- Email: [email protected]
A model for estimating the rate of chemical transformation of a VOC in the troposphere by two pathways: Photolysis by sunlight and hydroxyl radical attack
Chcmosphcre, Vol, 22, Nos 3-4, pp. 305-315. It)91 Printed in (ircat Britain
0045 C,535/'-~1$3.1111+ 0.00 l'crganv,'mPress plc
A MODEL FOR ESTIMATING THE RATE OF CHEMICAL TRANSFORMATION OF A VOC IN THE TROPOSPHERE BY TWO PATHWAYS: PHOTOLYSIS BY SUNLIGHT AND HYDROXYL RADICAL ATTACK
Nigel J. Bunce*, Jamie S. Nakai and Maritza Yawching Department of Chemistry and Biochemistry University of Guelph, Guelph, Ontario Canada, N1G 2W1 Abstract
A simple model has been developed to describe the transformation of a tropospheric constituent by two competing pathways: direct photolysis and attack by hydroxyl radicals. The model makes use of the observations of Platt et al. (1988) that under the condition of low NOx, the concentration of hydroxyl radicals appears to depend linearly on the rate of photolysis of ozone. It has been used to obtain a rapid but rough estimate of the rate of (photo)-chemical transformation of an organic tropospheric constituent and to estimate the tropospheric hydroxyl radical concentration under various conditions of geographical location, season, and time of day. In this work the model is used to describe the tropospheric chemistry of pentachlorophenol, but it is readily extended to other substances. Introduction
Many tropospheric pollutants have the potential for chemical or photochemical transformation prior to deposition. The rates of deposition and transformation determine whether such substances will be deposited in the same or a different chemical form, and whether they will be deposited close to their sources or become globally distributed. For example, PCB's are rather unreactive in the atmosphere and have low deposition rates. As a result, they may be deposited unchanged in locations remote from their source (Risebrough et aL, 1976; Swackhamer et al., 1988; Gregor and Gummer, 1989). By contrast, SO 2 is rapidly oxidized to SO3, and has a high rate of deposition because of the solubility of these gases in water. Consequently acidic deposition occurs as sulfate rather than as sulfite, and is localized relatively close to the source (Finlayson-Pitts and Pitts, 1986). Two common reaction channels for compounds in the troposphere are direct photochemical change under the influence of sunlight, and oxidation initiated by reaction with hydroxyl radicals. Direct photolysis is limited to substances having a chromophore with absorption at wavelengths greater than 290 nm, the short wavelength cut-off for solar radiation in the troposphere. 3O5
Hydroxyl radicals react with the majority of
atmospheric constituents (with the notable exception of chlorofluorocarbons), the common pathways being abstraction of hydrogen atoms and addition to unsaturated centres (Atkinson, 1986). The objective of the present work was to provide an approximation for the rates of chemical and photochemical transformation of a given tropospheric substance and its tropospheric half-life.
This was
undertaken by developing a model which accounted for geographical latitude during any season and at any time of day, and was simple enough to run on a personal computer using readily available spreadsheet software such as Lotus 1-2-3. A secondary objective of the work was to estimate the concentration of OH as a function of geographical location, season, and time of day. This is important because the diurnal variation of the concentration of OH in the troposphere is poorly documented. Experimental determination of the ambient concentration of this important species is technically very difficult, and few measurements have been made (Wang et al., 1984; Perner et al., 1987; Platt et al., 1988, Dorn et aL, 1988). Concept of the model The reactions of OH under tropospheric conditions are invariably second order kinetically, and hence require a knowledge of the hydroxyl radical concentration. [1]
rate
= kl.[X].[OH ]
These rates are often estimated by using a diurnally and seasonally averaged value of the hydroxyl radical concentration, together with experimental or estimated rate constants. This approach is satisfactory for longlived substances, but large diurnal and seasonal fluctuations in the reaction rate may be expected for shortlived compounds. This is because the concentration of OH shows large seasonal and diurnal variation, since its major tropospheric source is the photochemical cleavage of ozone by sunlight (equations [2]-[3]). [2] 03 hv, x = 290-320 nnk 02 + O [3]
O
+ H20
---
2 OH
The concentration of OH, and therefore the rate of reaction with substance X, change with the intensity of the solar flux, as well as with the concentrations of ozone and H20. At any instant, the quasi-steady state concentration of OH may be expressed by equation [4], in which is the proportionality constant between the solar flux I o and the rate of OH formation by ozone photolysis, :~kf[Y] is the rate of all source reactions other than ozone photolysis, and :~kl[X] is the total rate of all sink reactions corresponding to equation [1]. [4]
[OH] = (yIo + £kf[V])/:gkl[X]
The exact dependence of [OH] on the solar flux will be complex, because of the multitude of both sources and sinks of OH in the troposphere.
The work of Platt et al. (1988) suggests that in the unpolluted rural
troposphere the concentration of OH may depend linearly upon the rate of photolysis of ozone. Such a linear relationship (equation 5) implies that under these conditions ozone photolysis must be the predominant source of OH in the troposphere. [51
[OH] -
~,Io/Y.kl[X]
Since the solar flux I o capable of cleaving ozone can be calculated, the data of Platt et al. can be used to deduce the proportionality constant ,//I;kl[X ] between the solar flux and the concentration of OH.
