Fast sulfate formation from oxidation of SO2 by NO2 and HONO observed in Beijing haze

Severe events of wintertime particulate air pollution in Beijing (winter haze) are associated with high relative humidity (RH) and fast production of particulate sulfate from the oxidation of sulfur dioxide (SO2) emitted by coal combustion. There has been considerable debate regarding the mechanism for SO2 oxidation. Here we show evidence from field observations of a haze event that rapid oxidation of SO2 by nitrogen dioxide (NO2) and nitrous acid (HONO) takes place, the latter producing nitrous oxide (N2O). Sulfate shifts to larger particle sizes during the event, indicative of fog/cloud processing. Fog and cloud readily form under winter haze conditions, leading to high liquid water contents with high pH (>5.5) from elevated ammonia. Such conditions enable fast aqueous-phase oxidation of SO2 by NO2, producing HONO which can in turn oxidize SO2 to yield N2O.This mechanism could provide an explanation for sulfate formation under some winter haze conditions.

B eijing experiences severe air pollution events in winter, commonly called winter haze. The concentration of fine particulate matter with aerodynamic diameter less than or equal to 2.5 μm (PM 2.5 ) can exceed 200 μg m −3 on a 24-h average basis during these events 1 , considerably higher than the 24-h Chinese National Ambient Air Quality Standard of 75 μg m −3 . Winter haze events are often associated with high relative humidity (RH) [2][3][4][5] and a major contribution of sulfate to total PM 2. 5 6 . Sulfate is produced in the atmosphere by oxidation of sulfur dioxide (SO 2 ) emitted from coal combustion 7,8 . But the photochemical oxidants known to drive atmospheric oxidation of SO 2 (hydroxyl radical, hydrogen peroxide, ozone) have very low concentrations under typical winter haze conditions 7,9,10 . This has led to considerable debate regarding the mechanisms responsible for sulfate formation in winter haze 9,[11][12][13] .
The high-RH conditions characteristic of winter haze cause particulate matter to take up water, enabling aqueous-phase pathways for SO 2 oxidation. SO 2 is a weak acid with moderate water solubility (Henry's law constant K H = 1.2 M atm −1 at 298 K) that dissociates in water to form bisulfite (HSO 3 − ; pK a,1 = 1.9 at 298 K) and sulfite (SO 3 2− ; pK a,2 = 7.2 at 298 K). Bisulfite and sulfite are converted to sulfate by a number of aqueous-phase oxidants with rates dependent on pH 14 . As the air cools at night or through rising motions the haze can turn to fog and low clouds (RH > 100%), increasing the atmospheric liquid water content (LWC) by orders of magnitude and hence the importance of SO 2 aqueous-phase oxidation pathways.
Most previous studies of sulfate formation during Beijing haze events have focused on mechanisms taking place in the ubiquitous haze particles (RH < 100%) rather than in the more sporadic fog and cloud (RH > 100%) 13,[15][16][17] . Haze particles are concentrated aqueous solutions with pH that can be estimated from standard thermodynamics 18 . Aqueous-phase oxidation of SO 2 by nitrogen dioxide (NO 2 ) in haze has been proposed 9,11,13 , with NO 2 originating from vehicular emissions, but requires higher pH than the 4-5 range inferred from thermodynamic calculations [19][20][21] . Some studies have suggested that oxidation by NO 2 would be enhanced by fog 9,13,17 . Aqueous-phase autoxidation of SO 2 by molecular oxygen catalyzed by transition metal ions (TMI) has been proposed 22,23 but is poorly constrained due to the lack of information on TMI concentration, complexation, and solubility 24 . A recent study suggests that aqueous-phase oxidation by hydrogen peroxide (H 2 O 2 ) in haze could be significant 10 . Yet another suggestion is that some of the reported sulfate could actually be hydroxymethanesulfonate (HMS) produced by incloud complexation of HSO 3 − and SO 3 2− with formaldehyde (HCHO) 25,26 .
