comparison of theory and experiment
C. Calculation and comparison of rate coefficients
Rate coefficients of reactions (1a) and (1b) calculated with TST, CVT, CVT/ZCT, and
CVT/SCT methods in the temperature range 300 to 3000 K are presented in Fig. 6. As shown in panels A and B of Fig. 6, rate coefficients of reactions (1a) and (1b) predicted with TST are similar to those predicted with CVT because of their moderately high barriers. The rate coefficients predicted with CVT/ZCT are smaller than those predicted with CVT/SCT. At 300 K, rate coefficients of reactions (1a) and (1b) predicted with CVT/SCT are 24 and 10500 times that predicted with CVT, respectively.
The branching ratio of channels (1a) and (1b) predicted with the CVT/SCT method for 300−3000 K are plotted in Fig. 6C. Reaction (1a) is the major channel at low temperatures; its branching ratio decreases from 0.87 at 300 K to 0.50 at 1700 K. Above 1700 K, reaction (1b) becomes the major channel; its branching ratio increases from 0.50 at 1700 K to 0.62 at 3000 K.
In order to compare predicted rate coefficients with experimental data quantitatively, we fit rate coefficients predicted with CVT/SCT in the temperature range 300−1000 K to the
Arrhenius form to yield
k1a(T) = 1.77×10−11 exp [−(2298/T )] cm3 molecule−1 s−1 (15) k1b(T) = 1.50×10−11 exp [−(2845/T )] cm3 molecule−1 s−1 (16) At higher temperatures, rate coefficients increase more rapidly with temperature. We fit rate coefficients predicted with CVT/SCT in the temperature range 300−3000 K with a
three-parameters function to yield
k1a(T) = 8.80×10−20 T 2.61 exp [−(941/T)] cm3 molecule−1 s−1 (17) k1b(T) = 4.15×10−23 T 3.64 exp [−(974/T)] cm3 molecule−1 s−1 (18) Predicted total rate coefficients may be expressed with the three-parameter equation k1(T) = 1.93×10−21 T 3.20 exp [−(763/T )] cm3 molecule−1 s−1 (19) The total rate coefficients predicted with CVT/SCT in the temperature range 300−3000 K are plotted in Fig. 3 to compare with experimental data of KTSKM,5 GJ,6 FSPI,7 and this work. In general, rate coefficients predicted with CVT/SCT is in satisfactory agreement with experimental value reported previously, indicating that the SCT method treats tunneling effects adequately. At low temperatures, predicted rate coefficients are slightly greater than experimental values, but within expected uncertainties of calculation and experiments. At
high temperatures, predicted rate coefficients fit satisfactorily with experimental data of this work and of KTSKM5 and GJ.6
Our experimental data are about 20 % smaller than theoretically predicted rate coefficients, but the deviations are within expected uncertainties. The equation reported by Herron26
k1(T) = 3.99×10−19 T 2.50 exp [−(1550/T)] cm3 molecule−1 s−1 (20) is in satisfactory agreement with our experimental results in the overlapping temperature range 1000−1777 K. The equation reported by Tsang10
k1(T) = 6.44×10−19 T 2.50 exp [−(1550/T)] cm3 molecule−1 s−1 (2) is slightly greater than our experimental results but appears to fit well with calculated rate coefficients at high temperatures, as illustrated in Fig. 3.
V. CONCLUSION
Total rate coefficients of the reaction O(3P) + CH3OH in the temperature range 835−1777 K were determined using a diaphragmless shock tube with atomic resonance absorption
detection of O atoms. Our results extended the upper limit of the temperature range of study from 1006 to 1777 K and clearly indicate a non-Arrhenius behavior of the rate coefficient.
Rate coefficients obtained in this work correlate well with those determined previously by Keil et al.5; they were combined to yield the temperature dependence as k1 = (2.74±0.07)
×10−18 T 2.25±0.13 exp [−(1500±90)/T] cm3 molecule−1 s−1for 298 ≤ T/K ≤ 1777. Theoretical calculations at the CCSD(T)/6-311+G(3df, 2p)//B3LYP/6-311+G(3df, 2p) level predict transition states and barriers for various channels. Rate coefficients predicted with CVT/SCT show that branching ratios of two accessible reaction channels to form CH2OH + OH (1a) and CH3O + OH (1b) varies with temperature. At 300 K, reaction (1a) dominates, whereas above 1700 K, reaction (1b) becomes more important. Predicted total rate coefficients are in
satisfactory agreement with our experimental data at high temperature (835−1777 K) and those reported by Keil et al.5 at 298−998 K.
