Deviations from Henry’s law for hydrogen peroxide during a cloud lifetime

Ž where a is the droplet radius, d is the coefficient of diffusion in gaseous phase egal to g 2 y1 . 0.1 cm s , v is the mean molecular speed and a is the accommodation coefficient. As soon as cloud water is present, additional rate equation for the aqueous concentra- tion C has to be accounted for: aq dC k C aq t aq s P y L C q Lk C y 4 Ž . aq aq aq t g d t H RT eff Ž . In pure gas phase chemistry, the characteristic time scales lifetimes are expressed by the inverse of the term , and in gas-aqueous chemistry two different terms are involved: y1 k t y1 D q Lk and D q . 5 Ž . Ž . g t aq ž H RT eff The equilibration time is often taken as the characteristic lifetime of the species. In fact, the equilibration time t is just proportional to this lifetime for pure gaseous eq chemistry, and it is given by: C y C g g eq s D C 6 Ž . g g t eq Ž . where D is the inverse of the lifetime of the species chemical destruction rate and g C the equilibrium concentration. g eq With transfer to aqueous phase, this equation becomes: C y C g g eq s D C q Lk C 1 y q 7 Ž . Ž . g g t g t eq Ž where q s C rLH RTC expresses the deviation from Henry’s law equilibrium q aq eff g . equals 1 in Henry’s law equilibrium . This ratio q is linked to the partitioning of material between gas and liquid phases. If Ž . Ž . q 1 or q - 1 , this means that the species is preferably in the aqueous or gaseous phase. This ratio has been discussed by other authors but rather in experimental studies Ž . Laj et al., 1997; Ricci et al., 1997; Winiwarter et al., 1988, 1994 . Most of the time, it has been studied for very soluble species such as NH , HNO and HCOOH and its 3 3 Ž . evolution has been drawn versus either drop radius or pH. Laj et al. 1997 are the ones that complete the quantification of this partitioning process for H O , but the results 2 2 have also been discussed only as a function of pH. Here, we want to look at this ratio as a function of the variation of the liquid water content and consider various scenarios that include the limitation by mass transfer and Ž . the reactivity of the hydrogen peroxide with SO in particular . 2

3. Deviations from Henry’s law for hydrogen peroxide during a cloud lifetime

The evolution of hydrogen peroxide has been followed during a cloud event by Ž . means of a chemical box model Madronich and Calvert, 1990 , which interprets any chemical mechanism, including aqueous phase chemistry based upon Gregoire et al. ´ Ž . 1994 . The chemical system is a standard gas phase mechanism including methane and CO in the presence of NO and sulfur dioxide. The pH is held constant, equal to 4. x Tables 1–5 list the reactions, the initial concentrations of the species and values of accommodation coefficients used to calculate k coefficients. Since radiative properties t of the cloud are unknown, we neglect the modification of the radiation field by the cloud. To produce hydrogen peroxide mean photolysis rate values are only considered during this cloud event but photolysis inside the droplets is taken into account as shown Ž . in Table 3. In Table 4 the levels of concentrations for hydrogen peroxide 2 ppb and Ž . SO 1ppb are typical of a moderately polluted continental area. NO , O and CO 2 x 3 Table 1 Ž List of the