1153
Photolysis of Nitrogen Dioxide
Photolysis of Nitrogen Dioxide to Produce Transient 0 , NO3, and N205 Alan 6 . Harker and H. S. Johnston* Department of Chemistry and inorganic Materials Research Division, Lawrence Berkeley Laboratory, University of California, Berkeley, Callfornia 94720 (Received December 27, 7972) Publication costs assisted by The University of California
Nitrogen dioxide was photolyzed at room temperature in a long-path infrared cell. The concentrations of nitrogen dioxide and nitrogen pentoxide (N206) were followed as a function of time, and the molecular modulation spectrum of nitrogen dioxide was obtained in a steady-flow experiment. With 1 atm of nitrogen, the observations were the rate constant ratios and standard deviations: kl[M]/kz = 0.18 f 0.01, k 3 [ M ] / k 2 = 0.22 f 0.01, k4/K = 0.71 f 0.05 sec-1 where (1) NO 0 M NO2 + M; (2) NO2 + 1 0 + N O + 0 2 ; (3) NO2 + 0 M NO3 + M; (4) NO3 NO 2NOz; K = ([N2Oa]/[NOz][NO3])e,. By using literature values for k l (6.9 X 10-32 cm3 molecule-1 sec-I) and for K (1.24 X 10-11 cm-3), thle values of the elementary rate constants are kz = 9.2 X 10-12 cm3 molecule-1 sec-1, 123 = 8.2 X 10-:!2 cmgmolecule-2sec-1, and kq = 8.7 X 10-12 cm3 molecule-2sec-1.
+
-
+
Introduction The photolysis of nitrogen dioxide is a key reaction in photochemical air pollution,l is important in stratospheric photochemistry,z and is often used in the laboratory to measure light ihtensity between 300 and 400 nm. The reaction is complex, and there is disagreement in the literature as to the value of certain rate constants and rateconstant ratios. There is agreement in the literatures+ that the following mechanism describes the overall kinetics of the photolysis of small amounts of NO2 in an inert carrier gas
+
hv 0 + M
NO,
+
NO
+0 +0+M
+
+ + +
2N02 h ~ [ N O ~ I [ N O l
(4)
M *NOz
+
+
+M
0,
+
NO
0
NO
+
NO,
+
M h6M[N205] ( 6 )
NO
+
0,
+
-t
NO,
where ka is the empirical, first-order, decay constant. 1.f the initial concentration of nitric oxide is close to zero, the initial rate of formation of dinitrogen pentoxide is
At an early stage of the reaction ( t = t * ) dinitrogen pentoxide goes through a maximum, at which point
where reactions a a n d 1-6 are included and where K := k5/k6. The modulation amplitude of nitrogen dioxide in a steady-flow 'system illuminated with square-wave photolyzing light of frequency f is
+
d In [NO,] = -2aI dt >,+I
(
At 1 atm total pressure and with small initial NO concentration, the disappearance of NO2 is given (by reactions a , 1,2,3, and 5) as a good approximation by
+M
(7) h,[M][O,][O] O2 k,[NO][O,] (8) where 01 includes the absorption cross section u and the quantum yield $. The purpose of this study was to examine this system with the molecular modulation technique,6 and in particular to focus on the rate constants for reactions 2,3, and 4 a t room temperature. Quantities measured in this study were the decay of NOz, the buildup and decay of NzOs, and the molecular modulation of NO2 during intermittant illumination of a steady-flow system. In terms of the mechanism these measurements give the following information. At low pressures (below 50 Torr) the M gas dependent reactions (1 and 3) become negligible compared to reaction 2, and the decay of nitrogen dioxide can be described by 0 2
-
(3)
Nz05 + M h5M[N02][N03] ( 5 )
M
NO2
N206
(1) (2)
NO3
NO3
(a)
+ 0 2 h,[NO,][O] NO3 + M k,[MIINOzIIOl
NO, NO,
-
NO + O(,P) aI[N02] NO2 + M h,[M][NO][O]
-)c
+ +
-+
