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Kinetics of the reaction between nitrogen dioxide and water vapour
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Vd. 21. Na 7. pp. 029~IS& 1987.
KINETICS OF THE REACTION BETWEEN NITROGEN DIOXIDE AND WATER VAPOUR Dqutmcnt
R. SVENSSON, E. LJUNGSTR&I and 0. LINDQV~S~ of lnorgrnic Clkcmistry. Chalmers University of Technology and University of Giiteborg. S 412 96 Giiteboq, Sweden (Flnt rrceicuf 28 Murch 1985 and recei#d /a publication 15 Deembrr 1986)
AhtrsceTbe rate of diclppamnce of nitrogen dioxide @IOX) with water npour and fomution of nitrous was used to dctamim (HONO) in the dnrk has b&n invcstig&d in b&b cxpaimnts. IR mpy the concentrations of NO1, HONO and NO. Tbc r&on is 6rst order both with respect to NO1 and water
&d
npourrnd proccals hctcropnoudy on most unpoisuned surfaces.Initially. the amount of HONO formal is dose to half the NO* which has diippuual. When the surface in the present ractor (surface to volume ratio - 14 m -’ ) hasracbd iu limiting state of poisoning. tbc reaction is still active and the NOI disappearance follows the expression:
where k, = 4.1(* 0.8) lo-’
-d[NO&dt ppm- t
min- ’
%[NOzl [Hz01
-
(22°C).
Tbc S/ Yntio dependenceof the rrte
shows tkat a bcterogeaous r&on pr& but the existing cvideaa is not condusive about a pox&k homogcnou~contribution to the rrrmining activity. A rate expression which
derribcs the overall reaction at tcmpemturcs around 25°C. when the surface present is made passive. is: -d[NO1]/dr
= (S/V5.6(f0.9)10-9+2.3(~6.5)10-9)
[NO,]
[H*O].
Key word index IR spectroscopy, nte constant, nitrogen dioxide, nitrous acid, isotopic experiment. hctaogmous raction.
WTRODlJCllON
The importance of photochemically induced reactions for the transformation of a variety of air pollutants is well established (Baulch et al.. 1982). The rates of parallel, competing thermal reactions indicate that under conditions of photochemical activity, such reactions may generally he disregarded. In some areas, however. the latitude or meteorological conditions may cause severe restrictions on the flux of sunlight to the lower troposphere. One such area is Scandinavia where, during the winter, the photochemical activity in the troposphere is xmall or nonexistent for extended periods of time. The winter emission of most types of primary pollutants is often larger than the summer emission due to domestic heating, cold started automobile engines, etc. More often than not the maximum concentrations of S02, NO, N02. CO and hydrocarbons in urban areas are recorded during the winter. Under such conditions, tk relative importance of thcmul tr8nsforIMtion reactions increWs. One of the thermal reactions which is not well understood at present is that between NO2 and water vapour. The products from this reaction include HNO,, HONO and NO (England and Corcoran, 1974; S&am&i et ol, 1983; Kesskr, 1984, Pitts et al., 1984). HNO, may contribute significantly to the acidiikation of the environment whik HONO is a known nitrosating agent and ix auspc&d to particip8tc in ‘in uiuo’ formation of carcinogenic
nitrosamincs (Pitts, 1979, 1983). In polluted air, HONO often accumulates during the dark hours and the reaction between NOI and water is one of the likely sources. The results concerning the NO,-water vapour rcaction reported in the literature are not in total agreement, e.g. regarding the nature of the reaction mcchanism, reaction order or whether the reaction is homogeneous or heterogeneous.
EXPERIMENTS AND METHODS Tbc experiments were made in a batch reactor with N2 as tbc matrix pr The concentration of NO, NOI and HONO was followa! by FAIR spcctroxcopy.The ractor consistsof a borosilimte ghss pipe (dixmetcr 0.30 m, knflh 2.00 m) held by two st&kss steel cndphta rad four INVAR distance rods. The toti volume of tk -or ix 0.153 rn’ utd the 8urf8a to volume (S/ v) ntio is 14 m- ‘. The reactor has. attached to tbc mlphtcs. I thra-mirror White optical system (Wltik 1942) with a hw pth kttgth of 2 m. The thra ghss mirrorx, one of 0.21 m and two of 0.14 m diameter. are gold arlsd~hrverprolsc(inL~of~umRuoride.The mirrors may be adjuxtal by external controla to nry the number of relktioat. Pub kngtba between 8 and 120 m may be used. One of the endplates is fitted with KBr windows to 8llowtbe~~ofuulytAlr8diatkm.Intbcprcscnt investiption the rcrtor walls were either boroxiliate glus (Coming Ltd.) with endplxta of xtainkn Uecl, lined with 0.025 mm FEP (Du Pont) T&on film or lieal with stainkss stceishectmetaLFortbeiacmredS/Vntioqmimcnts.an inacrt of lmnging FEP T&n foil, dirnibuting the foil i&de tbccdlwithoutobstmuiaptheLgbtpuhwasusal.This umngcmmtinaaatdtbcS/Vntioto42m-‘.
1529
1530
R. SVEN~~ONet al.
The reactor can be evacuated with a two-stage rotary vane pump IO less than 5 Pa and is enclosed in an insulated box where the temperature can be set between 0 and 60°C and controlled to 1°C. The introduction of known quantities of NOx into the reactor was accomplished by filling the calibrated bulbs of a vacuum line gas handling system to aome predetermined pressure and then expanding the gas into the evacuated reactor. The pressure was measured with a Validync CD 233 pressure gauge (O-18 kPa or O-180 kFa) The water vapour concentration was calculated from a carefully measured quantity of liquid water which was evaporated and entered into the reactor by means ofa stream of Ns.The water vapour concentration was checked. after some of the experiments, with a cooled mirror hygrometer and found to agree well with the expected values. To promote rapid mixing of the reactants, a T&n tuhe fixed along the bottom of the reactor from one end to the other and perforated along the top side, was used. One end of the tube was closed while the other was connected to the reactor inlet. The NO2 used was > 98% pure with nitric acid as the major impurity. The nitrogen used contained less than 10 ppm 0s and less than 5 ppm HsO. Infmred spectra of the reactor content were recorded with a Nicolet MX-I Fourier Transform i.r. spectrometer coupled with a mirror arrangement IO the reactor (Fig. 1). The i.r. source is a globar element and the detector is a DTGS pyrcclectric bolometer. The path lengths employed during the experiments varied between 56 and 72 m. The spectra were taken with 1 cm-’ reaolution and collected from 4000 to 400 cm-‘. The time to collect a spectrum was 5 min. The box car apodizlltion was used when calculating the spectra from the interferograms.
The smallest detectableconcentrations in practical work with 72 m path length in this cell are: NO loOppb, NO1 3Oppb. HNO, HONO 20 ppb.
20 ppb and trans-
The majority of the experiments were conducted as follows: before the experiment the reactor was evacuated three limes to 1 LPaand refilled with pure Nr , then evacuated again and a background spectrum collected. A measured amount of NO2 was introduced, with N2, from the gas handling system into the reactor until the pressure was about 30 kPa. The water vapour was then added to the reaction mixture with a stream of Ns. The final reactor pressure was 100 kPa. The procedure took about 10 min from theaddition of the NO2 until the 6rst spectrum had been collected. The collection ofa spectrum was then initiated every 30 min for a total time of 540 min. Changes in HONO, NOa and NO concentrations were evaluated by subtracting the xero time spectrum from suhaequent spectra. The resulting diiferences between spectra thus show a positive absorption band for an increasing concentration and vice versa (Fig. 2). To investigate the water uptake on the FEP Teflon film used for the reactor lining, a sheetof the film was suspendedin the weighing chamber of a Cahn ekctrobalance. Air with known relative humidity (r.h.) was allowed to flow through the thermostatted chamber while the weight was recorded. The digerence in weight between the film in dry air (less than 0.005%r.h. at 2O”C)and theotable weight at acertain r.h. was taken as the massof water acquired by the !ilm at that r.h. To compare our measured NO,, HONO and NO data with
The following frequencies and extinction coefficients were used to evaluate the concentrations: sigma = 2.02(f0.06)10-‘ppmL*m-1 nitrogen dioxide 1599 cm-’ (in house calibration) trana-nitrous acid 1264 cm- * sigma= 3.84(f0.38)10-3 ppm-‘m-r with trans-nitrous acid/&nitrous acid = 229 to calculate total nitrous acid (Chan et 01.. 1976) nitric oxide 1876cm-’ sigma = 2.77(f0.03)10-4 ppm-‘m-l (Stockwell and Calvert, 1983) aigma = 1.75(f0.18)10-’ ppm-’ m-r nitric acid 878 cm-’ (Stockwell and Culvert, 1983) (ln(la/l) = sigma ‘c. I, base e).
Fig. I. FTIR-White cell system. I. Nkokt MX-I FTIR spcctromctcr. 2. Samplr compartment with interfacing optics. 3. Reactor with White optical system.
