Kinetics and mechanism of the photooxidation of formaldehyde. 2

Kinetics and Product Yields of the OH Initiated Oxidation of Hydroxymethyl ... C. Rivera-RiosFrank N. KeutschJason M. St. ClairThomas F. HaniscoKristi...
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J. Phys. Chem. 1989, 93, 2375-2382

2375

Kinetics and Mechanlsm of the Photooxidation of Formaldehyde. 2. Molecular Modulation Studies J. P. Burrows, G. K. Moortgat,* G. S. Tyndall, Air Chemistry Department, Max Planck Institut fur Chemie, D 6500 Mainz, FRG

R. A. Cox,* M. E. Jenkin, G. D. Hayman, Combustion Centre, Harwell Laboratory, Didcot, Oxfordshire, UK

and B. Veyret* Laboratoire de Chimie Physique A (UA 348 and 503, CNRS), UniversitP de Bordeaux 1 , 33405 Talence Cedex, France (Received: March 31, 1988; In Final Form: September 12, 1988)

Transient species in the photooxidation of formaldehyde in air have been investigated by using the technique of modulated photolysis-long path kinetic spectroscopy. A transient absorption spectrum consisting of a broad band with a maximum near 230 nm was observed, which is attributed to the HOCHZOzradical formed by the reaction HOz + HCHO HOCHz02 (1). The equilibrium constant, K1*, was estimated from these measurements of the HOCHzOz radical together with cm3molecule-I measurements of HOz obtained with diode laser infrared absorption spectroscopy: K1* = 4.0 (+4.0, -2.0) X at 298 K. Kinetic measurements of the two radicals allowed determination of the rate coefficients at 298 K for the following reactions: HOCHzOz + HOz products (3), k3 = (1.2 f 0.3) X lo-" cm3 molecule-l s-l; 2HOCHZOz HCOOH + CHz(OH)z O2(4b), klb = (5.6 f 2.8) X cm3 molecule-' s-I. The alternative pathway, 2HOCHZOz 2HOCH20 + O2(4a), followed by HOCHzO + Oz,leads to the chain generation of formic acid. The rate coefficient for reaction 4a, kla = (5.5 f 1.1) X cm3 molecule-' 8,was determined from the yields of formic acid.

--

-

+

Introduction

In the preceding paper, we have reported a flash photolysis-UV absorption study of the reaction of the HOz radical with formaldehyde.' The results gave strong support for the following mechanism based on an addition reaction of H 0 2 with HCHO, which has been proposed following the work of a number of groups on the photooxidation of formaldehyde.2" HOz

+ HCHO

[HOOCH20] HOz

ROz ROz

+ HO2

+ ROz

-

+ H02

-

--*

HOCHzOz (=ROz) H202

+0 2

HOCHZOZH

+0 2

+0 2 HCOOH + CH2(0H)2 + 0 2 RO + 0 2 HCOOH + HOz 2R0

-

(1) (2)

spectroscopy. There are several problems of calibration associated with this latter technique, and there was a need for further studies of the kinetics and equilibrium constant in this system. In this paper we report the results of a study of the HOZ + H C H O system using modulated photolysis with long path absorption kinetic spectroscopy in the infrared and ultraviolet spectroscopic regions to investigate transient spectra and kinetics. The photooxidation of H C H O in air at 700 Torr and the C12 photosensitized oxidation of HCHO at pressures in the 2-10-Torr range were used to generate H 0 2 radicals in the presence of H C H O at room temperature. In the latter system the reactions occurring in addition to reactions 1-5 are

(3a) (4a) (4b) (5)

In this study spectroscopic evidence was obtained for the hydroxymethylperoxy radical, formed by addition of H02to HCHO, and kinetic measurements for the forward and reverse reaction for its formation enabled direct determination of the equilibrium constant K l * . The value was not in very good agreement with that obtained in another recently reported study,7 where the equilibrium constant K I * was determined by cryotrapping H 0 2 and ROZradicals and measuring their concentrations by ESR

Clz

+ hv

C1+ H C H O

-+

--+

2 C1

HC1+ H C O

HCO+02+HOZ+CO

(6) (7)

(8)

The equilibrium constant was determined by direct gas-phase measurements of HOz, R02, and HCHO, and information on the kinetics of the self-reaction of ROz and its reaction with H02 was obtained. Experimental Section

11x5

The details of the setup for the UV-IR spectrometer at the Max Planck Institut fur Chemie, Mainz, have been given in a paper on the photooxidation of acetaldehyde.* Figure 1 shows an illustration of the setup. The 44-L quartz reaction cell is traversed by two separate multipass optical probes, one for detection of absorption in the UV region and the other in the infrared. The cell is surrounded by fluorescent lamps. For the experiments on H C H O photolysis, up to six "sunlamps" emitting in the spectral region 280 < X C 370 nm were operated with square-wave modulation with a period of 6 s. The UV source was a 30-W deuterium lamp, and after multipassing the reaction volume, the monitoring beam was focused

(6) Barnes, I.; Becker, K. H.; Fink, E. H.; Reimer, A,; Zabel, F.; Niki, H. Chem. Phys. Left. 1985, 115, I . (7) Zabel, F.; Sahetchian, K. A,; Chachaty, C. Chem. Phys. Left. 1987, 134, 433.

(8) Moortgat, G. K.; Cox, R. A.; Schuster, G.; Burrows, J. B.; Tyndall, G. S., submitted for publication in J . Chem. SOC.,Faraday Trans. 2.

