J. Phys. Chem. 1994, 98, 11452-11458
11452
Reactions of Atomic Oxygen (3P) with Selected Alkanes Akira Miyoshi; Kentaro TsuchiyaJ Noboru Yamauchi, and Hiroyuki Matsui Department of Reaction Chemistry, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113 Japan Received: May 17, 1994; In Final Form: August 25, 1994@
Rate constants for the reactions of atomic oxygen (3P) with selected alkanes (CZ-CS straight chain alkanes, c-CgH12, neo-CsHlz, and i-C4H10) have been determined directly by a laser photolysis-shock tube-atomic resonance absorption method at high temperatures (850-1250 K). For n-C6H14 and c-CgH12, rate constants have been also determined at lower temperatures (296-400 K) by a laser photolysis-vacuum ultraviolet laser-induced fluorescence method. Present results agree with the TST calculation by Cohen and Westberg [Znt. J . Chem. Kinet. 1986, 18, 991 within experimental error limits except for 0 -I-c-CgH12 and 0 -k neoC5H12. The group additivity of the rate constants for different C-H bonds (primary, secondary, and tertiary) is examined and neo-CsHlz and C - C ~ Hare I ~found to be good representatives of primary and secondary C-H bonds, respectively, for C4 and larger alkanes. A trial is made to investigate the J dependence of reactivity of atomic oxygen ( 3 P ~ with ) c - C ~ H ~toZ examine the adiabatic correlation of reactants and products. No evidence for such J dependence can be observed due to the rapid relaxation among the spin-orbit components. Rate constants for the intratriplet relaxation processes are evaluated for He as a collision partner.
Introduction
ment on the reactions of O(3P) with several alkanes. They suggested the J-selective reactivity of O(3PJ)from the preference of 21-13n spin-orbit components of product OH radical. Although such an effect was treated in theoretical calculations of rate constants,6,20J no direct experimental investigations have been reported. In the present study, (1) measurements of OUT previous study13 (for C1-C5 straight chain alkanes) were extended to n-C&4, c-CgH12, neo-CsH12, and i-Cd1o and to lower temperatures for some alkanes. Reactions of 0 CzH6 and C3Hg were also for reinvestigated. (2) The validity of the TST cal~ulation'~ the extrapolation of rate constants is discussed. (3) Group additivity for 0 alkane reaction was examined. And (4) a trial was made to investigate the J dependence of reactivity of atomic oxygen.
Reactions of atomic oxygen (3P) with alkanes are important initial steps of hydrocarbon combustion' and are the prototype of simple metathesis reactions in which a hydrogen atom is transferred via an apparent barrier in the reaction coordinate. The reaction of 0 methane has been extensively studied from 300 to 2200 K and several studies for 0 ethane cover the temperature range from 300 to 1270 K.2-4 For larger alkanes, however, only limited experimental information is available," and no measurement has been reported at high temperatures ('700 K) except for 0 propane? isobutane,' and neopentane.8 The development of the laserlflash photolysis-shock tube t e c h n i q ~ e ~enabled -'~ us to directly measure the rate constants for 0 alkanes at high temperatures (2850 K) and we have reported the results for C1 to C5 straight-chain alkanes.13 Recently, Cohen and Westberg4 extensively reviewed experimental data for 0 alkanes and presented recommended Experimental Section rate constants up to 2000 K. Because of the lack of experimental information at high temperatures, they used transitionShock Tube Experiments. For experiments at high temstate theory (TST) calculation^^^ to extrapolate rate constants peratures (850- 1250 K), a laser photolysis-shock tube-atomic to higher temperatures. resonance absorption spectrometry (LP-ST-ARAS) method was For systematic understanding of the reactions as well as for used in the present study. Details of the apparatus have been practical use, several attempts have been reported to examine described elsewhere.12 All experiments were performed in a the validity of the group additivity of the rate c o n ~ t a n t s , ~ J ~ - ' ~ diaphragmless stainless steel shock tube (5 cm i.d., 4 m long). Le., whether the rate constants for hydrogen abstraction reaction Atomic oxygen (3P) was generated by 193-nm photolysis of from alkanes can be expressed as the sum of site-specific rate SO2 behind reflected shock waves. The ArF excimer laser light constants for primary, secondary, and tertiary sites, or not. Group (193 nm) was introduced from the suprasil quartz window rate constants presented by Atkinson and co-workers18seem to located at the end of the test section. Oxygen atom concentrabe successful to estimate the rate constants for OH radical with tions were monitored with ARAS (atomic resonance absorption organic compounds. Tully and co-workersl' reported sophisspectrometry). A microwave discharge in a flowing mixture ticated studies on OH alkanes by using partially deuterated of 1% 0 2 in He at -7 Torr was used as a resonance lamp. The alkanes to determine site-specific rate constants. However, for radiation was passed through the shock tube (path length = 5 0 alkane reactions, only earlier investigation based on cm), filtered with a 20 cm vacuum UV (VUV) monochromator experiments by Herron and Huie,15 and theoretical investiga(with 1.O mm slits) and detected by a solar-blind photomultiplier tions6 on this subject have been reported. tube (Hamamatsu, R976). An example of the ARAS signal is Another interesting feature of the reaction was aroused by shown in Figure 1. The stepwise increase of baseline absorption Andresen and Luntz,lg who reported a molecular beam experiafter the arrival of incident and reflected shock waves was mainly caused by the absorption of SO2. The signal was On leave from National Institute of Resources and Environment, 16-3 converted to concentration of oxygen atoms with a calibration Onogawa, Tsukuba, Ibaraki, 305 Japan. curve obtained by the thermal decomposition of N20. The Abstract published in Advance ACS Abstracts, October 1, 1994.
