Yuri Bedjanian
email: yuri.bedjanian@cnrs-orleans.fr

Temperature Dependent Rate Constant for the Reaction of Hydroxyl Radical with 3-Hydroxy-3-Methyl-2-Butanone

Temperature-Dependent Rate Constant for the Reaction of Hydroxyl Radical with 3-Hydroxy-3-methyl-2-butanone

Yuri Bedjanian

INTRODUCTION

3-Hydroxy-3-methyl-2-butanone ((CH 3 ) 2 C(OH)C(O)CH 3 ) is a representative of hydroxyketones, chemical species belonging to a large family of Oxygenated Volatile Organic Compounds (OVOC) playing an important role in the tropospheric chemistry. [START_REF] Calvert | Mechanisms of Atmospheric Oxidation of the Oxygenates[END_REF] OVOCs are directly injected into the atmosphere as a result of anthropogenic and natural emissions, and can also be formed in the atmosphere upon degradation of primary emitted organic compounds. For example, hydroxyketones can be formed in the OH-initiated oxidation of alkanes, 2 alkane diols, [START_REF] Baker | Rate Constants for the Gas-Phase Reactions of OH Radicals with a Series of Hydroxyaldehydes at 296 ± 2 K[END_REF] alkenes 4 and alcohols. [START_REF] Reisen | Hydroxyaldehyde Products from Hydroxyl Radical Reactions of Z-3-Hexen-1-ol and 2-Methyl-3-Buten-2-ol Quantified by SPME and API-MS[END_REF] In particular, 3-Hydroxy-3-methyl-2-butanone was shown to be a product of OH-initiated oxidation of 2-methyl-2-butene in the presence of NO. [START_REF] Tuazon | Products of the Gas-Phase Reactions of a Series of Methyl-Substituted Ethenes with the OH Radical[END_REF] The atmospheric degradation of hydroxyketones is initiated by their reactions with atmospheric oxidants (OH, NO 3 ,O 3 , Cl), mainly with OH radical, and their photolysis. [START_REF] Calvert | Mechanisms of Atmospheric Oxidation of the Oxygenates[END_REF] The understanding of the degradation mechanism of hydroxyketones in the atmosphere requires information on their major photo-oxidation pathways, including kinetics and primary products of their reactions with the atmospheric oxidants. Reactions of OH radicals with hydroxyketones are also of great theoretical interest as proceeding through a complex kinetic mechanism leading to a non-Arrhenius temperature dependence of the reaction rate constant. The existing data base on the reactions of hydroxyketones with OH is limited to a number of relative rate measurements at room temperature. [START_REF] Calvert | Mechanisms of Atmospheric Oxidation of the Oxygenates[END_REF] Even for the reaction of OH with the smallest hydroxyketone, hydroxyacetone, the dependence of the rate constant on temperature and its potential pressure dependence is a matter of discussion. [START_REF] Vu | Absolute Rate Coefficient of the Gas-Phase Reaction between Hydroxyl Radical (OH) and Hydroxyacetone: Investigating the Effects of Temperature and Pressure[END_REF] For the title reaction three experimental studies are available. [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF][START_REF] Bouzidi | Reactivity of 3-Hydroxy-3-Methyl-2-Butanone: Photolysis and OH Reaction Kinetics[END_REF][START_REF] Aschmann | Atmospheric Chemistry of Selected Hydroxycarbonyls[END_REF] In two previous temperature-dependent studies of the reaction, realized in a rather narrow temperature range (277-356K), a slight positive [START_REF] Bouzidi | Reactivity of 3-Hydroxy-3-Methyl-2-Butanone: Photolysis and OH Reaction Kinetics[END_REF] and slight negative [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF] dependence of the reaction rate constant on temperature (with absolute values differing by up to a factor of 2) were reported. In addition, the reaction rate constant was theoretically calculated over the temperature range from 278 to 1000 K, showing slow decrease with temperature. [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF] In this regard, the objective of the present work was to measure the rate constant of the reaction

OH + CH 3 C(O)C(CH 3 ) 2 OH  products (1)
in a wide temperature range and to compare it with previous experimental data and theoretical predictions.