( I ) Veyret, B.; Lesclaux, R.; Rayez, M.-T.; Rayez, J.-C.; Cox, R. A,; Moortgat, G. K. J . Phys. Chem., preceding paper in this issue. (2) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. Chem. Phys. Left. 1980, 72, 72. ( 3 ) Su, F.; Calvert, J. G.; Shaw, J. H. J . Phys. Chem. 1979, 83, 3185. (4) Veyret, B.; Rayez, J.-C.; Lesclaux, R. J. Phys. Chem. 1982, 86, 3424. (5) Moortgat, G. K.; Seiler, W.; Warneck, P. J . Phys. Chem. 1983, 78,

0022-3654/89/2093-2375$0 1.5010

0 1989 American Chemical Society

2376 The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 UV

- IR

MULTIPATH

Burrows et al.

PHOTOCHEMICAL

SPECTROMETER

Cu G e DETECTOR

BOMEM

CONTROLLER

Figure 1. Schematic diagram of the MPI UV-IR multipath photochemical spectrometer.

f

5 ; l j n g b l e dsa2e lsier LCM

i

Lose'

Io"I.cl

\ r = M o d e s s r l n'; meddle

~ - ~ c f i c c l r o ~ ~0' ;c i- g Z C l e O e ' e c l o -

Figure 2. Schematic diagram of the Harwell tunable diode laser IR-UV photochemical spectrometer.

on the entrance slit of a 0.25-111 monochromator (Spex), and detected on a photomultiplier tube. The spectral slit width was 5 nm. Absorption-time profiles obtained during the modulated photolysis were fed to a signal averager (EG&G Model 4203) and processed by an Apple I1 minicomputer. For the infrared measurements, a Bomen DA03.0 1 Fourier transform infrared (FTIR) spectrometer was employed. A KBr beamsplitter and closed-cycle liquid-helium-cooled Cu-doped germanium detector were used to obtain spectra from 400 to 4000 cm-' at 1-cm-' resolution. The experiments were all conducted in a static mode, the gases being introduced to the cell from a grease-free vacuum system. HCHO, obtained by heating paraformaldehyde, was introduced directly into the cell through a trap at -78 OC to remove water and was measured by UV absorption and pressure. High-purity air was used as diluent, and a total pressure of 700 Torr was used for all experiments. The temperature of the cell was not controlled and was 303 f 3 K. The Harwell tunable diode laser infrared spectrometer was used for quantitative measurements of HO,, HCHO, and HCOOH in the photolysis of Cl,-HCHO-O, mixtures (Figure 2). The photochemical reactions were conducted in a 20-L cell made of Pyrex (100 cm long X 15 cm in diameter), with internally mounted gold-plated mirrors that provided path lengths for the infrared analyzing beam of up to 100 m by using multiple reflections. The gases were analyzed by a UV beam from a 30-W Xe arc lamp (Applied Photophysics, Ltd.), which made two passes, giving a path length of 214 cm, before it was dispersed by a double monochromator (Spex doublemate) and detected by a photomultiplier. Infrared radiation was obtained from a Pb-Sn-Te diode laser, tunable in the region 1030-1125 cm-' in modes

typically covering 0.5 cm-I. The laser was mounted in a spectrometer (Laser Analytics LS3) that provided facilities for cooling the diode laser to -12 K in a closed-cycle H e cryostat, for collimating the radiation, and for calibrating the laser frequency by using the combination of an air spaced etalon and known transitions in a reference gas. The laser was tuned by using well-stabilized temperature and current controllers and the radiation detected on a Hg-Cd-Te detector maintained at 77 K. Gas mixtures were introduced into the cell from a vacuum system. For photochemical experiments, mixtures containing C12, HCHO, and O2 flowed through the vessel at pressures approximately between 2.0 and 10.0 Torr and with a residence time of approximalely 10-30 s. The temperature of the vessel was 298 f 2 K. Entry and exit through several ports ensured that the gases in the cell were well mixed under the operating conditions. The cell was illuminated by three "black lamps" (Philips 40-W 4-ft TL/40/08) emitting light in the region 310 < X < 400 nm, powered by a special direct current supply providing square-wave modulation at selected frequencies of 0.2-5 Hz. The lamps were mounted radially around the cell. For measurement in the infrared region of HCHO and HCOOH conventional absorption spectroscopy was employed. Standard mixtures were prepared and the absorption by a selected rotational line measured by sweeping the laser frequency through the line. The laser beam was chopped mechanically at 400 Hz and detected with a lock-in amplifier. Standard mixtures of H C H O were prepared, with UV absorption at 338.8 nm and 0.675-nm resocm2 molecule-'). HCOOH mixtures lution (uHCHO = 5.3 X were prepared by dilution in N2 of a measured pressure of HCOOH with correction for the presence of formic acid dimer. All infrared absorption coefficients were measured at the appropriate total pressure with N2 used as diluent. For calibration and setting up of the infrared absorption detection of H 0 2 , the photolysis of C12-CH30H-02 mixtures was employed to provide known concentrations of this radical, modulated at frequencies around 0.5 Hz. A laser mode covering two 514) and 1110.2869 HO, absorption lines at 1110.254 (F2 6,, cm-I (F, 615 514) was ~ e l e c t e d . ~To improve sensitivity, these lines were detected in a first-derivative mode, the laser frequency being modulated by a low-amplitude triangular wave of 1-kHz frequency. The low-frequency chemical modulation of the H 0 2 absorption in the intermittent photolysis could be readily observed on a fast-response chart recorder when the laser frequency was coincident with the transitions. For time-resolved measurement of HO,, the laser frequency was fixed at a point corresponding to the maximum amplitude

-

-

(9)Johns, J. W. C.; McKellar, A. R. W.; Riggin, M. J . Chem. Phys. 1978, 68, 3957.

