Organic peroxides (OPs) are an important contributor to the atmospheric oxidation capacity, as they act as reservoirs for alkoxy radicals and organic peroxy radicals (ROx) (Ehn et al., 2014; Allen et al., 2022). Besides their well-known implication in the oxidation of biogenic volatile organic compounds and anthropogenic precursors, OPs were shown to contribute to secondary organic aerosols (SOAs) by forming an important link between sulfate and SOAs (Tkacik et al., 2012; Riva et al., 2015; Hettiyadura et al., 2017; Huang et al., 2020). Moreover, they are also known to regulate the distribution of HOx and ROx radicals through large-scale vertical and horizontal transport (Mari et al., 2000; Ravetta et al., 2001). OPs were ubiquitously detected in atmospheric media, including air and precipitation, fresh water, seawater, surface waters, and coastal environments (Sauer et al., 2001; Morgan and Jackson, 2002; Sun et al., 2021). Their sources are varied, depending on their chemical compositions and properties (Liu et al., 2014). In aqueous media, these sources include the self-reaction of photochemically formed organic radicals and partitioning from the gas phase to the particle phase (O'Sullivan et al., 2005; Sun et al., 2021; Riemer et al., 2000).

The primary sinks of OPs include SO2 oxidation in cloud and rain droplets and uptake on water surfaces and water ice, mainly forming water-soluble organic compounds and secondary sulfates (Böge et al., 2006; Hua et al., 2008). Previous studies have indeed shown that OPs are highly reactive towards dissolved SO2 in submicron aerosol (O'Sullivan et al., 1996; Liou and Storz, 2010), despite the incomplete detailed mechanisms and kinetics of their transformation. Such reactions in the aqueous phase are known to be driven by the change in solution pH. Specifically, bulk phase pH was shown to impact the rates of multiphase SO2 oxidation towards aqueous-phase aerosol formation by altering the reactions mechanisms and modifying the particle morphology, viscosity, and radiative effects (Turnock et al., 2019; Lei et al., 2022). While some of these pH impacts have been explored in detail, namely altering the aerosol radiative forcing (Turnock et al., 2019), the detailed effect on reaction mechanisms and kinetics remains not fully elucidated. The lack of comprehensive information on the pH impact on the mechanisms and kinetics of OP reactions towards SO2 hinders the complete assessment of the importance of such interactions in aquatic environments, for example in the chemical composition of dissolved organic matter (DOM).

Methyl hydroperoxide (MHP, CH3OOH), peracetic acid (PAA, CH3C(O)OOH), and benzoyl peroxide (BZP, C6H5-C(O)OO(O)C-C6H5) are typical examples of OPs both from natural and anthropogenic origins. MHP is the simplest and most abundant OP in the atmosphere and is most prevalent in the remote marine environment (Heikes et al., 1996; O'Sullivan et al., 1999). MHP is believed to form from the ozonolysis of alkenes and from biomass burning (Klippel et al., 2011; Zhang et al., 2012). PAA is one of the simplest OPs containing the carbonyl function, formed form the reaction between acetic acid and hydrogen peroxide in the presence of a strong acid catalyst. PAA is widely used as a disinfectant, sterilizing agent, oxidizer, polymerization catalyst, and sanitizer in wastewater treatment and various industrial applications and is known as a powerful degrading agent for aqueous organic micropollutants (Luukkonen et al., 2015; Zhang and Huang, 2020; Ao et al., 2021; Kiejza et al., 2021). BZP is an antiseptic much used for acne treatment and in the chemical industry (Kircik, 2013; Brammann and Mueller-Goymann, 2019). It can easily enter the human body via food intake and skin absorption, causing potential risks such as tissue damage and eventually acting as a tumor promoter (Kozan et al., 2010; Ding et al., 2019). As a strong reactive oxygen species, BZP can be reduced to benzoic acid, with the ability to inhibit the growth of some microorganisms in wheat flour and corn starch (Ding et al., 2019; Yu et al., 2022). Previous studies also mentioned the possibility of BZP thermolysis to yield benzoyloxy radicals and volatile benzene in the aqueous phase (Tu et al., 1996; Wang et al., 2023).

