J . Phys. Chem. 1985, 89, 192-199
192
Kinetics Study of the Reactions IO -I- NO2 -I- M and I O3 IO 4- O2
+
IONOp -I- M, IO 4- IO
-+
-
Products,
-+
M. E. Jenkin* and R. A. Cox Environmental and Medical Sciences Division, A.E.R.E. Harwell, Oxfordshire, OX1 1 ORA, England (Received: March 8, 1984)
A photochemicalmodulation technique was employed to investigate the title reactions. IO radicals were monitored in absorption at 426.9 nm where the absorption cross section at this wavelength was determined to be (2.2 f 0.5) X cm2 moleculed. ION02 + M, studied between 35 and 404 torr at 277 K, was found to be in the falloff The reaction IO NO2 + M region between second- and third-order kinetics for this pressure range. The limiting rate constants were ko = (4.3 f 2.0) X 10"' cm6 molecule-2 s-l and k , = [ 1.6$':] X lo-" an3molecule-' s-I. The self-reactionIO + IO products was investigated between 10 and 100 torr at 303 K and between 25 and 404 torr at 277 K. The reaction appeared to proceed by at least two pathways, one pressure dependent and the other pressure independent. The pressure dependence of the overall rate coefficient is described by (5.6 i 0.8) X [MI + (8.0 f 2.7) X 10-l2 cm3molecule s-l at 277 K. The results also allowed an estimate of (9.6 f 3.0) X cm3 molecule-I s-l for the rate coefficient of the reaction I + O3 IO + O2 at 26 torr and 303 K.
+
-
-
-
1. Introduction
The gas-phase chemistry of chlorine- and bromine-containing species has been reasonably well established over the past decade, in particular that of the photochemically initiated free-radical systems that have relevance to the atmosphere.' In contrast, little is known about the atmosphere chemistry of iodine, although both gaseous and particulate iodine species are known to be present in the atmosphere. Chameides and Davis2 have given a detailed discussion of the potential role of iodine in the chemistry of the troposphere and how it might influence tropospheric ozone and the NO, and HO, systems. They point out that iodine-containing species have electronic absorption spectra which extend into the visible region of the spectrum, and therefore photolysis plays a potentially important role in the behavior of atmospheric iodine. Quantitative understanding of the effects discussed is dependent on kinetic and photochemical data which, for the most part, were inferred from the properties of the C1 and Br counterparts. The behavior of iodine compounds in the atmosphere also has relevance to the nuclear i n d ~ s t r y .The ~ radioactive iodine, formed as a fission product of uranium fuels, is a potentially harmful airborne emission from nuclear power installations. The behavior of airborne iodine on a relatively short time scale determines the fate of I3II ( t I l 2= 8 days). An understanding of the fate of the long-lived nuclide 1291( t I l 2= 1.7 X lo7 year) requires a knowledge of the global atmosphere cycle of iodine. Photochemistry does not appear to have been considered in earlier models of the behavior of airborne radioactive iodine. The photolysis of many iodine species produces iodine atoms, for which the major reaction pathway in the troposphere is believed to be reaction 1. I +0 3 IO + 0 2 (1)
-
On the basis of the reported rate constant for reaction 1 ( k ,
of the association reaction of IO with NO2,reaction 2, and of the self-reaction of IO, reaction 3. IO NO2 M ION02 M (2)
+
+
IO
+ IO
-
+
-+
products
(3)
The reactions were studied by using a photochemical modulation technique with detection of IO by absorption spectroscopy. IO was produced mainly by using reaction 1 as a source, and the results also enabled a determination of the rate coefficient, k , , for which the only previously reported measurement has a large experimental uncertainty. Extensive studies of the reactions of C10 and BrO with NO2 show that they are rapid and that the rate coefficients exhibit a pressure dependence typical of association reactions of small radical specie^.^^^ The products of these reactions are the corresponding halogen nitrates, XON02 (X = C1 or Br), the properties of which have been extensively investigated by Schmeisser and Brandle.' Iodine nitrate, "IN03",has also been ider~tified,~ but reaction 2 has not been characterized in the gas phase. In the present work, the kinetics of reaction 2 have been investigated in the pressure range 35-404 torr by time-resolved observation of IO in the presence of NO2, with a view to establishing the occurrence and the rate of the association reaction. The kinetics of reaction 3 were first studied at 1 torr total pressure by Clyne and Cruse," who used a discharge flow technique with IO measured by absorption spectroscopy in the A211 X211 electronic transition. They observed second-order decay kinetics for IO and postulated a mechanism analogous to that for the BrO radical, reaction 3a. More recently, Cox and Coker* have inIO + IO I + IO0 21 + 0 2 (3a)
-
-
k3a = 5.3 x
-
cm3 molecule-'
s-l
(ref 4)
=8X cm3 molecule-l s-' 4, and a typical tropospheric ozone concentration of 30 ppb (= 10l2 molecule ~ m - ~iodine ), atoms are converted to IO radicals with a time constant of approximately 1.5 s. It is apparent, therefore, that IO radicals are important in atmospheric iodine chemistry, and a knowledge of subsequent reactions, and reliable kinetic data for these reactions, is essential. In this paper, we report an experimental study of the kinetics
vestigated IO radical kinetics at atmospheric pressure using molecular modulation/absorption spectroscopy. The reaction was found to be extremely rapid, resulting in formation of an iodine oxide condensation aerosol. The kinetics were complex, but an estimate of the overall rate constant for reaction 3 was obtained which was at least a factor of 10 larger than the earlier value. An additional, possibly pressure-dependent, channel, forming 1202 (reaction 3b) was proposed.