Here we present detailed chemical observations during a Beijing haze event in December 2016 where PM 2.5 concentrations reached 400 μg m −3 . We observe fast sulfate production as RH increases over the course of the event, leading to extensive nighttime fog and low clouds, and find a concurrent increase of nitrous oxide (N 2 O). N 2 O is a product of aqueous-phase SO 2 oxidation by dissolved nitrous acid (HONO) [27][28][29] , and observations of HONO during the event support this sulfate formation mechanism. Most of the HONO appears in turn to be produced by aqueous-phase SO 2 oxidation by NO 2 , leading us to propose a two-step fog-enabled mechanism for sulfate formation during winter haze events.

Results
Field observations. Figure 1 shows the time series of selected variables measured at our field site on the rooftop of an Institute of Atmospheric Physics (IAP) building in urban Beijing during December 4-22, 2016. The start of the campaign on December 4 sampled the end of a haze event that terminated on December 5 with passage of a cold front. Variable conditions were observed during December 6-15 (data not shown). An extended haze event then developed over the December 16-22 period, with 24-h average PM 2.5 exceeding 200 μg m −3 for 6 successive days before a cold front swept in with clean air on December 22.
Wind speed during the December 16-22 haze event was persistently low in the range of 0.3-1.5 m s −1 and the mixed layer height (MLH) was less than 600 m above ground level (AGL), decreasing to 300 m at night. The early part of the event on December 16-19 (labeled Stage I in Fig. 1) had moderate RH in the 40-75% range. On December 20-21 (Stage II) the RH rose to above 75% as temperatures cooled to an average of 271 K at night, and dense nighttime fog with LWC as high as 0.5 g m −3 was observed at the Beijing Observatory meteorological station 20 km to the south (Fig. 1). Beijing International Airport also reported fog during that period ( Supplementary Fig. 1). Dense fog was not observed at our site, but the visibility dropped below a few hundred meters and low clouds formed just 50 m above ground ( Supplementary Fig. 2). PM 2.5 concentrations rose to over 400 μg m −3 during the high-RH period (Stage II) in concert with a rise in sulfate, while nitrate remained at the same concentration as in Stage I (47 μg m −3 ). Black carbon (BC) increased from 9.4 to 13.1 μg m −3 . SO 2 concentrations were relatively high in Stage I but nearly depleted in Stage II, indicating rapid oxidation of emitted SO 2 to sulfate. Figure 2 shows that the sulfate particles measured by highresolution aerosol mass spectrometer (HR-AMS) shifted to larger sizes during Stage II while the organic particles did not, consistent with sulfate formation taking place in fog and low cloud (cloudmediated coagulation would have affected both sulfate and organic particles). Mean PM 2.5 increased from 210 μg m −3 in Stage I to 330 μg m −3 in Stage II, while sulfate measured by HR-AMS increased fourfold from 10 to 40 μg m −3 . The sampling efficiency of the HR-AMS instrument (PM 1 ) drops off rapidly for particles above 1-μm diameter 30 , implying that actual sulfate levels during Stage II were probably much higher than measured. Indeed, PM 2.5 sulfate concentrations measured at the site by online ion chromatography (URG-9000D Ambient Ion Monitor) were 1.5-2 times larger than the HR-AMS measurements during Stage II ( Supplementary Fig. 3). Some of the sulfate particles could even be larger than PM 2.5 due to swelling at high RH.
