Aqueous Reactions of Sulfate Radical-Anions with Nitrophenols in Atmospheric Context

Nitrophenols, hazardous environmental pollutants, react promptly with atmospheric oxidants such as hydroxyl or nitrate radicals. This work aimed to estimate how fast nitrophenols are removed from the atmosphere by the aqueous-phase reactions with sulfate radical-anions. The reversed-rates method was applied to determine the relative rate constants for reactions of 2-nitrophenol, 3-nitrophenol, 4-nitrophenol, 2,4-dinitrophenol, and 2,4,6-trinitrophenol with sulfate radical-anions generated by the autoxidation of sodium sulfite catalyzed by iron(III) cations at ~298 K. The constants determined were: 9.08 × 108, 1.72 × 109, 6.60 × 108, 2.86 × 108, and 7.10 × 107 M−1 s−1, respectively. These values correlated linearly with the sums of Brown substituent coefficients and with the relative strength of the O–H bond of the respective nitrophenols. Rough estimation showed that the gas-phase reactions of 2-nitrophenol with hydroxyl or nitrate radicals dominated over the aqueous-phase reaction with sulfate radical-anions in deliquescent aerosol and haze water. In clouds, rains, and haze water, the aqueous-phase reaction of 2-nitrophenol with sulfate radical-anions dominated, provided the concentration of the radical-anions was not smaller than that of the hydroxyl or nitrate radicals. The results presented may be also interesting for designers of advanced oxidation processes for the removal of nitrophenol.

Atmospheric sinks for nitrophenols include photolysis [50] and the gas-phase reactions with OH radicals and NO 3 radicals [51,52] which are characterized by the estimated residence time of several days. More efficient sinks may include partitioning to atmospheric aqueous phases followed by reactions with various radicals and/or photolysis [1,46]. More recently, Barsotti, et al. [53] demonstrated that the irradiation of aqueous solutions or viscous films containing several nitrophenols (2-NP, 4-NP, 2,4-DNP, and 2,6-DNP, i.e., 2,6-dinitrophenol) was an efficient source of HONO and NO 2 − ions. Vione, et al. [54] showed that OH radicals reacted faster than NO 3 radicals with 2-NP and 4-NP in aqueous solutions to lower the atmospheric levels of 2-NP below those of 4-NP. Hems and Abbatt [55] studied the aqueous-phase photo-oxidation of 2,4-DNP by OH radicals, identified numerous intermediate products thereof and showed the corresponding evolution of UV absorbance of the reacting solutions.

Estimation of the Rate Constants
The relative rate constants for reactions of nitrophenols with sulfate radical-anions were estimated using the reversed-rates method developed by Ziajka and Pasiuk-Bronikowska [84] and successfully applied to several organic compounds [83,85,86]. Briefly, the sulfate radical-anions are generated during chain autoxidation of sulfite anions catalyzed by Fe(III) cations. The mechanism of the autoxidation was presented in detail by Ziajka and Rudziński [83] and recalled in the SI. One runs several experiments with the autoxidation of S(IV) inhibited by two different compounds, inh1 and inh2, used at several different initial concentrations (e.g., Figure 1). Each experiment should attain a pseudo-stationary phase during which the autoxidation proceeds at a constant rate (e.g., Figure 2). Then, one plots the reciprocal stationary rates observed against the initial concentrations of the inhibitor used ( Figure 3). If both plots are linear, the ratio of rate constants for reactions of the inhibitors with sulfate radical-anions is equal to the ratio of the slopes of the linear plots (Equation (2)). If one knows the rate constant for reaction of one inhibitor with sulfate radical-anions, one can calculate the rate constant for the other inhibitor.
In the present work, ethanol was used as a reference inhibitor against which the rate constants for nitrophenols were calculated.