(1)"The Stratosphere-Present and Future"; Hudson, R. D., Reed, E. I., Eds.; U.S.National Aeronautics and Space Administration: Washington, DC, 1979;NASA Reference Publication 1049. (2) Chameides, W. L.; Davis, D. D. JGR, J. Geophys. Res. 19&85, 1383 (3)Chamberlain, A. C.; Eggleton, A. E. J.; Megaw, W. J.; M o h , J. B: Discuss. Faraday SOC.1960, 30, 1. (4) Clyne, M. A. A,; Cruse, H. W. Trans. Faraday SOC.1970, 66, 2227.
( 5 ) Cox, R. A.; Lewis, R. J. Chem. Soc., Faraday Trans. I 1979.75, 1649. ( 6 ) Sander, S . P.; Ray, G. W.; Watson, R. R. J . Phys. Chem. 1981, 85,
0022-3654/85/2089-0192$01.50/0
199. (7) Schmeisser, M.; Brandle, K. Angew. Chem. 1961, 11, 388. (8) Cox, R. A.; Coker, G. B. J. Phys. Chem. 1983.87, 4418.
Published ! 9 8 5 American Chemical Society
monochromator photomult Ipl ier c h a r t recorder/ multichannel analyser
from Tungsten- Halogen or Deuterium lamp
Figure 1. Diagrammatic representation of reaction vessel.
IO
k3,, = 4.0
+ IO(+M)
X
-
I,O,(+M)
cm3 molecule-’
s-l
Signal form
(ref 6)
In the present work, the self-reaction of IO was investigated in the pressure range 10-404 torr in an attempt to rationalize the difference between the high- and low-pressure rate constants. 2. Experimental Section
+-
w
Y
From photo-
Buffer memory
0 C reference y , L a m p s W21 Oscillator 1100 k H z )
2.1. The experiments were conducted in gas mixtures flowing through a silica reaction vessel 120 cm in length and 3.0 cm internal diameter. The vessel (Figure 1) was surrounded by a jacket through which a thermostated solution of 33% ethylene glycol in water was circulated, enabling regulation of the vessel temperature. Six 40-W fluorescent photolysis lamps, 120 cm in length, were radially mounted around the cylindrical reaction vessel. The lamps were powered by a square-wave-modulated 250-V dc supply. I O radicals were produced in chemical systems involving either photolysis of NOz using fluorescent lamps emitting at 350 f 50 nm (Philip T W 40/08,”Blacklamps”) in the presence of 1, or photolysis of 1, using 570 f 70 nm radiation (Thorn EM1 40 W Gold) in the presence of 03. The concentrations of the precursor species were measured by conventional absorption spectroscopy in the reaction vessel, using either a tungsten halogen lamp (e.g., for I2 at 500 nm, u = 2.14 X cm2) or a deuterium lamp source (e.g., for O3at 254 nm, u = 1.11 X lo-’’ cm2) with monochromator (0.75 m spex), photomultiplier (EM1 9781 B), and chart recorder. IO was monitored at 426.9-nm absorption (tungsten-halogen lamp). This corresponds to the (4,O) component of the A211 X211 t r a n ~ i t i o n . The ~ modulated absorption signals due to IO, resulting from intermittent photolysis of the precursor molecules, were detected by using a custom-built multichannel analyser incorporating an internally preprogrammed microcomputer (Harwell MOUSE type 6161) controlled externally by a CBM PET 3032. Figure 2 shows a schematic diagram of the setup. The signal from the photomultiplier, consisting of a carrier dc together with small modulated absorptions (typically lo4), was fed initially to a differencing amplifier, where the majority of the dc component was removed, and the residual signal containing the modulated component was amplified by a factor of 50. The signal was then digitized by a voltage-to-frequency converter (ANCOM 15 VF-1, 100 kHz V-I) and fed alternately to two scalers in MOUSE which were gated with a channel width r/200, where 7 is the modulation period. The contents of one scaler were transferred to the appropriate channel of a 200-channel buffer memory while the signal (9) Durie, R. A.; Ramsay, D. A. Can. J . Phys. 1958, 36, 35.