In addition, the reaction of OH radicals with Br 2 was studied as a part of this study. This reaction is very often used in our laboratory for indirect detection of OH by mass spectrometry via conversion of the radicals to HOBr [START_REF] Bedjanian | Reactions of OH Radicals with 2-Methyl-1-Butyl, Neopentyl and 1-Hexyl Nitrates. Structure-Activity Relationship for Gas-Phase Reactions of OH with Alkyl Nitrates: An Update[END_REF][START_REF] Bedjanian | Kinetics and Mechanism of the Reaction of OH with ClO[END_REF][START_REF] Bedjanian | Kinetic Study of OH + OH and OD + OD Reactions[END_REF] and as a reference reaction in the relative measurements of OH reactivity: [START_REF] Bedjanian | Gas-Phase Reaction of Hydroxyl Radical with p-Cymene over an Extended Temperature Range[END_REF][START_REF] Braure | Experimental Study of the Reactions of Limonene with OH and OD Radicals: Kinetics and Products[END_REF] OH + Br 2  HOBr + Br (2)

The rate constant of the reaction seems to be well established at low temperatures (T = 230-360K), [START_REF] Bedjanian | Kinetic Study of the Reactions of Br 2 with OH and OD[END_REF][START_REF] Gilles | Rate Coefficients for the Reaction of OH with Cl 2 , Br 2 , and I 2 from[END_REF] however, only one temperature dependence study is available at higher temperatures. [START_REF] Bryukov | Kinetic Study of the Gas-Phase Reaction of OH with Br 2[END_REF] In the present work, we report the measurements of the rate constant in an extended temperature range, T = 220 -950K.

EXPERIMENTAL

Experiments were carried out in a discharge flow reactor at total pressure of Helium of 2

Torr using a modulated molecular beam electron impact ionization quadrupole mass spectrometer (operated at 30 eV energy) as the detection method. [START_REF] Bedjanian | Reactions of OH Radicals with 2-Methyl-1-Butyl, Neopentyl and 1-Hexyl Nitrates. Structure-Activity Relationship for Gas-Phase Reactions of OH with Alkyl Nitrates: An Update[END_REF][START_REF] Bedjanian | Kinetics and Mechanism of the Reaction of OH with ClO[END_REF][START_REF] Bedjanian | Kinetic Study of OH + OH and OD + OD Reactions[END_REF][START_REF] Bedjanian | Gas-Phase Reaction of Hydroxyl Radical with p-Cymene over an Extended Temperature Range[END_REF][START_REF] Braure | Experimental Study of the Reactions of Limonene with OH and OD Radicals: Kinetics and Products[END_REF] Two flow reactors were used. The first one, used at low temperatures (220 -323 K), consisted of a Pyrex tube (45 cm length and 2.4 cm i.d.) with a jacket for the thermostated liquid circulation (ethanol) (Figure S1, Supporting Information (SI)).The walls of the reactor as well as of the movable injector of OH radicals were coated with halocarbon wax in order to minimize the heterogeneous loss of OH. The second flow reactor used at high temperatures (T = 299 -950 K), consisted of an electrically heated uncoated Quartz tube (45 cm length and 2.5 cm i.d.)

with water-cooled attachments (Figure S2, SI). [START_REF] Morin | Experimental Study of the Reactions of OH Radicals with Propane, n-Pentane, and n-Heptane over a Wide Temperature Range[END_REF] Temperature in the reactor was measured with a K-type thermocouple positioned in the middle of the reactor in contact with its outer surface. Temperature variation along the flow tube (Figure S1, SI) measured with a thermocouple inserted in the reactor through the movable injector was found to be less than 1%. [START_REF] Morin | Experimental Study of the Reactions of OH Radicals with Propane, n-Pentane, and n-Heptane over a Wide Temperature Range[END_REF] Hydroxyl radicals were produced in the movable injector through a rapid reaction of H 195 -2000). [START_REF] Su | Rate Constants, 1100 ≤ T ≤ 2000 K, for H + NO 2 → OH + No Using Two Shock Tube Techniques: Comparison of Theory to Experiment †[END_REF] OH radicals were detected at m/z = 96/98 (HOBr + ) after being scavenged with an excess of Br 2 (added in the end of the reactor 5 cm upstream of the sampling cone, as shown in Figure S2, SI) through reaction 2:

k 3 = (1.47 ± 0.26)  10 -10 cm 3 molecule -1 s -1 (T =
OH + Br 2  HOBr + Br (2) and their absolute calibration procedure was discussed in details in previous papers from this group. [START_REF] Bedjanian | Kinetic Study of OH + OH and OD + OD Reactions[END_REF][START_REF] Bedjanian | Kinetic Study of the Reactions of Br 2 with OH and OD[END_REF] In experiments on absolute measurements of the rate constant of reaction The purities of the gases used were as follows: He (>99.9995%, Alphagaz), passed through liquid nitrogen trap; H 2 (> 99.998%, Alphagaz); Br 2 (>99.99%, Aldrich); NO 2 (> 99%, Alphagaz); 3-hydroxy-3-methyl-2-butanone (> 95%, TCI Europe); Propane (>99.95%, Alphagaz). butanone are shown in Table 1. The flow velocity in the reactor was in the range (856-1695) cm s -1 . The pseudo-first-order rate constants were determined from the exponential fit to OH consumption kinetics: an example is shown in Figure 1. The consumption of the excess reactant, 3H3M2B, in reaction s -1 . [START_REF] Ivanov | HO 2 , and Ozone Gaseous Diffusion Coefficients[END_REF] The applied corrections were generally within a few percent, although reaching up to 17% in a few kinetic runs. were, as a rule, less than 10%. shown in Table 3. The combined uncertainty on k 2 was estimated to be ≈12% by adding in quadrature statistical error (≤ 5%) and those on the measurements of the flows (3%), pressure (2%), temperature (1%) and absolute concentration of Br 2 (≤ 10%). Gilles et al. [START_REF] Gilles | Rate Coefficients for the Reaction of OH with Cl 2 , Br 2 , and I 2 from[END_REF] have measured the reaction rate constant, k 2 = (1.98±0.51)10 -11 exp((238±70)/T) cm 3 molecule -1 s -1 at T = 235-357K, under pseudo-first-order conditions in OH by using a pulsed laser photolysis/laser-induced fluorescence (PLP/LIF) technique. In the earlier study from our group, [START_REF] Bedjanian | Kinetic Study of the Reactions of Br 2 with OH and OD[END_REF] the reaction rate constant, k 2 = (1.8±0.3)10 -11 exp((235±50)/T)cm 3 molecule -1 s -1 at T = 230 -360K, was derived both from the kinetics of Br 2 consumption in excess of OH radicals and HOBr formation kinetics in excess of Br 2 . The results from two studies are in excellent agreement and show a slight negative temperature dependence of k 2 . In the only high temperature study of reaction (2), Bryukov et al. [START_REF] Bryukov | Kinetic Study of the Gas-Phase Reaction of OH with Br 2[END_REF] using PLP/LIF method extended the measurements of k 2 to 766K and recommended k 2 =

k 2 =

RESULTS AND DISCUSSION

(1.85±0.32)10 -9 ×T -0.67±0.03 cm 3 molecule -1 s -1 at T = 230 -766K. As one can see in Figure 6, the experimental data from the present work are in excellent agreement with previous measurements of k 2 , except those of Bryukov et al. [START_REF] Bryukov | Kinetic Study of the Gas-Phase Reaction of OH with Br 2[END_REF] from the present work (solid line in Figure 6) provides the following Arrhenius expression:

k 2 = 2.1610 -11 exp(207/T) cm 3 molecule -1 s -1 at T = 220 -950K.
Fit of the data from the present work combined with the two previous low temperature measurements [START_REF] Bedjanian | Kinetic Study of the Reactions of Br 2 with OH and OD[END_REF][START_REF] Gilles | Rate Coefficients for the Reaction of OH with Cl 2 , Br 2 , and I 2 from[END_REF] results in an identical Arrhenius expression. The dotted lines in Figure 6 correspond to ± 10% deviation from this expression, showing that practically all temperature dependent data for k 2 fall into this range. Based on this, we would recommend the above expression for k 2 for use in the temperature range 220-950 K with conservative 10%

uncertainty.

The temperature dependence of k 1 observed in the present work is shown in Figure 7 along with previous measurements. [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF][START_REF] Bouzidi | Reactivity of 3-Hydroxy-3-Methyl-2-Butanone: Photolysis and OH Reaction Kinetics[END_REF][START_REF] Aschmann | Atmospheric Chemistry of Selected Hydroxycarbonyls[END_REF] Aschmann et al. [START_REF] Aschmann | Atmospheric Chemistry of Selected Hydroxycarbonyls[END_REF] and Bouzidi et al. [START_REF] Bouzidi | Reactivity of 3-Hydroxy-3-Methyl-2-Butanone: Photolysis and OH Reaction Kinetics[END_REF] have carried out relative rate measurements of the rate constant of reaction (1). The rate constant, k 1 = (0.94±0.37)10 -12 cm 3 molecule -1 s -1 at 296 K, originally reported by Aschmann et al., [START_REF] Aschmann | Atmospheric Chemistry of Selected Hydroxycarbonyls[END_REF] when placed on an absolute basis by use of a new recommendation for the reference reaction OH + n-octane, results in k 1 = (0.85±0.33)10 -12 cm 3 molecule -1 s -1 . [START_REF] Calvert | Mechanisms of Atmospheric Oxidation of the Oxygenates[END_REF] Priya et al. [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF] have carried out absolute measurements of the rate constant of reaction (1) over the temperature range 277

