Ionic-Equilibrium-Based Mechanism of •OH Conversion to Dichloride

Article Cite This: J. Phys. Chem. B 2019, 123, 528−533

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Ionic-Equilibrium-Based Mechanism of •OH Conversion to Dichloride Radical Anion in Aqueous Acidic Solutions by Kinetic and Theoretical Studies Lukasz Kazmierczak, Marian Wolszczak, and Dorota Swiatla-Wojcik* Institute of Applied Radiation Chemistry, Faculty of Chemistry, Lodz University of Technology, Zeromskiego 116, 90-924 Lodz, Poland

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S Supporting Information *

ABSTRACT: A new mechanism for the dichloride radical anion (Cl2•−) formation in diluted acidic chloride solutions is proposed on the grounds of pulse radiolysis measurements of the optical absorption growth at 340 nm and the density functional theory and Hartree−Fock computations. We show that the rate of •OH conversion into Cl2•− is determined by the equilibrium concentration of the ionic pair H3O+·Cl−. According to the proposed mechanism, the diffusional encounter of •OH and H3O+·Cl− is followed by fast concerted charge/proton transfer (k(25 °C) = 6.2 × 1012 s−1) to yield Cl•, which then reacts with Cl− to produce Cl2•−. The mechanism has been confirmed by the observed first-order growth of the Cl2•− absorption and a direct proportionality of the rate constant to the activities of H3O+ and Cl− ions. The salt effect on the rate of Cl2•− formation is due to the ionic strength effect on the equilibrium H3O+ + Cl− ⇄ H3O+·Cl−. Jayson et al.6 found the decay of •OH and the growth of Cl2•− absorption at 340 nm to occur at the same rate, which is not consistent with time-resolved consecutive reactions (1)−(3). If the formation of Cl2•− involves consecutive reactions (1)−(3) and the intermediate product •OHCl− absorbs weaker than Cl2•−, as suggested,6 then the absorption growth should be sigmoid in shape as observed for Br2•− and I2•− in aqueous solution.12,13,15 In our pulse radiolysis measurements, the growth of absorbance at 340 nm was pure first-order and the optical absorption spectra overlapped at different times after the electron pulse, indicating that no intermediate product is formed. Second, the reaction rate constants kexp obtained in our experiments significantly exceed the values kJPS calculated from the formula derived by Jayson et al.6 on the basis of reactions (1)−(3) (cf. Table S2 in the Supporting Information). Dissimilarity of the chloride systems has also been revealed by computational studies.16,17 Yamaguchi16 has demonstrated that the formation of •OHX− from the hydroxyl radical and halide anion X− is exothermic for bromide and iodide, but endothermic for chloride, whereas mechanistic analysis by Minakata et al.17 indicates that reactions involving •OHCl− do not adhere to the linear relationship between the calculated Gibbs free energy and the measured reaction rate constant,

1. INTRODUCTION The reduction of the hydroxyl radical (•OH) in diluted acidic aqueous solutions of chloride anions has been a topic of increasing interest because the aqueous-phase advanced oxidation processes, involving chlorine atoms, are used in chlorination of drinking water, disinfection, and wastewater reclamation for direct potable reuse.1−3 The aqueous oxidation of Cl− by •OH also occurs in natural environments, e.g., in water droplets or sea-salt aerosols.4,5 The three-step conversion mechanism of •OH in acidic chloride solution was first proposed by Jayson et al.,6 on the grounds of their pulse radiolysis experiments and the earlier studies by Anbar and Thomas.7 Later, the mechanism6 was generalized for bromide and iodide solutions and considered one of the paths of the formation of Br2•− and I2•−.8−14 The mechanism assumes the formation of the •OHX− radical anion (1), which in reaction (2) with H+ forms the halogen atom. The subsequent recombination (3) with the halogen anion leads to the dihalogen radical anion X2•−. •

OH + X− V •OHX− (X = Cl, Br, I)

(1)

•

OHX− + H+ V X• + H 2O

(2)

