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J. Phys. Chem. 1996, 100, 17202-17206
Studies on the Reactions of Atomic Sulfur (3P) with H2, D2, CH4, C2H6, C3H8, n-C4H10, and i-C4H10 Kentaro Tsuchiya,† Koichi Yamashita,‡ Akira Miyoshi,§ and Hiroyuki Matsui*,§ National Institute for Resources and EnVironment, 16-3 Onogawa, Tsukuba, Ibaraki, 305 Japan, Department of Applied Chemistry, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113 Japan, and Department of Chemical System Engineering, The UniVersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113 Japan ReceiVed: May 1, 1996; In Final Form: August 6, 1996X
Rate constants for the reactions of S(3P) atom with H2, D2, CH4, C2H6, C3H8, n-C4H10, and i-C4H10 have been measured at temperatures above 830 K by a laser photolysis-shock tube method coupled with atomic resonance absorption spectrometry. The activation energies for these reactions were found to be almost identical with the endothermicities, indicating the lack of pronounced barriers along the reaction coordinates, in contrast to the analogous reactions of O(3P) atoms. Group additivity of the rate constants for primary and secondary C-H bonds was found to be a good approximation for the reactions of S(3P) with alkanes. Ab initio (MRSDCI) potential energy surface calculations also revealed that the barrier height along the collinear S(3P) + H2 reaction coordinate is very small, only 8.3 kJ mol-1 above the SH + H asymptote.
Introduction The role of sulfur atoms and sulfur-containing species is important in combustion and atmospheric chemistry, especially in relation to the environmental SOx issues. In the previous paper,1 a new kinetic model was developed and proposed for the high-temperature oxidation mechanism of H2S based on the kinetic measurements on key reactions. An important and interesting feature has been revealed about the thermal decomposition mechanism of H2S,2-4 which mainly decomposes to S(3P) + H2, but not to H + SH, as was assumed in the earlier studies.5-7 Since a similar mechanism can be expected for the thermal decomposition of organic sulfur compounds, the formation of S(3P) atoms and their reactions with organic compounds may play some role in the early stage of the combustion of sulfur-containing fuels. However, the knowledge of the kinetics of sulfur atoms is limited to date. For the reactions with hydrocarbons, only the studies on the reactions with alkenes and alkynes have been reported.8-10 In addition to the practical importance, the reactions of sulfur atoms are interesting in contrast to those of oxygen, the element belonging to the same VIa group. Some features have been discussed concerning the difference between sulfur and oxygen systems. Hydrogen abstraction reactions by S(3P) are expected to be slower than those by O(3P) due to the smaller bond dissociation energy of S-H than O-H, while oxygen abstraction reactions by S(3P) are known to be faster than those by O(3P) [e.g., S(3P) + NO2 f SO + NO11 versus O(3P) + NO2 f O2 + NO12] due to the stronger SdO bond. The dominance of S(3P) atom formation in the pyrolysis of H2S has been ascribed2-4 to the intersection of triplet surfaces with the singlet surface, which lies lower than that of H2O system. Also the strong non-Arrhenius behavior of the S(3P) + O2 reaction may be due to the effects of low-lying multiplet surfaces.13 Previously,4 we reported the kinetic measurements on the reactions of S(3P) with H2 and H2S. The observed activation energies were approximately identical with the endothermicities. This indicates the lack of pronounced barrier between reactants and * To whom correspondence should be addressed. † National Institute for Resources and Environment. ‡ Department of Applied Chemistry, The University of Tokyo. § Department of Chemical System Engineering, The University of Tokyo. X Abstract published in AdVance ACS Abstracts, October 1, 1996.