-353 K and total pressure between 5 and 80Torr, by using PLP/LIF technique. One can see in Figure 7 that the present data obtained at 2 Torr total pressure are in good agreement with previous relative measurements of Aschmann et al. [START_REF] Aschmann | Atmospheric Chemistry of Selected Hydroxycarbonyls[END_REF] and Bouzidi et al. [START_REF] Bouzidi | Reactivity of 3-Hydroxy-3-Methyl-2-Butanone: Photolysis and OH Reaction Kinetics[END_REF] realized at 740 and 500-600 Torr total pressure, respectively. This can be considered as an indication that the rate constant of reaction (1) does not depend (at least substantially) on pressure. The present data for k 1 are by a factor of 1.3-1.9 higher than the absolute measurements of Priya et al. [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF] It is difficult to establish the exact cause of this discrepancy. One of the possible options is the measurements of the absolute concentrations of 3H3M2B. In the present work, 3H3M2B was directly monitored with mass spectrometer and absolute calibration of the 3H3M2B signals was realized by injecting known amounts of liquid 3H3M2B inside the flow tube as described in Experimental section. In the study of Priya et al. [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF] the concentrations of 3H3M2B in the reaction zone were calculated from mass flow rates of 3H3M2B/He mixtures stored in a 20 L bulb. This method could potentially lead to overestimation of the 3H3M2B concentrations. Indeed, we have observed a decrease in gaseous concentration of 3H3M2B over time (from day to day) during the storage of 3H3M2B/He mixtures in 10L Pyrex flask. This may be due to the adsorption of 3H3M2B on the surface of the flask, its decomposition, or other reasons; we did not attempt to carry out specific experimental work to clarify this issue. The present data are in contradiction with theoretical calculations of Priya et al. [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF] (black solid line in Figure 7), in particular, with the statement of the authors that "the calculated theoretical rate constants are in good agreement with the experimental data over the ) temperature range of 278 to 1000 K". [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF] Our experimental data exhibit positive temperature dependence, while computed k 1 decreases with temperature. The computed and experimental values of k 1 at T  800 K, highest temperature of this study, differ by an order of magnitude.

As one can see in Figure 7, in the present work, the rate constant of reaction (1) was observed to be temperature independent at T = 278-323K and increasing at higher temperatures. This non-Arrhenius behavior could be expected. Similarly to reaction of OH with hydroxyacetone (smallest hyrdoxyketone) [START_REF] Vu | Absolute Rate Coefficient of the Gas-Phase Reaction between Hydroxyl Radical (OH) and Hydroxyacetone: Investigating the Effects of Temperature and Pressure[END_REF][START_REF] Dillon | Reaction of HO with Hydroxyacetone (HOCH 2 C(O)CH 3 ): Rate Coefficients (233-363 K) and Mechanism[END_REF] and also with aldehydes and ketones, 1 reaction (1) can proceed via two mechanisms, through formation of hydrogen-bonded prereactive complex and direct H-atom abstraction with major contributions of these pathways at lower and higher temperatures, respectively. This mechanism, in combination with tunneling effect at low temperatures, results in non-Arrhenius, often U-shaped, behavior of the reaction rate constant observable experimentally if a sufficiently wide temperature range is considered. [START_REF] Calvert | Mechanisms of Atmospheric Oxidation of the Oxygenates[END_REF] In this regard, even upward curvature in the temperature dependence of k 1 can be expected at lower temperatures. Unfortunately, our measurements were limited to T = 278K because of the heterogeneous complications at lower temperatures, which were manifested in an anomalous increase of the OH consumption rate in the presence of even very low concentrations of 3H3M2B, probably due to reaction of OH with 3H3M2B on the surface of the flow reactor. At higher temperatures we have not observed any evidence of the heterogeneous reaction. In this regard, it can be noted that compatible values of k 1 were measured in different reactors at close temperatures (at T = 350 and 365K in halocarbon wax coated and uncoated quartz reactors, respectively). Finally, the present experimental data were fitted with Arrhenius expression at T = 400 -830K and modified Arrhenius expression at T = 278 -400K (blue solid lines in Figure 7), leading to: k 1 = 5.4410 -41 T 9.7 exp(2820/T) cm 3 molecule -1 s -1 (T = 278-400K), k 1 = 1.2310 -11 exp(-970/T) cm 3 molecule -1 s -1 (T = 400-830K) with conservative temperature independent 20% uncertainty (dashed lines in Figure 7). It is clear that the expression for k 1 at T = 278-400K has no physical meaning and should be considered only as a representation of the rate coefficients in this temperature range.

