Discussions 2891

I N F R A R E D A B S O R P T I V I T I E S A N D

I N T E G R A T E D B A N D I N T E N S I T I E S F O R

G A S E O U S P E R O X Y A C E T Y L N I T R A T E

( P A N ) *

Tsaikani and Toupance recently reported infrared absorp- tion coefficients and integrated band intensities of peroxyace- tyl nitrate (PAN). They compared their results with those of Gaffney et al. (1984) for PAN and suggested that some of the band intensities reported by Gaffney et al. (1984) were too large by up to 50%. This agrees with our conclusions (Rogers and Rhead, 1987), based on a comparison of the infrared intensities of peroxyglutaryl nitrate (PGN), HC(O)CH2CH 2 CHzC(O)OONOz, with those reported by Gaffney et al. (1984) for PAN and peroxyproprionyl nitrate (PPN). All of these measurements were made on gas-phase samples, and we noted that some of the reported band intensities for PAN seemed too large compared to PGN or to PPN. The new infrared intensities reported by Tsalkani and Toupance for PAN make it possible to identify similarities in several of the band intensities of PAN-type molecules.

Several of the vibrational modes of PAN, PPN and PGN involve the peroxynitrate group. These bands have similar absorption frequencies in these molecules and thus might be expected to have similar band intensities. They are the NO 2 scissors mode at 794 cm- 1, the C = O stretch at 1842 cm- 1, and the symmetric and antisymmetric NO2 stretches at 1302 cm- 1 and 1741 cm- 1, respectively. The assignments are from Varetti and Pimentel (1974) and from Gaffney et al. (1984).

Table 1 compares the infrared band intensities for the peroxynitrate group vibrations in PAN, PPN and PGN. The Table also includes the averages of all the data for these PAN-type molecules, excluding the data of Gaffney et al. (1984) for PAN. The uncertainties listed in Table 1 are all 2or values to provide a realistic estimate of the expected errors. For this comparison, the integrated band intensity for the antisymmetric NO2 stretch in PGN was obtained by sub-

tracting the intensity of the C = O stretch of the aldehyde group from the total integrated band intensity of the 1741 cm -1 band (see Rogers and Rhead (1987)) for more details.

The infrared intensities for the absorption bands of PAN, PPN, and PGN listed in Table 1 are quite dose. For the 794 cm- 1 band, the actual intensities for the three molecules are only 3-10% different from the average value; for the 1302 cm- 1 band, the actual intensities are 2-10% different; for the 1741 cm -1 band, the actual intensities are 1-4% different; and for the 1842 cm-1 band, the actual intensities are 6-13% different. Considering the uncertainties and the problems in measuring accurate band intensities, the in- tensities for these bands have nearly the same values. Regard- ing the infrared intensities for PAN reported by Gaffney et al. (1984), only the intensity for the 794 cm- 1 band is close to the average value; for the other three bands, the values differ from the averages by 30-50%.

Table 1 does not include a comparison of the infrared intensity of the C-O stretch in these PAN-type molecules, since the position and infrared intensity of the C-O stretch varies significantly. This band appears at 1163.5 cm -1 in PAN, with a band intensity of 332 __+ 14 cm- 2 as measured by Tsalkani and Toupanee. In PPN, however, the C-O stretch is shifted to 1048 cm- 1 and the band intensity decreases to 131 _ 11 cm-2 atm-1 (Gaffney et al., 1984), while in PGN, this band is probably the absorption band at 1050 cm- t, which has a band intensity of 157+ 12 cm -2 atm-1 (Rogers and Rhead, 1987). Thus, the frequency and intensity of this C-O stretching vibration is obviously affected by the nature of the acyl group, presumably because the carbon atom is directly bonded to the rest of the PAN-type molecule.

This analysis shows that the infrared intensities of PAN reported by Tsalkani and Toupance are more accurate than those reported by Gaffney et al. (1984). It also shows that some of the characteristic vibrational bands of the peroxyn- itrate group in PAN-type molecules have the same average infrared band intensities to within about 10%. These average intensities could be used to estimate approximate concentra- tions of other PAN-type molecules.

