Environ. Sci. Technol. 1982, 16, 45-52
(16) (17) (18) (19)
(3) Everitt, B. “Cluster Analysis”;Heinemann: London, 1974. (4) Kruskal, J. B.; Wish, M. “Multidimensional Scaling”;Sage Publications: Beverly Hills, CA, 1978. (5) Kruskal, J. B. In “Mathematical Methods for Digital Computers”; Enslein, K.; Ralston, A,; Wilt, H. S., Eds.; Wiley-Interscience: New York, 1977; Vol. 3, pp 296-339. (6) Emery, K. 0. “A Coastal Pond Studied by Oceanographic Methods”; Elsevier: New York, 1972. (7) Clark, R. C.; Finley, J. S.; Gibson, G. G. Environ. Sei. Technol. 1974,8, 1009-14. (8) NOAA. “Local Climatological Data. Boston,
Acad. Sei. U.S.A. 1974, 71, 2925-7. (20) Boehm, P. D.; Quinn, J. G. Geochim. Cosmochim. Acta 1973, 37, 2459-77. (21) Shaw, D. G. In “Fate and Effects of Petroleum Hydro-
carbons in Marine Organisms and Ecosystems”;Wolfe, D. A., Ed.; Pergamon Press: Elmsford, NY, 1977; pp 8-18. (22) McAuliffe,C. In “Petroleum in the Marine Environment”; Petrakis, L., Weiss, F. T., Eds.; Advances in Chemistry Series, American Chemical Society: Washington, DC, 1980;
Massachusetts”; Environmental Data and Information Service: Asheville, NC, 1978 and 1979. (9) Sauer, T. C., Jr.; Sackett, W. M.; Jeffrey, L. M. Mar. Chem.
p 203. (23) Schauenstein,E.; Esterbauer, M.; Zollner, H. “Aldehydes
1978, 7, 1-16. (10) Sauer, T. C., Jr. Limnol. Oceanogr. 1980,25, 338-51. (11) Cleveland, W. S.; Kleiner, B.; McRae, J. E.; Warner, J. L. Science 1976,191, 179-81. (12) Erhardt, M.; Blumer, M. Environ. Pollut. 1972,3,179-94. (13) Bray, F. E.; Evans, F. E. Geochim. Cosmochim. Acta 1961, 22, 2-15. (14) Farrington, J. W.; Meyers, P. A. In “Environmental
Chemistry”;Eglinton, G. Ed.; Chemical Society: London, 1975; Vol. 1, 109-35. (15) McAuliffe, C. J . Phys. Chem. 1966, 70, 1267-75.
McAuliffe, C. Science 1969, 163, 478-9. Button, D. Geochim. Cosmochim. Acta 1976,40,435-40. Hermann, R. B. J . Phys. Chem. 1972, 76, 2754-9. Reynolds, J. A.; Gilbert, D. B.; Tamford, C. Proc. Natl.
in Biological Systems: Their Natural Occurrence and Biological Activity”; Pion: London, 1977; p 192.
Received for review March 30, 1981. Accepted September 17, 1981. This work was supported in part by Department of Environment (U.K.) Grant D. G. 480/48 and OCE 74-22781. P.M.G. acknowledges partial support from the WHOI Education Office. R.F.C. acknowledges travel funds f r o m the WHOI Coastal Research Center.
Computer Modeling Study of Photochemical Ozone Formation in the Propene-Nitrogen Oxides-Dry Air System. Generalized Maximum Ozone Isopleth Fumio Sakamakl, Michio Okuda, and Hajime Akimoto”
Division of Atmospheric Environment, The National Institute for Environmental Studies, P.O. Tsukuba-gakuen, Ibaraki, 305 Japan Hideo Yamazakl
Department of Chemistry, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo 152 Japan Computer simulation for the propene-nitrogen oxides-dry air system was performed by using a detailed reaction model in order to represent previous experimental results. The proportional relationships between [O,],, and [O,],,,[NOx]01/2,and kI1I2 were successfully reproduced by the model. Based on the calculated data, the plot of [o,],,/[03],, vs. [C3H6]o/[N0,]owas found to fall on a single common curve, which is called a generalized maximum ozone isopleth. In the falloff region of the above plot, an approximate linear relationship between [03],,/[03] ,and ([C3H6I0/[N0,]o)1/2was obtained, implying that [03],, is linear with [C3H6]01/2 in the NO,excess region. In order to characterize ozone formation in photochemical air pollution, many attempts (1-8) have been made to correlate the maximum ozone concentration attained in smog-chamber experiments with the reaction parameters such as light intensity, initial concentrations of hydrocarbons and nitrogen oxides, temperature, or hydrocarbon reactivity. In our previous papers (1-3) on smogchamber studies of the olefin-nitrogen oxides system, an approximate, proportional relationship [O,lrnax 0: [03lp, (1) was proposed to hold in the hydrocarbon-excess region, where [O,],, is the maximum ozone concentration ultimately reached and [O,],, is the photostationary ozone concentration parameter in the absence of hydrocarbon. 0013-936X/82/0916-0045$01.25/0
