2560
The Journal of Physical Chernlstty, Vol. 83, No. 20, 1979
R. A. Cox and J. P. Burrows
Kinetics and MechanDsm of the Disproportionation of
Hopin the Gas Phase
R. A. Cox and J. P. Burrows* Environmental and Medical Sciences Division, Atomic Energy Research Establishment, Harwell, Oxfordshire, United Kingdom (Received Aprll 4, 1979)
-
The kinetics of the reaction HOz + HO, HzOZ+ O2 (1)have been investigated over the pressure range 3-760 torr and the temperature range 273-339 K by using molecular modulation/UV absorption spectrometry to monitor HOz. HOz was produced by reaction with O2 of H or CHO generated by photolysis of Clz in the presence of either Hz or HCHO. kl was invariant with pressure above 25 torr and its temperature dependence is given by kl = (3.8 f 1.4) X exp((1250 f 200)/T) cm3molecule-l s-l (error = 2 sd). The corresponding value of the absorption cross section for HOz at the monitoring wavelength (220 nm) was 3.45 X cm2. At pressures 110 torr, kl decreased with falling pressure and its temperature dependence was reduced. The presence of water vapor increased the effectivevalue of kl,in agreement with other recent work. A mechanism is proposed for the overall reaction involving an intermediate Hz04molecule, which offers a plausible explanation of the observed effects of temperature and pressure.
Introduction The central role of the hydroperoxyl radical, HO,, in low temperature combustion and in atmospheric chemistry is now widely recognized. However, compared to other atom and free radical species in these systems, e.g., 0, H, and OH, quantitative information on the kinetics of elementary reactions involving the H 0 2 radical is relatively sparse. Until recently the only reaction of H 0 2 for which direct measurements of the rate constant had been reported is the mutual combination reaction HO2 + HO2 ---* H202 t 02 (1) Rate constants for numerous other reactions of H02have been obtained by indirect methods but in many cases the values have depended on rather complex chemical modeling and on a knowledge of the absolute value for kl.l Reaction 1 assumes an added importance in this respect, and a detailed characterization of the reaction pathway and an accurate knowledge of its rate constant as a function of temperature and pressure are required. Unfortunately, the data available at this time do not allow this. The first direct measurement of k l was made by Foner and Hudson2 who used a low-pressure flow system with mass-spectrometric detection of H02. The value obtained, kl = 3 X cm3 molecule-l s-l, was of limited accuracy but was substantially confirmed in a later and more extensive kinetic investigation by Paukert and Johnston3 using molecular modulation spectrometry. In the latter study the absorption spectrum of HOz in the gas phase was characterized both in the UV and IR spectral regions. The kinetic measurements were made primarily by using the UV absorption of H 0 2 at -220 nm and the measurements allowed determination of both hl and the absorption cross section, u H O ~ , as a function of wavelength. Hochanadel et al.4 also used UV absorption spectrometry to follow the decay of H 0 2following the flash photolysis of H20-Hz-O2 mixtures. Accurate second-order decay of HOz was observed after correction for absorptions due to product Hz02. Their basic data gave kl/uzlo nm = 1.40 X lo6 cm s-l and u = 6.8 X 10-ls cm2 (from the amount of H202 formed) but the quoted value of k l = 9.4 X lo-', cm3 molecule-l s-l is a factor of -3 larger than the previous values. An indication of the origin of this discrepancy comes from the work of H a m i l t ~ nand , ~ Hamilton and Lii? who used pulsed radiolysis of gaseous mixtures containing HzO in 2 atm of H2to produce HOP Their measurements 0022-3654/79/2083-2560$01 .OO/O
show a variation of the second-order decay parameter, [H20]are consistent with the previous flash photolysis work and those at low H 2 0 were close to Paukert and Johnston's3 value. Experiments were conducted to try and characterize the water vapor effect; it was concluded that formation of a gas-phase HO2-HZ0 complex was responsible for the apparent acceleration of the combination rate of HO,. If complex formation with H 2 0is kinetically significant for H02reactions, this could be of profound importance in the chemistry of H 0 2 in the lower atmosphere. In the present paper we describe some results from a reinvestigation of reaction 1, using the technique of molecular modulation spectrometry, with a view to determining the dependence of kl on temperature, pressure, and added gases including water vapor. Our approach was similar in concept to that of Paukert and Johnston3 but different in respect of the chemical system employed, the experimental setup, and the treatment of the results. HOz radicals were produced by the photolysis of C12 either in the presence of excess H2 and 02: Cl2 + hv C1+ C1 (2) kl/u, with H20concentration; the values at high