3~17 One of the important reaction partners for OH is nitrogen dioxide, whose reaction with OH [6] has a pseudo-second order rate constant of ca. 1.2 x 10-11 cm 3 molecule 1 s -1 under tropospheric conditions (Lelieveld and Crutzen, 1990). [6]
NO 2 + OH
M .._ HNO3
The work of Dorn et al. (1988) indicates that the linear relationship between the rate of ozone photolysis and the hydroxyl radical concentration (equation [5]) holds only when the concentration of NO 2 is less than about 2 ppb. This condition was fulfilled for the data of Platt et al., and for part of the data set of Dorn et al., as can be seen by examination of Figures 4 and 6, respectively, of these two papers. The model described here is applicable only to tropospheric conditions of low [NO2], although it would be possible to develop an alternative model at high [NO2]. In that case the proportionality between J(O3) and [OH] would be given by 3/k f,[NO2], where k 6 is the rate constant for reaction [6], and [NO2] is given in molecules per cm 3. Development of the model The information needed is the rate of direct photolysis of the constituent (a w)latile organic compound, VOC) by sunlight and the rate of its reaction with OH. As already noted, the rate of reaction with OH requires knowledge of the concentration of OH. The rates of both these processes depend on the intensity of sunlight, although not necessarily over the same range of wavelengths, since the absorption spectrum of the VOC may differ from that of ozone. The substance whose behaviour is modelled here is pentachlorophenol (PCP), a chlorinated aromatic compound whose absorption lies at the short wavelength extreme of the tropospheric solar spectrum. However, the model is readily applied to other VOCs with different absorption characteristics. The following is an outline of the calculation. The rates of light absorption of both ozone and a VOC can be calculated using tabulations of solar intensity vs. wavelength, which are available for specified solar zenith angles, and the absorption spectra of ozone and the VOC. If the zenith angle is known for the time, date, and geographical location of interest, one can sum the total flux of photons absorbed by a given concentration of either ozone or the VOC over all relevant wavelengths. The rates of photolysis then follow if the reaction quantum yields are known. In the case of ozone photolysis, the concentration of OH is assumed to be proportional to the photolysis rate (see above), and the rate of reaction of the VOC with OH is calculable provided that the second order rate constant is known. The calculation is carried out in the following manner. 1. Calculate zenith angle; 2. obtain photon intensity absorbed per second by ozone and by the VOC, and hence calculate the rates of photolysis of ozone and of the VOC; 3. relate the rate of photolysis of ozone to the OH concentration, and use equation [1] to estimate the rate of reaction of the VOC with OH. Both the solar intensity and its spectral distribution depend on the solar zenith angle, which can be calculated using equation [7]-[9].
3(18
[7]
T = T G - (eo + ~r/12) + 1.002739(T L + d)
[8]
H = T -
[9]
cos Z = sin0. sin8 + cos0. coss- cos H
Sidereal time (T, equation [7]) at the appropriate longitude (¢,in radians) is obtained from the Greenwich hour angle of the equinox (TG), the local time of the observer (TL), and the clock difference 'd' between Greenwich Mean Time and the observer's local time. The hour angle (H) of the Sun (equation [8]) is calculated from sidereal time and the right ascension of the Sun (a) at the relevant local time. Finally (equation [8]), the zenith angle (Z) of the Sun is found from the hour angle, the declination (8) of the Sun at the relevant local time, and the observer's latitude (0). The next part of the calculation is to determine the solar fluxes capable of cleaving both ozone and the VOC. We consider first the case of ozone. The information available (Finlayson-Pitts and Pitts, 1986) is the solar intensity Ix, tabulated for different zenith angles as a function of wavelength, the ozone absorption cross section
1,
and the quantum yield Cx for photolysis of O 3 to O *. These parameters are all strongly
wavelength dependent in the range 290-325 nm where ozone absorbs in the troposphere. For weak absorption, the rate constant J(O3) x for photolysis of O 3 to O* per unit area at any wavelength is given by equation [10]. [10]
J(O3) x = I (ohotons) " ~ . ( ~ _ . ~ x -~"" cm2"s " molecule
The values of I x at several zenith angles, ,Ix, and ~ are all taken from the literature (Finlayson-Pitts and Pitts, 1986). At any time of the day, i.e., at each zenith angle, the term (I x ~ x +)x must be summed over the wavelength range 290 - 325 to obtain the overall photolytic rate constant (I x c, x q~)z" Estimates for (I x ~ x +)z at zenith angles between those found in the tables are obtained by fitting to equation [11], in which 'm' is an empirically adjustable parameter whose value is usually about 2.4. [11]
(I x c~x '~)z = (I x a x 6)2:=0 .(cos Z ) m
Equation [12] then gives the rate of photolysis of ozone to O . [12]
-d[03]/dt = (I x cr x ,)z.[O3] The rate of direct photolysis of the VOC is estimated analogously. However for PCP, as for most
organic pollutants, the wavelength dependence of the quantum yield of photolysis is not known at present, and so this parameter must be assumed independent of wavelength ('l~,Cl, = 0.018; Bunce and Nakai, 1989). Once again, interpolated values of (I x ~)z are obtained by fitting to an empirical cosine function (equation [13]). [13]
(I x epcp) Z = (I x a p c p ) z = 0 (cos Z) n
For the case of PCP, the adjustable parameter 'n' has a value near 2.1; in general we can expect 'm' and 'n' to have different values whenever the absorption range of the substance undergoing direct photolysis is different
1 For many organic pollutants, including PCP, molar absorptivities (~., units L mo1-1 em -1, to a logarithmic base of 10) are available rather than absorption cross sections (~). Tile conversion factor is cr = (3.824 x lO-2t).~.
from that of ozone. The relevant wavelength range for J(PCP)x is 290 - 350 nm, since PCP absorbs out to 350 nm. The instantaneous rate of reaction of PCP by direct photolysis is given by equation [14] and the corresponding rate of hydroxyl radical attack by equation [15]. [14]
Photo-rate = -d[PCP]/dt = (I x Crpcp)z . 00pcp • [PeP l
[15]
OH-rate = -d[PCP]/dt = k.[OH].[PCP] = k.13.(Ix, x e)z.[PCP].[O3]
In equation [15], the proportionality constant 13 between the ozone photolysis rate and the steady state concentration of OH has the value 4.3 x 109 (deduced from the work of Platt et aI., 1988). The model has been used under two different initial assumptions, either that the concentration of PCP remains constant during the reaction, or that no additional PCP enters the system once degradation begins. In either case, the calculation has been carried out as a numerical integration, equation [16], with the use of a spreadsheet; Z i and, for the second assumption, [PCP]i both take values appropriate for the time increment At.. l
[161
-a[PCP]i = {(I x apcp)zi - 4pcp + k.13.(Ix 4, x Cr)zi.[Og]}.[PCP]i.at~ Because Z i and hence [OH]i change with location, season, and time of day, equation [16] does not
correspond to a pseudo first order rate expression. This means that the atmospheric half-life of a VOC cannot be calculated directly. The simplest means of finding the half-life is to examine the spreadsheet to determine the time at which exactly half of the original substrate has reacted.