Estimation of the Rate Constants
The relative rate constants for reactions of nitrophenols with sulfate radical-anions were estimated using the reversed-rates method developed by Ziajka and Pasiuk-Bronikowska [84] and successfully applied to several organic compounds [83,85,86]. Briefly, the sulfate radical-anions are generated during chain autoxidation of sulfite anions catalyzed by Fe(III) cations. The mechanism of the autoxidation was presented in detail by Ziajka and Rudziński [83] and recalled in the SI. One runs several experiments with the autoxidation of S(IV) inhibited by two different compounds, inh1 and inh2, used at several different initial concentrations (e.g., Figure 1). Each experiment should attain a pseudo-stationary phase during which the autoxidation proceeds at a constant rate (e.g., Figure 2). Then, one plots the reciprocal stationary rates observed against the initial concentrations of the inhibitor used ( Figure 3). If both plots are linear, the ratio of rate constants for reactions of the inhibitors with sulfate radical-anions is equal to the ratio of the slopes of the linear plots (Equation (2)). If one knows the rate constant for reaction of one inhibitor with sulfate radical-anions, one can calculate the rate constant for the other inhibitor.
In the present work, ethanol was used as a reference inhibitor against which the rate constants for nitrophenols were calculated.

Estimation of the Rate Constants
The relative rate constants for reactions of nitrophenols with sulfate radical-anions were estimated using the reversed-rates method developed by Ziajka and Pasiuk-Bronikowska [84] and successfully applied to several organic compounds [83,85,86]. Briefly, the sulfate radical-anions are generated during chain autoxidation of sulfite anions catalyzed by Fe(III) cations. The mechanism of the autoxidation was presented in detail by Ziajka and Rudziński [83] and recalled in the SI. One runs several experiments with the autoxidation of S(IV) inhibited by two different compounds, inh1 and inh2, used at several different initial concentrations (e.g., Figure 1). Each experiment should attain a pseudo-stationary phase during which the autoxidation proceeds at a constant rate (e.g., Figure 2). Then, one plots the reciprocal stationary rates observed against the initial concentrations of the inhibitor used ( Figure 3). If both plots are linear, the ratio of rate constants for reactions of the inhibitors with sulfate radical-anions is equal to the ratio of the slopes of the linear plots (Equation (2)). If one knows the rate constant for reaction of one inhibitor with sulfate radical-anions, one can calculate the rate constant for the other inhibitor.
In the present work, ethanol was used as a reference inhibitor against which the rate constants for nitrophenols were calculated.

Experimental Runs
The experimental setup and procedure for carrying out the stationary autoxidation of S(VI) inhibited by organic compounds was described in detail elsewhere [83]. Briefly, the experiments were carried out in a well-mixed glass reactor of 60 cm 3 volume, closed with a Teflon cover and thermostatted at 298 K within a water jacket. For each run, the reactor was filled with aqueous solution of sodium bisulfite and oxygen so that it contained no gas phase. The pH of solution was adjusted to 3.1 with HClO4. The pH of the solution was recorded using a SenTix Mic combination pH electrode from WTW. Then, a small aliquot of aqueous solution of Fe(ClO4)3 catalyst was injected to start the reaction. Table 1 shows the initial concentrations of reactants. The autoxidation of S(IV) was followed by recording the concentration of oxygen using an Orion 97-08 from Thermo Fisher Scientific and a home-designed pH/oxygen meter and software. Equations (3a) shows the overall stoichiometry of uninhibited SIV autoxidation. Assuming the conversion of inhibitors was small, the stoichiometry of the autoxidation inhibited by a nitrophenol was defined by the same equation so that the rate of the autoxidation was defined by Equation (3b) [83].

Correction of the Diffusional Limitations of the Rate Constants
Since the reactions examined were very fast, we corrected the rate constants determined for diffusional limitations using a simple resistance-in-series model [87][88][89][90]

Experimental Runs
The experimental setup and procedure for carrying out the stationary autoxidation of S(VI) inhibited by organic compounds was described in detail elsewhere [83]. Briefly, the experiments were carried out in a well-mixed glass reactor of 60 cm 3 volume, closed with a Teflon cover and thermostatted at 298 K within a water jacket. For each run, the reactor was filled with aqueous solution of sodium bisulfite and oxygen so that it contained no gas phase. The pH of solution was adjusted to 3.1 with HClO 4 . The pH of the solution was recorded using a SenTix Mic combination pH electrode from WTW. Then, a small aliquot of aqueous solution of Fe(ClO 4 ) 3 catalyst was injected to start the reaction. Table 1 shows the initial concentrations of reactants. The autoxidation of S(IV) was followed by recording the concentration of oxygen using an Orion 97-08 from Thermo Fisher Scientific and a home-designed pH/oxygen meter and software. Equation (3a) shows the overall stoichiometry of uninhibited SIV autoxidation. Assuming the conversion of inhibitors was small, the stoichiometry of the autoxidation inhibited by a nitrophenol was defined by the same equation so that the rate of the autoxidation was defined by Equation (3b) [83].

