Second-Order Kinetic Rate Coefficients for the Aqueous-Phase Sulfate Radical (SO4•–) Oxidation of Some Atmospherically Relevant Organic Compounds

The sulfate anion radical (SO4•–) is a reactive oxidant formed in the autoxidation chain of sulfur dioxide, among other sources. Recently, new formation pathways toward SO4•– and other reactive sulfur species have been reported. This work investigated the second-order rate coefficients for the aqueous SO4•– oxidation of the following important organic aerosol compounds (kSO4): 2-methyltetrol, 2-methyl-1,2,3-trihydroxy-4-sulfate, 2-methyl-1,2-dihydroxy-3-sulfate, 1,2-dihydroxyisoprene, 2-methyl-2,3-dihydroxy-1,4-dinitrate, 2-methyl-1,2,4-trihydroxy-3-nitrate, 2-methylglyceric acid, 2-methylglycerate, lactic acid, lactate, pyruvic acid, pyruvate. The rate coefficients of the unknowns were determined against that of a reference in pure water in a temperature range of 298–322 K. The decays of each reagent were measured with nuclear magnetic resonance (NMR) and high-performance liquid chromatography–high-resolution mass spectrometry (HPLC-HRMS). Incorporating additional SO4•– reactions into models may aid in the understanding of organosulfate formation, radical propagation, and aerosol mass sinks.


■ INTRODUCTION
A wide variety of water-soluble condensed-phase compounds are formed during the oxidation of reactive carbon emissions in the atmosphere. 1−3 The oxidation of reactive carbon emissions in the aqueous phases of aerosols, fogs, and clouds initiated by hydroxyl (OH) radicals, nitrate (NO 3 ) radicals, and the sulfate anion radical (SO 4 •− ) has been reviewed previously (refs 4−6 and references therein). SO 4 •− radicals have been recognized as a potentially important source of surface-active organosulfates (OSs) in the environment, 7−10 which can modify aerosol cloud interactions. 11,12 A large variety of OSs have been identified in both field and laboratory studies, several of which are proposed to only be formed from SO 4 •− radicals. 9,13−17 The SO 4 •− radical is thought to be formed primarily in the autoxidation of SO 2 ; however, it can also be formed from the activation of sulfate and bisulfate anions with OH, NO 3 , 4 and to a small extent ferric ion complexes. 18,19 Although the atmospheric concentration of the SO 4 •− radical has not been directly measured, it has been estimated between 9.1 × 10 −13 and 5.5 × 10 −17 M, assuming known sources. 4 New mechanisms of reactive sulfur species relevant to sulfate aerosols have been recently reported, including SO 4 •− formation from irradiated sulfate aerosols, 20 OH-initiated oxidation of organosulfates, 21 and autocatalysis of the SO 4 2− anion in the presence of phenols. 22 The formation of reactive sulfur was also reported from the interfacial redox of ammonium sulfate aerosol particles. 23 Thus, the chemistry and environmental source calculations of SO 4 •− and other sulfur radicals may benefit from re-evaluation in models.
Experiments. Photochemical reactions of organic compounds of interest with sulfate radicals were examined in quartz reaction vessels using the UV irradiation of potassium persulfate (K 2  A relative rate technique 39 was used, where the second-order rate coefficients for the compound of interest with respect to oxidation by the SO 4 •− radical were determined against a reference compound with a known rate coefficient in the same reaction. The reference compound selected for study was erythritol (C 4 H 10 O 4 ), which has a rate constant of 4.56 × 10 7 M −1 s −1 with the sulfate radical when averaged over the experimental temperature range. 24 (2) Under the conditions of our study, J i is ∼5.5 × 10 −5 s −1 . Using known rate coefficients for the above reactions (e.g., k ii ∼ 400 s −1 ) 41 and those of erythritol with OH and SO 4 •− , 4 it was estimated that >99% of the reaction proceeded via SO 4 •− compared to OH (Table S1).
Rate coefficients for the reactions were obtained as follows: The unadjusted pH values for MGA, PA, and LA were 3, 5, and 2, respectively. To analyze 2-methylglycerate and lactate (pH 5), NaOH was added dropwise to the mixed solution until pH 5 was reached. MGA and pyruvic acid were analyzed at pH 2 by adding H 2 SO 4 dropwise to the mixed solution until pH 2 was reached. All other determinations were performed at pH 5−7. A quartz reaction vessel was filled with 10−15 mL of the sample mixture, placed in an enclosed compartment with a 254 nm UV lamp, and irradiated over the course of two hours (See Figure 1 for the experimental setup).