For substrates where only a small
percentage loss occurs in one day, the following approximation is useful. [17]
In [VOC](time zero) - In [VOC](1 day) = "k".l day
[18]
tl/a
= (ln 2) / "k"
The half-life, in days, is obtained under the pretense that loss of the VOC proceeds monotonically through the day, and can be described by the "rate constant", "k". However, when a large proportion of the VOC disappears in a single day, the half-life must be obtained literally by finding the elapsed time needed for the ccmcentration of substrate to fall to half its initial value. Results
Figure 1 shows typical profiles of the change in the zenith angle over the course of a day for different values of the minimum zenith angle. Since the rates of photolysis of both PCP and ozone are greatest near Z . , the period close to midday contributes most to the total amount of reaction during the day. mm
Figure 2 shows the best fit between the computed and fitted values of (I x ~ x e)z (Figure 2a) and between the computed and fitted values of (I x ~pcp) Z (Figure 2b). Both curves refer to the latitude of Toronto, Ontario (43.70°N, 79.42°W) on March 21. Parameters 'm' and 'n' are adjusted so that the optimum fit is obtained for minimum values of Z experienced on the day in question. The diurnal variation in the concentration of OH, calculated from the present model, is shown as the continuous line in Figure 3. These data refer to the Black Forest (47.88 ° N) on June 25, and thus represent the calibration data from the results of Platt et al (1988). The experimental values obtained by Platt et al. are included.
200 I / 175 1"~'~
o) Miami, Florida: Jcn 22 b) Toronto Ontario: March 21
I
150 +~--"...~
c) Toronto, Ontario: Jan 1
0/
I 3
0
I 6
I 9
I 12
/
I 18
t
15
21
24
Day (hr)
Time of
Figure 1: Variation of zenith angle over a full day (a) Miami, Florida, January 22; (b) Toronto, Ontario, March 21; (c) Toronto, Ontario, January 1.
2a
0
+-
I
10
20
I
I
I
I
.30 40 50 60 Zenith Angle (degrees)
,
-,
~
70
80
90
70
80
90
o o [2_ 0_
2b
~o 1.0 c o c © o
\
x n=2.1
0.5-
0.0
I-
0
10
20
30 40 50 60 Zenith Angle (degrees)
Figure 2: Best fit between the computed and fitted values of (I x ¢ x O)z (Figure 2a) and between the computed and fitted values of (I x ~rece) z (Figure 2b) for Toronto, Ontario on July l. Optimum values of parameters 'm' and
'n'
are 2.4 and 2.1 respectively.
9 ~
. . . . . . . . . . . . . . . . . . . . . . . .
8 c '1
o E -
~
T
7 -
6+
~#
/
//
4
6
,,
±
8
10
12
!4
16
\.\ 18
20
r i m e of Do}, (hr)
Figure 3: The diurnal variation in the concentration of OH in the Black Forest (47.88 ° N) on June 25. These data represent the calibration of the model to the results of Platt et al. (1988). Figure 4a shows the calculated rates of direct photolysis and OH attack for PCP at Windsor, Ontario (42.30°N, 83.00°W) on February 1. The gas phase rate constant for the reaction between OH and PCP was estimated as 5 x 10-13 cm 3 molecule -1 s -1 using the method of Zetsch (1982), and a value of 1 ng m -3 for the concentration of PCP was assumed (compare literature values ranging from 0.25 to 7.8 ng m -3, World Health Organization, 1987).
Direct photolysis is predicted to be the dominant process for this pollutant, as was
anticipated in a previous preliminary study from our laboratory (Bunce and Nakai, 1989).
9--
! u~ 6 co r~ 'F5 .
•
o
%
/ .
.
.
.
~ • 4-
Photolysis
•
\, ,
/,/ /
cJ o 5 x J 2&
xx \
\
\ /"
\\' ''\
/ OH A t t a c k
\ \,
5
10
12
14
!6
18
l i m e of Day (hr)
Figure 4a:
Calculated rates of direct photolysis and OH attack for PCP at Windsor, Ontario (42.30°N,
83.00°W) on February 1.
312
0.12-->~ U. I ' d -
o
48 £ c'os }
\ ,\
e/"
"N\ o co
= C'.06
\
:
',! "~ © 8.3,4 © <
-
0.02-
08,3 - - J - ~ -' 8
9
10
11
12
"3
14
15
16
17
18
Time of Day (h'-)
Figure 4b: Ratio of the rate of [OH radical attack / direct photolysis] for reaction of PCP at Windsor, Ontario
(42.30°N, 83.00°W) on February 1. As expected, the calculated rates of both processes maximize at solar noon, when Z is at a minimum and the solar intensity is greatest. However, the ratio of the rates {OH attack/direct photolysis} is not constant over the day; it is at a maximum at solar noon (Figure 4b). This is because PCP absorbs out to longer wavelengths than ozone; since the short wavelength end of the solar spectrum is attenuated the most at large Z, the relative importance of the direct photolysis is greatest when the Sun is low in the sky. A more detailed estimation of the atmospheric chemistry of PCP is now presented for the latitude of Toronto, Ontario (43.70°N, 79.42°W). Rates of reaction, in percent per hour, are given for several times of the year in Table 1. The half-life of PCP in the troposphere changes substantially with the season, ranging from 9 days in early January to less than one day in mid-summer. Note that in mid-summer, we cannot be more precise than this; it takes somewhat less than one day for half the PCP to react, but the actual time period depends on when the clock starts (see Figure 5). Table 1: Kinetic parameters for reaction of PCP at several seasons at 43.70 °N.
Date January 1 February 1 March 1 April 1 May 1 June 1 July 1
Percent per hour at noon 1.8 2.8 4.8 7.4 9.4 10.5 10.6
Half-life, days 9 5 2-3 1-2 1-2 <1 <1
313
.......
I
,{~,, E
0.8 ~
\~',~'\ ~"
-
~'~"~
~\
.E rD
\"~-
darn. 1 Feb. !
~ \
q
Ma~ch 1
___
I
6'2 ]
i
" Apri!
G
[
.
.
.
1
Ma>, i .