Despite MHP, PAA, and BZP being poorly soluble in water compared to hydrogen peroxide, for example, they are relatively present in aquatic media (Meylan and Howard, 1991; O'Sullivan et al., 1996; Sun et al., 2021). Some studies have investigated the chemistry of these OPs through particle uptake, wet and dry deposition, thermal and photochemical decomposition, and SO2 oxidation (Tan et al., 2020; Xu et al., 2021; Ignatov et al., 2011; Allen et al., 2022), yet there are still deficiencies in understanding their full chemistry in aquatic media. The current study applies quantum chemical calculation techniques to explore the aqueous-phase reactions of MHP, PAA, and BZP with dissolved SO2. The pH effect on the mechanism and kinetics of these reactions is evaluated, and their implication in altering the chemical composition of DOM is assessed.

The reactions with OPs were explored at three different pH ranges, according to the prevalent states of dissolved SO2: SO2⚫ H2O at pH < 1.81, HOSO2- at 1.81 < pH < 6.97, and SO32- at pH > 6.97. Details on the distribution of dissolved SO2 are given in the Supplement, Table S1. From this distribution, the following reactions were investigated: R2pH<1.81SO2⚫H2O+OP→products,R31.81<pH<6.97HOSO2-+OP→products,R4pH>6.97SO32-+OP→products.

In a series of experiments, the Abbatt group suggested that in peroxide reaction with S(IV), organosulfates are formed directly from peroxide–SO2 interactions instead of SO2 being first oxidized by peroxides to SO42- followed by the reaction between SO42- and organic species (Ye et al., 2018; Wang et al., 2019, 2021). The current study is in line with the observations of the Abbatt group and further explains in detail their suggested mechanisms for sulfate formation. Our calculations indicate that the importance of the degradation pathway of OPs by reaction with S(IV) to form (organo)sulfate in the aquatic environment is strongly dependent on the pH and is especially important under acidic pH. Besides reactions with dissolved SO2, other recent studies showed that hydronium ions effectively catalyze the decomposition of organic peroxides at acidic pH (Qiu et al., 2020; Hu et al., 2020; Enami, 2021). It should be noted that in these studies, the catalytic effect of the available proton was examined on specific classes of OPs, namely hydroperoxides with α-hydroxyalkyl, α-alkoxyalkyl, and α-acyloxyalkyl substituents. The presence of the hydroperoxide group (-OOH) and the α-substituent with the oxygen atom (-O-) at the β-position in these peroxides enables the formation of a hydrogen-bonded ring structure involving the two functions and further facilitate the decomposition. Although these two requirements are not met for OPs considered in this work, the potential role of the available proton in the degradation of OPs that have no substituents at the α-position is worth thorough analysis in our future investigations.

Wang et al. (2019) raised the aerosol pH effect to be one of the fundamental issues to model aqueous-phase sulfate formation from the reactions of OPs with dissolved SO2. We explored the conditions of pH 1–10, which are dominated by different prevalent states of dissolved SO2. While pH below 1.81 is not a favorable condition for the degradations of both investigated OPs by reaction with S(IV), these reactions exhibit different mechanisms and kinetics at a pH above 1.81. Based on the mechanisms shown in Figs. 1, 3, 4, 5, and S1, the kinetics of the degradation of investigated OPs were evaluated within the ranges of pH 1–10 and 240–340 K temperature. The reaction rate at each pH is driven by specific fractional populations of the different protonated states of S(IV): δ(SO2⚫ H2O) at pH < 1.81, δ(HOSO2-) at 1.81 < pH < 6.97, and δ(SO32-) at pH > 6.97. Details on these fractional populations are given in Table S1. At a given temperature, the effective rate constant, keff, for each reaction is calculated by weighing the overall rate constant (koverall, given by Eq. 4) of partial reactions at specific pHi over the fractional populations of S(IV) (xS(IV)) at that pH as follows: 7keff,i=∑ixS(IV),i×koverall,i. While koverall is independent of pH and simply gives the rate constant of the OP + S(IV) reaction based on the activation energy, keff gives the rate constant of the full process, by taking into account the population of different protonated states of S(IV) according to the pH value. Atmospheric lifetimes of OPs are calculated based on the effective rate constant of Eq. (7), and considering that self-degradation is an unlikely process given the simple structure of investigated OPs relative to those of, e.g., hydroperoxides with α-hydroxyalkyl, α-alkoxyalkyl, and α-acyloxyalkyl substituents, whose self-degradations are catalyzed by the proton (Enami, 2021), these lifetimes are estimated based on S(IV) reactions exclusively.