I
Timing circuits L
IPeriod = 7)
Gate
I f
Commodore
(r1200)
Preset and control
1
1
Print
65382 *mouse’ microcomputer
Figure 2. Schematic diagram of multichannel waveform analyzer for modulated absorption.
for the following channel was accumulated by the second scaler. In this way the modulated absorption signal for a single cycle was built up. Experiments were carried out for many modulation cycles and the signals accumulated. The reference dc signal was also digitized and updated for each cycle. The required timing signals for the photolysis lamp driver (7/2), the scaler controllers (r/200), and updating the dc carrier signal (7)were obtained from modulo-N counters operating on the output from a 100-kHz crystal-controlled oscillator. At the end of each experiment, the contents of the 200-channel memory was transferred to the PET and displayed. Experiments could be repeated and the new data added to the existing data until an acceptable amount of signal averaging was achieved. The total experimental time was generally in excess of 3000 modulation cycles for a favorable signal/noise ratio to be obtained. Typically the noise level in a single channel was 4 X 10” absorption unit. The gas mixtures were pumped through the reaction vessel, and the pressure and flow could be varied by adjustment of needle valves at the inlet and outlet. The total gas pressure was measured by an M.K.S. Baratron. Flow rates through the vessel were such that residence times were about 3 s. I2 was generated by a flow of N 2 (high purity, 6400 mL/min) over iodine crystals (BDH, Analar Grade). The vessel containing the crystals was immersed in a water bath, so the I2vapor pressure, and therefore the I, concentration in the mainstream, could be maintained at a constant value for the duration of each experiment. O3was generated by passing 0,(B.O.C.,Breathing Grade, < 150 mL/min) through a silent discharge ozonator into the vessel. Typical concentrations were 5 X l O I 4 molecule cm-3 of O3 and 5 x 1OI3 molecule cm-3 of I,. I, and O3 were mixed on the low-pressure side of the inlet needle valve because appreciable thermal reaction occurs a t high partial pressures of O3 and 1,. When NO2 was added, the reaction between O3 and NO, was
194 The Journal of Physical Chemistry, Vol. 89, No. I , 1985
Jenkin and Cox
avoided in the same manner. N 0 2 / N 2 mixtures (Air Products, 900 ppm NO2 in high purity N,) were taken from a cylinder and metered through a calibrated rotameter. Concentrations in the vessel were varied between 5 X lo1, and 1 X lOI4 molecule ~ m - ~ . Since NO, could not be measured accurately in absorption at these cm2 molecule-’ at 400 nm), concentrations ( u = 6.76 X concentrations were determined from the dilution in the manifold and the ratio of the pressure in the manifold to that in the vessel. The accuracy of this procedure was checked at greater [NO,], ,A, Absorption due to iodicol ~nsteody st& when the absorption was measurable. 7 Mcdulotion Period 2.2. Analysis of Time-Resolved Absorption Waveforms. Int ’ h l i i s e l , t’oitolll Chorxteristic half times foc rise to and loll formation regarding the kinetic behavior of the IO radical during hom steody state a modulation cycle could be obtained from an analysis of the recorded waveform. 1 During the “light-on” period, the radical concentration increases 0 t2 T (see Figure 3) until the removal rate is equivalent to the production Figure 3. A typical modulation waveform when radical lifetimes are rate, at which point steady state is achieved. During the dark comparable to modulation period. period, decay of the radical is observed. The modulation frequency can be varied, so that the decay time constant is comparable with 3. Results the period. In this way both the steady-state absorption and the half-times for rise to and fall from steady state can be obtained. 3.1. NO2 Photolysis System: The Absorption Cross Section In these experiments the modulation frequency was varied between ofZ0. The photolysis of NO2 in the presence of I, yields I O 0.5 and 4.0 Hz. radicals in the following manner: The behavior of I O during a photolysis cycle can be described NO, hv (A = 350 nm) NO 0 (4) by eq i and ii where n is the reaction order and B is the radical