Using 400 μL H 2 O spiked with xylitol (0.762 mM) as an internal standard, 100 μL aliquots of the reaction solution were analyzed at variable time points after dilution. Representative data are shown in Figure 2. All experiments were performed in triplicate, and uncertainty bounds represent one standard deviation.
Direct photolysis controls for compounds with chromophoric functional groups were performed identically to the experiment except without the erythritol reference and without K 2 S 2 O 8 . The spectral output from the lamp was measured using a portable spectrophotometer (Tidas series, WPI Inc.), and the photo flux ( Figure 3A) was calibrated using the neutral aqueous photolysis of uridine as a chemical actinometer according to protocol L09 from IUPAC. 42 Erythritol and other compounds without chromophores are assumed to undergo negligible photolysis during the experiment. A first-order loss rate (J) was extracted from the control experiments for the compounds of interest, and a correction to the raw data was performed where the k 1 /k 2 ratio was obtained by plotting ln For experiments with photolysis controls, the uncertainties in the J determinations (e.g., errors in slopes) were propagated together with the standard deviations from the data.
In order to understand the temperature fluctuations during an experiment, a control experiment with Milli-Q water was performed with continuous irradiation while the temperature was monitored with a thermocouple ( Figure S1). The temperature of the solution was recorded until temperature stabilization occurred. Thus, data are reported in the range of 298−322 K. The studied compounds are stable at these temperatures. Although the kinetic data are referenced and SO 4 •− reaction rates with similar compounds are weakly dependent on temperature, 26,40 it is not clear whether the temperature dependence of the rate coefficient for the reference compound is identical to that of the compound of interest. Partitioning to the gas phase may increase at higher temperatures in the capped quartz tube; however, all studied compounds have large Henry's Law coefficients that favor the aqueous phase by many orders of magnitude. 1,2-DHI is likely the most volatile compound in the study; its Henry's law coefficient may be estimated based on 1,2-pentanediol (K H = 1.4 × 10 5 M atm −1 or 3.4 × 10 6 mole ratio of aqueous to gas). 43 The temperature uncertainty can be considered a limitation of this work.
Analytical Measurements. All analytes, with the exception of 1,2-DHI, were analyzed using high-performance liquid chromatography (HPLC) coupled to high-resolution mass spectrometry (HRMS). The HPLC-HRMS analyses were performed using an Agilent 1100 HPLC coupled to a lineartrap-quadrupole Orbitrap (LTQ-Orbitrap) mass spectrometer (Thermo Corp., Waltham MA) operated at a mass resolving power of 60 000 m/Δm at m/z 400. Xcalibur 2.0 software was used to analyze the mass spectra. The separation of MT, MD-1,4-DN, MT-3-N, erythritol, and xylitol was performed using a Shodex Asahipak NH2P-40 2D column (2 × 150 mm, 4 μm, 100 Å) using a method recently reported elsewhere. 27 An Agilent Poroshell InfinityLab EC-C18 (2.1 × 100 mm, 2.7 μm,  The Journal of Physical Chemistry A pubs.acs.org/JPCA Article 120 Å) column was used to separate MD-3-S and MT-4-S using a previously reported method. 27 To analyze pyruvic acid, lactic acid, and MGA, including erythritol and xylitol, a Shodex HILICpak VG-50 2D column (2 × 150 mm,5 μm, 100 Å) was used. The mobile phases were MeCN (A) and 0.5% NH 3 (B), and the injection volume was 1 μL. To separate MGA from erythritol and xylitol, the mobile phase was held at 30% B for 2 min, increased to 90% B for 10 min, held at 90% for 3 min, decreased to 30% for 5 min, and held at 30% for another 5 min. The flow rate was 0.3 mL min −1 , and the total run time was 25 min. To separate pyruvic acid and lactic acid from erythritol and xylitol, the mobile phase was held at 30% B for 4 min, increased to 90% for 6 min, held at 90% for 1 min, decreased to 30% for 4 min, and held at 30% for 2 min. The flow rate was 0.1 mL min −1 , and the total run time was 17 min. A representative HPLC-HRMS data set for lactic acid is shown in Figure 2.