ACKNOWLEDGMENT
YPL thank the National Science Council of Taiwan (grant no. NSC93-2119-M-009-002) for
support. MCL, SCX, and ZFX thank the support from the Basic Energy Science, Department of Energy, under Contract DE-FG02-97-ER14784, and Cherry L. Emerson Center for
Scientific Computation of Emory University for the use of its resources, which are in part supported by a National Science Foundation Grant (CHE-0079627) and an IBM Shared University Research Award. MCL also acknowledges the support from the National Science Council of Taiwan for a Distinguished Visiting Professorship at the National Chiao Tung University in Hsinchu, Taiwan. SCX also thank the support from Cherry L. Emerson Center for Scientific Computation of Emory University for a Cherry L. Emerson Visiting Fellowship.
Table I. Summary of reported experimental rate coefficients using various methods Temperature
/ K
Pressure (gas) / Torr
k (~298 K) / 10−15, a
A / 10−12, a
Ea/R
/ K Methodb Reference
347−506 0.85 1560 DF/PCA Avramenko et al. (AKK)8 273−438 1.48−2.41 (O2, He) 51.5±5.8 2.82±1.10 1147±101 DF/ESR LeFevre et al. (LMT)2 300−830 232 7.11 1020 DF/ESR Basevich et al. (BKF)3 301−451 1.00−1.76 (N2, NO) 13.6±0.83 2.41±0.01 1540±144 DF/CL & MS Owens & Roscoe (OR)4 298 9.25 (Ar) 0.0598 FP/RF Lalo & Vermeil (LV)9 298−998 2.15−4.41 (O2, He) 5.82±0.54 27.0±5.0 2530±80 DF/RF Keil et al. (KTSKM)5
329−527 50−400 (Ar), 100−200 (Ar:N2=9:1)
FP/RF
300−1006 57.0±19.0 2750±150 DF/TOF Grotheer & Just (GJ)6 297−544 27.2−45.9 (NO, NO2) 8.28±0.623 16.3±4.5 2267±111 PM/CL Failes et al. (FSPI)7 835−1777 1086−1953 (Ar) 229±18c 4210±100c ST/ABS this workc
a in units of cm3 molecule−1 s−1. b DF: discharge flow; FP: flash photolysis; PM: phase modulation; ST: shock tube; PCA: product collection and analysis; ESR: electron spin resonance; CL: chemiluminescence; MS: mass spectrometry; RF: resonance fluorescence; TOF: time-of-flight mass; ABS: absorption. c k(T) = (2.74±0.07)×10−18 T
2.25±0.13 exp[−(1500±90)/T] cm3 molecule−1 s−1 for a combined fit of data from KTSKM and this work
Table II. Reaction models employed to derive rate coefficients of O + CH3OH
No.. Reaction Rate expression Ref.