i
~
-
+
d[IO]/dt = B - nk[IO]”, lamps on
(i)
d[IO]/dt = - nk[IO]”, lamps off
(ii)
production rate when the lamps are on. The steady-state condition applied to eq i gives eq iii (a is the absorption cross section, 1 the
A,, = ul[IO],, = al[
$1
‘In
(iii)
path length, and A , the absorption at steady state). While the steady state can give information on relative rates of production and removal of the transient species, the absolute removal rate can be obtained, for simple kinetic systems, from the half-times for rise to and fall from steady state. Integrating eq i and ii for the simple cases when n = 1 and n = 2 yields expressions iv and v. Hence, inspection of the ratios of half-times for fall and rise n-1
tlj2(fall) = tlj2(rise) = In 2 / k
(iv)
n=2
2 tli2(fall) = tl,,(rise)- In 3 = (2Bk)-0.5
(VI
gives an immediate indication of the kinetic order for removal of the radical and enables calculation of rate constants, although it must be noted that for the case when n = 2, B must also be known. In the more complex case, when the radical is removed by both first-order and second-order processes simultaneously, the steady-state situation is described by eq vi and the decay by eq vii. From eq vi, either removal constant can be calculated provided
+
k4 = 0.028 s-l (6 lamps; see text) 0 + I,
k5 = 1.38
X
-
IO
+I
(5)
10-Io cm3 molecule-‘
s-l
(ref 10)
The rate of production of IO is approximately equivalent to the NO, photolysis rate since reaction 5 is very rapidlo The only alternative reaction for 0 atoms, reaction 6, is slower” and only accounted for between 2% and 5% of the removal of 0 atoms in these experiments.
0 + NO2 ---+NO + 0
k6 = 9.3
X
lo-], cm3 molecule-I
(6)
2
s-l
(ref 11)
The primary photodissociation rate of NO,, k4, in the reaction cell was determined in separate experiments in which the photolytic decay of NO, was monitored in a static mode at 0.2 torr pressure in the absence of I,. k, was determined from the overall first-order decay constant, assuming a quantum yield for NO2 photolysis of 2.0, resulting from reaction 4 followed by reaction 6. IO production rates could be calculated accurately with a knowledge of NO2 and I, concentrations. It was expected that reaction 2 would be the major removal pathway for IO. However, a t finite reaction times when NO produced from NO2 photolysis is present, the reaction with NO, reaction 7, provides a further removal process for IO. The behavior IO
+ NO-
I
+ NO,
(7)
k7 = 1.67 X lo-” cm3 molecule-] s-I (ref 10)
-d[lolf - k,[IO], + 2kII[I0],2 -dt
(vii)
[IO], = A , / a l the other constant, the absorption cross section, u, and B are all known. Equation vii can be used to obtain estimates of both rate constants by considering two points on the decay curve where removal of IO is dominated by the first-order component (low [IO]) and the second-order component (high [IO]) and solving the resultant equations simultaneously. The absolute concentrations (Le., a) must be known for this procedure.
of IO during a typical modulation cycle is displayed in Figure 4. Rise to and fall from steady state occurred on a 50-ms time scale, showing that processes removing IO were rapid. The rise and fall times are equivalent, which is consistent with only first-order kinetics operating. This was confirmed in 14 experiments at total pressure ranging from 7 to 70 torr with initial [NO,] in the range and I, approximately 3 X 1013 (0.5-3.0) X lOI3 molecule molecule cmw3;the temperature was 306 K throughout. The overall first-order removal constants, kl, were obtained from the expression k , = In 2 / i (Le., eq iv), where i is the arithmetic mean of the half-times for fall from and rise to steady state. kI (10) Ray, G. W.; Watson, R. T. J . Phys. Chem. 1981, 85, 1955. ( 1 1 ) Baulch, D. L.; Cox, R. A.; Hampson, R. F.; Kerr, J. A,: Troe, J.: Watson, R. T. J . Phys. Chem. Ref. Dura 1980, 9, 336.
The Journal of Physical Chemistry, Vol. 89, No. 1. 1985 195
Kinetics Study of Reactions of IO lo5
Absorption iL26 9 nml
Figure 5. Modulation cycle from experiment involving the photolysis of I2 in the presence of O3 and NOz. Time lms1
F i i 4. Typical modulation cycle from experiments involving photolysis of NO2 in the presence of 12. Data averaged over 3600 cycles.
