Kinetics and Mechanism of the ChlorateâNitrous Acid Reaction

Article pubs.acs.org/IC

Kinetics and Mechanism of the Chlorate−Nitrous Acid Reaction Rafaela T. P. Sant’Anna and Roberto B. Faria* Instituto de Química, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, CT, Bloco A, 21941-909 Rio de Janeiro, Brazil S Supporting Information *

ABSTRACT: The chlorate-nitrous acid reaction was investigated in acid media, using a high concentration of reagents. It was followed via ultraviolet−visible light (UV-vis) spectroscopy and presented a complex behavior. The order of reagents, and the products formed by this reaction, are dependent on the concentration of reagents. For the high concentration set we used, the reaction has shown a first-order behavior for H+ and HNO2, and an order equal to 0.79 for chlorate. In this case, chlorine dioxide is formed. Moreover, chlorine dioxide starts to form only after all HNO2 has been consumed. This is the first time chlorine dioxide was observed to be formed by this reaction. Reduction of the concentration of reagents decreases the order of HNO2 to 0.91 and no chlorine dioxide is formed. An isosbestic point was found at 312 nm, which indicates a 1:1 ratio between nitrate ion and nitrous acid species. A model, with 14 independent species and 12 reactions is presented, which is able to simulate the experimental behavior for the low and high concentrations sets of reagents and it is a significant improvement in the understanding of the complex nitrogen and chlorine aqueous chemistry.

■

INTRODUCTION During our study of chlorate−iodine−nitrous acid clock reaction,1 we noticed that the chlorate−nitrous acid reaction, which was previously studied by Lowe and Brown2 and by Emeish,3 produces chlorine dioxide, together with nitrate. This was the first time that chlorine dioxide was observed to be formed by the reaction between chlorate and nitrous acid, suggesting that this reaction deserves to be reinvestigated. Reactions to produce chlorine dioxide are widely studied, because of its use as an oxidizing species in very important large-scale industrial processes, including kraft pulp bleaching, use as a fiber brightener in the textile industry, water purification, and treatment of industrial waste. One of the most important methods for the generation of chlorine dioxide is via the chlorate−chloride reaction in aqueous solution using high acid concentration.4,5 The production of chlorine dioxide radical was patented by several authors, including Haller6 and Hutchinson,7 which used methods that have the advantage of not producing chlorine simultaneously. Haller6 produced chlorine dioxide via the reaction between chlorate and nitrogen dioxide at neutral pH, while Hutchinson7 reported the chlorine dioxide formation by the use of chlorite and nitrogen dioxide in acidic pH and explained it by reactions R1−R4. None of them has considered the reaction between chlorate and nitrous acid. NO2• + NaClO2 → ClO2• + NaNO2

(R1)

NaNO2 + H 2SO4 → HNO2 + NaHSO4

(R2)

•

2HNO2 → H 2O + NO + NO2

•

© 2017 American Chemical Society

NO• +

1 O2 → NO2• 2

(R4)

Lowe and Brown2 investigated the chlorate−nitrous acid reaction in acid aqueous media (HNO3), following the reaction by the amount of AgCl precipitated by the addition of AgNO3. They considered reaction R5 and found the rate law given by eq 1. They did not observe the formation of chlorine dioxide. ClO3− + 3HNO2 → Cl− + 3NO3− + 3H+ d[Cl−] = k[ClO3−][HNO2 ][H+] dt

(R5)

(k = 0.7 L2 mol−2 s−1, 25 °C)

(1) 3

Emeish investigated the chlorate−nitrous acid reaction in acid aqueous media (HCl), following the concentration of N(III) using a colorimetric method based on the diazotization of sulfanilamide, and obtained the rate law given by eq 2 for the concentrations [ClO3−] = 6.587 × 10−3 mol L−1, [HNO2] = 3.646 × 10−4 mol L−1, and [H+] = 1.78 × 10−2 mol L−1. However, he did not observe the formation of chlorine dioxide. The mechanism suggested by this author is shown by reactions R6−R13. Received: June 12, 2017 Published: September 5, 2017