reactions and equilibrium in the gas phase with corresponding rate and equilibrium constants from . Lelieveld and Crutzen, 1991, G27 from De More et al., 1987 a Gas phase reaction scheme Rate constants P b G1 O qH Oq hn ™2OH qO J 3 2 2 eff P P y12 Ž . G2 O qOH ™HO qO 1.6=10 exp y940rT 3 2 2 P P y14 Ž . G3 O qHO ™OH q2O 1.1=10 exp y500rT 3 2 2 y13 Ž Ž . G4 2HO ™H O qO 2.3=10 exp 600rT 2 2 2 2 y33 w x Ž .. q1.7=10 M exp 1000rT y2 1 Ž w x Ž .. = 1q1.4=10 H O exp 2200rT 2 P y6 G5 H O q hn ™2OH 4.6=10 2 2 P P y12 Ž . G6 H O qOH ™HO qH O 3.3=10 exp y200rT 2 2 2 2 P P y12 Ž . G7 CH qOH qO qM ™CH O qH OqM 2.3=10 exp y1700rT 4 2 3 2 2 P P y12 G8 CH O qHO ™CH O HqO 4.0=10 3 2 2 3 2 2 P P y6 G9 CH O HqO q hn ™CH OqHO qOH 4.6=10 3 2 2 2 2 P y12 G10 CH O HqOH ™CH O qH O 5.6=10 3 2 3 2 2 P y12 G11 CH O HqOH ™CH OqOH qH O 4.4=10 3 2 2 2 y5 G12 CH Oq2O q hn ™COq2HO 1.7=10 2 2 2 y5 G13 CH Oq hn ™COqH 3.3=10 2 2 P P y11 G14 CH OqOH qO ™COqHO qH O 1.1=10 2 2 2 2 P P y13 G15 COqOH qO qM ™CO qHO qM 2.4=10 2 2 2 y12 Ž . G16 NOqO ™NO qO 2.0=10 exp y1400rT 3 2 2 y3 G17 NO O q hn ™ NOqO 5.6=10 2q 2 3 P P y12 Ž . G18 NOqHO ™NO qOH 3.7=10 exp 240rT 2 2 P P y12 Ž . G19 NOqCH O qO ™NO qCH OqHO 4.2=10 exp 180rT 3 2 2 2 2 2 y11 Ž . Ž . G20 NO qOH qM ™ HNO qM 1.2=10 2 3 y7 G21 HNO q hn ™NO qOH 3.2=10 3 2 P y15 E22 CH OqHO lO CH OH 6.7=10 2 2 2 2 P P y12 G23 O CH OHqHO ™HCO HqHO qO 2.0=10 2 2 2 2 2 2 P y12 G24 O CH OHqNOqO ™HCO HqHO qNO 7.0=10 2 2 2 2 2 2 P y13 G25 O CH OHqO CH OH ™2HCO HqHO qH O 1.2=10 2 2 2 2 2 2 2 P y13 G26 HCO HqOHqO ™CO qHO qH O 3.2=10 2 2 2 2 2 y12 Ž . G27 SO qOH qM ™H SO qHO k s1.5=10 ; Fc s 0.6; 2 2 4 2 ` y31 y3.3 Ž . k s 3=10 Tr300 a Reaction rate constants of first order reactions are in s y1 , of 2nd order reactions in molecule y1 cm 3 s y1 . b Ž 1 . y5 Ž 1 . y1 0 Ž 1 . Ž 3 . O q hn ™O qO D J s1.6=10 O D qH O ™2OH k s2.2=10 O D qN ™O P q 3 2 2 1 2 y1 1 Ž Ž .. Ž 1 . Ž 3 . y1 1 Ž Ž N k s 4=10 exp 67 1rTy1r298 O D qO ™O P qO k s 2.6=10 exp 110 1rTy 2 2 2 2 3 .. Žw x Ž w x w x w x.. 1r298 J s J k H O r k H O q k O q k N . eff 1 2 1 2 2 2 3 2 Table 2 List of the gas–aqueous phase equilibria with corresponding henry’s law constants and of aqueous equilibria Ž . with corresponding dissociation constants from Lelieveld and Crutzen, 1991 a Gas–aqueous and aqueous phase equilibria Henry’s law and dissociation constants K 298 q y y14 Ž Ž .. E1 H O lH qOH 1.0=10 exp y6716 1rTy1r298 2 y2 Ž . Ž . Ž Ž .. H1 O gas lO aq 1.1=10 exp 2300 1rTy1r298 3 3 4 Ž . Ž . Ž Ž .. H2 H O gas lH O aq 7.4=10 exp 6615 1rTy1r298 2 2 2 2 y q y12 Ž . Ž Ž .. E2 H O aq lHO qH 2.2=10 exp y3730 1rTy1r298 2 2 2 2 Ž . Ž . Ž Ž .. H3 CH O H gas lCH O H aq 2.2=10 exp 5653 1rTy1r298 3 2 3 2 3 Ž . Ž . Ž . Ž Ž .. H4 CH O gas lCH OH aq 6.3=10 exp 6425 1rTy1r298 2 2 2 5 Ž . Ž . Ž Ž .. H5 HNO gas lHNO aq 2.1=10 exp 8700 1rTy1r298 3 3 q y Ž . E3 HNO aq lH qNO 15.4 3 3 P P 3 Ž . Ž . Ž Ž .. H6 HO gas lHO aq 2.0=10 exp 6600 1rTy1r298 2 2 P q y y5 Ž . Ž . E4 HO aq lH qO aq 3.5=10 2 2 P P Ž . Ž . Ž Ž .. H7 OH gas lOH aq 25 exp 5025 1rTy1r298 y3 ` Ž . Ž . Ž Ž .. H8 NO gas lNO aq 6.4=10 exp 2500 1rT 1r298 2 2 ` 3 ` Ž . Ž . Ž Ž .. H9 NO gas lNO aq 1.9=10 exp 1480 1rT 1r298 P P 3 Ž . Ž . Ž Ž .. H10 CH O gas lCH O aq 2.0=10 exp 6600 1rTy1r298 3 2 3 2 3 Ž . Ž . Ž Ž .. H11 HCO H gas lHCO H aq 3.7=10 exp 5700 1rTy1r298 2 2 q y y4 Ž . Ž Ž .. E5 HCO H aq lH