5474
J . Phys. Chem. 1988, 92. 5474-5481
-
the cluster not satisfy rule 2: at least one quantum of 16a is always 16b1,which exchanged. A possible exception is the reaction 6a' has only been observed by Brumbaugh et al. as a channel of minor importance. Indeed, Heppener et al. did not find this reaction to occur. A manifestation of the symmetry restriction (rule 4) is hard to find in the tetrazine-argon system. One might try to attribute the absence of a large difference between the rates of the reactions 16a2 16a' and 6a1 16aZto rule 4. Even though the former reaction exchanges only one quantum, while the latter changes three, the exchange of one non-totally symmetric quantum is forbidden in our low-level analysis. The evidence remains sketchy, though, since the second reaction also exchanges more 16a quanta. The symmetry restriction on IVR reactions arises from neglecting the van der Waals bend motion. A more realistic treatment would include the effects of vibrational motion in the chemically bound molecule on the van der Waals bend motion. These effects will, in principle, induce reactions that are forbidden in our one-dimensional model. The relative unimportance of rule 4 suggests some of the aspects of the dynamics a more detailed theoretical treatment will have to include. New data are needed to further test our analysis. Experiments of the types already carried out, but with increased sensitivity,
-
-
should give information on less favorable reaction channels. Another test is to examine the rates of reactions that start from different initial states but yield the same product state. If our analysis is correct, the initial level with the larger vibrational band shift ought to react faster. It would also be extremely interesting to investigate the clusters of tetrazine with other rare gases, for example, krypton and xenon. These clusters exhibit almost the same van der Waals stretch frequency as does tetrazine-argon.I2 Therefore, the lower limit to energy transfer into the van der Waals bond of about 100 cm-I is again expected to be valid. Since the binding energies of the krypton and xenon clusters are presumably larger than that of the tetrazine-argon cluster, one might expect reactions to occur that deposit more energy into the van der Waals bond.
Acknowledgment. We thank Prof. P. H. Rettschnick for a preprint of his most recent work and Prof. D. H. Levy for many stimulating discussions. This research was supported by the National Science Foundation. Registry No. s-Tetrazine, 290-96-0;argon, 7440-37-1. (12)Weber, P. M.; Buontempo, J. T.; Novak, F.; Rice, S . A. J. Chem. Phys. 1988,88, 6082.
Thermal Decomposition of Methyl Nltrite: Kinetic Modeling of Detailed Product Measurements by Gas-Liquid Chromatography and Fourier Transform Infrared Spectroscopy Yisheng He, W. A. Sanders,* and M. C. Lin*,+ Department of Chemistry, The Catholic University of America, Washington, D.C. 20064 (Received: January 11, 1988; In Final Form: March I , 1988)
The thermal decomposition of C H 3 0 N 0 was studied in a static reactor at temperatures in the range 450-520 K. Stable products were analyzed by FTIR and gas-liquid chromatography to yield concentration-time profiles as functions of temperature and pressure. The species monitored included CHSONO, CHzO,CH,OH, NO, N20, and CO. The experimental data were kinetically modeled with the aid of Rice-Ramsperger-Kassel-Marcus (RRKM) calculations for pressure-dependent rate constants. The key reactions of this mechanism are the following: CH,ONO CH30 NO (1); CH,ONO CH20 + HNO (2); CHSO + NO CHSONO (3); CHSO + NO CH20 + HNO (4); CH30 + HNO CHSOH + NO (5); HNO + HNO N 2 0 + H 2 0 (7). The results showed that the initiation reaction, (l), is clearly pressure-dependent in the temperature and pressure ranges investigated. The data are consistent with the value k , = 1015~3f0~30 exp((-38 700 i 400)/RT) s-I at 710 Torr of He and with the extrapolated high-pressure rate constant k," = 1016.0'*0.30 exp((-39600 i 400)/RT) s-I. The rate constant ratio k4/k3for channels 3 and 4 was also found to depend on both temperature and pressure. At 710 Torr, k3 = 10'2,96*0.30 exp((0 i 200)lRT) and k4 = 10'2.92f0.30 exp((-2050 i 200)/RTj, both in units of cm3/(mol s). Kinetic modeling of CH30H and NzO formation over the entire range of temperatures and pressures investigated here exp((0 f 400)lRT) and k7 = 108~93*0~30 exp((-3100 i 300)lRT) cm3/(mol s). yielded k5 = 1013.5*0.4
-
-
---L
Introduction The pyrolysis and photolysis of methyl nitrite have been studied by many investigators because it is a convenient source of the methoxy radical, which is very important to combustion and atmospheric chemistry. Early pyrolytic work by Steacie and Shawl at temperatures in the range 470-520 K suggested that the fission of the MeO-NO bond was the first step in the thermal decomposition process. Their data were interpreted on the basis of the two-step mechanism CH30N0 C H 3 0 + CH,O
-
+ NO CHzO + C H 3 0 H
CH30
(1) (6)
This mechanism predicts that the stoichiometric ratio of methanol to formaldehyde should be 1:1, which appeared to be confirmed 'Chemistry Division, Code 6105,Naval Research Laboratory, Washington, DC 20375-5000.
