Photochemical Kinetics of Pyruvic Acid in Aqueous Solution - The

Article pubs.acs.org/JPCA

Photochemical Kinetics of Pyruvic Acid in Aqueous Solution Allison E. Reed Harris,†,‡ Barbara Ervens,‡,§ Richard K. Shoemaker,† Jay A. Kroll,†,‡ Rebecca J. Rapf,†,‡ Elizabeth C. Griffith,†,‡ Anne Monod,‡,∥ and Veronica Vaida*,†,‡ †

Department of Chemistry and Biochemistry, University of Colorado, UCB 215, Boulder, Colorado 80309, United States, CIRES, University of Colorado, UCB 215, Boulder, Colorado 80309, United States, § Chemical Sciences Division, Earth System Research Laboratory, National Oceanic and Atmospheric Administration, Boulder, Colorado 80305, United States ∥ Aix Marseille Université, CNRS, LCE FRE 3416, 13331 Marseille, France ‡

S Supporting Information *

ABSTRACT: Pyruvic acid in the atmosphere is found in both the gas and aqueous phases, and its behavior gives insight into that of other α-keto acids. Photolysis is a significant degradation pathway for this molecule in the environment, and in aqueous solution the major photoproducts are higher-molecular-weight compounds that may contribute to secondary organic aerosol mass. The kinetics of the aqueous-phase photolysis of pyruvic acid under aerobic and anaerobic conditions was investigated in order to calculate the first-order rate constant, Jaq, in solution. Analysis of the exponential decay of pyruvic acid was performed by monitoring both pyruvic acid and its photolytic products over the course of the reaction by 1H NMR spectroscopy. Detection of major and minor products in the 0.1, 0.05, and 0.02 M pyruvic acid photolyses clearly demonstrates that the primary reaction pathways are highly dependent on the initial pyruvic acid concentration and the presence of dissolved oxygen. The Jaq values were calculated with approximations based on the dominant pathways for limiting cases of the mechanism. Finally, a model study using the calculated rate constants demonstrates the importance of aqueous-phase photolysis as a sink for pyruvic acid in the atmosphere, compared with gas-phase photolysis and OH oxidation.

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INTRODUCTION Atmospheric aerosols directly impact the global radiative balance by absorbing and scattering incoming solar radiation, initiating cloud formation, and influencing atmospheric chemistry.1−3 Aerosol particles are also known to contribute to pollution-related smog and haze, negatively affecting the human cardiovascular and respiratory systems.4,5 Secondary organic aerosols (SOAs) are created when volatile organic compounds (VOCs) are oxidized in the atmosphere to give low-vapor-pressure products, which in turn condense and increase particulate matter.6 Field measurements of the mass of SOAs are significantly different than corresponding predictions from current atmospheric models, highlighting a gap in the fundamental understanding of their formation and growth.7 Recent work suggests that some of this discrepancy can be explained by accounting for SOAs formed from high-molecular-weight products of aqueous-phase photochemistry,1,2,8 prompting kinetic and mechanistic studies of aqueous organic reactions.9−13 This work explores the photochemical kinetics of aqueous-phase pyruvic acid under conditions relevant to deliquesced aerosols. Pyruvic acid, found in both the gas and aqueous phases in the atmosphere, is formed primarily from photooxidation of biogenic and anthropogenic precursors14−21 and provides insight into the chemistry of other important α-keto acids.17,22,23 Previous and current studies on pyruvic acid © 2014 American Chemical Society

span a variety of reactions: thermochemical decarboxylation, infrared multiphoton pyrolysis, direct UV−vis photolysis, and hydroxyl radical oxidation.24−37 Oxidation of pyruvic acid by OH in solution, which yields glyoxylic, oxalic, acetic, and formic acids, has been linked to aqueous SOA formation.24 While many studies of the atmospherically relevant aqueousphase processes have focused on organic reactions with OH radicals,9−13 the photolysis of ketones and aldehydes may also play a significant role in aerosol processing.38−42 The mechanism of the direct photolysis of pyruvic acid is complex and highly dependent on the reaction environment.12,39,43−46 For example, it is well-known that in the gas phase, UV absorption to the first excited singlet state causes decarboxylation and yields methylhydroxycarbene.27,32,33,35−37,47−49 However, the pathway for the aqueous-phase photolysis of pyruvic acid (as well as the resulting products) is different from that in the gas-phase and more controversial.31,40,50−54 Aqueous photolysis also begins with excitation to the S1 state, but intersystem crossing results in the 3(n, π*) state, which initiates radical chemistry that produces polymeric species and other minor products.31,34,40,50−52,55 [We use the term “polymer” in Special Issue: A. W. Castleman, Jr. Festschrift Received: March 3, 2014 Revised: April 9, 2014 Published: April 11, 2014 8505

dx.doi.org/10.1021/jp502186q | J. Phys. Chem. A 2014, 118, 8505−8516

The Journal of Physical Chemistry A

Article

geminal diol (see eq 1), only the unhydrated form absorbs in the UV−vis range available from this instrument. Therefore, absorbance values were calibrated to the concentration of pyruvic acid in the keto form (Figure S3 in the Supporting Information). The total pyruvic acid concentration ([PA]Tot = [PA]Keto + [PA]Diol) was calculated from a curve of the concentration of pyruvic acid in the keto form versus the geminal diol form, which was generated from 1H NMR absolute integrated intensities (Figure S4 in the Supporting Information). Products obtained after 9 h of photolysis for the starting concentration of 0.1 M were also analyzed with negative-ion electrospray ionization mass spectrometry (ESI-MS) (Figure S5 in the Supporting Information). Results. The photolytic decays determined from the 1H NMR absolute integrated intensities for 0.1, 0.05, and 0.02 M pyruvic acid are shown in Figure 1 with two standard