(R3) 11160

DOI: 10.1021/acs.inorgchem.7b01477 Inorg. Chem. 2017, 56, 11160−11167

Article

Inorganic Chemistry

reaction produces ClO2• after an induction period (clock reaction). However, no experimental evidence is shown in this article for the formation of ClO2• using any experimental method. They indicated that the reaction was also followed by spectrophotometry at 280 nm, but they did not present these results. In addition, this is not the best wavelength to follow the formation of ClO2•, which has a band with a maximum at 358 nm (see the Experimental Section). In the present work, we report a kinetic study of the chlorate−nitrous acid reaction, in acid media (HClO4), followed at 358 nm, which is the wavelength where both nitrous acid and chlorine dioxide absorb. In this study, we employed a range of concentrations that was ∼100 times higher than the concentrations used by Emeish.3 Different from the other authors that studied this reaction, our results show the formation of chlorine dioxide, in addition to the formation of nitrate. A reaction mechanism is presented that explains all of the experimental observations, being a significant improvement in the understanding of the complex nitrogen and chlorine aqueous chemistry.

⎛ 1 ⎞ d[N(III)] d[Cl−] −⎜ ⎟ = = k[ClO3−][HNO2 ][H+] ⎝3⎠ dt dt (k = 0.773 ± 0.02 L2 mol−2 s−1, I = 0.033 mol L−1, 25 °C) (2) +

H + HNO2 +

ClO3−

⇌ H 2NClO5

(R6)

H 2NClO5 ⇌ H+ + HNClO5−

(R7)

H+ + HNO2 ⇌ H 2NO2+

(R8)

H 2NO2+ + ClO3− ⇌ H 2NClO5

(R9)

HNO2 + HClO3 ⇌ H 2NClO5 H 2NClO5 → NO3− + ClO2− + 2H+

(R10) (rate‐determining step) (R11)

ClO2− + HNO2 → NO3− + ClO− + H+

(R12)

ClO− + HNO2 → NO3− + Cl− + H+

(R13)

■

8

Emeish and Howlett studied the chlorite−nitrous acid reaction (reaction R14), in the presence of chloride, following the reaction by the same colorimetric method employed by Emeish,3 obtaining the rate law given by eq 3. The second term of the rate law is important only at high concentrations of chloride. They also did not observe chlorine dioxide formation. 2HNO2 + ClO2− → 2NO3− + 2H+ + Cl−

All reagents were used as received (sodium chlorate, from Fluka; sodium perchlorate, from Vetec; sodium nitrite, from Carlo Erba; perchloric acid, from Vetec). All solutions were made using conductivity water (18 MΩ) from a Milli-Q Plus system (Millipore, Bedford, MA). The concentration of perchloric acid was determined by titration with standard NaOH solutions. Considering HNO2 as a weak acid, the reported HNO2 concentration is equal to the sodium nitrite concentration employed. The reported HClO4 concentration (which is the actual [H+] for all reported reaction’s mixtures) is the added HClO4 concentration minus NaNO2 concentration, considering that each mole of nitrite consumes one mole of perchloric acid to produce one mole of HNO2. The reaction was followed using UV-vis spectroscopy at 358 nm, one of the strongest absorption wavelength of nitrous acid (ε = 51 L mol−1 cm−1)13 and also the maximum of the chlorine dioxide absorbance band (ε = 1250 L mol−1 cm−1).14 For the set of kinetics experiments using a low concentration of reagents (runs 15−29), the reactor was a 3 mL quartz cell with a path length of 1 cm, inserted in a diode array spectrophotometer (Hewlett−Packard, Model 8452A), which has a single deuterium lamp. To follow the reaction obtaining full spectra at sequential time, this same spectrophotometer (resolution of 2 nm) was used. For the set of kinetics experiments using a high concentration of reagents (runs 1−14), we employed the Hi-Tech SFA-20 rapid kinetics accessory (stopped-flow), which has a quartz cell with 0.2 cm of path length. The quartz cell was inserted inside the Agilent 8453 spectrophotometer with only the tungsten filament lamp turned on, keeping the deuterium lamp off to prevent the incidence of UV light on the sample, especially to avoid the decomposition of the ClO2• formed under these conditions. A data point was obtained every 0.6 s. For the experiments using the 1 cm path length quartz cell as a reactor, the order of addition of reagents was sodium chlorate, sodium nitrite, and perchloric acid. For the experiments that employed the stopped-flow setup, a 0.2 cm path length quartz cell was used as a reactor, and the reaction was performed using two solutions: A (sodium nitrite and sodium chlorate) and B (perchloric acid and sodium perchlorate). All experiments were done at 25 ± 0.1 °C, and the ionic strength was adjusted with sodium perchlorate. The kinetic order of each reagent was determined by the slope of the straight line obtained in a log−log plot of concentration versus initial rate. The initial rates were determined as v0 = −[d[HNO2]/ dt]t=0, and the reported values are an average of at least five experiments. Simulation of the proposed mechanism was done by the use of a Turbo Pascal code, which employs a fourth-order Runge−Kutta semi-