0022-3654/88/2092-5474$01.50/0
-
-
+
-+
qualitatively by their experimental data. Subsequent work by Carter and Travers,z P h i l l i p ~and , ~ Gray and Williams: however, indicated that the actual mechanism is more complex. Several mechanisms have been proposed to account for the accumulated experimental observations,w but the reaction is still not fully understood, particularly at low temperatures and (1) Steacie, E. W. R.; Shaw, G. T. Proc. R. SOC., Ser. A
1934,A146,388. (2)Carter, A. G.; Travers, M. W. Proc. R. Soc., Ser. A 1937,A158, 495. (3) Phillips, L. J . Chem. SOC.1961,7, 3082. (4)Gray, P.; Williams, A. Nazure (London) 1960,188, 56. (5) Zaslonko, I. S.; Kogarko, S. M.;Mozzhukhin, E. V.;Petrove, Yu. P.; Borisov, A. A. Kinet. Kafal. 1970,11, 296. (6) Hsu, D. S . Y.; Burkes, G. C.; Beebe, M. D.; Lin, M. C. I n f . J. Chem. Kinef. 1984,16, 1139. (7) Batt, L.; Milne, R. T.; McCulloch, R. D. Int. J. Chem. Kinet. 1977, 9, 567. (8) Benson, S. W.; ONeal, H. E. Kinetic Data on Gas Phase Unimolecular Reacfions; NSRDS-NBS 21;National Bureau of Standards: Washington, DC, 1970;p 464. (9)MCGarvey, J. J.; McGrath, W. D.Trans. Faraday SOC.1964,60,2196.
0 1988 American Chemical Society
Thermal Decomposition of Methyl Nitrite TABLE I: Typical Carbon and Nitrogen Mass Balances of FTIR Product Analysis' time, s total C, lo-' mol/cm' total N, IO-' mol/cm3 0 5.26 5.26 300 5.27 5.20 600 5.40 5.14 900 5.34 5.24 1200 5.32 5.23 1500 5.30 5.23
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5475
4.0
k, I 4.0h I
I
'Experimental conditions for this run: temperature 483.3 K, pressure 710 Torr. high reagent concentrations. It is clear that the mechanism can be reliably determined only by following as many species as possible over a significant range of temperatures, pressures, and conversion ratios. We have studied the decomposition of methyl nitrite in a static reactor with good temperature control. The concentrations of methyl nitrite and stable products were analyzed by gas chromatography and quantitative FTIR spectroscopy. Concentration-time profiles were obtained for methyl nitrite, methanol, formaldehyde, nitric oxide, nitrous oxide, and small amounts of carbon monoxide for times up to 90 min as functions of temperature and pressure. Analysis of these data showed that (1) the overall rate of disappearance of methyl nitrite is clearly first order and (2) in the temperature range 450-520 K the relative yield of formaldehyde is substantially greater than that of methanol. As the temperature is increased, the yields of formaldehyde and nitrous oxide increase a t the expense of methanol and nitric oxide. Detailed kinetic modeling, aided by RRKM calculations for pressure-dependent rate constants, provides a quantitative description of the disappearance of methyl nitrite and the formation of all major products.
Experimental Section Reaction Vessel. The static reactor was a Pyrex sphere with a volume of 277.3 cm3, placed in a well-insulated cylindrical furnace with automatic temperature control to an accuracy of 0.1 O C . The reaction temperature was monitored with a thermocouple placed at the center of the sphere. The reactor was connected directly to the gas-handling system and to the gas chromatograph sampling loop. A removable cell was used for the collection of products for FTIR analysis. Materials. Methyl nitrite was prepared by the dropwise addition of 33% H2S04 to a saturated solution of N a N 0 2 in methanol. The gaseous products were passed through potassium bicarbonate and dry ice traps before being condensed at liquidnitrogen temperature. After purification by multiple distillations, the product was analyzed by gas chromatography and quantitative FTIR spectroscopy. The concentration of methyl nitrite was greater than 99.2%, with the balance composed of methanol. N o other impurities were detected. Product Analysis. Methyl nitrite, methanol, and formaldehyde could be separated well on a temperature-programmed GLC column 2 m long packed with PEG 400. The carrier gas was a 50 mL/min He flow, and a flame-ionization detector was used. Although the reproducibility was excellent, the mass balance was rather poor due to polymerization of formaldehyde in the GLC column. For this reason, most of the data were obtained by quantitative FTIR spectroscopy (Perkin-Elmer Model 1750), which gave excellent mass balances and offered a wider range of detectable products. GLC analysis was used as an independent measure of the CH30H concentration due to partial overlap with one of the methyl nitrite bands in the IR spectrum. Samples at total pressures in the range 0-500 Torr were collected in an IR cell with KCl windows and transferred to the spectrometer sample chamber. The species detected and infrared bands (in cm-l) utilized were formaldehyde (1745.7, 2782.5), methanol (1033.8), nitrous oxide (2223.7), nitric oxide (1904.9, methyl nitrite (821.4), and carbon monoxide (2171.2). The accuracy of the determinations was verified by absolute calibration
I t 6.0
tlme(rec)
Ii me( s e c )
Figure 1. Concentration-time profiles of various species produced by the thermal decomposition of 2.25% CH'ONO in He at different temperatures. In each case the total pressure was 710 Torr. The symbols represent experimental data points (0= CH30NO; = CH30H; 0 = NzO; A = NO; 8 = CH20; X = CO). The curves are the results of kinetic modeling (discussed in the text).
+
with mixtures of known composition. Table I is typical of the mass balances that were obtained from the FTIR analysis.