is made up of components of all the removal processes for IO. Subsequent analysis suggested that reaction 7 accounted for the majority of kI, since residence times in the reaction cell were sufficiently long for significant buildup of NO to occur. Consequently, these experimental results could not be used to obtain a value for the rate constant for the association reaction of IO and NO,, although it was clear that this reaction was occurring. The data could be used, however, to obtain a reliable value of the absorption cross section of IO at 426.9 nm, CT,since the radical production rates, B, the removal constants, kI, and the radical steady-state absorptions, A,, were known. The average value of CT calculated from equation iii (n = 1) for 14 experiments exhibiting first-order kinetic decay of IO gave a mean value of (2.2 f 0.5) X lo-’’ cmz molecule-’ (error limit = 2 standard deviations). No significant variation of CT over the pressure range was observed. 3.2. Photolysis of 1, in the Presence of O3 and NO,: The Reaction IO NO2 M IONOz M . When I, is photolyzed in the presence of 03,the production of I O radicals occurs via reactions 8 and 1. (Photolysis by gold fluorescent lamps, 500 nm C X C 700 nm.) I, hu (X = 500 nm) I I (8)
+
-
+
+
I
k , = 8.3 X
+ O3
+
-
-+
IO
+ Oz
cm3 molecule-’
(1) s-l
(ref 4)
Addition of NO2to the system provided the possibility of IO removal by the association reaction 2, without complication due to reaction with NO, since photodissociation of NO2 to product NO only occurs for X < 398 nm. Furthermore, any NO impurity in the NO2 was quickly converted to NO, via reaction with 03, before entry into the measurement zone, reaction 9.
NO k9 = 1.8 X
+ O3
-
NOz + O2
cm3 molecule-’
s-l
(9)
(ref 12)
NO, is also produced in this system by the slow reaction of NO2 with O3and is removed by the rapid association reaction with NOz. Its significance as a reactant for IO, or as a source of NO resulting from its photolysis was considered negligible, however, first because its steady-state concentration would have been less than 4 X lo9 molecule cm-j and second because its photolysis in the 500-nm region would have occurred too slowly to be important and results primarily in formation of NO, and oxygen atoms. It was not possible to calculate the IO radical production rates from I2 photolysis rates, since the latter could not be measured directly. A static system is necessary to enable measurement of (12) Baulch, D. L.; Cox, R. A.; Hampson, R. F.; Kerr, J. A.; Troe, J.; Watson, R. T. J . Phys. Chem. Ref. Darn 1980, 9, 350.
progressive photolysis of a reagent, but measurement of I2 decay in the presence of O3 is subject to interference from aerosol formation.s In the absence of 03, regeneration of Iz from the rapid recombination of iodine atoms precludes direct measurement of the I2 photolysis rate. The reaction of IO and NO, was investigated in this system for the pressure range 35-404 torr at 277 K and from 25 to 100 torr at 303 K. Figure 5 shows a typical absorption waveform obtained in these experiments. The rise and fall of IO to and from steady state occurred on a 25-ms time scale, reflecting the presence of rapid removal processes. At pressures up to 100 torr, equal rise and fall times were observed, indicative of pseudo-first-order removal of IO. At higher pressures, fall times were significantly longer than rise times, which was indicative of an additional second-order removal component. This is attributed to the pressure-dependent self-reaction of IO, which was the subject of a separate investigation described in the next section. In experiments displaying first-order kinetic decay of IO, removal constants (k,) were directly obtainable from the rise and fall times on the modulation cycles (eq iv). At each pressure, experiments were performed for various [NO,]. The resulting values of kI were plotted against [NO,] (see Figure 6a, Top), and the effective bimolecular rate constants for IO removal by reaction with NO, ( k b i ) were obtained from the slope. The presence of an intercept upon extrapolation to zero [NO,] indicated the existence of an additional first-order removal component, which appeared to be pressure independent and had a value of approximately 8 s-l. This was attributed to heterogeneous removal of I O at the vessel wall. It was also possible to estimate a value of the radical production rate ( B ) from experiments displaying first-order kinetics, usiing eq iii and the value of cr (426.9 nm) obtained in the experiments described in section 3.1 (2.2 X lo-’’ cmz molecule-’). The corresponding values for the I, photolysis rate, ks, assuming B = 2ks [I2], were determined in seven experiments, the mean value being 1.05 (fO.l) X lo-, s-’ for photolysis by two gold fluorescent lamps. There was no apparent pressure dependence of the value ks. In the experiments at higher pressures, the first-order decay constant could no longer be obtained directly from the rise and fall times, owing to the presence of a small higher order component of removal, which was assumed to be due to the self-reaction of IO. However, values of the first-order constants could be obtained from analysis of the IO steady states observed in the mixed firstand second-order system, using second-order rate coefficients for the IO + IO reaction obtained from the experiments described later (see section 3.3). The values of CT (426.9 nm) and ks determined above were used together with the appropriate value of the pressure-dependent rate constant for the IO + I O reaction to obtain a value of kI from eq vi. The resulting values of kI were once again plotted against [NO,] to obtain the effective bimolecular rate constants ( k b i ) for reaction of IO with NO, at each pressure, (Figure 6b, Bottom). The resulting values of k b i are listed in Table I and the 277 K data are plotted as a function of total gas pressure in Figure 7. There is a nonlinear pressure dependence of kbi showing that
196 The Journal of Physical Chemistry, Vol. 89, No. 1, 1985
Jenkin and Cox / /
I
0 // /
i il d
I
J
I
2.0
1.0 IN021/lO"molecule
0
,
cm-'
,
,
,
,
I
,
,
L
2
, 6
I
200
-
,
,
8
,
,
I
10
,
,
,
.