The tropospheric lifetime of 3-Hydroxy-3-Methyl-2-Butanone with respect to its gas phase reaction with OH, 16 days (calculated using the measured rate constants of 7.2510 -13 cm 3 molecule -1 s -1 at T=298 K and a 24 h average concentration of OH radical of 10 6 molecules cm -3 ), is comparable with atmospheric lifetime of 3H3M2B of 4-5 days with respect to its photolysis [START_REF] Bouzidi | Reactivity of 3-Hydroxy-3-Methyl-2-Butanone: Photolysis and OH Reaction Kinetics[END_REF] and supports the conclusions of the previous studies [START_REF] Priya | An Experimental and Theoretical Study of the Kinetics of the Reaction between 3-Hydroxy-3-Methyl-2-Butanone and OH Radicals[END_REF][START_REF] Bouzidi | Reactivity of 3-Hydroxy-3-Methyl-2-Butanone: Photolysis and OH Reaction Kinetics[END_REF][START_REF] Aschmann | Atmospheric Chemistry of Selected Hydroxycarbonyls[END_REF] on importance of the reaction (1) as a tropospheric loss process of 3H3M2B.

CONCLUSIONS

In this work, we investigated the kinetics of the reaction of OH radicals with 3-Hydroxy-3-Methyl-2-Butanone (3H3M2B) using a discharge flow reactor combined with an electron impact ionization mass spectrometer. The total rate constant of the reaction, k 1 = 5.4410 -41 T 9.7 exp(2820/T) and 1.2310 -11 exp(-970/T) cm 3 molecule -1 s -1 at T = 278-400K and 400-830K, respectively, was determined using both absolute and relative rate method for temperatures in the range 278 -830 K. Temperature dependence of k 1 , measured over a wide temperature range, is significantly different from that of available computational study and, apparently, is an interesting experimental basis for further theoretical developments. The temperature dependence of the rate constant of the OH + Br 2 reaction, measured as a part of this study,

ACKNOWLEDGEMENT

Financial support from CNRS is gratefully acknowledged.

  2.1610 -11 exp(207/T) cm 3 molecule -1 s -1 (T = 220 -950, this work). This reaction was also used for the determination of the absolute concentrations of OH through their chemical conversion to HOBr in excess of Br 2 : [OH] = [HOBr] = [Br 2 ], i.e. concentration of OH (HOBr) was determined from the consumed fraction of [Br 2 ]. The possible influence of secondary chemistry on this method of the detection of OH radicals

( 2 )

 2 , OH radicals were detected also at m/z = 144 (HOI + ) upon their conversion to HOI in a rapid reaction with excess I 2 ([I 2 ] = (1.0-1.5)×10 13 molecule cm -3 , added in the end of the reactor by flowing Helium through a column containing iodine crystals, Figure S1, SI): OH + I 2  HOI + I (4) k 4 = (2.1 ± 06)×10 -10 cm 3 molecule -1 s -1 (T = 240 -348). 16 The 3-hydroxy-3-methyl-2-butanone (3H3M2B) was delivered to the reactor by flowing the bath gas (He) over liquid 3H3M2B and was detected by mass spectrometry at m/z = 59 (C(CH 3 ) 2 OH + ) and its parent peak at m/z = 102 (CH 3 C(O)C(CH 3 ) 2 OH + ). The H 2 O impurity in the gaseous samples of 3H3M2B, directly detected at m/z =18 (H 2 O + ), was ≤ 1%. The absolute calibration of the mass spectrometer for 3H3M2B was realized under experimental conditions of kinetic measurements (pressure, temperature, total flow of bath gas, He) through injection of known amounts (0.2-1.0 μL) of 3H3M2B into the flow of helium and recording its parent peak intensity at m/z = 102. The integrated area of the mass spectrometric signal corresponding to known total number of 3H3M2B molecules injected into the reactor allowed the determination of the calibration factor. Absolute concentrations of stable species (NO 2 , C 3 H 8 and Br 2 ) were calculated from their flow rates obtained from the measurements of the pressure drop of their mixtures in He stored in calibrated volume flasks.

3. 1 .