Results and Data Analysis Experimental Results. Mixtures of 0.5-4.0% methyl nitrite in helium were pyrolyzed at 13 temperatures in the range 450-520 K at pressures between 10 and 900 Torr. Typical concentration-time profiles for representative temperatures and pressures in the measured range are shown in Figures 1 and 2. Several general conclusions can be drawn from an inspection of the concentration curves. Most striking is the fact that the forma1dehyde:methanol ratio differs from 1:1 at all temperatures investigated. Formaldehyde is the more important product by roughly a factor of 2 at the lowest temperatures and becomes increasingly dominant as the temperature is increased. At the lowest temperatures, most of the nitrogen appears as NO. As the temperature increases, however, N 2 0 accounts for a steadily increasing fraction of the nitrogen. These observations are generally consistent with those reported by P h i l l i p ~ . ~ Our data showed that the rate of disappearance of methyl nitrite is first order under our conditions, in agreement with the results of Steacie and Shawl and of Phillip3 Figure 3 shows the apparent first-order decay of methyl nitrite for different temperatures at a constant pressure of 710 Torr. Figure 4 is an Arrhenius plot of the apparent first-order rate constant k', in the range 450-520 K. Our values of k', are seen to be in close agreement with those of Steacie and Shawl but in rather poor agreement with those of Phillip~.~ We found kt1 to be only mildly pressure-dependent, in sharp contrast with the first-order rate coefficient for the unimolecular decomposition of methyl nitrite obtained by kinetic modeling. The significant difference between these two quantities can be seen clearly from Figure 5. This obvious difference is caused by the occurrence of reaction 3 (which is the reverse of reaction 1) in the very early stage of the decomposition, and it has led to confusion and misunderstanding of the overall reaction mechanism. The mechanism and the evaluation of the key rate constants will be discussed in more detail below. It is clear from our data and those of earlier workers that the simple two-step mechanism consisting of reactions 1 and 6 cannot
5476
The Journal of Physical Chemistry, Vol. 92, No. 19, I988
He et al.
1
-1
A @
I n k;
@,O
Ref. 1 Ref. 3 This work
1.0'
?CO
600 rine(secj
900
',ne!secj
L
1.88
2.12
2.04
1.96
2.20
2.2
1000/T
Figure 4. Arrhenius plot of the apparent first-order rate constant k',. r,me(sec)
rlme(,ec)
Figure 2. Concentration-time profiles of various species produced by the thermal decomposition of 2.25% CH30N0 in He at different total pressures. In each case the temperature was 483.3 K. The symbols represent experimental data points (0 = CH,ONO; + = CH,OH; = N20; A = NO; 0 = CH20; X = CO). The curves are the results of kinetic modeling (discussed in the text).
Results obtained by GLC analysis of CH,ONO are indicated by 0 and those from FTIR by 0.
1.0
0.5 0
."
0.3 0.2
0.1
0.05
J 600
300
1200
900
1800
1500
log P
tlme (set)
Figure 5. Effect of pressure on the first-order rate constant k l for the
Figure 3. Apparent first-order decay of CH30N0 at various temperatures. The total pressure was 710 Torr in all cases.
unimolecular decomposition of CHJONO and the apparent first-order decay constant k',.
describe the thermal decomposition of methyl nitrite, because it requires that the amounts of formaldehyde and methanol produced be equal under all conditions. Even a qualitative explanation of the observed product distributions requires that additional reactions be included; the following mechanism, established on the basis of earlier was employed to model the key products observed in our experiment: C H 3 0 N 0 CH30 NO (1)
product formation will be discussed later. Although a mechanism consisting of reactions 1-7 is capable of rationalizing the major product profiles, it does not account for the formation of a small but measurable amount of CO, which may derive from the following four reactions: CH30+ M CH20 H + M (8)
-
CH30NO CH30
+
CHzO
-
+ NO
+ NO CH,O + HNO H N O + HNO CH3O
+
+
+ HNO
(2)
CH,ONO
CHZO
(3)
+ HNO
CH30H
(4)
+ NO
(5)
+
HzO NzO (7) The relative importance of these reactions with respect to key -+
~~
~
-
+ CHZO CHSO + CH20 H
CHO
+M
+
+
CHO
+ H2
CH30H
CO
+ CHO
+H+M
(9) (10)
(11)
together with other minor radical-molecule reactions 12-16. The complete mechanism is listed in Table 11, along with the rate constants used in the initial and final modeling calculations. Kinetic Modeling. To test the various proposed mechanisms, we modeled our experimental data with the help of the CHEMEQ program.lg Several different mechanisms were tested, including
~~
(10) Mendenhall, G. D.; Golden, D. M.; Benson, S. W. Inr. J. Chem. Kiner 1975, 7, 125
( I 1) McGraw, G. E., Johnston, H. S. In?. J . Chem. Kinet. 1969, 1, 89.
