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Appendix A The Chemistry of Acid Formation It is well established that the oxides of sulfur--sulfur dioxide (SO2) and sulfur trioxide (SO3)--and nitrogen-- nitric oxide (NO) and nitrogen dioxide (NO2)--are converted (oxidized) in the troposphere to sulfuric acid (H2SO4) and nitric acid (HNC3), respectively. However, the most prevalent end products of these reactions--H2SO4, HNO3, ammonium bisulfate (NH4HSO4), ammonium nitrate (NH4NO3), etc.--give few clues about which of several oxidizing pathways are important. Yet for the develop- ment of scientifically sound, predictive models of acid deposition that define theoretical source-receptor rela- tionships r knowledge of the elementary chemical steps that are involved (among many other quantities such as deposition rates and transport rates) is required. The rates of these reactions follow well-defined mathematical laws (rate expressions) that relate reaction rates to concentrations of the reactants, temperature, pressure, and other variables. Considerable progress has been made in developing an understanding of the nature of this chemistry, but a large number of uncertainties still remain in key areas. As our knowledge of the atmospheric chemistry of SO2, NO, and NO2 continues to grow, it has become increasingly clear that many different pathways exist for generating H2SO4 and HNO3 in the troposphere. Reactions can occur in the gas phase; in the solution phase in cloud water and rainwater, for example; and in reactions on surfaces of solid particles in the atmosphere. Thus we are concerned with the rates of exchange of gaseous reactants and their reaction products between liquids and the surfaces of solids as well as the rates of interactions among gaseous molecules, aqueous phase molecules and ions, and species adsorbed on solid 155
156 surfaces. For current purposes, it is not necessary to review and evaluate every detail of these chemical processes, but we should note the nature of the many chemical processes, the variety of interactions among the many species involved, and the current state of knowledge related to the chemistry of acid deposition. We consider first the homogeneous gas-phase chemistry that results in oxidation of SO2, NO, and NO2 in the troposphere (Calvert and Stockwell 1983, Calvert et al. 1978). GAS-PHASE REACTIONS LEADING TO GENERATION OF ACID IN THE TROPOSPHERE Oxidation by Stable Atmospheric Molecules The thermodynamic properties of the oxides of sulfur indicate that sulfur dioxide has a strong tendency to react with oxygen in the air under normal tropospheric conditions: 2SO2 + O2 ~ 2SO3. (1) Thus the ratio of [SO3]/tSO2] is about 8 x 1011 at equi- librium in air at 1 atm and 25°C. (Square brackets indicate the concentration of the species inside the brackets.) Thermodynamic arguments also tell us that at humidities normally encountered in the lower troposphere, the SO3 produced by reaction (1) will be converted efficiently to sulfuric acid, H2SO4(aq), according to SO3 + H2O ~ H2SO4(aq). (2) The reaction of SO3 with H2O is so fast that any process in which SO3 is formed in the moist troposphere can be considered equivalent to the formation of H2SO4. Certain metal ions (Mn2+, Fe3+, etc.) in aqueous solutions of SO2(HSO5) can catalyze the overall sequence of reactions (1) and (2). However, thermo- dynamics tells us nothing about the rates of chemical reactions, and the rate of reaction (1) is so slow under catalyst-free conditions in the gas phase that it can be neglected as a source of sulfuric acid in the atmosphere. The thermal oxidation of NO and NO2 in the gas phase is also slow. Pathways that are thermodynamically favored are
157 2NO + O2 + 2NO2, 2NO2 + H2O ~ HNO3 + MONO. (3) (4) Reaction (3) requires literally days for the conversion of a significant fraction of the nitric oxide present [at concentrations of the order of parts per billion (ppb)] in the troposphere, and the homogeneous gas-phase reaction (4) is immeasurably slow (Schwartz and White 1982). Obviously, other, seemingly less direct reactions must be invoked to account for the observed rates of SO2, NO, and NO2 oxidation, which are between 1 and 100 percent/in. A number of the more complex pathways involve photo- chemistry. In one, sulfur dioxide absorbs light in the ultraviolet region of the solar radiation incident in the troposphere, and, in principle, excited states of SO2 generated in this fashion could lead to SO2 oxidation in the troposphere. Figure A.1 indicates that there is a significant overlap between the actinic flux incident in the lower troposphere and two distinct absorption regions of SO2. Excitation in the "forbidden," long-wavelength band forms the excited SCt(3B1) species, while excitation at the wavelengths below 330 nm generates higher excited states, presumably the 1A2 and 1B1 species. SO2(XlAl) + hv(340 < A < 400 nm) ~ So2(3Bl), SO2(XlAl) + hv(240 < ~ < 330 nm) ~ SO2(1A2, 1Bl). (6) These excited states of SO2 are nondissociative; only quanta of light at wavelengths below 218 nm (which do not penetrate to the troposphere) provide sufficient energy to allow photodissociation: ~1 SO2(X*A1) + hv(A < 218 nm) ~ S02(1B2) ~ 0(3P) + So(3£ ) e (7) The lower excited singlet states of SO2(1A1, 1Bl) appear to be very short lived in air at 1 atm, and they are rapidly converted by collisional perturbations to S02(3B1) molecules, possib~ SO2(3A2) and SO2(3Bk) molecules, and ground-state S02(X A1) molecules. The rate of excitation of SC2 through absorption of sunlight can be very sig- nificant. If this excitation were the rate-determining step in the photooxidation of SO2, that is, if every molecule of SO2 that is photoexcited were oxidized
158 400 _ 300 c, . _ cat - c' to 0 200 - c~ - x 111 100 _ O 240 1 1 1 " ~.~ 1 - 320 Wavelenoth (nary) 0.10 0.08 A, c . _ . _ - o 0.04 _ C1 0.02 400 FIGURE A.1 Comparison of the extinction coefficients (liters mole~1 cm~i, base 10) of SO2 within the first allowed band (left), the "forbidden" band (right), and a typical distribution of the flux of solar quanta (relative) at ground level (dashed curve). SOURCE: Calvert et al. (l978~. through subsequent reaction with O2 or other reactants, then the lifetime of SO2 in the lower troposphere with overhead sun should be as low as 52 minutes (Sidebottom et al. 1972). Of course, this is not the case. The SO2(3B1) species appears to be one of the most favored states, which is ultimately populated through absorption of sunlight and collisional processes in the lower atmosphere. The reactions of this species with various atmospheric gases and many atmospheric impurities have been studied extensively (Calvert et al. 1978). Quenching of SO2(3B1) by atmospheric gases is expected to be the dominant process. In air at 1 atm, 25°C, and 50 percent relative humidity, quenching by N2, 02, H2O, and Ar will occur 45.7, 41.7, 12.2, and 0.3 percent of the time, respectively. Quenching by impurity gases is highly improbable. Even when impurities are present at concentrations of the order of ppm, the rates of SO2 conversion by such species are very slow (Calvert et al. 1978). All available evidence suggests that the only . . . . . . significant chemical result of the major quenching reactions of SO2(3B1) occurs with O2, and this does not lead efficiently to any overall chemical change in the SO2, but low-lying, excited electronic states of molecular oxygen, O2(1Ag) and O2(1£+g), are formed by energy transfer.