Evidence for SO 2 oxidation by HONO. A remarkable feature of the observations in Stage II is the large rise in N 2 O concentrations concurrently with sulfate. N 2 O is a major greenhouse gas with a globally dominant biogenic source 31 . It is chemically inert in the troposphere. Vehicles and coal combustion may be a significant source of N 2 O in Beijing 32 , but this would not explain the N 2 O rise in Stage II because no parallel rise was observed for BC ( Fig. 1). Figure 3 shows the relationships between the concentrations of sulfate and different nitrogen oxide species (N 2 O, HONO, NO 2 , and PM 1 nitrate) observed in Stages I and II. The relationships are shown only for nighttime hours (19:00-06:00) to minimize strong common dependences on diurnal changes in mixed layer depth, and to avoid the effect of fast HONO photolysis in the daytime. Sulfate correlates positively with all species in Stage I, which may reflect common dependences on atmospheric mixing and ventilation. In Stage II, sulfate is positively correlated with N 2 O (including a step increase) and with HONO, but negatively correlated with NO 2 and nitrate. This suggests a change in the regime for sulfate production in Stage II with associated production of N 2 O. Looking back at the tail end of the previous haze event on December 4, which also featured high-RH conditions, we again see elevated N 2 O together with sulfate ( Fig. 1). N 2 O is a product of the aqueous-phase oxidation of SO 2 by HONO 28,29 . HONO is moderately soluble in water (Henry's law constant K H = 49 M atm −1 at 298 K) and dissociates as a weak acid (pK a = 3.2 at 298 K) to increase its partitioning in the aqueous phase 33 . The aqueous-phase oxidation of SO 2 by HONO can be expressed stoichiometrically as follows 28,29 : 2NðIIIÞ þ 2SðIVÞ ! N 2 O " þ2SðVIÞ þ other products: ðR1Þ Here N(III) ≡ HONO(aq) + NO 2 − denotes the dissolved HONO species, S(IV) ≡ SO 2 •H 2 O + HSO 3 − + SO 3 2− denotes the dissolved SO 2 species, and S(VI) ≡ H 2 SO 4 (aq) + HSO 4 − + SO 4 2− denotes the sulfate species. The other products may include H 2 O or H + depending on the speciation of N(III), S(IV), and S(VI). A laboratory study by Martin et al. 28 gives a rate expression for sulfate formation from reaction (R1) at pH < 4: where k 1 = 142 M −3/2 s −1 . Another study by Oblath et al. 27 gives a rate expression  Fig. 3 are similar for Stages I and II and not consistent with the 2:1 stoichiometry of reaction (R1). A possible explanation is that the PM 1 sulfate measurements underestimated total sulfate concentrations during Stage II, as shown above. In addition, it is likely that the correlations and slopes are mainly driven by mixing rather than M denotes mass and D va denotes particle vacuum aerodynamic diameter. The measurements were made by the HR-AMS instrument with 50% size cut at 1-μm diameter, hence the data are shown as PM 1 (particulate matter with less than 1-μm diameter). Mass modal diameters are shown as dotted lines. chemistry, as is frequently observed in polluted air masses 34,35 . The signature of the reaction (R1) taking place in Stage II would then be manifested by the step increase in N 2 O between the two Stages.
Importance of fog and cloud. Reaction (R1) requires fog or cloud to proceed at an appreciable rate. LWCs in haze are too low. It also requires a relatively high pH. The mean gaseous ammonia concentration observed during Stage II was 14 ppb (Fig. 1), typical of previous observations during haze events 36 and mainly attributable to emissions from fuel combustion 37 . Fog has a much higher pH than haze under high-ammonia conditions because of efficient scavenging of ammonia at high LWC. Whereas ammonia volatility limits the pH of haze aqueous solutions to a 4-5 range even with ammonia in large excess 19,20,[38][39][40] , the corresponding pH range in fog is 6-7 9,13,21,41,42 . Higher pH in haze can be achieved if dust is a significant component 9,21,42 but low LWC is still a limitation. PM 2.5 concentrations of dust cations (Ca 2+ , Mg 2+ ) were low at our site, as described in the "Methods" section.
Our sampling site did not actually experience fog during Stage II, but the cloud deck extended down to 50 m ( Supplementary  Fig. 2), and surface air would have been processed by that low cloud and/or by fog elsewhere. We estimate a fog/cloud pH of 5.7 on the basis of our mean measured value of 14 ppb total ammonia to be partitioned into the fogwater; a fog LWC of 0.15 g m −3 ; sulfate, nitrate, and chloride PM 2.5 present as their ammonium salts; and a temperature of 271 K (see "Methods"). Past observations for Beijing in winter indicate a fog/cloud pH range of 4.7-6.9 7,11,26,43,44 . Sensitivity to pH will be examined in the "Discussion" section.
