Thus for the transition state different geometries of C-O-Mg and C-0-Mg2 were taken into account. The first proposal may give effects close to the experimental ones but is not able to repro-duce their temperature independence. For the second proposal different bond lengths and interbond angles were tried. The best agreement with experiment was found with the transition state shown in Figure 1.
These results confirm that in CO reduction over a Mg surface, one adsorbed CO molecule reacts with two metal surface atoms, and that among ali the adsorbed CO molecules only those being adsorbed via the O atom to the surface at the moment of reaction are reactive.
B. Reduction of COi over Mg"
For this reaction the kinetic isotope effects determined in the temperature range of 773-873 K are: ki2/ki3 = 1.078 - 7.15 x T x 10"5 (± 2.2 x 10"3), ki2/ki4 = 1.156 -1.42 x T x 10"5 (± 3.2 x 10"3), and kie/kig = 0.909 + 1.12 x T x 10-4 (± 3.6 x 10"3).
In the slovvest step of the reaction mechanism, the at-techment of a C02 molecule to the surface, one CO bond is being weakened with simultaneous formation of a new Mg-0 bond. Thus for this reaction a four-centre transition state O-C-O-Mg was proposed. Varying bond lengths and interbond angles, two bent structures with Mg and the terminal O atom either in cis or trans posi-tion ali give three kinetic isotope effects in agreement with the experiment (Figure 2).
Figure 1: The agreement between the calculated and experimental kinetic isotope effects. <x=140°, t=0°, Fod=0, Fdd=0, Fa=20 Nm1, Ft=10 Nm"1. (—) Fd=1400 Nm'1. Fj=200 Nm'1; (- - -) FD=1800 Nm", Fd=600 Nm'1. (a) ki2/k|4), (b) ki2/ki3). Bars show experimental pomts Slika 1: Ujemanje med eksperimentalnimi (stolpci) in teoretično izračunanimi (krivulje) kinetičnimi izotopskimi efekti. a=140°, t=0°, Fdj=0 Fdd=0, Fa=20 Nm"1, Ft=10 Nm'1. (—) Fd=1400 Nm'1, Fd=200 •) Fd=1S00 Nm'1, Fj=600 Nm'1. (a) ku/ku), (b) ki2/ki3)
Nm'1; (-
We may conclude that a C02 reacting molecule on a Mg surface is not linear. This could be due to its excita-tion or an interaction of the terminal O atom with the surface; this is especially evident for the D type transition state.
12
C.	Catalytic oxidation of CO over Pd
C-13 kinetic isotope effects in the oxidation of CO with oxygen over a Pd/Al20? catalyst were determined in the temperature range of 323-413 K and the follovving temperature dependence was found: 100 ln(ki2/ki3 = 3.18 - 83 l/T (± 0.15). It has been widely accepted that the kinetics follow the Langmuir-Hinschelwood mechanism, and as the slowest step the reaction of adsorbed CO molecules with adsorbed O atoms was proposed13. For the transition state of this reaction both linear and bent O-C-O have been suggested14'15. Thus, in our analy-sis we took a C02 molecule with interbond angles from 80 to 180°. The linear model was found never to give kinetic isotope effects in agreement with the experiment. The best agreement was obtained with a transition state having the interbond angle close to 90°. One of the best choices is a symmetric C02 with an interbond angle of about 80°, bond lengths of 123 pm, and 1080 and 200 Nm'1 for the stretching and bending force constants, re-spectively. To save space the figure showing the agreement is omitted.
D.	Catalytic oxidation of CO over NiO
In the oxidation of CO with oxygen over a NiO cata-lyst, carbon kinetic isotope effects were determined in the temperature range of 523-773 K. They are practically temperature independent and amount to 1.0255 + 0.0014
1.030
1.025
oo 7 1.020 o
1.015
1.010,
1.050 1.045 >r 1.040 O 1.035 1.030 1.025
JL
_L
_L
760 800 840 880
T/K
\
TS-C
760 800 840 880 T/K
1.010
1.005
« 1.000 ■
° 0.995 0.990 0.985
TS-C TS-D
J_
J_
_L
760 800 840 880 T/K
t
TS-C
TS-D
Figure 2: The agreement between the calculated and experimental kinetic isotope effects. The parameters Nm"1 for force constants, nm for bond length for TS-C^and TS-D transition states, respectively; FCo=1700, 1700; Fco»=500, 300; FMgo*=150, 100; dco=113.6, 113.6; dco»=140.3, 153.2; dMgO*= 194.9, 225.0; «=(3=120°; FK=100, 100; Fp=50, 30; Ft=10, 20
Slika 2: Ujemanje med eksperimentalnimi (območje med črtkanima premicama) in teoretično izračunanimi (za aktivirana kompleksa C in D) kinetičnimi izotopskimi efekti. Vrednosti parametrov (F/Nm'1, d/nm): Fco=1700, 1700; Fco*=500, 300; FMgO*=150, 100; dco=113.6, 113.6; dco*=140.3, 153.2; dMgo»=I94.9, 225.0; a=p=120°; Fa=100, 100; Fp=50, 30; FT=10, 20
and 1.0493 ± 0.0013 for C-13 and C-14, respectively. Due to an isotopic exchange of oxygen on the surface, oxygen isotope effects could not be measured. For the rate determining and isotopic fractionation governing step of the reaction mechanism both CO2 and CO3 transition states may be taken into account16. With ali selec-tions of geometric parameters and force constants the CO3 transition states gave kinetic isotope effects much lower than the experimental values. Thus only the CO2 transition state may be considerd as acceptable for this reaction. Best agreement was achieved with the follow-ing parameter values: interbond angle from 110 to 130°; stretching force constants for both bonds 1600-1800 and 600-800 Nm-1, respectively; bending force constant: 50-150 Nm-1. To save space the agreement between the calculated and experimental values is omitted. This result supports the suggestion that in the slowest step a CO molecule, most probably adsorbed to the surface or maybe from the gas phase, interacts with one and not two adsorbed O atoms.