The same relationship has also been suggested to hold in the irradiation of sampled ambient air (4). On the other hand, in the flow reactor study of the cyclohexenenitrogen dioxide-air system, Shen et al. (7) have proposed that [0,]m,/(k,[N0,]o/k,)1’2 depends only on the ratio of the initial concentrations of the hydrocarbon and the nitrogen oxides and presented normalized maximum ozone concentration curves. Here kl and k 2 are the rate constants for the photolysis of NO2 and the reaction of NO and 03, respectively. Since a detailed mechanism for the photooxidation of the propene-NO, system based on the knowledge of chemical kinetic data has been reported (9) recently, it is of great interest to determine whether computer modeling can reproduce the above experimentally obtained relationship. For the purpose of establishing an ozone control strategy based on smog-chamber data with the aid of computer simulation, substantiation of the experimental data by means of the “theoretical” prediction and vice versa should be of key importance. This study presents the reaction model which can reproduce our previously reported C3H6(3 ppm)-NO, (1.5 ppm)-dry air runs where reaction products were fully analyzed by a long-path Fourier transform infrared spectrometer (IO). Lower-concentration runs were then simulated by using the same reaction model to obtain the theoretical relationship between [031mar and [C&6]0, [NO,lo, and the light intensity. The computer modeling was found to predict eq I successfully, and the proposal
0 1981 Amerlcan Chemical Society
Environ. Sci. Technol., Vol. 16, No. 1, 1982 45
Table I. Experimental and Calculated [O,Imax in the C,H,-NO,-Dry
run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
[C,H,lo, PPm
[NOXIO, PPm
[NO],, ppm
[NO,],, PPm
k, min-'
[C,H,IoI [NO, I o , ppm
0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.50 0.50 0.50 0.50 0.50 0.50 0.05 0.15 0.20 0.30 0.40 0.20 0.33 0.50 0.50 0.50 0.50 0.50
0.009 0.020 0.026 0.034 0.036 0.043 0.052 0.063 0.086 0.045 0.090 0.089 0.090 0.187 0.290 0.038 0.039 0.040 0.039 0.039 0.086 0.091 0.085 0.090 0.083 0.088 0.089
0.004 0.015 0.005 0.033 0.004 0.022 0.049 0.048 0.006 0.004 0.008 0.081 0.082 0.011 0.255 0.003 0.003 0.004 0.005 0.005 0.009 0.008 0.012 0.012 0.009 0.009 0.007
0.005 0.005 0.021 0.001 0.032 0.021 0.003 0.015 0.080 0.041 0.082 0.008 0.008 0.176 0.035 0.035 0.036 0.036 0.034 0.035 0.077 0.083 0.073 0.078 0.074 0.079 0.082
0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.37 0.31 0.25 0.19 0.13
11.1 5.0 3.8 2.9 2.8 2.3 1.9 1.6 1.2 11.1 5.6 5.6 5.6 2.7 1.7 1.3 3.8 5.6 7.7 10.2 2.3 3.6 5.9 5.6 6.0 5.7 5.6
by Shen et al. (7) was also verified. The "generalized ozone isopleth" for the reaction system will be presented.
Experimental Section Smog-Chamber Experiments and Computational Methods. All of the experimental data used in the present study as a data base are from the C3H6-N0,-dry air ([H20] 1 ppm) runs, which have been reported before (1, 10). Experiments were performed at 30 "C by the evacuable and bakable photochemical smog chamber at NIES (11). Typical wall decay rates of O3 (0.04 ppm) and NO2 (0.04 ppm) observed in this chamber were 2.0 X and 0.8 X s-l, respectively (11). The initial concentrations and the kl value for each run are given in Table I together with the experimental and calculated results for [Os1mar. Calculations were performed on a Hitac 180 computer using a CHEMK program for the integration of coupled differential equations written by Whitten and Hog0 (12). The subroutines employ the Gear algorithm (13) for the variable-step-size integration. All calculations were performed by using single precision and an error tolerance constant, E = Reaction Mechanism. The detailed reaction mechanism used in the present study is presented in Table 11. The mechanism is based on the one reported by