-
C1+ H2 H
-+
+ 02 + M
+H H02 + M
HCl -+
-
or in the presence of formaldehyde and 02: C1+ HCHO HC1+ CHO CHO + 02
HO2 t CO
(3)
(4) (5)
(6) In both systems the major products are HC1 and H20z, the latter resulting from reaction 1. We have already reported' measurements which indicated that, provided the concentration of H2 is high enough t o eliminate C1atom reactions which compete with (3), the simple mechanism involving (1)-(4) occurs at small extents of reaction. At low pressures this condition was not satisfied and also HOz formation by reaction 4 was too slow. For measurements of kl at total pressures 525 torr, the HCHO system was used. The rapid rates of the bimolecular reactions 5 and 6, h5 = 7.8 X lo-" cm3 molecule-I s-18t22 and k6 = 5 X cm3 molecule-' s-1,9-11ensured low [Cl] and efficient conversion of CHO to HOz. In the present work H 0 2 radical concentrations and lifetimes were measured by lock-in detection of the modulated absorption in the ultraviolet region near 220 +
0 1979 American Chemical Society
Disproportionation of H 0 2 in the Gas
Phase
The Journal of Physical Chemistry, Vol. 83,No. 20, 7979 2561
nm, which resulted from intermittent photolysis of the gas mixtures. This enabled determination of both the rate constant kl and the cross section for absorption by H 0 2 at the monitoring wavelength for a variety of conditions of temperature, pressure, and composition.
Treatment of Data In previous studies of the disproportionation of H02,the radical was observed to follow second-orderdecay kinetics. The equations describing this behavior in a system with intermittent photochemical production of H 0 2 are
Experimental Section The molecular modulation spectrometer and ancillary apparatus used in this work have already been described in some detail.12 Most experiments were conducted in a jacketed Pyrex vessel 120 cm long with 2.5-cm diameter quartz end windows. For the low pressure experiments (110 torr) a quartz cell, 120 X 4.0 cm, was used. This cell was coated internally with a thin layer of PTFE to minimize heterogeneous removal of H02, which proved troublesome at low pressures. Up to six fluorescent “blacklights” (Philips TL40/08,120 cm long) provided the square-wave modulated photolytic light source. Absorption was monitored on a beam from a D2lamp passing axially along the cell, and resolved on a double grating spectrometer (Spex Doublemate). The in-phase and inquadrature components of modulated absorption were detected on the previously described digital phase-sensitive detector.12 Gas mixtures were introduced to the reaction cell from a flowing stream of C12 and H2 (or HCHO) in an 02containing diluent in a manifold at atmospheric pressure. H 2 0 was introduced by passing a fraction of the diluent through a saturator containing distilled water at an appropriate temperature. The H 2 0 mixing ratio was determined from measurement of the relative humidity of the mixed streams, using a wet and dry bulb hygrometer. For most of the kinetic measurements at atmospheric pressure, the flowing mixture was stopped instantaneously by using electrically operated valves at each end of the vessel. The static mixture was then photolyzed and the modulated absorption measured after a 10-30-s warming period, an adequate sensitivity being obtained with a 30-100-5 measurement period. Measurements at low pressure were usually made on a flowing mixture with a cell residence time of -15 s. The overall extent of photolysis of C12 was never more than 10% and usually substantially less. Both the static and the flow technique gave identical results for otherwise similar conditions. The dissociation rate constant for C12, k2, was determined as a function of the number of fluorescent lamps activated, from measurements of the first-order decay of C12absorption at 310 nm in the presence of Hz and OB For this experimental study k2 was between 0.9 X and 1.9 X s-’ per lamp depending on age, and increased linearly with the number of lamps indicating good homogeneity of actinic radiation. In individual kinetic experiments the reaction rate was monitored by measurement of the formation of H202by its absorption at 220 nm (a = 2.8 X cm2molecule-’). Comparison of this rate with the calculated rate of C12dissociation allowed evaluation of the quantum yield of H202formation, 9(H202). Chlorine was taken from a cylinder containing 5% C12 in pure NP Formaldehyde was produced by passing a slow stream of 0 2 over paraformaldehyde heated to 85 “C. The HCHO/02 mixture was mixed with the diluent stream after passage through an acetone/dry-ice cooled trap. HCHO concentration was measured in the cell by monitoring its absorption at 303.8 nm. N2 (high purity), H2 (CP grade), and SFG (99.9%) were taken directly from cylinders. O2 (breathing grade) was passed over hot Cu turnings and soda-lime to remove any hydrocarbon impurities.