qHCO 1.8=10 exp y1510 1rTy1r298 2 2 P Ž . Ž . Ž Ž .. H12 SO gas lSO aq 1.2 exp 3120 1rTy1r298 2 2 P q P y2 Ž . Ž Ž .. E6 SO aq lH qHSO 1.7=10 exp y2090 1rTy1r298 2 3 P q 2y y8 Ž Ž .. E7 HSO lH qSO 6=10 exp y1120 1rTy1r298 3 3 a Henry’s law constants in mol l y1 atm y1 and dissociation constants in mol l y1 at 298 K. levels are rather representative of a remote area. These concentrations were chosen in order to fit the conditions at the Kleiner Feldberg in Germany, which is considered for the cloud observations and described below. Table 3 Ž List of the reactions in the aqueous phase with corresponding rate constants from Lelieveld and Crutzen, . 1991 a Aqueous phase reaction scheme Rate constants at 298 K P y1 Ž . A1 H O q hn ™ 2OH G5=1.6 in s 2 2 y1 Ž . A2 O q hn ™ H O q O G1=1.6 in s 3 2 2 2 P P 9 Ž . Ž Ž .. A3 CH OH qOH q O ™ HCO Hq HO q H O 2.0=10 exp y1500 1rTy1r298 2 2 2 2 2 2 P P 8 Ž Ž .. A4 HCO Hq OH q O ™ CO q HO qH O 1.6=10 exp y1500 1rTy1r298 2 2 2 2 2 y q P y 9 Ž Ž .. A5 HCO qOH O ™ CO q HO q OH 2.5=10 exp y1500 1rTy1r298 2 2 2 2 P P y 9 Ž Ž .. A6 O q O ™H O OH q OH q 2O 1.5=10 exp y1500 1rTy1r298 3 2 2 2 P y y 8 Ž Ž .. A7 HO q O qH O ™ H O q OH q O 1.0=10 exp y1500 1rTy1r298 2 2 2 2 2 2 P P 7 Ž Ž .. A8 H O q OH ™ HO q H O 2.7=10 exp y1715 1rTy1r298 2 2 2 2 P y y 7 Ž Ž .. A9 CH O q O q H O ™ CH O Hq OH q O 5.0=10 exp y1610 1rTy1r298 3 2 2 2 3 2 2 P 7 Ž Ž .. A10 CH O HqOH ™ CH O qH O 2.7=10 exp y1715 1rTy1r298 3 2 3 2 2 2y 7 Ž Ž .. A11 SO qO ™SO qO 1.9=10 exp y1860 1rTy1r298 3 3 42y 2 2y y 9 Ž Ž .. A12 SO qOH ™SO qOH 5.5=10 exp y1500 1rTy1r298 3 42y y 9 Ž Ž .. A13 HSO qOHqO ™SO qH O 9.5=10 exp y1500 1rTy1r298 3 2 3y 2 y q 7 Ž Ž .. A14 HSO qH O ™SO q H OqH 7.45=10 exp y4725 1rTy1r298 3 2 2 42y 2 a y1 y1 Ž . Rate constants are in mol l s except for A1 and A2 . Table 4 Initial values of the chemical species O H O SO CH O H CH O CO HNO HO OH NO NO CH O HCOOH 3 2 2 2 3 2 2 3 2 2 3 2 25 ppb 2 ppb 1 ppb 2 ppb 0.5 ppb 140 ppb 200 ppt 9 ppt 0.08 ppt 12 ppt 6 ppt 9 ppt 0.3 ppt In order to simulate a cloud event, a variable liquid water content has been introduced Ž . in the chemical model. The liquid water content evolution Fig. 1 corresponds to observations at Kleiner Feldberg on October 31th 1990 for a stratocumulus cloud, during Ž the 1990s Cloud Experiment EUROTRAC Subproject Ground-based Cloud Experi- . ment, Fuzzi, 1994 . The time duration of the simulation is four hours. The cloud is essentially maintained during 1 h and then it dissipates. The maximum water content was 0.2 grkg. In this simple cloud scenario, three sensitivity runs are performed. The first one only includes gas-phase chemical reactions and uptake of gases by the drops. The two others consider gas and aqueous phase chemistry and include or exclude sulfur dioxide chemistry. When SO is taken into account, higher reactivity is obtained in aqueous 2 Ž . phase for H O . The sensitivity of the drop size 10 mm vs. 100 mm is also examined 2 2 in each case. Then, the uptake of the gases by the drops can be either described using instantaneous Henry’s law equilibrium or full kinetic mass transfer following Schwartz Ž . 