Kinetics of the reaction between nieosa
1531
dioxide and water vnpour
-0.3:: fi 3 Q
-0.6-
-0.9
iI
1
-1.2 ’ I700
1325
950
1 575
Wavenumbers Fig. 2. Difference spectrum. found by subtracting the reactant spectrum from the product spectrum, showing bands after 180 min. N02(uS)1599 cm-‘, trans-HONO 1246 cm-‘, (ur) 794cm-’ and cis-HONO (u.) 852cm-‘.
proposed models it was ncccssary to integrate the resulting differential quations. This was done with FACSIMILE (Chance er al.. 1977).a computer program for the solution of initial value probkms arising as systems of difkential equations. The program may also fit rate constants to observed data by a least squares procedure. RESULTS
Reaction order
From a series of experiments in the Teflon lined reactor, the initial rate of NO2 disappearance (the first 30 min) was determined over a range of NO1 (5-80 ppm, 1000 ppm HzO) and Hz0 (lOOO20,000 ppm, 24 ppm NO1) concentrations. In Fig. 3, it is seen that for odr conditions, the reaction order is one within the raqe of experimental error both for NO1 and water. In an attempt to understand the reactions responsible for the concentration changes in the reactor, several sets of elementary reactions were tried on the experimental data. The rate constants were allowed to vary to obtain the best fit between the calculated concentrations from a model and the experimental data. To reproduce the first order behaviour of NO1 disappearance with respect to NO1 and water, reactions (1) and (2) were used. NO, + Hz0 + H2NOS HINO, + NOz + HONO + HNOJ.
(1) (2)
Hz0
(ppm)
Fig. 3. (a) Initial rate of NO* disappearance at constant Hz0 = 1000 ppm vs NO2 concentration. (b) Initial rate of NO* disappearance at constant NO1 = 24 ppm vs Hz0 conantration.
To make (1) the rate determining step in the refinement, kl was set at a value large enough to make (2) fast in comparison with (1). The proposed stoichiometry is supported since the initial rate of HONO formation in Fig. 4 is close to half the initial rate of NO2 disappcarante in Fig. 3. The values of kI obtained by fitting the observed NOz concentrations to (1)and (2)are given in Table 1. The above description is acceptable since kl is reasonably constant with varying initial NO1 and water concentrations. kl describes the overall disappearance of NO1 and is the quantity to be compared with previously reported values (Sakamaki et al.. 1983; Pitts et ol., 1984). If the data from the first 60 min in each run were excluded from the refinement, a significant improvement of the fit was obtained. It was evident that the second order tate ‘constant’ for reaction (1) decmased somewhat during the early parts of the experiments. This is interpreted as a high initial reaction rate caused by the preparation of the reactor before a run which to some extent reactivated the surface. After some time of reaction, the surface is passivated and a limiting rate is approached. The HONO production rate is correspondingly increa& in the initial part of the experiments which is consistent with the above explanation. The values of all constants givun in Table 1 are calculated with data excluding the &at 60 min. The error given corresponds to one standard deviation based on the fit between observed and calculated data
1532
R
%‘EN!BoN et d.
extinction coefficient. This explains why some values are missing in Fig. 6. The build-up appears to be tirst order in NO1. With water, however, the plot is linear up to about 1O$lOOppm Ha0 but the rate at 20,OCNlppm Hz0 is signiticantly higher than expected from a first order dependence. The reproducibility of the points in the graph was documented in several experiments. In most experiments, the NO observed is well predicted by reactions (l)-(3) (Fig. 5a) but at water vapour concentrations of 14BOO and 20,000 ppm, more NO is actually produced than is expected (Fig. 5b).
Temperature dependence Measurcmcnts in the Teflon-lined reactor, with an initial NO1 concentration of 24 ppm and with an Hz0 concentration of 10.000 ppm, were made at 7.22 and 50°C. The results show a decreasing rate constant with increasing temperature (Table 1). The apparent activation energy in the Arrhenius expression calculated from our data amounts to about - 32 kJ mole- ‘.
Surface dependence
Fi& 4. (a)Initialrateof HONO formation st con-
stant Ha0 = loDoppm M NO1 auieeatmtion. (b) Initial mte of HONO form&on at amstant NO1 = 24 ppm vs H1O concentration.
and is only a measure of the capacity of the model to describe the observed data. When the concentration of HONO, calculated by (1) and (2), wascompared to the experimental values it was clear that a loss mechanism was active. A second order decay as described by the reaction 2 HONO w NO1 + NO + Hz0
(3)
together with (1) and (2) produced a satisfactory description of the observed NO1 and HONO data (Fig 5). The re6ned rate constants for ki and k3 are giveninTabk l.Intheretinement,k_~wassettok,l.l x 10m6 ppm-’ (Kaiser and Wu, 1977). The decomposition of HONO has been studied by several authors (see e.g. Grosjean, 1979) and is known to proceed heterogenously to some extent. The literature values for the second order rate constant enclose the values obtained from the retinement. HNOs was never observed as a reaction product in the gas phase and was assumed to adsorb to the reactor wags (Ferm, 1982). HNO, in the gas phase appeared only in experiments with a high initial NOz concentration and was then visible only during the first 60 min. It is likely that this HNOs entered the reactor initially as an impurity in the NO*. In Fig 6 the initial rate of NO formation vs NO1 at Hz0 3 loo0 ppm and vs water at NO2 = 24 ppm are shown. The measurement of low NO concentrations is unartain and sometimes impossible due to its low
The condition of the reactor surface had a strong influence on the measured rates. A rate of NO1 disappearance much faster than normal was observed in the glass cell after washing the glass surface with dilute hydrochloric acid, and rinsing with distilled water and thorough pumping (Table 1). The same qualitative behaviour was seen when the cell was heated and pumped over night or when a new Teflon lining had been inserted. When the stainless steel insert was used, the observed NO2 disappearance rate was about eight times higher than normal while the HONO concentration never reached values seen in comparable experiments with the glass- or Teflon-lined reactor. In all experiments the rate of reaction (3) appears to be influenced by surface catalysis. The extent is dependent on, for example, water vapour concentration, type of surface and the condition of the surface. When experiments in the initially clean glass or Teflon-lined reactor were made with only mild cleaning between the experiments, pumping the reactor to 1 kPa and ret’& hng with nitrogen three times between the runs (i.e. the normal procedure), the rate constants converge towards a constant value, similar for both the glass and Teflon-lined reactor. In a number of experiments in the Teflon-lined reactor the S/ Yratio was increased by a factor of three by the Teflon film insert. The rate of NO1 disappearance in the increased S/Y experiments show a small (average 1.5) but significant rate increase compared with the experiments with a normal S/V ratio. In the increased surface experiments, the rate of formation of HONO is equal to, and the rate of formation of NO is twice that of an experiment with normal S/Y ratio.
24 24 24 5 5 24
36 D 33 D 19 D 15 rk 13 B 31 B
50 7
22 22 22 22
7500 1000 1000 1000
22 22 22 22 22
22 22 22 22
1.5 1.4
33
::
1342*
8.8 4.4 2.8 1.5 22 14 7.2 7.1 4.5
d HONO/dt (103ppm-1min-‘)
:z
E 29 23 9.5
20 13 6.0 1.1
-d NO,/dt Temp. ’ (“C) (103ppm-‘min-‘)
14,000 lO,aao 75W 5000 10,000 10,000
a~
looo 1000 1000 low
(Fg)
Initial
2.9 8.5 6.5
3.7 3.6
23 6.9 3.6 2.6 2.4
3.1 1.1 -
5.1
d NO/dt (lO’ppm_‘mm-’ 5.8 * 1.0 5.0 f 0.5 5.1* 0.6 5.3 j: 2.2 4.a*o.1 3.9iO.l 3.4 f 0.1 5.0 f 0.2 3.2 * 0.4 2.5 f 0.6 8.2 f 0.3 6.5 f 0.2 5.0* 1.3 302 f 8.0 36 f 2.0
kt ) (lOsppm_‘mitt-‘)
k, was calculated taking only reactions (1) and (2) in account, k; and k, were refined with reaction (3) included.
80 50 24 5 24 24 24 24 24
(s)
25 D 24 D 3c 6C 21 D 22 D 26 D 18 D IC
Run number
Initial
4.0 f 0.3 5.3 f 0.3 4.1 f 0.3 5.0,* 0.2 6.5 f 0.2 3.9 f 0.2 3.7 f 0.1 5.3 f 0.2 3.0 f 0.5 1.6iO.2 9.8 f 0.6 6.0 f 0.4 4.2 * 0.9 285*50 46*3.0
KI (lOsppm_‘min-‘) 4.9 f 0.7 9.5 f 4.1 4.2 f 1.5 9.3 f 14*0.5 1.9 f 0.7 15* IA 6.3 f 0.4 9.0 f 5.9 9.3f 1.5 * 1.6 5.0 * 0.8 lO* 161* 69*6.4
(ltippmk’rmin-r)
Increased surface Glass seasoned Glass clean Stainless steel
Teflon
Teflon
Teflon
Comments
Table 1. initial concentrations, rate of NO2 decrease, HONG-NO formation and refined rate constants for the reactions between nitrogen dioxide and water vapour
1534
R. SVENSSONC~ al. (a)
l
=CNOJ
l
=CHONOl
30
r-IN03
90
60 NO2 @pm)
(b)
I
_/m-m
“2
,
60
_,.-m--m-*
.L~--A-b
. 240
420
Tlme tmln)
7000
W
14300
2lcoo
n,o (PPrn)
20
Fig. 6. (a) Initial rate of NO formation at constant
l=INOJ =IHONOI h*CNOl
l
I
IS
HsO = loo0 ppm vs NOs concentration. (b) Initial rate of NO formation at constant NOs = 24 ppm vs NOz concentration.
F 8 IO
s
+G -•-.-.
_ 60
I
I
240
420
Time tmin) Fig. 5. (a) Observed and cakuktal concentrations at an initial water wpour concentration of 7SOOppm. The calculations were based on the r&ncd rateconstants. (b) Observed andcalculated concentrations at an initial water vapour conantration 0120300 ppm. Thccakuktions ware based on the refined rate constants.
