2946
(eaT
J. P b p . Chem. 1981,85,2946-2949
+ l)(emaT
m
in
-
I)($(ENJ+ ~ Z Z : E N ~ ) / A- ~ 1
+
(%(eaT- l)(ernaT- 1)]2C(ENi/A)((euTl)e-iaT- ( 1 +
1
1
,e-rnar))2 =
(eaT- l)(ernaT + 1 ) [ ( E N 2+ (%5',(ENi)1/2)2]/A2 =
(27(eaT- l)(ernaT - 1 ) ) 2 ~ (-1
1
rn
+
(eaT l)(ernaT - 1)(CT2(eaT - 1)2e-2iaT + 0P (A-l))1
(eaT- l)(ernaT + 1 ) ( ~ ~-(e-rnaT)z 1 + O&A-')] = O,(A-l) (IV)
-
as A 03, Substituting the expansions 11-IV into the formula for g(a), we deduce that
+
g(a) = 2(eaT I)(ernaT -~
rn
) E z ~ ( E N J-~ / ~ / A ~
(V) That is, A1/2g(a) is asymptotically normal N(O,k(a)). Finally, observe that 0 = g(&)= g(a) + (& - a)g'(a) + YZ(& - a)2g"(a) + ... = k(a)
Inverting this expansion, we see that & - CY
1
2(ea~ l)(emaT
+ I ) ( E N1? Z ~ ( E N J ~ /+~ o/ A, ( A~ - ~ )
m
= ( ~ T / A ) C Z , ( E N ~ +) ~l)(ernaT / ~ ( ( -~ 1~) ~ X 1
+
+
(eaT- l)e-iaT- (eaT- l)(ernaT 1 ) ( 1 - e-rnaT)) O,(A-') rn
= (27(eaT- l)(ernaT - 1)/A)CZi(ENi)1/2((eaT + l)e-iuT1
(1 + ernaT))+ 0,JA-l)
The series on the right is a sum of independent, zero-mean random variables, and it is readily proved that A112g(a) is asymptotically normally distributed with zero mean and variance equal to
31
-g(a)/g'(a)
As in the proof of Theorem 1, we have 'i- T and so 'i - 7 T2g(a)/g'(a)
N -T~(&
- a),
Combining this with eq I and V we see that All2(?- T ) is asymptotically normally distributed with zero mean and variance equal to x ~ ~ k ( a ) / ( h ( ( u=) (r3/TZ)(eaT ]~ - 1)2(1 (eaT 1)2(1 emaT e2maT) - (1 emaT)2 x 1 eaT e2aT (m(eaT- 1 ) - (e2maT - l)e-(m-l)aT/(eaT+ 1))-2
+
+
+
+
+
+
1
This completes the proof of Theorem 2.
Rate Coefflcient for the Reaction of CH302with NO from 218 to 365 K R. Slmonaitls and Jullan Helcklen' Department of Chemistry and Ionosphere Research Laboratory, The Pennsylvania State University, Unlversity Park, Pennsylvania 16802 (Received: April 6, 198 1)
-
The kinetics of reaction 1, CH302+ NO CH,O + NOz, were studied in the temperature range 218-365 K by using the flash photolysis of C12 in the presence of CHI and O2as a source of CH3O2 radicals. These radicals were monitored by ultraviolet absorption. The rate coefficient kl = (2.1 f 1) X exp((380f 250)/Tj cm3 s-l at 200-torr total pressure. The reaction is independent of pressure (70-600 torr, mostly CHI) at 296 K. Introduction CH302radicals are produced in the atmosphere from the oxidation of CH4: In the stratosphere their principle loss process is the reaction with NO: CH302+ NO CH30 + NO2 (1) However, in regions of low NO concentration, such as the clean troposphere, reaction 1may also compete with other CH302-losspr0cesses.l The kinetics of reaction 1 at room temperature have now been measured directly by several groups.2* The results
-
(1) R. Simonaitis, Proceedings of the NATO Advanced Study Institute on Atmospheric Ozone, U.S.Department of Transportation Report No. FAA-EE-80-20. 1979. (2) H. Adachiand N. Basco, Chem. Phys. Lett., 63,490 (1979). (3) J. C. Plumb, K. R. Ryan, J. R. Steven, and M. F. R. Mulcahy, Chem. Phys. Lett., 63, 255 (1979). (4) R. A. Cox and G. S. Tyndall, Chem. Phys. Lett., 66, 357 (1979). ( 5 ) S. P. Sander and R. T. Watson, J.Phys. Chem., 84, 1664 (1980). (6) A. A. Ravishankara, F. L. Eisele, N. M. Kreutter, and P. H. Wine, J. Chem. Phys., 74, 2267 (1981). ~
~
of the various studies are summarized in Table I. In general the agreement is good. However, in one study2 a significantly lower value for kl was found, but this has been e ~ p l a i n e d .In ~ this paper we report our kinetic measurements of reaction 1 over the temperature range 218-365 K. Since this work was completed, Ravishankara et al. have also completed a temperature study of reaction l!3' Experimental Section Apparatus. The kinetics of reaction 1 were studied by using the flash photolysis-ultraviolet absorption technique. The system consists of four principle parts: the reaction cell, the flash unit, the analysis lamp, and the detection system. The Pyrex reaction cell with quartz windows is 100 cm long and consists of three concentric chambers with an (7) Chemical Kinetic and Photochemical Data for Use in Stratospheric Modelling, National Aeronautics and Space Administration, Jet Propulsion Laboratory Publication 81-3, 1981.