 1 Rate constant of reaction (1): absolute measurements. The rate constant of the title reaction was determined under pseudo-first order conditions monitoring OH decays in excess of 3H3M2B, [OH] = [OH] 0 ×exp(-k 1 '×t), where [OH] and [OH] 0 are the time-dependent and initial concentrations of OH radicals, respectively, and k 1 ' = k 1 ×[3H3M2B]+k w is the pseudo-first-order rate constant with k w representing the loss of OH radicals in the absence of 3H3M2B in the reactor. Initial concentration of OH radicals in these experiments was in the range (1.5 -3.5)×10 11 molecule cm -3 ; the concentrations of 3-hydroxy-3-methyl-2-

( 1 )

 1 was observed to be insignificant due to its sufficiently high excess over OH radicals. The possible thermal decomposition of 3H3M2B at high temperatures of the study was also probed. Firstly, we have not observed any noticeable consumption of 3H3M2B on the time scale of our experiments. We have analyzed also the signals at m/z = 94/96, 96/98, 122/124, 138/140 and 166/168, corresponding to CH 3 Br, HOBr, CH 2 C(O)Br, BrC(CH 3 ) 2 OH and BrC(O)C(CH 3 ) 2 OH, respectively, which could be formed in reactions of possible products of 3H3M2B decomposition with Br 2 . The mass spectrometric signals corresponding to these species were found to be by at least a factor of 10 lower than those of OH radicals (detected as HOBr, see above) at highest concentrations of 3H3M2B and highest temperatures of the study. Given these observations, the thermal decomposition of 3H3M2B under experimental conditions of the study could be considered as insignificant and not affecting the rate constant measurements.

Figure 1 .Figure 2 .

 12 Figure 1. Examples of the exponential decays of OH in reaction with 3H3M2B at T = 745 K.

Figure 2 .

 2 Figure 2. Pseudo-first-order rate constant (k 1 ′) as a function of the concentration of 3H3M2B measured at different temperatures. Error bars represent typical uncertainties (≤ 5%) on the determination of k 1 ′.

Figure 3 ,

 3 Figure 3, corresponding to the data observed at T = 500K with different concentrations of Br 2 , have similar slopes (i.e. provide similar k 1 /k 2 ratios) and different intercepts in agreement with equation (I).

Figure 3 .

 3 Figure 3. HOBr yield from OH radical titration with Br 2 + 3H3M2B mixtures at different temperatures. Partially shown error bars represent typical uncertainties of the measurements (≤ 10%).

The intercepts in the examples shown in Figure 4 (

 4 as well as in other experiments), k w , were in the range (20 ± 15) s -1 , in good agreement with the rate of OH decay measured in the absence of Br 2 in the reactor. All the results of the absolute measurements of k 2 are

Figure 4 .

 4 Figure 4. Pseudo-first-order rate constant (k 2 ′) as a function of the concentration of Br 2 measured at different temperatures. Error bars represent typical uncertainties (≤ 5%) on the determination of k 2 ′.

a

  Number of data points. b Units of 10 14 molecule cm -3 . c Units of 10 13 molecule cm -3 d Units of 10 -11 cm 3 molecule -1 s -1 , estimated uncertainty on k 2 is approximately 15%.

Figure 5 .

 5 Figure 5. HOBr yield from OH radical titration with Br 2 + C 3 H 8 mixtures at different temperatures. The horizontal and vertical error bars represent the estimated uncertainties (≤ 10%) on the respective values.

3. 5 .

 5 Comparison with previous studies. Figure 6 summarizes the results of the most recent temperature dependent measurements of the rate constant of reaction (2).

Figure 6 .

 6 Figure 6. Reaction OH + Br 2 : summary of the measurements of the temperature dependence of the reaction rate constant. AM: absolute measurement, RM: relative rate method. Partially shown error bars correspond to estimated 12 and 15 % uncertainty on the measurements of k 2 in the present work by absolute and relative rate method, respectively, and to maximum systematic uncertainty of 5% estimated in ref. 17. Uncertainties on k 2 reported in two other previous studies are omitted for clarity. Red dashed line: previous recommendation; 17 black solid line: Arrhenius fit to the present data; dotted lines: present fit ±10%.

  at highest temperatures of their study, where a downward curvature in the Arrhenius plot was observed. The reason for this slight disagreement (the reported uncertainty ranges overlap) is unknown. It can be noted that the observed experimentally downward curvature in the Arrhenius plot was not supported by theoretical calculations realized by Bryukov et al.: 17 the computed temperature dependence of k 2 displayed a slight upward curvature at high temperatures. Least-squares fit to k 2 data

Figure 7 .

