Extinction Coefficients of NO2 and N2O4*

The extinction coefficient of NO2 has been measured in the spectral range 185 to 410 nm as a function of temperature between 235 and 298 K. In order to correct for the effect of the dimer absorption, the extinction coefficient of N2O4 has also been measured. The effect of a decrease in temperature upon the NO2 absorption is a reduction in the extinction coefficient of approximately 10 percent in the range 320 to 380 nm.


Introduction
. The absorption of solar radiation by O2 is of prime Importance in the c he mic al processes whic h may O?cur !n .the troposphe re and stratos ph ere. Th e photo-dI ssocIatIOn of N02 is an important so urce of oxyge n O(3P) a tom s in the a tmosphere. At all wavele ngths s ho~ter than the dissociation limit, 398 nm, a bsorption of lIght by N0 2 res ults in di ssociation of the molecule with th e formation of an oxygen a tom. The fate of th e o atom, ultimately O(3P) in large part, is to reac t with O 2 res ultin g in 0 3 , the c he mi s try and physics of whi ch are cr~c ia~ to th e dynami cs of the s tratosphe re. A de terminatIOn of the a tom yield in the atmos phe re depe nd s on a knowled ge of the N0 2 absorption crosssection , con centration and quantum yield of dissociation, and the solar flux over the wavele ngth range 185-410 nm.
The measure ments on N02 reported in the previously published literature have been made at room temper~ture. Considerations of the photoche mistry of N02 III the s tratosphere require a knowledge of the extinction coefficient s at ambient stratos pheri c conditions -low temperature and low press ure. Extrapolation of data obtained a t room te mpe rature to stratospheric te mpe rature re quires a knowledge of the states involved in the absorption. If any of the absorption is attributable to " hot-bands" the relative i~portan ce of. s uc h absorption will decrease markedly with decreaslllg te mpe rature. Since the de tails of the tra~s ition s involved in the N02 absorption s pec trum over thi s wavelength ran ge are not entirely under stood, we have unde rtake n to de termin e the experimental behavior of the extinction coeffi cient as a fun ction of temperature.
• Work suppo rt ed in part by the Clim ati c Im pact Assessment Program. Office of the Secretary, De partment of Transportatio n, a nd by th e Natio nal Aero naut ics and Space Administration.
The meas ure ment of th e extin ction coeffi cie nt of N02 at any te mperature is seve rely co mpli cated by th e presence of its dim er , N 20 4 • The equilibrium mole fraction of N20 4 is a fun ction of both te mperature a~d. p~e ss ure . It is well known that low press ures mlmmlze the N 20 4 contribution. Howe ver , as th e te mperature of a mixture is reduced, the mole fraction of N20 4 in c reases. It is a relatively simple matte r to de termin e the co ncentration ratio (N0 2/N 20 4) based upon th erm odyna mi c co nsideration s [1]. I While concentration corrections to the measured absorption may be s mall , a possibly greater error would res ult from the absorption by N 20 4 if the extinction coe fficient of N20 4 is large co mpared to that of N02• It was impe rative, therefore, to meas ure the extin ction coefficie nt of N20 4• Hall and Blace t [2] ha ve re ported values of the extinction coefficie nts for N20 4 • Their experime nts, howev er, were not performed under condition s where N20 4 formation was favored, i.e., low te mperature and high pressure.
Three previous photoelectric meas ure men ts of the ultraviolet absorption cross-sections for N0 2 have been reported. Nakayama et al. [3] examined the region from 108-270 nm with a spectral resolution of 0.02 nm. Corrections for the overlapping absorption by the dimer, N20 4 , were made at five selected wavelengths between 190 and 240 nm by making measurements at several press ures , and extrapolating to zero pressure. Hall and Blacet [2] made measurements from 240-500 nm with an ave rage spectral band width of 0.4 nm on three mixtures each of which contained appreciable N 20 4 • By usin g the equilibrium expres-sIOn of Verhoek and Daniels [4] and Beer's law, they were able to de termine the extinction coefficients for I Figu res in brackets indicate the lit e rature references a t the end of this paper. · both N02 and N20 4 • Johnston and Graham [5], in connection with a study of the absorption by nitric acid vapor, determined th e N02 extinction coefficient at low press ures and with a long optical path over the wavelength range 185-420 nm. Because of the low pressures used, the N20 4 was negligible.