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+
+
f
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0022-365419412098-11452$04.5010
0 1994 American Chemical Society
Reactions of 0 (,P) with Selected Alkanes
a, 0
5
z
r o + n-66~14
2000 -
1.1
1800
1.0
1600
5 0.9
1
T
39N
1400
~
I
8
C
2 0.8
+
2200
0+ ~ - c ~ H , ~
Incident Shock 1.2
. r IC,
1200
1000
0.7
800
0.6
600 l
1
l
1
1
1
l
1
1
1
1
1
1
1
-300-200-100 0 100 200 300 400 500 Time / ps Figure 1. An example of 0-atom ARAS signal. Experimental conditions: P = 1.09 atm (buffer gas: Ar),T = 1139 K, [GC&IIO]= 2.45 x [SO,] = 6.93 x IOl4 molecules ~ m - laser ~ , intensity = 1.2 x 10l6photons cm-,, [O]O= 3.6 x 1013atoms ~ m - ~ .
0
1
2
3
Time I ms Figure 2. 0-atom time profiles monitored by VWLIF. Experimental = conditions: P = 25.5 Torr (buffer gas: He), T = 345 K, [c-C~HIZ] 0 mTorr (0)/16.5 mTorr (0)/66.3 mTorr (0)/116.9 mTorr (m), [SO,] = 1.0 mTorr, laser intensity = 1.4 x 1015photons cm-,, [Olo = 2.0 x 10" atoms ~ m - ~ . initial concentration of oxygen atoms was kept smaller than onefifth of that of alkane to maintain the pseudo-first-order condition. WVLIF Experiments. For lower temperature studies, laser photolysis-vacuum ultraviolet laser-induced fluorescence (LPVWLIF) method was used. Atomic oxygen in different spinorbit components, i.e., ,Po, ,PI, and ,P2, were monitored at resonance transitions at 130.603 nm (3S1-3P0), 130.487 nm (3S1-3P1),and 130.217 nm (,SI-~P~), respectively. V W laser light was generated by a resonant difference-frequency mixing in The output of a XeCl excimer laser (Lambda Physik LPX 11Oi) pumped dye laser (Bis-MSB dyeLambda Physik LPD 3002E; -425.1 nm) was frequency doubled in a BBO crystal and tuned to two-photon resonance to the Kr 5p['/2,0] state (201 = 94 093.7 cm-'). The output of another simultaneously pumped dye laser (rhodamine 6G dyeRRA DL14P; -574 nm) was used as w2 to tune the VUV light, Le., w w = 201 - 0 2 . The two laser beams were combined coaxially and focused with a f = 70 mm quartz lens into a cell of 30 Torr Kr. Generated V W laser light was passed through the reaction cell and monitored by an ionization cell which contained a flowing NO/He mixture. Fluorescence was observed from right angle to the VUV laser beam with a solar-blind photomultiplier tube (Hamamatsu R972) and processed with a boxcar averager (Stanford Research System, SR250) interfaced to a microcom-
400
200
0
0
50
100
150
[n-CgH14] / mTorr Figure 3. Determination of the rate constants. Experimental conditions: P = 25.5 Torr (buffer gas: He), T = 296 K (0)/322 K (0)/345 K (0)/369 K (.)I399 K (A), [n-C&d] = 0-177 mTorr, [SO,] = 0.68 mTorr, laser intensity = 1.3 x 10l5photons cm-,, [O]O= 1.2 x 10" atoms ~ m - ~ .
puter. Detection limit of oxygen atoms was -1 x lo9 atoms cm-, when using the 3S1-3P2 transition and averaged over 10 laser shots. Oxygen atoms were generated by 193-nm (ArF laser) photolysis of S02. The time profile of oxygen atom concentration was obtained by changing the time delay between the ArF laser and VUV lasers. Figure 2 shows examples of time profiles of oxygen atom concentrations and results of least-squares regression to single-exponential functions. Rate constants were determined by plotting first-order decay rates vs alkane concentrations (Figure 3). Ar (Nihon Sanso; 299.9999%) was purified by passing a cold trap (-140 "C). Ethane, propane, n-butane, isobutane (Takachiho; 99.9%, 99.99%, 99.5%, 99.5%, respectively), n-pentane, n-hexane, c-hexane (Wako; 99.0%, 95%, 99.8%, respectively), neopentane (Tokyo Kasei; 96%) were purified by trap-to-trap distillation. He (Nihon Sanso; 299.9999%) and SO2 (Takachiho; 299.0%) were used as delivered. All indicated error limits in experimental values are at two standard deviations level.