X• + X− V X •− 2

(3)

Although the formation of •OHX− seems to be well established for bromide and iodide solutions,11−15 the role of •OHCl− as a precursor of Cl2•− is questionable for several reasons. First, © 2019 American Chemical Society

Received: October 26, 2018 Revised: December 20, 2018 Published: January 7, 2019 528

DOI: 10.1021/acs.jpcb.8b10452 J. Phys. Chem. B 2019, 123, 528−533

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The Journal of Physical Chemistry B exhibited by the majority of chlorine-derived radicals with other inorganic radicals, unless two or more water molecules are explicitly included in calculations.17 This suggests the importance of H2O molecules in stabilization of the •OHCl− geometry, and is consistent with the earlier ab initio calculations by Sevilla et al.,18 who showed that only fully optimized explicitly hydrated •OHCl− structure displays stronger ion-dipole interaction resulting in complete spin localization on the hydroxyl radical. Later, density functional theory (DFT) calculations for the •OHCl− intermediate revealed two minima on the ground-state potential-energy surface, interpreted as a hydrogen-bonded complex and a hemi-bonded compound.19 D’Auria et al.20 pointed out, however, that different configurations, a hydrogen-bonded complex •OH···Cl− and a hemi-bonded (HO•−Cl)−, depend on schemes employed in DFT calculations, self-interactioncorrected BLYP and the uncorrected one, respectively. Combined quantum mechanics/molecular mechanics calculations of the ground-state free-energy surfaces and absorption spectrum of covalently bonded HO•−Cl− revealed that hemibonded structures are the excited-state rather than the groundstate configurations.21 Although the absorption spectrum calculated for aqueous solution showed good agreement with the spectroscopic experimental data reported by Jayson et al.,6 the mechanism leading to the formation of Cl• has not been clarified. In this work, the •OH conversion to Cl2•− in aqueous acidic solutions has been investigated by pulse radiolysis measurements and quantum chemical calculations using DFT and Hartree−Fock (HF) methods. On the grounds of the experimental and theoretical data obtained, a new mechanism is proposed.

Figure 1. Selected kinetic traces and the nonlinear fits to the firstorder absorbance growth at 340 nm measured using 17 ns pulse radiolysis of aqueous solutions containing 10 mM HCl (upper traces) and 10 mM HCl and 200 mM NaClO4 (lower traces). For more details, see the text and Table S1 in the Supporting Information.

NaClO4 in the concentrations specified in Table S1. The fitted values of kexp depend on [H3O+] and [Cl−]. At the higher concentration of these ions, the absorption growth was faster but the increase in ionic strength by addition of NaClO4 resulted in a slower growth. The salt effect was particularly significant when NaClO4 was added to HCl solution. The value of kexp = (1.72 ± 0.07) × 106 s−1 obtained for [HClO4] = [NaCl] = 10 mM and [NaClO4] = 980 mM is slightly higher than (1.4 ± 0.1) × 106 s−1 reported by Jayson et al.6 for the decrease in optical density at 240 nm in the argon-flushed solution of the same composition. This slight difference is explained in Section 4.