Experimental Detail
All measurements were made with a 0.75 m Fastie-Ebert monochromator equipped with a 2400 groove/mm grating. With 10 I-t slits, the spectral resolution was 0.01 nm. The actual measurements were made at intervals of 0.125 nm with a spectral resolution of 0.015 to 0.04 nm. The light source for the absorption studies was either a low-pressure hydrogen discharge for the region 185-360 nm, or, in the region above 360 nm, a quartz-iodine incandescent lamp. The e ntire gas handling system was fabricated of stainless steel and monel to minimize surface decomposition of the N02• Pressures were measured by means of a capacitance manometer. OETECTOR Two distinct, separate measurements were made; one involving the spectrum of N20 4 and the other of N02• The spectrum of the form er was obtained by using a low-temperature cell which has been previously described [6]. A Pyrex 2 tube was sealed to one of several fused silica absorption cells of path lengths between 0.1 mm and 5.0 mm. The Pyrex portion was equipped with a side-arm whic h could be used as a cold trap. Purified N02 was distilled into the cell through polytetrafluoroethylene vacuum valves. This cell was immersed in another cell fabricated of stainless steel, shown in figure 1. The heat transfer fluid was either methanol or 2,2,2-triftuoroethanol both of which possess excellent light transmission p~operties at wavelengths as low as 185 nm at low tempera. ture. Constant temperature was attained using either n-pentanoic acid slush (240 K) or CC14 slush (250 K). At these temperatures and at the pressures used, the N0 2 -N 20 4. equilibrium mixture remains gaseous.
The absorptIOn cell temperature was measured with a chromel-constantan thermocouple whic h was in contact with the cell. As may be seen in figure 1 ~he .surrounding volume was evacuated thereby elim: matmg the problem of frost formation on the fus ed silica windows.
In a typical experiment, the transmitted light intensity was determined through both the cooled absorption cell and optical system. Then N02 was conde nsed into the side-arm of the absorption cell. Removal of the cold trap permitted the N0 2 -N20 4 mixture to vaporize once again and fill the entire cold absorption cell. The material was allowed to equilibrate thermally and then the transmitted intensity was measured. The system was assumed to be in equilibrium when the measured absorption at any given wavelength remained invariant with time.
To de scribe adequately the ratio of N02/N20 4 , determination of both the te mperature and press ure in the absorption cell are required. The temperature determination is straightforward. The pressure in the absorption cell could not be monitored during the course of an experiment (see fig. 2). Furthermore, portions of the cell we re us ually at two differe nt temperatures during any particular measurement, i. e., room and some reduced temperature. As a consequence of these two factors, the pressure and hen ce the concentration of both monomer and dimer in the cold portion of the cell was determined by calculation based upon the conservation of N atoms in the sys tem. . ' ~ M U l T I -P A~S->fS=:~~'HJc : .p.j~ ~~

ADJUSTMENT' "
"-" fI~ ': using the multiple-pass design of White [7a] and Berns tein and Herzbe rg [7b] path le ngth s up to a maximum of 10 meters co uld be used. Since th e cell was also to be used at low temperatures, the multiple-re fl ec ti on mirrors were connected to eac h otl:ter by rigid fused sili ca rods to ins ure that the path le ngth be twee n the mirrors remained fixed as the cell te mperature was c hanged. The arrangement also permitted adjustment of the opti cs on the benc h and in sertion, as a unit, into the cell. Th e end s of the cell were thermally isolated from the environment by gold-plated copper radiation s hields. The multiple-re fl ec tion mirrors were made of a low thermal expans ion material and were aluminized and overcoated with magnesium fluoride. Temperature control was obtained by circ ulation of a refrigerated fluid , usually me thanol, through the outer jacket of the cell. Further, the outer surface of the cell was coated with copper using a " flam es praying" process to further insure uniformity of temperature along the cell. Th e gas sample te mperature was measured by means of three calibrated c hromel-co nstantan thermocouples in side the cell. At a cell term pe rature of 220 K the te mperature variation of th e sampl e over the le ngth of the cell was approximately 1 0c.