Correction of the Diffusional Limitations of the Rate Constants
Since the reactions examined were very fast, we corrected the rate constants determined for diffusional limitations using a simple resistance-in-series model [87][88][89][90] where all k are second order rate constants (M −1 s −1 ), D are diffusion coefficients of reactants A and B (m 2 s −1 ), r are reaction radii of reactant molecules A and B (m), and N is the Avogadro number (mol −1 ). Details of the calculations are summarized in Section S3 of the SI.

Results
In this section, we present the experimental results obtained for 4-NP. The results for other nitrophenols were similar so we present them in the SI. Figure 1 shows consumption of oxygen during the autoxidation of S(IV) in the presence of 4-NP. The higher was the initial concentration of nitrophenol, the slower was the consumption of O 2 .
In each experiment, the autoxidation attained a quasi-stationary rate, as shown in Figure 2 for the run with [4-NP] = 0.28 mM. Figure 3 shows the plots of reciprocal stationary rates for autoxidation of S(IV) in the presence of 4-NP or a reference compound ethanol versus initial concentrations of each inhibitor. The plots were linear, so their slopes were used in Equation (2) to calculate the relative rate constant for the reaction of 4-NP with sulfate radical-anions Plots for other nitrophenols, all of them linear, were placed in the SI. The results of all experiments are collected in Table 2 and include the slopes of linear plots and the rate constants for reactions of nitrophenols with sulfate radical-anions, both observed and corrected for diffusional limitations. The uncertainties of the observed rate constants were estimated using the total differential method applied to Equation (6) with individual errors equal to the standard errors of the linear slopes and k EtOH ( Table 2). The uncertainties of the corrected rate constants were estimated in a similar way from Equation (4), assuming arbitrarily the uncertainty of k difffusion was 10%. Table 2. Experimental slopes of linear plots (Figure 3 and Figure S2) and rate constants for reactions of nitrophenols with sulfate radical-anions (observed and corrected for diffusional limitations).

Hammett's Correlations
The reactions of nitrophenols with sulfate radical-anions appeared quite fast, with observed second order rate constants of the order 10 9 s −1 M −1 (Table 2). However, the diffusional limitations were not significant because the rate constants corrected for diffusional limitations were higher for a  Figure 4a shows the uncorrected rate constants for reactions of sulfate radical-anions with phenol and substituted phenols-chlorophenols [83] and nitrophenols (this work)-correlate well with sums of Brown substituent coefficients for the compounds. The Brown coefficients for chlorophenols were taken after [83], while those for nitrophenols were: σ m + = 0.71, σ p + = 0.79 [91,92] and σ o + = 0.66 σ p + = 0.52 [93] for meta, para and orto substituents, respectively. The straight line in Figure 4a was obtained by linear regression covering all data (Equation (7)).
Atmosphere 2019, 10, x FOR PEER REVIEW 6 of 15 log = 9.9006 ± 0.0785 − 1.1513 ± 0.0970 ∑ , = 0.9663, Equation (7) can be used to estimate the second order rate constants for reactions of sulfate radical-anions with substituted phenols that had not been determined experimentally.