For the rate determinations of 1,2-DHI, proton nuclear magnetic resonance ( 1 H NMR) spectroscopy was used to quantify the decay of erythritol and 1,2-DHI due to the distinct proton environments of the alkene using a method similar to that we reported previously. 27 1,2-DHI is poorly ionizable in the HPLC-HRMS method. Due to the lower sensitivity of the NMR analysis, 100 mM concentrations of both reactants were mixed with 300 mM K 2 S 2 O 8 in order to increase the analytical signal. Reactions for NMR analyses were performed on a 400 MHz Bruker instrument (400 MHz Bruker Avance III HD Nanobay Spectrometer) using an autosampler and analyzed using TOPSPIN. The solution was irradiated over the course of 1.5 h and taken to the instrument without any workup at several time points.
A Shimadzu UV-1800 dual-beam spectrophotometer was used to measure the UV−visible extinction coefficients of organic reactants as referenced with pure water, primarily to assess which reactant required a direct photolysis correction. A 1 cm quartz cuvette was used for the absorbance measurements for 0.1−1 mM samples, which were diluted in order to maintain Beer's Law linearity when required. Extinction coefficients were then calculated based on the measured absorbances, the path length, and the known concentrations of the solution.  Figure 3B is shown in Figure S2. These compounds have chromophores such as carbonyl, alkenyl, and nitrato groups, so their absorbance in the 200−400 nm range is expected. Pyruvic acid has a carbonyl in the β-position relative to the acid, which increases its chromophoric properties compared to those of hydroxyacids such as lactic acid. Photolysis controls performed for these compounds ( Figure  S3) yielded first-order loss rates of approximately 5−40 × 10 −5 s −1 , which were used to correct the rate ratios against erythritol. Quantum yields under our lamp could be estimated to be in the range of ∼0.1−0.2 for the organonitrates and pyruvate (pH 5) but were larger than unity for pyruvic acid (PA) and 1,2-DHI (Table S2). Eugene et al. 44 reported that the photolytic loss of PA in water at pH 1 proceeds with a quantum yield of ∼2, in good agreement with our estimate (2.4). Effectively, each PA* molecule that is excited per absorbed photon consumes another molecule of PA in a highly efficient bimolecular process. Although the chromophore-loss quantum yield of pyruvate in water has not been reported, to our knowledge, the decarboxylation quantum yield for pyruvate is at least twenty times smaller than that for the acid, 45 in qualitative agreement with the much smaller quantum yield we extracted for pyruvate loss (0.19). Aqueous photolysis data for other compounds studied in this work were not available in the literature for further comparisons.
Kinetics Experiments. From the decay of erythritol, the steady-state concentrations of SO 4 •− used for experiments were determined in the range of 0.1−2 × 10 −11 M. Ratios of k 1 /k 2 for the different compounds of interest, derived from triplicate trials, are shown in Figures 4 and 5. Data points were fit linearly, with the slope being "k 1 /k 2 ". Direct photolysis corrections are shown in blue where appropriate. Table 1 shows the k SO4 values for the compounds under study after the application of the rate coefficient of erythritol to the respective rate ratios. Control experiments did not show appreciable reactions between organics and the K 2 S 2 O 8 reagent in the dark  Figure S4). Starting with the isoprene-derived polyols, organonitrates, and organosulfates (Figure 4), we see the largest rate coefficient in the reaction of 1,2-DHI versus erythritol. The unsaturation in 1,2-DHI enables an addition mechanism for SO 4 •− that is unavailable for the other compounds under study (Scheme 2a); thus, the reaction of SO 4 •− with 1,2-DHI is expected to contribute to the formation of organosulfates. 