Molecular Modulation Study of H C H O Photooxidation

20

The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2377

I

TABLE I: Steady-State Absorptions and Decay Kinetics for Transients in the Photolysis of HCHO-Air Mixturesa

steady-state ~O-IS[HCHO], absorption XlO' molecule cm-) 220 nm 250 nm 2.2 5.2 17.1 24.0

,

- 3'

I

I

3

6 9 Time (seconds1 Figure 3. Absorption (In Io/I)time profile (A = 250 nm) for the HOCH20, radical, formed during 0.17-Hz modulated photolysis of an HCHO-air mixture: pressure, 700 Torr; [HCHOIo= 2.4 X 10l6 mol-

ecule ~ m - ~ . of the first-derivative signal of the H 0 2 absorption. The firstderivative signal together with a known offset voltage was fed to a multichannel waveform analyzer, which averaged the signal for successive photolysis cycles. The absorption coefficient for H 0 2 , )determined from at a particular operating condition ( ~ ~ 0was measurement of the ratio k 2 / u , where k2 is the rate coefficient for the reaction HO2

+ HO2

-

H202

+0 2

(2)

which is known to have a value of (1.6 f 0.2) X cm3 molecule-' s-' at 300 K and 1 2 0 Torr of pressure.lo The ratio k 2 / uwas determined from time-resolved H 0 2 absorption in the modulated photolysis of C12-CH30H-02 mixtures. The absolute cross section for the F,, 615 SI., line was approximately 1.8 X lo-'* cm2 molecule-'; by use of the first-derivative mode, a detection limit of H02 of approximately 1 X lo9 molecule cm-3 was achieved with averaging over 100 photolysis cycles. One of the problems encountered in this work was the difficulty in handling gaseous formaldehyde, because of its tendency to polymerize on glass and other surfaces. In all of the current studies HCHO was produced when required by heating laboratory grade paraformaldehyde. By careful control of the temperature of the paraformaldehyde, a constant partial pressure of HCHO gas could be maintained in the system. Water, which is also given off from the paraformaldehyde, was removed by passing the gas through a U-tube cooled to -78 OC. The dried H C H O gas then passed into the reaction cell inlet through a Teflon stopcock, which could act as a restriction to the flow. Pure C12was taken directly from a cylinder (Imp. Chem. Industries) in order to maintain the required high concentrations at low total pressure. For the low-pressure experiments N2 and O2 were used as carrier gases and were taken from cylinders (British Oxygen Co., Ltd.). N2was of high-purity grade and 02, of breathing grade. Methanol was introduced to the system in a stream of O2passing through a bubbler of pure methanol (BDH, Analar grade) maintained at 0 OC to give the required low partial pressure of C H 3 0 H . +-

Results Photooxidation of HCHO-Air Mixtures at 700-Torr Pressure. Mixtures of H C H O (approximately 0.1 and 0.8 Torr) in air at 700-Torr total pressure were photolyzed, and the growth of products was observed by FTIR. Photolysis of H C H O was accompanied by the formation of C O and HCOOH, the relative rate of formation of the latter being noticeably greater at 0.8 Torr. Additional weaker infrared spectral features due to H202and H20 were observed but not the hydroperoxide HOCH202H,which has been reported from previous studies of H C H O photooxidations. (10) De More, W. B.; Margitan, J. J.; Molina, M. J.; Watson, R. T.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R. Chemical Kinetics and Photochemical Data for Use in Stratospheric Modelling, Evaluation No. 7; J.P.L. Publication, 1985, 85-37.

2.0 3.10 4.61 5.86

0.80 1.89 3.57 5.28

1o6ko/u, cm s-I 220 nm 250 nm 1.43 1.21 1.53 (f0.12)b 0.85 (f0.20) 0.63 (f0.25)