during illumination d[HO,]/dt = 2B - 2kl[HO2I2 (i) d[H02]/dt = -2k1[HO2I2
in the dark
(ii)
where 2B is the rate of photolytic production of H02. In the present work the value of B was assumed to be equal to the rate of photolysis of C12. Photodissociation of HCHO to produce H + HCO was negligible at the HCHO concentrations employed, i.e., 3-20 X 1015molecules ~ m - ~ . The absorption signals in the in-phase and in-quadrature channels in the digital phase sensitive detector are given by
P=
Q=
?[
“““[ 7
&7’2[H0 2] dt -
[HO,] dt]
J7
712
(iii)
J37/4[H02] 7/4 dt - ~ ~ ; ~ [ Hd0t ]2 ](iv)
where 1 is the path length, 7 the overall photolysis period, a the absorption cross section of H 0 2 at the monitoring wavelength, and C a calibration factor reflecting the sensitivity of the digital detector. At long photolysis periods the radical will reach a steady-state concentration after a short time relative to the “light” period and decay rapidly to near zero during the “ d a r k period. The absorption signal will be predominantly in phase and is given by
A,, = al(B/kl)’i2 As the photolysis period is decreased, the time to reach steady state becomes comparable with the photolysis period and the radical signal lags behind the light period. By integration of (i) and (ii) and substitution in (iii) and (iv), curves may be generated which give the variation of P and Q with 7 . A given combination of a and kl has a unique pair of curves for all B if the absorptions and photolysis periods are reduced by respectively dividing and multiplying by The characteristic form of the curves is exemplified in the illustrations of the experimental data given below. Solution of the equations for the curve crossing region when P and Q are equal gives 7,$’/2
= 2,2k,-’/2
A,, = 0.284A,,
Measurement of r0and A, allows preliminary estimates of k1 and a but optimum values of rate constants were obtained by fitting full curves to the data obtained over a range of modulation periods and radical production rates. In this work full curves were generated by numerical integration of the equations governing the radical chemistry and the operation of the detector with the Harwell computer program FACSIMILE.'^ Since the product of reaction 1, H202, possesses a sizeable absorption cross section at 220 nm, modulated absorption components due to H20zwere also detected. During static irradiation of C12-H2-02 mixtures at slow speeds, the change in signal due to H202is linear during photolysis and zero when the lights are off. The average rate of change of signal due to H202absorption is given by v = a’l9B/2 which results in apparent absorptions of -v7/4,in-phase, and v7/8,in-quadrature. In the flowing system a “saw tooth” concentration modulation of HzOZ
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979
2562 5
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R. A. Cox and J. P. Burrows
portant at low frequency. All modulated absorptions in the present work were corrected for components due to H202product by using the above approximations.
I
4
0
P
“E 3
s
[ h2
i 1
1
I
200
210
I
1
I
220 230 240 Wavclcngth(nm1
I
250
Flgure 1. Absorption spectrum of HO, as determined from modulated absorption components in the photolysis of Cl2-H2-O2 mixtures at 298 K. The resolution was 1.6 nm. Absolute cross sections, based on u = 3.5 X cm2 at 220 nm, were obtained from kinetic measurements.