* Tsalkani N. and Toupance G. (1989) Atmospheric Envir- onment 23, 1849-1854.

Environmental Science Department General Motors Research Laboratories, Warren, M I 48090-9055, U.S.A.

JERRY D. ROGERS

Table 1. Comparison of integrated band strengths (cm-2 a tm-l ) of selected absorption bands of peroxyacyl nitrates

Wave number (cm- 1 )

Species

794 1302 1741 1842 NO 2 symmetric antisymmetric C = O

scissors NO2 stretch NO2 stretch stretch

PAN * 239 _ 8 270_ 4 563 + 20 262 _ 8 PAN t 247 __+ 6 405 __+ 20 808 + 34 322 __+ 9 PPN t 210 + 14 306 __+ 18 537 _+ 25 262 _ 39 PGN :~ 246 + 13 327 __+ 17 523 __+ 50 213 _ 14 Average § 232 301 541 246

* Tsalkani and Toupance (1989). t Gaffney et al. (1984). :~ Rogers and Rhead (1987). §Excludes the measurements for PAN by Gaffney et al. (1984).

2892 Discussions

REFERENCES

Gaffney J. S., Fajer R. and Senum G. I. (1984) An improved procedure for high purity gaseous peroxyacetyl nitrate production: use of heavy lipid solvents. Atmospheric Envir- onment 18, 215-218.

Rogers J. D. and Rhead L. A. (1987) Peroxyglutary nitrate: formation and infrared spectrum. Atmospheric Environ- ment 21, 2519-2523.

Varetti E. L. and Pimentel G. C. (1974) The infrared spectrum of 15N-labeled peroxyacetylnitrate (PAN) in an oxygen matrix. Spectrochim. Acta 30A, 1069-1072.

T H E C H A R A C T E R I S T I C T I M E T O

A C H I E V E I N T E R F A C I A L P H A S E

E Q U I L I B R I U M I N C L O U D D R O P S *

works which Kumar cites (Schwartz and Freiberg, 1981; Schwartz, 1986; Seinfeld, 1986). However, it was not. For example the analysis of Schwartz and Freiberg (1981) re- sulted in expressions in which the quantity *phasc invariably appeared within a square root, and in Schwartz (1986) this quantity was abandoned in favor of the quantity ~") the - s a t ,

characteristic time for saturating the droplet as governed by interfacial mass transport, linear in the Henry's Law coeffi- cient, and equal to the quantity in Kumar's Equation 10. In retrospect the quantity ~phase is potentially misleading, resulting in the strong solubility dependence reflected in Kumar's table, and therefore should not have been intro- duced. However, I emphasize that the discrepancies implied in the comparison presented by Kumar are only apparent and do not indicate any problem in the analysis and inter- pretation presented in the cited papers.

Aside from the above point, the analysis presented by Kumar is flawed in several major respects. I briefly elaborate on items of concern with Kumar's analysis.

Dissolution of trace atmospheric gases into cloud droplets followed by aqueous-phase reaction is an important atmo- spheric transformation process. Accurate description of this process requires consideration not only of the aqueous-phase solubility and reaction kinetics of these species but also of the kinetics of mass transport coupling the two phases. However, in many circumstances of interest, this mass transport is sufficiently rapid that the rate of aqueous-phase reaction can with good accuracy be evaluated by assuming that the cloud droplets are saturated in the reagent gases. This greatly simplifies the treatment. The validity of the saturation as- sumption can be addressed heuristically by comparing the time constant for reaction of the dissolved gas with the time constants of each of the three pertinent mass transport processes, gas-phase diffusion, interracial mass transport, and aqueous-phase diffusion (Schwartz and Freiberg, 1981; Schwartz, 1986). Readily applicable quantitative criteria have also been presented to ascertain the onset of an arbitrary departure from the rate calculated under the saturation assumption due to each of these three possible sources of mass-transport limitation. These criteria have recently been applied to a re-examination of mass-transport limitation to the rate of in-cloud SO2 oxidation by H202 and 03, taking into account new determinations of the mass-accommoda- tion coefficients of these species (Schwartz, 1988). Expres- sions have also been presented that allow quantitative evalu- ation of single-drop reaction rates in situations where ap- preciable mass-transport limitation is indicated, and this formalism has been extended to permit evaluation of the rate of coupled mass-transport and chemical reactions in ensem- bles of drops, i.e. clouds.