"Total pressure = 700 Torr; temperature = 303 f 3 K. bError limits are two standard deviations from least-squares regression on plots of (absorbance)-' vs time. Rapid photochemical and heterogeneous decay of this species has been reported, and HCOOH is the major product of decomposition of this peroxide. The radical species in the photooxidation of H C H O were investigated by using the molecular modulation technique with modulation at 0.16 Hz. Absorption-time profiles at selected wavelengths in the 21 5-275-nm region were recorded in the modulated photolysis of HCHO-air mixtures containing several different H C H O concentrations in the range (2-26) X lOI5 molecule cm-3, with the total pressure constant at 700 Torr. Transient absorptions showed a characteristic rise and fall during the alternating photolysis and dark periods, which in spectral regions where products and reactants absorb was superimposed on a changing base line. Figure 3 shows a typical waveform recorded at 250 nm where absorption due to products was negligible. The amplitude of the modulation for a given set of conditions gives a measure of the absorption cross section while the shape of the waveform gives kinetic information. Analysis of the waveforms according to the previously described procedures" showed that the radical kinetics followed second-order to a good approximation. The steady-state absorptions and the ratio of the overall second-order rate coefficient to the absorption cross section kola (defined by -d[R]/dt = kO[Rl2) for two wavelengths, 220 and 250 nm, are shown in Table I. It will be seen that although the absorptions at the two wavelengths shown increased with increasing [HCHO], the absorption at 250 nm increased more rapidly than at 220 nm, indicating a change in radical population. The absorption cross section ratio ~ 2 2 0 / ~ 2 5 for 0 H 0 2 is 8.01° whereas the maximum observed ratio of steady-state absorption at these two wavelengths was only 3, indicating that one or more absorbing species additional to H 0 2 were present, even at the lowest H C H O concentration. The value of k o / u declined significantly with the increase in [HCHO], indicating that radical kinetics were also changing. At the highest H C H O concentration, modulated absorption was measured at 5-nm intervals in the range 215-280 nm. Accuracy at short wavelengths was diminished by the presence of strong absorption due to HCOOH product, and in order to determine the steady-state absorption of the transient, a correction had to be made for the product contribution, based on the observed rate of change of product absorption when the radical was in steady state. At wavelengths below 240 nm significant H 0 2 absorption may also contribute to the transient spectrum. This amount of H 0 2 can only be deduced from knowledge of the equilibrium constant K I * , which according to the results reported in the cm3 previous paper,' has a value of approximately 4 X molecule-' at 303 K, the temperature of these experiments. Correction to the transient absorptions at X < 240 nm was made by assuming H 0 2 contribution at 260 nm was zero and by using the aforementioned value of K l * . The maximum correction (at 215 nm) was only 7% of the total absorption, and therefore the spectrum is not very sensitive to the H 0 2 correction. The resultant transient absorption spectrum is plotted in Figure 4, together with the spectrum obtained by flash photolysis reported in our previous (1 1 ) Cattell, F. C.; Cavanagh, J.; Cox, R. A,; Jenkin, M. E. J . Chem. Soc., Faraday Trans. 2 1986, 82, 1999.

Burrows et al.

2378 The Journal of Physical Chemistry, Vol. 93, No. 6, 1989

,

"O

0

5!

71

0

HG2 HCHO +

I

1

I

1

1

I

0

5

10

15

20

[HCHGI molecule c W 3

Wavelength l n m l

Figure 4. UV absorption spectrum of HOCH200 obtained from photolysis of HCHO-air mixtures, after correction for HCOOH product absorption and H 0 2 absorption (based on value of K,* = 4.0 X

cm2). Line shows spectrum obtained from flash photolysis of C12-HCHO-02 mixtures as described in previous paper.

45

c

x

Figure 6. Ratio of steady-state concentrations of H02, formed during modulated photolysis of CI2-HCHO-O2 mixtures, as a function of

[HCHO]. [HO,], is the observed steady state of H02 when CH30H was under used as a source of H02,i s . [HCHO] 1.0 X 10l6 molecule cmT3)was photolyzed at a frequency of 0.5 Hz.

Molecular Modulation Study of H C H O Photooxidation

The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2379

TABLE II: Kinetic and Steady-State Parameters for R 0 2 Radicals"

TABLE 111: Calculated Equilibrium Constant K1* from UV Absorption Measurements in the Photooxidation of HCHO in Air at 303 -+ 3 K and 700 Torr concn, molecule cm-3 10'6K1*, cm3 HCHO R02 H02 molecule-I 2.2 X lOI5 0.89 X IO" 1.31 X 10" 3.10 5.2 X lOI5 2.41 X IO" 1.18 X IO" 3.93 17.1 X I O l 5 4.79 X IO" 0.72 X 10" 3.89

cm-) A, 1.18 X 10l6 6.97 X lo4 6.35 X lo5 1.95 X 10l6 7.56 X lo4 6.88 X 10'

3.88 X 3.16 3.23 X lo-'' 2.52 av o (250 nm) = 2.85 X

'Conditions: temp, 296 K pressure, 2.15 Torr; X = 250 nm; [CI,] = 8.85 10" molecules k, = 4.6 X 10" s-l. ko defined by - d[RO2I2/dr= 2ko[R0J2. X

Figure 7 shows the time dependence of this absorption, which is seen to show behavior similar to that of HO2, Le. rising to and falling from a steady state with a half-life of approximately 100 ms. Also shown in Figure 7 is the time dependence of HCOOH during a singte photolysis cycle, measured on the HCOOH absorption line, which was adjacent to that of H 0 2 at 11 10.3 cm-'. The HCOOH shows behavior typical of a product of a radical reaction; its formation rate increases with time as the radical builds up to steady state, and then on cessation of photolysis, continues to form but at a decreasing rate as the radical decays away. This shows clearly that formic acid is a product of the R 0 2 (or H02) radical reactions. Table I1 shows the steady-state concentrations of the R 0 2 radical measured in these experiments together with values of ko and u obtained by assuming second-order kinetic behavior for R 0 2 , which was approximated well at these higher [HCHO]. The basis for this analysis has been described previously." The rate of production of the HOZradical was obtained from the Clz photolysis rate, which was determined independently from measurements of the rate of loss of C12when static mixtures of C12-H2-02-N2 were photolyzed. Note from Table I1 that there is little change in the ROz steady state with an increase in HCHO, indicating that the radicals are predominantly R 0 2 in this H C H O concentration regime. The average value obtained for the absorption cross section of ROz is in good agreement with that obtained at 250 nm from the flash cm2 molecule-'. photolysis experiments, i.e. 3.1 X Estimation of the Equilibrium Constant Kl *. Measurement of the steady-state concentrations of ROZ and HOZ from the modulated absorptions in periodic photolysis can be used to determine KI* directly, assuming that the equilibrium between H 0 2 , HCHO, and the ROZradical was maintained on the time scale of the kinetic measurements. There is strong evidence from flash photolysis studies reported previously" that the forward and reverse reactions are rapid enough for this assumption to remain valid at the prevailing conditions in these studies. Thus: [ROJ = K1*[HCHO][HO2]