8,9 The aqueous SO 4 •− rate coefficient of 1,2-DHI for this work (1.14 × 10 8 M −1 s −1 ) is comparable to SO 4 •− rate coefficients that have been reported for other atmospherically relevant alkenes, such as methacrolein and methylvinylketone (9.9 × 10 7 and 1.1 × 10 8 M −1 s −1 , respectively). 25 The reaction of MT is ∼30% slower than that of erythritol, which may be rationalized on the basis of their structural differences. MT has the same basic structure as erythritol but has an additional methyl group at the second carbon; thus, MT has a less-    reactive primary-carbon abstraction site (R-(HO)(CH 3 )C-R) compared to the secondary-carbon abstraction site (R-(HO) HC-R) of erythritol (Scheme 2b and c). For the organic dihydroxy dinitrates of isoprene, 33 we expect the major isomer MD-2,3-DN to be formed from gas-phase oxidation. However, once formed and partitioned to the condensed phase, its aqueous oxidation will not be competitive with the fast hydrolysis fate. 46,47 The hydrolysis product formed from MD-2,3-DN, namely, 2-methyl-1,2,4-triol-3-nitrate (MT-3-N), was studied here due to its higher relevance for the aqueous reaction. The mononitrate MT-3-N participated in direct photolysis as well as the SO 4 •− reaction, and the corrected rate coefficient (∼3 × 10 7 M −1 s −1 ) was similar to that of MT within uncertainty. This could potentially suggest that substitution of an OH group with a ONO 2 group at a secondary carbon does not significantly change the SO 4 •− reactivity. As opposed to the major dinitrate MD-2,3-DN, the minor dinitrate isomers (nitrates at the 1,4-and 1,3-positions) are expected to build up in concentration in the condensed phase given their slow hydrolysis fates. 48 Thus, the aqueous oxidation of the minor dinitrate isomers such as MD-1,4-DN would be a competitive fate. However, we found that MD-1,4-DN was relatively slow with respect to its reaction with SO 4 •− (∼5 × 10 6 M −1 s −1 ). Its reaction with OH radicals is also relatively slow. 27 It is not clear at this time whether this finding is relevant to nitrates in the primary position or whether substitution with two nitrate groups has outsized effects compared to one. Relative to its rate coefficient with aqueous OH (∼2 × 10 8 M −1 s −1 ), 27 the SO 4 •− reaction of MD-1,4-DN may not be competitive unless the particle phase supplies a large reservoir of sulfate radicals.
We studied the organosulfates as their sodium salts, as the pK a values of these species are expected to be negative. 49 Both the primary organosulfate, MT-4-S (∼1 × 10 7 M −1 s −1 ), and the secondary organosulfate, MD-3-S (∼5 × 10 6 M −1 s −1 ), had low reactivities with SO 4 •− ; however, the third OH group in MD-3-S is absent, which does not allow for an exact structural comparison. This is drastically different from the OH rates, where MT-4-S has a k OH rate only 20% slower than that for erythritol. MT-4-S has a faster k SO4 than MD-3-S (about two times faster), a trend similar to what we observe with the OH radical. Within organic aerosols of isoprene, the sulfate in the tertiary position is expected to be the major isomer, either from the reaction of the sulfate radical with isoprene 50 or from the ring opening of the isoprene epoxydiols, 51 but the secondary species is also present. The equivalent primary OS has not been observed, although it was studied here due to the enhanced feasibility of its organic synthesis. Unlike the tertiary nitrates of isoprene, the tertiary sulfate is fairly stable with respect to hydrolysis, 52 so oxidation is a competitive fate. It is presumed that the SO 4 •− rate of the tertiary sulfate will be within a factor of two or three of the primary sulfate, assuming general substitution trends from OH oxidation can be applied here. 53−58 With this assumption, we can estimate a lower limit of 3.5 × 10 6 M −1 s −1 for the tertiary species.