Water uptake by FEP Teflon The obvious surface catalysis of the reaction raised the question of water uptake by FEP Teflon film. The water uptake was investigated with the Cahn electrobalance between 5 % and 90 % r.h. at 20°C. In Fig. 7 the mass of water gained by the film per m2 at various relative humidities is shown. About 70% of the mass increase for a certain r.h. in Fig. 7 was acquired within 20 min while the remaining 30% was taken up over a
R.H. IX)
Fig. 7. Water uptake on FEP Teflon vs relative humidity at 22°C. D = Ckan film, A = HNO, contaminated film.
period of days. This is interpreted as an initial, rapid adsorbtion of water to the surface followed by a much slower diffusion of water molecules into the Teflon film. Assuming one water molecule to occupy lo-r9m2, one monolayer would require a weight increase of about 0.3 mgmT2. Figure 7 shows that if the surface of the film was perfectly smooth it would already have about two monolayers of water at S % r.h. At 90% relative humidity it appears that condensation occurs on the film. The influence of HNOa on the water uptake was investigated by exposing the film to 250 ppm HN03 vapour at 10% r.h. for several h. The film was then exposed to dry air and it was observed
Kin&s of the reaction between nitrogen dioxide and water vapour
1535
value with’ageing’ofthe reactor surface. This indicates that the limiting value is not very dependent on the type of surface since FEP Teflon and borosilicate glass have widely dinering surface properties. HNO, was shown to adsorb to the Teflon film. both in the electrobaiance experiment acd by chemical Isotopic experiments analysis. This makes HNO, a prime candidate for the To gain further information about the reaction, substance poisoning the surface. The scatter in the rate an isotope experiment originally made by Sakamaki constant values determined by us and also by other et 01. (1983) was repeated. In a number of runs, “0 workers may well be due to dificulties in reproducing labelled water was used. Measurements were made the preparation ofthe reactor beforean experiment. In at NOI concentrations of 24 and 80ppm and with an attempt to resolve the nature of the limiting reaction Hz0 concentrations between 1000 and 10.OOOppm. the results obtained by us and by other workers will be Experiments with Hz0 concentrations of SOOO- examined. 10,COOppm showed the HONO bands normally found The disappearance of NO2 in our experiments has a at 1264.8S2and791 cm-‘tobedisplaazdto 1251,838 first order dependence both on NO, and water vapour. and 780 cm-’ in agreement with the bands found by This is the best description when considering both the McGraw et ol. (1966) for H “ON0 and by Sakamaki initial rate and the least squares lit to the data er al. (1983) indicating that H “ON0 was formed excluding the first 60 min. exclusively (Fig. 8a). Experiments with lower Hz0 The first order behaviour of the NO2 consumplion concentration, however, gave two sets of bands with respect to NO2 is in agreement with the obser(Fig. 8b). one set the same as with high Hz0 concenvations of Sakamaki et ol. (1983) and Pitts et al. (1984) tration and a second set found at 1257. 848 and but disagrees with the close to second order behaviour reported by England and Corcoran (1976). The recent 786 cm- ’ indicating that HON ‘so also was produced (McGraw et al., 1966). No bands were detected at the information thus shows an apparent first order depennormal positions showing that only labelled HONO dence of the NO1 decay on itself. Comparing the was formed. pseudo first order rate constant at about 13,ooOppm A double band also appeared at 2868 cm-’ close to Hz0 concentration and room temperature obtained the 2906cm-’ NOz(ul +ua) bands. The calculated by Sakamaki et 01. (1983) of 3.8 x lob4 min-’ and by displacement from the normal position for ON “‘0 is Pitts et 01. (1984) in two different reactors of 2.8 about 4Ocm-’ (Shvangiradze and Dzhamagidze, x lo-* min- ’ and 1.6 x lo-* min- ’ to that found by 1961) and it is concluded that “0 labelled NO3 is us of 10.9 x lo-* min- ’ it is seen that they are of the formed in the reactor (Fig. 9). The rate of labelled NO1 same order of magnitude. If the above rate constants production is proportional to the NOz concentration. relate to a gas phase reaction, the scatter is conbut no effect of Hz0 concentration could be seen in the siderable but if the constants relate to a heterogenous concentration interval lOOO-10,000 ppm. reaction the variation is easily understandable since, e.g. reactors with different surface to volume ratio were Mass balance Used.
that the initial weight of the film was not regained, i.e. some of the HNO, was strongly adsorbed to the film. When the flm wasexposed to water vapour, the weight increase at low relative humidities was higher than observed with the clean film.
In all experiments, a loss of nitrogen from the gas phase is observed as the reaction proceeds. In a few runs. a piece of the initially clean Teflon lining was withdrawn from the cell after the experiment and immediately rinsed with water. The liquid was analysed by ion chromatography and revealed an amount of nitrate which, if extrapolated to the entire surface of the cell, closes the mass balance. No other anionic species except traces of nitrite was detected in the liquid by the ion chromatograph. ’ DISCUSSION
From the experiments with the clean glass cell, where rate constants more than an order of magnitude greater than with the’seasoned’cell were observed,it is clear that the reactor walls have a profound influence on the reaction. it is concluded that it proceeds mainly via a heterogenous route in the clean glass cell at low Hz0 concentrations. Both in the giass and the Teflon-lined reactor the observed rate constant converges towards a similar
The water vapour dependence of the NO1 decay is slightly less clear. Sakamaki et 01. (1983) reports a first order dependence on water vapour for NO1 consumption. At Hz0 concentrations of less than 12,000 ppm. however, their NO* disappearance rate is significantly higher than predicted from a first order relation. England and Corcoran (1974) show a clear first order water behaviour. In conjunction with our data the indication exists that the NO2 consumption also has a first order water vapour dependence. The initial rate of HONO formation is first order in NOz as observed both by Sakamaki et al. (1983) and Pitts eta/. (1984) as well as by us. In the present investigation and in the work by Sakamaki, the HONO formation appears lo be first order also in water vapour. Although Pitts ef al. (1984) do not claim a first order behaviour for HONO with respect to water, there is nothing in their data which contradicts such a dependence. The kinetics for the reaction between NOa and water vapour may thus formally be described by reactions (l)-(2). The mechanism of the rate determin-
1536
R. SVENS~ON et al.
0.083-
0.0608 6 5 2 0.03?-
0’014: i
’
-0.009
1305
I155
1005 Wavenumbers
W
I-
Q
-0.011
. 1305
I
II55
1005
855
705
Wavenumbers
Fig. 8. Infrared absorption bands of nitrous acid formed in: (a) NOz = 24 ppm and Hz0 = 10,000 ppm. (b) NO2 = 80 ppm and Hz0 = 1000 ppm.
Kinetics of the rewtion between nitrogen dioxide and water vapour
1537
Wavenumbers Fig. 9. (a) Normal 165Ni65 (IQ+ q) absorption bands. (b) Spcctnun recorded during one of the H1*a5 cxpcrimcnts. (c) Spasrum b. withspectruma subtracted revealing additional bands from ‘60N1*0.
ing step, however, offers a number of possibilities. If the reaction is het~o~no~, one of several rate controlling steps may be involved. When the reaction is fast, mass transfer to the surface willbe rate controlling which, in turn. would give an apparent first order behaviour with respect to the limited component. Such an explanation is not feasible in our case since the experiments with the clean glass cell show that it is possible to supply a reaction, at least 10 times faster than the limiting rate, with reactants. Pitts et al. (1984)discussother ways of obtaining the observed first order behaviour on NOa in a heterogenous reaction. The attachment of a mol~ule to an active site on the surface is mentioned as a potential rate controlling step. If the molecule reacts as adsorbed, the adsorbtion step is less likely to be rate controlling since physical adsorbtion is generally a rapid process. For a molecule. reacting as a chemisorbed species and where the transfer from the ad- to the chemisorbed state has an appreciable activation energy, the chemi~rbtion may well be rate limiting. The rate of transfer wit1depend on the surface activity of the adsorbed molecule. Another possibility, according to Pitts et al. (1984).is that one adsorbed molecule of NO2 may react with one adsorbed molecule of water in the mte controlling step to form a reactive intermediate which rapidly reacts with another NO2 molecule. In addition, the intermediary may form from one
adsorbed reactant molecule with another impinging from the gas phase. The intermediary may also form in the gas phase with subsequent adsorbtion and reaction on the walls. Common to all heterogenous meohanisms outlined above is that the fate of a reaction, where the reactants are adsorbed to the surface, is controlled by the surface activity of the reactants. If the surface activity of a compound is assumed to be proportional to the mass of compound per unit surface, a fair assumption if the covemge is less than one monolayer, then the surface activity is linked to the gas phase concentration by the normally non-linear adsorbtion isotherm. If a substance has a high gas phase concentration, as is the case for water in some of our experiments, then liquid water is present at the surface. A change in gas phase water concentration may then change the mass but not the activity of surface water. Thus for a surface reaction, a linear rate response to a change of gas phase concentration is generally not expected. If a molecule impinges from the gas phase on another, already adsorbed molecule in the rate determining step, then the mte would be expected to show a first order dependena on the gas phase concentration of the impinging molecule. Another possibility to have a first order behaviour is when the coverage of the surface is su~~nt~lly less than one monolayer. The adsorbed molecules then interact little and the adsorbtion isotherm has a section which is approximately
1538
~!%ENSSON~d.