Results Rate constants for reactions 1-9 have been determined at high temperatures (2850 K) by a LP-ST-ARAS method, and for reactions 6 and 7 measurements were extended to low temperatures (300-400 K) with a LP-VUVLIF method: 0 CH, OH iCH, (1)
+
-
+ C2H5 0 + C,H, - OH + C,H, 0 + n-C,Hlo OH + C,Hg 0 + n-CSH12 - OH + C5H11 O + n-C6H14 - OH C6H13 0 + C-C,Hl, - OH + C(jH1, 0 + neo-C,HI2 -.OH + C5H,, 0 + i-C4Hlo- OH + C,Hg 0 -k C2H6
OH
-.
(2)
(3) (4)
(5) (6) (7)
(8)
(9) Rate constants determined in shock tube experiments are summarized in Table 1 with experimental conditions. It should
11454 J. Phys. Chem., Vol. 98, No. 44, 1994
Miyoshi et al.
TABLE 1: Rate Constants Measured at High Temperatures WlO-" cm3 molecule-'
T/K
S-1
[alkane]/10l4 molecules cm-3 T/K
WlO-" cm3 [alkane]/10L4 molecule-' molecules S-' cm-3 T/K
kll0-l' cm3 [alkane]/10l4 molecule-' molecules S-1 cm-3 T/K
WlO-" cm3 [alkar~e]/lO'~ molecule-' molecules 5-1 cm+
o+cw 1374 0.381 f 0.105 1399 0.581 f 0.013
23.7 23.7 42.6
1234 0.250 f 0.008 1367 0.301 f 0.011
25.6 21.9
938 0.287 0.037 967 0.319 f 0.072
17.9 8.81
1101 0.589 f 0.085 1111 0.645 f 0.076
0 6.94 12.2
929 0.390 f 0.018 948 0.293 f 0.016
34.8 35.4
950 0.262 f 0.013 974 0.458 f 0.021
0 35.2 35.7
0.962 f 0.030 0.937 f 0.033 1.26 f 0.04 1.19 f 0.03 1.63 f 0.04
10.2 10.4 4.41 9.57 4.29
980 0.0655 f 0.0034 1098 0.143 f 0.003 1219 0.167 f 0.031
*
0 939 943 946 952 957
0.844 f 0.036 0.692 f 0.037 0.580 f 0.022 0.783 f 0.031 0.763 f 0.030
9.70 9.93 18.6 18.6 18.8
1152 1.18 f 0 . 1 4 1172 0.974 f 0.071
+ C2H6'
987 0.410 f 0.018 993 0.351 f 0.035
+ C3Hsb
7.16 7.24
12.7 7.33
14.5 29.6
1065 0.577 f 0.019 1152 0.892 f 0.036
15.3 13.1
2.07 f 0.07 1.96 f 0.08 2.83 f 0.13 2.79 f 0.14
4.59 4.64 4.69 4.64
1080 2.74 f 0.11 1118 3.74 f O . 1 0
3.28 2.83
1138 2.96 f 0.19
2.89
2.66 f 0.08 2.67 f 0.11 2.78 f 0.13 2.38 f 0.08
0 n-C5H1zU 2.93 1040 2.35 f 0.09 7.02 1061 3 . 2 2 f 0 . 0 6 2.73 1071 2.59 f 0.11 4.60 1091 3.96 f 0 . 1 3
13.6 4.69 11.7 2.76
1105 1117 1127 1141
4.13 f 0 . 1 3 3.61 f 0.23 3.56 f 0 . 1 7 3.82 f 0 . 0 9
2.32 8.61 4.59 4.94
949 2.46 f 0.08 953 2.75 f 0.08 983 2.53 f 0.10
0 n-C6H14 2.35 998 3.43 f 0.16 2.82 1036 3.37 f 0.14 2.23
1.99 1.74
1072 3.85 f O . 1 0 1117 4 . 8 0 f 0 . 1 5
1.93 1.42
2.89 f 0.10 3.39 f 0.09 3.20 f 0.11 2.69 f 0.11
0 C-C~HIZ 1.88 1044 3.28 f 0.10 1.74 1103 5 . 0 0 f 0 . 1 2 1.65 1103 4 . 0 0 f 0 . 1 9 1.53
1.62 1.48 1.39
1111 3.73 f 0 . 1 2 1148 5.41 f 0.12 1178 4.97 f 0.17
1.64 1.43 1.46
5.86 6.04 8.34
1073 1.88 f 0 . 0 8 1095 2.24 f 0.07 1109 2.32 f 0.08
5.38 4.63 5.45
2.33 2.32 7.84 2.37 2.38 2.48 2.41 8.23 2.45
1136 1139 1144 1153 1176 1181 1186 1203 1205
2.80 f 0.07 2.51 f 0.07 2.62 f 0.09 2.76 f O . 1 1 3.20 f 0.09 3.54 f 0.12 3.52 f 0 . 1 6 3.62 f 0.12 2.97 f 0.09
2.45 2.45 2.46 2.47 2.51 2.52 2.52 2.54 2.55
0
1.83 f 0.06 2.21 f 0.08 2.41 f 0.05 2.30 f 0.10
6.15 3.19 6.69 2.99
967 1002 1003 1034
868 2.06 f 0.06 879 1.85 f 0.05 919 2.47 f 0.06
3.66 3.47 3.20
873 921 947 967
2.52 f 0.05 2.90 f 0.07 3.03 f 0.07 3.66 f 0.09
3.44 3.11 2.65 2.08
876 896 901 940
0.583 f 0.025 0.832 f 0.032 1.13 f 0.03 1.23 f 0.04
897 934 934 943 954 955 959 970 978
1.16 f 0.04 1.22 f 0.05 1.15 f 0.07 1.23 f 0.04 1.29 f 0.05 1.19 f 0.05 1.29 f 0.04 1.58 f 0.11 1.20 f 0.04
975 1018 1020 1038
+
+ +
955 1.44 f 0.07 956 1.32 f 0.04 1019 1.34 f 0.04
997 999 1013 1025 1027 1030 1032 1041 1048
1119 1159 1163 1217
+ n-CaHlo"
4.17 3.91
0
(I