Carter et al. (9) with some modification. Rate constants for primary photochemical reactions were calculated from the absorption cross section cA of the species, the quantum yields of the reaction, and the spectral intensity distribution JA of the photolyzing radiation which was determined experimentally (10). Photolysis rate constants are given in Table I as normalized to that of NO2 and were used after being adjusted proportionally to the kl value (the photolysis rate constant of NO2). Since only the dry-air runs were considered in the present study, neither the heterogeneous nor homogeneous loss reactions of N205by H20 were included in the model. 46
Air System
Envlron. Scl. Technol., Vol. 16, No. 1, 1982
1
[03Ips,
PPm 0.005 0.008 0.010 0.011 0.012 0.013 0.015 0.016 0.020 0.014 0.020 0.020 0.020 0.020 0.030 0.038 0.012 0.013 0.012 0.012 0.020 0.020 0.028 0.027 0.023 0.021 0.018
[o,lgg,
]eld,
[o,
PPm
ppm
0.026 0.068 0.078 0.116 0.106 0.115 0.126 0.164 0.148 0.151 0.236 0.232 0.217 0.363 0.443 0.085 0.139 0.136 0.136 0.139 0.216 0.232 0.390 0.366 0.307 0.271 0.233
0.066 0.097 0.112 0.125 0.131 0.137 0.146 0.154 0.171 0.175 0.267 0.251 0.252 0.379 0.403 0.104 0.150 0.158 0.164 0.163 0.221 0.258 0.373 0.359 0.313 0.286 0.239
Wall loss reactions of O3 and NO2 were included, and the s-l for O3 and first-order decay rate constants, 1.1X 7.2 X lo4 s-l for NO2, were used in the high-concentration run ([C3H6], = 3.0 ppm, [NO,], = 1.5 ppm). For the lower-concentration runs ([C3H6],< 1ppm, [NO,], < 0.5 ppm), the 50% increased decay rates, 1.6 X 10" s-l for O3 and 1.1X s-l for NOz, were employed. The reaction of ozone with propene was postulated to give vibrationally stabilized biradicals (CH200 and CH3CHOO) which react bimolecularly with NO, NO2, HCHO, and CH3CH0, and dioxiranes (CH200 and CH,CHOO) which decompose or isomerize unimolecularly. The branching ratios of the unimolecular decay of C H 2 0 0 were taken from the study of Whitten et al. (14). The ratio of the atom and radical formation from CH,CHOO was decreased to 50% of their values. The propylene glycol dinitrate (PGDN) formation mechanism was modeled according tci a scheme proposed previously (15). The 0-nitratopropoxy radical CH3CH(0)CH20N02was assumed to decompose faster than the recombination reaction with NO2,whereas the decomposition rate of CH3CH(ON02)CH20was assumed to be slow enough to compete with the reaction with NO2 to form PGDN. By analogy with the OH-propene reaction scheme, the NO3-added peroxy radicals (CH&H(OO)CHzONOzand CH3CH(ON02)CH200) were assumed to react with NO also to give PGDN, competing with the reaction to oxidize NO to NOz. Curve Fitting, Curve fitting of the experimental data was attempted for the C3H6 (3.05 ppm)-NO (1.477 ppm)-NOz (0.023 ppm) run where total analysis of the reaction products was made (10). Fitting to the time profiles of NO, NOz, C3H6, and 03,as well as to the maximum O3 level, was attempted as a first priority. The trials were mainly made by adjusting the following three rate parameters: (1) the relative rate constants of the reactions, OH-added peroxy radicals (CH3CH(OO)CH20H and CH3CH(OH)CHzOO) with NO to form nitrate
-
-
c O3
t
I
E0.2 E
e " C
" a c
0 V
-
10-
U
100
200
300
02
03 lC3H61O
l r r a d i o t i o n Time / m i n
e (b)
04
0.5
06
1 PPm
Flgwe 2. Comparison of observed (0, A) and predicted (0,A) [O,], as a function of [C3H6],. k , = 0.16 min-'; [NO,lo = 0.04 (0, 0) and 0.09 (A, A) ppm.
E
8
.a.1 0 C
0
04'
0-
L
e " C U
E
5 05
8 0.3-
u
0
100 200 Irradiation Time/ min
300
Flgure 1. Comparison of observed (symbols) and predicted (curves) concentrationsfor the C3H6(3.05 ppm)-NO (1.477 ppm)-NOp (0.023 ppm)-dry air run. k, = 0.27 min-l.