It can be seen that eq I gives d; with a1 so determined, eq I1 and 111 give two independent measures of the ratio kz/ k3; the combination of eq I, 11, and V gives kllkz. Thus by solving the five experimental relationships simultaneously, it is possible to obtain values for .I, k4/K, kl/k2, and k3/kz, with one equation redundant to use as a check. By taking the literature values for k1 and for the (1) A. J. Hagen-Smit, Ind. Eng Chem., 44, 1342 (1952). (2) (a) M. Nicolet, J. Geophys. Res., 70, 679 (1965); (b) P. J. Crutzen, Quart. J. Roy. Met. SOC., 06, 320 (1970); (c) H. S. Johnston, Science, 173, 517 (1971). (3) T. C. Hall, Jr., "Photochemical Studies of Nitrogen Dioxide and Suifur Dioxide," Ph.D. Thesis, University of California, Los Angeles. (4) H. W. Ford and N. Endow, J. Chem. Phys., 27,1156, 1277 (1957). (5) J. Troe, Ber. Bunsenges. Phys. Chem., 73, 906 (1969). (6) H. S.Johnston, G. E. McGraw, T. T. Paukert, L. W. Richards, and J. Van den Bogaerde, Proc. Nat. Acad. Sci., US.,57, 1146 (1967). The Journal of Physicai Chemistry, Vol. 77, No. 9, 1973
Alan 6.Harker and H. S. Johnston
1154
equilibrium constant K , it is possible to obtain the elementary rate constants kz, k3, and k4. Reactions 7 and 8 are not significant in this system.
Experimental Section The instrument used in this work is a long-path molecular modulation infrared spectrometer. A block diagram of the apparatus is shown in Figure 1. The reaction cell is a cylindrical quartz tube 91 cm long and 28.7 cm in diameter, with a volume of 67.0 1. The cell is equipped with gold-coated multiple-reflection mirrors which give it a spectroscopic path length adjustable from 4 to 40 m. The source of the ir radiation is a Nernst glower which is chopped a t $00 cps by an American Time Products tuning fork. The mohochromator is a McPherson Model 2051, 1-m grating monochromator equipped with a 150-line per mm grating and order sorting filters. The ir detector is a liquid helium cooled, copper-doped germanium photoconductor produced by the Santa Barbara Research Center. The photolytic light for these experiments was supplied by four, 32-in. G.E. 30-W, F30T8/BL black lamps. The photolytic photon flux in the cell is on the order of 1016 photons/cm2 sec. The photolysis lamp output for the cell is monitored by a phototransistor, which can be used as a reference to detect fluctuations in the lamp intensities. The photolysis lamps are driven by a regulated power supply which can electronically switch them on and off in response to a reference square wave from a crystal oscillator. The electronics for the instrument are designed to deteqt the periodic concentration fluctuations in the absorbing gases in the cell which are induced by the flashing of the photolysis lamps. This is done by two sequential stages of demodulation. The 400-cps ac signal from the detector carries the modulation information on sidebands a t 400 f f cps, where f is the frequency of the flashing lamps. The first demodulation is carried out by a 400-cps lock-in amplifier which produces a dc signal directly proportional to the spectroscopic light intensity. Riding on this dc signal as a low-frequency ripple is the modulation information. This de signal is split in two with one component being recorded while the other is ac coupled, filtered, and sent into the second stage of demodulation. The second-stage demodulator is a set of two lock-ins, operating a t frequency f, with one lock-in reference in
F
-
400 cpr Reference Si no1
9
L. F. Ret Generalor
7
I
*
Results A series of experiments was carried out in the closed cell with low total pressure, 19-56 Torr. The decay of NO2 was first order throughout an experiment, and the results are listed in Table I. When NO2 is photolyzed in a closed cell a t 1 atm, the initial decay is first order, but deviations from first-order kinetics appear a t later times, as illustrated by Figure 2. (The concentration of NO2 was followed by infrared absorption at 1600 cm-1.) Data for a series of experiments of this type are included in Table I. The buildup and decay of NzO5 is illustrated by Figure 3 for conditions a t 1 atm total pressure (N2) and 24". The concentration of N2O5 was followed by infrared absorption a t 1238 cm-1. The initial rate of formation of N205 is given in