Figure 7 shows the effects of pH and temperature on the effective rate constants while the numerical values are given in Tables 1, S2, and S3. In general, the effective rate constants of the reactions of OPs exhibit a positive temperature dependency, with the steepest increase being observed at a pH below 6.97, especially for the reaction of BZP. Above this range, the effective rate constant becomes almost insensitive to the pH. This indicates that the effect of pH change on the formation of organosulfates from reactions of OPs with dissolved S(IV) is most relevant in acidic aqueous environments.

In the pH range 1.81–6.97, the rate constant of the MHP + HOSO2- reaction to form methyl sulfate (Reaction R5) was estimated to be 2.38×10-14 M-1 s-1 at 298.15 K, ∼ 3 orders of magnitude lower than that of the reaction to form inorganic sulfate (Reaction R6; overall rate constant of 3.02×10-11 M-1 s-1) and 7 orders of magnitude higher than the overall rate constant of the MHP + SO2⚫ H2O reaction. The branching ratios estimated from the obtained kinetics for the MHP + S(IV) reaction are 99.92 % and 0.08 % for inorganic sulfate and methyl sulfate, respectively. This favored formation of inorganic sulfate relative to methyl sulfate is in agreement with the experimental observation that inorganic sulfate is the major product while methyl sulfate is the second product in the MHP + HOSO2- reaction (Lind et al., 1987). Regardless of the temperature, the effective rate constant within this pH range increases by 3 orders of magnitude as the pH increases.

The formation of methyl sulfate at a pH above 6.97 is much more favorable than in the preceding investigated pH range, occurring with an overall rate constant of 9.25×10-8 M-1 s-1 at 298.15 K. However, the effective rate constant in this range is almost insensitive to pH at all temperatures investigated (see Fig. 7). The estimated atmospheric lifetimes for MHP at 298.15 K, based on this reaction, are 1.34×10-5–5.05×1010 s in the pH range 1–10, and they are shown to decrease with increasing pH. This indicates that MHP degradation is more important in acidic waters and will alter the chemical composition of DOM by increasing the concentration of inorganic sulfate.

The kinetics of PAA + S(IV) reactions are essentially driven by the rates of inorganic sulfate formation, given the much lower energy barrier than in organosulfate formation. The rate constants for these processes at 298.15 K are 9.37×10-6 and 1.10×104 M-1 s-1 for organosulfate and inorganic sulfate formation, respectively. Despite quantum chemical calculations predicting the pathways for the formation of both inorganic sulfate and organosulfate from the PAA + S(IV) reaction, the kinetics show that inorganic sulfate formation is more than 9 orders of magnitude faster than organosulfate formation in the whole pH range investigated, simply indicating that the organosulfate formation from PAA reaction is insignificant. Regardless of the pH range, the branching ratios estimated from the kinetics are 100 % for inorganic sulfate formation and 0 % for organosulfate. This is in line with the experimental observation that the reaction of PAA with dissolved SO2 almost exclusively forms inorganic sulfate (Lind et al., 1987). Lind et al. (1987) measured a rate constant of (6.10±2.60)×102 M-1 s-1 for this reaction at 291 K and pH 2.9–5.8. At the same temperature and pH 5.8, we obtained an effective rate constant of 4.20×102 M-1 s-1, in reasonable agreement with the experimental value. At pH 1–10 and 240–340 K, we obtained a positive dependency for the effective rate constant (plot and numerical values are shown in Fig. 7, Tables 1 and S3). From these kinetics, the estimated atmospheric lifetimes for PAA based on the reaction with dissolved SO2 at 298.18 K and pH 1–10 are within the range of 1.12×10-16–8.71 s. This indicates that PAA is much more reactive than MHP towards dissolved SO2 under the investigated conditions.