June
i
i 0
10
20
50
40
50
60
Time (hr)
Figure 5: Reaction of PCP in the atmosphere at Toronto, Ontario over 4 days at several seasons (Jan. 1, Feb. 1, March 1, April 1, May 1, June 1). Limitations of the model 1. Ozone photolysis and OH radical concentration
We have assumed that the OH concentration is proportional to the rate of ozone photolysis, equation [5]. This assumption is not valid for urban atmospheres containing high concentrations of NO 2 (Dorn et at., 1988). Whether it is generally valid in the "clean" troposphere will not be known until many more experimental determinations of the actual concentration of OH in the troposphere have been made.
Since the
proportionality constant 13is based on a single set of measurements (Platt et al., 1988), it will undoubtedly need updating in the future. Additionally, its variation, for example on the concentration of water vapour, is not taken into account. As noted by Finlayson-Pitts and Pitts (1986), the fraction (f) of O* which reacts with water vapour is given by equation [19], where k 2 and k 3 are the rate constants for reactions [2] and [3], and 'M' is a third body (any atmospheric component). [191
f =
k2.lH20 ]
k2[H20] + k3[M] At 1 atm, 25 °C, and 50% relative humidity ([H20 ] = 3.9 x 1017 molecules cm-3), f has the value 0.11. This fraction changes with the water content of the atmosphere, and presumably with temperature, since k2 and k3 are unlikely to have the same temperature dependence. 2. Other reaction channels
Although direct photolysis and hydroxyl radical attack are important reaction channels for VOC's, the model ignores other reactions such as those of the substrate with 0 3 and NO 3. Direct reaction with ozone
314 may be important for unsaturated organics, while hydrogen abstraction by the nitrate free radical can be a significant sink for organic comopounds during darkness, when the concentration of OH is essentially zero. 3. PCP photolysis The quantum yield for decomposition of PCP was taken to be independent of wavelength. The wavelength dependence of the quantum yield is known for very few organic reactions. However, should the wavelength dependence of this parameter become available, it would be a simple matter to modify equation [14] to be the analog of equation [12]. Conclusions We have achieved our goal of developing a simple model to describe the transformation of an atmospheric pollutant in the troposphere by the competing routes of direct photolysis and hydroxyl radical attack. Pentachlorophenol was chosen as a model pollutant, but the calculation is applied to other constituents of the atmosphere, simply by incorporating the appropriate absorptivity data and quantum yield of phototysis, and the rate constant for the reaction with OH. This model can be useful for estimating rates of reaction of a target VOC by these two major reaction channels, to identify which of these pathways is likely to predominate in the atmosphere, and to provide an approximation for the tropospheric half-life for the VOC under a variety of geographical and seasonal conditions. It allows one to estimate whether the lifetime is of the order of hours, days or months. To obtain a more precise estimate, one would need to know the diurnal and seasonal dependence of several parameters, such as the concentrations of ozone and water vapour, the temperature, and the temperature dependence of the rate constants in equation [19] and of the rate constant for the reaction of the pollutant with OH. This information is frequently unavailable, besides which, the refinement for large files of input data is inconsistent with the goal of a simple model. By comparison with estimates of the rates of transport and deposition, it will be possible to determine whether the VOC is likely to undergo chemical or photochemical transformation in the atmosphere, and hence whether deposition is likely in the original chemical form or a different one. More detailed modelling studies may then be undertaken if necessary. Acknowledgements We thank the Ontario Ministry of the Environment (Air Resources Branch) and Environment Canada (Atmospheric Environment Service) for financial support, and Dr. J.L. Hunt of the Department of Physics, University of Guelph, for discussions on the calculation of zenith angles. References Atkinson, R. (1986) Kinetics and mechanisms of the gas-phase reactions of the hydroxyl radical with organic compounds under atmospheric conditions. Chem. Rev. 86 69-201. Bunce, N.J. and Nakai, J.S. (1989) The atmospheric chemistry of chlorinated phenols. JAPCA 39 820-823. Crutzen, P.J. (1982) The global distribution of hydroxyl. In Atmospheric Chemistry, pp. 313-328. Goldberg, D.G. (ed.), Ann Arbor Press, Ann Arbor, MI.
315
Dorn, H-P., Callies, J., Platt, U., and Ehhalt, D.H. (1988) Measurement of tropospheric OH concentrations by laser long-path absorption spectroscopy. Tellus 40B 437-445. Finlayson-Pitts, B.J. and Pitts, J.N., Jr. (1986) Atmospheric Chemistry, pp. 93-199, 645-713. Wiley, New York. Gregor, D.J. and Gummer, W.D. (1989) Evidence of atmospheric transport and deposition of organochlorine pesticides and polychlorinated biphenyls in Canadian Arctic snow. Environ. Sci. Technol., 23, 561-565. Lelieveld, J. and Crutzen, P.J. (1990) Influences of cloud photochemical processes on tropospheric ozone. Nature, 343, 227-233. Perner, D., Platt, U., Trainer, M., Hubler, G., Drummond, J., Junkermann, W., Rudolph, J., Schubert, B., Volz, A. and Ehhalt, D.H. (1987) Tropospheric OH concentrations: a comparison of field data with model predictions. J. Atmos. Chem. 5 185-216. Platt, U., Rateike, M., Junkermann, W., Rudolph, J. and Ehhalt, D.H. (1988) New tropospheric OH measurements. J. geophys. Res. 93 5159-5166. Risebrough, R.W., Walker, T.T., Schmidt, de Lappe, B.W. and Connors, C.W. (1976) Transfer of chlorinated biphenyls to Antactica. Nature 264 738-739. Swackhamer, D.L., McVeety, B.D., and Hites, R.A. (1988) Deposition and evaporation of polychlorinated biphenyl congeners to and from Siskiwit Lake, Isle Royale, Lake Superior. Environ. Sci. Technol., 22, 664672. Wang, C.C., Davis, L.I., Jr., Wu, C.H., Japar, S., Niki, H. and Weinstock, B. (1984) Hydroxyl radical concentrations measured in ambient air. Science 189 797-800. World Health Organization (1987) "Environmental Health Criteria 71: Pentachlorophenor', United Nations Environmental Program. Zetsch, C. (1982) Predicting the rate of OH-addition to aromatics using ~+-electrophilic substitutent constants for mono- and polysubstituted benzene. From "15th Informal Conference on Photochemistry" Abstract A11, Stanford, CA; cited by Atkinson (1986).