1177 0.633 f 0.051 1192 0.981 f 0.077
+ C2H6'
1221 1233 1239 1254
968 2 . 1 6 f 0 . 0 4 1020 2.25 f 0.06
6.89 7.11 7.13 7.62 7.22 7.27 7.55 7.33 7.36
20.8 20.2
4.30 8.17 4.44 4.57
5.13 4.79
12.6 6.69 6.06 7.71
1404 0.458 f 0.015 1522 0.785 f 0.020
1.63 f 0.04 1.95 f 0.08 1.89 f 0.07 2.65 f 0.15
987 1004 1039 1058 1107
896 1.88 f 0.04 931 1.60 f 0.03 852 900 942 950
45.8 21.9
+ neo-CsH12
5.60 5.29 7.04
1020 1.61 f 0.06 1020 1.65 f 0.06 1041 1.65 f 0 . 0 9
O + i -C4H10 7.48 1052 7.60 1053 2.26 1064 7.66 1073 2.28 1089 7.71 1102 7.84 1111 7.73 1128 2.31 1128
1.53 f 0.06 1.51 f 0.05 1.90 f 0.06 1.40 f 0.05 1.90 f 0.04 1.54 f 0.06 1.43 f 0.08 1.71 f 0.07 1.94 f 0.04
1.83 5 0.05 1.91 f 0.04 1.69 f 0.07 2.22 f 0.06 2.38 f 0.08 2.87 f 0.11 2.05 f 0.05 2.17 f 0.11 2.25 f 0.07
Reanalysis of experiments in the previous reportI3 (see text). New experiments after the previous report.13
be noted that experimental data for reactions 1, 4,and 5 in the previous report13 have been reanalyzed with a recently reconstructed better ARAS calibration curve for the 0 atom and listed again in Table 1. For reactions 2 and 3, rate constants were reinvestigated experimentally. Since the initial oxygen atom concentrations were not so low (typically (1-4) x 1013 atoms ~ m - ~ contributions ), of side reactions such as reactions of oxygen atoms with CH3, OH, or C2H5 may not be neglected completely in the shock tube experiments. Computer kinetic simulations showed that the maximum errors in measured rate constants due to side reactions were +6 to +21% (typically -13%). In the kinetic simulations, reactions of OH alkanes, H alkanes, thermal decomposition of alkanes and alkyl radicals, 0 OH, OH OH, 0 alkyl radicals, OH alkyl radicals, H alkyl radicals, and CH3 alkyl radicals were included. Because these errors were always
+
+
+
+ +
+
+
+
smaller than the experimental error limits and rate constants and mechanism of subsequent reactions have not been well established (especially for large alkanes), no corrections were made for rate constants listed in Table 1. It must be noted that present measurements at high temperatures may be slightly affected by side reactions, and they may therefore be overestimated by about 10%. The thermal decomposition of large branched chain alkanes, such as i-C4H10 and neo-CsH12, is expected to be fast and may affect the present measurements at high temperatures. Thus the thermal decomposition of these two alkanes (i-Ca10 and neo-CsHl2) has been investigated in our shock-tube apparatus by measuring the absolute hydrogen atom concentrations. The measured thermal decomposition rate constants were in agreement with, or slightly higher than, the previous report^.^^^*^ Computer kinetic simulations including the thermal decomposi-
Reactions of 0 (3P) with Selected Alkanes
J. Phys. Chem., Vol. 98, No. 44, 1994 11455
TABLE 2: Rate Constants Measured at Low Temperatures
TE
rate const/10-l3 cm3 molecule-' s-'
0 296 322 345 369 399
0.600 f 0.040 1.10 f 0.05 1.52 f 0.20 2.47 f 0.10 3.46 f 0.39
297 297 297 344 344 345 392
0.872 f 0.046 0.866 f 0.068 0.824 f 0.040 1.93 f 0.20 1.84 f 0.26 1.81 f 0.32 3.91 f 0 . 4 4
0
[alkane]/ mTorr
total press/ Torr
0-174 0-176 0-177 0-176 0-177
25.5 25.5 25.5 25.5 25.5
3P~ 3P~ 3P~ 3P~ 3P~
0-244 0-166 0-163 0-99 0-117 0-117 0-115
25.6 25.6 25.6 25.4 25.5 25.5 25.5
3P~
+ n-CrjH14
+ c-cd-I12
0.75
monitored state
0.70
U
3P~
O 0.08
3P~ 3P~
reaction
+ + +