Care was taken to avoid the use, as far as possible, of any materials which would be subj ect to corrosion by N02. The vacuum seals were made by compressed gold O-rings. Two layers of aluminized-mylar were wrapped around the outer s hell to provide in sulation of the cell from room te mperature.
The absorption cells we re placed in the exit beam of the monochromator. Immediately in front of th e cell , a sapphire plate was used to split the light beam so that a portion of the signal illuminated a I3-stage photomultiplier tube. Th e signal meas ured by thi s photomultipli er monitored the variation of th e light so urce. Corrections for c hanges in the in ciden t li ght signal were applied in the data red uction process. A seco nd photomultipli er tube recorded th e light flux tran s mitted throu gh the absorption cell.
In all experime nts, data acquisition was automated by photon countin g equipm e nt in conjunction with a stepping motor co ntrol for the monoc hrom ator wavelen gth drive. Th e operation of the equipme nt has been previo usly described [8].
The procedure used in a t ypi cal N02 meas ure me nt involved a scan over the wavelength region to be examined, with the cell evac uated. The ratio of th e incident signal to the transmitted signal (through the multpile-reflection cell) as a function of wav ele ngth was determined. Then the cell was filled with a known pressure of N02 as measured with a capacitance manometer and the scan repeated. The data were reduced by computer calc ulation after corrections were made for both the concentration and absorption due to N 20 4• The N02 was obtained commercially and purified by reaction with excess O2• When cooled to -78°C, a pure white solid was obtained which, followin g thorough pumping, was warmed, di stilled throu gh P 205 and subsequently stored in the dark in a glass bulb. NO, a probable impurity, was absent in a 1 torr 3 sample of N02 as indicated by the absence of absorption of the stron g (A -X) syste m at 226 nm. , I Torr = 133,3 Pa, A mInImUm of 0.005 torr NO would be observable under these conditions. To minimize errors in the determination of the extinction coefficients of both N 2 0 4 and N0 2 , the following procedure was followed. Initial measurements were performed at low pressure over the complete wavelength region. Under these conditions, the concentration of N 20 4 was minimal and a correction due to its concentration, but not its absorption, could be made. The values obtained are an upper limit for EN0 2 since some of the absprption.
is undoubtedly due to N20 4 • The next series of experiments involved measurement of the N20 4 absorption as previously described. Here again, a correction due to the presence of N02 could be made; both as to its concentration and absorption. In the region where the relative values of E(N02 ) and E(N20 4) are about equal, the correction is less than 1 %. At shorter wavelengths, where E(N20 4 ) ~ E(N02 ), an error in the latter has but a small effect on the determination of the former.
With an adequate determination of E(N20 4 ), an accurate value of E(N02) was readily obtainable.

Results and Discussion
The extinction coefficient E IS ~efined by the Lambert-Beer equation: I/Io=exp (-EPX) where 1 and 10 are the transmitted and incident light intensities, P the pressure in atmospheres at 273 K,4 and x the path length in cm.
The N20 4 absorption measurements were performed at -23°C at pressures of about 30 torr and at room temperature at high pressures (117-500 torr).
Under these conditions, the mole fraction of N20 4 41 n computing E, the ex perime ntal press ures havc4-bee n con vert ed to the eq uival e nt va lues at 273 K. To convert to absorption cross section s (em:! molecule-I), multiply E by 3.72 X 10 -"'. represents between 40-80 percent of the sample.
The actual . experimental conditions are shown in table l. The results, which are shown in figures 3 and 4 and in table 3, were obtained at low and room temperature but have been corrected to the equivalent press ure at 273 K and represent the non-weighted average of at least 2 and usually 3 values at each wavelength. No temperature effect on the spectrum was observed. The data, then, represent the extinction coefficient of N20 4 • There have been only two reported examinations of the N20 4 spectrum with which our results may be compared. In the shorter wavelength region, (185-240 nm) an approximate value for E(N20 4 ) = 950 atm -I cm-1 at 197 nm has been reported as the maximum value [3] which is to be compared to our value of -!l80 atm -1 cm-1 at 197 nm. Since the previous work is, in reality, an estimate and was obtained in systems with low N20 4 concentrations (-3 percent in measurements at 195 nm), the discrepancy of 20 percent is small. Of greater significance is the observation that the maximum absorption appears in the present work not at 197 nm, but at-190 nm. Any rationale for the discrepancy would, of course, be speculative, but it should perhaps be noted that the values for E (N0 2 ) determined by Nakayama et al.