Atmospheric Significance
The atmospheric significance of the aqueous-phase reactions of nitrophenols with sulfate radical-anions was evaluated using the approach developed in [81]. The rate of the total conversion of a nitrophenol NP by a reactant X (OH or NO3) in the gas phase (rX,g) and in the aqueous phase (rX,aq × ω) was compared to the rate of conversion of this NP by sulfate radical-anions in the aqueous phase within the gas phase (rSO4,aq ω) as the ratio RX,tot-aq defined by Equation (10). The concentrations of the gas-phase and aqueous-phase reactants were assumed to follow the Henry's Law.
where ω m 3 m −3 is the atmospheric liquid water contents; kX,g and kX,aq dm 3 mol −1 s −1 are the rate constant for the reaction of X with NP in the gas phase and the aqueous phase, respectively; kSO4,aq dm 3 mol −1 s −1 is the rate constant for the reaction of SO4  Equation (7) can be used to estimate the second order rate constants for reactions of sulfate radical-anions with substituted phenols that had not been determined experimentally.
The Brown substituent coefficients can estimate the relative strength of the O-H bonds in substituted phenols with a linear correlation developed by Jonsson et al. [93] (Equation (8)).
Therefore, the rate constants for reactions of sulfate radical-anions with phenol and substituted phenols can also be correlated against ∆D O-H (Figure 4b). The corresponding linear regression is given by Equation (9).
Equation (9) can estimate the second order rate constants for reactions of sulfate radical-anions with substituted phenols in place of Equation (7).

Atmospheric Significance
The atmospheric significance of the aqueous-phase reactions of nitrophenols with sulfate radical-anions was evaluated using the approach developed in [81]. The rate of the total conversion of a nitrophenol NP by a reactant X (OH or NO 3 ) in the gas phase (r X,g ) and in the aqueous phase (r X,aq × ω) was compared to the rate of conversion of this NP by sulfate radical-anions in the aqueous phase within the gas phase (r SO 4 ,aq ω) as the ratio R X,tot-aq defined by Equation (10). The concentrations of the gas-phase and aqueous-phase reactants were assumed to follow the Henry's Law. , (10) where ω m 3 m −3 is the atmospheric liquid water contents; k X,g and k X,aq dm 3 mol −1 s −1 are the rate constant for the reaction of X with NP in the gas phase and the aqueous phase, respectively; k SO 4 ,aq dm 3 Tables 2 and 3 while more details are available in the SI. The ranges of radical concentrations considered in Figure 5 fit well within the realistic ranges estimated by modeling for the atmospheric systems (Table 4) [94].
Atmosphere 2019, 10, x FOR PEER REVIEW 7 of 15 Figure 5 compares the total conversion of 2-NP due to the gas-phase and the aqueous-phase reactions with OH radicals to the aqueous-phase reaction with SO4 •-radical-anions (a) as well as the conversion of 2-NP due to the gas-phase and aqueous-phase reactions with NO3 radicals to the aqueous-phase reaction with SO4 •− radical-anions (b). Data required for the calculations behind the plots are given in Tables 2 and 3 while more details are available in the SI. The ranges of radical concentrations considered in Figure 5 fit well within the realistic ranges estimated by modeling for the atmospheric systems (Table 4) [94].  (10)).
In most cases, the total OH radical sink for 2-NP dominates over the SO4 •− aqueous sink in all atmospheric aqueous phases. Sulfate radical-anions take the lead only if they are in significant excess in clouds, rains, and storms (red line in Figure 5a . In other cases, the SO4 •− aqueous sink prevails. The above rationale is based on the assumption that the hydroxyl and nitrate radicals as well as 2-NP are at Henry's equilibria in the gas phase and in the aqueous phase while the sulfate radical-anions exist only in the aqueous phase.  [52,95]; (b) [54]; (c) [96]; (d) [81]; (e) [97]. •− ] aq > 36). In other cases, the SO 4 •− aqueous sink prevails. The above rationale is based on the assumption that the hydroxyl and nitrate radicals as well as 2-NP are at Henry's equilibria in the gas phase and in the aqueous phase while the sulfate radical-anions exist only in the aqueous phase.  [52,95]; (b) [54]; (c) [96]; (d) [81]; (e) [97]. Table 4. Ranges of radical concentrations in gas phase, clouds and deliquescent particles [94].  Table 3.