Recently Kumar (1989) has re-examined certain aspects of this problem. His principal point appears to be that the time constant for approach to a steady state diffusive flux of a non- reacting gas into solution in semi-infinite planar geometry (Danckwerts, 1970; Seinfeld, 1986) is qualitatively different from that for a saturating spherical drop, exhibiting a quadratic, rather than linear dependence on the Henry's Law solubility constant of the dissolving gas. The different ex- pressions yield vastly different characteristic times--10 or- ders of magnitude or more--as displayed in Kumar's Table 1. Kumar concludes that it is inappropriate to use the quadratic expression in ascertaining whether the saturation approx- imation is valid in evaluating rates of reaction in spherical drops, a point in which I certainly concur. This point would be a major concern if that had been the approach taken in the

* Kumar S. (1989) Atmospheric Environment 23, 2299- 2304.

This research was performed under the auspices of the United States Department of Energy under contract No. DE- AC02-76CH00016.

(1) Kumar correctly realizes that the time constant for reaching the steady state condition is much smaller in the gas-phase than in solution. (Incidentally, in the example he gives at the bottom of the first column of page 2300, drop radius a=10/~m, gas-phase expression coefficient D~ = 0.1 cm 2 s - ~, the time constant should read 3 × 10- 6 s, not 3 x 10-4s as given.) However, from this realization Kumar

concludes, incorrectly, that the gas-phase concentration of a substance reacting in the aqueous phase can be treated as uniform spatially from the bulk up to the surface of the drop. Constant (temporally) is not equivalent to uniform (spatial- ly). Gas-phase diffusion is in fact more restrictive to achieving a uniform spatial profile than is aqueous-phase diffusion for high-solubility gases, i.e. having Henry's Law coefficient H greater than about 100 M atm-1 (Schwartz and Freiberg, 1981; Schwartz, 1986). Contrary to Kumar's assertion, this source of departure from the saturation condition cannot be neglected.

(2) Since for a reactive species aqueous-phase diffusion and reaction occur concurrently, accurate description of this process requires a differential equation incorporating both processes. Since the differential equation which Kumar sets up and solves (his Equation 3) examines diffusion only in the absence of reaction, it cannot serve as other than a qualitative indication of possible mass-transport limitation to the rate of aqueous-phase reaction. For a quantitative analysis both of the onset of mass-transport limitation and of the magnitude of departure in reaction rate from that calculated under the saturation assumption the reader is referred to Schwartz and Freiberg (1981), especially Equation 18 and Figure 5.

(3) Kumar confuses the issue of achieving phase equilib- rium locally at the interface with that of establishing a uniform spatial profile within the drop. Kumar's Equation (3) indeed yields a time constant which, in the limit of high or low Henry's Law coefficient, corresponds to the character- istic time for saturating the drop (by a non-reactive gas) as governed by aqueous phase diffusion or by the rate of interracial mass transport, respectively (Schwartz, 1986). However, these limits represent entirely different physical phenomena. It is not conducive to physical insight to ascribe mass-transport limitation resulting from the finite rate of aqueous-phase diffusion (e.g. the example in Kumar's Table 2 of ozone reacting at pH 5 with SO 2 at 15 ppb) to a failure to achieve interfacial equilibrium. By applying Figure 4 of Schwartz (1988) to this situation it may be seen that the source of mass-transport limitation is aqueous-phase diffu- sion, not interracial mass-transport; the departure in reaction rate from that calculated under the saturation assumption is about 20%. Interfaciai mass-transport limitation is negli- gible. In other words, the mass-transport limitation is due to a decrease in concentration of ozone as a function of distance from the interface into the interior of the drop, not to a departure from Henry's Law equilibrium at the interface.