(R14)

⎛ 1 ⎞ d[N(III)] d[Cl ] −⎜ ⎟ = = k[NO2−]1.5 [ClO2−]0.5 [H+]1.5 ⎝2⎠ dt dt −

+ k′[NO2−]1.5 [ClO2−]0.5 [H+]1.5 [Cl−] (k = 0.39 × 106 dm 7.5 mol−2.5 s−1, k′ = 7.2 × 106 dm10.5 mol−3.5 s−1, 25 °C, I = 0.215 mol L−1)

(3)

Nagaishi et al.9 studied the chlorate−nitrite reaction (reaction R15) in the pH range of 3−4, and they found the rate law given by eq 4, but these authors did not observe the formation of chlorine dioxide: 3NO2− + ClO3− → 3NO3− + Cl− −d[NO2−] = k[NO2−][ClO3−][H+]2 dt

(R15)

(4)

10

Lahoutifard et al. studied the kinetics of nitrite oxidation by hypochlorous acid in aqueous phase in the pH range of 5−11 (reaction R16). These authors obtained the rate law given by eq 5, where kobs is a complex function of [H+] and [NO2−]. To explain their results, they proposed a mechanism that involved the intermediate NO2Cl suggested initially by Pendlebury and Smith.11 NO2− + HOCl → NO3− + Cl− + H+ −d[HOCl]total = kobs[HOCl]total dt

EXPERIMENTAL SECTION

(R16)

(5)

12

Lengyel, Gáspár, and Beck studied the reaction between chlorite and nitrous acid, in the pH range of 2.4−4.0, and observed oligo-oscillations in excess of chlorite. They followed the reaction by the potential of a platinum electrode. Different from the other authors indicated above, they report that this 11161


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Inorganic Chemistry implicit method.15 The steps of the proposed mechanism were converted to a system of differential equations, which was submitted to numerical integration. The [H+] was fixed during numerical integration calculations. The model results were compared to the absorbance versus time curves obtained experimentally using different concentration of the reactants. The entire procedure is analogous to that used in the similar kinetic study of chlorate−bromide reaction made recently by our group.16

■

RESULTS AND DISCUSSION Since it is known that nitrous acid decomposes in strongly acid solution,17 we decided, initially, to follow this process under low pH conditions ([HClO4] = 1.000 mol L−1). The experimental results (Figure 1) showed no significant disproportionation of nitrous acid at the maximum time employed in our kinetics experiments for the chlorate−nitrous acid reaction. Figure 2. Plot for Experiment 1. Concentrations employed: [HNO2] = 0.008 mol L−1, [NaClO3] = 0.200 mol L−1. Spectra were obtained every 10 s. Range of time: 0−1200 s.

Experiment 2 was made with addition of perchloric acid to produce a higher acidity than Experiment 1. The results are shown in Figure 3.

Figure 1. Nitrous acid stability in a strong acid medium. Concentrations employed: [HNO2] = 0.03 mol L−1, [HClO4] = 1.00 mol L−1.