2. EXPERIMENTAL SECTION Electron pulse radiolysis experiments were carried out using 17 ns pulses from a 6 MeV ELU-6 linear accelerator, coupled with optical detection at 340 nm, which is the absorption maximum of Cl2•− as confirmed by the absorption spectrum recorded in the wavelength range of 250−450 nm. Solutions were prepared using 1 M HCl, 60%(m/m) HClO4 stock aqueous solutions, sodium chloride (NaCl), and sodium perchlorate monohydrate (NaClO4·H2O); all of these were of the purest commercially available grade and purchased from Sigma-Aldrich. The concentrations of H3O+ and Cl− ions varied from 2 to 50 mM. Sodium perchlorate was used to increase the ionic strength. The solutions were deoxygenated by purging with high-purity N2. In acidic solutions, the hydrated electron (eaq−) is converted to a hydrogen atom in the reaction with H3O+. The growth of transient absorption of Cl2•− was traced at room temperature (24 ± 1 °C). The optical path of the cell was 1 cm. The optical absorption was recorded using a monochromator ARC SpectraPro275, a photomultiplier R 928 Hamamatsu Photonics, and an oscilloscope Tektronix TDS 500 MHz. Time intervals for data analysis were chosen to avoid artifacts resulting from Cherenkov radiation. The kinetic traces were fitted to the first-order growth using the Levenberg−Marquardt iteration algorithm, implemented in Origin 2018b software. The correlation coefficients, ranging from 0.917 to 0.995, confirm pure first-order formation of Cl2•− (see Figure 1). All of the determined rate constants are collected in Table S1 in the Supporting Information. The formation of Cl2•− has been observed at varied ionic strengths. Electrolyte solutions contained HCl, HClO4, NaCl, and

3. QUANTUM CHEMICAL CALCULATIONS Calculations were performed using Gaussian 09W22 and the unrestricted open-shell DFT and unrestricted Hartree−Fock (UHF) methods coupled with the Pople’s split-valence 6-311G ++(3df,3pd) basis set or the Dunning’s correlation-consistent triple-zeta aug-cc-pVTZ one. The hybrid three-parameter functional UB3LYP was employed in DFT calculations. The polarizable continuum model with integral equation formalism IEF-PCM or the SMD model was assumed in the selfconsistent reaction field method. The optimization by the Berny algorithm was controlled by the quadratically convergent method, involving linear searches when far from convergence, and Newton−Raphson steps otherwise. After the optimization, the force constants and vibrational frequencies were computed, and the natural orbital bond analysis (NBO) was performed to specify the thermodynamic output, atomic charge distribution, and orbital energies. The DFT and HF computations performed for negatively charged, doublet structure consisting of Cl, O, and H atoms failed in obtaining • OHCl− as a transient product because the tight convergence criteria in searching either the local minima or the first-order saddle points were not fulfilled. Instead, the convergence was obtained for the system consisting of H3O+, Cl−, and •OH, and this system was taken for further modeling. The convergence to either the local minimum (LM) or the first-order saddle point (SP) revealed four configurations of 529

DOI: 10.1021/acs.jpcb.8b10452 J. Phys. Chem. B 2019, 123, 528−533

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The Journal of Physical Chemistry B stationary points of the H2O(h)·H2O(r)·Cl• complex, depicted in Figure 2, where (h) corresponds to the atoms originally

tion: the up-SP complex shows the negatively charged chlorine atom, whereas the atomic charge on Cl in the up-LM complex is nearly zero. Because the vibrationally promoted proton transfer and the charge compensation occur simultaneously, the overall process is considered a concerted charge/proton transfer. The DFT rigid scans including single-point energy evaluations over a rectangular grid versus the distance O(h)− H(h) indicate that the concerted charge/proton transfer is activationless (see Figure 4). This implies the value of

Figure 2. Four configurations of the stationary points of the H2O· H2O·Cl• complex classified according to the position of the hydronium hydrogen atoms bound to O(h) and the vector connecting O(h) and O(r) atoms. (a) Down: hydronium hydrogen atoms are placed below the O(h)−O(r)−Cl plane; (b) left: hydronium hydrogen atoms and the chlorine atom are on the opposite sides of the O(h)− O(r) axis; (c) right: hydronium hydrogen atoms and the chlorine atom are on the same side of the O(h)−O(r) axis; (d) up: hydronium hydrogen atoms are above the O(h)−O(r)−Cl plane.