about a mean value of [H20,] given by the steady-state solution of eq v will result: Here, kf is the effective decay coefficient due to flowout from the cell. The resultant modulation signal appears, to a first approximation, in-quadrature only and has a . both cases the product absorption value of u ’ l @ B ~ / 8In signals increase linearly with T and are in fact only im-
Results and Discussion The Ultraviolet Absorption Spectrum of H 0 2 . Figure 1 shows the wavelength dependence of the in-phase component of modulated absorption normalized to the value of the absorption cross section of 3.5 X cm2at 220 nm, derived from the kinetic measurements (quod vide). The data are averaged values from several experiments with a flowing mixture of C12and H2 in 1atm of 02,with a relatively short photolysis period, T = 0.4 s, so that the effect of absorptions due to H202product was negligible. The spectral resolution was 1.6 nm. The shape of the absorption feature is very similar to that obtained by Paukert and Johnston3using the molecular modulation technique, by Hochanadel et ala4using conventional flash photolysis, and also by Troe14who studied the shock-wave thermal decomposition of H202at 1000 K. The spectrum can therefore be attributed to the H 0 2 radical with some confidence. Paukert and Johnston obtained a maximum cm2 at 210 nm which agrees with value of u = 4.5 X the present work. The absolute cross sections deduced by Hochanadel et al. were approximately 50% higher, cm2, a,,(205 nm) = 6.8 X Measurement of kl a t Atmospheric Pressure. To investigate the kinetics of H 0 2 in the C12-02-H2 system, measurements of the in-phase and in-quadrature absorption at 220 nm as a function of photolysis period were made by using a range of HO, generation rates, B, obtained by varying the concentration of C1, and the number of photolysis lamps. The data for total pressures near 760 torr and 298 K are plotted in reduced form in Figure 2. B ranged from 1.7 X 10l2to 5.83 X 1013molecules cm-3 s-l, [H,] from 2.7 to 8.0 X 1017molecules ~ m -and, ~ , in some experiments, 380 torr of either SF6or N2was present. It will be seen that none of these changes in conditions produced any systematic variation in the kinetic behavior of H02. The data were well fitted with a pair of sec-
I
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C
0
30 -
-
0
0
-
-g Sn N,
-
9 20-
-Y 0
E
$7
5 G0
?lo-
A
0
0
-
4 0
0
. -
0
0 0
01
1
o
U
10
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10
100
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979 2563
Disproportionation of HOP in the Gas Phase
TABLE I : Summary of Rate Constant Data for HO, t HO, = H,O, t 0, k , cm3
~
~~
temp, K 298 298 298 298 298 298 273 274 27 8 318 338 339 27 8 298
press., torr 760 347 25 2 5' 10a,b 1oa 5.34b 3.0a3d 760 1oa 7 60 760 760 1oa
molecule-' s-l x 10"
u cm2 molecule-' x
2.35 i 0.2 2.5 1.6 2.3 1.8 1.P 1.5d l.lC 3.4 2. le 3.5 1.9 1.5 1.4
3.49 3.5 2.6 3.7 3.2 3.3 3.3 3.3 3.2 3.3 3.6 3.6 3.2 3.5
i
lo1*
0.4
Runs in the Presence of H,O All at 760 torr Total 4.8 3.4 1.0 [H,O] 3.0 3.6 1.9 [H,O] 3.1 3.4 2.6 [H,O] 2.1 3.5 4.0 [H,O]
k / o cm s-'
x
Q(HZO2) 0.75 i 0.15
0.68 i 0.08 0.71 0.62 0.62 0.56 0.55 0.45 0.33 1.06 0.64 0.98 0.52 0.46 0.40
0.92 0.90 0.83 0.84 0.82 0.55 0.61 0.60 0.80 0.80 0.93
Pressure 1.44 0.84 0.91 0.61
0.29 0.45 0.42 0.85
318 Obtained with a 40-mm diameter Obtained by using the C1,-HCHO system; all other data from the Cl,-H, system. First-order component used in derivation of k , with k 1 PTFE coated vessel; all other data obtained with a 26-mm vessel. First-order component used in derivation of k , with k' = 1 0 s-'. e First-order component used in derivation of = 1 2 s-'. k , with k' = 18 s-', a
ond-order curves, except at very long photolysis period when a systematic departure from the model was apparent, in a sense that both in-phase and in-quadrature absorptions were greater than expected for pure second-order kinetics. This anomaly will be discussed later. The rate constant for H 0 2 recombination obtained from these cm3 molecule-l s-' and the curves is kl = 2.3 f 0.3 X corresponding absorption cross section for HO2 at 220 nm cm2, The errors given are the is u = 3.5 f 0.4 X estimated experimental errors averaged over 1 2 experiments and do not include systematic uncertainty arising from the assumption that (a) B is equal to the Clz dissociation rate and (b) that the rate constant can be accurately derived by fitting the model second-order