(i)

The measurements of R 0 2 and HO2 in the C12-photosensitized oxidation of H C H O at an H C H O concentration of 1.2 X 10I6 molecule cm3, presented in the previous section, were used to calculate Kl*. Using the value of uRo2= 3.1 X cm2 molecule-' (determined in the flash photolysis experiments)' and the HOZcalibration determined in this study, we obtain for [HCHO] = 1.2 x 10l6 molecule cm4: [RO2lm= 1.04 X 10l2 molecule cm-3 [HO,],, = 2.18 X 10'' molecule cm-3 and

KI* = 4.0

X

cm2 molecule-' at 298 K

The absolute accuracy of this single determination is no better than f a factor of 2, but nevertheless it agrees well with the value of Kl* = 4.5 X cm3 molecule obtained directly from the rates of the forward and reverse reaction (1) as measured by flash photolysis. A further estimate of KI* can be obtained from the steady-state absorptions at 220 and 250 nm in the H C H O photooxidation experiments at 700 Torr shown in Table I. The steady-state R 0 2 and H 0 2 concentrations can be evaluated if the absolute cross

-

0

_--_ _ * - -

----

I

I

0

5

10 15 [HCHOI molecule ~ r n - ~ x

20

,

~

Figure 8. Quantum yields for HCOOH formed during photolysis of Cl2-HCHO-O2 (filled points) and C12-CH30H-02 (open points) mixtures, as a function of [HCHO]. Filled line shows simulation with kdP = 5.5 X cm3 molecule-' S-I, and broken lines indicate effect of changing kla by f20%.

sections of the two radicals are known for both wavelengths, by solution of the following simultaneous equations:

+ ulR[R02])l A2 = absorption (220 nm) = ( u , ~ [ H O ~+] uzR[R02])1

A I = absorption (250 nm) = (ulH[HO2]

(ii) (iii)

I = path length, 2422 cm Literaturelo values were as follows for H 0 2 : uzz0= 4.0 X cm2 molecule-' and u250/u220= 0.125. For ROz we estimated a = 1.2 from the spectrum shown in Figure 4, and ratio u220/u250 we used the above-mentioned value of uRO2at 250 nm. Table 111 shows the results of these calculations, which are clearly consistent with the value of Kl* obtained from the flash photolysis study and the measurements in the CI2-HCHO-O2 system. The value of K1* shows no significant variation over an 8-fold change in HCHO concentration, providing further support for the assumption that equilibrium is established. Quantum Yieldsfor HCOOH Formation. The quantum yield for HCOOH formation was determined in the C12-HCHO-02 system at a total pressure of 2 Torr. The quantum yield 0 is defined as @ = [HCOOH] /nHo2

(iv)

where nH02 is the number of H 0 2 radicals produced in the reaction time, t , (corresponds to average residence time in the cell), calculated from the amount of C12 photolysis. Concentrations of HCOOH and H C H O were determined by direct optical density measurements on their characteristic lines near 11 10.2 cm-I. Figure 8 shows the values of @ plotted as a function of [HCHO] . the quantum in the range (1-20) X lOI5 molecule ~ m - ~Initially yield increases rapidly and seems to start leveling off at higher [HCHO]; the highest values are well in excess of 1, indicating that HCOOH is formed in a chain reaction. The formation of HCOOH was also noticed in the photolysis of C12-CH30H-02 mixtures. This can result from the reaction of H 0 2with the relatively low concentrations of HCHO produced with H 0 2 in reaction 9. Use was made of this to determine @ CH2OH 0 2 ---c H C H O + HO2 (9)

+

at [HCHO] < 1 X loL5molecule cmW3.The amount of H C H O present could be changed by adjusting the extent of reaction

Burrows et al.

2380 The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 TABLE IV: Quantum Yields of HCOOH Formation at Low lHCH01 at 296 K and 10.4 rt 0.4 Torr photolysis rate, 10-15[HCHO], molecule s-I X molecule O(HC0OH) 0.22 0.096 1.24 0.40 0.12 2.23 0.17 3.11 0.55 0.27 4.06 0.72 0.30 5.23 0.93 1 .oo 0.39’ 4.30 1.25 0.41” 4.30 1.37 0.52” 4.30

“ Determined in the conventional way with Cl2-HCH0-O2 mixtures.