1986 . Fig. 2 shows the time evolution of hydrogen peroxide in every run. In Fig. 2a, the assumption of instantaneous Henry’s law equilibrium is valid for droplets of 10 mm radius but gives slightly different result for larger drops. This is due to the fact that for soluble species, equilibrium between gas and aqueous phases is Ž . established more slowly for larger drops Iribarne and Cho, 1989; Huret et al., 1994 . Ž . If aqueous phase reactions are now added Fig. 2b , some deviations arise between the run assuming Henry’s law equilibrium and the run including mass transfer. This is essentially true for larger drops as explained before. There is 16 discrepancy for large drops at the entrance of the cloud. During cloud dissipation, differences between the two assumptions are of 13 for the smaller droplets and 8 in the case of larger ones. Table 5 Values of the mass accommodation coefficients Species Mass accommodation Reference coefficient Ž . O 2E-3 Utter et al. 1992 3 Ž . H O 0.18 Ponche et al. 1993 2 2 Ž . CH O H 0.05 Worsnop et al. 1992 3 2 Ž . CH O 0.05 Lelieveld and Crutzen 1991 2 Ž . HNO 0.125 Van Doren et al. 1990 3 Ž . HO 0.2 Lelieveld and Crutzen 1991 2 Ž . OH 0.05 Lelieveld and Crutzen 1991 Ž . NO 6.3E-4 Lelieveld and Crutzen 1991 2 Ž . NO 1E-4 Lelieveld and Crutzen 1991 Ž . CH O 0.05 Lelieveld and Crutzen 1991 3 2 Ž . HCOOH 0.05 Lelieveld and Crutzen 1991 Ž . Ž Fig. 1. Time evolution of the liquid water content in vrv during the Kleiner Feldberg Experiment Fuzzi, . 1994 . The more drastic discrepancies are observed if furthermore SO chemistry is added 2 Ž . Fig. 2c . For hydrogen peroxide, by considering Henry’s law equilibrium, gas phase concentration is greatly overestimated whatever the drop size is. Especially, for low Ž . Ž water contents from 10 to 11 h , the two assumptions Henry’s law equilibrium and . mass transfer severely deviate for smaller drops. The second assumption leads to higher amount of gas uptake when entering the cloud because of higher speed of transfer. For bigger drops, the speed of transfer is diffusion limited and deviations from Henry’s law are less important. Hence, soluble and reactive species such as H O may not be 2 2 considered in an instantaneous equilibrium between the gas and aqueous phases during the formation stage or the dissipation of clouds. On Fig. 3, the factor q has been drawn for small and large drops in the three runs described previously: the first run considers only gas phase chemistry plus mass transfer, while the two others take into account both gas and aqueous phase chemistry and either exclude or include SO chemistry. The curves of Fig. 3 just reflect what we have 2 already seen on Fig. 2 but will be helpful in the following section to compare the chemical behaviour of H O in a cloud simulated by a mesoscale model. 2 2 In fact, this q factor represents the partitioning of the species among phases and is linked to the equilibration time of the species in the presence of clouds. Before the occurrence of the aqueous phase, q is equal to zero and the driving term of the equilibration is D . g Ž . At a sudden introduction of aqueous phase, the term Lk C 1 y q with q close to t g zero, becomes the driving term of the equation for most of the species. When Henry’s law equilibrium is established, the relaxation time will be driven by D again. Any g deviation from Henry’s law can therefore significantly increases the equilibration time in each phase. For the aqueous phase, the equilibration time can be derived in the same