curves, notwithstanding the deviations at low frequency. Pressure Dependence of kl. In order to investigate any possible pressure dependence of kl, we conducted kinetic measurements (at 298 K) at 347 and 25 torr using the C12-H2-02 system and at 25,10,5.3, and 3.0 torr using the Cl2-HCHO-OZ system. With the exception of some of the H2 data at 25 torr, all measurements were made under flowing mixture conditions with residence times from 8 to 20 s. A summary of the rate constants, k l , together with the correspondingabsorption cross sections, the ratio kl/p, and the quantum yields for H2O2formation is given in Table I. Considering first the H2 system, the H 0 2 absorptions exhibited second-order kinetic behavior at all pressures but the apparent value of kl at 25 torr was lower by about 30% than the value at 347 and 760 torr. However, there was also a reduction in u so that the ratio kl/u exhibited no significant pressure dependence. These effects were observed both in the static and the flow system and can be explained in terms of failure of the assumption that E = k2[C12].In these experiments [H2]was relatively low and competitive wall removal of C1 atoms would easily have led to a reduction in the photochemical source of H 0 2 without affecting the H 0 2decay kinetics. By replacing Hz with HCHO this problem was apparently eliminated, at least at 25 torr where the values of hl, u, and k l / u were all equal to the 760-torr values. On reduction of the total pressure to 10 torr in the C12-HCHO-02 system, we observed changes in the kinetic behavior of HOz, inasmuch as the size of the H 0 2 ab-
sorption and the lifetime parameter, r0,did not exhibit the B1i2dependence expected for second-order kinetics. As B was decreased by reducing the photolytic intensity, both r,$'J2 and the reduced absorption components decreased, indicating the presence of an additional loss process for H 0 2 of smaller kinetic order. First-order removal of H 0 2 could result from reaction with HCHO: H 0 2 + HCHO products (7) The available data on reaction 7 yields k7 5 2.5 X cm3molecule-' s-l at 298 K, which for our conditions gives a first-order rate constant of k' I 0.5 s-l and is therefore too slow to account for the observed phenomena. However, recent work by Niki and co-workers (personal communication) on the C12-HCHO-02 system suggests that k7 = 1X cm3molecule-' s-' at 298 K, with the product of the reaction possibly being an adduct which apparently does not regenerate H02. This would account, at least in part, for the observed first-order loss of H02. An alternative process is removal of HOz at the vessel wall, and to test this possibility measurements were conducted in the larger diameter (40 mm) PTFE coated reaction cell. With this cell there was no significant departure from model second-order behavior over a sevenfold change in B at a pressure of 10.3 torr. The values of kl and kl/u obtained from these data showed a significant reduction compared to values for pressures 2 2 5 torr. The magnitude of the effect of the first-order component is illustrated in Figure 3 which shows experimental absorption measurements in both the 40- and 26-mm vessels at a pressure of 10 torr, together with model curves cm3 molecule-'^-^ and computed by using kl = 1.8 X = 3.3 X 10-ls cm2. For clarity not all of the data from the 40-mm vessel are shown but it will be seen that these are well described by curves calculated with k' (the effective first-order removal rate constant) = 0. The optimum value of k1 was then chosen to simulate the dependence of the size of the reduced absorptions and the lifetime parameter, rail2, on B, which was observed in the 26-mm vessel. As will be seen a reasonable description of the results was obtained by using k' = 12 s-'. As the pressure was further reduced to 5.3 and 3.0 torr,
-
(T
2564
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979
R. A. Cox and J. P. Burrows
Figure 3. Reduced in-phase and in-quadrature absorptions due to Hop undergoing mixed first- and second-order decay plotted as function of reduced photolysis period: temperature, 298 K; pressure, 10 torr; [HCHO] = 5 X loi5, [Cl,] = 6.7 X loi5 molecules ~ m - (0) ~ ; 40 mm-vessel, SIX lamps;
(A)26-mm vessel, six lamps; (0) 26-mm vessel, one lamp; open points, In-phase; filled points, in-quadrature. Curves from computer slmulatlon obtained with k, = 1.8 X lo-'* cm3 molecule-' si, (r = 3.3 X cm2, and values of k* and 6 (= k2[CI2])shown on figure.