TABLE V Reaction Mechanism Used for Simulation of HCHO + H 0 2

Reaction System

reacn reaction no. 1 H02 + HCHO R02 -1 ROz HO2 + HCHO 2 H02 + HO2 H202 + 0 2 3a R02 HO2 4 ROOH 0 2 3b R02 + HO2 HCOOH + H2O + 0 2 4a R02 + R02 2R0 + 0 2 4b RO2 RO2 HCOOH + CH2(OH)2 5 RO + 0 2 HCOOH H02 6 C12 + hv C1 + C1 7 C1+ HCHO HCI + HCO HCO + 0 2 HO2 + CO 8

k (298 K), cm’ molecule“ S-I

-+

4

+

-+

+

-+

+

4

+

+

+02

+

6.6 X see text 1.6 X 7.2 x 10-12 4.8 X 5.2 X 7.0 X lo-” 3.5 x 1 0 4 4 4.5 x 10-3 (PI) 7.3 X lo-” 5.6 X

dependence at low [HCHO] are sensitive to the value off and at high [HCHO] to the value of k&. These parameters are also very sensitive to the value of K l * , but the equilibrium constant and the other rate parameters in eq v have all been determined reasonably precisely from the experiments discussed above and in the previous paper.’ Values off and k4, were determined by comparing curves generated by the function in eq v with the experimental data shown in Figures 8 and 9 with use of the following rate parameters (as is discussed later):

1 0

U 0

5. 05

K l * = 4.6

X 10-l6cm3 molecule-’

at 2 Torr and 298 K

k2 = 1.6 X 0.5

0

[HCHO] m o l e c u l e ~

1.0 m x - 10l5 ~

1.5

Figure 9. Quantum yields for HCOOH formation during photolysis of CI2-CH3OH-O2 mixtures. Full line shows computer simulation with the fraction of H 0 2 + HOCH202’reaction forming HCOOH + H20 + 0 2 as products, f = 0.4. Broken lines show effect of extreme values off.

occurring in the fixed residence time in the cell, by varying the photolysis rate with different [Cl,] and photolytic intensities (by varying the number of photolysis lamps). The “steady-state” HCHO was calculated from the production rate and the ”flow-out” term, which was determined independently by following HCHO decay from a measurable concentration present when illumination was stopped. Table IV shows the HCOOH quantum yields at low [HCHO] determined in this way. These data are plotted in Figure 9 and also in Figure 8 where they are seen to be consistent with the data from higher [HCHO]. There are at least three reactions providing routes to HCOOH formation in the H 0 2 HCHO system. The formation of HCOOH in a chain reaction can be explained by reaction 4a followed by reaction 5, as originally proposed on the basis of FTIR In addition the “terminating’! reaction k4bproduces HCOOH, together with methanediol, CH2(OH)2,postulated by analogy with the products of the equivalent channel in the selfreaction of methylperoxy radicals. A third route to HCOOH is the alternative channel in the H 0 , reaction with the hydroxymethylperoxy radical: RO2 H02 HCOOH + H20 + 0 2 (3b)

cm3 molecule s-’

k, = 1.2 X

cm3 molecule-l s-I

k4b = 7.0 X

cm3 molecule-’ s-I

and The curve in Figure 8 shows simulation of the data over the whole range of [HCHO] using a value off = 0.5 and three different values of k4a; the “best-fit” value is estimated to be given by

k4, = (5.5 f 1.1) X lo-’, cm3 molecule-’

s-l

at 298 K

Figure 9 shows simulation of the data at the lower HCHO concentration range where the shape and magnitude of the curve depend o n j Using the above values of k,-k4, the best fit is given by f = 0.40 f 0.15 It is therefore concluded that approximately 40% of the reaction of H 0 2 with R 0 2 gives HCOOH directly; the remaining 60% is assumed to form H O C H 2 0 0 H since this product has been positively identified by other worker^.^,^ Computer Simulation of HOz Absorption in C12-HCHG02 Modulated Photolysis. Determination of k,. The infrared diode laser absorption measurements provided an unambiguous measure of the shape of the concentration modulation waveform for H 0 2 and, within the limits of accuracy of the cross section determination, a measure of absolute H 0 , concentration. Over the HCHO concentration range (1-10) X lOI5, the amplitude of the modulated absorption waveforms is a strong function of the equilibrium constant, K I * , and the rate coefficient k,; the shape This reaction was included in order to explain the production of of the waveform depends on k3 at low [HCHO] and on K I * at formic acid at very low [HCHO], when [HO,] >> [RO,], and the higher [HCHO], although the latter dependence is rather the R 0 2 self-reaction is unimportant. weak. The general expression for @ H C m H obtained from steady-state In order to ascertain whether the mechanism gave an accurate analysis is fit to the experimentally observed H 0 2 waveforms, computer KI*fk3[HCHO] + (2k4, + ~ ~ ~ ) ( K I * [ H C H O ] ) ~ simulation of the kinetic system was performed with the Harwell @HCOOH = program FACSIMILE.^, The complete mechanism used in these 2kz + 2k3K*[HCHO] 2k4b(Kl*[HCHO])’ simulations is given in Table V together with the rate constant (v) for the elementary reactions. The concentrations of the reactant molecules (C12, HCHO, 0,) were fixed at the average concenHere f is the fraction of the ROz + HO, reaction that gives trations present in the cell, as measured during the experiments. HCOOH directly in reaction 3b. The solution of the differential equations governing the production Equation v predicts that at very low [HCHO], i.e. when 2k2 >> 2k3K*[HCHO], @(HCOOH) should increase linearly with [HCHO] and at high [HCHO] should approach a limiting value (12) Chance, E. M.; Curtis, A. R.; Jones, I. P.; Kirby, C. R. AERE Report R-8775; HMSO: London, 1977. of (2k4, + k&)/2k4b. Thus the values of @ and the functional

+

+

-+

+

The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 2381

Molecular Modulation Study of HCHO Photooxidation

30

1 /

[HCH01=1~72~10~~

1.0

3t

I

\

1.5

2.0

Time lsecondsl

Figure 10. Computer simulations of H 0 2 absorption profiles in modulated photolysis of C12-HCHO-02 mixtures. The broken curves show the effect of varying k3 and the equilibrium constant K,*.