(CH,CH (ONOz)CHzOH and CH,CH(OH) CH20NOZ)to those to form oxy radicals (CH3CH(0)CH20H and CH,CH(OH)CH,O); (2) the percentage of the radical formation (CzH5+ CHO) in the reaction of oxygen atom with C3H6;(3) the branching ratios to form the biradicals and the dioxiranes in the 03-C3H6 reaction. All calculations for the lower-concentration runs were performed by using the same reaction model and rate constants except the increased wall decay of O3and NOz as described before. The time profile of each species reproduced using the present reaction model is shown in Figure 1, a and b. Slight initial delay of the NO and C3H6 decay rate in the computer simulation as compared to the experimental data can be noted in Figure 1,a and b. Such an initial delay was also observed in all of the lower-concentration runs. The same type of discrepancy was reported by Carter et al. (9) and Hendry et al, (16))and an unknown radical source of OH and H 0 2 was invoked in those studies, respectively, to obtain the acceptable fits to the experimental data. In the present study, however, a hypothetical radical source was not included since the discrepancy between the modeling and the experiment was not as pronounced as found by Carter et al. (9) and such an initial delay does not affect the conclusions of the present study.
Results and Discussion Figures 2-4 show the comparison of [O,],, in the C3H6-N0,-dry air system obtained by computer modeling
0
I
'
I
001
,
I
005
010
02 [NOx10 / ppm
I
03
Figure 3. Comparison of observed (0,A) and predicted (0,A) [O,], as a function of [N0x]0112.The abscissa is In a square-root scale. k l = 0.16 min-l; [C3H6], = 0.50 (0, 0) and 0.10 (A, A) ppm.
and the smog-chamber study as a function of [ C ~ H ~ I O , [N0,]01/2,and JtI1I2, respectively. Initial conditions used for the simulation are the same as those for each experimental run. In Figure 2, the leveling off of the [O,],, is found to be reproduced when [C3H6],is increased keeping [NO,], constant, although the computer simulation overpredicted [O,],, by up to 15% in this series of runs. Experimentally the leveling off was noted to occur at a ratio of [C,H6],/[N0,], 2 3, and this region was defined as a C3H6-excessregion (I). In the present model, the [O,], at the ratio of [C,H,],/[NO,], = 3 corresponds to 90% of the plateau value, thus showing satisfactory agreement with the smog-chamber data within experimental error. More complete leveling off was noted a t a ratio of [C3H6]o/[N0,]o2 5. The values of [O,],, at several points with a higher [C3H6],/[N0,], ratio than experimentally available were also predicted and included in Figure 2. Although a slight decrease of [O,],, was observed at [C3H6]0/[NOx]0 > 15, the leveling off of [O,],, can be regarded as representative behavior of [O,],, in the region of practical interest in this reaction system. Environ. Sci. Technol., Vol. 16, No. 1, 1982 47
Table 11. List of Reactions and Rate Constants Used in t h e C,H,-NO,-Dry reaction no. reaction
Air Model
rate constant"
ref
Photochemical Reactionsb
11
NO, + hv -+ NO + o ( 3 ~ ) 0, t hu + O('D) t 0. + 0 ( 3 p j + 0,' HONO + hv -+ OH + NO H-0, t hu + 2 0 H NO3&+hv + N O + 0, +NO, t o ( 3 ~ ) HCHO t hu -+ H + HCO + H, + CO CH3CH0 t hv CH, t HCO C,H,CHO t hv + C,H, + HCO
12
CH,COCHO
1
2 3 4 5 6 7 8 9 10
1.0 3.9 x 2.0 x 1.5 X 4.9 x 4.3 1.3 X 2.0 x 6.3 x 2.6 x 2.6 x
-+
+ hu -0, + CH,C(O)O,
t HCO
0,
13 14
CH,COCH,OH t hv --+CH,C(O)O, + CH,OH CH,CH(OH)CHO + hv -+ CH,CHOH + HCO
15
CH,CO t hu
16 17 18
0, -+
+ CO CH,OO + CO
-+
7
-+
10-4
lo1 10-3 10-3 10-3 10-3
+ M + 0, t M o(3~) + NO, -+ NO + 0, t NO, t M + NO, + M o(3~ +)NO + M NO, t M + 0, -+ 2 0 ,
t t
Inorganic Reactions
1 . 5 X 10-'
d
9.0 x 10-4 2.6 x 10-3
e c
1
lo-%
o(3~)
1.0x 10-31 1.1x 10-31 9.6 x 10-15
o ( ~ D )t M + o ( 3 ~t)M O('D) t H,O -+ 2 0 H O('D) t 0, + 2 0 , 0, + NO NO, + 0, 0, t NO, +NO, + 0, 0, t O H + H O , + 0, 0, + HO, + OH + 2 0 , 2 N 0 + 0, 2N0, NO t NO, + 2N0, NO + OH HONO NO + HO, + OH + NO, NO, t NO, -+ N,O, N,05 + NO, t NO, NO, t OH + HNO, NO, + HO, -+ HO,NO, HO,NO, + HO, t NO, HO, + HO, -+ H,O, + 0, H,O, t OH -+ HO, t H,O C O + O H + H t CO, H + 0, t M + H O , t M
2.8 X 2.3 X 2.4 X 1.8 x 3.7 x 5.5 x 1.1 x 1.9 x 1.9 x 1.2 x 8.1 X 1.9 x 3.7 x 1.2 x 1.3 X 2.5 X 2.5 X 8.4 x 3.0 x 1.7 x
lo-" lo-'' lo-'' 1044 lo-"
44
0, + 0, (wall)
45
NO,
46 47
C,H,
o(3~)
-+
-+
-+
-+
+ NO,
+
(wall)
t HCO