manner: C y C k aq aq t eq s D C q C 1 y q rq 8 Ž . Ž . aq aq aq t H RT eq eff aq Hence, three types of equilibria determine the equilibration time of each species: the physical equilibrium between the two phases and the chemical equilibrium of each phase. Fig. 3. Time evolution of the factor q sC r LH RTC , for the three sensitivity runs: gas phase chemistry aq eff g Ž . and mass transfer are considered ‘‘transfer’’ , gas phase chemistry, aqueous phase chemistry and mass Ž . transfer are considered ‘‘aqueous’’ and SO chemistry, gas phase chemistry, aqueous phase chemistry and 2 Ž . Ž . Ž . mass transfer are considered ‘‘SO ’’ and two drop sizes: a drops with 10 mm radius and b drops with 100 2 m m radius. Assuming that the equilibration time is mainly due to chemical reactions, this leads to consider that the partition between the aqueous and gaseous phases always follows the Ž . Henry’s law instantaneous Henry’s law equilibrium . This assumption requires that for most species the fluxes at the interface are faster than gas or aqueous chemistry which means that the characteristic times of chemical reactions D y1 and D y1 are, respectively, g aq Fig. 2. Time evolution of the hydrogen peroxide concentration in molecrcm 3 for various hypothesis, indicated Ž in the right-hand side legend Henry’s law equilibrium is assumed, then mass transfer is considered for small . Ž . and large drops, respectively and for the three sensitivity runs, which are described as follows: a gas phase Ž . chemistry and mass transfer are considered; b gas phase chemistry, aqueous phase chemistry and mass Ž . transfer are considered and c SO chemistry, gas phase chemistry, aquaeous phase chemistry and mass 2 transfer are considered. Ž . y1 Ž . y1 higher than Lk and k rH RT . This is observed for H O scavenged by small t t eff 2 2 drops of 10 mm radius when no SO chemistry is involved as can be seen on Fig. 3a. 2 For big drops, the total content of H O in a single drop may become so important in 2 2 phase equilibrium, that the resulting equilibration time seriously exceeds the chemical . equilibration times and the model timestep , even with fast exchanges at the interface of Ž . the drops Lk term . In such case, deviations from Henry’s law is observed with q - 1 t at the onset of the cloud and q 1 during the dissipation stage of the cloud. Fast exchanges are also revealed through the high variations in the q factor. Ž . In the second run without SO the value of D of the hydrogen peroxide is small 2 g compared to Lk for both 10 mm and 100 mm cases, as D is small compared to t aq Ž . Ž Ž .. k rH RT. It is noteworthy that both D q Lk and D q k rH RT decreases t eff gas t aq t eff by a factor of 100 between the 10 mm and 100 mm cases, meaning that the equilibration time is much longer for big drops. When sulfur dioxide is added, Lk is still higher than t D , while D becomes higher than k rH RT by a factor of 2000 in the case of small g aq t eff Ž . drops and only by a factor of 2 up to 8 in the big drop case. The driving time scale in Ž . y1 the aqueous phase equilibrium is then k rH RT . Hence, the method assuming t eff instantaneous Henry’s law equilibrium is not applicable anymore, and the q factor is Ž . always less than 1 Fig. 3 .

4. Deviations from Henry’s law for hydrogen peroxide in a polydisperse cloud