and removal of H 0 2 , RO, and R 0 2was performed explicitly with no assumption concerning equilibrium in reaction 1, and therefore any effects on the time dependence of H 0 2 arising from the formation and decomposition of R 0 2 would be accounted for. The effect of varying KI* was investigated by using a fixed value of cm3 molecule-' s-l and varying the value of k-, kl = 6.6 X around a median value of 140 s-' corresponding to K1* = 4.7 X cm3 molecule-I. Figure 10 shows some typical simulated curves, illustrating the dependence of the shape of the waveforms at different [HCHO] on the values of k3 and K,* used in the simulations. In the figure the absolute magnitudes of the absorptions have been scaled to fit the experimental steady-state values. At high [HCHO], the shape was unaffected by the value of k3 but showed a weak dependence on Kl*; at low [HCHO] the shape was quite sensitive to k3, the best fit being obtained with k3 = (1.2 f 0.3) X lo-" cm3 molecule-I s-', this value being rather insensitive to Kl * in the range (2-10) X cm2 molecule-I. The amplitude of the absorption modulation was dependent on KI* at all [HCHO]. The best fits were obtained by using the values of K1* in the range cm3 molecule when the experimental value of (3.9-5.1) X the effective absorption cross section for H 0 2 was used. This result is in good agreement with that obtained by flash photolysis reported in the previous paper.' Determination of kQ. Knowledge of Ki* allows an independent value of k4bto be obtained from the overall second-order decay constant for ROz, ko, measured as a function of [HCHO] (data from Tables I and 11). Assuming equilibration of H 0 2 and R 0 2 , the differential equation for time dependence of R 0 2 can be written d[R02] B.KF ----..

1 + KF

dt

(2k2

+ k3KF + 2k4b(KF)2)[R02]2 ( KF(l + KF)

0

IO

where KF is the product Kl*[HCHO] and B is the total rate production of H 0 2 radicals by secondary reactions of photochemically generated H or CI atoms or HCO radicals. The overall second-order rate coefficient can be identified with the complex coefficient in the [RO2I2term, which gives the following ex-

30

Figure 11. Plot of the left-hand size of eq vii (see text) against H C H O concentration. Open points are from modulated photolysis of H C H O a i r mixtures at 700 Torr; half-filled points are from modulated photolysis of C12-HCHO-02 mixtures at 2.0 Torr.

value of k4 is (5.6 f 2.8) X cm3 molecule-' s-', which although less accurate, is in agreement with that derived from the flash photolysis resu1ts.l

Discussion The value of the equilibrium constant Kl* at room temperature determined in this study from measurement of "equilibrium" concentrations of H 0 2 and the hydroxymethylperoxy radicals RO2, as a function of HCHO concentration, confirms the value derived from measurement of the forward and reverse reactions, kl and k-,, reported in the previous paper.' The value of K1* is substantially lower than all previous estimates near room temperature but is consistent with the value reported at 273 K6 by Barnes et al., when the temperature dependence of Kl* is taken into account. A more detailed discussion of the values of K1* is given in the previous paper.' The present experiments also provide further demonstration that the reaction of H 0 2 with R 0 2 is relatively fast compared to the few other peroxy radical + H 0 2 reactions that have been studied kinetically at room temperature. In addition to the normally assumed peroxide product, HOCH202H,which has been identified by FTIR spectroscopy in previous we find strong evidence for a channel forming HCOOH directly, presumably via a six-membered ring intermediate: H

HOCH200 -4- HO2

- PH-d \p 0 -

Ho

4

20

[HCHO] molecule ~ m x' I ~O l 5

I

H

\c'

/ HO

-4- HOH

-

02

H

This mechanism would be similar to the reaction forming HCHO and H 2 0 for which we have recently found evidence in the analogous reaction of methylperoxy radi~a1s.I~The "termination" channel in the self-reaction of CH3O2 (eq 10) is probably the best 2CH302 HCHO C H 3 0 H + O2 (10)

-

+

(vii)

known example of this class of reaction channels in the low-temThis perature radical-radical interactions of peroxy radi~a1s.l~ type of reaction also occurs for higher alkylperoxy radicals at room temperature.' 1 ~ 1 5 ~ 1 6

A plot of the left-hand side of eq vii against [HCHO] is shown in Figure 11. The data are rather scattered, but the formation does increase with [HCHO]. Linear regression gives a slope of (4.5 f 2.3) X cm6 molecule-2 s-l (=2k4K*) and intercept of (1.27 0.43) X lo-'' cm3 molecule-' s-' ( = k 3 ) . The resulting

(13) Jenkin, M. E.; Cox, R. A.; Hayman, G. D.; Whyte, L. J. J . Chem. Sor., Faraday Trans. 2 1988, 84, 913. (14) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. J . Phys. Chem. 1981, 85, 817. (15) Kirsch, L. J.; Parkes, D. A.; Waddington, D. J.; Woolley, A. J . Chem. Soc., Faraday Trans. 1 1919, 75, 2678.