159 SO2 ( B1) + O2 ( Eg) + SO2 (X A1) + O2 ( fig) ~ SO2(2 Al) + O2( Ag) (8) . (9) These reactions are not unique sources of excited oxygen, species that are also formed in other atmospheric reactions at much higher rates (Calvert et al. 1978). Thus we conclude that photooxidation of SCt is also not an important source of acids in the atmosphere. Similar conclusions are reached from a study of the photochemistry of NO and NO2. NO does not absorb solar radiation in the wavelength range available near the Earth's surface, so its photochemistry is not important in the troposphere. NO2 does absorb radiation over a wide range, and absorption of the wavelengths below 430 nm leads to dissociation (NO2 + he ~ O + NO). However, formation of acid as a direct result of the photochemistry . of NO and NO2 is unimportant. Reactive Transient Species in the Troposphere Most of the gas-phase tropospheric chemistry of SO2, NO, NO2, and other impurity molecules involves reactions with a variety of reactive excited molecules, atoms, and free radicals (neutral fragments of stable molecules) formed by absorption of sunlight by trace gases in the atmosphere. As a background to discussions to come we review briefly here some of this important chemistry since it enters directly or indirectly into many of the reaction pathways that lead to the formation of acids in the troposphere. In the polluted troposphere, NO2 is dissociated by sunlight absorption (A < 430 nm) to form reactive, ground state oxygen atoms, O(3P), and NO, while the oxygen atom reacts rapidly to form ozone (O3): NC: + hv(A < 430 nm) + O(3P) + NO, O(3P) + O2(+M) ~ O3(+M). Ozone can reoxidize NO to NC2 in (12) or react with alkenes to give highly reactive ozonides in (13) and Criegee intermediates in (14): (10) Ill)
160 0 3 + NO ~ O2 + NO2 0 - 0 - 0 O3 + RHC=CHR ~ RHC- CHR 0 - 0 - 0 1 1 RHC - CHR ~ RCHO2 + RCHO Ozone can also oxidize NO2 to the reactive transient NO3 in (15), and this can lead to N2O5 in (16): O3 + NO2 + O2 + NO3, Net + Net (+M) By N2O5 (+M) . (12) (13) (14) (15) (16) The photodecomposition of ozone may generate electroni- cally excited oxygen atoms, O(1D), and excited molecular oxygen with absorption in the short-wavelength region of the spectrum: O3 + hv(290-306 nm) ~ O(1D) + O2( fig), O3 + hv(290-350 nm) ~ O(1D) + O2 or O + 02(1Ag' 3£g)' O3 + hv(450-700 nm) ~ O + O2. (17) ( 18) (19) The O(1D) species formed in (17) is much more reactive than the ground-state oxygen atoms [O(3P), often simply symbolized by O]. O(1D) reacts efficiently when it collides with a water molecule to form a highly important transient in atmospheric chemistry, the hydroxy radical, HO: O (ID) + H2O ~ 2HO. (20) This radical, unlike many molecular fragments formed from carbon-containing molecules, is unreactive toward oxygen, and it survives to react with most atmospheric impurities such as the hydrocarbons, aldehydes, NO, NO2, SO2, and CO. Its reactions with carbon monoxide and the hydro- carbons (RH) lead to another important class of reactive transients, the peroxy radicals: HO + CO ~ H + CO2, (21)
161 H + O2(+M) + HO2(+M), HO + RH ~ H2O + R. R + O2(+M) ~ RO2(+M). (22) (23) (24) Here R represents the alkyl groups such as methyl (CH3), ethyl (C2H5), or another larger group derived from the parent hydrocarbons, methane (CH4), ethane (C2H6), or larger hydrocarbon (RH), respectively. The reaction of the HO radical with aldehydes (RCHO) forms the acyl (RCO) and acylperoxy (RCO02) radicals in similar reactions: RCHO ~ HO ~ RCO + H2O, RCO + O2(+M) ~ RC002(+M). (25) (26) The peroxy radicals react rapidly with NO to form NO2 and other classes of reactive species. In the case of the HC2-No reaction, HO is regenerated, while with the RO2 and SCOW radicals, alkoxy (RO) and acyloxy (RCO2) radicals, respectively, are formed: HO2 + NO ~ HO + NO2, RO2 + NO ~ RO + NO2, RCOO2 + NO ~ RCO2 + NO2 (27) (28) (29) The most common fate of the smaller alkoxy radicals in the lower atmosphere is reaction with oxygen, leading to HO2 radicals and a carbonyl compound. For example, with the simplest alkoxy radical, methoxy (CH3O), the following reaction occurs: CH3O + O2 + HO2 + CH2O (30) The RCC: radicals are of short lifetime, decomposing to form an alkyl radical (R) and CO2, with the subsequent generation of another peroxyalkyl radical: RCO2 ~ R + CO2, R + O2(+M) ~ RO2(+M) (31) (32) Reactions (14)-(26) combined with reactions (27)-(32) form a chain reaction. That is, a single initial HO radical
162 may oxidize CO, hydrocarbon, or aldehyde, and additional HO radicals will be regenerated as NO is oxidized to N02; the subsequent steps occur again and again in a repeating cycle of events. The peroxy radicals and ozone are the principal oxidizing agents for NO in the lower atmosphere [reactions (IS) and (27)-(29)] (Demerjian et al. 1974). When peroxy radicals react with NO2, an additional class of highly reactive compounds is generated--the peroxynitrates: HO2 + NC2 ~ HC2NC2, RO2 ~ NO2 ~ RO2NO2 ~ RCOO2 + NO2 ~ RCOO2 NO2 Peroxynitric acid formed in (33), and the alkyperoxy- nitrates formed in (34) are relatively unstable in the lower troposphere at temperatures common in summer months; they dissociate readily to reform peroxy radicals and NC2. However, during the cold winter months or in the stratosphere they can act as temporary sinks for HO2 and RO2 radicals and NO2. Peroxyacylnitrates (RC ~ NO2), of which peroxyacetylnitrate (CH3COCtNC2) is the most common, have longer lifetimes and can be the source of radical generation even during the nighttime hours. The excited singlet delta molecular oxygen, O2(1Ag), product of reactions (17) and (18), and excited singlet sigma oxygen, O2(1~+)' the product of reaction (8), can also be created by ~irect absorption of sunlight by atmospheric O2 and by energy transfer reactions from other photoexcited species such as NO2(\ > 430 nm) and excited triplet aromatic hydrocarbons. (33) (34) (35) For current purposes the complex array of interactions that occur among the reactive species outlined here and with the various atmospheric impurities need not be considered. It suffices to say that many aspects of tropospheric chemistry, including photochemical "smog" and ozone generation, depend on these happenings (Demerjian et al. 1974). It is important, however, to evaluate the potential significance of the many highly reactive transient species of the atmosphere for reactions that oxidize SO2 and NO2 to acids.
163 Atmospheric Oxidation of SO2 by Reactive Transient Species There are a large number of potentially significant gas-phase reactions of the reactive transients leading to oxidation of SC: in the troposphere. The potential candidate reactions, summarized in Table A.1, have the thermodynamic potential to occur as measured qualitatively by the sign of the change in enthalpy (aH°) for the overall reaction. Rate constants for most of these elementary reactions have been determined. These data, coupled with estimates of the concentrations of the transients in the atmosphere, allow us to evaluate the significance of each reactant in oxidizing SO2 in the atmosphere. Such evaluations have shown that reactions (42), (50), (56), and (59) or (61) are potentially sig- nificant sources of SO2 oxidation; some of these reactions are only important for certain peculiar atmospheric conditions. By far the most important of the gasphase reactions is the reaction of HO radicals with so2 HO + SO2(+M) ~ HOSO2(+M) . (56) The rate-constant data for reaction (56) have been reviewed recently (Calvert and Stockwell 1983) and are summarized in Figure A.2. The theoretical effect on this rate constant of the altered temperature and pressure of the atmosphere at various altitudes is shown in Figure A.3. The "best" values of kII(56) suggested from the analysis given by Calvert and Stockwell (1983) are somewhat larger than those chosen by Moortgat and Junge (1977), Zellner (1978), and the values recommended for use by the CODATA (1980) group and the NASA (1979) panel and are more consistent with currently available infor- mation on the HO-SO2 reaction. One must, however, retain considerable pessimism about the accuracy of all these data; realistic confidence limits should include +50 percent of the suggested value. Evidence is good that HOSO2 formed in reaction (56) ultimately leads to the generation of sulfuric acid aerosol. However, HOSO2 is not a stable molecule; it is a free radical that is probably highly reactive with several atmospheric compounds. It is not now clear what elementary reaction conversion to H2SO4. pathways are important in its Although there has been a great
164 TABLE A. I Enthalpy Changes and Recommended Rate Constants for Potentially Important Reactions of Ground State SO~ and SO~ Molecules in the Lower Atmosphere - -~H ~kh Reaction (kcal/mole) (25°C) (cm3/molec-sec) (36) O. ('~g) + SO. ~ SO4 (biradical; cyclic) ~25, ~28 (37) O. ('Ax) + SO. ~ SO,3-O (3P) -13.5 3.9 x l0-2° (3X) O. (~Ag) + SO.-O. (~5g) + SO. 22.5 (39) O. (~5g) + SO2-SO4 (biradical: cyclic) ~40, ~43 (40) O. ('Ig) + SO.-SO~ + O (3P) 1.5 6.6 x 10-~6 (41) O2 (~g) + SO.-SO. + O. ('/`,~) 15.0 (42) O (3P) + SO~ (+M)-SO~ (+M) 83.0 5.7 x 10-~4 (43) O3 + SO2-O. + SO; 57.6 <8 x 10-24 (44) NO2 + SO2-NO + SO3 9.9 8.8 x 10-3° (45) NO,3 + SO2-NO2 + SO3 32.6 <7 x 10-2' (46) ONOO + SO.-NO. + SO,3 ~30 <7 x 10-2' (47) N2O~ + SO2 ~ N.O4 + SO3 24.0 <4 x 10-23 (48) HO. + SO'-HO + SO3 16.7 ) <1 x 10-'8 (49) HO. + SO. (+M)-HO.SO2 (+M) ~7 (50) CH3O2 + SO2-CH3O + SO3 ~27 <1 x 10-'8 (51) CH,;02 + SO2 (+M) _ CH3O2SO2 (+M) ~31 ~1.4 x 10-'4C (52) (CH,3),~CO2 + SO2-(CH3)3CO + SO,3 ~26 / <7.3 x 10-~9 (53) (CH~),~CO2 + SO2 _ (CH,~)3CO2SO2 ~30 (54) CH,~COO. + SO2-CH3CO. + SO,1 ~33 <7 x 10-19 (55) CH,~COO2 + SO2-CH3COO,SO2 ~37 (56) HO + SO2 (+M) ~ HOSO2 (+M) ~37 1.1 x lo-~2 (57) CH30 + SO2 (+M)_ CH3OSO2 (+M) ~24 ~5.5 x 10-13 Q~ ,0 (58) RCH-CHR + SO2 ~ 2RCHO + SO3 ~69 See text Q o,-O RCH-CHR + SO2-2RCHO + SO3 ~89 See text (59) RCHOO- + SO2_ RCHO + SO,~ ~79 k59/k60~ 6 x 10-5 (60) RCHOO- + H2O-RCOOH + H2O ~121 (R = CH3) (61) RCHO ~ SO2-RCHO + SO3 ~58 k6l/k62 ~ 4 Q Q (62) RCHO + CH2O ~ RCHOCH2O ~12 (63) SO3 + H2O ~ H2SO4 24.8 (R = H) , ,, 9.1 x 10 'Enthalpy change estimates were derived from the data of Benson (1978), Harding and Goddard (1978), and Domalski ( 1971). ~Rate constants are expressed as second-order reactions for I atm of air at 25°C; see Calvert and Stockwell (198,3) for the references to the original literature. ''The reverse reaction is so fast that the rate of oxidation of SO2 via (51) is very dependent on alternate fates of the CH3O2SO2 species.