0 CH4' 0 c~H.5~ 0 C3Hsd 0 n-C4H1oc 0 n-C5H12' 0 -t n-c1jHI4
+ +
+ 0+ 0+
0
Aa/cm3 molecule-' s-I
4.70 x 6.59 x 1.34 x 3.93 x 3.05 x 8.91 x 5.56 x c-C&IIZ 3.29 x 3.64 x neo-CsH12 1.26 x i-CdH10 1.13 x
10-"(2.8) lo-'' (3.0) (1.7) 10-"(3.3) lo-'' (2.1) 10-'O(2.1) lo-" (1.6) 10-"(2.5) lo-" (1.5) (3.0) (1.6)
EaM mol-'
F(k)b
T/K
54.1 f 10.7 42.0 f 9.3 41.0 f 4.6 23.6 f 10.0 20.2 f 6.4 27.8 f 5.8 16.8 f 1.3 19.0 f 7.6 15.0 f 1.2 37.0 f 8.8 35.7 f 4.3
1.52 1.48 1.26 1.31 1.29 1.19 1.11 1.33 1.12 1.34 1.27
980-1520 930-1190 940-1250 900-1140 850-1140 870-1120 296-399 870-1180 297-392 880-1110 900-1210
0.04
+
m
0
2
4
6
8
1012
Figure 4. Intratriplet relaxation of O(%). Experimental conditions: P = 450 mTorr (buffer gas: He), T = 298 K, [SO21= 2.5 mTorr, laser intensity = 1.1 x 1015photons cm-2, [0It0d = 4.6 x 10" atoms cmW3.Solid lines denote reproduced time profiles with derived rate constants (see text).
tween 3P0and 3P1states is forbidden to the first order. Quantal close coupling calculation^^^ also showed that k01 is only 10% of kQ2 and k12 at around room temperature, where ku denotes rate constant for the relaxation process from 3Pi to 3Pj state. With this assumption of kQl = 0, an integration of rate equations can be simplified as
N, = N,' - k12Jh12 dt where Nu is nonequilibrium number density defined as
+
+
0
Time I ps
a Values in parentheses indicate uncertainty factors of preexponential factors. Uncertainty factors of rate constants in the specified temperature range. Experiments in the previous reportL3were reanalyzed (see text). Rate constants have been reexamined experimentally after the previous report.13
tion rate constants obtained here showed that the effects of the thermal decomposition of alkanes on the 0 alkane rate measurements are less than 3% at the highest temperature, 1200 K. The total error caused by the side reaction due to high initial oxygen atom concentrations as discussed above and by the thermal decomposition of alkanes was evaluated to be less than 10% at 1200 K for 0 i-C4H1o and neo-CsHlz. Rate constants obtained in the LP-VUVLIF experiments are summarized in Table 2 with experimental conditions. Since the initial concentrations of oxygen atoms were sufficiently low ((1-3) x 10" atoms cmP3), the contribution of subsequent reactions was estimated to be negligible. Measured rate constants both at high and low temperatures are summarized in Arrhenius form in Table 3 with error limits and temperature ranges. Difference of reactivity between spin-orbit components of atomic oxygen was investigated in 0 C-CgH12 reaction at 297 and 344 K. As shown in Table 2, rate constants determined by monitoring 3P0, 3P1, and 3P2 states are in agreement within experimental error limits, and no difference in reactivity was found. However, this does not lead to the straightforward conclusion that the reaction is completely diabatic because the intratriplet relaxation can be expected to be very fast due to the small separation in energies. Thus, a trial was made to measure the intratriplet relaxation rate using He as a collision partner. A clear relaxation phenomenon was found when SO2 was photolyzed with 193-nm light at pressures around 500 mTorr on the microsecond time scale (Figure 4). On the basis of the S2-conserving appro xi ma ti or^,^^^^^ the collisional transition be-
l
0.06
TABLE 3: Arrhenius Expression for the Measured Rate Constants k = A exp(-Ea/RT)
,
N,. v = Ni - K i FI .