1a O + CH3OH → OH + CH2OH fitted
1b O + CH3OH → OH + CH3O k1b/k1a calculated from theory
8a CH3OH (+ M) → CH3 + OH (+ M) k∞: 1.9×1016 exp [−(46140/T)] 10a, b k0 : 4.9×1020T −7.35 exp [−(48017/T)]
8b CH3OH (+ M) → CH2OH + H (+ M) k∞: 2.96×1016T −0.08 exp [−(49768/T)] 10a, c k0 : 3.89×1016T −6.33 exp [−(51860/T)]
9 CH2OH + O → H2CO + OH 7.0×10−11 10
10 CH3 + O → H2CO + H 1.41×10−10 27
11a O + SO → S + O2 3.0×10−11 exp [−(6980/T)] 28
11b O + SO (+ M) → SO2 (+ M) 3.3×10−26T −1.84 29 12a O + SO2 (+ M) → SO3 (+ M) 1.21×10−33 exp (3136/T) 30 12b O + SO2 → O2 + SO 8.3×10−12 exp [−(9800/T)] 31 21 SO (+ M) → S + O (+ M) 6.61×10−10 exp (−53885/T) 32 22 S + O2 → SO + O 9.02×10−19T 2.11 exp (730/T) 33 23 O + SO3 → O2 + SO2 2.19×10−12 exp (−3070/T) 30 24 O + O (+ M) → O2 (+ M) 5.21×10−35 exp (900/T) 34 25 CH3 + O2 → CH3O + O 4.9×10−11 exp (−15340/T) 35 26a CH3 + CH3 (+ M) → C2H6 (+ M) k∞: 1.5×10−7T −1.18 exp [−(329/T)] 36a, d
k0 : 8.77×10−7T −7.03 exp [−(1389/T)]
26b CH3 + CH3 → C2H5 + H 5.25×10−11 exp (−7384/T) 37 27 CH3 + H (+ M) → CH4 (+ M) k∞: 2.31×10−8T −0.534 exp [−(270/T)] 38a, e
k0 : 7.23×10−15T −4.76 exp [−(1227/T)]
28a CH3 + OH → CH2OH + H 3.16×10−11 39
28b CH3 + OH → CH3O + H 3.32×10−8 exp (−13800/T) 27 29a CH3 + CH3OH → CH4 + CH2OH 5.29×10−23T 3.2 exp (−3609/T) 10 29b CH3 + CH3OH → CH4 + CH3O 2.39×10−23T 3.1 exp (−3490/T) 10
30a HCO + O → CO + OH 5×10−11 40
30b HCO + O → CO2 + H 5×10−11 40
31 HCO (+ M)→ H + CO (+ M) 1.15×10−6T −1 exp (−8550/T) 41 32 H2CO + O → HCO + OH 3.0×10−11 exp [−(1552/T)] 42 33 H2CO + OH → HCO + H2O 6.47×10−11 exp [−(705/T)] 43 34 H2CO + H → HCO + H2 3.62×10−16T 1.77 exp [−(1509/T)] 44
35a CH3O + O → H2CO + OH 1.0×10−11 34
35b CH3O + O → CH3 + O2 3.55×10−11 exp [−(239/T)] 45
36 CH3O + OH → H2CO + H2O 3×10−11 34
37 CH3O + H → H2CO + H2 3×10−11 40
38 CH3O + CH3O → CH3OH + H2CO 1×10−10 34
39 CH3O + HCO→CH3OH + CO 1.5×10−10 34
40 CH3O (+ M)→ H2CO + H (+ M) 9.04×10−11 exp (−6794/T) 46
41 CH2OH + OH → H2CO + H2O 4×10−11 10
42a CH2OH + H → CH3 + OH 1.6×10−10 10
42b CH2OH + H → H2CO + H2 1.66×10−11 47
43 CH2OH (+ M) → H2CO + H (+ M) k∞: 2.8×1014T −0.73 exp [−(16509/T)] 10a, f k0 : 9.98×109T −5.39 exp [−(18209/T)]
44a CH2OH + CH2OH → HOCH2CH2OH 1.6×10−11 10
44b CH2OH + CH2OH → CH3OH + H2CO 8×10−12 10
45 CH2OH + CH3O → CH3OH + H2CO 4×10−11 10
46a CH2OH + HCO → CH3OH + CO 2×10−10 10
46b CH2OH + HCO → 2H2CO 3×10-10 10
47a CH3OH + OH → CH2OH + H2O 2.39×10−18T 2 exp (423/T) 48 47b CH3OH + OH → CH3O + H2O 1.66×10−11 exp [−(854/T)] 49 48a CH3OH + H → CH2OH + H2 2.72×10−17T 2 exp [−(2273/T)] 48 48b CH3OH + H → CH3 + H2O 3.32×10−12 exp [−(2670/T)] 50 48c CH3OH + H → CH3O + H2 6.64×10−11 exp [−(3067/T)] 49 49 CH3OH + CH3O → CH2OH + CH3OH 5×10−13 exp [−(2050/T)] 10
50 OH + O → H + O2 2.3×10−11 exp (110/T) 51
51 O + H2O → 2OH 9.21×10−11 exp [−(9611/T)] 52
a k0 and k∞ refer to low- and high-pressure limits, respectively. The Fc parameters in the Troe equation are listed separately. Unless otherwise noted, all species are assumed to have a third body efficiency of 1.0.