I2
Rewre &mm H ~ I ~lHl/lOwmolecu~ecm~'
Figure 7. Pressure dependence of effective bimolecular rate constant for the reaction IO NO2 M IONOz M at 277 K.
+
J
I
1.o
0.5
0
[N021/ 10" molecule cm-3
-
Figure 6. (a, Top) Variation of first-order removal constant (from rise and fall times) with [NOz] for experiments at 100 torr (Ag)and -55 torr ( 0 ) . (b, Bottom) Variation of first-order removal constant (from steady-state analysis) with [NO,] for experiments at 150 torr ( 0 )and -210 torr (A).
-
TABLE I: Rate CoeMcients for Reaction of IO with NO2 1 013kbi,
cm3 molecule-'
temp, K
press. torr
303
25.0 60.0 100.7
2.5 (11.3)' 3.3 (11.7) 4.7 (f2.0)
277
35.0 100.7 149.2 208.0 404.0
4.5 (f2.2) 8.4 (11.7) 10.8 (13.2) 14.6 (13.9) 20.4 (16.4)
s-'
-
BrONO,
+M
cm6
k, = [1.6!?&] X lo-" cm3 molecule-'
(10)
and employs eq viii to describe the bimolecular rate constant in
the falloff region. Here, ko is the third-order rate constant at the low pressure limit and k , is the second-order constant which is asymptotically approached at high pressures. The parameter F, modifies the simple Lindemann model which predicts kbi = ko[M]/(1 + k o [ M ] / k , ) . The high-pressure limit k , is approached much more slowly than the simple theory predicts. F, characterizes the "broadening- of the falloff curve, which occurs because the probability of decomposition of the vibrationally excited adduct back into reactants before collisional deactivation is dependent on the energy of the adduct above a threshold. F, is the product of two factors, F:, and FcWc, which account for strong and weak (13) Troe, J. J . Phys. Chem. 1979, 83, 114.
+
+
ko = (4.3 f 2.0) x
association reaction 2 is in the "falloff" region between the lowpressure third-order regime and the high-pressure limit where the kinetics are second order. The limiting low- and high-pressure rate constants for reaction 2 were determined on the basis of the theoretical treatment of Troe.13 The method followed that used by Sander et a1.6 for the analysis of the rate data for reaction of BrO with NOz (eq 10)
+ NOz + M
+
collision effects, respectively. These factors can be calculated from physical properties of the adduct, such as the vibrational partition function and the critical energy for decomposition. The complete procedure has been carried out for BrONOZ6where the resulting value of F, agreed well with that obtained from a nonlinear least-squares curve fitting of the experimental data to eq viii. Evidently, for an expression containing three parameters, good fits to experimental data can be obtained for a wide range of parameter values. Sander et a1.6 had also carried out low-pressure (1-6 torr) discharge flow mass spectrometric experiments and thus obtained an independent estimate of the low-pressure limit, ko, which aided interpretation of the results of curvefitting procedures. In the present study, values of kbi a t pressures low enough for purely third-order kinetics to be operating were unobtainable, due to the dominance of the wall-removal reaction at these pressures. Hence a curve-fitting procedure with these independent parameters, which is unlikely to give a unique solution, would be difficult to interpret. Accurate theoretical determination of F, was also not possible owing to a lack of spectroscopic and thermodynamic data for IONOZ. In order to fit the experimental data, therefore, a value of F, equivalent to that obtained for BrO NOz M BrONOz M in ref 6 was assumed. Figure 7 shows the resultant fitted curve, which corresponds to
-
Estimated experimental error in determination.