+ CH,CHCH,O
+ C,H,CHO
HCO + 0, + HO, + CO CH, t 0, CH,O, C,H, + 0, -+ C,H,O, CH30, + NO CH30 + NO, C,H,O, t NO + C,H,O + NO, CH,O, + NO, CH,O,NO, CH30,N0, + CH,O, t NO, C,H,O, t NO, C,H,O,NO, C,H,O,NO, -+ C,H,O, + NO, CH,O, + HO, -+ C H 3 0 0 H t 0, C,H,O, t HO, -+ C,H,OOH t 0, 2CH30, -+ 2CH30 t 0, -+ CH30H t HCHO t 0, + CH,OOCH, 2C,H,O, + C,H,OOC,H, -+
-+
-+
-+
Envlron. Sci. Technol., Vol. 16, No. 1, 1982
1044 10-15
10-38
10-l'
lo-" lo-'' lo-', 10-l lo-', 10-l
10-13 10-13
10-32
1.6 x 10-5 7.2 X 1.1 x 10-5 2.3 X
lo-''
1.1 x 1.1 x
lo-',
5.6 X fast fast 8.0 X 8.0 X 1.3 X 1.0 x 1.3 X 1.0 x 2.9 X 2.9 X 1.6 x 2.7 x 3.0 x 4.5 x
lo-"
27, f 24 24 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 23 28 28 5 29 28 28 28 28
1.1x 10-5,
Propene t O(,P) Reaction System
o(3~ -+ )C,H,
24, 25 26
3.6 x 9.1 x
o(3~ t)0 ,
23
c
1.3 X 10-'
Wall Loss Reactions
48
10-'
9.7 2*4 x 10-3 1.3 X 10"
CH,ONO + hu CH30 t NO C,H,ONO + hu + C,H,O t NO
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
lo-,
CH,O, I
0,
17, 18 19 20 21 22
10-3
i
lo-'' lo-" lo-" lo1 lo-" lo1 loM1' lo-'' 10-13
io-', 10-14 10-i4
g
g
30, h 5 31 1
5 5 5 5 5 5 28 28 28 j
Table I1 (Continued) reaction no. 64 CH,O
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
reaction CH,ONO -+ HCHO + HNO C,H,O -+ C,H,ONO -+ CH,CHO + HNO CH,O + NO, CH,ONO, -+HCHO + HNO C,H,O + NO, -+ C,H,ONO, -+ CH,CHO + HNO CH,O + 0, HCHO + HO, C,H,O + 0, -+ CH,CHO + HO, CH,C(O)O, + NO -+ CH, + CO, + NO, CH,C(O)O, + NO, -+ CH,C(O)O,NO, CH,C(O)O,NO, -+ CH,C(O)O, + NO, CH3C(0)0, + HO, -+ CH,C(O)O,H + 0, C,H,C(O)O, + NO + C,H, + CO, + NO, C,H,C(O)O, t NO, -+ C,H,C(O)O,NO, C,H,C(O)O, + NO, C,H,C(O)O,NO, C,H,C(O)O, t HO, C,H,C(O)O,H + 0, Propene + 0, Reaction System C,H, + 0, -+ CH,CHO,* t HCHO CH,CHO + CH,O,* CH,O,* -+ CH,O,
+ NO
-+
-+
-+
-+
-+
--f
1.7 X lo-" 3.0 X lo-'' 1.7 X lo-" 3.0 X lo-'' 1.4X lo-" 2.4 X lo-'' 1.4 X lo-" 2.4 X lo-'' 6.8X 6.8 X 2.0 x lo-" 1.3 X lo-" 8.0 X 3.0X lo-'' 2.0 x lo-" 1.3 X lo-" 8.0 x 10-4 3.0 X lo-''
-+*cy00
CH,CHO,
1
88 89 90 91 92 93 94 95
.+ CH,CHOO CH,O, + NO -+ HCHO + NO, CH,CHO, + NO -+ CH,CHO + NO, CH,O, t NO, HCHO + NO, CH,CHO, + NO, -+ CH3CH0 + NO, CH,O, + HCHO product CH,O, + CH,CHO product CH,CHO, t HCHO -+ product CH,CHO, t CH,CHO -+ product
96 97 98 99
C y 0 0 -+ H, + CO, 'CO + H - 0 -+ 2H + C 6 , -+ HCHO
-+
-+
--f
(0.50) 1.9x lo-" 1.9 x lo-" 2.0 x lo-1z 2.0 x lo-', 1.4 x 10-13 1.4 x 1 0 - 1 3 1.4 x 1 0 4 3 1.4x 10-13
5
5 5 5 28 28 5
5 5
5 5 5 5 5
t
(0.50) (0.50)
+ CH3CH0,
t i t 1
5.5 x 10-18 5.5 x (0.50)
I
85 86 87
ref
rate constanta
28
1
adj, k , 1
}
adj 5 5 14 14
adj
1
(0.18) (0.67) (0.09) (0.06)
1 100 101 102 103 104
105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
CH,CHOO
CH, + CO, CH, + CO + OH Cy, t H + CO, -+ CH,O + H t CO -+CH,CO t H,O Propene
(0.24) (0.27) (0.35) (0.06) (0.08)
-+ -+ --f
+ OH Reaction System
0,
C,H, t OH -+ CH,CH( O,)CH,OH 0, --+ CH,CH(OH)CH,O,
C,H, + OH C&CH(O,)CKOH
+
NO -+ CH,CH(O)CH,OH CI~,CH(ONO,)CH,OH CH,CH(OH)CH,O, . - .t NO -+ CH.CH(OH)CH,O + NO, CH;CH(OHjCH;ONO, ' CH,CH(O,)CH,OH + NO, -+ CH,CH(O,NO,)CH,OH CH,CH(O,NO,)CH,OH -+ CH,CH(O,)CH,OH t NO, CH,CH(OH)CH,O, + NO, CH,CH(OH)CH,O,NO, CH,CH(OH)CH,O,NO, -+ CH,CH(OH)CH,O, + NO, CH,CH(O)CH,OH -+ CH,CHO + CH,OH CH,C(OH)CH,O -+ CH,CHOH + HCHO CH,OH + 0, -+ HCHO + HO, CH;CHOH t' 0, -+ CH,CI-~O 5 HO, CH,CH(O)CH,OH + 0, + CH,C(O)CH,OH + HO, CH,CH(OH)CH,O + 0, -+ CH,CH(OH)CHO + HO, CH,CH(O,)CH,OH + HO, -+ CH,CH(O,H)CH,OH + 0, CH,CH(OH)CH,O, t HO, CH,CH(OH)CH,O,H + 0 , CH,C(O)CH,OH + OH -+ CH,C(O)CHOH + H,O CH,C(O)CHOH + 0, CH,C(O)CHO + HO, CH,CH( 0H)CHO + OH -+ CH,C( 0H)CHO + H,O CH,C(OH)CHO + 0, -+ CH,C(O)CHO + HO, CH,CH(OH)CHO t OH -+ CH,CH(OH)CO + H,O CH,CH(OH)CO + 0, CH,CH(OH)C(O)O, CH,CH(OH)C(O)O, + NO CH,CH(OH)CO, + NO 1 CH,CH(OH)CO, CH3CHOH + CO, -+
-+
-+
-+
-+
-+
-f
-+
14
1.6 X
lo-"
8.6 X 10'lz 1.9 x lo-" 8.0 x 10-13 1.9 x lo-" 8.0 x 1 0 4 3 1.3 x 10'" 1.0x l o 1 1.3 x 10-l' 1.0 x 10' 4.7 x lo5 6.0x 10, fast fast
1.2 x lo-', 1.2x 10-15 2.9 x 10-1, 2.9 x 10-11 7.0 x lo-', fast
1.3 X fast
lo-"
1.6 x
fast
2.0 x
fast
!