Thermal Decomposition of Methyl Nitrite
The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 5477
TABLE II: Elementary Reactions and Rate Constant Values Used in the Initial and Final Modelings of Methyl Nitrite Pyrolysis' reaction A E E ref 1. CH30N0 CH30 NO 6.3 X 10l5 0.0 41.2 7
-
+
-- + + + + - + + - + + - + + + + + + + - + + - + + + - ++ + + - + + + - +
2. CH30N0 CH20 NHO 3. CH30 + NO CHpONO 4. CH30
NO
5. CH30 NO
HNO
CH20 HNO CH30H
6. CH30 CH30 CH,OH CH2O 7. HNO HNO H20 N20
1015 0.0 lOI3 0.0 1013 0.0 l o L 2 0.0 10l2 0.0 l o L 2 0.0 10') 0.0
38.7) 38.5 0.0 0.0)
(3.2 x 1013 0.0 7.0 X 10" 0.0
0.0)
(1.7 X 4.0 X 1.3 x (7.2 X 2.0 X (8.4 X 3.0 X
4.0 X 10' (8.5 X lo8
+
b
0.0
0.0 0.0
12 13 c
17.2 1.9
15 16 17 18
0.0
1.9
18
0.0 0.0
0.0
10" -0.40
d
'The tabulated constants are defined by k = ATB exp(-E/RT), where E is in kcal/mol and bimolecular rate constants are in cm3/(mol s). Final values for the most important reactions are shown in parentheses. bThis work given for 710 Torr of He. cThis work. dVeyret, R.; Lesclaux, R. J . Phys. Chem. 1981, 85, 1918. as many as 19 elementary steps. Whenever possible, rate constants were obtained from the literature or from calculations based on the RRKM theory. Unknown values were adjusted within physically reasonable limits to obtain the best fit to the experimental data over the temperature and pressure ranges investigated. In our initial modeling, the key reaction rate constants involving the unimolecular decomposition of C H 3 0 N 0 and the reaction of C H 3 0 with N O (i.e., kl, k2, k3,and k4) were based on those recommended by Batt et al.7 and listed in Table 11. Surprisingly, however, these values were found to be incompatible with the observed concentration profiles of C H 3 0 N 0 , C H 2 0 , and NO, as illustrated in Figure 6 for a representative temperature. These rate constants were varied systematically in our subsequent detailed kinetic modeling. In modeling calculations, the rate constant for reaction 4 was initially estimated with the RRKM theory (to be described below), and kl was adjusted to fit the decay of C H 3 0 N 0 and to reproduce the value of k3. The latter was determined from the relationship k3 = kl/KI, where K1 is the equilibrium constant for the reaction C H 3 0 N 0 s C H 3 0 + NO. For K1, the thermochemical data for C H 3 0 N 0 were taken from the compilation of Stull et al.,20 based on the averaged AH0f,29s= -15.3 kcal/mol. The thermochemical data for C H 3 0 and N O were taken from the recommendations of Tsang and HampsonI2 and JANAF,21respec~
2'
12 14 12
lOI7 -1.0 lo1* 0.0 10" 0.7 10" 0.0 10"
~ = 4 a 3 . 3K
7 7 b 0.0 7 2.05) b 0.0 11
0.0 3.1) 3.9 X lo3' -6.65 33.3 2.5 X lo9 1.27 2.64 1.0 X 10" 0.0 2.98
8. CH30 M CHzO H M 9. H CH2O CHO H2 10. CH30 CH20 CH30H CHO 11. CHO M CO H M 1.9 X 12. H + H N O - H 2 + N O 4.8 X 13. CHO HNO CH20 NO 2.0 X 14. H CH3ONO-CH3OH 1.2 X NO 15. H CH30N0 H2 CH20 1.4 X NO 16. CHO NO CO HNO 7.2 X
1
61
~~
(12) Tsang, W.; Hampson, R. F. J . Phys. Chem. Ref: Data 1986, IS, 1087. (13) Kohout, F. C.; Lampe, F. W. J . Chem. Phys. 1967, 46, 4075. (14) Hsu, D. S.Y.;Shaub, W. M.; Blackburn, M.; Lin, M.C. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 909. (15) Timonen, R. S.; Ratajczak, E.; Gutman, D.; Wagner, A. F. J . Phys. Chem. 1988, 92, 651. (16) Baulch, D. L.; Drysdale, D. D.; Horne, D. G.; Lloyd, A. C. Evaluated Kinetic Data for High Temperature Reactions; Butterworths: London, 1973; Vol. 2. (1 7) Westley, F. Table of Recommended Rate Constants f o r Chemical Reactions Occurring in Combustion; NSRDS-NBS67; National Bureau of Standards: Washington, DC, 1980. (18) Moortgat, G. R.; Slemr, F.; Warnock, P. Int. J . Chem. Kine?. 1977, 9, 249. (19) Young, T. R., Boris, J. P. J . Phys. Chem. 1977, 81, 2424. (20) Stull, D. R.; Westrurn, E. F., Jr.; Sinke, G . C. The Chemical Thermodynamics of Organic Compounds; Wiley: New York, 1969.
0
300
600
900
1200
1500
TIME ( s e c )
Figure 6. Comparison of the experimental concentration-time profiles (curves with symbols) with those obtained from kinetic modeling, with Batt's recommended values for the rate constants k l , k3, and kd (curves without symbols). n l
-1
1.88
1.96
2.04
2.12
2.20
1000/T
Figure 7. Arrhenius plots of the rate constant k , and the extrapolated kl". Results obtained by GLC analysis of CH30N0 are indicated by 0
and those from FTIR by 0.
tively. The rate constants for reactions 5 and 7, the key processes responsible for C H 3 0 H and N 2 0 production, were adjusted to fit the profiles of these products. Reaction 6 was found to be unimportant under all conditions employed in this study because of the low concentration of C H 3 0 . Reactions 8-16, which were introduced to account for the trace amount of CO formed, were essentially insignificant, and their rate constants were not varied in the modeling. Figures 1 and 2 show comparisons of the measured and modeled concentration-time profiles for a variety of temperatures and pressures, by using the final values of rate constants k l , k3, k4, k5, and k7 given in Table 11. The agreement can be seen to be very good in most cases. At very low pressures the concentrations of nitrous oxide, methanol, and carbon monoxide could not be measured accurately. Under these conditions, therefore, modeling was limited to the disappearance of methyl nitrite and the for-
5478 The Journal of Physical Chemistry, Vol. 92, No. 19, 1988
He et al.