S0022-3654(96)01252-X CCC: $12.00
products, in clear contrast to the analogous reactions14,15 of O(3P) with H2 and H2S, which proceed via substantial barriers. In the present study, for the extension of the kinetic information and for the further understanding of the chemical nature of sulfur atoms, the measurements on the S(3P) atom reactions were extended to the reactions with D2, CH4, C2H6, C3H8, n-C4H10, and i-C4H10:
S + H2 f SH + H
∆H298K ) 84.4 kJ mol-1
(1)
S + D2 f SD + D
∆H298K ) 87.2 kJ mol-1
(2)
S + CH4 f SH + CH3 S + C2H6 f SH + C2H5
∆H298K ) 87.0 kJ mol-1
(3)
∆H298K ) 59.3 kJ mol-1 (4)
S + C3H8 f SH + n-C3H7
∆H298K ) 58.0 kJ mol-1 (5a)
f SH + i-C3H7
∆H298K ) 46.3 kJ mol-1 (5b)
S + n-C4H10 f SH + n-C4H9
∆H298K ) 58.0 kJ mol-1 (6a)
f SH + s-C4H9
∆H298K ) 45.7 kJ mol-1 (6b)
S + i-C4H10 f SH + i-C4H9
∆H298K ) 56.9 kJ mol-1 (7a)
f SH + t-C4H9
∆H298K ) 32.8 kJ mol-1 (7b)
where thermodynamic data were taken from refs 16, 17, and 18. Experimental results are discussed in comparison with the reactions of O atoms. Ab initio (MRSDCI) calculations of the potential energy surfaces of collinear S(3P) + H2 and O(3P) + © 1996 American Chemical Society
Reactions of S(3P) with H2 and Alkanes
J. Phys. Chem., Vol. 100, No. 43, 1996 17203
H2 systems have been conducted in order to clarify the reason for the difference between O(3P) and S(3P) reactions. Experimental Section The rate constants for the reactions of S(3P) atoms were directly measured by monitoring the pseudo-first-order decrease of S atoms with a laser photolysis-shock tube technique coupled with atomic resonance absorption spectrometry. Details of the apparatus have been described previously.19,20 Only a brief description will be given here. The shock tube used in this study is a diaphragmless one with a 5-cm diameter and a 4-m length and is made of stainless steel. The sample gas mixtures were irradiated by a KrF excimer laser beam through a rectangular quartz window (3 cm × 1 cm) located at the end plate of the shock tube. The laser was fired with a 100-µs delay after the reflected shock wave passed through the observation section located 3 cm upstream from the end plate. S(3P) atoms were detected by using atomic resonance absorption spectrometry. Resonant radiation at 182.6 nm emitted from a microwave discharge lamp (containing a flowing mixture of 0.1% SO2 in He maintained at ∼9 Torr) was isolated by using a 20-cm VUV monochromator and then sensed by a solar-blind photomultiplier (Hamamatsu, R976). COS was used as a precursor for S(3P) atoms. S(1D) atoms produced in the 248-nm photolysis of COS are rapidly quenched to its ground state (3P) under the shock tube conditions.21 The initial concentration of S(3P) atoms was always kept low enough to satisfy the pseudo-first-order kinetic condition for the decay of S atoms. The procedure to construct the calibration curve for S atoms has been given previously.4 The concentrations of the reactants in the sample gas mixtures (buffer Ar) were [D2] ) 2.02 or 0.50%; [CH4] ) 1.13%; [C2H6] ) 0.522 or 1.10%; [C3H8] ) 0.0506 or 0.255%; [n-C4H10] ) 0.209%; and [i-C4H10] ) 0.114%. The concentrations of COS were 59-89 ppm through all sample gas mixtures. CH4, C2H6, C3H8, n-C4H10, and i-C4H10 (Takachiho; 99.5%, 99.95%, 99.7%, 99.9%, 99.5%, and 99.5%, respectively) and COS (Matheson; 97%) were purified by trap-to-trap distillation. D2 (Takachiho; 99.5%) and Ar (Nihon Sanso, 99.9999%) were passed through a cold trap kept at -120 °C before use.
Figure 1. An example of the time profile of the absorption intensity at 182.6 nm in the KrF laser photolysis of a COS/D2/Ar mixture behind a reflected shock wave (0.503% D2 + 73 ppm COS, T ) 1418 K, F ) 6.75 × 1018 molecules cm-3).
of the measured rate constants for reaction 2 as well as those for reaction 1 is shown in Figure 2. A least-squares fit gives the following Arrhenius expression for the rate constants for reaction 2.
k2 ) 10-9.54(0.25 exp[-(90.6 ( 6.5) kJ mol-1/RT] cm3 molecule-1 s-1, T ) 1200-1680 K Arrhenius plots of the rate constants for reactions 3-7 are shown in Figure 3. A least-squares analysis gives the following Arrhenius expressions.