linear.giving a linear relation between gas and surface concentration. In our investigation, this may be the case for NOZ. The gas phase water concentration was, for the Teflon-lined reactor, varied over the non-linear part of the adsorbtion isotherm (cf. Fig. 7) with an approximately linear rate response.This experimental evidence indicates that adsorbed water is not a direct participant in the rate determining step. A reaction seq~enat. where an adsorbed or chemisorbed NOz molecule reacts with an impinging water molecule and where the formation of a reactive intermediary or the chemisorbtion is the rate controlling step, offer, together with a pure gas phase reaction, mechanisms compatible with the available rate information. Due to the symmetric structure of any likely gas phase transition compkx between NO* and water, it is not easy to see how only labelkd HONO is formed. A surface reaction offers better possibilities to fix a transition complex and to produce only specific types of HONO. Mow 5OtM ppm Hz0 concentration both H ‘*ON0 and HON ‘so are produced which suggest two pathways producing HONO where one of the pathways is being inhibited by increasing water vapour concentration. The formation of specific types of labelled HONO and the change in isotopic composition of the reaction product strongly suggeststhat a heterogenous reaction is involved. The observed oxygen isotope exchange in the NOz molecule rquires hydrogen-oxygen bonds and nitrogen-xygen bonds to he broken and reformed. This is also needed to form the labelkd HONO observed.The labelkd NO2 formed is in excessof what is possible to form through decomposition of labelkd
HONO. The water dependence of the labelkd NOz formation also differs from that of HONO formation. This indicates that labelled NO2 is formed through a process not involved in the HONO production. The negative temperature dependence observed in the present work for the NO2 disappearance was also seen by England and Corcoran (1974) who found an activation energy of about - 4 kJ mole- ’ in the temperature interval 25-5OC. Pitts et d. (1984) report no clear temperature dependence on the HONO formation. We believe that the etTectis due to a change in the adsorbtion of some important reactant or intermediary with temperature. The large diliirence in apparent activation energy is the likely result of dilferent adsorbtion characteristics of the reactors. The temperature behaviour may be interpreted as still another indication of a heterogenous reaction. If the limiting reaction proceeds entirely via a hcterogenous route and if no mass transfer limitation occurs then an increased S/V ratio would be expected to increase the rate in the same proportion. This is not the case in our study sincea S/ V increase by a factor of three only gives 1.5 times rate increase. The same observation was made by England and Corcoran (1974) who saw ‘very little increase’ for a S/V change with a factor of 3.4. Kessler (1984). on the other hand, usedaglasssmogchamhcr witha S/Vratioof7.6 m‘ ’
which was increased with a factor of 3.5 by introduction of glass Raschig rings, whereupon the HONO formation rate was also increasedabout 3.5 times. Due to the insensitivity to the change in S/V ratio the possibility that some of the observed activity in our reactor may he due to a gas phase reaction remains. Assuming that the limiting reaction is composed of one part from a gas phase and one part from a heterogenous surface reaction, then a plot of rate constants vs S/V ratios for comparable experiments could beextrapolated to S/V = 0 which would give the gas phase rate. This was done with kt values from the present work and with values calculated from Sakamaki er 01. (1983) (Table 2, runs 15-18) and from Pitts et al. (1984) (Table 1. runs 555-6, 558. 753-4, 757-8. 761. 763. 774A. 779 and 781-2) under the assumption of a first order NO1 and water dcpendence (Fig. 10). The line has an intercept at S/V = 0 of 1.1 (+3.3)10v9 ppm-’ min-‘. Due to the error associated with this figure it is possible that the reaction is purely heterogenous. If, however, the line in Fig. 10 is accepted as an estimate for k, then a rate expression taking both homo- and heterogcnous reactions into account is: -d[NO,]/dr
= 2*d[HONO]/dr = (S/V5.6( f0.9)10-9 + 2.3( + 6.2)10-9)[N0,][H,0].
(4)
According to expression (4). when the reaction proceedsat its low limiting rate, about 97 % of the activity in our cell is due to the wall reaction. Several dificulties appear when expression (4) is to be applied to ambient conditions, e.g. a city. The rate expression is valid if the available surface is made passiveso that the reaction proceeds at its low limiting rate. In real life, this may not be the case. Glass can be made passive during dry weather but reactivated during rain, resulting in changing catalytic activity. Some building materials with basic properties, e.g. limestone, may also react with the agent inducing passivity. The result would be an under-estimation of the reaction rate. In a city, a ‘macro’ S/V ratio of
S/Y
Cm“)
Fig. Iu. Rale wnstant k, vs S/V ratio
Kinetics of
the reaction between nitrogen dioxide and water vapour
0.2m-’
to roof top level (25 m) is reasonable. The catalytically active surface may be an order of magi& tude greater due to porosity and roughness of building materials, etc. For very porous materials mass transfer may become rate limiting. The effective mixing height is also crucial for the determination of a useful S/Y ratio. During the daytime, the large mixing height would cause the S/Y ratio to approach that based on aerosol surface alone, while at night the surface supplied by the ground may dominate. If the rate expression is used to calcuiate the production of HONO assuming inversion episode values of the participating reactants, NO1 = 0.1 ppm, Hz0 = 15,000 ppm and with a mixing height of 50 m, giving anelT&iveS/Ymtioofl m-l.then1.1 ppbHONOis produced in 3 h. Accumulation of HONO in the atmosphere is expected to take place mainly during the night when the mixing often is poor and when the photolysis into NO and OH has ceased. At night the temperature very often is considerably lower than the temperatures of the quoted experiments (22-30”). According to our results, the reaction rate increases with decreasing temperature which may double the production of HONO at night, compared to the number given by Equation (4). In GZiteborg, Sjijdin et 01. (1984) measured l-2 ppb HONO as 12-h mean values, and in Los Angeles, Harris et 01. (1982) found concentrations of HONO up to 8 ppb. Based on these considerations, it is likely that the reaction between NO2 and water vapour is responsible for a significant fraction of the HONO observed in polluted air. Acknmvledgemenr-The authors wish to thank the Swedish Environmental Protection Agency (SNV) for financial support.
REFERENCES
Baulch D. L., Cox R. A., Crutzcn P. J.. Hampson R. F.. Kerr J. A.. Tree J. and Watson R. T. (1982) Evaluated kinetic and photochemical data for atmospheric chemistry. 1. Phys. Chem ReJ Dara II, 327. Chan W. H., Nordstrom R. J.. Calvcrt J. G. and Shaw J. H. (1976) Kinetic study of HONO formation and decay reactions in gaseousmixtures of NO, N02, Hz0 and N1. Enuir. Sci. Tcehnol. 10. 674-682.
1539
Chance E. M.. Curtis A. R, Jones I. P. and Kirby C. R. (1977) FACSIMILE: a computerprogram for flow and chemistry simulation and gcneml initial value probkms. United Kingdom Atom Energy Authority HanveIl Report R 8775. England C. and Cotcoran W. H. (1974) Kineti and mcchan-
ismx of the gwphmc reactionof watervaporand nitrogen
dioxide. lmf. Enan~. Chem. Fumdam 13.373-384. Fum M. (1982) M&d for determination of gaseous nitric acid and particulate nitrate in the atmosphere. EMEP expert meeting on chemical matters_Geneva, 10-12 March 1982. Grosjean D. (1979) Nitrogenous Air Pdlutants, Chemical and Biological fmplicotions, p. 51. Ann Arbor Science, Ann Arbor. Harris G. W., Carter W. P. L, Wincr A. M.. Pitts J. N.. Platt U. and Pcmer D. (1982)Observation ofnitrousmzid in the Los Angeles atmosphere and implications for predictions of ozone-prsursors relationships. En&. Sci. Techno/. 16, 414-419. Kaiser E. W. and Wu C. H. (1977) A kinetic study of the gas phase formation and decomposition reactions of nitrous acid. 1. Phys. Chem. 81, 1701-1706. Kessler C. (1984)Gasfiirmigc Salpctrigc Siiurc ( HNOz) in da Bclastcten Atmosphiire. Thesis, Univ. of Kiiln. McGraw G. E.. Bcmitt D. L. and Hisatsune I. C. (1966) Infrared spectra of isotopic nitrous acid. 1. Chcm. Phys. 45. 1392-1399. Pitts J. N. Jr (1979) Photochemical and biological implications of the atmospheric reactions of amines and bcnzo(o)pyrene. Phil. Truns. R. Sue. A 290, 551-576. Pitts, J. N. Jr (1983) Formation and fate of gaseous and particulate mutagens and carcinogens in real and simulated atmospheres. Envir. Hlrh Perspec. 47, 115-140. Pitts. Jr. J. N.. Sanhucza E.. Atkinson R.. Carter W. P. L. Wincr A. M.. Harris G. W. and Plum C. N. (1984) An investigation of the dark formation of nitrous acid in environmental chambers. Int. J. C/tern. Kin. 16.919-939. Sakamaki F.. Hatakeyama S. and Akimoto H. (1983) Formation of nitrous acid and nitric oxide in the hctnogcnousdark reaction of nitrogen dioxide and water vapour in a smog chamber. Inr. J. Chem. Kin. 15, 1013-1029. Shvangiradxe R. R. and Dxhamagidzc S. Z (1961) Use of the frqucncia of isotopic molecules for the determination of the force constants of symmetric molecules of the type XY,. Opt. Specrr. 12, 200-202. Sj6din A., Ferm M. and Grennfeldt P. (1984) Measurements of nitrous acid in the city of GGteborg. IVL B-publ. 749 Gijtcborg. Jan. 1984. Stockwell W. R. and Calvert J. G. (1983) The mechanism of the HO-SO2 reaction. Atmospheric Enuironmenr 17, 2231-2235. White J. U. (1942) Long optical paths of large apperturc. J. Opt. Sot. Am. 32.285-288.
ooM-+9rl/l7 s3.00+0.00 rcrpmOaJCUMbLld.