this paper to describe high-molecular-weight products from the photolysis of pyruvic acid, including dimethyltartaric acid (a dimer of pyruvic acid) and other compounds of similar molecular weight. These are the same products as described in previous literature as oligomers.] This paper demonstrates that the photolysis of pyruvic acid is sensitive not only to the phase but also to the presence of dissolved oxygen and the initial pyruvic acid concentration. In this study, the aqueous-phase photolysis of pyruvic acid was investigated in order to obtain kinetic information as a function of the pyruvic acid concentration and presence of dissolved oxygen. The photolysis of pyruvic acid at three atmospherically relevant concentrations (0.02, 0.05, and 0.1 M) was studied both aerobically and anaerobically. On the basis of a detailed mechanism, first-order rate constants (Jaq values) in solution were estimated by monitoring reactants and products over the course of the photolysis. The results were then used in a modeling experiment to compare the rate of direct photolysis of pyruvic acid to the rate of OH oxidation under atmospheric conditions in both the gas and aqueous phases.

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EXPERIMENTAL METHODS AND RESULTS Methods. Pyruvic acid (98%, Sigma-Aldrich) was distilled once under reduced pressure and diluted with deionized water to 0.1, 0.05, or 0.02 M. A volume of 250 mL of solution was photolyzed for 9 h in a temperature-stabilized water bath at 4 °C with a 450 W Xe arc lamp (Newport) and stirred for the duration of the photolysis. A Pyrex lens was placed between the light source and reacting solution to filter out wavelengths λ < 300 nm. Throughout the photolysis, 5 mL aliquots were taken, wrapped in foil, and refrigerated to prevent further reaction. The time intervals between samples ranged from 5 to 90 min, and all of the samples were equilibrated to room temperature before analysis. The photolysis was also performed in an anaerobic environment at all three concentrations. For these experiments, the solutions were purged with N2 to displace dissolved O2 and then isolated from the surroundings to prevent oxygen from reentering the system. Experiments at each concentration were run as described above, removing samples with a syringe via a silicon septum to avoid oxygen contamination. NMR experiments were performed using a Varian INOVA500 NMR spectrometer operating at 499.60 MHz for 1H observation. Quantitative 1H NMR spectroscopy (QNMR) was performed using WET suppression of H2O followed by wellcalibrated 90° excitation pulses (7.1 μs). To ensure absolute quantitation, a constant receiver gain was used in all of the experiments. Absolute integrated intensities from QNMR experiments were calibrated versus molar concentration of analyte using samples of known concentration (see Figure S1 in the Supporting Information). During aerobic and anaerobic photolysis experiments, aqueous samples were prepared volumetrically (640 μL + 50.0 μL of D2O for NMR fieldfrequency lock) for QNMR analysis, enabling the determination of the pyruvic acid concentration as well as the molar concentrations of other products, including acetoin and acetic acid. Samples were also analyzed with UV−vis spectroscopy using an Ocean Optics USB2000 miniature fiber optic UV−vis spectrometer with wavelengths ranging from 250 to 880 nm. Spectra of aliquots taken throughout a 0.1 M photolysis are shown in Figure S2 in the Supporting Information. Although about 60% of pyruvic acid is hydrated in solution to give its

Figure 1. Decay of 0.1 M (red ●), 0.05 M (green ■), and 0.02 M (blue ▲) pyruvic acid over a 9 h photolysis. Concentrations and errors (two standard deviations) were determined from 1H NMR absolute integrated intensities. The exponential decays from regression analysis −5

are as follows: [PA]Tot = 0.102e−(2.13×10 −5

−(4.29×10 )t

0.0519e 0.02 M.

)t

for 0.1 M, [PA]Tot =

for 0.05 M, and [PA]Tot = 0.0199e−(4.07×10

−5

)t

for

deviations. The exponentiality of this curve is illustrated by the linear relationship between ln[PA]Tot and time (Figure S6 in the Supporting Information). A regression analysis was performed, assuming that the concentration of pyruvic acid would go to zero as time goes to infinity, in order to find the function for each curve in Figure 1. First-order rate constants (J values) for limiting cases were then calculated by equating the experimentally determined decay rates to the results from a kinetic analysis. Similar plots and results were obtained from UV−vis spectroscopy and are shown in Figures S7 and S8 and Table S1 in the Supporting Information. Hydration of the carbonyl group of aldehydes and ketones in solution, including pyruvic acid, is well-known.34,56−66 The kinetic treatment of pyruvic acid in this study requires analysis of its hydration to the geminal diol, 2,2-dihydroxypropanoic acid (eq 1), to determine the amount of photoreactive pyruvic acid.56,67 CH3C(O)CO2 H + H 2O ⇄ CH3C(OH)2 CO2 H

(1)

The equilibrium constant, KHyd = [CH3C(OH)2CO2H]/ [CH3C(O)CO2H], was determined throughout the reaction by measuring the keto and diol forms of pyruvic acid separately by 1H NMR spectroscopy. Pocker et al.67 showed that KHyd is highly dependent on both temperature and pH, reporting a 8506