assigned to the hydronium ion and (r) to the atoms initially assigned to the hydroxyl radical. The atomic charges on the chlorine atom resulting from UHF and DFT calculations are (−0.004e) and (−0.269e), respectively. The former result can be regarded as more reasonable because UHF methods are better suited for electron density modeling of open-shell systems.19,20 Detailed characteristics of the distinguished configurations are given in the Supporting Information. These include zero-point energy (ZPE)-corrected free energies (Table S4) and enthalpies (Table S5) and imaginary frequencies resulting from the vibrational−rotational analysis of SPs (Table S6). High vibrational frequencies were obtained for the up-SP using both UHF and DFT methods and the IEFPCM solvent model, although the DFT method more often failed in searching LM and SP. A close proximity of the Oh, Or, and Cl atoms results in a highly inhomogeneous distribution of positive and negative charges, and promotes proton transfer, shown by the displacement vector in Figure 3a. The intrinsic reaction coordinate analysis confirmed that the up-SP is the transition state for an attachment of the H(h) atom to the O(r) atom followed by relaxation to the up-LM complex, depicted in Figure 3b. This process is associated with charge compensa-

Figure 4. Rigid scans of potential energy along the O(h)−H(h) coordinate, obtained for up-LM using 6-311G++(3df,3pd) basis set and the IEF-PCM water-solvent model: DFT method (dashed line); UHF method (solid line).

6.21 × 1012 s−1 for the reaction rate constant. As seen in Figure 4, the UHF calculations show a small activation energy of 13.5 kJ mol−1 and, consequently, the value of 2.66 × 1010 s−1 for the concerted charge/proton-transfer rate constant. We consider the DFT value as more reliable because the HF methods tend to overestimate the energy barrier.23 At the same time, the scans in Figure 4 indicate that the reverse process requires very high activation energies, i.e., 110.4 kJ mol−1 shown by the UHF method and 276.5 kJ mol−1 resulting from the UB3LYP DFT calculations. In general, the UHF energies and enthalpies of the water-dimer-stabilized complex H2O·H2O·Cl• are much higher than the DFT ones (see Tables S4 and S5), and both UHF and DFT results are rather insensitive to the basis set assumed.

4. RESULTS AND DISCUSSION Applying steady-state approximation to the mechanism based on reactions (1)−(3) and assuming that equilibrium (3) is shifted to the right and is fast compared to reaction (2), Jayson et al.6 derived eq 4 describing the rate constant, kJPS, for the formation of Cl2•− as a function of the activities of chloride and hydrogen ions k k a −a + k JPS = 1 2 Cl H k −1 + k 2a H+ (4) In our experiments, equilibrium (3) was shifted to the right because [Cl−] ≥ 2 mM is far above the limiting value of 10−4 M.6 Table S2 in the Supporting Information shows that kJPS values calculated using eq 4 are noticeably lower than kexp. This

Figure 3. Vibrationally promoted proton transfer from H3O+, coupled with charge transfer from Cl−, results in the water-dimer-stabilized Cl•: (a) up-SP; (b) up-LM obtained at the UHF/aug-cc-pVTZ level of theory and using the IEF-PCM solvent model. 530

DOI: 10.1021/acs.jpcb.8b10452 J. Phys. Chem. B 2019, 123, 528−533

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The Journal of Physical Chemistry B indicates that the rate of formation of Cl2•− is not determined by equilibrium (1) and reaction (2). Therefore, an alternative mechanism is proposed as described below. 4.1. Kinetic Model. Instead of reactions (1) and (2), we assume that in chloride solutions the formation of Cl2•− is controlled by equilibrium (5) established between free H3O+ and Cl− ions and the ionic pairs H3O+·Cl−. H3O+ + Cl− V H3O+ ·Cl−

keff =

k50k 7 × γ±2[H3O+][Cl−] k −5

(12)

The critical test of the proposed model is presented in Figure 5. Details of the calculations of γ± can be found in the Supporting Information.