[3], in the region below 200 nm are significantly greater than determined in the present work. It is possible that the absorption, incorrectly attributed to N O 2 , was in fact due to N20 4 whose concentration could have been incorrectly determined.
The N 20 4 data with which we have the widest correspondence are those of Hall and Blacet [2]. The results of both sets of data have the same general shape with the first maximum at -340 nm and a second, less pronounced, in the vicinity of -265 nm.
At shorter wavelengths, the absorption increases sharply to what appears to be another maximum in  [plot is a computer reconstruction of averaged dala. S ee tex t.J the region of -190 nm. The apparent discontinuity amounting to -20 percent in the value of E at 275 nm is an artifact and is caused by the method used to collect the data, i.e., the wavelenth overlap between successive determinations was not sufficient to eliminate the error at that point. The difference at 275 nm is a likely indication of the maximum error due to all causes in our determination of the extinction coefficient.
Hall and Blacet indicate the absence of structure in the spectrum of N 20 4 • Since the error in our determination is probably of the order of 20 percent, it is uncertain whether the features observed in the region between 275-390 nm are indeed resolved structure or simply indicative of the "noise" in the experiment. In any case, no obvious regular pattern is apparent. It is important to note the large value of the extinction coefficient at short wavelengths, which indicates that extreme care is required to account adequately for N 20 4 absorption in any measurement of the NO z spectrum.
Although the general shape of the absorption curve agrees well with that of Hall and Blacet, the differences between the two measurements are not constant over the complete wavelength region. Between 260 and 335 nm, the two sets of measure me nts lie within 10 percent of each other but outside of th ese limits (i.e., 240-260 and 335-390 nm) the difference is closer to 20 percent. The explanation for this discrepancy may lie in the fact that in our experime nts, the ratio of N 20 4 /NO z was usually close to 4 while those of Hall reached a maximum of 1.3. Thus, the correction due to N02 absorption is larger in Hall's work than in ours.

. N02
The room temperature absorption spectrum of N02 is shown in fi gures 5 and 6 and in table 3. The spectrum shown has been corrected for the contribution of N 20 4 to the measured pressure . The N Z0 4 mole fraction was obtained from the calculated value of the equilibrium constant, Kp , based upon spectroscopic and thermodynamic considerations [1]. At the pressures 'IS ed, usually less than about 0.1 torr, the correction due to N20 4 concentration was less than about 0.1 percent. Similarly, a correction for the absorption due to N20 4 could be made using the measured values for E(N20 4 ). In particular, at shorter wave-   lis hed lite rature [2,3,5]. Th e major diffe re nce be tween the present and previously publis hed work is related to the spec tral band-pass used. The larger amount of struc ture evide nt in figures 5 and 6 as compared to pre vious work is a conseque nce of th e greate r resolving power in the prese nt experiments.
The appearan ce of the sp ectrum and positions of the ab sorption peak s agree well with th e data in the pub- ::: [plot is a c omputer recon struction of averaged data. See te xt. J 150 1 Bayes [9] has carefully reexamined the data of Hall and Blacet [2] and presented the values in tabular form at 0.5 nm intervals. Over the range from 250 to 410 nm our values for the extinction coefficients are 10-20 percent lower than those of Hall and Blacet. Comparison with Johnston [5] indicates good agreement (within 10 percent) over the range from 245-410 nm. Although the present values are slightly lower than those of Johnston, the latter are also lowe r than those of Hall and Blace t. At shorter wavele ngths (245-190 nm) the agreement betwee n Johnston and us is not quite so good, but ge nerally it is within 15 percent. Presumably th e di scre pan cy may be attributed to the methods used to correct for the NZ0 4 absorption.
A comparison betwee n the room-temperature and low temperature (235 K) absorption spectrum is shown in figure 7. It is clear that the discernible effect is no greater than about 10 pe rcent and appears be tween 320-380 nm. It is apparent that no sin gle fe ature is re mov ed at low te mperature but rath er a reduction in th e unde rlyin g co ntinuum is noticed.