 7 Figure 7. Reaction OH + 3-hydroxy-3-methyl-2-butanone: summary of the measurements of the reaction rate constant. AM: absolute measurement, RM: relative rate method. The error bars correspond to estimated 15 and 20 % uncertainty on the measurements of k 1 in the present work by absolute and relative rate method, respectively; uncertainties on previous measurements are given as reported in respective studies.

k 2 = 2 .

 22 1610-11 exp(207/T) cm 3 molecule -1 s -1 , and found to be in good agreement with previous data, was extended to lower (T = 220K) and higher (T = 950K) temperatures.ASSOCIATED CONTENTSupporting Information. Diagrams of the low and high temperature flow reactors (FiguresS1 and S2, respectively); dependence of k 1 ' on initial concentration of OH radicals (FigureS3); examples of the exponential decays of OH in reaction with Br 2 (FigureS4); HOBr yield from OH radical titration with Br 2 + C 3 H 8 mixtures at different temperatures (FigureS5).

Table 1 . Summary of the absolute measurements of the rate constants of the reaction OH + 3- hydroxy

 1

	T (K)	Number of kinetic runs	[3H3M2B] (10 13 molecule cm -3 )	a k 1 (10 -13 cm 3 molecule -1 s -1 )
	278	12	0.68-13.7	7.33
	298	11	0.38-14.8	7.25
	323	10	0.66-14.8	7.52
	350	10	0.50-14.0	8.28
	365	9	0.95-17.6	9.44
	390	9	0.62-11.9	10.4
	400	9	0.65-15.1	11.1
	460	9	0.67-12.9	14.6
	550	9	0.60-10.2	20.1
	630	16	0.49-9.88	24.4
	745	11	0.24-9.87	32.3
	830	12	0.42-8.72	39.9

-3-methyl-2-butanone.

a Statistical uncertainty on k 2 is ≤ 5%, total estimated uncertainty is approximately 15%.

Table 1 .

 1 The measurements of k 1 at temperatures between 278 and 350K have been carried out in a Pyrex reactor coated with halocarbon wax and those at T ≥ 365K in an uncoated quartz reactor. The combined uncertainty on k 1 was estimated to be about 15% by adding in quadrature statistical error (≤ 5%) and those on the measurements of the flows (3%),

	pressure (2%), temperature (1%) and absolute concentration of 3-hydroxy-3-methyl-2-
	butanone (10%).
	3.2. Rate constant of reaction (1): relative measurements. Relative rate measurements
	were conducted with reaction of OH with Br 2 as a reference. Fast titration of the initial
	concentration of OH radicals, [OH] 0 , by a mixture of Br 2 and 3H3M2B was performed, and
	the yield of HOBr was measured as a function of the [3H3M2B]/[Br 2 ] ratio:
	OH+3H3M2B  products	(1)
	OH + Br 2  HOBr + Br	(2)
	The concentration of HOBr formed is defined by the fraction of [OH] 0 reacting with Br 2 in
	reaction 2:
	HOBr

3H3M2B

OH

Rearrangement of this expression leads to:

Table 2 . Experimental Conditions and Results of the Relative Measurements of the Rate Constant of the Reaction OH + 3-hydroxy-3-methyl-2-butanone.

 2 Units of 10 14 molecule cm -3 . c Units of 10 13 molecule cm -3 . d Units of 10 -13 cm 3 molecule -1 s -1 , estimated uncertainty on k 1 is approximately 20%.

	T (K)	No./exp. a	[3H3M2B] b	[Br 2 ] c	k 1 /k 2	k 1 d
	285	6	1.71-16.0	0.98	0.0166	7.41
	310	13	0.32-11.1	0.94	0.0164	6.91
	370	8	0.19-1.79	0.72	0.0257	9.71
	420	8	0.22-1.71	1.02	0.0367	13.0
	500	13	0.06-1.30	1.25-1.85	0.0526	17.2

a Number of data points. b 2 : in all cases the average concentration of excess reactant along the reaction zone was used in the calculation of the reaction rate constant. Figure

4

shows typical dependences of the pseudo-first-order rate constant, k 2 ' = k 2 ×[Br 2 ]+k w , on concentration of Br 2 . Diffusion corrections applied to k 2 '

Table 3 . Summary of the absolute measurements of the rate constant of the reaction OH + Br 2 .

 3

	T (K)	Number of kinetic runs	[Br 2 ] (10 13 molecule cm -3 )	a k 2 (10 -11 cm 3 molecule -1 s -1 )
	263	12	0.08-1.07	4.78
	325	9	0.08-1.58	4.14
	455	10	0.11-1.85	3.35
	575	9	0.11-2.18	3.15
	865	8	0.17-2.19	2.81

a Statistical uncertainty on k 2 is ≤ 5%, total estimated uncertainty is approximately 12%.