(5)

Because at equilibrium, rates of the forward and reverse steps are the same, the equilibrium concentration of the ionic pairs is +

−

[H3O ·Cl ]∞ =

k50γ±2 k −5

× [H3O+]∞ × [Cl−]∞

(6)

In eq 6, the square of the mean activation coefficient γ2± accounts for the salt effect on the forward rate constant.24 The proposed kinetic model (7)−(9) assumes the diffusional encounter of •OH and H3O+·Cl− pair and the formation of the complex H3O+·•OH·Cl−. As shown in Section 3, the proximity of the hydroxyl radical induces vibrationally promoted charge redistribution. This concerted charge/proton transfer results in the decay of the proximity complex H3O+·•OH·Cl− to water-dimer-stabilized Cl•, which then reacts with Cl− to produce Cl2•−. H3O+ ·Cl− + •OH V H3O+ · •OH·Cl−

(7)

H3O+ · •OH·Cl− V H 2O·H 2O·Cl•

(8)

H 2O·H 2O·Cl• + Cl− V H 2O·H 2O·Cl 2•−

(9)

Figure 5. Rate constants kexp for the pseudo-first-order conversion of • OH to Cl2•− in chloride solutions obtained from pulse radiolysis measurements of the absorbance growth at 340 nm. Linear regression (dotted line) confirms direct proportionality k exp = a × γ ±2 [H3O+][Cl−] predicted by eq 12. Inset: Rate constants kexp measured in pure HCl solutions.

The direct proportionality is particularly well reproduced in pure HCl solutions (see the inset) because H3O+ and Cl− ions are not involved in other equilibria. Interplay between equilibria is seen by comparison of the data obtained for pure HCl and HCl and 200 mM NaClO4 solutions. As seen from Table S2 in the Supporting Information, because of the engagement of H3O+ ions in the equilibrium H3O+ + ClO−4 ⇄ H3O+·ClO−4 , the decrease in kexp is more significant than exclusively expected from the salt effect predicted by the approximate formula (12). The role of equilibrium (5) is also evidenced by a slightly higher value of kexp obtained for N2saturated solutions compared to that measured in Ar-saturated systems. The difference in kexp was observed at low concentration of H3O+ and Cl− ions. At ambient conditions, the solubility of N2 in water is more than twice as low as the solubility of Ar. Because in the presence of neutral gases equilibrium (5) shifts to the left, the equilibrium concentration [H3O+·Cl−]∞ is higher in N2-saturated solutions, explaining faster formation of Cl2•−. Considering the effects resulting from the composition of a solution, the value of (3.1 ± 0.1) × 1010 M−2 s−1 obtained for the proportionality coefficient a in pure HCl solution has been

According to the quantum chemical calculations (see Section 3), the forward reaction (8) is fast (k8 = 6.2 × 1012 s−1) and the reverse step requires a high activation energy. The measured value for k−8 is 2.5 × 105 s−1.25 Therefore, k−7 and k−8 can be neglected as small compared to the forward reaction rate constants k7 and k8. Reaction (9) is virtually the same as equilibrium (3). The reverse step can be neglected because in our experiments [Cl−] ≥ 2 mM. Applying steady-state approximation to Cl• and H3O+·•OH·Cl−, one can show that the rate of formation of Cl2•− is equal to the rate of decay of • OH and depends on equilibrium (5) as follows d[Cl •− d[•OH] 2 ] =− = k 7 × [H3O+ ·Cl−]∞ × [•OH] dt dt (10) −

When [H3O ·Cl ]∞ is in excess, the pseudo-first-order rate constant keff for the formation of Cl2•−, or for the conversion of • OH to Cl2•−, is given by +

keff =

k50k 7 × γ±2[H3O+]∞ [Cl−]∞ k −5

assumed to be the most reliable estimate of the ratio

(11)

k50k 7 . k −5

To

verify the obtained value, an alternative assessment is provided below. The diffusion-controlled reaction rate constant k7 can be calculated from the Smoluchowski equation24