(12)
N/ denotes number density of O(3Pj)and Ku denotes equilibrium constant between 3Pi and 3Pj states (=NielNF = kjilku). Superscripts 0 and e denote quantities at time = 0 and at the equilibrium, respectively. Plots of Ni against .@?i2 dt gave ki2 as the slopes and N? as the intercepts. From experiments at [He] = 320-720 mTorr, kQ2 and k12 were determined to be k,, = (4.4 f 1.0) x lo-" cm3 molecule-'
s-l
k,, = (2.3 f 0.5) x lo-" cm3 molecule-' s-' for He as a collision partner and at room temperature (298 f 2 K). Experimental data can be well reproduced with these values (solid lines in Figure 4). These rate constants are more than 100 times faster than the measured rate constants for 0 alkane (c-hexane and n-hexane) at room temperature. From the analysis described above, nascent spin-orbit populations of O(3P~)produced in 193-nm photolysis of SO2 were also evaluated as F(3P~)= 0.09 f 0.02, F(3P1)= 0.25 f 0.04, and F(3P2)= 0.66 f 0.04.
+
Discussion Comparison with the TST Calculations and Earlier Measurements. The present results are compared with the TST calculation by Cohen and Westberg,14 and with earlier
Miyoshi et al.
11456 J. Phys. Chem., Vol. 98, No. 44, 1994
L
10
15
20
25 30 35 -4 -1 T - ' I 10 K Figure 5. Arrhenius plot for the reaction of 0 C2Hs: (0)present (+) Mahmud et al. study (LP-ST-ARAS), (-) TST calc~lation,'~ (1988),28(A) Mix and Wagner (1983),29(0) Caymax and Peeters (1982),3O (0)Tanzawa and Klemm (1980),31(V)Papadopoulos et al. (1971),32 (0) Herron and Huie (1969)lS [for 0 + CZHSD],(0) Westenberg and DeHaas ( 1967/1969),33(V)Saunders and Heicklen ( 1966).34
+
- 4 1 T - ' I 10 KFigure 7. Arrhenius plot for the reaction of O + n-Ca14. (0)present study (LP-ST-ARAS), (A) present study (LP-VUVLIF), (-) TST (0)Herron and Huie (1969).lS calc~lation,'~ 10-1Ot,,.., , , ,
I
I
, ,
~
,
I
, , , ,
I
, , , ,
I
, , , ,
~
10-l1
T
10-131
I
10-14
-4 -1 T-' I 1 0 K Figure 8. Arrhenius plot for the reaction of 0 + c-CgH12. (0)present T-I I IO-~K-I study (LP-ST-ARAS), (A) present study (LP-VUVLIF), (-) TST (0)Washida and Takagi (1982),39(+) Kim and Timmons cal~ulation,'~ Figure 6. Arrhenius plot for the reaction of 0 + C3Hs. (0)present (1975),@(0) Huie and Herron (1972):' (V) Stucky and Heicklen (0)Washida (1987)3s[for study (LP-ST-ARAS),(-) TST calc~lation,'~ (1967),42(0)Avramenko et al. (1965).43 0 (CD3)2CH2],(V)Jewel1 et al. (1981),36(0)Tanzawa et al. (1980); (+) Harker and Burton (1975),3' (0)Stockburger and Heicklen (1971),38 the number of secondary C-H bonds. Solid lines in Figure 11 (V)Saunders and Heicklen ( 1966).34 denote estimated rate constants from those for single primary and secondary C-H bond derived for 0 m e a ~ u r e m e n t s ~ ~in~ Figures ~ ~ * ~ ~5~ 10. ~ * -The ~ ~present results neo-CsHlz and for 0 C2H6, 0 C3H8,O n-C6H14, and 0 i-Cd10 agree c-CgH12. respectively. Rate constants for C4 and larger straightchain alkanes agreed with the estimates within experimental with earlier measurements and the TST calculation within the error limits. When we use the TST rate constants14for C-CgH12 experimental error limits. However, for 0 C-CaHlz and 0 instead in the above estimate, poorer agreement was found since neo-CsHlz, obvious differences were found between the present measurements and the TST calculations. The results of TST the TST rate constants are about 2 times larger than the present calculation were apparently biased on the earlier measurements measurements. A similar situation was found at lower temfor 0 c-C~HIZ (refs 40 and 41) and 0 ne0-CsH12.