(P,cceixcd m Gcrnmn'~ 15 December 1990; acccpted 26 January 1991)
0045 C,535/'-~1$3.1111+ 0.00 l'crganv,'mPress plc
A MODEL FOR ESTIMATING THE RATE OF CHEMICAL TRANSFORMATION OF A VOC IN THE TROPOSPHERE BY TWO PATHWAYS: PHOTOLYSIS BY SUNLIGHT AND HYDROXYL RADICAL ATTACK
Nigel J. Bunce*, Jamie S. Nakai and Maritza Yawching Department of Chemistry and Biochemistry University of Guelph, Guelph, Ontario Canada, N1G 2W1 Abstract
A simple model has been developed to describe the transformation of a tropospheric constituent by two competing pathways: direct photolysis and attack by hydroxyl radicals. The model makes use of the observations of Platt et al. (1988) that under the condition of low NOx, the concentration of hydroxyl radicals appears to depend linearly on the rate of photolysis of ozone. It has been used to obtain a rapid but rough estimate of the rate of (photo)-chemical transformation of an organic tropospheric constituent and to estimate the tropospheric hydroxyl radical concentration under various conditions of geographical location, season, and time of day. In this work the model is used to describe the tropospheric chemistry of pentachlorophenol, but it is readily extended to other substances. Introduction
Many tropospheric pollutants have the potential for chemical or photochemical transformation prior to deposition. The rates of deposition and transformation determine whether such substances will be deposited in the same or a different chemical form, and whether they will be deposited close to their sources or become globally distributed. For example, PCB's are rather unreactive in the atmosphere and have low deposition rates. As a result, they may be deposited unchanged in locations remote from their source (Risebrough et aL, 1976; Swackhamer et al., 1988; Gregor and Gummer, 1989). By contrast, SO 2 is rapidly oxidized to SO3, and has a high rate of deposition because of the solubility of these gases in water. Consequently acidic deposition occurs as sulfate rather than as sulfite, and is localized relatively close to the source (Finlayson-Pitts and Pitts, 1986). Two common reaction channels for compounds in the troposphere are direct photochemical change under the influence of sunlight, and oxidation initiated by reaction with hydroxyl radicals. Direct photolysis is limited to substances having a chromophore with absorption at wavelengths greater than 290 nm, the short wavelength cut-off for solar radiation in the troposphere. 3O5
Hydroxyl radicals react with the majority of
atmospheric constituents (with the notable exception of chlorofluorocarbons), the common pathways being abstraction of hydrogen atoms and addition to unsaturated centres (Atkinson, 1986). The objective of the present work was to provide an approximation for the rates of chemical and photochemical transformation of a given tropospheric substance and its tropospheric half-life.
This was
undertaken by developing a model which accounted for geographical latitude during any season and at any time of day, and was simple enough to run on a personal computer using readily available spreadsheet software such as Lotus 1-2-3. A secondary objective of the work was to estimate the concentration of OH as a function of geographical location, season, and time of day. This is important because the diurnal variation of the concentration of OH in the troposphere is poorly documented. Experimental determination of the ambient concentration of this important species is technically very difficult, and few measurements have been made (Wang et al., 1984; Perner et al., 1987; Platt et al., 1988, Dorn et aL, 1988). Concept of the model The reactions of OH under tropospheric conditions are invariably second order kinetically, and hence require a knowledge of the hydroxyl radical concentration. [1]
rate
= kl.[X].[OH ]
These rates are often estimated by using a diurnally and seasonally averaged value of the hydroxyl radical concentration, together with experimental or estimated rate constants. This approach is satisfactory for longlived substances, but large diurnal and seasonal fluctuations in the reaction rate may be expected for shortlived compounds. This is because the concentration of OH shows large seasonal and diurnal variation, since its major tropospheric source is the photochemical cleavage of ozone by sunlight (equations [2]-[3]). [2] 03 hv, x = 290-320 nnk 02 + O [3]
O
+ H20
---
2 OH
The concentration of OH, and therefore the rate of reaction with substance X, change with the intensity of the solar flux, as well as with the concentrations of ozone and H20. At any instant, the quasi-steady state concentration of OH may be expressed by equation [4], in which is the proportionality constant between the solar flux I o and the rate of OH formation by ozone photolysis, :~kf[Y] is the rate of all source reactions other than ozone photolysis, and :~kl[X] is the total rate of all sink reactions corresponding to equation [1]. [4]
[OH] = (yIo + £kf[V])/:gkl[X]
The exact dependence of [OH] on the solar flux will be complex, because of the multitude of both sources and sinks of OH in the troposphere.
The work of Platt et al. (1988) suggests that in the unpolluted rural
troposphere the concentration of OH may depend linearly upon the rate of photolysis of ozone. Such a linear relationship (equation 5) implies that under these conditions ozone photolysis must be the predominant source of OH in the troposphere. [51
[OH] -
~,Io/Y.kl[X]
Since the solar flux I o capable of cleaving ozone can be calculated, the data of Platt et al. can be used to deduce the proportionality constant ,//I;kl[X ] between the solar flux and the concentration of OH.