pression:

ko(l

2k2 + KI*[HCHO]) - = k3 + 2k4K1*[HCHO] KF

*

2382 The Journal of Physical Chemistry, Vol. 93, No. 6, 1989 Our flash photolysis work shows that k3 has a large negative temperature coefficient overall, but we cannot distinguish the temperature dependences of the two channels. Knowledge of the temperature dependence of the branching ratio would provide useful clues concerning the kinetics and mechanism of the reaction. These results show that the self-reaction of hydroxymethylperoxy radicals also occurs by two channels. The value obtained for the rate coefficient k4,, at 300 K confirms the flash photolysis resu1ts.I The reaction is a factor of 3-4 faster than the analogous reaction of CH302,10possibly reflecting the presence of a weaker C-H bond in the HO-substituted radical, allowing more facile transfer in a six-centered intermediate complex: H

\cP-"\o

,

I \

/ 'H-0'

I

Ho

CH2(OH)

The slower rate of the reaction, compared to the formation of HCOOH in reaction 3b, could be due to the steric hindrance effects of the larger CH2(OH) group compared to those of H. The "radical" channel in the self-reaction of the R 0 2 radical, reaction 4a, is a factor of 50 faster than the analogous reaction of the C H 3 0 2radical. The higher alkylperoxy radicals react in this way even more slowly, and moreover, appear to have positive activation energies. The thermochemistry of the alkylperoxy radicals is not sufficiently well-known to determine whether the reaction enthalpy AH' controls the activation barrier in these reactions, which are assumed to proceed via an R 0 4 R tetraoxide intermediate. It is clear from the rapid rate of reaction 4a at 298 K that there is little or no activation energy for this reaction of hydroxymethylperoxy, which is consistent with our knowledge of the thermochemistry of R 0 2 and R0,'s4 which predicts that reaction 4a is exothermic, Le. AHr'(R0,) > AHf"(R0). It is of interest to examine the implications of the measured rate and equilibrium parameters for the occurrence of the H 0 2 H C H O reaction in the atmosphere. The two main questions that arise are (a) is this reaction a significant sink for atmospheric H C H O and (b) does it provide a significant source of HCOOH? The rate a t which equilibrium between HO;, R 0 2 , and H C H O is achieved can be calculated from the rates of reactions 1 and -1 under atmospheric conditions. At a representative [HCHO] 2 X 10" s-l at 298 of 1 ppt (lower atmosphere), kl[HCHO] K. Reaction -1 is much more rapid ( 100 d),so the time for equilibrium to be established (=(kl[HCHO] + k-JI) is governed by the reverse reaction, and the equilibrium strongly favors H 0 2 and HCHO. Apart from reaction 1, the main reaction of the R 0 2 radical will be with NO,4 and HCOOH will be formed via the reactions RO2 NO R O NO2

+

N

+

RO

+0 2

-+

-+

+

HCOOH

+ HOz

(5)

(16) Anastasi, C.; Waddington,D. J.; Woolley, A. J . Chem. Soc., Faraday Trans. I 1983, 79, 505.

Burrows et al. The rate constant k l l has a value of (4.0 f 1.9) X lo-" cm3 molecule-' s-' at room t e m p e r a t ~ r e . ~ If [NO] = 1 ppb, a typical daytime value in the continental boundary layer, the removal rate of R 0 2 by reaction 1 1 can be estimated to be approximately 1.2 s-', Le. too slow to disturb the equilibrium. In the absence of NO, R 0 2 is expected to react via reaction 3, also leading eventually to HCOOH formation. The overall rate of conversion of H C H O to HCOOH is given by (viii) R = KI * [HCHO] [HOZ]kl1 [NO] For typical boundary layer daytime conditions, [HO,] I5 X lo8 molecule ~ m - giving ~ , a lifetime of H C H O with respect to this removal process of >25 days, which is negligibly slow compared to the other loss process operating, Le. photolysis and reaction with OH. Formic acid formation from this process is also very slow; even in the polluted boundary layer, with [HCHO] = [NO] = 10 ppb, the production rate of HCOOH calculated from eq viii is less than 0.08 ppb h-l. Other sources such as the ozone-alkene reaction must be responsible for the relatively high concentrations of formic acid that are present in photochemical pollution episodes.

Summary The results of the flash photolysis and molecular modulation experiments carried out in our studies of the H C H O + H 0 2 system have demonstrated that the original mechanism proposed for the photooxidation of formaldehyde2s3 is correct. We have observed the transient peroxy radical formed by isomerization of the initial adduct produced in the gas-phase reaction of H 0 2 to HCHO and have demonstrated the equilibrium of this addition reaction. The equilibrium constant is a factor of 10 or more lower at room temperature than has been previously suggested, but the reaction enthalpy, based on the temperature dependence of the equilibrium constant, is consistent with earlier theoretical estimates. The reactions of the new peroxy radical forming HCOOH and other products have been characterized. The rate coefficients of these reactons are much larger than those for analogous reactions of the methylperoxy radical, upon which earlier estimates were based. The results provide an interesting insight into the reactivity of peroxy radicals. The reaction of H 0 2 with formaldehyde is unimportant in the atmosphere, either as a loss process for HCHO or as a source of formic acid. Acknowledgment. This work was conducted within the framework of a "Stimulation Action" project financed by the Commission of the European Communities (Contract ST2J-0193). The work at Harwell was supported by the UK Department of the Environment. Registry No. HCHO, 50-00-0;HOz, 3170-83-0; HOCH202,278285 1-9; HCOOH, 64-18-6; 0 2 , 7782-44-7; C11, 7782-50-5. (17) Finlayson, B.; Pitts, J. N., Jr. Atmospheric Chemistry; Wiley: New

York, 1986.