b Fc = (1−0.414) exp [−(T/279)] + 0.414 exp [−(T/5459)].
c Fc = (1−0.773) exp [−(T/693)] + 0.773 exp [−(T/5333)].
d Fc = (1−0.619) exp [−(T/73.2)] + 0.619 exp [−(T/1180)]. Enhanced third body coefficient (relative to N2):ηAr = 0.7.
e Fc = (1−0.783) exp [−(T/74)] + 0.783 exp [−(T/2941)] + exp [−(6964/T)]. Enhanced third body coefficient (relative to N2):ηAr = 0.7.
f Fc = (1−0.96) exp [−(T/67.6)] + 0.96 exp [−(T/1855)] + exp [−(7543/T)].
Table III. Experimental conditions and rate coefficients k1 for the reaction O + CH3OHa
40.2 2000 2.51 1550 2.22 3.46 14.78 14.42±0.48 1.39 35.0 2000 2.60 1649 1.99 2.79 13.29 16.60±0.90 1.61
SO2 (100 ppm) + CH3OH (300 ppm), 193 nm
190.2 2000 1.78 835 2.28 3.95 67.95 1.60±0.09 1.31 140.2 2000 1.85 893 1.78 5.56 53.11 2.19±0.05 1.33 113.9 2000 1.96 991 1.58 3.61 47.00 3.03±0.10 1.07 111.1 2000 1.97 995 1.54 3.56 46.01 3.26±0.08 1.05 80.5 2000 2.12 1139 1.23 3.30 36.84 4.94±0.11 0.94 60.0 2000 2.28 1295 1.00 2.75 29.89 8.25±0.20 1.14 50.8 2000 2.42 1446 0.91 1.79 27.03 11.89±0.57 1.24 40.1 2000 2.53 1566 0.75 1.50 22.29 16.38±0.91 1.08
SO2 (101 ppm) + CH3OH (500 ppm), 193 nm
160.1 2000 1.80 849 1.96 4.35 96.51 1.67±0.07 0.98 120.1 2000 1.93 963 1.63 4.66 80.51 3.08±0.07 1.23 100.0 2000 2.02 1039 1.44 3.31 71.17 3.32±0.09 1.06 81.4 2000 2.10 1122 1.24 3.20 61.29 4.66±0.12 1.19
SO2 (900 ppm) + CH3OH (136 ppm), 248 nm
60.2 2000 2.27 1284 8.93 2.71 13.53 7.73±0.36 1.28 50.0 2000 2.30 1315 7.53 1.97 11.40 9.30±0.45 1.13 50.3 2000 2.37 1393 7.84 2.91 11.88 9.54±0.35 1.21 45.3 2000 2.43 1455 7.24 2.08 10.97 10.37±0.64 1.25 41.0 2000 2.48 1513 6.70 2.76 10.14 12.18±0.59 1.24 35.3 2000 2.59 1641 6.02 2.83 9.12 18.11±1.41 1.82 30.3 2000 2.70 1766 5.36 3.18 8.11 23.87±3.83 2.40 30.3 2000 2.71 1775 5.37 2.10 8.13 27.15±3.97 1.63
aP1: pressure of reactant gas mixture; P4: pressure of driver gas; Ms: Mach number; T5: temperature of reaction.
Concentrations are in units of molecule cm−3; k1 in cm3 molecule−1 s−1 are fitted with kinetic modeling and k1' are derived from pseudo-first-order decays; see text.
Table IV. Total and relative energiesa of reactants, transition states, and products of the reaction O + CH3OH
Species or
reactions ZPE B3LYP/
6-311+G(3df, 2p)
CCSD(T)b/
6-311+G(3df, 2p) ∆Hexptc
O + CH3OH 0.0511 −190.864006 −190.4686391
TS1 −2.3 −1.2 6.3
TS2 −4.7 3.4 10.6
TS3 −2.4 44.7 52.7
CH2OH + OH −3.5 −7.7 −5.5 −6.8±0.8
CH3O + OH −4.1 −0.5 2.4 1.2±1.1
HO2 + CH3 −4.5 24.1 28.1 26.3±0.9
a Total energies are in a.u. and relative energies are in kcal mol−1.
b Based on optimized geometries calculated at B3LYP/6-311+G(3df, 2p).
c At 0 K, ∆Hf (in kcal mol−1) are as follows: O, 58.98 (Ref. 53); CH3OH, 45.43 (Ref. 54); OH, 8.85±0.07 (Ref.