We can estimate the e-folding lifetime for SO 2 oxidation by HONO in nighttime fog on the basis of a fog with pH 5.7 and LWC of 0.15 g m −3 , and assuming a mean nighttime total HONO concentration of 9 ppb as measured during Stage II (Fig. 1). This involves applying the rate expression for reaction (R1) with Henry's law and acid dissociation constants computed at 271 K (Supplementary Table 1). We find a fogwater nitrite (N(III), mainly as NO 2 − ) concentration of 2.2 μmol L −1 , which leads to an e-folding SO 2 lifetime of 3.8 h using the rate expression of Martin et al. 28 extended to pH 5.7 but 79 h using the rate expression of Oblath et al. 27 . The former would imply a major role of HONO as SO 2 oxidant while the latter would imply an insignificant role. As we will see, the HONO concentration in fog could actually be much higher than measured at our site, which would increase the importance of reaction (R1). The observed increase of N 2 O in Stage II does suggest an important role for reaction (R1).

Evidence for SO 2 oxidation by NO 2 and production of HONO.
A remarkable result in Fig. 3 is the positive correlation of sulfate with HONO during Stage II, and the negative correlations with NO 2 and nitrate. Aqueous-phase loss of NO 2 during haze and fog is generally thought to be driven by particle-phase disproportionation to HONO and HNO 3 11 , but if this were the case we would expect an increase in nitrate during Stage II in contrast to what was observed (Figs. 1 and 3). Aqueous-phase oxidation of S(IV) by NO 2 (aq) in fog is an alternative explanation for the depletion of NO 2 and produces both HONO and sulfate 28 , which would be consistent with the positive correlation observed between the two (Fig. 3): ðR2Þ Laboratory studies give a rate expression for reaction (R2) as with k 2 = 2 × 10 6 M −1 s −1 for the pH range 5.8-6.4 (Lee and Schwartz 45 ) and k 2 = 1.2-1.5 × 10 7 M −1 s −1 for the pH range 5.3-6.8 (Clifton et al. 46 ). For a mean nighttime NO 2 concentration of 50 ppb during Stage II (Fig. 1), and a fog with LWC = 0.15 g m −3 and pH = 5.7, we find an SO 2 e-folding lifetime of 1-7 min against loss by reaction (R2) depending on which value of k 2 is used, sufficiently short in any case for SO 2 depletion. Reaction (R2) further produces N(III) as NO À 2 , which in a fog of pH 5.7 would remain in the aqueous phase and may thus go on to oxidize SO 2 by reaction (R1). If reaction (R1) is sufficiently fast, following the rate expression of Martin et al. 28 , then a steady state would be established at night between production of NO À 2 in the fog by reaction (R2) and loss by reaction (R1), resulting in an effective sulfate mass yield of 2 from reaction (R2).