OH NO 3 OH NO 3 SO 4 •− [OH]/[SO 4 •− ] [NO 3 ]/[SO
The rate of aqueous-phase reaction of a nitrophenol NP with sulfate radical-anions can also be compared to the rates of gas-phase reactions with OH or NO 3 sinks alone, assuming the gas-phase and aqueous-phase reactants follow the Henry's Law The results obtained for 2-NP ( Figure 6) show that the gas-phase sinks dominate in the aerosol and haze waters and in clouds and rains provided hydroxyl or nitrate radicals are in excess. Surprisingly, there is little difference observed between the hydroxyl radicals and nitrate radicals in spite of significant difference between the rate constants for their gas-phase reactions with 2-NP ( Table 2). This is explained by lower solubility of NO 3 in water. When the aqueous-phase concentrations of both radicals are equal, the gas-phase concentration of NO 3 is higher than the concentration of OH and compensates for its lower rate constant. For reference, one can compare the gas-phase and the aqueous phase conversions of 2-NP by hydroxyl radicals or nitrite radicals alone ( Figure S3). Conversion by OH in the gas phase dominates in over conversion in aerosol and haze water but not over that in clouds and rain. Conversion of 2-NP by NO 3 in the gas phase always dominates over conversion in atmospheric waters.   3 1.2 × 10 7 8.0 × 10 −12 3.0 × 10 −13 9 × 10 −13 1.6 × 10 5 6.0 × 10 3 (a) calculated using Henry's constants from Table 3.
The rate of aqueous-phase reaction of a nitrophenol NP with sulfate radical-anions can also be compared to the rates of gas-phase reactions with OH or NO3 sinks alone, assuming the gas-phase and aqueous-phase reactants follow the Henry's Law The results obtained for 2-NP ( Figure 6) show that the gas-phase sinks dominate in the aerosol and haze waters and in clouds and rains provided hydroxyl or nitrate radicals are in excess. Surprisingly, there is little difference observed between the hydroxyl radicals and nitrate radicals in spite of significant difference between the rate constants for their gas-phase reactions with 2-NP ( Table 2). This is explained by lower solubility of NO3 in water. When the aqueous-phase concentrations of both radicals are equal, the gas-phase concentration of NO3 is higher than the concentration of OH and compensates for its lower rate constant. For reference, one can compare the gas-phase and the aqueous phase conversions of 2-NP by hydroxyl radicals or nitrite radicals alone ( Figure S3). Conversion by OH in the gas phase dominates in over conversion in aerosol and haze water but not over that in clouds and rain. Conversion of 2-NP by NO3 in the gas phase always dominates over conversion in atmospheric waters. Rate of conversions of a NP by X (OH or NO3) and by SO4 •− in the aqueous phases alone were compared using Equation (12).  Figure 7 shows that the aqueous-phase conversion of 2-NP by OH radicals dominates over that by SO4 •− radical-anions when the ratio of the radicals concentrations is higher than ~0.15. A similar Figure 6. Rate of 2-NP conversion in the atmosphere due to the gas-phase reaction with OH radicals (a) or with NO 3 radicals (b) compared to the rate of the aqueous-phase reaction of 2-NP with sulfate radical-anions for various proportions of radicals in the aqueous phase [OH] aq /[SO 4 •− ] aq and varying liquid water contents (ω) (based on Equation (11)).
Rate of conversions of a NP by X (OH or NO 3 ) and by SO 4 •− in the aqueous phases alone were compared using Equation (12). r X,aq r SO 4 ,aq = k X,aq Atmosphere 2019, 10, 795 9 of 14 Figure 7 shows that the aqueous-phase conversion of 2-NP by OH radicals dominates over that by SO 4 •− radical-anions when the ratio of the radicals concentrations is higher than~0.15. A similar domination of NO 3 radicals over SO 4 •− radical-anions requires the corresponding concentration ratio is greater than~40.
Atmosphere 2019, 10, x FOR PEER REVIEW 9 of 15 domination of NO3 radicals over SO4 •− radical-anions requires the corresponding concentration ratio is greater than ~40. Figure 7. Comparison of the rates of aqueous-phase conversion of 2-NP due to reaction with SO4 •− radicals and OH radicals (blue line) or NO3 radicals (red line).
We expect the comparison of gas-phase and aqueous-phase conversions for other nitrophenols studied would provide similar results when the gas-phase rate constants for these nitrophenols are available.