165 1 000 E ~ 00 - 10 ~ 1 ~ 1 1 0.01 0.1 _ I 1--l rilill r -Al l-:lil --I 1-l 1 IrTl ~-r I I Al ITT: C Corrected data of Castleman and Tang (1976-1977) O Leu (1982) a Range of values reported by Harris and Wayne (1975) Cox and Sheppard (1980) O Davis et a I. ( 1979) D' ,/ o i I I I l_L / 1/[M] (cm3/molec x 1018) 3' new , MU _4 ~ J /^ / / / I 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1.0 1n 100 10 FIGURE A.2 Comparison of the experimental data for the effective second-order rate constants for the reaction (56) with M = N2. SOURCE: Calvert and Stockwell (1983~. amount of speculation in this regard, there is little experimental evidence to help determine the relative importance of suggested alternative routes. Thus Cox (1974-1975, 1975), Calvert and McQuigg (1975), Calvert et al. (1978), Davis et al. (1979), Friend et al. (1980), Leu (1982), Benson (1978), and others have suggested that the HOSO2 radical may participate in a variety of radical-radical and radical-molecule reactions. These reactions are summarized in Figure A.4. Although the mechanism of H2SO4 generation following (56) is unclear today, it is probable that reaction (56) is the rate- determining step in the sequence. Recent evidence suggests that the concentration of HO in photooxidizing mixtures of MONO, NO, NO2, and CO is insensitive to even large additions of SC2 (Stockwell and Calvert 1983). Thus the following sequence of reactions seems favored:
166 10 \\/ \\~ _ _ ~I_ _ ~ - 1 1 1 1 1 0 10 20 30 40 50 Altitude (km) / Pressure \\ \ \ - All' '\ \ \ \ \ \ 0.01 300 250 a) Q ~ 200 a) 1 000 100 - 1 0 <:, in a) Cal 1 o FIGURE A.3 Pressure, temperature, and the apparent second-order rate constant for the reaction (56) as a function of altitude. SOURCE. Adapted from Calvert and Stock- well (1983) for the conditions of pressure and temperature defined for the standard atmosphere (Valley 1965~.
167 HO + SO2 - - ' (HOSO2t) (1~ O2 ) (+24) HO + SO3 (+40) 1 (-11) ('k 02) HC SO2 O ~- c~ ce ._ u, c~ c~ (+M) (-37) HO SO2 _~ HO2 + SO3 (°21(-16)~ HOSO2 H2O HOSO2 O (NO) (-25) \H2 O~ HOSO2 O2 H2 O (HO2 )W HOSO2O+NO2 ~ HOSO2 O + NO ~ ~(-14) /-26) ('h °2)-.` (-8)(H2 O)~ HOSO2 ONO ~ (-10) - (1~2 02)~ HOSO2 O2 H (+O2 ) HOSO2 O + NO2 H2 SO4 + HONO-(-14) (1~ o2 5-_ H2 SO4 + HNO3 I (H2 O) H2 SO4 (aq) + HNO3 (aq) - (H2O) (-12) ', (-22) ~~ HOSO ONO2 (iso-C4 H 1O) 12) _ HOSO2 O /~) ~\~VJ\~-~UJ (NO2 )~ (-24:C2 H4 ) \ HOSO2 ONO2 HOSO2 OC2 H4 ~ ~ - ~ H2SO4 + t-C4H9 / (NO)\(-26) HOSO2 ONO FIGURE A.4 Enthalpy relationships between various possible products of the HO- radical reaction with SO2. SOURCE: Calvert and Stockwell (1983~.
168 HOSO2 + O2 ~ HO2 + SO3, HO2 + NO ~ HO + NO2, SO3 + H2O ~ H2SO4. Atmospheric Oxidation of NO2 by Reactive Transient Species A great variety of experimental evidence supports the view that a very important pathway for the tropospheric oxidation of NO2 is similar to reaction (56) for SO2: HO + NO2(+M) ~ HONO2(+M). (64) Estimates of k~(64) are well characterized for conditions applicable to the troposphere (M = N2). Using Anderson's (1980) recommendations for this rate constant, we have made the plot shown in Figure A.5 of the effective second- order rate constant for various altitudes and conditions of [M] and temperature characteristics of the standard atmosphere. The same general trends in kII(64) with altitude are seen as observed for the HO-SO2 reaction rate constant kII(56) in Figure A.3, but the values of kII(56) are roughly a factor of 10 larger than those for kII(64) for a given temperature and pressure in the troposphere. A second homogeneous mode of potential formation of HONO2 involves N2O5: H2O + N2O5 ~ 2HONO2 (65) It is difficult to distinguish the homogeneous component of this reaction in laboratory experiments, since reaction at a moist cell wall can be more important than the homogeneous reaction for most experimental systems. Morris and Niki (1973) reported an upper limit for this constant of 1.3 x 10-2° cm) molec~1 sec~l. For theoretically expected concentrations of N2O5 in the troposphere (<2.5 x 109 molec cm~3) during the daylight hours (Demerjian et al. 1974), the rate of (65) is insignificant compared with that of (64). In theory the reaction (65) can be important at night when NO3 and N2O5 concentrations may rise.
169 10 5 2 0.5 x a) - a, o E mp 0.05 cat - 0.2 0.1 0.02 0.01 \ \ \ /k \ my\ / \ \ Pressure \ ~ 1 1 1 1 1 1 1 1 1 1 1 1 0 5 10 15 20 25 30 1 000 100 Al 10 ' in 1 o 35 40 45 50 Altitude (km) FIGURE A.5 Pressure and the apparent second-order rate constant for reaction (64) as a function of altitude. SOURCE: Calculated from the equations of Anderson (1980) for the conditions of pressure and temperature defined for the standard atmosphere (Valley 1965) (from Calvert and Stockwell 1983~. Theoretical Rates of SO2 and NO2 Conversion to H2SO4 and HONO2 Through Gas-Phase Reactions in the Troposphere The major homogeneous processes for SC2 and NO2 conversion to H2SO4 and HONO2, respectively, are governed by the rates of reactions (56) and (64), which depend on the concentrations of the reactants, N02, S02, and HO. Knowledge of [HO] in the troposphere is needed to make theoretical estimates of the minimum rates of the gas-phase generation of the H2SO4 and HONO2.