TABLE 111: Comparison of Measured and Calculated Values of the Rate Constants /r2 and kd" sourceb TIK P 1% k3 log k4 phot 443-473 -0.9 atm, i-C4Hlo 13.1 f 0.6 12.3
pyro, MeOOMe
383-423
-700 Torr, CF4
phot
298-423
-700 Torr, N,
sw
780-1000
PYro
403
-
(12.91-12.92 13.2 f 0.4 (12.83-12.84
11.72-11.82 11.9 11.61-11.74
13.16 12.94-12.96 13.22 12.85-12.88
(12.71-12.75
11.47-11.87
12.75-12.81
(12.60-1 2.32
12.52-1 2.78
12.87-12.9 1
(12.38 11.26 (12.71
12.06 10.6 1 11.47
(1 2.22
11.97
12.55 11.31 12.79 13.10 f 0.02 12.42
(12.71
1 1.47
12.79
1.6 atm, Ar
1 atm, NO
phot
298
1 atm, N,
phot
295
15 f 5 Torr, SF6
296
log ( k , + k4)
1 atm,
N2
k4/k3
ref
0.17 0.06-0.08) 0.05 0.06-0.08) 0.17 0.06-0.13) 0.5 0.85-2.90) 0.5 0.48) 0.5 0.06)
7 22 23 24 25 11 26
0.57) 0.13 0.06)
27
For each set of experimental conditions, the values calculated by the RRKM theory are given for parentheses. The units of the rate constants are cm3/(mol s). The step sizes for collisional energy transfer for mono-,di-, and polyatomic partners were taken to be 1.4, 4.0, and 6-8 kcal/mol, respectively. *phot, photolysis; pyro, pyrolysis; sw, shock wave. The source molecule was MeONO except as noted. 3l.t P.710
torr
30.0
29.0
28.0
27.0 1.90
1.98
2.06
2.22
2.14
~~
1.0
1.8
1.4
2.2
2.6
3
log P
Figure 8. Plots of the rate constants k, and k4 as functions of the total pressure at 483.3 K. Curves are calculated values based on the RRKM
theory. mation of nitric oxide and formaldehyde. From both the kinetic modeling and RRKM calculations, it is clear that k3 is independent of temperature but dependent on pressure. On the other hand, k , and k4 depend strongly on both pressure and temperature. The values of kl as functions of pressure (at T = 483.3 K) and temperature (at P = 710 Torr) are shown in Figures 5 and 7, respectively. In Figure 7, the extrapolated high-pressure rate constant for the unimolecular decomposition of C H 3 0 N 0 , k,", is also included for comparison. The extrapolation procedure will be discussed in the following section. The modeled values of k3 and k4 as functions of pressure (at T = 483.3 K) and temperature (at P = 710 Torr) are presented in Figures 8 and 9, respectively. Values of the ratio k 4 / k 3 obtained by previous investigators show a substantial amount of variation, undoubtedly due in part to the effects of both temperature and pressure as shown. Our data are summarized in Table I11 and compared with values from the literature. These two important reactions are discussed in more detail in a later section. The value of k5 determined by fitting the yield of C H 3 0 H was found to be independent of temperature and pressure. The averaged value (3.2 0.5) X lOI3 cm3/(mol s), derived from
*
1000/T
Figure 9. Arrhenius plots of the rate constants k, and k4 at a total pressure of 710 Torr. The solid curves are least-squares fits to the modeled data, while the dashed curves are calculated from the RRKM theory.
modeling more than a dozen experimental runs covering different temperatures and pressures, agrees closely with that of McGraw and Johnston" given in Table 11. Because the concentration of HNO is considerably higher than that of CH30, C H 3 0 H derives primarily from reaction 5. Reaction 6 is essentially unimportant, in spite of its apparently much larger rate constant as given. The N 2 0 detected in our system is believed to come solely from reaction 7. The alternative process H N O NO N 2 0 O H [ k = 2 X lo" exp(-26000/RT)], which was first proposed by Wilde2*to account for N20 production from the pyrolysis of NO
+
-
+
(21) JANAF Thermochemical Tables, 2nd 4.;Stull, D.R., Prophet, H., et al., Eds.; NSRDS-NBS 37; National Bureau of Standards: Washington, DC, 1971. (22) Batt, L.; Rattrary, G. N. Int. J . Chem. Kinet. 1979, I I , 1183. (23) Wiebe, H. A,; Villa, A,; Hellman, T. M.; Heicklen, J. J. Am. Chem. SOC.1973, 95, 1. (24) Erimin, A. V.; Zaslonko, I. S.; Kogarko, S. N.; Mozzivkhin, E. V.; Petrov, Yu.-P.;Borisov, A. A. Kinet. Katal. (USSR)(Engl. Transl.) 1970, 1 1 , 249, 711. (25) Baker, G.; Shaw, R. J . Chem. SOC.1965, 6965. (26) Sanders, N.; Butler, J. E.; Pasternak, L. R.; McDonald, J. R. Chem. Phys. Lett. 1980, 46,203.
The Journal of Physical Chemistry, Vol. 92, No. 19, I988 5479
Thermal Decomposition of Methyl Nitrite 17.8
150 140
T
.-.-.-. H-f-O--N=O
,O,;H!-
H--N=O
E*
;1 7 . 6 Y) 01
.
3 0
3
0
\
50
U
U
5
A
9
y 11.4 3 e
40
0
oi
30 17.2
lw
20
Eo I
10
I
CH20+RN0
. -.
17.C
1.88
\
2.04
1.96
2.
2.12
0
fleONO
lOOOlT
Figure 10. Arrhenius plot of the rate constant k,. The data shown here were obtained at a total pressure of 710 Torr (helium).
K TORR
T.483.3
P.710
6
Figure 12. Diagram illustrating the energy relationships among the reactant, the initial products, and the transition states.