BZP is more reactive than MHP and PAA towards S(IV) at all pH above 1.81. Despite the mechanisms being nearly similar in the investigated pH ranges, the overall rate constants of the formation of benzoyl sulfate at 298.15 K are 1.55×10-6 and 2.47×106 M-1 s-1 from BZP + HOSO2- and BZP + SO32-, respectively. The full pH and temperature dependencies of the total rate constant of the BZP + S(IV) reaction are given in Table 1 and plotted in Fig. 7. It should be noted that there is no direct formation of inorganic sulfate in BZP reactions in the pH range investigated. Sufficient evidence has been gathered about aromatic organosulfate formation connected to anthropogenic activities, namely benzyl sulfate and phenyl sulfate detected in ambient aerosols from urban sites (Kuang et al., 2016; Huang et al., 2018). These aromatic and other organosulfates derived from polycyclic aromatic hydrocarbons are believed to form from aromatics interacting with sulfur-containing species (Blair et al., 2017; Riva et al., 2015). It is likely that the investigated BZP + S(IV) mechanism in this work would explain some of such aromatic organosulfate formation mechanisms.

The calculated lifetimes for benzoyl peroxide in the investigated pH range and 298.15 K are in the range of 5.02×10-19–8.25×10-3 s (see Table 1), decreasing with increasing pH. These lifetimes are much lower than measured lifetimes of ∼ 6 d in Los Angeles from the photolysis of OPs (Krapf et al., 2016), indicating more efficient degradation in the aqueous phase. The current results highlight the strong pH impact on the degradation of BZP by S(IV). A previous study also showed that aerosol pH can substantially alter the formation of organosulfate from the reaction uptake of isoprene epoxydiols onto a mixture of ammonium sulfate and sulfuric acid particles (Lei et al., 2022).

The overall rate constants of SO3- reactions with MHP and BZP were determined to be 7.66×10-3 and 9.13×10-8 M-1 s-1, respectively, regardless of the pH. Compared to the rate constants of S(IV) reactions, the pathway for SO3- may also significantly contribute to degrade MHP and BZP and form organosulfate. Our results further show that sulfate formation from PAA + S(IV) and BZP + S(IV) reactions is more effective than from MHP + S(IV), and this pronounced reactivity can be attributed to electron-withdrawing effects of -C(O)R substituents (-C(O)-CH3 and -C(O)-C6H5 in PAA and BZP, respectively) that activate the -O-O- function. This finding further highlights that the specific nature of different substituents to the -O-O- function may play a determinant role in (organo)sulfate formation. It is obvious that OPs containing the hydroperoxyl function will most likely contribute to both organic and inorganic sulfate mass, whereas those not containing this function will only form organosulfates. Although OPs may not compete with, e.g., OH radicals in S(IV) oxidation, their contribution to sulfate formation may be important in low OH radical conditions. These pathways can adequately account for sulfate formation under conditions of low solar radiation such as haze events, where there is insufficient production of OH radicals. Further, the proposed mechanisms not only improve our understanding of the pH impact on the degradation efficiency but also show that different OPs would alter the chemical composition of DOM in different ways, both in terms of organic and inorganic sulfate mass fractions. Of particular importance, the investigated pathways for the degradation of OPs have direct implications for aqueous-phase sulfate aerosol formation. This provides grounds for a deeper evaluation of the pH impact of the kinetics of organic and inorganic sulfate formation from various OP+S(IV) reactions for a more complete kinetic data set. Such investigations will further guarantee a better understanding of the impacts of various sources of sulfates in aqueous-phase aerosol formation and unveil a broader impact of OPs in altering the composition of DOM in natural waters.