170 Although the direct measurement of [HO] in the troposphere is very difficult, there are both theoretical and experi- mental estimates of this quantity that are of some value for our considerations here t Table A.2). We have excluded early estimates based on laser-induced fluorescence of the HO radical because the generation of HO by the probing laser beam itself was then an unrecognized problem. Data based on the 14CO-chemical method of Campbell et al. (1979), the laser-induced fluorescence data of Wang et al. (1981), and the HO absorption data of Perner et al. (1976) are all reasonably consistent both among themselves and with theoretical estimates based on computer models (Calvert and McQuigg of the complex atmospheric chemistry 1975, C hang et al. 1977, Crutzen and Fishman 1977, Demerjian et al. 1974, Graedal et al. 1976, Hecht and Seinfeld 1972, Hov and Isaksen 1979, Levy 1974, Niki et al. 1972). We may use these data to make reasonable estimates of the gas-phase oxidation rates for SO2 and NO2 in order to judge the potential of reactions the ingredients for "acid rain." (56) and (64) to develop At high concentrations of HO radical characteristic of midday sunny summer skies in a polluted atmosphere (about 9 x 106 molec cm~3), we anticipate from our selected rate constant data that SO2 will oxidize at a rate of ~3.7 + 1.9 percent/in through HO-radical attack in reaction (56). . . . . .. Rates of HONO2 generation in (64) are expected to be about 34 + 17 percent/in for these conditions. Somewhat lower midday solar intensities typical of the winter months in a polluted atmosphere for which the maximum noontime value for [HO] ~ 2.4 x 106 molec cm~3 lead to rates of about 1 + 0.5 percent/in for SO2 and about 18 + 9 percent/in for N ~ . Of course, these rates are expected to track [HO] during the day and thus to drop rapidly to near zero at night. Computer simulations (Stockwell and Calvert 1983) show that for conditions that provide a maximum summertime value for [HO] of about 9.1 x 106 moles cm~3, the 24-h average [HO] is about 1.7 x 106 molec cm~3, leading to a daily average rate of SO2 oxidation through reaction (56) of 0.7 percent/in or 16.4 percent/24-in period. The equiva- lent NO2 oxidation rate in (64) is 6e2 percent/in or 150 percent/24-in period. oxidation is much lower: for SO2 it is about 0.12 percent/in or 3 percent/24-in period and for NO2 about 1.1 percent/in or 25 percent/24-in period. In theory therefore we expect the homogeneous gas-phase conversion of SO2 ~ . The average wintertime rate ot
171 TABLE A.2 Measured and Theoretical Estimates of the [HO] in the Troposphere [HO1. molec/cm3 A. Experimental Methods 1. Chemical Method: 14co + HO ~ '4CO2 + H (Campbell et al. 1979) Pullman, Wash. (46.7° N. 770 m) New Zealand (44° S' 1030 m) Tennessee (rural, 36° N. 270 m) Los Angeles (34° N. 270 m) Arizona (desert, 37° N. 2300 m) Laser-Induced Fluorescence, 282.07-nm excitation, 309-nm emission, 302-nm N2 Raman (Wang et al. 1981) Niwot Ridge, Colo. (3048 m) Los Angeles, Calif. ( 1 1 ,886 m) San Bernadino, Calif. (10,057 m) San Diego, South, Calif. (10,667 m) Denver, Colo. (10,057 m) 3. Absorption Spectroscopy, 307.995 nm (Perner et al. 1976) Julich, Germany (51° N) B. Theoretical Estimates: Typical recent estimates found in simu- lations of Calvert, Demerjian, Seinfeld, Niki, Graedel, Isaksen, etc., and their co-workers (values are sensitive to ultraviolet solar irradiance at point of interest, levels of impunities, NO, NO2, RH's, RCHO's, etc.): Daytime maximum (summer, 40° N) Daytime maximum (winter, 40° N) Nighttime (5.8+2.4)x lo6 (1.1+0.4)x lob (1.9+0.7)x lo6 (S.0 + 1 .2) x 106 (57 + 23) x 106 (40 to 6) x 106 (2.5 + 2) x 106 (20 + 6) x lob (10 + 4) x lo6 (1+3)x 106 (11+6)x lob usually (6 + 3) x 106 ~ (9 + 4) x 106 ~(2+1)x 106 <2 x 10S SOURCE: Calvert and Stockwell (1983). and NO2 to provide a significant quantity of sulfuric and nitric acids in the troposphere. When making such estimates for the gas-phase SO2 oxidation rates, we must remember that other as yet unevaluated contributions from the alkene-C3 products, the CH3O2-radical, and probably other unidentified reactants may contribute to the total SO2 oxidation rate as well. For example, the reaction (42) of 0(3P) with SO2 can be significant in a highly NC~-polluted atmosphere such as that present in the early stages of dilution of a stack gas plume. In this case, reaction (42) can theoretically account for an initial burst of SO3 (H2SO4) formation at a maximum rate of about 1.4 percent/in (Calvert et al. 1978). In addition, the methyl- peroxy (CH3O2) and possibly other primary alkylperoxy
172 radicals may lead to SO2 oxidation in the tropospher e under special circumstances of high NO-NO2 pollution, although the evidence for the significance of reaction (50) is not unambiguous (Ken et al. 1981). Also the products of the ozone-alkene reactions oxidize SO2 readily, presumably through the Criegee intermediates in reactions (59) or (61). The aldehydes, water vapor, carbon monoxide, NO, and possibly other atmospheric impurities compete with SO2 for these reactive inter- mediates, and the effectiveness of the competition of SO2 with NO remains unclear today (Calvert and Stockwell 1983). If the rate constants for these RCHO2 species with NO and SO2 are similar and/or the ratio of [NO]/ [SO21 is low, then SO2 oxidation by Criegee intermediates can be significant in alkene-ozone-containing atmospheres (a few tenths of a percent per hour). Although the contribution of SO2 oxidation from reactions other than (56) may be important, the theo- retical rates given here for the HO reactions alone appear to match reasonably well those observed in relatively dry SO2 urban plumes (Eatough et al. 1981, Forrest et al. 1981, Garber et al. 1981, Gillani and Kohli 1981, Hegg and Hobbs 1980, McMurry and Rader 1981, Meagher et al. 1981, Newman 1981, Williams et al. 1981, Wilson and McMurry 1981, Zak 1981). Certainly a large part of the observed oxidation in the cloud-free ambient troposphere during the daylight hours arises from the HO-SO2 reaction. The conversion rates for NO2 observed by recent worker s are also consistent with the estimates presented here (Spicer 1982). THE SOLUTION-PHASE OXIDATION OF SO2 IN THE TROPOSPHERE In recent years the role of the aqueous-phase reactions in the development of acid precipitation has received increased attention. The results of field and laboratory studies suggest that the relative importance of the gas-phase and solution-phase pathways may vary depending on a variety of meteorological conditions such as the extent of cloud cover, relative humidity, the amount of precipitation, the intensity of the solar radiation, and the presence and concentration of various pollutants. Rates of oxidation of SO2 through gas-phase reactions are relatively slow (a few percent per hour during daylight), whereas in theory those for the solution-phase pathways may be as high as 100 percent/in fo r seemingly realistic concentrations of the reactants in cloud
173 water. Despite the considerable difference in rates of oxidation pathways in the aqueous and gaseous phases, both must be regarded as participating in the development of acid deposition in the eastern United States because air masses in this region are more likely to be free of clouds and precipitation a large fraction of the time (Niemann 1982). There appears to be little question that both gas-phase and liquid-phase processes can contribute significantly to the formation of H2SO4 in the atmosphere. Clear evidence of the relative importance of the two processes for various conditions is not now available. Field data taken in dilute stack plumes in relatively cloud-free atmospheres show that formation of sulfuric acid at night is very slow and that during daylight hours the rate correlates with solar intensity (Hegg and Hobbs 1980, Wilson and McMurry 1981). Measurements are not frequently made at night, however, and there is no clear test, of which we are aware, of cloud chemistry for conditions that minimize the possible gas-phase processes. Wilson and McMurry (1981) have observed the evolution of aerosol size distributions as a result of gas-to-particle conversion. From these data they suggest that droplet-phase conversion of SCAN to sulfate may be important at high humidities (>50 percent), where up to 20 percent of the growth of the aerosol was attributed to this reaction. Aerosol from gas-phase processes dominated the plume chemistry for low humidities and in the absence of clouds. The clearest evidence of the major input from precipi- tating clouds was derived in the Acid Precipitation Experiment (APEX) (Lazrus et al. 1983). The investigators found significant production of both sulfuric and nitric acids in clouds. The acidity of dry air south of a warm front was measured before it ascended and produced a large area of warm frontal precipitation. Comparison of the chemical composition of the dry air and precipitation at the base of the cloud showed that rapid production of acid had occurred in the cloud. Rates of HNO3 and H2SO4 production in the cloud were estimated to be of the order of 0.5 ppb/h and 1.2 ppb/h, respectively. Although analyses Of H2O2 in the cloud suggested the involvement of this oxidizing agent, unidentified interferences in the luminol method for H2O2 detection discovered later leave the nature of the oxidizing agent unresolved. Recently, transport and transformation chemistry of SO2 were studied in an air mass tagged with SF6 along the coast of southern California (sass and Shair 1983). These studies appear to provide the first unambiguous evidence