RRKM theory was utilized to calculate these rate constants for the experimental conditions employed. Both reactions 3 and 4 were assumed to take place via the chemically activated methyl nitrite molecule, CH30NO+,as follows:
h
U
CH30
Y)
. U
U 43 0
(CH30NO)t A C H 2 0
d
+M
v
C
.s:
+ NO
CH3ONO
+ HNO
(4)
(3)
The energy diagram for this system is shown in Figure 12; it was constructed on the basis of the Arrhenius parameters for C H 3 0 N 0 dissociation via channels b and c previously recommended by Batt et aL7 For channel b, leading to C H 3 0 NO, a transition state with two free rotations was assumede6Channel c, yielding C H 2 0 HNO, was assumed to involve a four-centered state by using the activated complex parameters proposed by Batt et aL7 for the initial calculations. The rate constants k3 and k4 were calculated by using the following expressions previously employed by Lin and co-work-
4
Y
U 01
+
w 0
01
+
Y
a
2
...
ers:29-31
.....
1200
600
1800
k3 =
tirne(sec)
Figure 11. Time dependence of the rates of the most important elementary reactions in the final mechanism used for kinetic modeling. The initial concentration of CH30N0for this run was 5.25 X lo-’ mol/cm3,
with helium as the background gas. and H2 mixtures at higher temperatures, was found to be too slow to account for the observed N 2 0 yields under the conditions of our experiments. Figure 10 is an Arrhenius plot of the values of k7 obtained from the kinetic modeling of our experimental data. The straight line was obtained by least-squares fitting of the data for a total pressure of 710 Torr and corresponds to k7 = 108.930*0.30 exp((-3310 f 300)/RT) cm3/(mol s) The kinetic modeling calculations indicated that the most important steps of the mechanism are reactions 1-5 and 7 . Figure 11 is a plot of the rates of these reactions as functions of the total elapsed reaction time. The remaining reactions are significantly slower at these low temperatures. RRKM Calculationsfor k3 and k,+ Because of the wide scatter of the k4/k3 ratios reported in the literature and the expected pressure and possibly temperature dependence of k3 and k4, the (27) Glasson, W. A. Enuiron. Sci. Technol. 1975, 9, 1048. (28) Wilde, K. A. Combusr. Flame 1969, 13, 173.
k4
=
where q* is the product of the translational and rotational partition functions of the transition state b, and q A and q B are the total partition functions of CH30 and NO, respectively. k, and kb are the energy-dependent rate constants of the elementary steps shown in the above scheme. The rate constant for the collisional stabilization of the energized molecule is w = PZp, where Z is the collision number and P is Troe’s collision e f f i ~ i e n c y . ~The ~ step size for collisional energy transfer was taken to be 1.4 kcal/mol. Collision cross sections were estimated from data in ref 33 for (29) Berman, M. R.; Lin, M. C. J . Phys. Chem. 1983, 87, 3933. (30) Berman, M. R., Lin, M. C. J . Chem. Phys. 1984,80, 5743. (31) Hsu, D. S . Y . ;Shaub, W. M.; Creamer, T.; Gutman, D.; Lin, M. C. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 909. (32) Troe, J. J . Chem. Phys. 1977, 66, 4745. Curtiss, C. F.; Bird, R. B. Molecular Theory of (33) Hirschfelder, J. 0.; Gases and Liquids; Wiley: New York, 1954.
5480 The Journal of Physical Chemistry, Vol. 92, No. 19, 1988 TABLE IV: Molecular Parameters Used for TST-RRKM Calculations property CH30 CH,ONO TSb TSC 16.79 32.55 35.06 moments of 5.11
inertia"
31.80 31.89
vibrational 3050 (3) frequenciesb 2340 (1) 1450 (2) 1350 (1) 1315 (1) 900 (1)
250.95 189.24 3033 3015 2890 1620 1458 1440 1400 1239 995 838 650 624 346 220 125
355.59 286.24
260.74 242.84
2980 (3) 1620 (1) 1435 (3) 1239 (1) 600 (2) 150 (1) 110 (1)
3000 (2) 2297 (2) 1412 (3) 800 (1) 450 (2) 260 (2) 125 (2)
energy barriers: E, = 0; E', = 25.1 kcal/mol statistical factors: 1, = 1; lb = 1; I, = 3 Runitsare lo4 g cm2 bunits are cm-I. Numbers in parentheses are degeneracies.