the presence of a first-order component in HOz kinetics became noticeable again, even in the 40-mm diameter vessel. Although the accessible conditions did not allow an unambiguous direct measurement of kl,it could be estimated quite reliably by fitting pairs of values of kl and k' to the data obtained over a range of B. Initial values of kl and k' for the simulations were obtained by comparing the experimental values of T~ on a computergenerated functional plot of T ~ - ' vs. B112for a range of values of kl and k'. In view of this indirect method the values of kl are less accurate than those measured at higher pressure. However, from analysis of these data it was clear that kl decreased with pressure in this region, while k' tended to increase. I t is concluded from these results that kl is invariant with pressure in the range 25-760 torr but there is a falloff in kl at pressures of 10 torr and below. This falloff with pressure is consistent with a recent measurement of kl, using laser magnetic resonance, which showed that at -2 torr pressure of helium kl I 1.25 X cm3 molecule-l s-' at 298 K.16 Temperature Dependence of kl. The effect of temperature on kl was investigated over the range 273-339 K, using total pressures of 760 torr (Clz+ H2 system) and 10 torr (C12 HCHO system) in the 26-mm diameter vessel. At least two values of B were used for each temperature and pressure, obtained by a sixfold variation in photolytic intensity. Data for 273 and 338 K are presented in reduced form in Figure 4 and the derived kinetic parameters given in Table I. At 338 K the results at both pressures followed second-order model behavior for all values of B and T employed, and any effect of pressure on kl could not be detected within the experimental error. At 273 K and 10 torr a substantial first-order component in the H02 kinetics was present. Data obtained over a 16-fold change in B were best described by a value kl = 2.1 X cm3 molecule-' s-l with k' = 18 s-l. There appears to be a substantial negative temperature dependence of kl,since an upper limit of k' 5 3 s-l could be set for the same system
+
at 338 K. At 760 torr and 273 K the second-order B112 dependence of T~ and absorption was observed but absorption at low frequency exhibited the same departure from the model curves as found at 298 K and 760 torr. This behavior indicates the presence of a kinetic component of higher order than 2. We have observed a similar deviation in the absorption components at low frequency in studying the mutual decay kinetics of the C10 radical by MMSI2 and it could be interpreted in terms of the involvement of a moderately stable ClZO2molecule in the decay mechanism. The magnitude of the effect in the H02 experiments described here was much less than for C10, but the observation may suggest the involvement of an H204species in the disproportionation of H 0 2 at low temperature. The results at 760 torr nevertheless show clearly a strong decrease in the effective second-order rate constant as the temperature increases, as manifested in the greater reduced absorptions and 7$'12 value at the higher temperature, see Figure 4. At the lower pressure, 10 torr, the temperature dependence was much reduced although the effect tended to be masked by the significant temperature-dependent first-order component in H 0 2 decay, which the evidence suggests is a wall removal process. Also shown in Table I are the mean quantum yields for hydrogen peroxide formation at each temperature and pressure. There was rather a large variability in this parameter which is reflected in the spread of values at 760 torr and 298 K. In most cases 9(H202)was less than unity and it showed a significant decrease with decreasing temperature. At the lower pressures when HCHO was used as a source of HOz, 9(H2O2)tended to be closer to unity than at 760 torr. This confirms that the simple mechanism assumed for the photolysis of C12-HCHO-02 mixtures is correct. In our previous work7 we found appreciable heterogeneous thermal decompositions of H202at 308 K but only a slow decomposition rate at room temperature (298 K). This temperature dependence, together with the observation in the present work that [H202]increased linearly
Disproportionation of
Hopin the Gas Phase
The Journal of Physical Chemistry, Vol. 83, No. 20, 1979 2565
338K
Flgure 4. Temperature dependence of reduced in-phase and in-quadrature absorption due to Hop as a function of reduced photolysis period: (0) one-lamp, (A)six-lamp photolysis at 760 torr, C12/H2system; (+) one-lamp, (X) six-lamp photolysis at 10 torr, CI,/HCHO system; filled points, in quadrature. Computed curves (left, 273 K): kl = 3.4 X lo-", k' = 0,(---) k = 2.1 X IO-", k' = 18 s-', B = 0.6 X l O I 3 molecule C f r 3 s-l (as in one lamp run, +); (right, 338 K): k, = 1.5 X lo-'' cm3 molecule-' s-I. All with u = 3.5 X IO-" cm2.