14 NO 2 12 10 8 6 4 2 o (b) OR _ _ . Y/80 JUN JUL AUG SEPT OCT Nit DEC ~/81 FED ~ARK ~T JUT BUS AUK 80: PPR 8 1 - - - 704 . ~ * 1 2.5ppb PPB 18 16 Sal _ _ . 174 ~8 1 WEST STATION CENT STATION EAST STATION ~ . ~1 82 . / A 83 that SO2 conversion to sulfate can occur at a measurable rate at night (about 10 percent/in) in low stratus clouds over the coastal waters. Strong seasonal variations in the sulfate and SO2 in precipitation (measured as H+ and HSO3) have been seen in the MAP3S precipitation chemistry data (Henderson and Wingartner 1980). A more direct and quantitative measure of seasonal variations in the atmospheric chemis- try involved in acid deposition has been presented by Shaw and Paur (1983). They measured gaseous NO, NO2, SO2, and airborne sulfate aerosol at three sites in the Ohio River Valley during the period May 1980 to August 1981 (Figure A.6). Two sites (labeled west and central in the figure) were located in rural farming communities (Union County, Kentucky, and Franklin County, Indiana), and the third (east) was in a forest clearing (Ashland County, Ohio). Figure A.6 indicates that while monthly average concentrations of NO remained relatively constant throughout the period of the experiment, NO2 and SO2 (gas-phase sulfur) increased in the winter months. Airborne particulate sulfate shows a minimum in winter, as does the percentage of total sulfur existing as
17S 25 20 in 6 4 66 ol ~ PERCENT ~ICR=~S/CU81C METER I GAS-PHASE SULFUR 12 . 5 . . . - 63 , ~ ,. ~ ~ _ B2 . ~ ~ :[ 7 MICROGRAMS/CUBIC METER _ PARTICULATE SULFUR 71 80 Ir ~ / 68 . ? _: (C) red ~1 (d) 12 |= WEST STATION I | CENT STATION 5////> EAST STATION ret 11 ~ .' it. L; 79 R ~ ~ ::/ _ :. AL ': 80 e3 t] 60 1 1 I PERCENT PARTICUlATE SULFUR so ~ to ~Y/" JUN JUL AUG SEPT 73 67 66 1: 2~ 1 :~ (e) ~ _ .. . ~. ~ . . . . . OCT NOV DEC JAN/81 FEe MAR APR MAY JUN JUL I: ~ I' V) 1::~ 1 ~ 1' V) 1::~ I: YE 1.K 1: k? it' 1::~ I V) 1::~ 1~ 1::~ 1L AUG FIGURE A.6 Average monthly concentrations of airborne pollutants at three sites in the Ohio River Valley in 1980-1981. (a) NO, (b) NO2, (c) SO2, (d) sulfate aerosol, (e) percentage of total airborne sulfur existing as sulfate aerosol. SOURCE: Shaw and Paur (1 983~. sulfate aerosol. The results are consistent with the general expectations of pathways for oxidation in both the gaseous and the aqueous phases since.higher concen- trations of the oxidizing agents (HO, H2O2, and O3) are anticipated in the summer months when both solar inten- sities and the length of daylight are higher.
176 Evidence concerning the relative contributions to SO2 oxidation by gaseous- and liquid-phase processes has also been presented using the isotopic abundance of 180 in sulfate formed in various laboratory experiments and in natural samples of snow and rain collected near Argonne, Illinois (Holt et al. 1981, 1982, 1983). The method is based on the fact that oxygen atoms in sulfate ions in water do not reach equilibrium with those of water for temperatures and times characteristic of acidification of droplets in acid Precipitation. Differences also exist in the ratios of 80 to 160 in O2 and H2O. Therefore, in principle, measured differences in the 180 content of cloud-water sulfate should provide evidence of the origins of the sulfate. An isotopic ratio typical of H2O would suggest solution-phase origins, whereas a ratio typical of atmospheric O2 or species derived from the O2 (O3, H2O2, HO, etc.) would suggest that gaseous-phase chemistry was more important. In their 1981 report, Holt et al. (1981) suggested that solution-phase oxidation of SO2 is the more effective pathway for observed isotopic ratios in sulfate in natural precipitation water. However, the most recent interpreta- tion of Holt et al. (1982, 1983) of the measured isotopic ratios in samples of atmospheric water and controlled laboratory experiments using a variety of homogeneous gas and liquid-phase and catalytic methods of SO2 oxidation is more ambiguous (Figure A.7). Note that the oxidation reaction of SO2 with aqueous H2O2, currently the most favored reaction,\gives isotopic ratios that are least in accord with the values observed for sulfate in snow and rain in field studies. The authors now conclude that some currently unknown source of sulfate (possibly primary sulfate) with enriched isotopic ratio must exist that dilutes that formed by one or more of the currently known reactions leading to sulfate formation. An abundance of data based largely on laboratory measurements points to the probable involvement of the oxidizing agents hydrogen peroxide and/or ozone in the formation of acids in cloud water. Also suggested in theory as having a possible influence in these trans- formations are free radicals such as HO and HO2 either formed in the gas phase and transported to the liquid phase or formed in the liquid phase. Soot (carbonaceous
177 2. 30 20 - ~ 1 0 Q - , O In -10 -20 1 -30 1 Aqueous air oxidation with Fee catalyst Aqueous air oxidation with charcoal catalyst 3. Aqueous H2O2 oxidation 4. Electric spark in humidified air 5. NO2 in humidified air 6. Gamma irradiation in humidified air 7. Water vapor, air, and SO2 absorbed on charcoal at 22 C - Snow o Rain ~ ~1 O ~ 00 0 0;~ O _~ at/ _ - _ - ,-_ ,- , - - _- i' _ _ - Aqueous-phase oxidation of SO2 Non-aqueous-phase oxidation of SO, 2 1 1 1 1 -20 -1 0 OLiqu id water (percent) ° Ef/fsmow) -1] x 103, where f = 1 80/160 and fsmow= 2.005 x 10-3, the isotopic ratio of standard mean oceanic water. 0 10 20 FIGURE A.7 Comparison of isotopic ratios in sulfates formed by seven laboratory methods and in precipitation water. SOURCE: Holt et al. (1982, 1983~. material) and various metal ions (copper, iron, manganese, and vanadium, for example) can act as catalysts for solution-phase oxidation of SO2. Ammonia and other basic materials (such as metal carbonates) can influence the rates of solution-phase oxidation of SC2 through alteration of the pH of the solution. We will review
178 briefly here the kinetic results that define the reaction rates for the solution-phase oxidation of SO2. Many of the rate data presented here are from the review of sulfite oxidation by Martin (1983). Aqueous-Phase Oxidation of SO2 Sulfur dioxide dissolves in water to form the hydrate SO2-H2O and the ions HSO3, H+, and SO3; these species are related by the following equilibria, which are established rapidly: SO2(g) + HzO(liq) =~ SO2.HzO(aq), KH = 1.23 M/atm (25°C), SO2 HzO(aq) K1 = HSO3(aq) K2 = H+(aq) + HSO3(aq), 10 2 M, H+(aq) + SO3(aq), 1o~8 M The concentration of undissociated H2SO3 is insignificant. The solubility of gaseous SO2 or the concentration of total dissolved S(IV) equilibrated in water at some specified pH with gaseous SC: at a pressure PSO2is given by the relation: [S(IV)] PSo KH (1 + K1/[H+] + K1K ~[H+]2), 2 where [S(IV)] = [SO2.H2O(aq)] + [HS03(aq)] + [S03(aq)]. It is apparent that SO2 becomes less soluble as the acidity of a solution increases. Freiberg and Schwartz (1981) and Schwartz and Freiberg (1981) have shown that the times required to establish gas-liquid equilibrium between SO2 and aqueous aerosol droplets are usually much shorter than the chemical reaction times for reactant concentrations typical of the ambient atmosphere. The expected 1S(IV)] in aqueous aerosols of pH 3.0 in equi- librium with SO2 in the atmosphere ranges from about