3~17 One of the important reaction partners for OH is nitrogen dioxide, whose reaction with OH [6] has a pseudo-second order rate constant of ca. 1.2 x 10-11 cm 3 molecule 1 s -1 under tropospheric conditions (Lelieveld and Crutzen, 1990). [6]
NO 2 + OH
M .._ HNO3
The work of Dorn et al. (1988) indicates that the linear relationship between the rate of ozone photolysis and the hydroxyl radical concentration (equation [5]) holds only when the concentration of NO 2 is less than about 2 ppb. This condition was fulfilled for the data of Platt et al., and for part of the data set of Dorn et al., as can be seen by examination of Figures 4 and 6, respectively, of these two papers. The model described here is applicable only to tropospheric conditions of low [NO2], although it would be possible to develop an alternative model at high [NO2]. In that case the proportionality between J(O3) and [OH] would be given by 3/k f,[NO2], where k 6 is the rate constant for reaction [6], and [NO2] is given in molecules per cm 3. Development of the model The information needed is the rate of direct photolysis of the constituent (a w)latile organic compound, VOC) by sunlight and the rate of its reaction with OH. As already noted, the rate of reaction with OH requires knowledge of the concentration of OH. The rates of both these processes depend on the intensity of sunlight, although not necessarily over the same range of wavelengths, since the absorption spectrum of the VOC may differ from that of ozone. The substance whose behaviour is modelled here is pentachlorophenol (PCP), a chlorinated aromatic compound whose absorption lies at the short wavelength extreme of the tropospheric solar spectrum. However, the model is readily applied to other VOCs with different absorption characteristics. The following is an outline of the calculation. The rates of light absorption of both ozone and a VOC can be calculated using tabulations of solar intensity vs. wavelength, which are available for specified solar zenith angles, and the absorption spectra of ozone and the VOC. If the zenith angle is known for the time, date, and geographical location of interest, one can sum the total flux of photons absorbed by a given concentration of either ozone or the VOC over all relevant wavelengths. The rates of photolysis then follow if the reaction quantum yields are known. In the case of ozone photolysis, the concentration of OH is assumed to be proportional to the photolysis rate (see above), and the rate of reaction of the VOC with OH is calculable provided that the second order rate constant is known. The calculation is carried out in the following manner. 1. Calculate zenith angle; 2. obtain photon intensity absorbed per second by ozone and by the VOC, and hence calculate the rates of photolysis of ozone and of the VOC; 3. relate the rate of photolysis of ozone to the OH concentration, and use equation [1] to estimate the rate of reaction of the VOC with OH. Both the solar intensity and its spectral distribution depend on the solar zenith angle, which can be calculated using equation [7]-[9].
3(18
[7]
T = T G - (eo + ~r/12) + 1.002739(T L + d)
[8]
H = T -
[9]
cos Z = sin0. sin8 + cos0. coss- cos H
Sidereal time (T, equation [7]) at the appropriate longitude (¢,in radians) is obtained from the Greenwich hour angle of the equinox (TG), the local time of the observer (TL), and the clock difference 'd' between Greenwich Mean Time and the observer's local time. The hour angle (H) of the Sun (equation [8]) is calculated from sidereal time and the right ascension of the Sun (a) at the relevant local time. Finally (equation [8]), the zenith angle (Z) of the Sun is found from the hour angle, the declination (8) of the Sun at the relevant local time, and the observer's latitude (0). The next part of the calculation is to determine the solar fluxes capable of cleaving both ozone and the VOC. We consider first the case of ozone. The information available (Finlayson-Pitts and Pitts, 1986) is the solar intensity Ix, tabulated for different zenith angles as a function of wavelength, the ozone absorption cross section
1,
and the quantum yield Cx for photolysis of O 3 to O *. These parameters are all strongly
wavelength dependent in the range 290-325 nm where ozone absorbs in the troposphere. For weak absorption, the rate constant J(O3) x for photolysis of O 3 to O* per unit area at any wavelength is given by equation [10]. [10]
J(O3) x = I (ohotons) " ~ . ( ~ _ . ~ x -~"" cm2"s " molecule
The values of I x at several zenith angles, ,Ix, and ~ are all taken from the literature (Finlayson-Pitts and Pitts, 1986). At any time of the day, i.e., at each zenith angle, the term (I x ~ x +)x must be summed over the wavelength range 290 - 325 to obtain the overall photolytic rate constant (I x c, x q~)z" Estimates for (I x ~ x +)z at zenith angles between those found in the tables are obtained by fitting to equation [11], in which 'm' is an empirically adjustable parameter whose value is usually about 2.4. [11]
(I x c~x '~)z = (I x a x 6)2:=0 .(cos Z ) m
Equation [12] then gives the rate of photolysis of ozone to O . [12]
-d[03]/dt = (I x cr x ,)z.[O3] The rate of direct photolysis of the VOC is estimated analogously. However for PCP, as for most
organic pollutants, the wavelength dependence of the quantum yield of photolysis is not known at present, and so this parameter must be assumed independent of wavelength ('l~,Cl, = 0.018; Bunce and Nakai, 1989). Once again, interpolated values of (I x ~)z are obtained by fitting to an empirical cosine function (equation [13]). [13]
(I x epcp) Z = (I x a p c p ) z = 0 (cos Z) n
For the case of PCP, the adjustable parameter 'n' has a value near 2.1; in general we can expect 'm' and 'n' to have different values whenever the absorption range of the substance undergoing direct photolysis is different
1 For many organic pollutants, including PCP, molar absorptivities (~., units L mo1-1 em -1, to a logarithmic base of 10) are available rather than absorption cross sections (~). Tile conversion factor is cr = (3.824 x lO-2t).~.
from that of ozone. The relevant wavelength range for J(PCP)x is 290 - 350 nm, since PCP absorbs out to 350 nm. The instantaneous rate of reaction of PCP by direct photolysis is given by equation [14] and the corresponding rate of hydroxyl radical attack by equation [15]. [14]
Photo-rate = -d[PCP]/dt = (I x Crpcp)z . 00pcp • [PeP l
[15]
OH-rate = -d[PCP]/dt = k.[OH].[PCP] = k.13.(Ix, x e)z.[PCP].[O3]
In equation [15], the proportionality constant 13 between the ozone photolysis rate and the steady state concentration of OH has the value 4.3 x 109 (deduced from the work of Platt et aI., 1988). The model has been used under two different initial assumptions, either that the concentration of PCP remains constant during the reaction, or that no additional PCP enters the system once degradation begins. In either case, the calculation has been carried out as a numerical integration, equation [16], with the use of a spreadsheet; Z i and, for the second assumption, [PCP]i both take values appropriate for the time increment At.. l
[161
-a[PCP]i = {(I x apcp)zi - 4pcp + k.13.(Ix 4, x Cr)zi.[Og]}.[PCP]i.at~ Because Z i and hence [OH]i change with location, season, and time of day, equation [16] does not
correspond to a pseudo first order rate expression. This means that the atmospheric half-life of a VOC cannot be calculated directly. The simplest means of finding the half-life is to examine the spreadsheet to determine the time at which exactly half of the original substrate has reacted.