~ The peratures. By using the present rate constant for C - C ~ Hand ~Z previous for neo-CsHlz as standards, rate constant for present measurements for 0 c - C ~ H ~ atZlower temperatures agree well with values reported by three g r o ~ p s ~but~ are , ~ ~ , ~n-C6H14 ~ was evaluated to be 5.96 x cm3 molecule-' s-l smaller by a factor of 2 than those reported by the other two at 297 K, which is in good agreement with the present group^^,^^ and the TST calculation. The present measurements measurement, (6.0 & 0.4) x however, it was calculated for 0 neo-CsHl2 seem to agree with the extrapolation of rate with TST rate constants for C-CgH12 and to be 9.97 x constants reported by Herron and Huiels but are larger by a neo-CsH12. factor of 3 than those by Michael et aL8 at the overlapping Present results shows that neo-C~Hlzand C - C ~ H are ~ Z good temperature, -900 K. The reasons for these differences are representatives for the reactivity of primary and secondary C-H not clear. bonds, although it is a crude assumption and must be investiExamination of the Group Additivity. In Figure 11, rate gated carefully with more examples. Detailed theoretical constants for straight-chain alkanes (c2-c6) are plotted against approach, e.g. TST, cannot lead to such a simple conclusion
+
+
+
+
+
+
+
+
+
+
Reactions of 0 (3P)with Selected Alkanes
10-l1
1
p\
J. Phys. Chem., Vol. 98,No. 44,I994 11457
0 + neo-CgH12
-3
0 + i-C4H10
t
FL
8
.'....,. 1
1
1
10
1
I
I
k
I
15
I
I ( I I *I
20
d.
25
30
+ ( I
1
1
1
35
o* I i
10
15
T-ItlO K
Figure 9. Arrhenius plot for the reaction of 0
+
neo-CsHtz. (0) present study (LP-ST-ARAS),(-) TST calc~lation,~~ (0 Michael et al. (1982)8 [O discharge-flow studym flash-photolysis study], (0) Herron and Huie (1969),15(+) Wright (1965).44 straightforward since characteristic structures of c-CgH12 and neo-CsHl2 give different effect in entropy (and enthalpy) terms from straight-chain alkanes. Present conclusion may be the results of accidental cancellation of various effects. For the reactions of OH alkane, much more experimental information is availablelgaand the group additivity has been examined and discussed in detail.16-18 It has been shown that the crude assumptions, such as equal reactivity of every kind of secondary C-H bonds, are not enough to estimate the rate constants and the effects of neighboring group must be taken into account.16-18 An empirical model presented by Atkinson and co-workers'* seems successful, and was also examined by TST calculations.16 For the reactions of atomic oxygen, experimental information is still insufficient for such analysis. Finally, the expressions for the rate constants for 0 4-single C-H bond derived in this study are presented for the convenience of practical applications. Although these expressions seems successful for L C alkanes ~ studied here, they must be checked with many more examples:
kp~" = 2.30 x 10-22 ?,469 exp(-1556/T) cm3 molecule-' s-'
ksecondary = 9.37 x 10
,267
?
exp(-832/T) cm3 molecule-' s-'
ktertiary= 4.17 x 10-16T',444 exp(-821/T) cm3 molecule-' s-' temperature range:
25
Figure 10. Arrhenius plot for the reaction of O
30
35
300- 1100 K
J Dependence of Reactivity of Atomic Oxygen (3P~). In the present study, a trial was made to examine the difference of reactivity between spin-orbit components of atomic oxygen (3P0, 3P1, 3P2) in the 0 -b c-CsHlz reaction at low temperature. However, no difference could be observed due to rapid intratriplet relaxation. In the adiabatic limit, 3P0state is expected to be completely nonreactive.20,21The present finding of the rapid intratriplet relaxation implies that the intratriplet exchange easily occurs at a very early stage of the potential energy surface of the reaction, and the reaction will not be completely adiabatic. Andresen and Luntz19 concluded that the reaction is neither completely in the adiabatic nor diabatic limit from their
+
i-C.&O. (0) present (0)Provencher et al. study (LP-ST-ARAS), (a)TST calc~lation,~~ (1982): (v)Jewel1 et al. (1982),"5(0)Washida and Bayes (1980),& (0)Cvetanovic and Doyle (1969):'
In I
+
-22
20
T-' I 10-4 K-1
-4 -1
-a, 3
'
$ 3
E
m E 2 0 ?