With the objective of identifying the chlorate−nitrous acid reaction products, two experiments were performed to observe the UV-vis spectral changes during the reaction time, as well the influence of perchloric acid concentration, since nitrous acid is a weak acid (pKa = 3.35 at 18 °C).18 Experiment 1 shows the reaction between chlorate and nitrous acid, without the addition of perchloric acid (except for the amount necessary to produce HNO2 from sodium nitrite, as explained in the Experimental Section). As can be seen in Figure 2, decay of the nitrous acid concentration (bands at 346, 358, 370, and 386 nm) occurs and the formation of nitrate is observed (λmax = 302 nm). Moreover, an isosbestic point was observed at 312 nm. These results allowed us to conclude that the nitrous acid is being oxidized to nitrate by chlorate. The presence of an isosbestic point indicates that the stoichiometric HNO2:NO3− ratio is 1:1, which allows us to propose the sequence of reactions R17−R19 that give the net reaction that is described by reaction R5, proposed initially by Lowe and Brown.2 ClO3− + HNO2 → NO3− + HClO2

HClO2 + HNO2 →

NO3−

+ HOCl + H

HOCl + HNO2 → NO3− + Cl− + 2H+

Figure 3. Plot for Experiment 2. Concentrations employed: [NaClO3] = 0.150 mol L−1, [HNO2] = 1.50 × 10−2 mol L−1, [HClO4] = 0.300 mol L−1. Spectra were obtained every 10 s. The acquisition of spectra started only 30 s after the mixture of reagents (range of time: 30−300 s).

Figure 3 shows clearly that, under acidic conditions, the formation of chlorine dioxide occurs (λmax = 358 nm, ε = 1250 L mol−1 cm−1).14 The chlorine dioxide band encompasses the band of nitrate (λmax = 302 nm, ε = 7.24 L mol−1 cm−1),19 which apparently increases, because the chlorine dioxide band extends below the nitrate band. Experiment 2 can also be seen in another range of time, from 0 to 50 s, in a three-dimensional composition (Figure 4). In this figure, it is possible to observe that the formation of chlorine dioxide (which has only one broad band centered at 358 nm) starts only after the nitrous acid (which has four thin bands, one of them centered at 358 nm; see Figure 2) has been completely consumed. Despite of the complexity of this reaction, we tried to obtain a simple rate law for the chlorate−nitrous acid−perchloric acid reaction, in acid media and using a range of concentrations

(R17) +

(R18) (R19) 11162


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Table 2. Orders Obtained for H+, Chlorate, and Nitrous Acid (See Table 1 for Concentrations) species +

H ClO3− HNO2

order

correlation coefficient, R2

1.06 ± 0.03 0.79 ± 0.05 0.97 ± 0.04

0.998 0.989 0.995

trations in Table 1. To check this behavior, we reinvestigate this reaction using the low concentration values indicated in Table 3. The initial rates values for runs 15−19, runs 25−29, and runs Table 3. Concentrations and Initial Rates Used to Determine the Reagent’s Orders and Rate Law of the Chlorate−Nitrous Acid Reaction, under Acidic Conditions, at a Low Concentration of Reagentsa

Figure 4. Spectra evolution in time for Experiment 2. Concentrations employed: [NaClO3] = 0.150 mol L−1, [HNO2] = 1.50 × 10−2 mol L−1, [HClO4] = 0.300 mol L−1. Spectra were obtained every 1 s. Time = 0 s shows the spectra of HNO2 (347, 358, 372, and 386 nm) in the back; final time = 50 s shows the spectra of ClO2• (λmax = 358 nm) in the front.

run

[NaClO3] (mol L−1)

[HNO2] (mol L−1)

[HClO4] (mol L−1)

v0b(× 104 mol L−1 s−1)

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

0.010 0.010 0.010 0.010 0.010 0.025 0.020 0.015 0.010 0.0050 0.010 0.010 0.010 0.010 0.010

0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.025 0.020 0.015 0.010 0.0050

0.510 0.410 0.310 0.210 0.110 0.510 0.510 0.510 0.510 0.510 0.510 0.510 0.510 0.510 0.510