For substrates where only a small
percentage loss occurs in one day, the following approximation is useful. [17]
In [VOC](time zero) - In [VOC](1 day) = "k".l day
[18]
tl/a
= (ln 2) / "k"
The half-life, in days, is obtained under the pretense that loss of the VOC proceeds monotonically through the day, and can be described by the "rate constant", "k". However, when a large proportion of the VOC disappears in a single day, the half-life must be obtained literally by finding the elapsed time needed for the ccmcentration of substrate to fall to half its initial value. Results
Figure 1 shows typical profiles of the change in the zenith angle over the course of a day for different values of the minimum zenith angle. Since the rates of photolysis of both PCP and ozone are greatest near Z . , the period close to midday contributes most to the total amount of reaction during the day. mm
Figure 2 shows the best fit between the computed and fitted values of (I x ~ x e)z (Figure 2a) and between the computed and fitted values of (I x ~pcp) Z (Figure 2b). Both curves refer to the latitude of Toronto, Ontario (43.70°N, 79.42°W) on March 21. Parameters 'm' and 'n' are adjusted so that the optimum fit is obtained for minimum values of Z experienced on the day in question. The diurnal variation in the concentration of OH, calculated from the present model, is shown as the continuous line in Figure 3. These data refer to the Black Forest (47.88 ° N) on June 25, and thus represent the calibration data from the results of Platt et al (1988). The experimental values obtained by Platt et al. are included.
200 I / 175 1"~'~
o) Miami, Florida: Jcn 22 b) Toronto Ontario: March 21
I
150 +~--"...~
c) Toronto, Ontario: Jan 1
0/
I 3
0
I 6
I 9
I 12
/
I 18
t
15
21
24
Day (hr)
Time of
Figure 1: Variation of zenith angle over a full day (a) Miami, Florida, January 22; (b) Toronto, Ontario, March 21; (c) Toronto, Ontario, January 1.
2a
0
+-
I
10
20
I
I
I
I
.30 40 50 60 Zenith Angle (degrees)
,
-,
~
70
80
90
70
80
90
o o [2_ 0_
2b
~o 1.0 c o c © o
\
x n=2.1
0.5-
0.0
I-
0
10
20
30 40 50 60 Zenith Angle (degrees)
Figure 2: Best fit between the computed and fitted values of (I x ¢ x O)z (Figure 2a) and between the computed and fitted values of (I x ~rece) z (Figure 2b) for Toronto, Ontario on July l. Optimum values of parameters 'm' and
'n'
are 2.4 and 2.1 respectively.
9 ~
. . . . . . . . . . . . . . . . . . . . . . . .
8 c '1
o E -
~
T
7 -
6+
~#
/
//
4
6
,,
±
8
10
12
!4
16
\.\ 18
20
r i m e of Do}, (hr)
Figure 3: The diurnal variation in the concentration of OH in the Black Forest (47.88 ° N) on June 25. These data represent the calibration of the model to the results of Platt et al. (1988). Figure 4a shows the calculated rates of direct photolysis and OH attack for PCP at Windsor, Ontario (42.30°N, 83.00°W) on February 1. The gas phase rate constant for the reaction between OH and PCP was estimated as 5 x 10-13 cm 3 molecule -1 s -1 using the method of Zetsch (1982), and a value of 1 ng m -3 for the concentration of PCP was assumed (compare literature values ranging from 0.25 to 7.8 ng m -3, World Health Organization, 1987).
Direct photolysis is predicted to be the dominant process for this pollutant, as was
anticipated in a previous preliminary study from our laboratory (Bunce and Nakai, 1989).
9--
! u~ 6 co r~ 'F5 .
•
o
%
/ .
.
.
.
~ • 4-
Photolysis
•
\, ,
/,/ /
cJ o 5 x J 2&
xx \
\
\ /"
\\' ''\
/ OH A t t a c k
\ \,
5
10
12
14
!6
18
l i m e of Day (hr)
Figure 4a:
Calculated rates of direct photolysis and OH attack for PCP at Windsor, Ontario (42.30°N,
83.00°W) on February 1.
312
0.12-->~ U. I ' d -
o
48 £ c'os }
\ ,\
e/"
"N\ o co
= C'.06
\
:
',! "~ © 8.3,4 © <
-
0.02-
08,3 - - J - ~ -' 8
9
10
11
12
"3
14
15
16
17
18
Time of Day (h'-)
Figure 4b: Ratio of the rate of [OH radical attack / direct photolysis] for reaction of PCP at Windsor, Ontario
(42.30°N, 83.00°W) on February 1. As expected, the calculated rates of both processes maximize at solar noon, when Z is at a minimum and the solar intensity is greatest. However, the ratio of the rates {OH attack/direct photolysis} is not constant over the day; it is at a maximum at solar noon (Figure 4b). This is because PCP absorbs out to longer wavelengths than ozone; since the short wavelength end of the solar spectrum is attenuated the most at large Z, the relative importance of the direct photolysis is greatest when the Sun is low in the sky. A more detailed estimation of the atmospheric chemistry of PCP is now presented for the latitude of Toronto, Ontario (43.70°N, 79.42°W). Rates of reaction, in percent per hour, are given for several times of the year in Table 1. The half-life of PCP in the troposphere changes substantially with the season, ranging from 9 days in early January to less than one day in mid-summer. Note that in mid-summer, we cannot be more precise than this; it takes somewhat less than one day for half the PCP to react, but the actual time period depends on when the clock starts (see Figure 5). Table 1: Kinetic parameters for reaction of PCP at several seasons at 43.70 °N.
Date January 1 February 1 March 1 April 1 May 1 June 1 July 1
Percent per hour at noon 1.8 2.8 4.8 7.4 9.4 10.5 10.6
Half-life, days 9 5 2-3 1-2 1-2 <1 <1
313
.......
I
,{~,, E
0.8 ~
\~',~'\ ~"
-
~'~"~
~\
.E rD
\"~-
darn. 1 Feb. !
~ \
q
Ma~ch 1
___
I
6'2 ]
i
" Apri!
G
[
.
.
.
1
Ma>, i .
