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

Abstract

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.

1. Introduction

Nitrophenols are well known environmental trace compounds and pollutants [1,2], which have been detected in various environmental matrices including air [3,4,5,6], rainwater [3,7,8,9], cloud water [10], fog [10,11], snow [1], atmospheric aerosol [4,5,6,12,13,14,15,16,17,18,19,20,21,22,23,24,25], soils [26,27], and surface waters [10,28,29,30,31,32]. They originate from many anthropogenic and natural sources including: the incineration of wastes [33], industrial chemical processes [34], combustion of coal and biomass as well as vehicle and aviation fuels [35,36,37], degradation of pesticides [34,38,39], release of wood preservatives [34], and atmospheric chemical reactions. 4-nitrophenol (4-NP) and 2,4-dinitrophenol (2,4-DNP), along with sugar anhydrides such as levoglucosan, serve as markers of biomass burning in ambient aerosol [40,41,42,43]. These compounds and 2-nitrophenol are recognized components of atmospheric brown carbon, i.e., a collection of light absorbing organic compounds in the atmosphere [22,44,45]

Atmospheric reactions that yield nitrophenols take place both in the gas phase and in the aqueous phase. For instance, the gas-phase nitration of phenol involves hydroxyl radicals ^•OH and NO₂ in the daytime or nitrate radical ^•NO₃ and NO₂ in the night to respectively produce 2-nitrophenol (2-NP) or 2-NP and 4-NP. The chemical mechanisms of both processes were thoroughly reviewed [1]. Formation of nitrophenols in atmospheric waters of all kinds is at least equally important but less understood. The possible pathways include oxidation of phenols with NO₂ and OH or NO₃ radicals [46], electrophilic nitration initiated by N₂O₅ and ClNO₂ [1,47], photolytic and dark reactions involving nitrate radicals, inorganic nitrates, nitrites and nitrous acid HONO [48,49], and photolytic reactions with nitrogen dioxide in the presence of iron oxide and oxygen [49].

Atmospheric sinks for nitrophenols include photolysis [50] and the gas-phase reactions with OH radicals and NO₃ 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 NO₂⁻ ions. Vione, et al. [54] showed that OH radicals reacted faster than NO₃ 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. In addition, many laboratories studied the aqueous-phase reactions of other substituted phenols of atmospheric interest like guaiacol, nitro-guaiacol, vanillin, or syringol [55,56,57,58,59].

Much of the nitrophenol chemistry has been studied for the sake of advanced oxidation processes aimed at mitigation of nitrophenols in aquatic and industrial environments [60]. The technologies considered include: Fenton and photo-Fenton reactions based on H₂O₂ [34,61], TiO₂ based photocatalysis [62,63,64], electrocatalysis [65], photo-electrocatalysis [66,67], and wet catalysis [68,69]. Among the latter, a promising process was proposed which utilized reactions of nitrophenols with sulfate radical-anions generated by the cobalt-mediated decomposition of peroxymonosulfate anions [70].

For years, some nitrophenols (2-NP, 4-NP, 2,4-DNP) have been listed as priority or hazardous pollutants [71,72,73]. Generally, mono- and di-nitrophenols are considered toxic in plants and mammals [74], while 4-nitrophenol is highly toxic in humans [75]. Although EPA USA has not considered 4-nitrophenol carcinogenic [38], a laboratory experiment showed the compound can destroy DNA in vitro [76].

This work was aimed at elucidating how fast nitrophenols are removed from the atmospheric waters by reaction with sulfate radical-anions, which are important atmospheric oxidants known to react fast with numerous atmospheric pollutants [77,78,79,80,81,82,83].

2. Experiments

2.1. Chemicals

The following chemicals were used as purchased: 2-nitrophenol (R.G.), 3-nitrophenol (REAGENTPLUS™, 99%), 4-nitrophenol and 2,4,6-trinitrophenol (1 wt % solution in water) from Sigma Aldrich, 2,4-dinitrophenol (97% + 15% H₂O) from Alfa Aesar, Fe(ClO₄)₃·9H₂O (purum) from Fluka, Na₂S₂O₅ (EMSURE^® ACS, Reag. Ph Eur. > 98%) and HClO₄ (pro analysis) from Merck, argon (99.999%) from Multax. For each experiment, aqueous solutions of reactants were prepared freshly using Milli-Q water (18.2 MΩ cm, Milli-Q Advantage System from Merck Millipore). Buffer standards used for the calibration of pH electrodes were from Thermo Fisher Scientific. To avoid the contact with the atmospheric oxygen, Milli-Q water was deoxygenated by a stream of argon bubbled through for 20 min. Solutions of sodium bisulfite were obtained by dissolving Na₂S₂O₅ in deoxygenated Milli-Q water

$${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_5+{\mathrm{H}}_2\mathrm{O}\rightleftarrows {2\mathrm{Na}}^{+}+2{\mathrm{HSO}}_3^{-},$$

(1)

The acidity of solutions was adjusted to pH = 3.1 with 0.1 M HClO₄ so the species in solutions were predominantly Na⁺ and HSO₃⁻ ions.