0022-3654/81/2085-2946$01.25/00 1981 American Chemical Society
Rate Coefficient for the Reaction of CH,02 with NO
The Journal of Physical Chemistry, Vol. 85,No. 20, 1981 2947
TABLE I : Summary of Measured Rate Coefficients for C H 3 0 , + NO + CH,O + NO, methodu P,torr lO'*A, cm3 s" EIR, K 1012k(296),cm3 s-'
ref
2 2.0 3 2.0 5 mol mod 1.4 4 FP-UV LFP-UV 6.3 i: 2.5b -86 f 112b 1.7 6 0 f 500 1.9 7 evaluation 7.4 FP-UV 70-600 (CH,) 2.1 f 1' -380 k 250' 0.9 this work FP-UV, flash photolysis-ultraviolet absorption; DF-MS, discharge flow-mass spectrometry; mol mod, molecular modulaOver the temperaOver the temperature range 240-339 K. tion; LFP-UV, laser flash photolysis-ultraviolet absorption. ture range 218-365 K. FP-UV DF-&;IS
3.0 8.0 t 6.5 * 7.1 * 7.4 * 7.4 f 7.7 ?1
75-100 (Ar) 2-3 (Ar) 50 (Ar + CH,) 540 (N,) 75-700 (He)
outside diameter of 5 cm. The inside chamber is 2 cm in diameter, and entrance and exit ports at each end provide for the continuous flow of reactants. The flow rate was adjusted such that the mixture was flashed only once to prevent secondary reactions and to reduce NO consumption. Through the middle jacket, cooled or heated fluids were circulated for temperature control. The outside jacket is evacuated for insulation. A 1-pF capacitor charged to 8-15 kV and discharged through two 1-m long Xe flash lamps placed adjacent to the cell provides the flash radiation. The flash lamp duration at half-intensity is 15 ps, but the afterglow made measurements possible only after -40-50 ps. A dual-beam mode of analysis with a single pass was employed for increased detection sensitivity. The analysis radiation was from a high-pressure 100-W Hg arc (Oriel Corp.). The collimated beam was passed through a 150-cm long cell containing 1atm of chlorine to remove radiation that could came photolysis before being split into analysis and reference beams. Analysis of the effluent for the NO concnetration showed no NO removal (*lo%) due to the analysis beam. The analysis beam was detected by an Hamamatsu 1P28 photomultiplier tube after passing through a Bausch and Lomb 33-86-45 monochromator blazed at 0.3 pm with 1200 grooves/mm and having a reciprocal linear dispersion of 1.6 nm/mm. The monochromator was set at 270 nm, and the entrance and exit slits were set at 1 mm giving a band-pass of 16 nm. The reference beam, after passing through a monochromator, was also detected by an Hamamatsu 1P28 photomultiplier tube. The current from the photomultiplier tubes is converted to a voltage pulse which is amplified with a differential pulse amplifier. The output of the amplifier is fed to a Biomation 805 transient recorder interfaced with a Tracor-Northern signal averager. The signal averager output is fed to an Aim 65 microcomputer, and the data are stored on tape. With signal averaging of 5-20 flashes, the limiting absorption which can be detected is 4-5 parts in lo4with a signal/noise ratio of 10. This corresponds to CH302densities of -3 X 10l2 cm-3 for X = 270 nm with an absorption cross section u = 1.5 X 10-l8 cm2.8p9 Of course, since 270 nm is not at the maximum in the CH3O2 absorption band, the detection sensitivity for CH302at the maximum (- 245 nm, CT = 3.0 X cm2)8,9is correspondingly greater. Measurements were made at 270 nm of the CH302absorption band rather than at the maximum in order to minimize absorption by the CH30N0 product. Materials. C12(Matheson Research Purity) was purified by pagsage over KOH and trap-to-trap distillation. The oxygen (Matheson, extra dry) was used directly from the
-
N
(8)C. S. Kan, R. D. McQuigg, M. R. Whitbeck, and J. G. Calvert,Znt. J. Chem. Kinet., 11, 921 (1979). (9) C. J. Hochanadel, J. A. Ghormley, J. W. Boyle, and P. J. Ogren, J. Phys. Chem., 81, 3 (1977).
1
I
.i" 0
100
200
300
4CO
TIME, psec
Figure 1. Decay of absorption. [NO], = 53.1 mtorr; [CH302], = 1.2 mtorr. Average of five flashes.
cylinder. The methane (Matheson, ultrahigh purity) in some runs was distilled trap to trap, but usually was used without further purification. Its consensable hydrocarbon content was determined to be