Vd. 21. Na 7. pp. 029~IS& 1987.
KINETICS OF THE REACTION BETWEEN NITROGEN DIOXIDE AND WATER VAPOUR Dqutmcnt
R. SVENSSON, E. LJUNGSTR&I and 0. LINDQV~S~ of lnorgrnic Clkcmistry. Chalmers University of Technology and University of Giiteborg. S 412 96 Giiteboq, Sweden (Flnt rrceicuf 28 Murch 1985 and recei#d /a publication 15 Deembrr 1986)
AhtrsceTbe rate of diclppamnce of nitrogen dioxide @IOX) with water npour and fomution of nitrous was used to dctamim (HONO) in the dnrk has b&n invcstig&d in b&b cxpaimnts. IR mpy the concentrations of NO1, HONO and NO. Tbc r&on is 6rst order both with respect to NO1 and water
&d
npourrnd proccals hctcropnoudy on most unpoisuned surfaces.Initially. the amount of HONO formal is dose to half the NO* which has diippuual. When the surface in the present ractor (surface to volume ratio - 14 m -’ ) hasracbd iu limiting state of poisoning. tbc reaction is still active and the NOI disappearance follows the expression:
where k, = 4.1(* 0.8) lo-’
-d[NO&dt ppm- t
min- ’
%[NOzl [Hz01
-
(22°C).
Tbc S/ Yntio dependenceof the rrte
shows tkat a bcterogeaous r&on pr& but the existing cvideaa is not condusive about a pox&k homogcnou~contribution to the rrrmining activity. A rate expression which
derribcs the overall reaction at tcmpemturcs around 25°C. when the surface present is made passive. is: -d[NO1]/dr
= (S/V5.6(f0.9)10-9+2.3(~6.5)10-9)
[NO,]
[H*O].
Key word index IR spectroscopy, nte constant, nitrogen dioxide, nitrous acid, isotopic experiment. hctaogmous raction.
WTRODlJCllON
The importance of photochemically induced reactions for the transformation of a variety of air pollutants is well established (Baulch et al.. 1982). The rates of parallel, competing thermal reactions indicate that under conditions of photochemical activity, such reactions may generally he disregarded. In some areas, however. the latitude or meteorological conditions may cause severe restrictions on the flux of sunlight to the lower troposphere. One such area is Scandinavia where, during the winter, the photochemical activity in the troposphere is xmall or nonexistent for extended periods of time. The winter emission of most types of primary pollutants is often larger than the summer emission due to domestic heating, cold started automobile engines, etc. More often than not the maximum concentrations of S02, NO, N02. CO and hydrocarbons in urban areas are recorded during the winter. Under such conditions, tk relative importance of thcmul tr8nsforIMtion reactions increWs. One of the thermal reactions which is not well understood at present is that between NO2 and water vapour. The products from this reaction include HNO,, HONO and NO (England and Corcoran, 1974; S&am&i et ol, 1983; Kesskr, 1984, Pitts et al., 1984). HNO, may contribute significantly to the acidiikation of the environment whik HONO is a known nitrosating agent and ix auspc&d to particip8tc in ‘in uiuo’ formation of carcinogenic
nitrosamincs (Pitts, 1979, 1983). In polluted air, HONO often accumulates during the dark hours and the reaction between NOI and water is one of the likely sources. The results concerning the NO,-water vapour rcaction reported in the literature are not in total agreement, e.g. regarding the nature of the reaction mcchanism, reaction order or whether the reaction is homogeneous or heterogeneous.
EXPERIMENTS AND METHODS Tbc experiments were made in a batch reactor with N2 as tbc matrix pr The concentration of NO, NOI and HONO was followa! by FAIR spcctroxcopy.The ractor consistsof a borosilimte ghss pipe (dixmetcr 0.30 m, knflh 2.00 m) held by two st&kss steel cndphta rad four INVAR distance rods. The toti volume of tk -or ix 0.153 rn’ utd the 8urf8a to volume (S/ v) ntio is 14 m- ‘. The reactor has. attached to tbc mlphtcs. I thra-mirror White optical system (Wltik 1942) with a hw pth kttgth of 2 m. The thra ghss mirrorx, one of 0.21 m and two of 0.14 m diameter. are gold arlsd~hrverprolsc(inL~of~umRuoride.The mirrors may be adjuxtal by external controla to nry the number of relktioat. Pub kngtba between 8 and 120 m may be used. One of the endplates is fitted with KBr windows to 8llowtbe~~ofuulytAlr8diatkm.Intbcprcscnt investiption the rcrtor walls were either boroxiliate glus (Coming Ltd.) with endplxta of xtainkn Uecl, lined with 0.025 mm FEP (Du Pont) T&on film or lieal with stainkss stceishectmetaLFortbeiacmredS/Vntioqmimcnts.an inacrt of lmnging FEP T&n foil, dirnibuting the foil i&de tbccdlwithoutobstmuiaptheLgbtpuhwasusal.This umngcmmtinaaatdtbcS/Vntioto42m-‘.
1529
1530
R. SVEN~~ONet al.
The reactor can be evacuated with a two-stage rotary vane pump IO less than 5 Pa and is enclosed in an insulated box where the temperature can be set between 0 and 60°C and controlled to 1°C. The introduction of known quantities of NOx into the reactor was accomplished by filling the calibrated bulbs of a vacuum line gas handling system to aome predetermined pressure and then expanding the gas into the evacuated reactor. The pressure was measured with a Validync CD 233 pressure gauge (O-18 kPa or O-180 kFa) The water vapour concentration was calculated from a carefully measured quantity of liquid water which was evaporated and entered into the reactor by means ofa stream of Ns.The water vapour concentration was checked. after some of the experiments, with a cooled mirror hygrometer and found to agree well with the expected values. To promote rapid mixing of the reactants, a T&n tuhe fixed along the bottom of the reactor from one end to the other and perforated along the top side, was used. One end of the tube was closed while the other was connected to the reactor inlet. The NO2 used was > 98% pure with nitric acid as the major impurity. The nitrogen used contained less than 10 ppm 0s and less than 5 ppm HsO. Infmred spectra of the reactor content were recorded with a Nicolet MX-I Fourier Transform i.r. spectrometer coupled with a mirror arrangement IO the reactor (Fig. 1). The i.r. source is a globar element and the detector is a DTGS pyrcclectric bolometer. The path lengths employed during the experiments varied between 56 and 72 m. The spectra were taken with 1 cm-’ reaolution and collected from 4000 to 400 cm-‘. The time to collect a spectrum was 5 min. The box car apodizlltion was used when calculating the spectra from the interferograms.
The smallest detectableconcentrations in practical work with 72 m path length in this cell are: NO loOppb, NO1 3Oppb. HNO, HONO 20 ppb.
20 ppb and trans-
The majority of the experiments were conducted as follows: before the experiment the reactor was evacuated three limes to 1 LPaand refilled with pure Nr , then evacuated again and a background spectrum collected. A measured amount of NO2 was introduced, with N2, from the gas handling system into the reactor until the pressure was about 30 kPa. The water vapour was then added to the reaction mixture with a stream of Ns. The final reactor pressure was 100 kPa. The procedure took about 10 min from theaddition of the NO2 until the 6rst spectrum had been collected. The collection ofa spectrum was then initiated every 30 min for a total time of 540 min. Changes in HONO, NOa and NO concentrations were evaluated by subtracting the xero time spectrum from suhaequent spectra. The resulting diiferences between spectra thus show a positive absorption band for an increasing concentration and vice versa (Fig. 2). To investigate the water uptake on the FEP Teflon film used for the reactor lining, a sheetof the film was suspendedin the weighing chamber of a Cahn ekctrobalance. Air with known relative humidity (r.h.) was allowed to flow through the thermostatted chamber while the weight was recorded. The digerence in weight between the film in dry air (less than 0.005%r.h. at 2O”C)and theotable weight at acertain r.h. was taken as the massof water acquired by the !ilm at that r.h. To compare our measured NO,, HONO and NO data with
The following frequencies and extinction coefficients were used to evaluate the concentrations: sigma = 2.02(f0.06)10-‘ppmL*m-1 nitrogen dioxide 1599 cm-’ (in house calibration) trana-nitrous acid 1264 cm- * sigma= 3.84(f0.38)10-3 ppm-‘m-r with trans-nitrous acid/&nitrous acid = 229 to calculate total nitrous acid (Chan et 01.. 1976) nitric oxide 1876cm-’ sigma = 2.77(f0.03)10-4 ppm-‘m-l (Stockwell and Calvert, 1983) aigma = 1.75(f0.18)10-’ ppm-’ m-r nitric acid 878 cm-’ (Stockwell and Culvert, 1983) (ln(la/l) = sigma ‘c. I, base e).
Fig. I. FTIR-White cell system. I. Nkokt MX-I FTIR spcctromctcr. 2. Samplr compartment with interfacing optics. 3. Reactor with White optical system.