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decrease in KHyd at 0 °C from 1.64 to 0.593 as the pH rises from 1.95 to 2.53. The equilibrium constant obtained in this study for the concentration of 0.1 M pyruvic acid at an initial pH of 2.06 is KHyd = 1.54. As the photolysis proceeds and pyruvic acid is consumed, the pH increases, and this is accompanied by the expected decrease in the hydration equilibrium constant. At the end of the 9 h photolysis, the pH had increased to 2.2 and KHyd was found to be 1.38, which is consistent with the results of Pocker et al. and other published literature values. 40,56,67 A full table of the experimentally derived, time-dependent KHyd values is given in Table S2 in the Supporting Information. Because of the variability of KHyd throughout a photolysis reaction, effective values of KHyd (time average over the 9 h reactions) at the different concentrations of pyruvic acid (Table 1) were found and were used in the calculation of the J values.

effective KHyd value

0.1 0.05 0.02

1.50 ± 0.05 1.3 ± 0.1 1.0 ± 0.1

DISCUSSION

Effects of Dissolved Oxygen on the Product Distribution. The concentrations of pyruvic acid used in this study (0.02, 0.05, and 0.1 M) are similar to the concentrations of condensed-phase pyruvic acid in the atmosphere if particulate pyruvic acid were dissolved in the aqueous phase of hygroscopic, acidic aerosol particles (see Atmospheric Implications).68,69 The overall concentration, however, does not represent the amount of photoactive pyruvic acid. 1H NMR results from this study show that pyruvic acid is 60% hydrated in a 0.1 M solution. The resulting geminal diol, 2,2dihydroxypropanoic acid (2,2-DHPA), does not absorb in the near-UV available in this experiment but may absorb through high-energy vibrational overtones with very low cross sections.70 Therefore, 2,2-DHPA was not considered a contributor to the photolytic decay of aqueous pyruvic acid in this work.50 Furthermore, pyruvic acid (pKa = 2.18)67 in this study is ∼23−43% in its anionic form, pyruvate, which Leermakers and Vesley51 have shown to be about 20 times less photolyzable than undissociated aqueous pyruvic acid. Thus, this kinetic and mechanistic study of the aqueous photolysis of pyruvic acid considers the protonated keto form to be the predominant reactive compound. The scheme used for the analysis is shown in Figure 2 and is discussed in detail below. The first step in the photolysis of pyruvic acid is the electronic excitation of the reactive keto form from the ground state to the 1(n, π*) (S1) state, followed by intersystem crossing and internal conversion to the 3(n, π*) (T1) state (eq 2, rate constant Jaq).50

Table 1. Effective Values of the Equilibrium Constant KHyd over 9 h Photolyses at Different Concentrations of Pyruvic Acida concentration (M)

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a

Error bars are one standard deviation. The ratio of keto form to geminal diol form was calculated from 1H NMR absolute integrated intensities.

A sensitivity study of Jaq with respect to KHyd was employed to check the validity of using the effective values in this manner (see the Discussion).

Figure 2. Summary of the main reactions involved in the kinetics of the photolysis of pyruvic acid. Rate constants used in the kinetic analysis are shown in red. The label 2,2 DHPA represents 2,2-dihydroxypropanoic acid, the hydrated form of pyruvic acid. 8507



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Figure 3. 1H NMR spectra for (a) 0.1 M, (b) 0.05 M, and (c) 0.02 M pyruvic acid after 9 h of photolysis. The location for acetoin and lactic acid (∼4.4 ppm) is indicated by *, and the acetic acid peak at 2.06 ppm is indicated by **. The 1H NMR signals from CH3 protons of pyruvic acid (2.4 ppm) and 2,2-DHPA (1.55 ppm) are indicated by # and ##, respectively. The peak of glyoxylic acid at 5.30 ppm is indicated by ⧧. For visual clarity, the vertical scale of the downfield portion (3.2−4.5 ppm) has been expanded vertically approximately 64 times for all three traces. Jaq

CH3C(O)CO2 H + hν → [CH3C(O)CO2 H]*

here to test the effect of O2 over the range of pyruvic acid concentrations considered in this paper. The second step in Figure 2 shows only the reaction of [PA]* with 2,2-DHPA (eq 3). While [PA]* can also react with pyruvic acid in the keto form (eq 4), it is more likely to react with 2,2-DHPA because of its higher concentration in solution and favorable energetics.50 Therefore, the remainder of the kinetic scheme focuses on the more probable pathway, namely, the reaction with 2,2-DHPA (eq 3). The reaction of [PA]* with 2,2-DHPA (eq 3) results in concerted H atom transfer and decarboxylation, yielding two radical species, PȦ and AȦ .50 These two radicals can undergo many reactions to produce various products; the following 1H NMR analysis demonstrates that the initial concentration of pyruvic acid determines which are the dominant pathways. The reactions considered in Figure 2 are limited to ones with products identifiable by 1H NMR spectroscopy that provide details regarding the mechanism for the aqueous-phase photolysis of pyruvic acid. Additional polymers were observed in the 1H NMR analysis but are not shown in this scheme. After the initial creation of radicals, the studied reactions can be separated into two categories: radical−radical recombinations (k5, k6, and k7) and radical reactions with O2 (k8 and k9).50,71,72 The three radical−radical recombinations are those reported by Griffith et al.50 to form acetoin (k5), lactic and acetic acid (k6), and dimethyltartaric acid (k7):

(2)

The excited T1 state, [CH3C(O)CO2H]*, is denoted in this paper by [PA]*. The first-order rate constant for the reaction shown in eq 2, Jaq, is the aqueous J value for pyruvic acid decay and will be determined for limiting cases in this study. After the initial excitation, [PA]* can react with either 2,2DHPA or pyruvic acid via eqs 3 and 4, respectively:50 [PA]* + CH3C(OH)2 CO2 H k3