1.47 ± 0.02 1.15 ± 0.04 0.912 ± 0.11 0.603 ± 0.19 0.332 ± 0.08 2.83 ± 0.02 2.45 ± 0.03 1.98 ± 0.02 1.47 ± 0.02 0.792 ± 0.08 3.20 ± 0.05 2.75 ± 0.03 2.05 ± 0.02 1.47 ± 0.02 0.752 ± 0.02

higher than that used by Emeish3 (necessary to observe the ClO2• formation). With this intention, we made several experiments using stopped-flow apparatus and the initial concentrations indicated in Table 1. The measured initial rate values for these experiments are also shown in Table 1. Table 1. Concentrations and Initial Rates Used to Determine the Reagent’s Orders for the Chlorate−Nitrous Acid Reaction under Acidic Conditions, Using a Stopped-Flow Apparatusa run

[NaClO3] (mol L−1)

[HNO2] (mol L−1)

[HClO4] (mol L−1)

v0b (× 10−2 mol L−1 s−1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.025 0.050 0.075 0.100 0.125 0.050 0.050 0.050 0.050 0.050 0.025 0.025 0.025 0.025

0.050 0.050 0.050 0.050 0.050 0.025 0.050 0.075 0.100 0.125 0.025 0.025 0.025 0.025

1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.900 0.800 0.700

3.32 ± 0.002 6.09 ± 0.003 8.77 ± 0.003 10.4 ± 0.003 11.5 ± 0.005 3.12 ± 0.0008 5.78 ± 0.002 8.43 ± 0.004 11.3 ± 0.005 15.3 ± 0.0002 1.93 ± 0.0002 1.74 ± 0.0002 1.51 ± 0.002 1.33 ± 0.0002

a

All experiments were conducted at an ionic strength (I) equal to 1.18 mol L−1, adjusted with sodium perchlorate. bv0 = −[d[HNO2]/dt]t=0.

20−24 indicate a first-order for H+ and orders slightly lower than one are observed for HNO2 and chlorate, respectively, as shown in Table 4. Table 4. Orders Obtained for H+, Chlorate, and Nitrous Acid under Low Concentration Conditions (See Table 3) species +

H ClO3− HNO2

a

All experiments were done at an ionic strength (I) equal to 1.18 mol L−1, adjusted with sodium perchlorate. bv0 = −[d[HNO2]/dt]t=0.

Using the initial rates values for runs 1−5, we obtained (from a plot of log [NaClO3] vs log v0) an order equal to 0.79 ± 0.05 for chlorate; from runs 6−10, we obtained (from a plot of log [HNO2] vs log v0) an order equal to 0.97 ± 0.04 for HNO2; and using the initial rate values from runs 11−14, we obtained (from a plot of log [HClO4] vs log v0) an order equal to 1.06 ± 0.03 for H+. All these order values are shown in Table 2, and they are valid for the range of initial concentrations shown in Table 1, which are much higher than the concentrations used by Emeish.3 As indicated previously, Emeish3 observed a first-order behavior for ClO3−, HNO2, and H+, using concentrations equal to 6.587 × 10−3, 3.646 × 10−4, and 1.782 × 10−2 mol L−1, respectively, which are significantly lower than the concen-

order

correlation coefficient, R2

0.97 ± 0.02 0.79 ± 0.03 0.91 ± 0.02

0.999 0.996 0.998

If we consider first-order for all reagents, the data on Table 3 allow one to calculate a rate constant equal to 0.92 ± 0.08 L2 mol−2 s−1, which is very close to the values obtained by Lowe and Brown2 and Emeish,3 which are equal to 0.7 and 0.773 L2 mol−2 s−1, respectively, despite the fact that we used a much higher ionic strength (I = 1.18 mol L−1) than Emeish3 (I = 0.033 mol L−1). However, considering the orders on Table 4 the rate law can be given by eq 6, which indicates that the reaction has a complex mechanism. ⎛ 1 ⎞ d[HNO2 ] −⎜ ⎟ = k[ClO3−]0.8 [HNO2 ]0.9 [H+] ⎝3⎠ dt (k = 0.237 ± 0.008 L2 mol−2 s−1) 11163