Kinetics of the reaction between nieosa
1531
dioxide and water vnpour
-0.3:: fi 3 Q
-0.6-
-0.9
iI
1
-1.2 ’ I700
1325
950
1 575
Wavenumbers Fig. 2. Difference spectrum. found by subtracting the reactant spectrum from the product spectrum, showing bands after 180 min. N02(uS)1599 cm-‘, trans-HONO 1246 cm-‘, (ur) 794cm-’ and cis-HONO (u.) 852cm-‘.
proposed models it was ncccssary to integrate the resulting differential quations. This was done with FACSIMILE (Chance er al.. 1977).a computer program for the solution of initial value probkms arising as systems of difkential equations. The program may also fit rate constants to observed data by a least squares procedure. RESULTS
Reaction order
From a series of experiments in the Teflon lined reactor, the initial rate of NO2 disappearance (the first 30 min) was determined over a range of NO1 (5-80 ppm, 1000 ppm HzO) and Hz0 (lOOO20,000 ppm, 24 ppm NO1) concentrations. In Fig. 3, it is seen that for odr conditions, the reaction order is one within the raqe of experimental error both for NO1 and water. In an attempt to understand the reactions responsible for the concentration changes in the reactor, several sets of elementary reactions were tried on the experimental data. The rate constants were allowed to vary to obtain the best fit between the calculated concentrations from a model and the experimental data. To reproduce the first order behaviour of NO1 disappearance with respect to NO1 and water, reactions (1) and (2) were used. NO, + Hz0 + H2NOS HINO, + NOz + HONO + HNOJ.
(1) (2)
Hz0
(ppm)
Fig. 3. (a) Initial rate of NO* disappearance at constant Hz0 = 1000 ppm vs NO2 concentration. (b) Initial rate of NO* disappearance at constant NO1 = 24 ppm vs Hz0 conantration.
To make (1) the rate determining step in the refinement, kl was set at a value large enough to make (2) fast in comparison with (1). The proposed stoichiometry is supported since the initial rate of HONO formation in Fig. 4 is close to half the initial rate of NO2 disappcarante in Fig. 3. The values of kI obtained by fitting the observed NOz concentrations to (1)and (2)are given in Table 1. The above description is acceptable since kl is reasonably constant with varying initial NO1 and water concentrations. kl describes the overall disappearance of NO1 and is the quantity to be compared with previously reported values (Sakamaki et al.. 1983; Pitts et ol., 1984). If the data from the first 60 min in each run were excluded from the refinement, a significant improvement of the fit was obtained. It was evident that the second order tate ‘constant’ for reaction (1) decmased somewhat during the early parts of the experiments. This is interpreted as a high initial reaction rate caused by the preparation of the reactor before a run which to some extent reactivated the surface. After some time of reaction, the surface is passivated and a limiting rate is approached. The HONO production rate is correspondingly increa& in the initial part of the experiments which is consistent with the above explanation. The values of all constants givun in Table 1 are calculated with data excluding the &at 60 min. The error given corresponds to one standard deviation based on the fit between observed and calculated data
1532
R
%‘EN!BoN et d.
extinction coefficient. This explains why some values are missing in Fig. 6. The build-up appears to be tirst order in NO1. With water, however, the plot is linear up to about 1O$lOOppm Ha0 but the rate at 20,OCNlppm Hz0 is signiticantly higher than expected from a first order dependence. The reproducibility of the points in the graph was documented in several experiments. In most experiments, the NO observed is well predicted by reactions (l)-(3) (Fig. 5a) but at water vapour concentrations of 14BOO and 20,000 ppm, more NO is actually produced than is expected (Fig. 5b).
Temperature dependence Measurcmcnts in the Teflon-lined reactor, with an initial NO1 concentration of 24 ppm and with an Hz0 concentration of 10.000 ppm, were made at 7.22 and 50°C. The results show a decreasing rate constant with increasing temperature (Table 1). The apparent activation energy in the Arrhenius expression calculated from our data amounts to about - 32 kJ mole- ‘.
Surface dependence
Fi& 4. (a)Initialrateof HONO formation st con-
stant Ha0 = loDoppm M NO1 auieeatmtion. (b) Initial mte of HONO form&on at amstant NO1 = 24 ppm vs H1O concentration.
and is only a measure of the capacity of the model to describe the observed data. When the concentration of HONO, calculated by (1) and (2), wascompared to the experimental values it was clear that a loss mechanism was active. A second order decay as described by the reaction 2 HONO w NO1 + NO + Hz0
(3)
together with (1) and (2) produced a satisfactory description of the observed NO1 and HONO data (Fig 5). The re6ned rate constants for ki and k3 are giveninTabk l.Intheretinement,k_~wassettok,l.l x 10m6 ppm-’ (Kaiser and Wu, 1977). The decomposition of HONO has been studied by several authors (see e.g. Grosjean, 1979) and is known to proceed heterogenously to some extent. The literature values for the second order rate constant enclose the values obtained from the retinement. HNOs was never observed as a reaction product in the gas phase and was assumed to adsorb to the reactor wags (Ferm, 1982). HNO, in the gas phase appeared only in experiments with a high initial NOz concentration and was then visible only during the first 60 min. It is likely that this HNOs entered the reactor initially as an impurity in the NO*. In Fig 6 the initial rate of NO formation vs NO1 at Hz0 3 loo0 ppm and vs water at NO2 = 24 ppm are shown. The measurement of low NO concentrations is unartain and sometimes impossible due to its low
The condition of the reactor surface had a strong influence on the measured rates. A rate of NO1 disappearance much faster than normal was observed in the glass cell after washing the glass surface with dilute hydrochloric acid, and rinsing with distilled water and thorough pumping (Table 1). The same qualitative behaviour was seen when the cell was heated and pumped over night or when a new Teflon lining had been inserted. When the stainless steel insert was used, the observed NO2 disappearance rate was about eight times higher than normal while the HONO concentration never reached values seen in comparable experiments with the glass- or Teflon-lined reactor. In all experiments the rate of reaction (3) appears to be influenced by surface catalysis. The extent is dependent on, for example, water vapour concentration, type of surface and the condition of the surface. When experiments in the initially clean glass or Teflon-lined reactor were made with only mild cleaning between the experiments, pumping the reactor to 1 kPa and ret’& hng with nitrogen three times between the runs (i.e. the normal procedure), the rate constants converge towards a constant value, similar for both the glass and Teflon-lined reactor. In a number of experiments in the Teflon-lined reactor the S/ Yratio was increased by a factor of three by the Teflon film insert. The rate of NO1 disappearance in the increased S/Y experiments show a small (average 1.5) but significant rate increase compared with the experiments with a normal S/V ratio. In the increased surface experiments, the rate of formation of HONO is equal to, and the rate of formation of NO is twice that of an experiment with normal S/Y ratio.
24 24 24 5 5 24
36 D 33 D 19 D 15 rk 13 B 31 B
50 7
22 22 22 22
7500 1000 1000 1000
22 22 22 22 22
22 22 22 22
1.5 1.4
33
::
1342*
8.8 4.4 2.8 1.5 22 14 7.2 7.1 4.5
d HONO/dt (103ppm-1min-‘)
:z
E 29 23 9.5
20 13 6.0 1.1
-d NO,/dt Temp. ’ (“C) (103ppm-‘min-‘)
14,000 lO,aao 75W 5000 10,000 10,000
a~
looo 1000 1000 low
(Fg)
Initial
2.9 8.5 6.5
3.7 3.6
23 6.9 3.6 2.6 2.4
3.1 1.1 -
5.1
d NO/dt (lO’ppm_‘mm-’ 5.8 * 1.0 5.0 f 0.5 5.1* 0.6 5.3 j: 2.2 4.a*o.1 3.9iO.l 3.4 f 0.1 5.0 f 0.2 3.2 * 0.4 2.5 f 0.6 8.2 f 0.3 6.5 f 0.2 5.0* 1.3 302 f 8.0 36 f 2.0
kt ) (lOsppm_‘mitt-‘)
k, was calculated taking only reactions (1) and (2) in account, k; and k, were refined with reaction (3) included.
80 50 24 5 24 24 24 24 24
(s)
25 D 24 D 3c 6C 21 D 22 D 26 D 18 D IC
Run number
Initial
4.0 f 0.3 5.3 f 0.3 4.1 f 0.3 5.0,* 0.2 6.5 f 0.2 3.9 f 0.2 3.7 f 0.1 5.3 f 0.2 3.0 f 0.5 1.6iO.2 9.8 f 0.6 6.0 f 0.4 4.2 * 0.9 285*50 46*3.0
KI (lOsppm_‘min-‘) 4.9 f 0.7 9.5 f 4.1 4.2 f 1.5 9.3 f 14*0.5 1.9 f 0.7 15* IA 6.3 f 0.4 9.0 f 5.9 9.3f 1.5 * 1.6 5.0 * 0.8 lO* 161* 69*6.4
(ltippmk’rmin-r)
Increased surface Glass seasoned Glass clean Stainless steel
Teflon
Teflon
Teflon
Comments
Table 1. initial concentrations, rate of NO2 decrease, HONG-NO formation and refined rate constants for the reactions between nitrogen dioxide and water vapour
1534
R. SVENSSONC~ al. (a)
l
=CNOJ
l
=CHONOl
30
r-IN03
90
60 NO2 @pm)
(b)
I
_/m-m
“2
,
60
_,.-m--m-*
.L~--A-b
. 240
420
Tlme tmln)
7000
W
14300
2lcoo
n,o (PPrn)
20
Fig. 6. (a) Initial rate of NO formation at constant
l=INOJ =IHONOI h*CNOl
l
I
IS
HsO = loo0 ppm vs NOs concentration. (b) Initial rate of NO formation at constant NOs = 24 ppm vs NOz concentration.