BrO
+
+
s-l s-l
and for F, = 0.4. The broken line in the figure represents the Lindemann falloff curve with the same limiting rate constants, thus emphasizing the deviation of the true curve from that predicted by simple theory. The data were also fitted, assuming the value of k , to be that for the BrO NOz reaction, 2 X lo-'' cm3 molecule-l s - ' . ~ The resulting values of ko and F, were 4.2 X cm6 molecule-z s-l and 0.35, respectively. This set of parameters fitted the experimental data equally well as those above, indicating the difficulty in defining a unique set of parameters. The data at 303 K could not be fitted in a similar manner, since the pressure range covered was narrow, and only three data points were obtained. The values of kbi (Table I) are lower than the corresponding values at 277 K, and there appears to be an exaggerated falloff, since kbi at 100 torr and 303 K is only just greater than half the value a t 277 K, whereas at 25 torr, the value of kbl at 303 K is only marginally lower than that at 277 K. 3.3. Photolysis of Iz in the Presence of 03.3.3.1. The Reaction IO + IO Products. In the absence of NOz, it was anticipated that the self-reaction of IO could be investigated in competition with the first-order loss attributed to wall removal of IO. Two series of experiments were performed in which IO kinetics were investigated. The first series at 303 K covered the pressure range 10 to 100.7 torr and the second, at 277 K, the pressure range 25 to 404 torr. Iz and O3concentrations were typically 5 X 1013and 5 x ioi4 molecule ~ m - respectively. ~, In these experiments formation of low volatility products was indicated by visible fogging of the reaction vessel with a yellow-
+
-
The Journal of Physical Chemistry, Vol. 89, No. 1, 1985
Kinetics Study of Reactions of IO ish-white film. This caused a small but progressive decrease in transmitted light intensity. The residence times were kept short (- 3 s) so that attenuation due to condensation aerosol formation, such as observed in the earlier experiments at atmospheric pressure: was avoided. Clearly solid oxides of iodine were formed by removal of I atoms, IO radicals, and/or IO, reaction products at the surface. A typical modulation waveform for IO in the photolysis of an 12-03mixture at 69.8 torr pressure is shown in Figure 8. Analysis of the waveforms showed complex kinetic behavior indicative of mixed first- and second-order kinetics for IO removal. Thus the rise time, tl12(rise), was consistently shorter than the fall time, and the steady-state IO concentrations, [IO],,, did not show a consistent relationship with the rate of photolysis of 12. For a given [I2],the steady state of IO exhibited an approximately 0.65 power dependence on the photolytic intensity, but the amount of IO formed at a given light intensity increased with [I2]by a smaller power dependence than would be expected if all I atoms formed IO radicals. Furthermore [IO], decreased at low [O,], for constant photolysis intensity and [I2]. These observations indicate that [IO], is influenced not only by complex decay kinetics but also by a complex relationship between photolysis rate, k,[I,], and IO production, presumably due to competing reactions of I atoms. For this reason the steady state could not be used for kinetic analysis, and determination of the rate coefficients for the first- and second-order components of IO removal were determined by analysis of the time-dependent decay measurements according to eq vii, utilizing the absorption cross section, u = 2.2 X cm2 molecule-l, determined earlier in this work, to obtain absolute IO concentrations. In practice it was found that at low pressures (95% of the I atoms regenerate IO rapidly through the I + O3 reaction at the O3concentrations used. If a fraction a of I atoms is lost by other routes (e.g., wall removal), then the above reaction will contribute ak3* to the overall second-order rate constant. Current information therefore suggest the following pathways: IO + 1 0 21 + 0, (3a)
IO
-+
+ IO
-
I, M
+ 0, --+
1202
(3c)
+M
(3b)
(14) Clyne, M. A. A.; Coxon, J. A. Proc. R.SOC.London, Ser. A 1968, 303, 207.
J . Phys. Chem. 1985, 89, 199-200 The pressure-independent component of the second-order rate constant obtained in this work can be regarded as the sum kjc akjaand the pressure-dependent component, k3b. The very large magnitude of the third-order rate constant for the pressure-dependent channel has been noted before in the previous work.8 It is unreasonably close to the bimolecular collision rate for a simple association reaction and therefore indicates a chaperone mechanism. Complications due to aerosol particle enhancement of IO decay rate advocated previous19 are less likely in the present work, considering the lower pressures and much shorter reaction times employed. Whatever the mechanism, it seems likely that this channel is responsible for formation ultimately of aerosol products, which are believed to be amorphous oxides 1408and 1409.15,16 These could be produced by “polymerization” of IO2 species formed as follows: I + I202 I2 I02
+
-
IO2 + IO2 I,Ozn
+
- -- + Iz04
+0 3
102
1408
102
+
1409
0 2
Our work also indicates that the polymerization process can also occur on the vessel walls. (15). Cotton, F. W.; Wilkinson, G. “Advanced Inorganic Chemistry“, 3rd ed.; Wiley-Interscience: New York, 1972; p 475. (16) Wikjord, A.; Taylor, P.; Torgerson, D.; Hacchkowski, L. Thermochim. Acta 1980, 336, 367.