Table 11, and the concentrations of NO, NOz, and NzO5 a t the maximum value of NzO5 are given in Table 111. A plot of ([Nz05]/[NOz])* against ([N02]/[NO])* is given as Figure 4 (compare eq IV) . Along with these conventional measurements, a molecular-modulation study of NO2 photolysis was carried out. The molecular-modulation method consists of monitoring the periodic concentration fluctuations induced in the reacting species by flashing the photolysis lamps on and off. In this work the NO2 modulation was studied in a steady-flow system with the photolysis lamps flashing a t 1 cps. Under these conditions the NO3 radicals and oxygen atoms will be a t their steady-state concentrations and N2O5 will be equilibrium. The behavior of the concentration modulation of NOz can be described by a differential equation with the flashing lamps represented by the Fourier series for a square wave
computer DCto-
LOW
Amp3
Figure 1. Schematic diagram of experimental apparatus. The Journal of Physical Chemistry, Vol. 77, No. 9, 1973
phase with the photolysis lamps and one reference exactly 90" out of phase. The outputs of these two lock-ins represent the amplitude of the sine and cosine components of the first fundamental of the modulation signal. From these values the phase shift and amplitude of the modulation signal can be calculated. The output of all three lockin amplifiers are recorded and time averaged in a signal averaging computer. The carrier gases used in the experiments were highpurity nitrogen and argon, both of which are passed through a Matheson water-and-particulate removal filter before use. The nitrogen dioxide used in the closed cell photolysis experiments was prepared by vacuum distillation from bulk liquid Nz04. The NO2 used in the flow experiments was commercial mixed gas supplied by Matheson. The gas was analyzed by ir and uv spectroscopy in this laboratory and found to contain 970 5 ppm of NO2 and 38 f 4 ppm of NO, with the remainder being N2. The concentrations of all NO, species involved in this work were determined spectroscopically from calibration curves measured in this laboratory.
Frequency
with F = flow rate of chemicals; V = volume of the reaction cell; [NOzIin = the NO2 concentration flowing into the cell; [NOzlout = the NO2 concentration flowing out of
1155
Photolysis of Nitrogen Dioxide TABLE I: Initial Rate of Decay of NO2 as a Function of Pressurea [NO2], molecules cm-3
8.6 X 8.8 X 4.8 x 8.8 X 12 x 6.7 x 9.6 x 10.5 x 11.6 x 2.1 x 2.4 x 3.1 x 19.7 x a
Total pressure, Torr
Relative light int.
19.5 19.5 22 27 56 756 756 756 756 756 756 756 756
1.oo
IOl4 IOl4 10'4 1014
1014 1014
10.14 10.14 10'14 10.14 10.14 10'14 10'14
1 .oo
0.56
1.47 1.44 1.50 1.52 1.52 1.23 1.20 1.25 1.22 0.69 0.71 0.68 0.68
I
I
X X X
X
x
10-2
X
x X X X
10-2 Thn II Indlcatea the concontration a t the tlme a t the N ~ O S concentration maximum, t "
lo-' lo-'
Figure 4. Concentration ratios where nitrogen pentoxide is a maximum (eq IV).
X
TABLE 11: Initial Rate of Formation of
1.91 2.5 2.6
N
z
I
X X
[NO2], molecuies cm-3
0
I
I
I
ka. sec-' (eq 11)
Temperature, 24"; NO2 followed by infrared absorption at 1600 cm-
-
I
I
-
-
10-
x 1015 x 1015 x 1015
[N02], molelim(d[NaO5]/ cules c ~ n - ~ dt)t-o/[tf&], sec-
lim(d[N2051/ dt)t-0/[?02], sec-
0.73 0.69 0.64
x x x
N2Q5
10-3 10-3 10-3
2.8 3.3 3.3
x x x
1015 1015 1015
0.63 0.70 0.79
TABLE I l l : Conditions at Maximum Concentration of initial concn
moiecules
molecules cm-3
x 10-3 x 10-3 x 10-3
N2O5
Concn at N2O5 maximum
molecuies ~ m -
moiecuies ~ cm- 3
i
[No#
x
108
~~~
3.28 3.26 2.50 2.84 1.85 1.61 2.56 2.56 2.26 2.36
0
10
20
30
40 50 Time (seconds)
60
70
00
Figure 3. N2O5 decay as observed by infrared absorption at
1237 cm- l; comparison of experimental points and calculated curve based on rate constants in Table VIII. Initial concentration of N O 2 = 2.8 X loi5 molecules ~ m and - [NO] ~ = 0.