m
5 5 5 adj 5 adj 5 5 5 5 adj adj 5 5 5 5 5 5 5
lo-"
5
Envlron. Scl. Technol., Vol. 16, No. 1, 1982 40
TABLE I1 (Continued) reaction no. reaction 131 CH,CH( OH)C(O)O,t NO, -+ CH,CH( OH)C( O)O,NO, 132 CH,CH(OH)C(O)O,NO, -+ CH,CH(OH)C(O)O, t NO, 133 CYC(0)CHO t OH -+ CH,C(O)CO t H,O 134 CH,C(O)CO + CH,CO t CO
rate constant" 1.3 X 10." 8.0 X lo-' 1.6 X lo-" fast
ref 5 5 5
Propene-NO, Reaction System 135
C,H, t NO,
0, --+
CH,CH(O,)CH,ONO,
0,
136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152
CH,CH( ONO,)CH,O, CH,CH(O,)CH,ONO, t NO -+ CH,CH(O)CH,ONO, t NO, CH,CH(ONO,)CH,ONO, CH,CH(ONO,)CH,O, t NO -+ CH,CH(ONO,)CH,O t NO, -+ CH,CH(ONO,)CH,ONO, CH,CH(O,)CH,ONO, t NO, -+ CH,CH(O,NO,)CqONO, CH,CH(O,NO,)CH,ONO, + CH,CH(O,)CH,ONO, t NO, CH,CH(ONO,)CH,O, t NO, CH,CH(ONO,)CH,O,NO, CH,CH( ONO,)CH,O, t NO, CH,CH( ONO,)CH,O,NO, CH,CH(O,)CH,ONO, t HO, -+ CH,CH(OOH)CH,ONO, t 0, CH,CH(ONO,)CH,O, t HO, CH,CH(ONO,)CH,OOH t 0, CH,CH( O)CH,ONO, t NO, -+ CH,CH(ONO,)CH,ONO, CH,CH( ONO,)CH,O t NO, + CH,CH(ONO,)CH,ONO, C&CH( O)CH,ONO, t 0, + CH,C(O)CH,ONO, t HO, CH,CH(ONO,)CH,O t 0, + CH,CH(ONO,)CHCHO t HO, CH,CH(O)CH,ONO, + CH,CHO t HCHO t NO, CH,CH(ONO,)CH,O -+ CH,CHO + HCHO t NO,
153
HCHO t OH -+ HCO
154
--+
--f
-+
-+
--f
CH,CHO
+ OH
0, -+
+ H,O
Aldehyde Reactions
CH,CO(O,) t H,O
0,
155 156
C,H5CH0 t OH 4 C,€I,CO(O,) t H,O HCHO t NO, + HCO t HNO,
157
CH,CHO
+ NO,
0, -+CH,CO(O,) t
HNO,
52.7 * 5x 1.9 x 8.0 X 1.9 x
10-15
lo-11 lo-', lo-" 8.0 X 1.3 X lo-" 1 . 0 x 10' 1.3 X lo-" 1.0 x lo1 2.9 X lo-', 2.9 X lo-" 1.4 X 10." 1.4 X lo-" 3.0 X lo-'* 3.0 X lo-'*
I
5, n 5
adj 5
adj 5 5 5 5 5 5 5 5
adj
3.1 x 105 3.0 X 10'
adj adj
9.4 x 10-12
5
1.6 X
lo-'' 1.6 X lo-"
5
1 . 8 x 10-15
5 5
2.0 x
5
10-15
0,
158 C,H,CHO t NO, -+C,H,CO(O,) t HNO, 2.0 x 10-15 5 a Units are s-', cm3 molecule-'s-', and cmc molecule-2 s-' for first-, second-, and third-order rate constants, respectively. All rate constants are given for 30 "C. Values in parentheses are branching ratios normalized to unity. The photolysis rate constants were calculated by the summation .Z hJicrh@husing the absorption cross section and quantum yield given by the cited references, and relative rates t o that of NO, are presented. Assumed t o be the same as CH,CHO. Assumbed t o be the same as (CH,CO),. e Assumed to be the same as CH,C(O)C,H,. f The branching ratio was assumed t o be 3 : l . g The first value is for the C,H, ( 3 . 0 ppm)-NO, ( 1 . 5 ppm) run, and the second value is for all other lower-concentration runs. h The total rate constant of 4 . 5 x was taken from ref 30, and the branching ratio of reaction 4 6 was adjusted. Assumed t o be the same as reaction 52. Assumed t o be 50%larger than the rate constants of reaction 62. Su e t al. (32) reported this branching ratio as 0.38 for reaction 84 and 0.62 for reaction 85. All of the values shown in Table I1 as "adjusted" are the finally selected values. The fraction of the radical-forming reactions 101-103 were reduced to be -50% of that used in ref 14. The fraction of reaction 104 was estimated t o be 8%of the total unimolecular decomposition
n
of CH,CHOO. The branching ratio to the addition to the terminal carbon was estimated t o be equal t o that for the reaction of C,H, t OH.
The linear dependences of [O,], against [N0,101/2and kl1I2were proposed in our previous paper (1)introducing a useful photostationary parameter [O3lPs,i.e.
-kl [O,lps =
+ (k1' + 4klk2[NOx]o)1/2 2kZ
E
[(ki/k2) [NOxlo1112
(11) (111)
where k2 is the rate constant of the reaction of NO and O3 Figure 3 depicts the comparison of the calculated and experimental [O,], against As for the run with [C3H6jo= 0.5 ppm, the agreement of the calculated and experimental values is within 10% and the linear relationship between [O,], and [NO,], was reproduced except at the highest point of [NO,], = 0.29 ppm. Since this run was started from NO, containing mainly NO, a calculation was performed starting with an NO2-richmixture 50
Environ. Sci. Technol., Vol. 16, No. 1, 1982
keeping the total NO, concentration the same as the experimental run. The result is included in Figure 3 (@). This demonstrates that the difference in [O,],, between the run starting with the NO2-rich mixture and the NOrich mixture is less than 10% and the deviation from the linear plot is apparent even for the run starting with the NO2-richmixture. The insensitivity of [O,], to the initial NO, composition was verified by several other model calculations with different initial conditions and confirmed our previous statement ( I ) , derived experimentally, that the initial content of NO, only affects the time for 0 3 to reach a maximum and does not appreciably affect the maximum concentration of 0, reached. Although the [O,],, obtained by the present model for the run with [C3H6], = 0.10 ppm is roughly 20 ppb higher than the experimental values, it is interesting to note that the plot for the computer runs with [C3H6I0= 0.10 ppm is superimposed on that for the runs with [C3H6], = 0.50 ppm in the C3H6-excessregion. The slight disagreement with the experimentalvalues might be due to the experimentalerror