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Inorganic Chemistry Table 5. Mechanism of Chlorate−Nitrous Acid Reaction in Acid Media rate lawa

reaction R20 R21 R22 R23 R24 R25 R26 R27 R28 R29 R30 R31 a

v v v v v v v v v v v v

= = = = = = = = = = = =

ref

1.50[HNO2][ClO3−][H+] 0.60[O2NOClO] 30[HClO2][HNO2] 7.40 × 103[HOCl][ HNO2] 80.0[NO2Cl] 2.20 × 104[HOCl][Cl−][H+] − 22.0[Cl2] 1.90 × 104[HOCl][HClO2] 1.50 × 109[ClOClO][HClO2] 1.70 × 107[ClOClO] 900[ClO2•][HNO2] − 9 × 103[HClO2][NO2•] 5.0 × 107[NO2•]2 1.8 × 109[Cl2][ Cl−] − 1.0 × 1010[Cl3−]

this work this work this work 25 10 26 27 27 28 this work 29 30

The units of the rate coefficients are s−1, L mol−1 s−1, and L2 mol−2 s−1 for first-, second-, and third-order reactions, respectively.

Considering, as a starting point, first-order for all reagents, the results of Experiments 1 and 2 (Figures 2 and 3), and the fact that chlorine dioxide starts to form only after nitrous acid has been consumed (Figure 4), a mechanism for the chlorate− nitrous acid reaction in an acid medium was developed. The two first two steps consider the formation of the intermediate O2NOClO (reactions R20 and R21). HNO2 + ClO3− + H+ → O2 NOClO + H 2O

(R20)

H 2O + O2 NOClO → NO3− + HClO2 + H+

(R21)

conditions than the rate law obtained by Emeish and Howlett.8 Since pH of the medium is below the pKa of nitrous acid (3.35 at 18 °C)18 and chlorous acid (1.72),24 we rewrote the rate law as v = k′[HNO2][HClO2] and we calculated the rate constant as k′ = 9.13 × 103 L mol−1 s−1. To obtain the best fit between the model results and experimental data, it was necessary decrease this rate constant. The reduction of this rate constant can be justified by the absence of any buffer in our experiments, which may have accelerate the reaction in the experiments by Nagaishi et al.23 A much higher value for reaction R22 rate constant can be found in the work by Lengyel et al.12 These authors considered the rate law v = k [ClO2−][HNO2][H+] (k = 5 × 109 L mol−1 s−1), which, when converted to v = k[HClO2−][HNO2], must have the rate constant k = 9.5 × 107 L mol−1 s−1, based on the pKa = 1.72 for HClO2. This rate constant value is much higher than k′ indicated above and produce a strong deviation for the calculated results, when compared with our experimental results. The rate coefficients for reactions R23 and R24 have been reported by Whiteman et al.25 and Lahoutifard et al.,10 respectively. The insertion of the NO2Cl hydrolysis in the mechanism is justified by the fact that this species is very reactive and was not observed as a product of the chlorate− nitrous acid reaction. The rate coefficients for the chlorine hydrolysis (reaction R25) were taken from Lengyel et al.26 Experiment 2 (see Figures 3 and 4) clearly shows that chlorine dioxide radical is formed in this reaction when the acid concentration is high. Therefore, we added reactions involved in the production and also consumption of ClO2•.

This intermediate is similar to the intermediate proposed by Emeish (H2ClNO5)3 but with one water molecule less, and it is analogous to other asymmetric intermediates recently proposed to explain reactions involving different halogen species, such as OClOIO3 (proposed in the mechanism of the chlorite− periodate reaction),20 BrIO3 or BrOIO2 (proposed in the mechanism of the bromide−periodate reaction),21 and also with one of the first asymmetric intermediates, ClOClO, proposed by Taube and Dodgen.22 Including reactions R22−R25, this mechanism was able to model the first part of absorbance versus time experimental curves, corresponding to the decay of the nitrous acid concentration. The sum of reactions R20−R24 gives reaction R5. HClO2 + HNO2 → HOCl + NO3− + H+