the cell; w = 2ir/T, where T is the period of the square wave. This equation neglects the ozone reactions, since the system contains no initial oxygen and the 0 3 buildup will not be significant. Under these conditions the flow system has reached a steady state with respect to reactants and products, so the unmodulated or dc terms in eq VI cancel leaving only the modulation or ac terms
0.0 0.0 0.0 0.0 8.1 10.2 16.5 25.2 25.8 40.8
2.1 2.0 1.43 1.66 0.89 0.65 0.84 0.68 0.80 0.57
2.82 2.79 2.'13 2.43 1.59 1.37 2.21 2.19 1.95 2.00
1.14 1.13 1.06 1.08 1.11 1.11 0.91 0.87 1.16 1.05
where d0 = 2irf dt; 0 = ut; and f = flashing frequency. Selecting the conditions so that the modulation will be less than one part per thousand leaves the reactant concentrations essentially constant, allowing eq VI1 to be integrated in closed form to give
2
-aI[N02]2hz n-2 cos (ne)
By electronically filtering out all but the first Fourier component of the modulation signal, and taking the pealrto-peak amplitude gives the experimental relationship
Comparison of eq VI11 and VI shows the NO2 modulation wave form to be triangular, phase shifted 90" froim the exciting light. The amplitude of this wave form and its phase shift from the exciting light can be determined experimentally and related to eq IX. The Journal of Physical Chemistry, Vol. 77, No. 9, 197'3
1156
Alan B. Harker and H . S.Johnston
TABLE IV: Data for NO? Modulation at 1 atm Total Pressure, 24’
TABLE VII: Observed Values of k p _ k l , cm6 m o l e c u k 2 sec - 1
Steady-state
n
x
~ ~ ~ co ! ’ cn 1 4[NO] 10-15
Carrier gas
1.02 1.19 0.68 1.13 1.87 1.68 1.55 2.12 1.34
N2 N2
N:, N2
N~ N2 Ar
Ar* Ar
Phase, shift, deg
k, Xsec-1 103
0.74 1.22 1.49 2.04 2.12 1.60 1.38 1.30 1.34
8.3 8.3 8.3 8.3 8.3 7.2 8.3 4.6 8.3
A [NO,] X mod.
93.6 89 70 a2
ao 94 88.2 87.8 91.8
kl
1.43 1.31 1.40 0.83 1.62 13 8 1.78 1.65 1.41
k2 [MI/
0.163 0.179 0.189 0.185 0.190 0.178 0.190 0.206 0.198
Observed value
7.45 X lO-3sec-’ 1.22 X 10-2sec-1 0.22 8.9 x 10-21 0.20
Based Source of oneq data
I
x 10-21 0.71sec-I
11 I1 II Ill Ill IV
0.18 7.3x 10-2’ 0.20 8.1 x 10-2’
V V V
8.1
V
Table I Table I Table I
Constant
1 atm of Nz 1 atm of Nz
=M
1 atm of N2
N2
=M
Table I I I , Figure 4 Table I V 1 atm of N2 N2 = M Table I V 1 atm of Ar Ar = M
TABLE VI: Comparison of the Resuits of This Work with the
Literature Valuesa
0.18 f 0.01
0.221
0.18 f 0.004 0.10 f 0.05 0.36
0.33 0.08 0.27 f 0.03 1.9
0.005
0.71 f 0.02
296
This work 7 5 4
0.60A 0.06
296 295 300 296
*
a Total pressure
a
= 1 atm, M gas = nitrogen.
A summary of the steady-state concentrations with the .phase shift and amplitude measurements are recorded in Table IV. The photolytic light intensity for the modulation experiments was found to be 11.2% greater than in the initial slope experiments, when measured by the phototransistor mounted in the cell, and the values of d have been normalized by this factor.
Discussion The observed rate constant ratios are assembled in Table V. The two independent values of k3/k2 agree within 10%; the value based on eq I1 was more precise and is preferred. The three observed ratios, k l / k z , k3/kz, and k 4 / K , are compared with values reported in the literature in Table This study gives only rate ratios. To evaluate absolute values of rate constants, either k l , k2, or ka must be taken from the literature. Of the three, the most extensive and most precise data are those for k l . Literature values are ~
.