̇ ̇ → CH3C(OH)CO 2 H + CH3C(OH)2 + CO2

(3)

[PA]* + CH3C(O)CO2 H k

4 ̇ ̇ → CH3C(OH)CO 2 H + CH3C(O) + CO2

(4)

Throughout the remainder of this paper, CH3Ċ (OH)CO2H is denoted as PȦ and CH3Ċ (OH)2 as AȦ . Because these reactions contribute to the overall depletion of pyruvic acid, the J value cannot be directly equated to the decay rate from Figure 1. A summary of the pathways important for this kinetic analysis is shown in Figure 2 and provides the framework for determining the values of Jaq for photolysis of pyruvic acid in solution. Griffith et al.50 presented this mechanism for 0.1 M pyruvic acid without the oxygen radical reactions (eqs 8 and 9), which are insignificant at that concentration, as is demonstrated in this work. The possibility of these reactions was reconsidered 8508



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Figure 4. 1H NMR spectra after 9 h of photolysis of 0.05 M pyruvic acid (a) with and (b) without oxygen in the solution. 1H NMR signals from acetoin and lactic acid at ∼4.4 ppm and acetic acid at 2.06 ppm are indicated by * and **, respectively. The signal identified as glyoxylic acid at 5.30 ppm is indicated by ⧧. The 1H NMR signals from CH3 protons of pyruvic acid (2.4 ppm) and 2,2-DHPA (1.55 ppm) are indicated by # and ##, respectively. For visual clarity, the vertical scale of the downfield region (2.4−4.5 ppm) has been expanded vertically approximately 64 times for both traces. k

5 PȦ + AȦ → H 2O + CO2 + CH3CH(OH)COCH3

The small polymeric species (the major products for the reaction of 0.1 M pyruvic acid) are treated together at shifts from 1.2 to 1.55 ppm. This region was chosen empirically to represent 1H NMR signals that appear from the formation of small polymers because it can be integrated without interference from other signals. Minor products in the spectrum after the 0.1 M pyruvic acid photolysis include acetoin and lactic acid, with nearly overlapping signals at 4.4 ppm, and acetic acid at 2.06 ppm. It is clear from the presence of acetoin, lactic acid, and small polymers in Figure 3a that eqs 5, 6, and 7 represent active pathways in the 0.1 M pyruvic acid photolysis. The comparable peak intensities of lactic acid and acetic acid imply that they are produced at similar rates, and thus, eq 6 is responsible for much of the acetic acid production. This indicates that radical−radical reactions are dominant at this concentration. Further, Henry’s law was used to estimate the concentration of dissolved oxygen at PO2 = 0.21 atm (assuming air at 1 atm with 21% O2). After adjustment for the temperature of the solution (4 °C), the ratio of dissolved oxygen to 0.1 M pyruvic acid was ∼1:40 under our experimental conditions.73 Because of this high initial pyruvic acid concentration relative to O2, it is likely that dissolved oxygen concentrations are depleted quickly by reaction with radicals,13 favoring radical−radical recombinations throughout the remainder of the photolysis. Therefore, we assumed that the oxygen radical reactions could be neglected when analyzing the 0.1 M pyruvic acid photolysis.

(5)

k

6 PȦ + AȦ → CH3CO2 H + CH3CH(OH)CO2 H

(6)

k

7 2PȦ → (CH3C(OH)(CO2 H))2

(7)

All of the products from these reactions were identified in the present study as well as in previous literature.31,40,50,51 The reactions of oxygen with organic radicals can proceed with PȦ to reproduce pyruvic acid (k8) and with AȦ to form acetic acid (k9): k

8 PȦ + O2 → CH3C(O)CO2 H + HȮ 2

(8)

k

9 AȦ + O2 → CH3CO2 H + HȮ 2

(9)

For the photolysis of a 0.1 M solution of pyruvic acid, two primary peaks were seen by ESI-MS (Figure S5 in the Supporting Information), which is consistent with previous studies for the aqueous photolysis of pyruvic acid.40,50 Griffith et al.50 identified one of these products as a dimer of pyruvic acid at m/z 175. The other peak, at m/z 177, is of similar molecular weight to dimethyltartaric acid, so these products are termed small polymers throughout this paper. The 1H NMR spectrum of the aliquot taken after 9 h of photolysis of 0.1 M pyruvic acid (Figure 3a; see Figure S9 in the Supporting Information for the full, unedited spectrum) matches the product distribution as observed by Griffith et al.50 8509



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First-Order Rate Constants for Photochemical Decay of Pyruvic Acid. This section includes a kinetic analysis of the photolysis of pyruvic acid based upon the mechanism given in Figure 2 and the 1H NMR results discussed above. First-order rate constants for the photolysis of pyruvic acid in aqueous solution, Jaq, were calculated for the initial concentrations of 0.1 and 0.02 M. These concentrations were chosen as limiting cases for the photolysis of pyruvic acid to estimate and compare the rate of photolysis when dominated by radical−radical recombination reactions to the rate of photolysis when oxygen radical reactions are most important. The analysis here is not a full kinetic treatment of the rate equations but makes use of steady-state approximations to find approximate Jaq values. No rate constant was calculated for the photolysis of 0.05 M pyruvic acid because all of the reaction pathways are significant at this concentration, and the system cannot be treated with either limiting case in order to solve for Jaq. To model the decay of pyruvic acid, the rate equation for d[PA]Tot/dt based on the mechanism and rate constants in Figure 2 was considered:

There is a difference in the distributions of minor products in the photolyses of 0.1 and 0.02 M pyruvic acid. In the 1H NMR spectrum of 0.02 M pyruvic acid after 9 h of photolysis (Figure 3c), the peaks for lactic acid and acetoin are absent, and there is a large decrease in the final peak intensities of small polymers compared with the 0.1 M pyruvic acid reaction (Figure 3a and Figure S10 in the Supporting Information). The significant loss in the three products formed only via radical−radical recombination reactions implies that eqs 5, 6, and 7 are less important at this lower initial concentration of pyruvic acid.13 However, the yield of acetic acid increased substantially with decreasing pyruvic acid concentration. Since eq 6 yields both lactic acid and acetic acid and no lactic acid was present after photolysis of 0.02 M pyruvic acid, we assume that eq 9, the oxygen radical reaction, is responsible for the increase in acetic acid. This change in mechanistic pathway is consistent with the change in the ratio of dissolved oxygen to pyruvic acid, which increased to ∼1:8. In this case, O2 is not depleted as quickly, and oxygen radical reactions remain competitive throughout the photolysis. Peroxy radical is a product of both oxygen radical reactions (eqs 8 and 9), and it can generate H2O2 and Ȯ H. While no H2O2 was detected by 1H NMR analysis, a product at 5.4 ppm in the 1H NMR spectrum for the aerobic photolysis of 0.02 M pyruvic acid was identified as glyoxylic acid (Figure S11 in the Supporting Information). Carlton et al.24 reported glyoxylic acid as a product of the reaction of pyruvic acid with OH radical, and thus, its identification in the 1H NMR spectrum suggests that there may be some hydroxyl radical chemistry during the 0.02 M pyruvic acid photolysis. However, the model results included in this study show that the Ȯ H oxidation of pyruvic acid is not competitive in terms of pyruvic acid loss under our experimental concentrations (i.e., pH < 3), and therefore, the hydroxyl radical reactions are not likely responsible for the bulk of the photochemical destruction of pyruvic acid (see Atmospheric Implications). The active pathways for the aqueous photolysis of 0.05 M pyruvic acid include all of the reactions presented in Figure 2. The 1H NMR spectrum after 9 h of photolysis of 0.05 M pyruvic acid (Figure 3b) shows the presence of acetoin, lactic acid, and the small polymers (at reduced concentrations from that of the 0.1 M photolysis), indicating the importance of radical−radical recombination reactions. However, the intensity of the acetic acid peak is much higher than that of the lactic acid peak, so reactions of dissolved oxygen with radicals must also play a significant role at this concentration. To verify that the differences in the product distributions at different concentrations are due to the activation of oxygen radical reactions, the photolysis was performed anaerobically at the same concentrations. Figure 4 directly compares the 1H NMR spectrum after 9 h of photolysis of 0.05 M pyruvic acid purged with N2 (Figure 4b) with that of the corresponding aerobic reaction (Figure 4a) (see Figure S12 in the Supporting Information for the full, unedited spectra). In the 0.05 M pyruvic acid reaction without oxygen in the solution, we see acetoin and lactic acid return strongly, while the concentration of acetic acid is greatly reduced from that in the original 0.05 M pyruvic acid photolysis. This matches the products expected without the oxygen radical reactions (eqs 8 and 9), confirming that the mechanistic difference between the photolyses of 0.02, 0.05, and 0.1 M pyruvic acid is in fact due to dissolved O2 playing a role only at reduced radical concentrations.

d[PA]Tot = −Jaq [PA]Keto − k 3[[PA]*][PA]Diol dt ̇ − k4[[PA]*][PA]Keto + k 8[PA][O 2]

(10)

By application of the steady-state approximation for [PA]*, it can be shown that Jaq [PA]Keto = k 3[[PA]*][PA]Diol + k4[[PA]*][PA]Keto (11)

which can be used to simplify eq 10. As per the discussion in the Results section, KHyd is known throughout the reaction, and thus [PA]Keto can be expressed in terms of the total concentration of pyruvic acid and KHyd:

[PA]Keto =

[PA]Tot 1 + KHyd

(12)

After substitution of eqs 11 and 12 into eq 10, the remaining unknowns are the concentrations of PȦ and O2, and further simplification must be made in order to solve for Jaq from the exponential decay of pyruvic acid. Depending on the initial concentration of the solution, either k 8 [PȦ ][O 2 ] ≪ 2Jaq[PA]Keto or k8[PȦ ][O2] ∼ 2Jaq[PA]Keto. The choice between these two approximations can be made with the support from the 1H NMR spectra. If k8[PȦ ][O2] ≪ 2Jaq[PA]Keto, then the term k8[PȦ ][O2] in eq 10 is negligible, and solving the differential equation we obtain ⎛ ⎞ 2Jaq [PA]Tot = [PA]0Tot exp⎜⎜ − t ⎟⎟ ⎝ KHyd + 1 ⎠

(13)

where [PA]0Tot is the initial concentration of pyruvic acid. On the other hand, if k8[PȦ ][O2] ∼ 2Jaq[PA]Keto, then applying the steady state approximation to PȦ , we find that ̇ Jaq [PA]Keto ≈ k 8[PA][O 2]

(14)

Substituting eq 14 into eq 10 and solving for the concentration of pyruvic acid yields 8510