(R22)

HOCl + HNO2 → NO2 Cl + H 2O

(R23)

NO2 Cl + H 2O → NO3− + Cl− + 2H+

(R24)

HOCl + Cl− + H+ ⇌ Cl 2 + H 2O

(R25)

Reactions R20 and R21 do not have rate coefficients established in the literature, and the values were adjusted to allow the mechanism to simulate the absorbance versus time curves for several different initial concentrations of reagents. Reaction R22 was studied by Emeish and Howlett,8 who obtained a complex rate law for the reaction between chlorite and nitrite, in an acid medium, in the presence of chloride, as cited in the Introduction. Another study on this reaction was conducted by Nagaishi et al.,23 from which the following rate law was obtained: v = k[NO2−][ClO2−][H+]2 (k = 1.08 × 109 L3 mol−3 s−1). Since our experiments do not have significant chloride concentrations, at initial times, we considered the rate law by Nagaishi et al.23 to be more appropriate to our

HClO2 + HOCl → ClOClO + H 2O

(R26)

ClOClO + HClO2 → 2ClO2• + Cl− + H+

(R27)

ClOClO + H 2O → Cl− + ClO3− + 2H+

(R28)

Reaction R26 was studied by Kormányos et al. and provided an additional route for ClO2• formation, followed by reaction R27.27 Reaction R28 avoids excessive production of ClO2•.28 The reactions proposed until now were not able to reproduce the fact that chlorine dioxide is formed only after nitrous acid is consumed (see Figure 4). To account for this behavior, we added two reactions. The first (reaction R29) avoids that the ClO2• concentration builds up before complete consumption of HNO2. There are rate constant values for this equilibrium, obtained in a pH range higher than we used in our 11164


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Inorganic Chemistry experiments.29 Then, for the adjustment of the model, it was necessary to increase the previously established value for the forward reaction. The second reaction, reaction R30, was required since the spontaneous hydrolysis of the NO2• is wellestablished.29 If this last reaction was not included, the mechanism will forecast a high concentration of nitrogen dioxide, which was not observed, since the rate coefficient for reaction R30 is very high. ClO2• + HNO2 ⇌ HClO2 + NO2•

(R29)

2NO2• + H 2O → HNO2 + NO3− + H+

(R30)

Reaction R31 was also included to obtain a good fit between the simulated and experimental results. Cl− + Cl 2 ⇌ Cl3−

(R31)

The rate constants for reaction R31 were adjusted to produce the average experimental equilibrium constant given by Wang et al.30 The rate laws and rate coefficients used to simulate the chlorate−nitrous acid reaction are presented in Table 5. Despite the fact that reaction R5 shows the formation of chloride as a product, the production of ClO2• is not a consequence of the very well-known chlorate−chloride reaction (2ClO3− + 2Cl− + 4H+ → Cl2 + 2ClO2• + 2H2O),5 which needs an H+ concentration equal to 2 mol L−1 or higher, to occur with significant speed, which is not the case of the concentrations indicated in Table 1. The inclusion of chlorate− chloride reactions in the model does not change the results, supporting this interpretation. The chlorine dioxide is formed indeed by the reaction between the intermediates ClOClO and HClO2 (reaction R27), and the intermediate ClOClO is formed by the reaction between HOCl and HClO2 (reaction R26). The isosbestic point observed at 312 nm in Figure 2 is related to the reaction of nitrous acid and formation of nitrate in a ratio of 1:1, before chlorine dioxide radical formation occurs. The proposed mechanism (Table 5) obeys these conditions, since HNO2 is consumed by three different reactions (reactions R20, R22, and R23) and NO3− is produced by three different reactions (reactions R21, R22, and R24). Figures 5−7 and Figures S1−S3 in the Supporting Information show that the mechanism described by reactions R20−R31 correctly simulates the experimental results of the effect of chlorate, nitrous acid, and H+ concentrations, for the concentrations indicated in Table 1 (high concentration set), where the formation of the chlorine dioxide radical occurs, and for the low concentrations indicated in Table 3 (low concentration set). As described in the Experimental Section, experiments of Table 1 were performed in a quartz cell with 0.2 cm of path length. The absorbance readings for runs 1−14 were multiplied by a factor of 5 to generate Figures 5−7.