A number of organic acids that have been observed in atmospheric aerosols 59 were investigated in this study. As these acids exist in the environment as either their neutral or anionic forms depending on the pH, two atmospherically relevant pH values were studied: pH 2 for relevance to sulfate-based aerosols and pH 5 for relevance to cloud droplets. In general, we found the k SO4 coefficients of the organic acids under study to be slightly lower at pH 2 compared to pH 5 ( Figure 5), although in some cases it was challenging to reach this conclusion within uncertainty. This general trend was also observed for other organic acids, with differences between the reaction of the carboxylate and the acid most severe for formic acid (∼2 orders of magnitude) and less so for larger acids and diacids (within 10% for malic acid). 60 SO 4 •− radicals efficiently decarboxylate carboxylic acids through electron transfer (Scheme 2d and e), 61 and the carboxylate form facilitates this reaction for some compounds. 62 For lactate at pH 5, our k SO4 coefficient (∼2 × 10 7 M −1 s −1 ) in the range of 293−322 K is in reasonable agreement with a previously determined value (∼1.6 × 10 7 M −1 s −1 ) at pH 9, which was controlled at 298 K. 60 Our value for lactic acid at pH 2 (∼1.4 × 10 7 M −1 s −1 ) is also within error of the value determined previously (∼1.0 × 10 7 M −1 s −1 at pH 1); discrepancies are likely due to the temperature difference between our study and the cited study. Methylglycerate at pH 5 was found to have a k SO4 similar to that of lactate. Both methylglycerate and lactate have one −CH 2 − carbon and one −CH 3 carbon, so perhaps their similar rate coefficients can be rationalized through structural similarities. Methylglyceric acid (MGA) at pH 2 was originally determined to have a slightly higher rate coefficient than methylglycerate; however, there is possibly a photolysis correction that should be applied. Although MGA did not have a high extinction coefficient at 254 nm (∼10 M −1 cm −1 ), the possibility for a quantum yield higher than unity could make direct photolysis a concern. We did not have additional MGA samples with which to study the direct photolysis. We applied the same chromophore loss quantum yield for pyruvic acid to estimate a maximum correction due to direct photolysis and found that up to a 15% reduction in k SO4 could be expected if MGA behaved like PA with respect to direct photolysis. We do not expect MGA to be quite as photolytically labile as PA as it is missing the carbonyl chromophore of PA. Within error, we conclude that MGA has a rate coefficient similar to methylglycerate. Otto, Schaefer, and Herrmann 26 found a weak pH dependence for the k SO4 of terpene-derived organic acids, an observation that also applies to this data set.
The SO 4 •− reaction of pyruvate was found to be twice as fast as those of lactate and methylglycerate. The direct photolysis of pyruvate was slow; thus, the correction is fairly minor at pH 5. At pH 2, pyruvic acid (PA) has the fastest direct photolysis rate ( Figure S3), which led to a greater than 50% correction to its observed rate of decay. PA appears slower than pyruvate in its SO 4 •− reaction after the correction, although this is not clear within uncertainty. It is safe to say, however, that PA reacts faster with SO 4 •− than the other studied carboxylic acids. The data here appear to be in good agreement with those of Otto, Schaefer, and Herrmann, 26 who found the k SO4 of cispinonic acid (a keto acid) to be ∼3 × 10 7 M −1 s −1 and that of camphoric acid (diacid without the carbonyl group) to be roughly half this value. It is possible that a carbonyl group in the structure of an organic acid increases the rate of reaction with SO 4 •− due to the production of an acyl radical (Scheme 2 d and e) compared to an alkyl radical, but this remains to be further explored.
1,4-DN reacted the slowest, which is similar to their relative reactivities with OH radicals. 27 There are also different trends that may highlight the greater selectivity of SO 4 •− reactions; for example, MT-4-S reacted with SO 4 •− faster than MT when that trend was reversed with OH. The C 3 −C 5 acids under study did not have significantly different reactivities with SO 4 •− compared to their carboxylates within the uncertainties of the analyses. Of particular interest may be the reaction of 1,2-DHI with SO 4 •− , which is able to form surface-active organosulfates, [8][9][10]50 or the potential reaction of MT-4-S with SO 4 •− to propagate sulfur radicals. 21 For other compounds, the k SO4 rates determined here may help improve the understanding of aerosol mass loss, which may be underpredicted in current models. 63 However, even with a better understanding of k SO4 and k OH rate coefficients, a comparison of SO 4 •− versus OH sinks for various organics may still be qualitative at this time. Oxidant concentrations in deliquesced particles and clouds are major sources of uncertainty in multiphase modeling. Models predict a vast range of steady-state OH concentrations in the atmospheric aqueous phase 64  •− ] aq at 1 × 10 −14 M and allow the full range of measured [OH] aq to compete, the SO 4 •− reaction would span from 10−70% of the summed reactivity of the organic using kinetic data reported by our group (assuming 2-methyltetrol and 1,2-DHI as the organics). We ignore the reactivity with NO 3 radical for now, as its rate coefficients with the compounds under study have yet not been determined. Thus, there may be situations in mixed urban−biogenic environments (such as regions of the Southeast US) for SO 4 •− to be a competitive fate of some organics in aerosols; however, better constraints on aqueous oxidant sources are likely needed in order to improve the understanding of the reactive fates of aerosol-phase compounds.

Kinetic competition calculation between SO 4
•− and OH, direct photolysis parameters, photolysis correction calculations, temperature of the reaction medium, magnified view of extinction coefficients, plot of direct photolysis control data, and plot of dark control data (PDF)