55); HO2, 4.0±0.8 (Ref. 56); CH3, 35.86±0.07 (Ref. 57); CH2OH, −2.1±0.7 (Ref. 58); CH3O, 5.9±1.0 (Ref. 59).
Table V. Vibrational wave numbers and moments of inertia Ii for the reactants, transition states, and products of the reaction O + CH3OH calculated with B3LYP/6-311+G(3df, 2p)
Species Ii (a.u.) Vibrational wave numbers (cm−1) OH 0.0, 3.2, 3.2 3722
HO2 2.9, 53.2, 56.1 1171, 1443, 3613
CH3 6.3, 6.3, 12.5 539, 1407, 1407, 3108, 3284, 3284
CH2OH 9.3, 60.2, 68.9 411, 528, 1054, 1204, 1356, 1483, 3130, 3272, 3851 CH3O 11.4, 64.1, 64.5 684, 960, 1108, 1355, 1366, 1513, 2885, 2959, 3002
CH3OH 14.0, 72.9, 75.5 288, 1043, 1077, 1174, 1366, 1481, 1500, 1511, 2991, 3038, 3107, 3856
TS1 51.5, 357.3, 392.3 137, 289, 476, 958, 1068, 1137, 1160, 1312, 1380, 1420, 1491, 3026, 3138, 3834, 426i
TS2 49.1, 285.7, 323.1 142, 167, 189, 616, 1030, 1129, 1150, 1235, 1427, 1435, 1506, 2985, 3043, 3070, 1313i
TS3 18.0, 360.8, 366.5 86, 216, 257, 427, 607, 669, 983, 1203, 1422, 1434, 3102, 3258, 3274, 3784, 942i
Caption of Figures
FIG. 1. Arrhenius plots of k1 for the reaction O + CH3OH. Our data are shown as symbols
○. Previous results are shown as lines of various types drawn for the temperature range of study. A combination of first character of each author's last name is used to indicate previous reports, as listed in Table I.
FIG. 2. A typical temporal profile of [O] observed after irradiation of a sample containing SO2 (300 ppm) and CH3OH (200 ppm) in Ar. T = 1372 K and total density = 8.79×1018 molecule cm−3. The thick solid line represents fitted results using the model described in text.
FIG. 3. Comparison of total rate coefficient k1 predicted with theoretical calculations (CVT/SCT, dashed line) with experimental results of this work (△), KTSKM (■),5 GJ (○),6 and FSPI (▽),7 and recommendation from Tsang (dotted line)10 and Herron (solid line).26 Insert: Expanded view of our experimental and calculation results. ○:
SO2(302 ppm) + CH3OH(102 ppm); □: SO2(500 ppm) + CH3OH(101 ppm); ▲:
SO2(208 ppm) + CH3OH(151 ppm); ▼: SO2(300 ppm) + CH3OH(200 ppm); ■:
SO2(100 ppm) + CH3OH(300 ppm); ◆: SO2(101 ppm) + CH3OH(500 ppm); ◇:
SO2(900 ppm) + CH3OH(136 ppm), irradiation at 248 nm. Unless otherwise specified, photolysis wavelength is 193 nm.
FIG. 4. Geometries of reactant CH3OH, three transition states (TS1, TS2, TS3) and products OH, HO2, CH3, CH2OH, CH3O of the O + CH3OH system optimized at the
B3LYP/6-311+G(3df, 2p) level. Listed bond lengths are in Å and bond angles are in degree.
FIG. 5. Potential energy diagram for various channels of the reaction O + CH3OH based on energies calculated with CCSD(T)/6-311+G(3df, 2p)//B3LYP/6-311+G(3df, 2p).
Listed energies are in kcal mol−1.
FIG. 6. Theoretically predicted rate coefficients for the reaction O + CH3OH in the temperature range 300－3000 K. Solid line: CVT with SCT tunneling correction;
dotted line: TST; dashed line: CVT; dot dashed line: CVT with ZCT tunneling correction. (A) k1a, (B) k1b, and (C) branching ratios for reactions (1a) and (1b).