From the material balance, equilibrium concentrations of free H3O+ and Cl− ions can be expressed as follows: [H3O+]∞ = [H3O+] − [H3O+·Cl−]∞ − ∑i[H3O+·X−i ]∞ and [Cl−]∞ = [Cl−] − [H3O+·Cl−]∞ − ∑i[Y+i ·Cl−]∞, where the last terms account for other equilibria established in multicomponent electrolyte solution. At sufficiently high concentration of H3O+ and Cl− ions in solution, [H3O+]∞ ≅ [H3O+] and [Cl−]∞ ≅ [Cl−], and eq 11 takes the form

k 7 = 4πNA(DH3O+·Cl− + DOH)R enc

(13)

Substituting Avogadro’s number NA, the encounter distance Renc of 0.32 or 0.30 nm, resulting from UHF or DFT 531

DOI: 10.1021/acs.jpcb.8b10452 J. Phys. Chem. B 2019, 123, 528−533

The Journal of Physical Chemistry B

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calculations, respectively, and taking the diffusion coefficients DH3O+·Cl− ≈ DOH ≈ DH2O = 2.3 × 10−9 m2 s−1 at room temperature, one obtains 1.11 × 1010 M−1 s−1 or 1.04 × 1010 M−1 s−1, respectively. Because k50 k −5

=

1 γ±2

×

[H3O+·Cl−]∞ [H3O+]∞ [Cl−]∞

=

1 γ±2

×

(1 − α) , α 2[HCl]

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.8b10452. Fitted rate constants for the pseudo-first-order growth of the Cl2•− absorbance; parameters describing the ionic strength dependence for the mean activity coefficient γ± and the values calculated for the measured systems; zero-point energy (ZPE)-corrected sum of the electronic and thermal free energies and enthalpies of H2O·H2O· Cl•; imaginary frequencies obtained from the vibrational−rotational analysis of the first-order saddle points (PDF)

of dissociation, we used the conductivity data for 2 mM HCl in water26 and the theoretical models of electrolyte conductance.27 Expressing the ion-pair-separation parameter by the sum of H3O+ and Cl− radii in aqueous solution, i.e., (0.135 + 0.181) nm, and substituting γ± = 0.965 from Table S2 in the −1

k50 k −5

ASSOCIATED CONTENT

S Supporting Information *

where α is the degree

Supporting Information, we calculated α = 0.9948 and

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=

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2.82 M . Thus, the alternative assessment results in the value of 2.93 × 1010 or 3.13 × 1010 M−1 s−1, depending on the estimate of k7. Such good agreement with the pulse radiolysis data confirms that the conversion of •OH to Cl2•− in acidic solutions results from a diffusional encounter of •OH and the ionic pair H3O+·Cl−, initiating the concerted charge/proton transfer to give Cl•, which reacts with Cl− to produce Cl2•−. The rate of the overall process is determined by [H3O+·Cl−]∞ and therefore is sensitive to the composition of aqueous solution. Although the mechanism based on the ionic equilibrium (5) is proposed for diluted acidic solutions, it is consistent with the pulse radiolysis observations made for neutral and alkaline solutions of sodium chloride.7 These experiments showed that at pH 7 the Cl2•− signal appeared immediately within 0.1 μs and the measured yield of Cl2•− was negligible at low concentration of Cl− ions but increased with the salt concentration. The radiation chemical yield of Cl2•− was significantly reduced by the addition of NaOH to the solution. To interpret these experimental facts, one has to know that although the bulk solution is neutral the radiation spur is acidic.28 The equilibrium (5) is established between Cl− and the H3O+ ions escaping from the spur when the intraspur chemistry is complete, i.e., within 0.1 μs. In the presence of NaOH, the yield of H3O+ is reduced because of the reaction with OH−, and [H3O+·Cl−]∞ is lower, resulting in a lower yield of Cl2•−.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Dorota Swiatla-Wojcik: 0000-0002-8863-9807 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr George V. Buxton for useful and fruitful discussion. L.K. thanks the Faculty of Chemistry, Lodz University of Technology for the financial support under the Young Scientists’ Fund (Grant number 13-19-2-6267).