81
16
0
2
4
6
8
1 0 1 2 1 4
[ C ~ H ~/I O[ N O x I o
Figure 4. Comparison of observed (0)and predicted (0)[O,], as a function of kl.”* The absclssa is In a square-root scale. [C&]O 0.09 ppm. = 0.50 ppm; [NO,], 05
04
E, 0 3 CL \
;I
-E
02
0
I
01
(
ii 0 01
; i
t’
002 [O3lps
0.03
(
/ pprn
Figure 5. Plot of predicted [O,], vs. [03]ps for the variable [NO,], runs (H) ([C,H,], = 0.50 ppm; k l = 0.16 min-I) and the variable kl 0.09 pprn). runs (0)([C3H6],= 0.50 ppm; [NO,],
in the low-concentration runs. The deviation from the linear relationship with [N0,]01/2is apparent at the region of [C3H6IO/[NOxIO -< 2. The agreement between the calculated and experimental values of [O,], is excellent in the series of light-intensity variation as presented in Figure 4. The proportional relationship between [O,],, and kl1l2has been well demonstrated. Since the linear dependence of [O,],, on [NOx]01/2 and kl1l2 has thus been obtained by the computer modeling, the proportionality between [O,],, and [O,] calculated by using eq I1 is next verified in Figure 5. f: Figure 5, values of [O,], obtained from two different sets of data, one for variable [NO,], at constant values of [C3H6I0= 0.5 ppm and k1 = 0.16 min-l, and another for variable kl at constant values of [C3H6]! = 0.5 ppm and [NO,], = 0.09 ppm, were plotted, resulting in a common straight line. It should be noted that the plot for the [NO,], variation runs has a small negative intercept when
Flgure 6. Generalized maximum ozone curve using the calculated data. Variable [NO,], runs for [C3HBI0= 0.50 (0)and 0.10 (A)ppm; 0.09 (0)and 0.04 (0) ppm; kl variable [C3H6IOruns for [NO,], = 0.16 min-‘.
plotted against [NOx]01/2but passes through the origin when plotted against the [O,], calculated with eq 11. This behavior was also observed ( I ) in our previous analysis of experimental data. An attempt is now made to coordinate these results to construct a generalized ozone isopleth for the C3H6NO,-air mixtures. A trial plot of all of the present calculated data in the form of [03],,/[0,1 vs. [C&&/ [NO,], was performed, giving the result sfown in Figure 6 . The data fall on a single common curve within scattering error. This lends validity to the idea of a normalized ozone formation curve, or generalized ozone isopleth. Such a concept was first proposed by Shen et al. (7). They proposed that [O,],,/ (kl[N0,]o/k2)1/2depends only on the ratio of the [HC], and [NO,], from their flow reactor study of the cyclohexene-NO-air mixtures, and a common single curve was presented for the reaction system. Although they also presented normalized maximum ozone curves for several other hydrocarbons and aldehydes obtained in earlier smog-chamber studies, the presence of a single curve for each hydrocarbon was somewhat ambiguous both because of the scatter of the data and because of the narrow variation of the [HC],-[NO,], combinations. In our previous experimental study of the C3H6-N0,-dry air system, the attempt to find a generalized curve was thought to be unsuccessful since the data for [C3H6I0= 0.1 and 0.5 ppm did not fall on a common curve. Judging from the results of the present study, however, the deviation might be due to the experimental error in the lower-concentration runs, as was discussed before, and the existence of the generalized ozone isopleth in the form of [O,],,/ [O,],, vs. [HC],/[NO,], is now thought to be established. This means that [O,], is characterized by [O,], not only in the hydrocarbon-excess region but also in the NO,-excess region, and the invariance of [O,],,/ [O,],, with [HC],/[NO,]o seems to be correct. As for the normalizing parameter [O,] the values defined in eq 11, rather than (kl[NO,lo/k~)l/~~should be used since the proportionality between [O,],, and [O,] defined in eq I1 is better than between [o,],, and [Nd,]01/2. The practical usefulness of the generalized ozone isopleth is apparent. The so-called ozone isopleth or equiconcentration contours of [O,],, against either [HC], or Environ. Sci. Technoi., Voi. 16, No. 1, 1982 51
(5) A generalized ozone isopleth curve of [03],/[03], vs. 9 [HC],/[NO,], conveys all of the information on the max-
imum ozone yield in the hydrocarbon-NO,-air
system.
Literature Cited
I
I
02
10 [ C ~ H ~ /I O[ N O x I o
05
I
I
20
30
1
Flgure 7. Piot of [03]max/[03]ps vs. ([CBH&/[NO~],J”* using the calculated data in the NO,-excess region. The symbols are the same a s in Figure 6 except for the run wlth [C3H8IO= 0.20 ppm (V)and k , = 0.16 min-’. The abscissa is in a square-root scale.