179 10 9 M for 0.2 ppb SO2 to about 10-6 M for 200 ppb SO2. At pH 4.0, [S(IV)] varies from about 10-8 M for 0.2 ppb to about 10 5 M for 200 ppb SO2. At pH 5.0, [S(IV)] is about 10-7 M for 0.2 ppb SO2 and 10-4 M for 200 ppb SO2. Of the various oxidizing agents that can oxidize S(IV) in solution, two species, H2O2 and O3, appear to be especially significant for ambient levels of impurities. The possibility that H2O2 and O3 could be important oxidants was first suggested by Penkett et al. (1979). The overall reactions are represented by H2O2(aq) + HSO3(aq) ~ SO4(aq) + H+(aq) + H2O(aq), (66) O3(aq) + HSO3(aq) ~ S 4(aq) + H+(aq) + O2(aq). (67) Martin and Damschen (1981) have summarized all the pertinent rate data for reaction (66) (Figure A.8) and derived the following rate equation for the reaction: d[S(IV)] 8 x 104[H2O2]1SO2.H2O(aq)] = dt 0.1 ~ [H+(aq)] mole liter~1 sec~l. When [H+] << 0.1 M, the expression (68) shows the oxidation rate to be independent of pH. This system is unique in this regard among the potential oxidizers of SC~ in solution, and hence the H202 oxidation mechanism is favored at low values of pH common in atmospheric aerosols and precipitation water. The apparent activation energy for the reaction is about 8 kcal/mole in the pH range 4-6 and 6.7 kcal/mole at pH 2 (no buffer). Hoffman and Edwards (1975) proposed a mechanism consistent with rate law (68): HSO3(aq) + H2O2(aq) ~ HOSOO2(aq) + H2O(aq), HOSOO2(aq) + HA(aq) + 2H+(aq) + SO4(aq) + A (aq), in which HA is H3O+ or a suitable weak acid in the solution. According to this mechanism, the reaction occurs via a nucleophilic displacement by H2O2 on HOSO2 to form a peroxymonosulfurous acid intermediate, HOOS~ (aq), which then undergoes a rate-determining rearrangement assisted by H3O+ or HA. (68)
180 1o6 105 c' 1 0 v, o E ~ 1 03 . _ - 4. 4 - ° 10' a, 4 - cr: 10' 10° 1o-l 1 1 0 1 2 3 \ t ~. Martin and Damschen (1981 ) O Pen kett et al. (1979) Hoffman and Edwards ( 1975) O Mader (1958) \ \o \ ~ \ o 1 1 1 1 1~1 4 5 6 7 8 9 10 11 12 pH FIGURE A.8 Rate constant (k) for the bisulfite H2 O2 reaction as a function of pH from the expression -d LS(IV)] /aft = k [H2 O2 ~ [S(IV)] with the effect of buffer removed and all results converted to 25°C. SOURCE; Martin (1983~. The oxidation of SO2 by O3 in solution has been studied by several groups. Available data are summer ize d in Figure A.9 (Martin 1983). For aqueous solutions with pa in the range 1-3, the rate of oxidation via ozone follows - = 1.9 x 104[H+(aq)]~l/2 [03(aq)] [S(IV)] mole liter-1 sec~1 -. (6 9)
- c~ In - 181 103 2 a, 4_ 10 J 01 1 1 1 0 1 7 3 · O · O O O ad 0 1 · ~ O _' - · Martin (1983) ~ Penkett et al. (1979) O Larson et al. ( ~ 978) O Erickson et al. ( 1977) -Maahs (1982) c pH FIGURE A.9 Pseudo-first-order rate constant for ozone loss as a function of pH in the reaction of ozone with bisulfite with initial [03 ~ = 1 X 10 ~ and [S(IV)] = 5 x 10 ~ M. SOURCE: Martin (1983~. For pH between 3 and 6.5, the rate law has this form: d[O3(aq)] dt = 4.19 x 105[03(aq)][S(IV)] + lOO[H+(aq)] 1 lS(IV)][O3(aq)] mole liter~1 sec~l. (70) The inverse dependence of the rate of the C3-S(IV) reaction on [H+(ag)] decreases the potential importance of the O3 reaction with acidic solutions characteristic of the troposphere. The apparent activation energy of the reaction is 8.2 kcal/mole (Maahs 1982). There is a strong link between the gas-phase and liquid-phase atmospheric chemistry related to acid precipitation. The major contributors to solution-phase oxidation of S(IV) in the troposphere, presumed to be H2O2 and C3, are both products of the homogeneous
182 gas-phase reactions. Hence the gas-phase and liquid- phase pathways of acid generation in the troposphere are not independent. The major sources of H202 in the gaseous tropo- sphere are reactions (71) and (73), involving the HO2 and the hydrated HO2 radicals: 2HO2 ~ H2O2 + O2, HO2 + H2O + H2O HO2, H2O-HO2 + HO2 ~ H2O2 + H2O + O2. (71) (72) (73) The complex H2O-HO2 represents only a few percent of the total HO2 concentration in the atmosphere; however, the inequality of the rate constants, k73 > k71, ensures that its role in H2O2 formation is not insignificant. Of course, if water is available to gaseous H2O2, this compound will end up largely in the aqueous phase because of the large Henry's law constant for H2C2 in water (7.1 x 104 M atm~ at 25°C). In the polluted atmosphere, there is strong competition for the HO2 radicals through reactions (27), (74), (75), and possibly others. HO2 ~ NO ~ HO + NO2, (27) HO2 + CH2O =-HO2CH2O + O2CH2OH, (74) HO2 + O~H2OH + HO2CH2OH + O2. (75) The efficiency with which H2O2 is generated in the polluted troposphere through (71) and (73) is a complex function of [NO] and [CH2O] as well as the concentra- tions of CO, hydrocarbons (RH), and aldehydes (RCHO) from which the HO2 radical is derived. [See reactions (21), (22), (30), and others.] Simulations of the complex chemistry of the polluted troposphere show that with a highly polluted air mass ([NOk] = 100 ppb, [RH] = 500 ppb, [RCHO] = 30 ppb), H2O2 development is unimpor- tant until the [NO] has been depleted late in the day (Calvert and Stockwell 1983). However, for conditions more typical of a nonurban air mass, where it is not uncommon to have very low NOx levels (~1 ppb) and somewhat higher RH and RCHO concentrations in this cir- cumstance, generation of H2Ok can begin early in the day. When [NOx] is very high (100 ppb) and [RH] and [RCHO] are low initially ( [RH] = 50 ppb, [RCHO] = 3 ppb),
183 little H2O2 forms. However, with small levels of all the pollutants, HACK formation in (71) and (73) can be significant. In theory, the amount of H2C2 formed in these gas-phase reactions can often be sufficient to oxidize a large fraction of the bisulfite usually present in cloud water and precipitation. Production of C3 in the troposphere follows a some- what different pattern. Its development is most favored in the highly polluted atmosphere, although significant concentrations (0.08 ppm) may be generated in relatively clean urban and rural atmospheres. The Henry's law constant for O3 in water (0.01 M atm 1 at 25°C) and normal concentrations of O3 found in the relatively clear tropo- sphere (30-60 ppb) ensure that the aqueous droplets in the atmosphere will contain ozone concentrations of about 3-6 x 0~10 M These limited observations suggest that conditions of low NOX and high hydrocarbon and aldehyde impurity levels favor H2O2 formation, whereas those of relatively high NOy, RH, and RCHO favor high O3 generation rates. If homogeneous air masses containing preformed H2O2 and O3 encounter cloud water, rainwater, high aqueous acid aerosol levels, etc., then solution phase pathways for H2SO4 formation are favored as well. Because the optimum impurity levels for generation of O3 can be very different from those for H2O2 formation, the components of the H2O2 and C3 oxidation of SC2(HSO5) in the solution phase will not proceed exactly in phase with fixed fractions occur- ring by each pathway. The rates of SO2 oxidation in the homogeneous gas-phase oxidation and those of the solution- phase reactions will depend on two quite different, complex functions of pollutant concentrations. However, it is clear that the two processes are not entirely independent. Other interesting possibilities for the oxidation of S(IV) to sulfuric acid in cloud water have been suggested but remain untested. Chameides and Davis (1982) studied theoretically the contribution to aqueous-phase chemistry of HO and HC2 gas-phase radicals scavenged by and incorporated into cloud droplets during daylight. A seemingly logical series of chemical reactions involving these species and their products was suggested, and calculations indicated that for small water droplets (<20 ~m) this scavenging process may be a very important source of oxidant (H2O2, HO2, HO) for acid development provided that the sticking coefficent for these species impingin, upon the water droplets is greater than about 10- . 1
184 Both NO2 and HONO can oxidize sulfite in dilute solutions. Martin et al. (1981) report that HONO2 does not react significantly for any of the pH conditions employed. Lee and Schwartz (1981) and Schwartz and white (1982) estimated the oxidation rate of NO2(aq) with S(IV) to be 2.4 x 10-6 M/h at OH 5 and Paws= MYTH= 10 ppb in the Has Phase. ~ ~ eve -TV ~ Their preliminary data suggest that for relatively high NC2 and SO2 pollution levels the acid generation from the NO2-SC2-H2O(liq) system could be significant. In laboratory experiments, nitrous acid can oxidize sulfite at a reasonably fast rate. Martin et al. (1981) report that the rate law for this system is given by d[S(IV)1 = 142[H+(aq)]l/2[N(III)][S(IV)] dt mole literal sec~l. (76) The rate constant data are summarized in Figure A.10. The nitrogen-containing product of the reaction up to pH 3.5 was N2O. Above this pH, hydroxylamine disulfonate (HON(SC3)2-) forms. Further reactions of this species occur to give hydroxylamine and nitrous acid. At the very low levels of gaseous HONG in the atmosphere both anticipated theoretically and observed experimentally, it is not likely that this reactant will contribute signifi- cantly to the oxidation of S(IV) in the troposphere. The truly uncatalyzed oxidation of sulfite solutions by oxygen is very slow, and there is some question whether small impurities of metal ions such as iron may not account entirely for observed ~uncatalyzed" rates (Martin 1983). O2(aq) + 2HSO3(aq) ~ 2H+(aq) + 2SO4(aq). Both iron (Fe3+) and manganese (Mn2+) ions catalyze the reaction effectively. The rate law derived by Martin (1983) for the iron-containing system is given by d[SO4(aq)]= 0.g2[H+(aq)]~l[Fe3+~[S(IV)] at mole literal sec~ -. (77)