k3 ) 10-9.47(0.18 exp[-(83.3 ( 4.4) kJ mol-1/RT] cm3 molecule-1 s-1, T ) 1140-1480 K k4 ) 10-9.69(0.61 exp[-(61.7 ( 11.2) kJ mol-1/RT] cm3 molecule-1 s-1, T ) 880-1150 K k5 ) 10-10.02(0.43 exp[-(46.3 ( 8.1) kJ mol-1/RT] cm3 molecule-1 s-1, T ) 890-1160 K
Results Rate constants for reactions 2-7 were measured at temperatures above 830 K. The experiments were limited in the temperature ranges where the influences of thermal decomposition of COS and alkanes are negligible. After subtracting the background absorption by COS, the absorption intensities were converted to concentrations of S atoms using the calibration curve. Initial concentrations of S atoms were (0.8-1.6) × 1013 atoms cm-3. An example of the absorption profile of S atoms (at 182.6 nm) is shown in Figure 1. The first-order decay rate of S(3P) atoms was determined by a least-squares fit. The net decay rate of S(3P) atoms by the reaction with D2 or alkanes was derived by subtracting the contribution of the S + COS reaction (always less than 20% of the whole rate) using the rate constants determined previously.4,22 The rate expression determined in the previous report4 for the S(3P) + H2 reaction was
k1 ) 10-9.58(0.16 exp[-(82.5 ( 4.0) kJ mol-1/RT] cm3 molecule-1 s-1, T ) 1050-1660 K Experiments for S + D2 were performed under conditions similar to the previous S + H2 experiments. An Arrhenius plot
k6 ) 10-10.22(0.53 exp[-(39.7 ( 9.3) kJ mol-1/RT] cm3 molecule-1 s-1, T ) 830-1050 K k7 ) 10-10.47(0.31 exp[-(33.9 ( 5.5) kJ mol-1/RT] cm3 molecule-1 s-1, T ) 830-1060 K Discussion The activation energies for reactions 1 and 2 (82.5 and 90.6 kJ mol-1, respectively) were found to be almost identical with the endothermicities (84.4 and 87.2 kJ mol-1, respectively), indicating the lack of pronounced barriers for the reverse reactions. The observed isotope effect in the rate constant is reasonable for such reactions, in which the effective transition state is presumably located at the later part of the reaction coordinate. The observed ratios of k2/k1 were 0.6 at 1600 K and 0.5 at 1250 K, which are close to those predicted from the difference in the collision frequency and the enthalpy of reaction, i.e., k2/k1 ) Z2/Z1 exp(-∆∆E/RT), where Z2/Z1 is the ratio of collision frequencies [)(µS+D2/µS+H2)-1/2 ) 0.728] and ∆∆E ()2.8 kJ mol-1) is the difference in the enthalpy of reaction. In terms of the transition-state theory, such a magnitude of the
17204 J. Phys. Chem., Vol. 100, No. 43, 1996
Figure 2. Arrhenius plot of the rate constants for the S(3P) + D2 reaction [Experimental conditions: (b) 2.02% D2 + 74 ppm COS, (O) 0.50% D2 + 73 ppm COS]. The solid line denotes the result of a leastsquares fit of the present experimental data, and the dashed line denotes the rate constants for the S(3P) + H2 reaction determined in the previous report.4
Tsuchiya et al.
Figure 4. Examination of the group additivity. Rate constants for the S(3P) + C2H6, C3H8, and n-C4H10 reactions are plotted against the number of secondary C-H bonds. Solid lines denote the results of least-squares fits, and dashed lines denote the rate constants calculated from eq 8.
channels. Therefore, a trial was made to resolve the overall rate constants into the rate constants for individual channels by assuming the group additivity. In Figure 4, the overall rate constants for C2H6, C3H8, and n-C4H10 at temperatures of 900 and 1000 K are plotted against the number of secondary C-H bonds. The good linear relationship in the plot indicates the validity of the group additivity for the reactions of S(3P) atoms with alkanes studied here. By assuming that the rate constants for the primary hydrogen abstraction in C3H8, n-C4H10, and i-C4H10 are the same as those for C2H6, the following expressions were derived for C3H8, n-C4H10, and i-C4H10:
k5,6 ) 6 × 3.43 × 10-11 exp(-61.7 kJ mol-1/RT) + ns × 1.91 × 10-11 exp(-42.5 kJ mol-1/RT) cm3 molecule-1 s-1 (8) k7 ) 9 × 3.43 × 10-11 exp(-61.7 kJ mol-1/RT) + 0.76 × 10-11 exp(-24.7 kJ mol-1/RT) cm3 molecule-1 s-1 (9)
Figure 3. Arrhenius plot of the rate constants for the reactions S(3P) with CH4, C2H6, C3H8, n-C4H10, and i-C4H10 [Experimental conditions: (O) 1.13% CH4 + 61 ppm COS, (0) 0.522% C2H6 + 60 ppm COS, (]) 1.10% C2H6 + 61 ppm COS, (4) 0.0506% C3H8 + 59 ppm COS, (3) 0.255% C3H8 + 88 ppm COS, (b) 0.209% n-C4H10 + 73 ppm COS, (9) 0.114% i-C4H10 + 79 ppm COS]. Solid lines denote the least-squares fits of the experimental data, and dotted lines denote the rate constants calculated from eq 8 (see text).