Lennard-Jones potentials. From the RRKM theory, these rate constants are given by (111)
where E P ( E * )is the sum of vibrational states for the transition state at the energy E* and N(E) is the density of vibrational states of the excited C H 3 0 N 0 at the energy E (see Figure 12). Ib and I, are the ratios of the overall rotational partition functions for channels b and c, with symmetry numbers excluded. The factors and 1, are the statistical factors for channels b and c, respectively. The energy barrier for the recombination of C H 3 0 and NO at 0 K, E,, was taken to be zero. The molecular parameters used for the RRKM calculations of the absolute rate constants are listed in Table IV. The sum of vibrational states was evaluated by direct count up to E* = 10 kcal/mol, and the Whitten-Rabinovitch approximation was used for higher energies. As a starting point for the RRKM calculations, we used the set of parameters recommended by Hsu et aL6 for channel b and that by Batt and co-workers' for channel c. Only slight adjustments of the parameters of the two transition states (mainly varying the overall moments of inertia and/or the lowest vibrational frequencies associated with the breaking bonds) were required for a self-consistent fit of k l , k,, and k,. The values of kl and k3,of course, are related through the equilibrium constant K1,and kl was determined by kinetic modeling to account for the observed decay rate of C H 3 0 N 0 as noted above. Using the experimental k , and the calculated k l / k l " ratio for the conditions ( T and P ) employed, we obtained the first-order rate constant a t the high-pressure limit, kl". The Arrhenius parameters of the high-pressure rate constant covering the entire temperature range (450-520 K) were then used to readjust the transition-state parameters for channel b. The high-pressure rate constants for this channel, Le., the unimolecular decomposition of C H 3 0 N 0 into C H 3 0 NO, obtained from this second iteration are presented in Figure 7; they agree closely with those from the first extrapolation based on the parameters of Hsu et aL6 A least-squares fit of all data points given in Figure 7 gives
+
kl" = 101601*030 exp((-39600
* 400)/RT)
s-l
Both k3 and k4 are pressure-dependent, and k4 also exhibits a significant temperature dependence; the computed curves for these
H e et al. two rate constants as functions of pressure and temperature are compared with the modeled results in Figures 8 and 9. The calculated k4/k3ratio, which is also a strong function of temperature and pressure, is given in Table I11 for comparison with the literature values.
Discussion Overall Reaction Mechanism. The kinetic modeling of detailed product measurements by FTIR and GLC has firmly established for the first time the mechanism of the thermal decomposition of C H 3 0 N 0 up to very high conversions in the low-temperature regime (450-520 K). The mechanism summarized in Table 11, together with the recommended rate constants for reactions 1-7, can account quantitatively for the disappearance of C H 3 0 N 0 as well as the key products formed in the decomposition reaction: CH20, NO, CH,OH, and N20. Reactions 8-16 are included only to account for the small amount of C O detected at the higher end of the temperature range. The decomposition reaction takes place primarily by reaction 1, giving rise to C H 3 0 and NO. The subsequent interaction of C H 3 0 and N O via reaction 4 produces C H 2 0 , the major carbon-containing decomposition product. The direct production of C H 2 0 from the four-centered channel, reaction 2, was found to produce a smaller fraction of the observed C H 2 0 under the conditions employed. Another carbon-containing product, C H 3 0 H , which was formed in much smaller quantities than CH,O, was concluded to derive mainly from reaction 5 rather than 6, contrary to common belief. The rate constant obtained from the present modeling of C H 3 0 H production, k5 = (3.2 f 0.5) X 1OI3 cm3/(mol s), agrees closely with that measured by McGraw and Johnston" at rmm temperature, (3.0 f 0.6) X lo1, cm3/(mol s), using the UV photolysis-IR absorption modulation technique. The relative yield of NO and C H 2 0 , the two most abundant products, varies in an interesting manner with temperature (see Figure 1). N O dominates a t low temperatures, but CHzO overtakes it at temperatures above 493 K, at which point both yields are approximately equal. The observed change, which can be quantitatively modeled, results mainly from the conversion of N O to N,O via reaction 7; this reaction is believed to be the sole source of N,O detected under the present conditions. Further comments on the mechanism of this reaction will be given below. The key to the present success in quantitatively modeling the overall reaction mechanism lies in our judicious and systematic evaluation of the three interrelated rate constants k , , k,, and k4 with the help of the RRKM theory. Satisfactory modeling of the disappearance of C H 3 0 N 0 and the formation of C H 2 0 and N O over the entire range of temperature and pressure employed was found to be quite difficult when we first utilized the greatly scattered literature values for these rate constants. Clearly this was due to the compounded temperature and pressure effects. Further comments on the kinetics of these important reactions will be included below. Unimolecular Decomposition of CH,ONO. The unimolecular decomposition of C H 3 0 N 0 under the present experimental conditions is clearly pressure-dependent, as illustrated in Figure 5. Its fall-off behavior can be quantitatively described by the RRKM theory. Since most of the measurements we made to examine the effect of temperature on k l were carried out at a constant pressure of 710 Torr using H e as a diluent, the highpressure first-order rate constant for the decomposition reaction could only be obtained by extrapolation with the RRKM theory as described above. The extrapolated rate constant can be expressed in the form k," = 1016.01*0.30 exp((-39600
* 400)/RT)
s-I
This result is in fair agreement with that of Batt and Stewart, 7.8 X l O I 5 exp(-40680/RT) s-I, also obtained by RRKM extrap~lation.~~ The extensive fall-off of kl was realized only recently as a result of the work of Hsu et aL6 and Batt and Stewart.34 The slow (34) Batt, L.; Stewart, P. H., private communication.