The Journal of Physical Chemistry A [PA]Tot =

[PA]0Tot

⎛ ⎞ Jaq exp⎜⎜ − t ⎟⎟ ⎝ KHyd + 1 ⎠

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calculated on the basis of the 1H NMR spectra for each concentration (see the Results section). The J values shown in the middle column of Table 2 were found with this effective value of KHyd. The sensitivity of the J values to the equilibrium constant was explored by calculating Jaq over the range of possible equilibrium constants in order to check the validity of using the effective value of KHyd. In the first column of Table 2, Jaq was calculated using the smallest observed ratio of 2,2DHPA to pyruvic acid over the course of the reaction (the 9 h ratio). Conversely, the third column shows the J value calculated with the highest observed KHyd (the initial ratio). This analysis shows that Jaq is only slightly sensitive to KHyd, as the low-KHyd and high-KHyd J values are all within 8% error of the Jaq value calculated from the effective value of KHyd. The differences between the J values for the aerated and nonaerated photolysis reactions confirm the key role of the dissolved O2 in the mechanism. For the initial pyruvic acid concentration of 0.1 M, where O2 does not play a significant role, the aerobic J value is only slightly lower than the anaerobic J value. This may result from some reaction of PȦ with O2, which was neglected in the aerobic analysis, regenerating pyruvic acid and slowing the decay. The difference in the Jaq values for the aerated and nonaerated reactions at 0.02 M pyruvic acid is more pronounced. The Jaq value for the aerobic photolysis of 0.02 M pyruvic acid is about 3 times that of 0.1 M pyruvic acid, which indicates that, when significant, the rate of the reaction of radicals with dissolved oxygen is higher than that of the radical−radical recombinations. This is in very good agreement with the literature.72,74 When the oxygen is removed from 0.02 M pyruvic acid solution, Jaq decreases to within one standard deviation of the 0.1 M pyruvic acid anaerobic J value, indicating a constant J value when oxygen is negligible. The mechanistic detail provided here is important for further studies of pyruvic acid and its decomposition in the atmosphere because it indicates that its gas-phase J value (Jgas) cannot be simply scaled down to determine a J value in aqueous solution. The aqueous-phase photolysis proceeds via a separate mechanism than the gas-phase photolysis, and thus, its rate is defined by completely different chemistry. Furthermore, the data presented in Table 2 reveal that the aqueous J value for pyruvic acid is dependent on both the concentration of pyruvic acid and the concentration of dissolved oxygen. In summary, at low concentrations of pyruvic acid (0.02 M), organic radicals are quickly quenched by O2, resulting in a Jaq value of (8.1 ± 0.9) × 10−5 s−1. Conversely, a higher concentration of pyruvic acid (0.1 M) yields a lower Jaq value of (2.66 ± 0.09) × 10−5 s−1, in which slower radical−radical recombination reactions dominate. The model section below scales up these experimental results to atmospherically relevant conditions in order to deduce their atmospheric significance.

(15)

This analysis is written out in full in section 2 in the Supporting Information. To solve for Jaq, absolute integrated intensities from 1H NMR spectra were converted to total concentrations of pyruvic acid ([PA]Tot = [PA]Keto + [PA]Diol) and plotted versus the irradiation time (Figure 1). The data were fit to exponential curves, yielding equations of the form derived from the above analysis, and Jaq values were obtained using the appropriate approximation as determined by inspection of the minor products in the 1H NMR spectra. Table 2 lists the calculated aqueous J values for the aerobic and anaerobic photolysis reactions. Table 2. Jaq Values Calculated for Aerobic and Anaerobic Photolysis of Pyruvic Acid at Initial Concentrations of 0.1 and 0.02 Ma Jaq (10−5 s−1) [PA]0Tot

(M)

Aerobic 0.1 0.02 Anaerobic 0.1 0.02

low KHyd

eff. KHyd

high KHyd

2.55 ± 0.09 7.43 ± 0.9

2.66 ± 0.09 8.08 ± 0.9

2.72 ± 0.09 8.68 ± 1

3.23 ± 0.2 3.50 ± 0.4

3.40 ± 0.2 3.80 ± 0.5

3.43 ± 0.2 4.08 ± 0.5

a

The aerobic values (top section of the table) were calculated from integrated peak intensities of 1H NMR spectra, while the anaerobic values (bottom section) were calculated from UV−vis spectra. The three columns show the possible range of J values calculated with the lowest observed value of KHyd, the effective value (eff.) of KHyd, and the highest observed value of KHyd (listed in Table S2 in the Supporting Information).

For the aerobic photolysis of 0.1 M pyruvic acid and both anaerobic reactions, the 1H NMR spectra indicated that radical−radical recombination reactions dominate, as discussed above. Thus, it could be approximated that k8[PȦ ][O2] ≪ 2Jaq[PA]Keto, and eq 13 was used to determine Jaq. However, at 0.02 M pyruvic acid, the 1H NMR spectra indicated that radical−radical reactions could be neglected because of the very low or absent product concentrations, and Jaq was calculated using eq 15 based on the second approximation (k8[PȦ ][O2] ∼ 2Jaq[PA]Keto). It should be noted that there is a high percentage (∼43%) of anion present at the low concentration. However, calculations incorporating the photoreactivity of the anion compared with pyruvic acid showed that pyruvate initiates less than ∼4.5% of the total photolysis;51 therefore, because of its much lower photosensitivity than pyruvic acid, its presence was ignored in this analysis. Since neither approximation applied to the 0.05 M pyruvic acid data, no J value was calculated for this concentration. A similar analysis was performed for each of the reactions analyzed with UV−vis spectroscopy. These results are tabulated in Table S1 in the Supporting Information and show agreement between the NMR and UV−vis analyses as well as reproducible J values for the photolyses of 0.1 and 0.02 M pyruvic acid. KHyd is needed to solve for Jaq using either approximation. Because the hydration equilibrium constant varies over the course of a photolysis reaction, an effective value for KHyd was