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REFERENCES

(1) Wang, D.; Bolton, J. R.; Hofmann, R. Medium Pressure UV Combined with Chlorine Advanced Oxidation for Trichloroethylene Destruction in a Model Water. Water Res. 2012, 46, 4677−4686. (2) Watts, M. J.; Rosenfeldt, E. J.; Linden, K. G. Comparative OH Radical Oxidation Using UV-Cl2 and UV-H2O2 Processes. J. Water Supply: Res. Technol.–AQUA 2007, 56, 469−477. (3) Watts, M. J.; Linden, K. G. Chlorine Photolysis and Subsequent OH Radical Production During UV Treatment of Chlorinated Water. Water Res. 2007, 41, 2871−2878. (4) Knipping, E. M.; Lakin, M. J.; Foster, K. L.; Jungwirth, P.; Tobias, D. J.; Gerber, R. B.; Dabdub, D.; Finlayson-Pitts, B. J. Experiments and Simulations of Ion-enhanced Interfacial Chemistry on Aqueous NaCl Aerosols. Science 2000, 288, 301−306. (5) Spicer, C. W.; Chapman, E. G.; Finlayson-Pitts, B. J.; Plastridge, R. A.; Hubbe, J. M.; Fast, J. D.; Berkowitz, C. M. Unexpectedly High Concentrations of Molecular Chlorine in Coastal Air. Nature 1998, 394, 353−356. (6) Jayson, G. G.; Parsons, B. J.; Swallow, A. J. Some Simple, Highly Reactive, Inorganic Chlorine Derivatives in Aqueous Solution. J. Chem. Soc., Faraday Trans. 1 1973, 69, 1597−1607. (7) Anbar, M.; Thomas, J. K. Pulse Radiolysis Studies of Aqueous Sodium Chloride Solutions. J. Phys. Chem. 1964, 68, 3829−3835. (8) Zehavi, D.; Rabani, J. Oxidation of Aqueous Bromide Ions by Hydroxyl Radicals. Pulse Radiolytic Investigation. J. Phys. Chem. 1972, 76, 312−319. (9) Behar, D. Pulse Radiolysis Studies on Br− in Aqueous Solution. Mechanism of Br2− Formation. J. Phys. Chem. 1972, 76, 1815−1818. (10) Mamou, A.; Rabani, J.; Behar, D. Oxidation of Aqueous Bromide by Hydroxyl Radicals, Studies by Pulse Radiolysis. J. Phys. Chem. 1977, 81, 1447−1448. (11) Büchler, H.; Büchler, R. E. The Radical Ion Complex IOH−: Spectrum and Reactions Studied by Pulse Radiolysis of Aqueous Iodide Solutions. Chem. Phys. 1976, 16, 9−18. (12) Yamashita, S.; Iwamatsu, K.; Maehashi, Y.; Taguchi, M.; Hata, K.; Muroya, Y.; Katsumura, Y. Sequential Radiation Chemical

5. CONCLUSIONS According to the mechanism proposed here, the rate of •OH conversion to Cl2•− in acidic chloride solution is determined by the concentration of H3O+·Cl− ionic pairs established in equilibrium (5). The conversion proceeds via the H3O+·•OH· Cl− complex, formed in the diffusional encounter of •OH and H3O+·Cl−, undergoing a fast concerted charge/proton transfer to give water-dimer-stabilized Cl•, which subsequently reacts with Cl− to give Cl2•−. The rate constant for a diffusional encounter has been estimated to be (1.0 ± 0.1) × 1010 M−1 s−1 at room temperature. For the concerted charge proton-transfer rate constant, the DFT/6-311G++(3df,3pd)/IEF-PCM calculations provide the value of 6.2 × 1012 s−1, corresponding to the activationless process. We showed that the observed negative salt effect on the rate of the Cl2•− formation results from the left-shift of equilibrium (5) under the increasing ionic strength of solution. 532

DOI: 10.1021/acs.jpcb.8b10452 J. Phys. Chem. B 2019, 123, 528−533

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DOI: 10.1021/acs.jpcb.8b10452 J. Phys. Chem. B 2019, 123, 528−533