185 103 1o2 - a, c' 10 o - a) . _ - a, 10-1 10-2 10-3 10-4 ~ Data from Martin et al. (1981 ) - \ Data from Oblath etal. (1981) __ 4 5 6 pH FIGURE A.10 Rate constant (k) for the reaction of HONG with bisulfite as a func- tion of pH in the expression d~S0V)] /aft = k [N(III)] [S(IV)] . SOURCE: Martin (1983~. These data and those of previous workers are summarized in Figure A.ll. An increase in [H+(aq)] typical of a reacting mixture in cloud water or rainwater tends to lower the rate of this reaction pathway. In the high pH range (pH > 4), a condition uncommon for most natural atmospheric situations, ferric ion concentrations fall below 10-8 M, and the inconsistency of the rate laws observed in the laboratory for this system in this pH range may reflect the unrecognized problem of iron ion removal as a precipitate. Catalysis of sulfite oxidation by manganese ions is governed by different mechanisms and rate laws depending on the concentrations of reactants. Martin (1983) reported the following expression for the [S(IV)] regime from 10 3 to 10 4 M:
186 105 - c) a, <a a) ~ 1 04 - ._ - 4J o a) to 103 1o2 10 1 O Aubuchon (1976), two-term rate law · Aubuchon ( 1 976J, one-term rate law O Neytzell-de Wilde and Taverner (1958) Brimblecombe and Speddi ng ( 1974) ~ Fuzzi (1978) - Martin (1983) o 2 _ . _ ~- 0/ / ~ /^ 0/ 0 O. 1 1 1 1 1 0 1 2 3 4 5 pH FIGURE A.11 Rate constant (k) for the iron-catalyzed oxidation of bisulf~te as a function of pH in the expression d~S(IV)] /aft = k tFe3~] [S(IV)] with data corrected to 25°C. SOURCE: Martin (1983~. d[SO4(aq)] = 4 7[H+(aq)]~l[Mn (aq)] dt mole liter~1 sec~ · (78) The rate is independent of [S(IV)] for these conditions. This and other estimates of the rate constants for this reaction are shown as a function of pH in Figure A.12. The activation energy for the reaction is 27.3 kcal/mole (Hoather and Goodeve 1934a,b). At low [S(IV)] (less than 10-6 M), Martin (1983) finds the rate law to be d[S(IV)1 = 25[H+(aq)] 1[Mn2+][S(IV)] dt mole liter~1 sec~1 -. (79)
187 For the entire range of concentration the rate is inversely proportional to [H+(aq)]. For the conditions of relatively high concentrations of Fe3+ or Mn2+ in atmospheric precipitation or urban fogs (Hoffman and Jacob 1983), the rates of S(IV) oxidation through these catalyzed reactions can be very significant. These conditions usually do not prevail in the free troposphere in nonurban areas, however. Barrie and Georgii (1976) found that when both Fe3+ ~ . and Mn~= ions are present in sulfite solutions, the rate of sulfite oxidation is enhanced over that expected from the sum of the Mn2+-S(IV) and Fe3+-S(IV) rates alone. Martin (1983) studied these systems in detail and con- firmed this finding. For the combined Fe-Mn system the rate of sulfite oxidation was typically 3 to 10 times faster than that anticipated from the sum of the inde- pendent rates in the individual systems. 104 - c' ~ 103 o E ._ - of 1 o2 o 10 1 ~ _ / ,,,,/' / ,~W Hoather and Goodeve (1934a,b) \~ Coughanowr and Krause ( 1 965) .~ ,' - Matteson et al. ( 1969) Neytzell-de Wilde and Taverner (1958) - Martin (1983) , 1 0 1 2 3 pH FIGURE A.12 Rate constant (k) for the Mn2+ ion catalyzed oxidation of bisulfite as a function of pHin the expression d[S(VI)~/dt =k[Mn2+~2. SOURCE: Martin (1983~.
188 Ions of other metals such as Cu and Co are much less effective catalysts for sulfite oxidation than Mn and Fe for the low values of pH encountered in the environment (Martin 1983). The mechanism by which the catalytic reactions occur has been studied by Hoffman et al. (1982) and others. A basic hypothesis being tested by Hoffman et al. is that the presence of certain trace metals in atmospheric aerosols and the occurrence of H2O2, HO, and HO2 may be interrelated phenomena. Hoffman et al. illustrate this notion by the following mechanistic sequence: Cu+(aq) + O2(aq) ~ Cup (aq), CuO+2(aq) + H+(aq) ~ Cu2+(aq) + HO2(aq), Cu+(aq) + HO2(aq) ~ Cu2+(aq) + HO2(aq), H+(aq) + HOi(aq) = H2O2(aq). For example, in atmospheric systems, Cu+, Co+, and Fez+ could be generated by photoinduced reduction of Cu2+, Co2+, and Fe3+. Cu2+(aq) + he ~ Cu2+*(aq), Cu2+ + H2O(aq) ~ Cu+(aq) + HO(aq) + H+(aq). Subsequent catalytic decomposition of the intermediate hydrogen peroxide may produce HO and additional HO2 free radicals. This hypothetical sequence of reactions could proceed according to the mechanism suggested for the classical "Fenton's reagent" reaction for the decom- position of H~O2. This mechanism involves a catalytic couple for Fe + and Fe3+ and a chain reaction that may proceed as follows: Fe2+(aq) + H2O2(aq) ~ Fe(OH)2+(aq) + HO(aq), Fe3+(aq) + H2O2(aq) ~ Fe2+(aq) + H+(aq) + HO2(aq), Fe3+(aq) + HO2(aq) ~ Fe2+(aq) + H+(aq) + O2(aq), HO(aq) + H2O2(aq) ~ H2O(aq) + HO2(aq), HO2(aq) + H2O2(aq) ~ O2(aq) + H2O(aq) + HO(aq).
189 The reactive intermediates, H2O2, HO, and HO2, in the overall sequence described in the equations may oxidize S(IV) to H2SO4. Hoffman et al. (1982) postulate another mechanism by which transition metals or transition metal complexes may catalyze the autooxidation of trace-level hydrocarbons present in cloud droplets. For a generalized hydrocarbon (RH) a possible sequence is as follows: M2+(aq) + O2(aq) + M}+-O2(aq), M3~-O2(aq) + RH(aq) ~ ~ +(aq) + R(aq) + HO2(aq), M or2(aq) + RH(aq) ~ M)+-O2H + R (aq), M3+-O2(aq) + RH(aq) ~ ~ +(aq) + R (aq) + HO2(aq) ~ M3+(aq) + R(aq) + HO2(aq), HO2(aq) + H+(aq) ~ H2O2(aq). There is some field evidence for such reactions in the atmosphere; rainwater analyses from Norway show signifi- cant numbers of alkanes, polycyclic aromatic hydrocarbons, fatty acids and esters, benzoic acids, etc. The interesting facet of this reaction scheme is the production of peroxide in the cloud droplet by gas-phase scavenged hydrocarbon products. Hoffman et al. suggest that complexes of Fe2+'3+, Mn2+~3+, Co2+~3+, and V3+~4+ should be the most effective catalysts for the autooxida- tion of sulfite. They also showed that certain metal- catalyzed reactions of sulfite may be enhanced by a photoassisted pathway. The coupling of photolytic and metal-catalyzed processes is also consistent with the observed difference between daytime and nighttime SO2 conversion rates. Dissolved organic molecules can act as competitive complexing agents for metals. The presence of complexing agents of this type will accelerate the dissolution of Fe2O3 and MnC2, which are the likely sources of soluble iron and manganese in cloud droplets. Another area of potential importance is that involving solid catalysts. Chang et al. (1978, 1981), and Brodzinski et al. (1980) showed that carbon can be an important catalyst for oxidation of sulfite in urban smog. They found from experiments at 20°C that the following rate expression decribed their results:
190 d[S(IV)] - 1.69 x 10-5[CX][O2(aq)] . (1.5 x 1012[S(IV)]2 ~ I . (80) t1 + 3.06 x 106[S(IV)] + 1.5 x 101~1S(IV)]~ J The rates are in moles per liter per second, concentra- tions of soluble species are in moles per liter, and [Cx] is the suspended carbon content of the suspension in grams per liter. The rate is independent of the pH (1.45-7.5), but it is dependent on the type of carbon (graphite, soot, etc.) employed and the surface area of the carbon particles. Comparison of Reaction Pathways for Solution-Phase Oxidation of SO2 The potential contributions of the various reactions we have considered here to solution-phase chemistry are compared for several realistic atmospheric conditions in Figure A.13. To obtain Figure A.13, Martin (1983) assumed that there are no limitations due to mass transport rates. The rate constants presented here have been applied to a hypothetical cloud containing 1 ml of liquid water per cubic meter of air at 25°C. The con- centrations of reactants assumed in the calculation are listed on the figure. Rates for other impurity concenr "rations may be derived easily by recognizing that most of the processes are first order in each species so that the conversion rates are independent of SO2 and linearly proportional to the concentration of the other species. The following are exceptions: (1) The mechanism for manganese-catalyzed oxidation changes at pH 4, because the equilibrium concentration of S(IV) goes above 10-6 M at higher values of pH; the shape of the curve is sensitive to the assumed concentrations of sulfur and manganese. (2) Oxidation by carbon catalysis is nonlinear in sulfur, and the curve of Figure A.13 will change in shape if the sulfur concentration is changed. (3) The upper portion of the curve for iron catalysis is nonlinear in sulfur. For iron-catalyzed oxidation at high pa, Martin used the result of Brimblecombe and Spedding (1974) converted to a third-order rate. The dotted part of the curve between pH 3 and 5 is very uncertain, and there may be local maxima in this region. No synergism has been included in deriving the data of Figure A.13.