Figure 5. Experimental results and simulation (see Table 5) of acid concentration effect (see Table 1, runs 11−14). Perchloric acid concentrations (mol L−1) are indicated in the figure. Other constraints: [NaClO3] = 0.025 mol L−1, [HNO2] = 0.025 mol L−1, I = 1.18 mol L−1. Dotted lines represent experimental data; continuous lines represent simulations. Experimental data were measured using a quartz cell with a 2 mm path length.

Figure 6. Experimental results and simulation (see Table 5) of chlorate concentration effect (see Table 1, runs 1−5). Sodium chlorate concentrations (mol L−1) are indicated in the figure. Other constraints: [HClO4] = 1.000 mol L−1, [HNO2] = 0.050 mol L−1, I = 1.18 mol L−1. Dotted lines represent experimental data; continuous lines represent simulations. Experimental data were measured using a quartz cell with a 2 mm path length.

The formation of ClO2• is not a consequence of the very well-known chlorate−chloride reaction:5

■

2ClO3− + 2Cl− + 4H+ → Cl 2 + 2ClO2• + 2H 2O

CONCLUSIONS The chlorate−nitrous acid reaction is a complex reaction. The order of reagents and the products formed is dependent on the concentration of reagents. Using the reagent concentrations shown in Table 1 (the high concentration set), the chlorate−nitrous acid reaction forms ClO2•. For the low reagent concentrations shown in Table 3 (the low concentration set), it presents first-order for H+ and fractional orders for chlorate and also HNO2, as shown by the rate law given by eq 6.

The chlorine dioxide is formed indeed by a sequence of reactions, which forms the intermediate ClOClO, followed by the reaction between ClOClO and HClO2. As shown in Figure 4, the formation of chlorine dioxide starts only after HNO2 has been consumed. This can be explained by the reaction of HClO2 and HOCl with HNO2 (reactions R22 and R23, respectively), preventing reactions R26 and R27 to occur at significant speed. In addition, any ClO2• formed is consumed by reaction with HNO2 (reaction R29). In other words, there is an induction period before ClO2• starts to form. 11165


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ACKNOWLEDGMENTS

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REFERENCES

We thank Dr. Istvan Lengyel for the use of his Turbo Pascal code to make the simulations by numerical integration. We also thank three anonymous reviewers, who made several suggestions and comments that significantly improved the final version of this article.

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Figure 7. Experimental results and simulation (see Table 5) of nitrous acid concentration effect (see Table 1, runs 6−10). Nitrous acid concentrations (mol L−1) are indicated in the figure. Other constraints: [NaClO3] = 0.050 mol L−1, [HClO4] = 1.000 mol L−1, I = 1.18 mol L−1. Dotted lines represent experimental data; continuous lines represent simulations. Experimental data were measured using a quartz cell with a 2 mm path length.

Nitrate is formed in the same amount as HNO2 is consumed, evidenced by the presence of an isosbestic point at 312 nm. A mechanism containing 12 reactions and 14 independent species simulates several different experimental sets of initial concentrations of reagents, allowing explain the complexity of this reaction.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01477. Experimental kinetic curves for the experiments in Table 3 and calculated kinetic curves based on the mechanism in Table 5 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Fax: +55 21 3938 7559. E-mail: [email protected]. ORCID

Roberto B. Faria: 0000-0001-9337-4324 Author Contributions

The manuscript was written through contributions of both authors. Both authors contributed equally and have given approval to the final version of the manuscript. Funding

We thank the Conselho Nacional de Desenvolvimento ́ e Tecnológiico-CNPq (Grant Nos. 306.050/2016-1 Cientifico and 141.341/2014-9) and Fundaçaõ Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro-FAPERJ (Grant No. E-26/111.749/2011) for funding this research. Notes

The authors declare no competing financial interest. 11166


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Kinetics and Mechanism of the ChlorateâNitrous Acid Reaction

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