June
i
i 0
10
20
50
40
50
60
Time (hr)
Figure 5: Reaction of PCP in the atmosphere at Toronto, Ontario over 4 days at several seasons (Jan. 1, Feb. 1, March 1, April 1, May 1, June 1). Limitations of the model 1. Ozone photolysis and OH radical concentration
We have assumed that the OH concentration is proportional to the rate of ozone photolysis, equation [5]. This assumption is not valid for urban atmospheres containing high concentrations of NO 2 (Dorn et at., 1988). Whether it is generally valid in the "clean" troposphere will not be known until many more experimental determinations of the actual concentration of OH in the troposphere have been made.
Since the
proportionality constant 13is based on a single set of measurements (Platt et al., 1988), it will undoubtedly need updating in the future. Additionally, its variation, for example on the concentration of water vapour, is not taken into account. As noted by Finlayson-Pitts and Pitts (1986), the fraction (f) of O* which reacts with water vapour is given by equation [19], where k 2 and k 3 are the rate constants for reactions [2] and [3], and 'M' is a third body (any atmospheric component). [191
f =
k2.lH20 ]
k2[H20] + k3[M] At 1 atm, 25 °C, and 50% relative humidity ([H20 ] = 3.9 x 1017 molecules cm-3), f has the value 0.11. This fraction changes with the water content of the atmosphere, and presumably with temperature, since k2 and k3 are unlikely to have the same temperature dependence. 2. Other reaction channels
Although direct photolysis and hydroxyl radical attack are important reaction channels for VOC's, the model ignores other reactions such as those of the substrate with 0 3 and NO 3. Direct reaction with ozone
314 may be important for unsaturated organics, while hydrogen abstraction by the nitrate free radical can be a significant sink for organic comopounds during darkness, when the concentration of OH is essentially zero. 3. PCP photolysis The quantum yield for decomposition of PCP was taken to be independent of wavelength. The wavelength dependence of the quantum yield is known for very few organic reactions. However, should the wavelength dependence of this parameter become available, it would be a simple matter to modify equation [14] to be the analog of equation [12]. Conclusions We have achieved our goal of developing a simple model to describe the transformation of an atmospheric pollutant in the troposphere by the competing routes of direct photolysis and hydroxyl radical attack. Pentachlorophenol was chosen as a model pollutant, but the calculation is applied to other constituents of the atmosphere, simply by incorporating the appropriate absorptivity data and quantum yield of phototysis, and the rate constant for the reaction with OH. This model can be useful for estimating rates of reaction of a target VOC by these two major reaction channels, to identify which of these pathways is likely to predominate in the atmosphere, and to provide an approximation for the tropospheric half-life for the VOC under a variety of geographical and seasonal conditions. It allows one to estimate whether the lifetime is of the order of hours, days or months. To obtain a more precise estimate, one would need to know the diurnal and seasonal dependence of several parameters, such as the concentrations of ozone and water vapour, the temperature, and the temperature dependence of the rate constants in equation [19] and of the rate constant for the reaction of the pollutant with OH. This information is frequently unavailable, besides which, the refinement for large files of input data is inconsistent with the goal of a simple model. By comparison with estimates of the rates of transport and deposition, it will be possible to determine whether the VOC is likely to undergo chemical or photochemical transformation in the atmosphere, and hence whether deposition is likely in the original chemical form or a different one. More detailed modelling studies may then be undertaken if necessary. Acknowledgements We thank the Ontario Ministry of the Environment (Air Resources Branch) and Environment Canada (Atmospheric Environment Service) for financial support, and Dr. J.L. Hunt of the Department of Physics, University of Guelph, for discussions on the calculation of zenith angles. References Atkinson, R. (1986) Kinetics and mechanisms of the gas-phase reactions of the hydroxyl radical with organic compounds under atmospheric conditions. Chem. Rev. 86 69-201. Bunce, N.J. and Nakai, J.S. (1989) The atmospheric chemistry of chlorinated phenols. JAPCA 39 820-823. Crutzen, P.J. (1982) The global distribution of hydroxyl. In Atmospheric Chemistry, pp. 313-328. Goldberg, D.G. (ed.), Ann Arbor Press, Ann Arbor, MI.
315
Dorn, H-P., Callies, J., Platt, U., and Ehhalt, D.H. (1988) Measurement of tropospheric OH concentrations by laser long-path absorption spectroscopy. Tellus 40B 437-445. Finlayson-Pitts, B.J. and Pitts, J.N., Jr. (1986) Atmospheric Chemistry, pp. 93-199, 645-713. Wiley, New York. Gregor, D.J. and Gummer, W.D. (1989) Evidence of atmospheric transport and deposition of organochlorine pesticides and polychlorinated biphenyls in Canadian Arctic snow. Environ. Sci. Technol., 23, 561-565. Lelieveld, J. and Crutzen, P.J. (1990) Influences of cloud photochemical processes on tropospheric ozone. Nature, 343, 227-233. Perner, D., Platt, U., Trainer, M., Hubler, G., Drummond, J., Junkermann, W., Rudolph, J., Schubert, B., Volz, A. and Ehhalt, D.H. (1987) Tropospheric OH concentrations: a comparison of field data with model predictions. J. Atmos. Chem. 5 185-216. Platt, U., Rateike, M., Junkermann, W., Rudolph, J. and Ehhalt, D.H. (1988) New tropospheric OH measurements. J. geophys. Res. 93 5159-5166. Risebrough, R.W., Walker, T.T., Schmidt, de Lappe, B.W. and Connors, C.W. (1976) Transfer of chlorinated biphenyls to Antactica. Nature 264 738-739. Swackhamer, D.L., McVeety, B.D., and Hites, R.A. (1988) Deposition and evaporation of polychlorinated biphenyl congeners to and from Siskiwit Lake, Isle Royale, Lake Superior. Environ. Sci. Technol., 22, 664672. Wang, C.C., Davis, L.I., Jr., Wu, C.H., Japar, S., Niki, H. and Weinstock, B. (1984) Hydroxyl radical concentrations measured in ambient air. Science 189 797-800. World Health Organization (1987) "Environmental Health Criteria 71: Pentachlorophenor', United Nations Environmental Program. Zetsch, C. (1982) Predicting the rate of OH-addition to aromatics using ~+-electrophilic substitutent constants for mono- and polysubstituted benzene. From "15th Informal Conference on Photochemistry" Abstract A11, Stanford, CA; cited by Atkinson (1986).
(P,cceixcd m Gcrnmn'~ 15 December 1990; acccpted 26 January 1991)