An SO 2 oxidation mechanism in nighttime fog involving reaction (R2) followed by reaction (R1) would be consistent with our observed enhancement of N 2 O. In that mechanism, one mole of N 2 O is produced for every three moles of SO 2 oxidized. Starting from a SO 2 level of 20 ppb in Stage I (Fig. 1), complete oxidation of that SO 2 to sulfate would produce 7 ppb N 2 O, consistent with the ≈5 ppb increase of N 2 O observed between Stage I and Stage II (Fig. 3). The mechanism both produces and consumes HONO in the oxidation of SO 2 , whereas N 2 O is a terminal product, which may explain why HONO shows a positive correlation with sulfate in Stage II but not a step increase. One would similarly expect one mole of NO 2 to be consumed for  Fig. 3 is only −0.2 mol mol −1 , which could suggest additional NO 2 sinks associated with fog, an underestimate of sulfate in the Stage II observations as previously discussed, or a dominance of atmospheric mixing in determining the slope. Figure 4a illustrates our proposed mechanism for sulfate formation involving reactions (R1) and (R2) in nighttime fog and cloud associated with winter haze events. We conducted air parcel model calculations to study the pH dependence of sulfate formation in this mechanism. For reaction (R1) we used the rate expression from Martin et al. 28 , because the much slower rate expression of Oblath et al. 27 would not explain the observed N 2 O enhancement. For reaction (R2) we followed the rate constant (k 2 ) estimates of Lee and Schwartz 45 as 1.4 × 10 5 M −1 s −1 for pH < 5 and 2 × 10 6 M −1 s −1 for pH > 6, with linear interpolation between these two pH ranges. Henry's law and acid dissociation equilibrium constants for SO 2 , NO 2 , and HONO are in Supplementary Table 1. The air parcel was initialized with concentrations taken from the field observations during Stage I including [SO 2 ] = 20 ppb, [NO 2 ] = 80 ppb, [HONO] = 5 ppb, and then allowed to evolve as a closed system for 5 h in a nighttime fog with LWC = 0.15 g m −3 and T = 271 K. The time scale for equilibration between the gas and aqueous phases in fog is less than a few minutes 47 , so that Henry's law can be applied to all three gases. In the case of HONO, N(III) has a lifetime against oxidation of S(IV) of 1.5 h for 20 ppb SO 2 and pH = 5.7, and this lifetime becomes longer as SO 2 is depleted.

Discussion
As shown in Fig. 4b, we find in this air parcel model that reactions (R1) and (R2) are sufficiently fast for complete conversion of SO 2 to sulfate at pH > 5.5, with a maximum contribution from reaction (R1) at pH 5.5. At higher pH, the faster kinetics of reaction (R2) decrease the role of reaction (R1) in competing for SO 2 oxidation, resulting in a lower yield of N 2 O. The N 2 O yield would also be low (<2 ppb) if we used the faster kinetics for (R2) from Clifton et al. 46 . The observed N 2 O enhancement of ≈5 ppb is most consistent with the kinetics of Lee and Schwartz 45 for (R2) and Martin et al. 28 for (R1), with a fog/ cloud pH of 5.5 (Fig. 4b), but uncertainties are obviously large. Further analysis will require better kinetic information for reactions (R1) and (R2). Decreasing ammonia emissions to bring cloud pH below 5 would shut down the mechanism (Fig. 4b), but other SO 2 oxidation pathways may then take over such as TMIcatalyzed autoxidation 22 .
The role of (R2) + (R1) as a source of HONO and N 2 O is of interest, considering that HONO photolysis is a major source of radicals during winter haze 48 and that N 2 O is a major anthropogenic greenhouse gas. Previous studies have found that HONO in Beijing haze has a large source from direct vehicular emissions 48,49 and this could explain the rise of HONO observed during Stage I (Fig. 1). However, the doubling of HONO concentrations from Stage I to Stage II suggests that (R2) could be an important source of HONO during haze events. With regard to N 2 O, the most relevant comparison is to the national anthropogenic source for China, estimated to be 2141 Gg a −1 with a dominant contribution from agriculture 50 . For a rough estimate, let us assume that (R2) + (R1) is the dominant SO 2 sink during high-RH winter haze, accounting for~8% of winter days (data downloaded from https://rp5.ru/), and that the N 2 O molar yield is 20% based on the upper limit (pH 5.5) of Fig. 4b. The Multi-resolution Emission Inventory for China estimates a national SO 2 emission of 13.4 Tg a −1 in 2016 51 , which would then imply a corresponding N 2 O source of 36.8 Gg a −1 . This is small compared with the national inventory total, but not negligible as a component of N 2 O emission from the energy sector estimated to be 232.7 Gg a −1 in 2012 50 .