Thermal Decomposition of Methyl Nitrite
The Journal of Physical Chemistry, Vol. 92, No. 19, I988
recognition of this pressure dependence could be attributed in part to the fact that the effect of pressure on the rate constant for the disappearance of C H 3 0 N 0 , k’’, was negligible, as indicated by the data shown in Figure 5. Thus k’] is less sensitive to pressure because the rapid reverse reaction, Le., reaction 3, is also pressure-dependent . From the extrapolated high-pressure rate constant one can readily obtain the energy barrier for the reaction C H 3 0 N 0 C H 3 0 NO at 0 K, E o l = 38.4 f 0.5 kcal/mol. This value corresponds to D0298(CH30-NO) = 39 f 1 kcal/mol, which compares reasonably well with the recommended value, 0’298(CH30-NO) = 41.8 f 0.9 k~al/mol,~’ based on Batt’s earlier data,7 E , = 41.2 f 1 kcal/mol. It should be mentioned that in the most recent work by Batt and Stewart a value of Eo,= 38.3 kcal/mol was used in their RRKM calculation^.^^ Recently Hsu et aL6 have measured rate coefficients for C H 3 0 N 0 decomposition in shock waves using Ar as diluent under two sets of conditions: P = 1.7-2.0 atm, T = 850-900 K and P = 0.6-0.8 atm, T = 680-955 K. Their results revealed that “the decomposition reaction is well into the fall-off region” under their conditions and that their data, which cover more than 3 decades in magnitude, falling nicely on a single straight line, could be effectively represented by the second-order rate parameters
kol = 1017.90i0.21 exp((-34200 f 8 0 0 ) / R T ) cm3/(mol s ) This finding is fully supported by the results of the present RRKM calculations within their experimental scatter. It should be pointed out that an individual shock-tube data point typically has an accuracy of f50%. However, this seemingly large error is usually compensated for by the large temperature range that can be achieved easily in shock-tube experiments. Reaction of C H 3 0 with NO. As discussed in the preceding section, the reaction of C H 3 0 with N O can lead to C H 3 0 N 0 by recombination reaction 3 and to C H 2 0 H N O by disproportionation reaction 4. The modeled and calculated RRKM results presented in Figures 8 and 9 support the assumption that the reaction takes place via CH30NOt as depicted in Figure 12. The facts that both k3 and k4 are pressure-dependent and k4 is mildly temperature-dependent can account for the large scatter of the various reported values for k3,k4,and/or the k4/k3ratio (see Table 111). We have calculated these quantities according to the conditions employed, using the finalized RRKM parameters listed in Table IV. The agreement between the calculated and some of the reported data is reasonable. To provide data for combustion and atmospheric chemistry modeling, we have calculated k3 and k4 over the temperature range 200-1000 K for four pressures between 50 and 760 Torr (He, Ar, or N2). Our calculated values are plotted in Figure 13, and the least-squares fits to these curves for values between 200 and 700 K are given here: P = 50 Torr
+
k3 = 10’2.18i0.30exp((0 f 200)/RT) cm3/(mol s) k4 = 1012.81i0.30 exp((-1280 f 200)/RT) cm3/(mol s) P = 760 Torr k3 = 1012.96i0.30exp((0 f 200)/RT) cm3/(mol s) k4 = 10’2.92*0.30exp((-2050 f 200)/RT) cm3/(mol s) It should be pointed out that the value of k3 derived from the present study depends on the value of the equilibrium constant K,(or, more precisely, the heat of formation of CH30NO) used. Thus k3 should be adjusted accordingly if AH0f,300 of C H 3 0 N 0 is changed from -15.3 kcal/mol:O the value adopted for our analysis. HNO HNO NzO + H 2 0 . This reaction has also been the subject of much confusion and controversy.I6 It has been proposed
+
32
I\
30 .
-
+
-
(35) Handbook of Chemistry and Physics; Weast, R.C., Ed.; CRC Press: Boca Raton, FL, 1986-87; Vol. 67.
5481
1 2
100 TORR
3 I
100 TORR 50 TORR
300 TORR
k3
’
28 1
c
3
’
26
1 2
.
24
22
I
i
1
0
3
2
5
4
1000/T
Figure 13. Temperature dependence of the rate constants k3 and k4 at various total pressures.
+
as the source of NzO in the H N O system. The only direct evidence for the occurrence of this process came from the study of Kohout and Lampe13 in the Hg-photosensitized reaction of Dz and NO, from which a rate constant of (4.0 f 1.3) X lo8 cm3/(mol s) was derived for 2 D N 0 N z O + DzO at 300 K. However, the H N O HNO reaction was ruled out as the source of N 2 0 by WildeZ8on the basis of kinetic modeling of the Hz N O reaction at high temperatures. An alternative reaction, HNO NO NzO + OH, with k = 2 X 10l2 exp(-26000/RT) cm3/(mol s), was introduced instead. Our present kinetic modeling of the N 2 0 production profiles at lower temperatures (450-520 K), however, clearly shows that the H N O N O reaction is too slow to account for the NzO yields under these conditions. Our modeling of all N z O profiles led to
-
+
+
-
+
+
k7 = 108.93i0.30exp((-3100 f 300)/RT) cm3/(mol s) At 300 K, k, is calculated to be 4 X lo6 cm3/(mol s), which is 2 orders of magnitude lower than that of Kohout and Lampe cited above. On the surface, the low A factor given above appears to be questionable. On the other hand, it may not be unreasonable if one considers the complex nature of the reaction, which can be depicted schematically as follows: H-N=O
2HNO
I
O=N-H
r
=
H-N-OH O=N
I
T
-
&O
+
HO ,
Other dimeric structures, including HON-NHO and HON=NOH, may also be involved in the reaction.36 The formation of the (HNO)2 dimer, according to Melius,36is exothermic by about 19 kcal/mol, which is due to the activation energy for the (CH3NO)z decomposition reaction, 23 kcal/m01.~’ Thus, reaction 7 may very likely take place with multiple reaction paths more complex than the case of C H 3 0 + NO: the deactivation, decomposition, and isomerization of (HNO),+ and the redissociation of the thermalized (HN0)2 Accordingly, the rate expression given above should not be extrapolated too far beyond the range of experimental conditions employed in this study. Further experiments on this interesting process are underway.
Acknowledgment. W e are pleased to acknowledge the US Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, for supporting this work through Contract NO. DE-FG05-85ER13373. Registry No. C H 3 0 N 0 , 624-91-9. (36) Melius, C. F., private communication. (37) Batt, L.;Gowenlock, B. G.; Trotman, J. J. Chem. SOC.1960, 2222.