isotope effect is expected if the reaction proceeds with very late (or very early) barriers. Also, the activation energies for reactions 3 and 4 (83.3 and 61.7 kJ mol-1, respectively) are close to the endothermicities (87.0 and 59.3 kJ mol-1, respectively). Since C3H8, n-C4H10, and i-C4H10 contain different types of C-H bonds in a molecule, the observed activation energies cannot be directly compared with the reaction enthalpies for the individual abstraction
where ns is the number of secondary H atoms. Broken lines in Figure 3 denote the rate constants for C3H8 and n-C4H10 calculated from eq 8. Although more information on the rate constants for larger alkanes is necessary for the detailed examination of the group additivity, each activation energy for the abstraction of primary, secondary, and tertiary hydrogen atoms was evaluated to be Ea(primary) ≈ 62 kJ mol-1, Ea(secondary) ≈ 43 kJ mol-1, and Ea(tertiary) ≈ 25 kJ mol-1. These are also close to the endothermicities of the respective channels (∼58, ∼46, and ∼33 kJ mol-1, respectively). The Arrhenius pre-exponential factors derived for a single primary, secondary, and tertiary hydrogen atom are 3.43 × 10-11, 1.91 × 10-11, and 0.76 × 10-11, respectively. This falloff trend of the pre-exponential factors may be ascribed to the steric hindrance due to the large size of the S atom, such that the secondary or tertiary hydrogen is difficult to be approached by the surrounding primary hydrogens. In addition to the result for H2 and H2S in the previous work,4 the present experiments for alkanes showed that the activation energies are also close to the endothermicities. This indicates the lack of pronounced barriers other than endothermicities for these hydrogen abstraction reactions by S(3P) atoms. This fact is in clear contrast with the analogous reactions of O(3P) atoms, which proceed via substantial barriers between reactants and products. An Evans-Polanyi plot for the reactions of O(3P) and S(3P) atoms is shown in Figure 5. Activation energies for O + alkanes, O + H2, and O + H2S reactions were taken from
Reactions of S(3P) with H2 and Alkanes
Figure 5. Evans-Polanyi plots for the S(3P) + alkanes and O(3P) + alkanes reactions.
J. Phys. Chem., Vol. 100, No. 43, 1996 17205 examine these two possibilities and to examine the difference between S and O reactions, ab initio calculations were performed for the collinear 3Π potential energy surfaces (PESs) of S(3P) + H2 and O(3P) + H2 reactions. Ab initio multireference single and double configuration interaction (MRSDCI) calculations of PESs have been done by using the MOLPRO code24 with the valence triple-zeta (VTZ) basis set.25 The details of our ab initio calculations are described in a previous paper.4 The collinear approach between S(3P)/ O(3P) and H2 produces the 3Π and 3Σ- states. The 3Σ- state is repulsive and the 3Π state correlates to the product ground state, SH(2Π) + H. Figure 6 shows the 3Π PES for the collinear approach of (a) the sulfur atom and of (b) the oxygen atom to the hydrogens. A characteristic difference between these reactions is the location of the transition state. In the case of S(3P) + H2, the transition state was found at the geometry RSH ) 1.419 Å and RHH ) 1.167 Å, indicating a “late” barrier; that is, the corresponding bond lengths of the transition state and the reactant H2 (0.74 Å) or the product SH (1.34 Å) differ 58% and 6%, respectively. On the other hand, a “middle” transition state was found for the O(3P) + H2 reaction; that is, both of the bond lengths, ROH ()1.184 Å) and RHH ()0.926 Å), stretch about 20% in comparison with those of the OH radical (0.97 Å) and H2 molecule (0.74 Å). The 3Π direct-abstraction potential energy surface of the S(3P) + H2 reaction has a very small barrier, only 8.3 kJ mol-1 above the SH + H asymptote, while a pronounced barrier was found for the O(3P) + H2 reaction (41.5 kJ mol-1 above the OH + H asymptote). Although either mechanism, the direct abstraction or the intersystem crossing mechanism, is consistent with the observed activation energies, the former (the direct abstraction) is more probable since the observed Arrhenius pre-exponential factors seem too large for the latter mechanism involving the entropically less favored intersystem crossing. References and Notes
Figure 6. (a) Contour plot of the 3Π PES for S(3P) + H2 with a “late” barrier. The contours are drawn for each 0.15 eV. Note that the bottom right end corresponds to S(3P) + H2. (b) Contour plot of the 3Π PES for O(3P) + H2 with a “middle” barrier. The contours are drawn for each 0.17 eV. Note that the bottom right end corresponds to the O(3P) + H2 channel.