[NO,lo can be drawn for any desired kl value from the generalized isopleth, thus allowing comparison of experimental smog-chamber data in a systematic and quantitative way. Our previous research establishing the proportionality between [O,],, and [O,],, made such a comparison possible in the hydrocarbon-excess region, whereas the generalized ozone isopleth allows it in any of the combination of [HC],, [NO,],, and kl. Therefore, if the generalized ozone isopleth is determined for each hydrocarbon and also for hydrocarbon mixtures, it offers a reliable characterization for ozone formation. The plateau region of the generalized curve defines the previously proposed ozone formation potential. Finally, the shape of the generalized ozone isopleth in the falloff region (the NO,-excess region) in Figure 6 suggests that the [O,],,/[O,] might be linearly proportional to ( [C3H6],/ [NO,]o)p/z. The relationship is verified in Figure 7. Although it is difficult to obtain [O,], for a [C3H6],/[N0,], ratio of less than unity in the smog chamber because of the impractically long irradiation time, several more trial computer runs other than those shown in Figure 6 were performed to complement the low [C3H6]o/[N0,]oregion of Figure 7. As shown in Figure 7, in the NO,-excess region of 0.5 C [C,H~]O/[N~,]O 3.0, [O,],,/ [O,],, is found to be approximately linearly proportional to ( [C3H6l0/[N0,]o)1/2, which means [O,],, is approximately linearly proportional to [C3H&1/2 when [NO,], and kl are kept constant. The slope of the plot (7.8 f 0.8) should be related to the reactivity of hydrocarbons and should be useful for characterization of the ozone formation in hydrocarbon mixtures like ambient polluted air. Summarizing the results, it can be concluded that photochemical ozone formation in the hydrocarbonNO,-air mixture can be characterized by the following rules. (I) In the hydrocarbon-excess region, [OJ,, is approximately linearly proportional to [N0,]01/2under the condition of constant [HC], and kl. (2) In the NO,-excess region, [O,],, is approximately linearly proportional to [HC]ol/zunder the condition of constant [NO,]o and kl. (3) [O,],, is, in general, proportional to k11/2under the condition of constant [HCIo and [NO,],. (4) [O,],, is proportional to [O,],, in the hydrocarbon-excess region.
52
Environ. Scl. Technol., Voi. 16, No. 1, 1982
Akimoto, H.; Sakamaki, F.; Hoshino, M,; Inoue, G.; Okuda, M. Enuiron. Sci. Technol. 1979, 13, 53. Sakamaki, F.; Akimoto, H.; Okuda, M. Environ. Sci. Technol. 1980, 14, 985. Sakamaki, F.; Akimoto, H.; Okuda, M. Enuiron. Sci. Technol. 1981, 15, 665. Shibuya, K.; Nagashima, T.; Imai, S.; Akimoto, H. Enuiron. Sci. Technol. 1981, 15, 661. Carter, W. P. L.; Winer, A. M.; Darnall, K. R.; Pitts, J. N., Jr. Enuiron. Sci. Technol. 1979, 13, 1094. Winer, A. M.; Darnall, K. R.; Atkinson, R.; Pitts, J. N., Jr. Environ. Sci. Technol. 1979, 13, 822. Shen, C. H.; Springer, G. S.; Stedman, F. D. Enuiron. Sci. Technol. 1977, 11, 151. Dimitriades, B. Enuiron. Sci. Technol. 1972, 6 , 253. Carter, W. P. L.; Lloyd, A. C.; Sprung, J. L.; Pitts, J. N., Jr. Znt. J. Chem. Kinet. 1979, 11, 45. Akimoto, H.; Bandow, H.; Sakamaki, F.; Inoue, G.; Hoshino, M.; Okuda, M. Environ. Sci. Technol. 1980, 14, 172. Akimoto, H.; Hoshino, M.; Inoue, G.; Sakamaki, F.; Washida, N.; Okuda, M. Enuiron. Sci. Technol. 1979,13,471. Whitten, G. Z.; Hogo, H. “Modeling of Simulated Photochemical Smog with Kinetic Mechanisms”, CHEMK: A Computer Modeling Scheme for Chemical Kinetics, EPA600/3-80-0286, Feb 1980; Vol. 2. Gear, C. W. “Numerical Initial Value Problems in Ordinary Differential Equation”; Prentice-Hall: Englewood Cliffs, NJ, 1971. Whitten, G. Z.; Killus, J. P.; Hogo, H. “Modeling of Simulated Photochemical Smog with Kinetics Mechanisms”, Final Report, EPA-600/3-80-028a, Feb 1980; Vol. 1. Bandow, H.; Okuda, M.; Akimoto, H. J. Phys. Chem. 1980, 84, 3604. Hendry, D. G.; Baldwin, A. C.; Golden, D. M. “Computer Modeling of Simulated Photochemical Smog”, EPA-600/ 3-78-059; Environmental Protection Agency: Research Triangle Park, NC, Feb 1980. Bass, A. M.; Ledford, A. E., Jr.; Laufer, A. H. J.Res. Natl. Bur. Stand., Sect. A 1976, 80, 143. Jones, I. T. N.; Bayes, K. D. J. Chem.Phys. 1973,59,4836. Brock, J. C.; Watson, R. T. Chem. Phys. 1980, 46, 477. Griess, M. J. Chem. Phys. 1968, 49, 857. Stockwell,W. R.; Calvert, J. G. J.Photochem. 1978,8,193. Lin, C. L.; Rohatgi, N. K.; De More, W. B. Geophys. Res. Lett. 1978,5, 113. Graham, R. A.; Johnston, H. S. J. Phys. Chem. 1978,82, 254. Calvert, J. G.; Pitts, J. N., Jr. “Photochemistry”; Wiley: New York, 1966; Chapter 5. Horowitz, A.; Calvert, J. G. Znt. J. Chem. Kinet. 1978,10, 805. Weaver, J.; Meagher, J.; Heicklen, J. J. Photochem. 1976, 6, 111. Okabe, H. “Photochemistry of Small Molecules”; WileyInterscience: New York, 1978; p 310. Hampson, R. F., Jr., Garvin, D., Eds. NBS Spec. Publ. (US.) 1978, No. 513. Graham, R. A.; Winer, A. M.; Pitts, J. N., Jr. J. Chem. Phys. 1978, 68, 4505. Atkinson, R.; Pitts, J. N., Jr. J. Chem. Phys. 1977,67,38. Plumb, I. C.; Ryan, K. R.; Steven, J. R.; Mulcahy, M. F. R. Chem. Phvs. Lett. 1979, 63, 255. Su, F.; Calveri, J. G.; Shaw,J. H. J. Phys. Chem. 1980,84, 239.
Received for review April 7, 1981. Accepted August 25, 1981.