191 104 103 1o2 - ~ 10 a) Q - LL 1 CC A O 10 0 10 2 10-3 10-4 10-5 H 2O2 M// / / / Mn: /NO2 0 1 2 /NO2 3 4 5 6 Gas-Phase Concentrations (ppb) H2O2 1 O3 50 HNO2 2 NO2 1 Liquid-Phase Concentrations Fe3+ 3 x 10-7 M Mn2+ 3 x 10~ M C 1x10~2g/liter pH FIGURE A.13 Theoretical rates of liquid-phase oxidation of SO2 assuming 5 ppb of SO2, 1 ml/m3 of water in air, and concentrations of impurities as shown. SOURCE: Martin (1983~. For the hydrated NO2 oxidation, Martin used the Henry's law constant and rate constants of Schwartz and White (1982) and Lee and Schwartz (1981). The concen- trations of NO2, MONO, and NO are related thermo- dynamically, and so they may not be regarded as completely independent. The trend of rising conversion rates with increased pH results from either the rising equilibrium concentration of sulfur (IV) or the sensitivity of the rate constants to pH, or both. The relative conversion rate increases with rising concentrations of sulfur (IV) in this range of pH values and for this amount of liquid. H2O2, which
192 undergoes an acid-catalyzed reaction, is the only oxidant for which the rate dependence on [H+] compensates for the decreased solubility of SO2 with increased [H+]; hence the rate of oxidation by H2O2 is nearly independent of pH. Martin emphasized that the relative positions of the curves in Figure A.13 differ for differing assumptions about the composition of the droplets. For example, an aerosol with less liquid water will, as a rule, have higher concentrations of nonvolatile species such as carbon, iron, and manganese but a smaller reaction volume, so the relative positions of the curves may differ in this situation. The relative positions will also be different at night, when the concentration of photochemically derived oxidants drops. At temperatures below 25°C, the rate constants are lower in accordance with the activation energies of the given reactions, and the Henry's law coefficients are higher. The two effects act in opposite directions. In some cases, such as that for H2O2 oxidation, the net rate rises as the temperature falls (at constant gas-phase concentration). In other cases, such as for iron catalysis, the net rate falls with temperature. The concentrations of reactants used in deriving Figure A.13 are representative of those that might be anticipated in the atmosphere. Oxidation by H2O2 dominates all reactions for conditions of low pH. Oxidation rates can be greater than 100 percent/in. The rate for oxidation by ozone varies from about 10 percent/in at pH 4.5 to about 1 percent/in at pH 4.0. The contributions from the Fe3+, Mn/+, and carbon-catalyzed reactions (for the conditions specified) are below 1 percent/in for solutions of pH ~ 4.5. Oxidation by NO2 and HONO is even less significant under these conditions. An additional influence on the rates and kinetics of sulfite oxidation in clouds and rainwater can arise from the complexation of HSOi(aq) by aldehydes scavenged by the droplets. The common gaseous products of atmospheric oxidation of the impurity hydrocarbons, CH2O, CH3CHO, CH3COCH3, and possibly other carbonyl compounds, can in principle complex with HSO3. The result of such interactions could increase the solubility of SO2 in the droplet and conceivably retard sulfite oxidation by the oxidants. Although there is significant theoretical evidence that H2O2 may be the most important oxidizing agent for acid generation in cloud water and rain, unambiguous
193 experimental measurements of H2O2 levels in air and in cloud water and rain have not been possible to date. Peroxide development in the sampling train and lack of selectivity of the luminol technique employed in previous work prevents a firm conclusion about the H2O2 levels in the atmosphere and in precipitation (Heikes et al. 1982, Zika and Saltzman 1982). Theoretical simulations of the atmospheric chemistry of a mixture of reactants in a highly diluted urban atmosphere show that H2Ok generation through reactions (71) and (73) can provide substantial levels of H2O2, CH302H, and other hydroperoxides in the gas phase. If these species are absorbed i non In aerosols, cloud water, or rainwater, for example, as is probable for H2O2 in view of its very high Henry's law constant, then oxidation by H2O2, and possibly other peroxides, can be most significant. The possible roles for peroxyacetylnitrate, peroxynitr~c acid, CH3C2H, and other peroxides in solution-phase sulfite oxidation remain to be evaluated. Solution-Phase Generation of Nitric and Nitrous Acids in the Troposphere There is some evidence of the formation of HONO2 in clouds and rainwater. Recently, both theory and experi- ment suggest that HONO2 may be formed rapidly from a combined gasphase/liquid-phase process. Through simulation, Heikes and Thompson (1981) have suggested that N205 generated by O3-NO2 reactions (15) and (16) may be scavenged effectively by H2O droplets to form HONO2 in clouds or rainwater. NO2 + O3 ~ O2 + NO3, N ~ ~ NO>(+M) ~ N2O5(+M), N2O5 + H2O(liq) ~ 2H+(aq) ~ 2NO3(aq) (15) (16) (81) A preliminary report of the experimental observation of this process has been made recently by Gertler et al. (1982). An evaluation of the contribution of this mechanism to the total [HONO2] found in the atmosphere is not now possible. Lee and Schwartz (1981) studied the rates of reactions (82) and (83):
194 2NO2(g) + HzO(liq) ~ 2H+(aq) + NO3(aq) + NO2(aq), (82) NO(g) + NO2(g) + H2O(liq) ~ 2H+(aq) + 2NO2(aq). (83) They found that at the lower partial pressures character- istic of moderately polluted atmospheres the rates are slow (10-9 to 10-8 M/h). Unless high partial pressures (e.g., 10-7 atm) of these gases are maintained in contact with liquid water for substantial periods of time (tens of hours), reactions (82) and (83) cannot represent a substan- tial source of atmospheric acidity. Lee and Schwartz found no evidence of Fez+ ion catalysis of these reactions, but they suggested that possibly other metal ions could enhance these rates. There is no evidence related to this pos- sibility now available. Although significant uncertainty remains concerning the source of HNO3 in clouds and rainwater, the limited evidence currently available favors the probable importance of the formation of N2O5 in (15) and (16) followed by its reaction in water droplets to form HNO3. SUMMARY In summary, a wide variety of interrelated homogeneous gas-phase, solution-phase, and heterogeneous chemistry may result ultimately in oxidation of SO2 to sulfuric acid and NOX to nitric acid. The homogeneous gas-phase oxidation of SC2 by the HO radical and the solution-phase oxidation of S(IV) through H2O2, O3, and possibly other species appear to be the major sources of H2SO4. In the cloud-free, ambient, sunlight-irradiated troposphere, nitric acid is probably generated largely by the reaction of HO radicals with NO2. Both HONO2 and H2SO4 produced in the gas phase can be scavenged effectively by cloud water and precipita- tion. NO2 may be oxidized to HONO2 if sufficient O3 and NO2 are present. Following its gas phase generation, N2O5 may be scavenged effectively by water droplets to form HONO2. All the various pathways that lead to the oxidation of SO2 and NOX are coupled by common products and reactants that can directly and indirectly influence the rates of reaction by the other pathways. In general the homogene- ous gas-phase reactions can lead to maximum daylight rates of acid formation of a few percent per hour for SO2 and 20-30 percent/in for NOk. Solution-phase reactions involving H2O2 and O3 can in principle
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