T I
Z1 4
Y
-
0 0
2
4
6
a
%ec C-H Figure 11. Examination of group additivity. Rate constants for 0 with CZ-cS straight chain alkanes are plotted against number of secondary C-H bonds ( n s e c c - ~ )Rate . constants and error limits were calculated from the Arrhenius expressions in Table 3. (0)rate constants at 900 K, (A)at lo00 K, (0)at 1100 K. Solid lines denote estimated rate constants using nm-CsH12 and c-Cd-I12as representatives of primary and secondary C-H bonds.
observation of spin-orbit branching of OH radicals in molecular beam experiments. Since a complete diabaticity is a basic assumption in the TST, such a discussion on the spin-orbit effect does not alter the results of conventional TST calculations which use only the degeneracy of the reactive surface (in other words, the electronic partition function of the transition state) and are indifferent to which spin-orbit component is reactive.14 However, the assumption of complete diabaticity must be proved by detailed experimental and/or theoretical investigations. The spin-orbit effect has been studied in more for atoms with larger spin-orbit splittings such as halogen atoms. In the present study, the intratriplet relaxation rate constants were measured for He as a collision partner. These values fit fairly well to the empirical relationship between the intramultiplet relaxation cross section and the energy gap which was found for metal atoms.49 The present values are close to the recent measurements for Kr or Xe as a collision partnerz6 and in reasonable agreement with the quantal close coupling calculation^.^^ Nascent spin-orbit distribution of O(3P~)produced in the 193-nm photolysis of SO2 was evaluated to be [3P~]:[3P~l:[3P2] = 0.09:0.25:0.66, which is apparently different from the statistical distribution (0.11:0.33:0.56). The present
11458 J. Phys. Chem., Vol. 98, No. 44, 1994
Miyoshi et al.
measurements agreed well with those measured with VUVLIF method26 (0.09:0.23:0.68) but were different from those measured with two-photon LIF method50 (0.11:0.30:0.59). Site-Specific Rate Contants for 0 Alkane: Future Studies. The important kinetic information for 0 alkane reactions is not only the overall rate constants but also the branching fractions for the abstraction of different C-H sites. Because of the difficulties of selective and quantitative measurements of product alkyl radicals, no direct experimental information on the branching has been reported. Branching fractions are usually estimated from group additivity or from the results of TST calculation^.^ For OH alkane reactions, Tully and co-workers17 derived “site-specific’’ rate constants by using partially deuterated alkanes. Although these studies were sophisticated and fruitful, the results are not strictly “sitespecific”, since they were based on the assumption that the deuterium substitution on neighboring group does not affect the specific C-H bonds. Thus, experimental determination of the branching fractions from quantitative measurements on the product is needed to investigate the group additivity more precisely and to examine the validity of TST calculations. Recently, we have started experiments to determine the branching fractions for the 0 C3Hg reaction utilizing the difference of thermal decomposition of n-C3H7 and i-C3H7 radicals. At temperatures above 900 K, thermal decomposition of these radicals are known to be fast:51,52
+
+
+
+
n-C3H7
+M
CH,
+ C2H4+ M
(134
Since (13a) is the dominant process of thermal decomposition of n-C3H7,52 the branching fraction for secondary hydrogen abstraction can be determined by quantitative observation of H atoms. Preliminary results show that the yield of K3H7 radical averaged for 0 f C3H8 and OH f C3H8 is -0.2 at 1150 K and -0.3 at 950 K, which are smaller than the results of TST calculations [0.46 for 0 f C3H8 (ref 14) and 0.42 for OH C3H8 (ref 16) at 1150 K]. In these experiments, it was shown that branching fractions can be determined with fairly good accuracy, although they suffered from side reactions to some extent. Detail of the experiments will be published in the near future.
Conclusions Rate constants have been determined at high temperatures (850-1250 K) for the reactions of O(3P) with c2-c6 straightchain alkanes, C-C&2, neo-CsHl2, and i-Ca10, and at low temperatures (296-400 K) for 0 f c-CgH12 and mC6H14. Measured rate constants agree well with the TST calculation by Cohen and Westberg14 except for 0 -k C-C&2 and neoC5H12. The additivity of the rate constants was examined and C-C&12 and neo-CsH12 were found to be good representatives for the reactivity of primary and secondary hydrogen for the reactions of C4 and larger alkanes studied here. The J dependence of reactivity of atomic oxygen (3P~)could not be clarified due to the rapid intratriplet relaxation. This, however, suggests that the reactions will not be completely adiabatic. The rate constants for the intratriplet relaxation by He were evaluated.
References and Notes (1) Warnatz, J. In Combustion Chemistry; Gardiner, W. C., Jr., Ed.; Springer-Verlag: New York, 1984.
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