4
,
5
3
7
3
8
The Journal of Physical Chemistry, Voi. 77, No. 9 , 1973
= 6.9 X
02,Nz,Ar Ar, 0 2 02
296 300 297 297 293 298 298 296
NP
02,He, Ar Ar NP
Nz
9 10 11 11
12 13 14 15
cm6/molecule2/sec
Value
Source
Ref
Condition
N:,
Table II
a Average value
Ref
T, “K
TABLE VIII: Elementary Rate Constants for Nitrogen Dioxide Photolysis (297 O K , 1 atm of N2)
TABLE V: Observed Rate Constant and Rate-Constant Ratios Rate constant function
* *
7.0 0.08 x 10-32 7.6 0.05 X 6.4 f 0.8 x 10-32 7.3 i 0.9 x 10-32 5.1 i 0.2x 10-32 5.3 x 10-32 6.1 x 1 0 - 3 2 10.0i 0.14x 10-32
M gas
_
6.9X cm6 sec-I 9.2X cm3 sec-I 8.2 x IO-32cm6sec-i 1.24 X 10-l’ 8.7 x l o - ” cm3 sec-1 0.104sec-1 1.29 X 10-l2cm3 sec-’ 6.24X 1 0-34 cm6 sec2.1 x 10-’4cm3sec-’
Literature
9-1 5
ki, ki/kz k2, k s / k z
Table V Table V
Literature K , k4/K
Literature
16
Table V 17
K , k6M
Literature Literature
18 19
summarized in Table VII,9-15 and the value 6.9 X 1 0 - 3 2 cm3 molecule-l sec-l was taken for N2 as foreign gas at room temperature. The observed quantity k 4 / K is reduced to k4 by the literature value of K . With these values of K and k l , the elementary rate constants k2, k3, and k4 are evaluated and listed in Table VIIIQ-19with the other eight elementary rate constants in this system. With these eight elementary reactions, a computer program was written that integrated the simultaneous rate equations to give NO2 and N205 as a function of time. In Figures 2 and 3 the circles represent observations and the smooth curves are those calculated from the elementary rate constants in Table VIII. There is good agreement between the calculated and observed curves over the full course of observations.
Acknowledgment. This work was supported in part by the U. S. Atomic Energy Commission through the Inorganic Materials Research Division, Lawrence Berkeley Laboratory, and in part by AP-104 Air Pollution Control Office, Environmental Protection Agency. (7) E. A. Schuck, E. R. Stephens, and R. R. Schrock, J. Air Pollut. Contr. Ass., 16, 695 (1966). (8) I. C. Hisatsune, B. Crawford, Jr., and R. A. Ogg. Jr.. J. Amer. Chem. SOC., 79, 4648 (1957). (9) F. Kaufman. Proc. Roy. SOC.,Ser. A, 247, 123 (1958). (IO) P. Hastek, R. R. Reeves, and G. G. Mannella, Air Force Cambridge Research Center, Technical Report No. AFCRC-TR60-264 (1960). (11) M. A. A. Clyne and 8.A. Thrush, Proc. Roy. Soc., Ser. A, 269, 404 (1962). (12) E. A. Ogryzloand H. I. Schiff, Can. J. Chem., 37, 1690 (1959). (13) S. Takahashi and S. Miyazakl, Mem. Def. Acad., Jap., 8, 611 (1968). (14) S.Takahashi, Mem. Def. Acad., Jap., 8, 777 (1968). (15) F. S. Klein and J. T. Herron, J. Chem. Phys., 41, 1285 (1964). (16) G. Schott and N. Davidson, J. Amer. Chem. Soc., 80, 1841 (1958). (17) R. L. Mills and H. S. Johnston, J. Amer. Chem. Soc., 73, 938 (1951). (18) H. S. Johnston, “Gas Phase Reaction Kinetics of Neutral Oxygen Species,” NSRDS-National Bureau of Standards, 20. (19) H. S. Johnston and H. J . Crosby, J. Chem. Phys., 22,689 (1954).
~