E. Catalytic oxidation of CO over ZnO17
The temperature range investigated was 473-773 K. Also here the carbon kinetic isotope effects were found
to be temperature independent and amounted to 1.0101 ± 0.0010 and 1.0204 ± 0.0019 for ki2/ki3 and ki2/ki4, re-spectively. Due to oxygen isotopic exchange reactions we were not able to determine the oxygen kinetic isotope effects. As on NiO, also here both CO2 and CO3 transition states may be considered as acceptable. In the con-trast to NiO, we vvere not able here to distinguish be-tween these two possibilities because both give a good agreement with experiment. In a symmetrical CO2 transition state the follovving parameter values give the best agreement: interbond angle: 80-90°; stretching force constants: 600-900 Nm"1; bending force constant: 200-300 Nm1. The CO3 transition state is planar with ali interbond angles of 120° and the follovving force constants in Nm1: 1700-1720 for one bond and 450-500 for the other two, 60 for two bending and 50 for out-of-plane bending. Again the graph presenting the agreement be-tvveen the calculated and experimental values is not shown.
3 Conclusions
These examples have shown that investigation of kinetic isotope effects in a chemical reaction gives addi-tional information about the transition state of that step
of the reaction mechanism which determins the overall rate and governs the isotopic fractionation. It often hap-pens that the numerical values of the geometric parame-ters and force constants are obtained, but a selection of only one transition state out of several possibilities is im-possible. In this čase additional criteria should be introduced, for instance activation energy, or pre-exponen-tials18. A good support for a particular choice among various possible transition states can also be made by quantum chemical calculations19.
4 References
1 J. Bigeleisen and H. Goeppert-Mayer, J. Chem. Phys., 15, 1972, 1953 - W. A. Van Hook, Isotope Effects in Chemical Reaction. edt. C. J. Col-lins and N. S. Bowman (Van Nostrand Reinhold, New York, 1970) 1 S. Gasstone, K. Laidler, and H. Eyring, The Tlieory ofRate Processes (McGraw Hiti, New York, 1965) 4 E. B. Wilson. J. C. Decius, and P. C. Cross. Molecular Vibrations (McGraw Hill, New York, 1965)
5 K. Nakamoto, Infrared Spectra of Inorganic and Coordination Com-pounds (Wiley, New York, 1965)
61. Kobal. M. Senegačnik, and H. Kobal. J. Catal., 49, 1, 1977
7	L. H. Jones, Inorganic Vibrational Spectroscopy (Marcel Dekker. Inc., New York, 1971)
8	B. Barlič, M. S. Thesis, University of Ljubljana, 1973
91. Kobal, M. Senegačnik. and B. Barlič, J. Chem. Phys., 69, 1978. 1, 174
101. Kobal and M. Senegačnik, J. Chem. Soc. Faraday Trans. 86, 1990, 12, 2283
11 P. Vidmar. A. Lesar. 1. Kobal, and J. Koller, J. Chem. Phys„ 100, 1996, 14, 5781
121. Kobal, N. Ogrinc, M. Senegačnik. 70th Colloid and Surface Science Syrnposiurn, Potsdam, New York, 1996
13 R. P. H. Gasser, in An Introduction to Chemisorption and Catalysis of Metals Claredon Press, Oxford, 1985
14T. Matsushima and H. Asada, J. Chem. Phys„ 85, 1986, 3, 1658
15 T. Matsushima, J. Chem. Phys. 91, 1983, 9, 5722
,6 Yu. D. Pankrefev, Kinet. Katal., 15, 1974, 635
171. Kobal, M. Senegačnik, and H. Kobal, J. Chem. Phys„ 78, 1983, 4, 1815
18	A. Lesar and M. Senegačnik, J. Chem. Phys„ 99, 1993, 1, 187
19	K. Polanec, J. Vernik, M. Hodošček, I. Kobal and M. Senegačnik, Vest. Slov. Kem. Druš. 39, 1992, 2, 213