2.2. 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.

$$k_{\mathrm{inh}1+{\mathrm{SO}}_4^{-}}=\frac{{\mathrm{slope}}_{\mathrm{inh}1}}{{\mathrm{slope}}_{\mathrm{inh}2}}{k}_{\mathrm{inh}2+{\mathrm{SO}}_4^{-}},$$

(2)

In the present work, ethanol was used as a reference inhibitor against which the rate constants for nitrophenols were calculated.

2.3. 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 cm³ 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. Initial concentrations of reactants used in the experiments.

Compound	Abbreviation	Concentration Range, mM
2-nitrophenol	2-NP	0.032–0.347
3-nitrophenol	3-NP	0.019–0.089
4-nitrophenol	4-NP	0.073–0.711
2,4-dinitrophenol	2,4-DNP	0.169–1.325
2,4,6-trinitrophenol	2,4,6-TNP	0.197–0.788
HSO3−		2
O2		~0.25
Fe(ClO4)3		0.01

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].

2SO₃²⁻/2HSO₃⁻ + O₂ = SO₄²⁻/HSO₄⁻,

(3a)

$$r_{autoxidation}=-\frac{d\left[\mathrm{S}\left(\mathrm{IV}\right)\right]}{dt}=\frac{d\left[\mathrm{S}\left(\mathrm{VI}\right)\right]}{dt}=-2\frac{d\left[{\mathrm{O}}_2\right]}{dt},$$

(3b)

2.4. 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]

$$k_{observed}^{-1}=k_{reaction}^{-1}+k_{diffusion}^{-1},$$

(4)

$$k_{diffusion}=4\pi \left(D_A+D_B\right)\left(r_A+r_B\right)N\times {10}^3,$$

(5)

where all k are second order rate constants (M⁻¹ s⁻¹), D are diffusion coefficients of reactants A and B (m² 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.

3. 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 O₂.

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

$$k_{4-\mathrm{NP}+{\mathrm{SO}}_4^{-}}=k_{\mathrm{EtOH}+{\mathrm{SO}}_4^{-}}\frac{{\mathrm{slope}}_{4-\mathrm{NP}}}{{\mathrm{slope}}_{\mathrm{EtOH}}}=4.3\times {10}^7\frac{2.665\times {10}^9}{1.735\times {10}^8}=6.636\times {10}^8 {\mathrm{M}}^{-1}{\mathrm{s}}^{-1},$$

(6)

Plots for other nitrophenols, all of them linear, were placed in the SI. The results of all experiments are collected in

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).

Compound	Slope, s M−2	kobserved, M−1s−1	kdiffusionA, M−1s−1	kreaction, M−1s−1	(kr − ko)/ko, %
EtOH (reference)	(1.735 ± 0.001) × 108			(4.30 ± 0.86) × 107
2-NP	(3.662 ± 0.235) × 109	(9.08 ± 2.40) × 108	2.01 × 1010	(9.50 ± 4.58) × 108	4.74
3-NP	(6.957 ± 0.277) × 109	(1.72 ± 0.41) × 109	2.01 × 1010	(1.89 ± 0,89) × 109	9.53
4-NP	(2.665 ± 0.985) × 109	(6.60 ± 3.77) × 108	2.01 × 1010	(6.83 ± 5.42) × 108	3.41
2,4-DNP	(1.154 ± 0.152) × 109	(2.86 ± 0.95) × 108	2.13 × 1010	(2.90 ± 1.58) × 108	1.51
2,4,6-TNP	(2.865 ± 0.180) × 108	(7.10 ± 1.87) × 107	2.18 × 1010	(7.12 ± 3.31) × 107	0.33

A—assumed unceratinty 2 × 10⁹ M⁻¹ s⁻¹(10%).

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%.

4. Discussion

4.1. Hammett’s Correlations

The reactions of nitrophenols with sulfate radical-anions appeared quite fast, with observed second order rate constants of the order 10⁹ 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 few percent only. The rate constants decreased with the number of NO₂ groups in the molecule with the exception of 3-NP. 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)).

$$\log \left(k_{S{O}_4}\right)=\left(9.9006\pm 0.0785\right)-\left(1.1513\pm 0.0970\right){\displaystyle \sum }{\sigma }^{+}, R^2=0.9663,$$

(7)

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)).

$$\Delta {\mathrm{D}}_{\mathrm{O}–\mathrm{H}}=-2+29.9\left({\sigma }_{o2}^{+}+{\sigma }_{m3}^{+}+{\sigma }_{p4}^{+}+{\sigma }_{m5}^{+}+{\sigma }_{o6}^{+}\right), {\mathrm{kJ}\mathrm{mol}}^{-1},$$

(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).

$$\log \left(k_{S{O}_4}\right)=\left(9.9498\pm 0.0828\right)-\left(0.0508\pm 0.0043\right)\Delta {\mathrm{D}}_{\mathrm{O}–\mathrm{H}}, R^2=0.9665,$$

(9)

Equation (9) can estimate the second order rate constants for reactions of sulfate radical-anions with substituted phenols in place of Equation (7).