Table 4 . Experimental Conditions and Results of the Relative Measurements of the Rate Constant of the Reaction OH + Br 2 .

 4 ×10 11 molecule cm -3 , concentrations of Br 2 and C 3 H 8 are shown in Table 4. Examples of the observed experimental data are shown in Figures 5 and S5 (SI). Final values of k 2 , shown in Table4, were calculated using the values of k 5 /k 2 determined from the slopes of the linear dependences in Figures5 and S5and k 5 = 2.6410 -17 T 1.93 exp(-114/T) cm 3 molecule -1 s -1 , which is well established over a wide temperature range T = 190 -1300K.[START_REF] Morin | Experimental Study of the Reactions of OH Radicals with Propane, n-Pentane, and n-Heptane over a Wide Temperature Range[END_REF]

	reference:
	OH + Br 2  HOBr + Br

3.4. Rate constant of reaction (2): relative measurements. In this series of experiments,

we have carried out relative rate measurements with reaction of OH with propane as

TOC Graphic


Fatima Hara
email: fatimahara1@gmail.com.

Mohammed Achab

Anas Emran

Badr Gil Mahe

El Fhel

Badr El Fhel

Estimate the risk of soil erosion using USLE through the development of an Open Source desktop application: DUSLE (Desktop Universal Soil Loss Equation)

Keywords: Water erosion, Loss in soil, USLE model, DUSLE development, Open Source, java, watershed

Introduction

Water erosion is the main factor of the deterioration of the soil resource. The soil loss phenomena have accelerated around the world [START_REF] De Graaf | Price of soil erosion: an economic evaluation of soil conservation and watershed development[END_REF]. Water erosion risk assessment involves mapping and analyzing many factors involved in the erosive process: rainfall erosivity, soil erodibility, slope length, vegetal cover (Wischmeier and Smith, 1978).

The development of computer tools and Geographic Information Systems (GIS) have facilitated and solved the problems of water erosion through modeling. In this context, our main objective is to develop a desktop application for open source soil erosion risk using the USLE empirical equation. The source code of the application can be used, modified and improved by all users.

Material and Methods

Development tools

Java

Java is an object-oriented computer programming language for developing applications. This language is intended to work in multiple computer environments and on different types of computers.

Netbeans

Netbeans is an integrated development environment (IDE) for Java, placed open source by Sun in June 2000. It also supports different other languages, such as Python, C, C ++, PHP, XML and HTML.

DUSLE desktop application

The desktop application DUSLE was composed of an interface with six button. Each button allows to load a factor involved in the USLE method, the last button allows to define the result path. The calculated button allows to create the USLE map which combines the five factors previously loaded via the directory path in picture format (jpg),(Conservation practice factor (P) is considered a number between 0 and 1), and calculate the average loss. Two buttons were added to interface with the intuitive functionality, Help button & Cancel button. The application can be easily installed on a PC with desktop shortcut and practical interface.

Figure 1 shows the general methodological organization followed in this work, and the development of the proposed DUSLE application.

Results and Discussion

The developed application has been tested in an area near the " Sidi Mohammed ben Abdallah Dam " located north west of Morocco. The spatial resolution of the raster files used in this case study was defined as 5 m. This resolution is the same of the DEM used. All the data were in the Merchich/North coordinate reference system (EPSG: 26191). The interface screen is shown on figure 3.

DUSLE application interface

Figure2: Authentication interface Figure3: DUSLE interface for each USLE parameter

Comparing the results of the DUSLE application and ArcGis software

The analysis of the risk map of soil erosion obtained via DUSLE application (Figure 4a) and that obtained via ArcGIS (Figure 4b) are similar. We are in the process of developing the DUSLE application for better results. The average soil loss values in the chosen zone obtained by DUSLE is close to the value obtained via ArcGis.

Conclusion

DUSLE application that we developed in this work allowed us to estimate the risk of soil erosion over the chosen area. The results obtained from the DUSLE application are similar to those obtained by USLE via ArcGis. These preliminary results are suitable for further uses.This work opens the way for broad use of programming for geoprocessing desktop or online at Morocco from open source tools.

Figure 1 :

 1 Figure 1: Diagram of the DUSLE application

Figure 4a :

 4a Figure 4a: The soil erosion risk map on DUSLE (Open source).

Figure 4b :

 4b Figure 4b: The soil erosion risk map on Arcgis (proprietary software).