It may be argued th at the differe nce spectrum is an artifact due to the in correc t numerical adjustment of the spec trum caused by the prese nce of N 20 4 at low te mpe rature. However, although N Z0 4 does have a broad absorption peak in thi s region (figure 4) the appearan ce of a " te mperature effect" at 360 nm and no observable effect at ;.... 290 nm whe re th e NZ0 4 absorption is similar to that at 310 or 360 nm would rule out thi s interpretation.
W e have attempted to estimate the possible sources of error in our measurements. The wavelength scale of the monoc hromator has been calibrated with the known e mi ssion lin es of Hg and is accurate to about 0.02 nm. Inacc uracies in th e pressure measurements we re of th e order of 1 percent and were limited to the accuracy in r eading the analog output from the manome te r. Significantly larger e rrors may result from th e intensity measure me nt and in partic ular, the ratio of 1110 although eac h individual meas ure me nt is probably accurate to within 5 pe rcent of the " true" value. Errors in the NZ0 4 measureme nt may be more significant. For example, at a pressure of -30 torr at a temperature of -250 K, a one degree temperature error res ults in a 1.25-pe rce nt error in the N Z04 mole fraction. The method used to de termine th e concentration in the absorption cell involves th e temperature of th e cell so that an error in te mpe rature is manifes ted in se ve ral ways and res ults in an overall N20 4 concentration which is only accurate to ± 5 pe rcent. In all experime nts, scatter be twee n run s amounted to 10 pe rcent or less. Consideration of those factors suggest th e final value for E (N20 4 ) is probably correct to within ± 20 perce nt, and for E (NOz) to within ± 10 percent. Table 3 li s ts th e extinction coe ffi cie nts of N02 and N20 4 corrected to th e eq uiv ale nt press ure a t 273 K.

. Appendix A
Consider a volume , V, in which IS measured a certain press ure, PT , of an N0 2 -N 2 0 4 equilibrium mixture at te mperature T. The number of nitroge n atoms is N= (V/RT) (PI +2P2 ) where PI and P2 refe r to the pressure of monomer and dimer, respectively.
If we follow th e procedure utilized in the experiments, the gas is now tran sferred co mpletely to the cell with volume, V', and sub seq ue ntly vaporized. A fraction (I) of the cell is maintained at a reduced temperature, T * and the remainder at T. The number of nitrogen a toms in the warm fraction is then N -IV' (p * P * -RT* 1+ 2 2)' Since th e numbe r of N atoms is conserved: (3) (P; + 2P;) + T* (Pi +2Pf) v = RT (PI +2P2 ).
If we set (1-f)/T= a and J/T* = b, eq (3) reduces to: wh ere XI is th e mole fraction of N0 2 . Since the volume ratio, VjV' , may be measured, the RHS of eq (4) is known. Recognizing that th e pressure throughout th e cell is constant, P' = P *, and eq (4) may be solve d by iteration. An initial estimate is made of the total press ure in th e absorption cell and then usin g the equilibrium constant, Kp , appropriate to th e te mperature (either room or reduced), a new pressure may be obtained. The process is co ntinued until s uccessiv e calculations yield similar res ults. Typi cal values for our a pparatus are VjV' = 8.9 and J= 0.5.

Appendix B
Chao e t al.
[l] calculated the thermodynamic properti es of N02 and N Z0 4 -The me thod involv ed a s tatistical th ermodynamic calc ulation based upon a ri gid rotor a nd harmonic oscillator model. £quilibrium constants were obtained from the th ermodynamic fun c tion s; from a least squares fit the folrowin g e mpirical relationship was obtained.
The equilibrium constants us ed here have been compared with thos e de rivable from the molec ular parameters used in the JANAF Thermoc hemical Tables. 5 Chao's expression (1) yields Kp uniformly 4 percent higher than the JANAF value. Kp from (1) is also in good agreement with the ex perime ntal Kp's reported by Vosper,6 agreei ng within 4 percent below 290 K. In both cases th e agreement is well within the accuracy of th e available thermoche mi cal and molecular data.