4.2. 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 (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_SO4,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.

$$R_{X,tot-aq}=\frac{r_{\mathrm{X},g}+r_{\mathrm{X},aq}\omega }{r_{S{O}_4,aq}\omega }=\frac{k_{X,g}{\left[X\right]}_g{\left[NP\right]}_g+k_{X,aq}{\left[X\right]}_{aq}{\left[NP\right]}_{aq}\omega }{k_{S{O}_4,aq}{\left[X\right]}_{aq}{\left[S{O}_4^{·-}\right]}_{aq}\omega }=\frac{\frac{k_{\mathrm{X},g}}{H_{d,\mathrm{X}}{H}_{d,\mathrm{NP}}}+k_{\mathrm{X},aq}\omega }{k_{{\mathrm{SO}}_4,aq}\omega }·\frac{{\left[X\right]}_{aq}}{{\left[S{O}_4^{·-}\right]}_{aq}},$$

(10)

where ω m³ m⁻³ is the atmospheric liquid water contents; k_X,g and k_X,aq dm³ 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_SO4,aq dm³ mol⁻¹ s⁻¹ is the rate constant for the reaction of SO₄^•− with NP in the aqueous phase; H_d is the dimensionless Henry’s constant (H_d = H × gas constant × absolute temperature) for X or for NP; [X]_aq and [SO₄^•−]_aq are the aqueous-phase concentrations of X and SO₄^•−.

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 Table 2 and

Table 3. Rate and Henry’s constants for selected atmospheric reactants at 296–298 K.

Reaction X + NP	kX,g		kX,aq	HdX	HdNP
	cm3 molecule−1 s−1	dm3 mol−1 s−1	dm3 mol−1 s−1
OH + 2-NP	9.00 × 10−13 (a)	5.42 × 108	5.90 × 109 (b)	6.11 × 102 (d)	5.17 × 103 (e)
NO3 + 2-NP	2.00 × 10−14 (a)	1.20 × 107	2.30 × 107 (c)	1.47 × 101 (d)

^(a) [52,95]; ^(b) [54]; ^(c) [96]; ^(d) [81]; ^(e) [97].

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. Ranges of radical concentrations in gas phase, clouds and deliquescent particles [94].

	Gas Phase (a)		Aqueous Phase
	OH	NO3	OH	NO3	SO4•−	[OH]/[SO4•−]	[NO3]/[SO4•−]
	molecule cm−3		mol dm−3
Minimal	1.4 × 102	7.9 × 106	1.4 × 10−16	1.6 × 10−16	5 × 10−17	1.6 × 10−4	1.8 × 10−3
Maximal	6.6 × 103	1.2 × 107	8.0 × 10−12	3.0 × 10−13	9 × 10−13	1.6 × 105	6.0 × 103

^(a) calculated using Henry’s constants from Table 3.

) [94].

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, [OH]_aq/[SO₄^•−]_aq < 0.16). The total NO₃ radical sink for 2-NP dominates over the SO₄^•− aqueous sink in aerosol and haze waters and in clouds and rains if in significant excess (red line in Figure 5b, [NO₃]_aq/[ SO₄^•−]_aq > 36). 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.

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

$$R_{X,g-aq}=\frac{r_{\mathrm{X},g}}{r_{S{O}_4,aq}\omega }=\frac{k_{X,g}{\left[X\right]}_g{\left[NP\right]}_g}{k_{SO4,aq}{\left[NP\right]}_{aq}{\left[S{O}_4^{·-}\right]}_{aq}\omega }=\frac{k_{\mathrm{X},g}}{k_{S{O}_4,aq}{H}_{d,\mathrm{X}}{H}_{d,\mathrm{NP}}\omega }·\frac{{\left[X\right]}_{aq}}{{\left[S{O}_4^{·-}\right]}_{aq}},$$

(11)

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).

$$\frac{r_{\mathrm{X},aq}}{r_{{\mathrm{SO}}_4,aq}}=\frac{k_{\mathrm{X},aq}}{k_{{\mathrm{SO}}_4,aq}}·\frac{{\left[\mathrm{X}\right]}_{aq}}{{\left[{\mathrm{SO}}_4^{·-}\right]}_{aq}},$$

(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 domination of NO₃ radicals over SO₄^•− radical-anions requires the corresponding concentration ratio is greater than ~40.

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.

5. 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 m³ m⁻³), gas-phase reactions always prevail over the aqueous-phase reactions. In cloud, rain and fog water (10⁻⁸ < ω < 10⁻⁶ m³ 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.