refs 23, 14, and 15, respectively. Obviously, the reactions of S(3P) atoms are classified into a different series from the reactions of O(3P) atoms. The activation energies and the isotope effect measured in the present study suggest the lack of pronounced barriers in the triplet direct-abstraction potential energy surfaces. However, an alternative explanation is possible for the observed activation energies; that is, the reactions proceed via intersystem crossing with singlet surfaces (which is the ground 1A1 surface of H2S for S + H2). For the case of S + H2, the intersystem crossing occurs at an energy below that of the products, H + SH.4 To
(1) Tsuchiya, K.; Kamiya, K.; Matsui, H. Int. J. Chem. Kinet., in press. (2) Woiki, D.; Roth, P. J. Phys. Chem. 1994, 98, 12958. (3) Olschewski, H. A.; Troe, J.; Wagner, H. Gg. J. Phys. Chem. 1994, 98, 12964. (4) Shiina, H.; Oya, M.; Yamashita, K.; Miyoshi, A.; Matsui, H. J. Phys. Chem. 1996, 100, 2136. (5) Higashihara, T.; Saito, K.; Yamamura, H. Bull. Chem. Soc. Jpn. 1976, 49, 965. (6) Bowman, C. T.; Dodge, L. G. Symp. (Int.) Combust. [Proc.] 1976, 16, 971. (7) Roth, P.; Lohr, R.; Barner, U. Combust. Flame 1982, 45, 273. (8) Davis, D. D.; Klemn, R. B.; Braun, W.; Pilling, M. Int. J. Chem. Kinet. 1972, 4, 383. (9) von Roodselaar, A.; Safarik, I.; Strausz, O. P.; Gunning, H. E. J. Am. Chem. Soc. 1978, 100, 4068. (10) Strausz, O. P.; O'Callaghan, W. B.; Lown, E. M.; Gunning, H. E. J. Am. Chem. Soc. 1971, 93, 559. (11) Clyne, M. A. A.; Whiltefield, P. D. J. Chem. Soc., Faraday Trans. 2 1979, 75, 1327. (12) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson, R. F., Jr.; Kerr, J. A.; Troe, J. J. Phys. Chem. Ref. Data 1992, 21, 1125. (13) Miyoshi, A.; Shiina, A.; Tsuchiya, K.; Matsui, H. Proc. 26th Symp. (Int.) Combust., in press. (14) Warnatz, J. In Combustion Chemistry; Gardiner, W. C., Jr., Ed.; Springer-Verlag: New York, 1984. (15) Tsuchiya, K.; Yokoyama, K.; Matsui, H.; Oya, M.; Dupre, G. J. Phys. Chem. 1994, 98, 8419. (16) Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Fruip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables. J. Phys. Chem. Ref. Data 1985, 14, Suppl. 1. (17) Nicovich, J. M.; Kreutter, K. D.; van Dijk, C. A.; Wine, P. H. J. Phys. Chem. 1992, 96, 2518. (18) McMillen, D. F.; Golden, D. M. Annu. ReV. Phys. Chem. 1982, 33, 493. (19) Koshi, M.; Yoshimura, M.; Fukuda, K.; Matsui, H.; Saito, K.; Watanabe, M.; Imamura, A.; Chen, C. J. Chem. Phys. 1990, 93, 8703.
17206 J. Phys. Chem., Vol. 100, No. 43, 1996 (20) Matsui, H.; Koshi, M.; Oya, M.; Tsuchiya, K. Shock WaVes 1994, 3, 287. (21) Woiki, D.; Markus, M. W.; Roth, P. J. Phys. Chem. 1993, 97, 9682. (22) Oya, M.; Shiina, H.; Tsuchiya, K.; Matsui, H. Bull. Chem. Soc. Jpn. 1994, 67, 2311. (23) Miyoshi, A.; Tsuchiya, K.; Yamauchi, N.; Matsui, H. J. Phys. Chem. 1994, 98, 11452.
Tsuchiya et al. (24) MOLPRO is a package of ab initio programs written by H.-J. Werner and P. J. Knowles, with contributions from J. Almlof, R. F. Amos, M. J. O. Deegan, S. T. Elbert, C. Hampel, W. Meyer, K. Peterson, R. Pitzer, A. J. Srone, and P. R. Taylor. (25) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007.
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