199
The value of k , = (9.6 f 3.0) X cm3 molecule-’ s-l at 303 K obtained in the present work agrees well with the single previously reported room temperature values of Clyne and Cruse cm3 molecule-’ s-l determined by observation of of 8.3 X the decay of O3 in the presence of I atoms in a flow tube at 1 torr pressure. The experimental details given are rather brief, but the authors claim an accuracy of only f a factor of 2 on the measurement, due to experimental difficulties. In the present work the time-resolved observation of product IO gave a more direct measurement of the kinetics of reaction, but modeling techniques involving a postulated chemical scheme were necessary to extract the rate coefficient. In the absence of large systematic errors arising from the assumed chemical model, the quoted error limits of *30% are believed to be representative of the uncertainty on this determination. The value of k l is close to that for the analogous rate coefficient cm3 molecule-’ s-l at 298 for the Br + O3reaction (1.1 X K) which is reasonably well-defined. The rate coefficients for the reactions of F and C1 with O3 are a factor of 10 faster at 298 K, the difference in rate compared to Br arising from the lower activation energy ( E I R = 251/T, 226/T and 760/T for C1, F, and Br respectively). Normally the activation energies for gasphase reactions of I atoms with closed shell molecules are higher than for the corresponding reactions of Br; the I + O3reaction may be an exception to this pattern, but a temperature dependence study of k , is required for a firm conclusion to be drawn.
Acknowledgment. Thanks are due to D. W. Stocker, University of Birmingham, for his help in performing some of the experiments.
COMMENTS Energy Loss Scaling for Small-Angle Rotationaliy Inelastic Scattering Sir: In a previous publication’ we reported a method to calculate rotational energy transfer distributions for atom (ion)-linear molecule small-angle scattering from a few to several hundred electronvolts. The calculations made use of classical perturbation scattering theory (CPST)2 and Monte Carlo techniques. In the development of the theory we assumed an initially nonrotating rigid rotor and calculated AE,, from a consideration of the change in orbital angular momentum in the collision system. The formulas can be found in ref 1 and 3. Interestingly, we found that for scattering at a given reduced deflection angle r = Et9, where E is the initial center-of-mass translational energy and t9 is the center-of-mass scattering angle, the rotational energy transfer AE,,,scales as the collision energy E EAEm
=As)
(1)
whereflr) is a complicated function dependent on the potential function and the collision masses. Several researchers commented on the seemingly unusual nature of the E M , scaling relationship. Because of this we have verified this result using full 3-D classical trajectories. Calculations. We considered a model Li+-CO potential of the form (1) F. E. Budenholzer and C. C. Lee, Chem. Phys., 73, 323 (1982). (2) E. A. Gislason and J. G. Sachs, Chem. Phys., 25, 155 (1977). (3) J. G. Sachs, Ph.D. Thesis, University of Illinois at Chicago Circle, 1978, p 93.
0022-3654/85/2089-0199$01.50/0
where R is the distance between the molecular center of mass and the ion, the angle between R and the molecular axis, P I and P2 are Legendre polynomials, D is the CO dipole moment (0.1 12 esu cm2), and e is D), Q is the quadrupole moment (2.0 X the electronic charge. The constants C, and c6 (14.20 eV A4 and 18.4 eV A6) are the long-range spherically symmetric potential terms calculated in the usual way: and C, (3.09 X lo5 eV A16) is chosen in such a way that the potential fits reasonably close to the experimentally determined symmetric part of the Li+-CO potential.’ The C O molecule has bond length r and its potential Vco was represented by a Morse function. Trajectories were run over this surface with a modified version of the classical trajectory program of Chapman et a1.* 600 trajectories were run for an initial translation energy of 2.4 eV and 600 for an energy of 4.8 eV. They were checked by noting conservation of energy and back-integration. The impact parameter was randomly selected with b,,, = 6.0 A. The initial vibrational and rotational energies were set to zero. All other parameters were randomly selected in the usual way. Four ranges (bins) of r = Et9 were selected. If the scaling (4) H. Loesch in “Potential Energy Surfaces”, K. P. Lawley, Ed., Wiley, New York, 1980, p 468. (5) R.Bottner, U. Ross,and J. Toennies, J . Chem. Phys., 65,733 (1976). (6) E. W. McDaniel and E. A. Mason, ‘The Mobility and Diffusion of Ions in Gases”, Wiley, New York, 1973, pp 248-254. (71 P. M. Polak-Dinaels, Ph.D. Thesis, University of Illinois at Chicago Circle, 1979, p 62. (8) S . Chapman, D. Bunker, and A. Gelb, QCPE, 11, 273 (1975).
0 1985 American Chemical Society