In summary, we have shown from field observations of an extended winter haze PM 2.5 pollution event in Beijing that aqueous-phase oxidation of SO 2 by NO 2 and HONO in nighttime fog and low cloud provides a plausible mechanism for explaining the rapid production of sulfate PM 2.5 . Production of sulfate in fog and cloud is consistent with the observed shift in the sulfate size distribution to larger sizes. High-RH conditions with widespread fog and low cloud formation are typical of severe winter haze events in Beijing 2,26 . This provides high LWCs for aqueous-phase reactions to occur, together with high pH (>5.5) from efficient uptake of ammonia. Based on available aqueous-phase kinetic data, such high-LWC high-pH conditions should allow fast oxidation of SO 2 by NO 2 to produce HONO, and subsequent fast oxidation of SO 2 by HONO to produce N 2 O. There remains large uncertainty in these kinetic data. But such a mechanism is consistent with our field observations of N 2 O enhancement, HONO enhancement, NO 2 depletion, and near-complete SO 2 depletion concurrent with fast sulfate production as RH increased during the haze event. Further work should target better understanding of the laboratory kinetics and products of the aqueous-phase reactions of SO 2 with NO 2 and HONO. December of 2016. This site is located around the 3rd ring road of north Beijing, surrounded by residential infrastructure and an arterial road to the east (360 m). Measurements were made from a rooftop laboratory 8 m above ground and with no interference from neighboring buildings. All data presented in this paper were hourly averaged (local time, UTC+8).
A HR-AMS was deployed during the field campaign to obtain chemical composition and size distributions of non-refractory particulate matter smaller than 1-μm diameter (NR-PM 1 ). A shared PM 2.5 cyclone inlet (Model URG-2000-30ED) and a diffusion dryer were used prior to the sampling. Detailed information on the operation of HR-AMS during the sampling campaign can be found in previous literature 4,52 . Additional measurements of aerosol composition were made with a URG-9000D Ambient Ion Monitor for water-soluble ions including a BGI-VSCC PM 2.5 cyclone upstream. Anion analysis was performed using the IonPac AS19 hydroxide-selective anion-exchange column, which can effectively separate sulfate from HMS. PM 2.5 mass concentration was measured by a TDMS-TEOM PM 2.5 analyzer (Thermo Fisher Scientific, Model 1405) at the Beijing Olympic Center Observatory, which is 4 km to the northeast of the sampling site. Fog LWC was measured by a TP/W VP-3000 ground-based 12-channel microwave radiometer (Radiometrics Corp.) at the Beijing Observatory of the China Meteorological Administration (CMA), 20 km to the south of our sampling site.
Gaseous and meteorological data were also collected at the site. An Aerodyne high-resolution time-of-flight chemical ionization mass spectrometer measured HONO concentrations 53   Calculation of fog/cloud pH. We estimated fog/cloud pH values during Stage II by assuming a pre-fog atmosphere with the mean composition observed at the IAP field site, and adding to that atmosphere an LWC of 0.15 g m −3 . The IAP field site did not experience fog during Stage II, but cooling of a few degrees would have caused fog to form (as apparent in the low clouds observed 50 m above the site, Supplementary  Fig. 2) and drive partitioning of gases into the aqueous phase. We can then estimate the fog/cloud pH from the partitioning of the relevant chemicals initially present in pre-fog air as defined by the mean conditions of Stage II (Fig. 1). This includes 14 ppb NH 3, 2 ppb SO 2 , and PM 2.5 with electroneutral composition [SO 4 2− ] = 3 × 10 −3 mol L −1 , [NO 3 − ] = 6 × 10 −3 mol L −1 , [Cl − ] = 1 × 10 −3 mol L −1 , and [NH 4 + ] = 1.3 × 10 −2 mol L −1 . We also include 400 ppm CO 2 , and neglect organic acids which are low under winter haze conditions 56 . Alkaline dust would increase the pH and is found to be important in precipitation data for winter Beijing 14,57 but our mean Stage II PM 2.5 measurements show [Ca 2+ ] = 1.2 × 10 −5 mol L −1 and [Mg 2+ ] = 2.1 × 10 −5 mol L −1 for the principal crustal cations, negligible relative to [NH 4 + ]. Thus we ignore the contribution of dust in the pH calculation, acknowledging that this may cause an underestimate of pH since dust could be present in larger particle sizes. We performed the pH calculation for a temperature of 271 K with the Henry's law and acid dissociation constants in Supplementary Table 1. We obtain in this manner a fog/cloud pH of 5.7.