F 8 IO
s
+G -•-.-.
_ 60
I
I
240
420
Time tmin) Fig. 5. (a) Observed and cakuktal concentrations at an initial water wpour concentration of 7SOOppm. The calculations were based on the r&ncd rateconstants. (b) Observed andcalculated concentrations at an initial water vapour conantration 0120300 ppm. Thccakuktions ware based on the refined rate constants.
Water uptake by FEP Teflon The obvious surface catalysis of the reaction raised the question of water uptake by FEP Teflon film. The water uptake was investigated with the Cahn electrobalance between 5 % and 90 % r.h. at 20°C. In Fig. 7 the mass of water gained by the film per m2 at various relative humidities is shown. About 70% of the mass increase for a certain r.h. in Fig. 7 was acquired within 20 min while the remaining 30% was taken up over a
R.H. IX)
Fig. 7. Water uptake on FEP Teflon vs relative humidity at 22°C. D = Ckan film, A = HNO, contaminated film.
period of days. This is interpreted as an initial, rapid adsorbtion of water to the surface followed by a much slower diffusion of water molecules into the Teflon film. Assuming one water molecule to occupy lo-r9m2, one monolayer would require a weight increase of about 0.3 mgmT2. Figure 7 shows that if the surface of the film was perfectly smooth it would already have about two monolayers of water at S % r.h. At 90% relative humidity it appears that condensation occurs on the film. The influence of HNOa on the water uptake was investigated by exposing the film to 250 ppm HN03 vapour at 10% r.h. for several h. The film was then exposed to dry air and it was observed
Kin&s of the reaction between nitrogen dioxide and water vapour
1535
value with’ageing’ofthe reactor surface. This indicates that the limiting value is not very dependent on the type of surface since FEP Teflon and borosilicate glass have widely dinering surface properties. HNO, was shown to adsorb to the Teflon film. both in the electrobaiance experiment acd by chemical Isotopic experiments analysis. This makes HNO, a prime candidate for the To gain further information about the reaction, substance poisoning the surface. The scatter in the rate an isotope experiment originally made by Sakamaki constant values determined by us and also by other et 01. (1983) was repeated. In a number of runs, “0 workers may well be due to dificulties in reproducing labelled water was used. Measurements were made the preparation ofthe reactor beforean experiment. In at NOI concentrations of 24 and 80ppm and with an attempt to resolve the nature of the limiting reaction Hz0 concentrations between 1000 and 10.OOOppm. the results obtained by us and by other workers will be Experiments with Hz0 concentrations of SOOO- examined. 10,COOppm showed the HONO bands normally found The disappearance of NO2 in our experiments has a at 1264.8S2and791 cm-‘tobedisplaazdto 1251,838 first order dependence both on NO, and water vapour. and 780 cm-’ in agreement with the bands found by This is the best description when considering both the McGraw et ol. (1966) for H “ON0 and by Sakamaki initial rate and the least squares lit to the data er al. (1983) indicating that H “ON0 was formed excluding the first 60 min. exclusively (Fig. 8a). Experiments with lower Hz0 The first order behaviour of the NO2 consumplion concentration, however, gave two sets of bands with respect to NO2 is in agreement with the obser(Fig. 8b). one set the same as with high Hz0 concenvations of Sakamaki et ol. (1983) and Pitts et al. (1984) tration and a second set found at 1257. 848 and but disagrees with the close to second order behaviour reported by England and Corcoran (1976). The recent 786 cm- ’ indicating that HON ‘so also was produced (McGraw et al., 1966). No bands were detected at the information thus shows an apparent first order depennormal positions showing that only labelled HONO dence of the NO1 decay on itself. Comparing the was formed. pseudo first order rate constant at about 13,ooOppm A double band also appeared at 2868 cm-’ close to Hz0 concentration and room temperature obtained the 2906cm-’ NOz(ul +ua) bands. The calculated by Sakamaki et 01. (1983) of 3.8 x lob4 min-’ and by displacement from the normal position for ON “‘0 is Pitts et 01. (1984) in two different reactors of 2.8 about 4Ocm-’ (Shvangiradze and Dzhamagidze, x lo-* min- ’ and 1.6 x lo-* min- ’ to that found by 1961) and it is concluded that “0 labelled NO3 is us of 10.9 x lo-* min- ’ it is seen that they are of the formed in the reactor (Fig. 9). The rate of labelled NO1 same order of magnitude. If the above rate constants production is proportional to the NOz concentration. relate to a gas phase reaction, the scatter is conbut no effect of Hz0 concentration could be seen in the siderable but if the constants relate to a heterogenous concentration interval lOOO-10,000 ppm. reaction the variation is easily understandable since, e.g. reactors with different surface to volume ratio were Mass balance Used.
that the initial weight of the film was not regained, i.e. some of the HNO, was strongly adsorbed to the film. When the flm wasexposed to water vapour, the weight increase at low relative humidities was higher than observed with the clean film.
In all experiments, a loss of nitrogen from the gas phase is observed as the reaction proceeds. In a few runs. a piece of the initially clean Teflon lining was withdrawn from the cell after the experiment and immediately rinsed with water. The liquid was analysed by ion chromatography and revealed an amount of nitrate which, if extrapolated to the entire surface of the cell, closes the mass balance. No other anionic species except traces of nitrite was detected in the liquid by the ion chromatograph. ’ DISCUSSION
From the experiments with the clean glass cell, where rate constants more than an order of magnitude greater than with the’seasoned’cell were observed,it is clear that the reactor walls have a profound influence on the reaction. it is concluded that it proceeds mainly via a heterogenous route in the clean glass cell at low Hz0 concentrations. Both in the giass and the Teflon-lined reactor the observed rate constant converges towards a similar
The water vapour dependence of the NO1 decay is slightly less clear. Sakamaki et 01. (1983) reports a first order dependence on water vapour for NO1 consumption. At Hz0 concentrations of less than 12,000 ppm. however, their NO* disappearance rate is significantly higher than predicted from a first order relation. England and Corcoran (1974) show a clear first order water behaviour. In conjunction with our data the indication exists that the NO2 consumption also has a first order water vapour dependence. The initial rate of HONO formation is first order in NOz as observed both by Sakamaki et al. (1983) and Pitts eta/. (1984) as well as by us. In the present investigation and in the work by Sakamaki, the HONO formation appears lo be first order also in water vapour. Although Pitts ef al. (1984) do not claim a first order behaviour for HONO with respect to water, there is nothing in their data which contradicts such a dependence. The kinetics for the reaction between NOa and water vapour may thus formally be described by reactions (l)-(2). The mechanism of the rate determin-
1536
R. SVENS~ON et al.
0.083-
0.0608 6 5 2 0.03?-
0’014: i
’
-0.009
1305
I155
1005 Wavenumbers
W
I-
Q
-0.011
. 1305
I
II55
1005
855
705
Wavenumbers
Fig. 8. Infrared absorption bands of nitrous acid formed in: (a) NOz = 24 ppm and Hz0 = 10,000 ppm. (b) NO2 = 80 ppm and Hz0 = 1000 ppm.
Kinetics of the rewtion between nitrogen dioxide and water vapour
1537
Wavenumbers Fig. 9. (a) Normal 165Ni65 (IQ+ q) absorption bands. (b) Spcctnun recorded during one of the H1*a5 cxpcrimcnts. (c) Spasrum b. withspectruma subtracted revealing additional bands from ‘60N1*0.
ing step, however, offers a number of possibilities. If the reaction is het~o~no~, one of several rate controlling steps may be involved. When the reaction is fast, mass transfer to the surface willbe rate controlling which, in turn. would give an apparent first order behaviour with respect to the limited component. Such an explanation is not feasible in our case since the experiments with the clean glass cell show that it is possible to supply a reaction, at least 10 times faster than the limiting rate, with reactants. Pitts et al. (1984)discussother ways of obtaining the observed first order behaviour on NOa in a heterogenous reaction. The attachment of a mol~ule to an active site on the surface is mentioned as a potential rate controlling step. If the molecule reacts as adsorbed, the adsorbtion step is less likely to be rate controlling since physical adsorbtion is generally a rapid process. For a molecule. reacting as a chemisorbed species and where the transfer from the ad- to the chemisorbed state has an appreciable activation energy, the chemi~rbtion may well be rate limiting. The rate of transfer wit1depend on the surface activity of the adsorbed molecule. Another possibility, according to Pitts et al. (1984).is that one adsorbed molecule of NO2 may react with one adsorbed molecule of water in the mte controlling step to form a reactive intermediate which rapidly reacts with another NO2 molecule. In addition, the intermediary may form from one
adsorbed reactant molecule with another impinging from the gas phase. The intermediary may also form in the gas phase with subsequent adsorbtion and reaction on the walls. Common to all heterogenous meohanisms outlined above is that the fate of a reaction, where the reactants are adsorbed to the surface, is controlled by the surface activity of the reactants. If the surface activity of a compound is assumed to be proportional to the mass of compound per unit surface, a fair assumption if the covemge is less than one monolayer, then the surface activity is linked to the gas phase concentration by the normally non-linear adsorbtion isotherm. If a substance has a high gas phase concentration, as is the case for water in some of our experiments, then liquid water is present at the surface. A change in gas phase water concentration may then change the mass but not the activity of surface water. Thus for a surface reaction, a linear rate response to a change of gas phase concentration is generally not expected. If a molecule impinges from the gas phase on another, already adsorbed molecule in the rate determining step, then the mte would be expected to show a first order dependena on the gas phase concentration of the impinging molecule. Another possibility to have a first order behaviour is when the coverage of the surface is su~~nt~lly less than one monolayer. The adsorbed molecules then interact little and the adsorbtion isotherm has a section which is approximately
1538
~!%ENSSON~d.