Conclusions
Nitrophenols (2-NP, 3-NP, 4-NP, and 2,4-NP) react fast with SO4 •− radical-anions in aqueous solutions. Rate constants for these reactions, along with rate constants of several chlorophenols and phenol, correlate linearly with Brown substituent coefficients and with the relative strength of the O-H bonds in the molecules. The correlation allows estimation of rate constants for reactions of other substituted phenols with sulfate radical-anions.
The aqueous-phase reaction of 2-NP with sulfate radical-anions dominates over the aqueous-phase conversion of 2-NP by OH radicals only when SO4 •-radicals are at least 10 times more abundant than the OH radicals. Similar domination over NO3 radical requires the concentration of sulfate radicals is at least a quarter of the concentration of nitrate radicals.
The comparison of gas-phase conversion of 2-NP by OH or NO3 radicals against the aqueous-phase conversion by sulfate radical-anions depends on the liquid water contents of a particular atmospheric system considered. In deliquescent aerosol and haze water (ω < 10 −10 m 3 m −3 ), gas-phase reactions always prevail over the aqueous-phase reactions. In cloud, rain and fog water (10 −8 < ω < 10 −6 m 3 m −3 ), the aqueous-phase reaction of 2-NP dominates over the gas-phase conversion of 2-NP by hydroxyl or nitrate radicals provided the aqueous-phase concentration of sulfate radical-anions is not smaller than the aqueous-phase concentration of hydroxyl or nitrate radicals. These conclusions are based on the assumption that the gas-phase and aqueous-phase concentrations of OH, NO3, and 2-NP are bound by Henry's equilibria.
The gas-phase and aqueous-phase conversions of other nitrophenols are expected to follow similar patterns. However, this expectation should be confirmed by calculations when constants of the gas-phase reactions of the nitrophenols with hydroxyl and nitrate radicals are available.
Last not least, we hope that the rate constants determined in the present work for atmospheric purposes may appear useful for designers of advanced oxidation processes aimed at removal of nitrophenols from various waste effluents utilizing sulfate radical-anions. We expect the comparison of gas-phase and aqueous-phase conversions for other nitrophenols studied would provide similar results when the gas-phase rate constants for these nitrophenols are available.

Conclusions
Nitrophenols (2-NP, 3-NP, 4-NP, and 2,4-NP) react fast with SO 4 •− radical-anions in aqueous solutions. Rate constants for these reactions, along with rate constants of several chlorophenols and phenol, correlate linearly with Brown substituent coefficients and with the relative strength of the O-H bonds in the molecules. The correlation allows estimation of rate constants for reactions of other substituted phenols with sulfate radical-anions. The aqueous-phase reaction of 2-NP with sulfate radical-anions dominates over the aqueous-phase conversion of 2-NP by OH radicals only when SO 4 •− radicals are at least 10 times more abundant than the OH radicals. Similar domination over NO 3 radical requires the concentration of sulfate radicals is at least a quarter of the concentration of nitrate radicals. The comparison of gas-phase conversion of 2-NP by OH or NO 3 radicals against the aqueous-phase conversion by sulfate radical-anions depends on the liquid water contents of a particular atmospheric system considered. In deliquescent aerosol and haze water (ω < 10 −10 m 3 m −3 ), gas-phase reactions always prevail over the aqueous-phase reactions. In cloud, rain and fog water (10 −8 < ω < 10 −6 m 3 m −3 ), the aqueous-phase reaction of 2-NP dominates over the gas-phase conversion of 2-NP by hydroxyl or nitrate radicals provided the aqueous-phase concentration of sulfate radical-anions is not smaller than the aqueous-phase concentration of hydroxyl or nitrate radicals. These conclusions are based on the assumption that the gas-phase and aqueous-phase concentrations of OH, NO 3 , and 2-NP are bound by Henry's equilibria.
The gas-phase and aqueous-phase conversions of other nitrophenols are expected to follow similar patterns. However, this expectation should be confirmed by calculations when constants of the gas-phase reactions of the nitrophenols with hydroxyl and nitrate radicals are available.
Last not least, we hope that the rate constants determined in the present work for atmospheric purposes may appear useful for designers of advanced oxidation processes aimed at removal of nitrophenols from various waste effluents utilizing sulfate radical-anions.