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ATMOSPHERIC IMPLICATIONS Model Description. A box model study was conducted to determine the conditions under which the aqueous-phase photolysis of pyruvic acid might be a significant sink compared with other known loss processes (specifically, the OH reaction in the gas and aqueous phases as well as gas-phase photolysis). We applied a multiphase box model in which the aqueous phase is composed of small water droplets with a diameter of 150 nm, which can be considered a typical size of deliquesced particles in the atmosphere. For the first set of simulations, an assumed particle concentration of Na = 10 000 cm−3 resulted in a total liquid water content (LWC) of 17.6 μg m−3, a value that 8511



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Figure 5. Box model results showing the relative contributions of gas- and aqueous-phase photolysis and OH reactions to the total loss of pyruvic acid in the multiphase system (eq 17). (top) Fractions of total loss at LWC = 17.6 μg m−3 as functions of pH assuming (a) KH* = 2 × 109 M atm−1 and (b) K*H = 3.1 × 105 M atm−1. (bottom) Fractions of total loss at pH 3 as functions of aerosol water mass assuming (c) K*H = 2 × 109 M atm−1 and (d) KH* = 3.1 × 105 M atm−1.

corresponds to a typical order of magnitude in the atmosphere when deliquesced aerosol particles are present. In sensitivity studies we increased this value to 0.5 g m−3 (droplet diameter = 10 μm, Na = 100 cm−3), a concentration typical for clouds. We did not consider any solutes other than OH and pyruvic acid in our simulations (i.e., any effects on uptake or reaction rates due to ionic strength effects were ignored). The uptake of pyruvic acid and the OH radical into aqueous particles was described kinetically by the resistance model.75 All of the reaction and uptake parameters are summarized in Table S3 in the Supporting Information.37,47,76−78 The thermodynamic partitioning of soluble compounds between the gas phase and the dilute aqueous phase is often described by Henry’s law. However, simultaneous measurements of pyruvic acid and related compounds in the gas and particle phases have shown that these compounds are partitioned much more strongly into the particle phase than expected on the basis of Henry’s law.68,69,79,80 Therefore, their fractions in the particle phase as related to the total budget (gas phase + condensed phase) can be substantial and could potentially exceed the amount in the gas phase. In order to capture these effects and contrast them with the results expected for ideal systems (dilute aqueous phase), we used two different (effective) Henry’s law constants, KH* = 3.1 × 105 M atm−1 and KH* = 2 × 109 M atm−1. The former is a standard Henry’s Law constant,81 and the latter value was chosen in such a way that gas/particle partitioning as observed in the atmosphere was reproduced.68,69,79

Partitioning increases with increasing pH when pyruvic acid dissociates (with pKa = 2.18), and the effective Henry’s law constants, including dissociation, were calculated as follows: ⎛ Ka ⎞ * = KH*⎜1 + KH,eff ⎟ ⎝ [H+] ⎠

(16)

These effective Henry’s law constants, KH,eff * , already include hydration (KHyd) (i.e., we did not consider any additional term to eq 16). The resulting particulate pyruvic acid concentrations are on the order of 10−5 M (K*H = 3.1 × 105 M atm−1) and 10−2 M (KH* = 2 × 109 M atm−1). The lower concentration is similar to that of organic acids in cloud or fogwater.82,83 Under the assumption that all particulate pyruvic acid (or pyruvate) is dissolved, the upper limit of this concentration range might correspond to pyruvic acid concentration in aerosol water69 and is comparable to the range used in the above laboratory experiments. Since the photolysis rates experimentally derived in this work for aerobic and anaerobic conditions differ by only a factor of 2 and the aim of our model studies was to seek an order-of-magnitude estimate, any uncertainties introduced by the photolysis rates are expected to be small. The aqueous photolysis rates were linearly scaled-up from the experimental conditions (0.1043 W m−2 at λ = 325 nm) to those of sunlight at a zenith angle of 63° using the corresponding actinic fluxes at this wavelength.84 As a result, the aqueous photolysis rate constant (J in the presence of oxygen; Table 2) was multiplied by a factor of ∼15. The zenith angle used here was chosen arbitrarily but did not dramatically 8512



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change the Jaq value unless it had an extreme value (near 0° or 90°). The gas-phase photolysis rate constant was calculated on the basis of spectra by Horowitz et al.,47 and the OH rate constants were taken from the literature.10,76,85 In agreement with results from Pocker et al.67 and those discussed above, we assumed hydrated fractions of 58%, 12.5%, and 6.3% at pH 1, 3, and 6, respectively. While kOH,aq represents an overall rate constant for the reactivity of the mixture of the keto and diol forms, the photolysis occurs only on the keto form, and thus, the pyruvic acid fraction used in the model is reduced by its hydrated fraction. In order to initialize the box model, we assumed a constant OH concentration (5 × 106 cm−3) and a mixing ratio of 0.1 ppb pyruvic acid in the gas phase, in agreement with measurements in urban air masses.19 It should be noted that the choice of initial pyruvic acid concentration does not greatly affect the results (as discussed in the following section) since we seek only trends in the relative contributions of the four loss pathways. Model Results. In the following we discuss the relative contributions of all four processes (gas- and aqueous-phase photolyses as well as gas- and aqueous-phase OH reactions) in the multiphase system. Here the “fraction of total loss” for each process is related to the total loss, that is, the sum of all of the loss rates:

likely represent upper and lower limits of realistic partitioning of pyruvic acid into the atmospheric water phase, respectively. The overall pyruvic acid loss rate in the multiphase system also depends on the size of the chemical reactor, or, more specifically, on the amount of water present in the system (LWC in eq 17). In order to explore the role of LWC in determining the relative contributions to the overall loss rates, we performed simulations at a fixed pH of 3 with water volumes of 5.5 μg m−3, 17.5 μg m−3, 53 μg m−3, and 0.5 g m−3, with the first three values being typical for aerosol water and the latter one for clouds. Figure 5c indicates that at high LWC, the aqueous-phase photolysis of pyruvic acid is of similar importance as the gasphase photolysis. With increasing water mass, the overall importance of the aqueous-phase photolysis increases from ∼5% to ∼40% while the aqueous-phase OH reaction contributes a factor of 2−4 less. When the fraction of pyruvic acid in the aqueous phase is less than 1% (K*H = 3.1 × 105 M atm−1 and water mass ≤ 17.6 μg m−3; Figure 5d), the increase in the importance of the aqueous-phase photolysis scales linearly with the LWC, while the gas-phase photolysis dominates the loss. The last set of bars in Figure 5d shows results from a much larger water mass (0.5 g m−3), which can be considered typical for clouds. The resulting dissolved pyruvic acid fractions for a small K*H (3.1 × 105 M atm−1) are similar to those predicted with a high effective Henry’s law constant and a smaller water volume. Under these conditions, the aqueous-phase photolysis is the dominant sink for pyruvic acid (∼90%). Overall, the results in Figure 5 show that the aqueous-phase photolysis can be an important sink process for pyruvic acid in acidic aerosols or droplets with a high enough LWC in the atmosphere. In a series of previous exploratory studies, it was suggested that (i) aqueous-phase losses of pyruvic acid might be significant compared with gas-phase losses86 and (ii) photolysis might be at least as important as the OH reaction in the aqueous phase.87 These statements are consistent with our findings. In the second study, however, it was assumed that the gas- and aqueous-phase photolysis rates can be scaled by each other, with the latter one having a lower rate. Our present study has shown that this approach is not applicable. Since the chemical mechanisms of the gas- and aqueous-phase photolyses are different, Jaq might be much higher than Jgas under certain conditions and thus play an important role in loss of pyruvic acid, even if the aqueous-phase volume is very small compared with the gas-phase volume. While not explored by our model studies, the transition from the gas phase to the aqueous phase dominating pyruvic acid losses has consequences for the modification of the chemical composition of the multiphase system. Under conditions where gas-phase losses dominate, fragmentation of pyruvic acid leads to small volatile products,37 which do not affect the particle phase composition. When sufficient aerosol water is available for the aqueous-phase photolysis to be as important as or more important than the gas-phase photolysis, the partitioning and subsequent aqueous photolysis of pyruvic acid leads to less volatile compounds (small polymers) that might remain in the particle phase upon water evaporation and contribute to secondary organic aerosol loading.

total loss = [PA]{k OH,gas[OH]gas + Jgas + (k OH,aq[OH]aq + Jaq )LWC}

(17)

where LWC is the liquid water content (aqueous volume/gas volume). Both K*H,eff and the pH determine the fraction of pyruvic acid that is present in the particle phase. The numbers at the bottom of Figure 5a (aq/gas) show that ∼30% of all pyruvic acid is predicted to be in the particle phase, which is in rough agreement with findings on gas/particle partitioning on ambient particles.79,80 Figure 5a shows that for the assumption of a high partitioning constant (KH* = 2 × 109 M atm−1) in the presence of an acidic aerosol (pH 1), the aqueous-phase photolysis is equally as important as the gas-phase photolysis. The fraction of total loss through aqueous-phase photolysis decreases with increasing pH. The gas-phase photolysis dominates at pH 6, as might be encountered in marine aerosols, where both aqueous-phase processes make minor contributions to the loss, with ∼0.01% by photolysis and ∼8% by OH reaction. With increasing pH, the importance of the reaction with OH radical increases because of the higher rate constant of OH with pyruvate relative to pyruvic acid (Table S3 in the Supporting Information). In agreement with previous findings, the loss by OH in the gas phase is negligible under all conditions.37 These trends show that pyruvic acid photolysis in the aqueous particle phase might be an important sink under conditions where the undissociated acid is present (pH < 3), conditions typical of continental aerosols. The particulate fraction is greatly reduced in acidic aerosol if the partitioning is described by the Henry’s law constant K*H = 3.1 × 105 M atm−1 (Figure 5b). Only at pH 6, when the effective Henry’s law constant (eq 16) is higher by several orders of magnitude than KH*, is there a significant fraction of pyruvic acid (pyruvate) present in water. Since the parameters that determine the partitioning of pyruvic acid between the gas and particle phases are not clear and thus cannot be extrapolated to various conditions, panels a and b of Figure 5 8513



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ASSOCIATED CONTENT

S Supporting Information *

Calibration data for UV−vis and 1H NMR analysis; UV−vis spectra, kinetic data, and tabulated Jaq values; additional 1H NMR spectra and data; complete tabulated values for KHyd; tabulated model parameters; and full presentation of the kinetic analysis described above. written out in full. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Pascal Renard for valuable discussions regarding the calculations for this paper. This work was supported by grants from the National Science Foundation. E.C.G. and R.J.R. also acknowledge funding from National Aeronautics and Space Administration Earth and Space Science Graduate Fellowships. B.E. acknowledges support from NOAA’s Climate Goal, and A.M. acknowledges support from CIRES at the University of Colorado and the French National Research Agency ANR through the CUMULUS Project (ANR2010-BLAN-617).

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