linear.giving a linear relation between gas and surface concentration. In our investigation, this may be the case for NOZ. The gas phase water concentration was, for the Teflon-lined reactor, varied over the non-linear part of the adsorbtion isotherm (cf. Fig. 7) with an approximately linear rate response.This experimental evidence indicates that adsorbed water is not a direct participant in the rate determining step. A reaction seq~enat. where an adsorbed or chemisorbed NOz molecule reacts with an impinging water molecule and where the formation of a reactive intermediary or the chemisorbtion is the rate controlling step, offer, together with a pure gas phase reaction, mechanisms compatible with the available rate information. Due to the symmetric structure of any likely gas phase transition compkx between NO* and water, it is not easy to see how only labelkd HONO is formed. A surface reaction offers better possibilities to fix a transition complex and to produce only specific types of HONO. Mow 5OtM ppm Hz0 concentration both H ‘*ON0 and HON ‘so are produced which suggest two pathways producing HONO where one of the pathways is being inhibited by increasing water vapour concentration. The formation of specific types of labelled HONO and the change in isotopic composition of the reaction product strongly suggeststhat a heterogenous reaction is involved. The observed oxygen isotope exchange in the NOz molecule rquires hydrogen-oxygen bonds and nitrogen-xygen bonds to he broken and reformed. This is also needed to form the labelkd HONO observed.The labelkd NO2 formed is in excessof what is possible to form through decomposition of labelkd
HONO. The water dependence of the labelkd NOz formation also differs from that of HONO formation. This indicates that labelled NO2 is formed through a process not involved in the HONO production. The negative temperature dependence observed in the present work for the NO2 disappearance was also seen by England and Corcoran (1974) who found an activation energy of about - 4 kJ mole- ’ in the temperature interval 25-5OC. Pitts et d. (1984) report no clear temperature dependence on the HONO formation. We believe that the etTectis due to a change in the adsorbtion of some important reactant or intermediary with temperature. The large diliirence in apparent activation energy is the likely result of dilferent adsorbtion characteristics of the reactors. The temperature behaviour may be interpreted as still another indication of a heterogenous reaction. If the limiting reaction proceeds entirely via a hcterogenous route and if no mass transfer limitation occurs then an increased S/V ratio would be expected to increase the rate in the same proportion. This is not the case in our study sincea S/ V increase by a factor of three only gives 1.5 times rate increase. The same observation was made by England and Corcoran (1974) who saw ‘very little increase’ for a S/V change with a factor of 3.4. Kessler (1984). on the other hand, usedaglasssmogchamhcr witha S/Vratioof7.6 m‘ ’
which was increased with a factor of 3.5 by introduction of glass Raschig rings, whereupon the HONO formation rate was also increasedabout 3.5 times. Due to the insensitivity to the change in S/V ratio the possibility that some of the observed activity in our reactor may he due to a gas phase reaction remains. Assuming that the limiting reaction is composed of one part from a gas phase and one part from a heterogenous surface reaction, then a plot of rate constants vs S/V ratios for comparable experiments could beextrapolated to S/V = 0 which would give the gas phase rate. This was done with kt values from the present work and with values calculated from Sakamaki er 01. (1983) (Table 2, runs 15-18) and from Pitts et al. (1984) (Table 1. runs 555-6, 558. 753-4, 757-8. 761. 763. 774A. 779 and 781-2) under the assumption of a first order NO1 and water dcpendence (Fig. 10). The line has an intercept at S/V = 0 of 1.1 (+3.3)10v9 ppm-’ min-‘. Due to the error associated with this figure it is possible that the reaction is purely heterogenous. If, however, the line in Fig. 10 is accepted as an estimate for k, then a rate expression taking both homo- and heterogcnous reactions into account is: -d[NO,]/dr
= 2*d[HONO]/dr = (S/V5.6( f0.9)10-9 + 2.3( + 6.2)10-9)[N0,][H,0].
(4)
According to expression (4). when the reaction proceedsat its low limiting rate, about 97 % of the activity in our cell is due to the wall reaction. Several dificulties appear when expression (4) is to be applied to ambient conditions, e.g. a city. The rate expression is valid if the available surface is made passiveso that the reaction proceeds at its low limiting rate. In real life, this may not be the case. Glass can be made passive during dry weather but reactivated during rain, resulting in changing catalytic activity. Some building materials with basic properties, e.g. limestone, may also react with the agent inducing passivity. The result would be an under-estimation of the reaction rate. In a city, a ‘macro’ S/V ratio of
S/Y
Cm“)
Fig. Iu. Rale wnstant k, vs S/V ratio
Kinetics of
the reaction between nitrogen dioxide and water vapour
0.2m-’
to roof top level (25 m) is reasonable. The catalytically active surface may be an order of magi& tude greater due to porosity and roughness of building materials, etc. For very porous materials mass transfer may become rate limiting. The effective mixing height is also crucial for the determination of a useful S/Y ratio. During the daytime, the large mixing height would cause the S/Y ratio to approach that based on aerosol surface alone, while at night the surface supplied by the ground may dominate. If the rate expression is used to calcuiate the production of HONO assuming inversion episode values of the participating reactants, NO1 = 0.1 ppm, Hz0 = 15,000 ppm and with a mixing height of 50 m, giving anelT&iveS/Ymtioofl m-l.then1.1 ppbHONOis produced in 3 h. Accumulation of HONO in the atmosphere is expected to take place mainly during the night when the mixing often is poor and when the photolysis into NO and OH has ceased. At night the temperature very often is considerably lower than the temperatures of the quoted experiments (22-30”). According to our results, the reaction rate increases with decreasing temperature which may double the production of HONO at night, compared to the number given by Equation (4). In GZiteborg, Sjijdin et 01. (1984) measured l-2 ppb HONO as 12-h mean values, and in Los Angeles, Harris et 01. (1982) found concentrations of HONO up to 8 ppb. Based on these considerations, it is likely that the reaction between NO2 and water vapour is responsible for a significant fraction of the HONO observed in polluted air. Acknmvledgemenr-The authors wish to thank the Swedish Environmental Protection Agency (SNV) for financial support.
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Chance E. M.. Curtis A. R, Jones I. P. and Kirby C. R. (1977) FACSIMILE: a computerprogram for flow and chemistry simulation and gcneml initial value probkms. United Kingdom Atom Energy Authority HanveIl Report R 8775. England C. and Cotcoran W. H. (1974) Kineti and mcchan-
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dioxide. lmf. Enan~. Chem. Fumdam 13.373-384. Fum M. (1982) M&d for determination of gaseous nitric acid and particulate nitrate in the atmosphere. EMEP expert meeting on chemical matters_Geneva, 10-12 March 1982. Grosjean D. (1979) Nitrogenous Air Pdlutants, Chemical and Biological fmplicotions, p. 51. Ann Arbor Science, Ann Arbor. Harris G. W., Carter W. P. L, Wincr A. M.. Pitts J. N.. Platt U. and Pcmer D. (1982)Observation ofnitrousmzid in the Los Angeles atmosphere and implications for predictions of ozone-prsursors relationships. En&. Sci. Techno/. 16, 414-419. Kaiser E. W. and Wu C. H. (1977) A kinetic study of the gas phase formation and decomposition reactions of nitrous acid. 1. Phys. Chem. 81, 1701-1706. Kessler C. (1984)Gasfiirmigc Salpctrigc Siiurc ( HNOz) in da Bclastcten Atmosphiire. Thesis, Univ. of Kiiln. McGraw G. E.. Bcmitt D. L. and Hisatsune I. C. (1966) Infrared spectra of isotopic nitrous acid. 1. Chcm. Phys. 45. 1392-1399. Pitts J. N. Jr (1979) Photochemical and biological implications of the atmospheric reactions of amines and bcnzo(o)pyrene. Phil. Truns. R. Sue. A 290, 551-576. Pitts, J. N. Jr (1983) Formation and fate of gaseous and particulate mutagens and carcinogens in real and simulated atmospheres. Envir. Hlrh Perspec. 47, 115-140. Pitts. Jr. J. N.. Sanhucza E.. Atkinson R.. Carter W. P. L. Wincr A. M.. Harris G. W. and Plum C. N. (1984) An investigation of the dark formation of nitrous acid in environmental chambers. Int. J. C/tern. Kin. 16.919-939. Sakamaki F.. Hatakeyama S. and Akimoto H. (1983) Formation of nitrous acid and nitric oxide in the hctnogcnousdark reaction of nitrogen dioxide and water vapour in a smog chamber. Inr. J. Chem. Kin. 15, 1013-1029. Shvangiradxe R. R. and Dxhamagidzc S. Z (1961) Use of the frqucncia of isotopic molecules for the determination of the force constants of symmetric molecules of the type XY,. Opt. Specrr. 12, 200-202. Sj6din A., Ferm M. and Grennfeldt P. (1984) Measurements of nitrous acid in the city of GGteborg. IVL B-publ. 749 Gijtcborg. Jan. 1984. Stockwell W. R. and Calvert J. G. (1983) The mechanism of the HO-SO2 reaction. Atmospheric Enuironmenr 17, 2231-2235. White J. U. (1942) Long optical paths of large apperturc. J. Opt. Sot. Am. 32.285-288.