with time during the initial stages of reaction, is inconsistent with a first-order heterogeneous removal of H202 as an explanation of the low quantum yields. The absorption cross section exhibited no significant temperature dependence as expected. It should be noted that all values of h and n given here are based on values of B calculated from the rate of Clp decay. If H202formation reflects the total amount of HOz formed, then both h and u should be increased by a factor of (@H202)-l and this would result in an apparent small temperature dependence of n. The ratio k/ u is independent of B and can be expressed in Arrhenius form as kln(220 nm) = (1.1f 0.8) X lo4 exp((1245 f 184)/T) cm s-l at 760 torr and hl(r(220 nm) = (7.6 f 1.2) X lo4 exp((581 f 44)/T) cm s-l at 10 torr. Error limits given here are 2 sd from least-squares analysis and do not include possible systematic errors. Effect of Water Vapor. The effect of added water vapor on the modulated absorptions at 220 nm as a function of the photolysis period was investigated at 278,298 and 328 K with H20concentrations (molecules cm-3 X of 1.03, 1.93-6.35, and 3.96 at the three temperatures, respectively. At 278 K only one photolysis lamp was employed because higher intensities resulted in interference with the monitoring beam by condensation on the internal cell surface and "fog" formation, presumably promoted by the HC1 and/or HzOzproducts. At 298 K the monitoring beam was noisier than usual when H20 was present, and, when H,O concentrations were 14 X lo1' (12 torr), it was found that the kinetics of H02 changed from near second-order behavior to a complex dependence on [Cl,] and intensity, tending to first-order kinetics at low B. This was strongly indicative of the participation of surface reactions, possibly promoted by multilayer absorption of water on the walls, which commences at -40% relative humidity at ambient temperatures. Only data at low relative humidity exhibiting near second-order kinetic behavior will be presented. Figure 5 shows reduced absorption data obtained at 298 K with 1atm of O2 as diluent and with 2.6 X 1017molecules
cm-3 (8.1 torr) of H 2 0 present. They may be compared with the full lines which are the pair of second-order curves which gave the best fit to the H20 free data at 760 torr and 298 K shown in Figure 2. It will be seen that there was a small but significant effect of water vapor, inasmuch as the absorptions were decreased and shifted to higher frequency on the time axis. The data are reasonably well described by a pair of curves calculated by using kl = 3.1 x cm2. Thus cm3 molecule-l s-l and u = 3.5 X our results suggest, in agreement with Hamilton: that the effective second-order HOZdecay constant is noticeably increased by the presence of a few torr of H20. However, in view of the possible participation of a first-order component in our system, the results are not entirely conclusive. Also it will be seen by comparison of Figures 2 and 5 that the deviation from second-order behavior at low frequency is more marked in the presence of water vapor. Thus, H20 seems to increase the importance of the slow intermediate in the reaction. A change of similar magnitude in the rate constant was observed from the single set of data at 278 K, but with lower [H20]present. The 318 K experiments were conducted with a range of C12 concentration and light intensities (1and 6 lamps), at a constant H20concentration. The effect of H 2 0 on the reduced absorptions was barely significant and the departure from model second-order behavior at low frequency was, as in the H20-freecase, very much less pronounced than at the lower temperatures. The rate constants, absorption cross sections, and the ratio k / n from these experiments are shown in Table I. Note that, to within the experimental error, there was no effect of HzO on the absorption cross section of H02, as was assumed by Hamilton and Lii.6 Figure 6 illustrates graphically the H 2 0 dependence of kl/u(230 nm) at total pressures I 1atm. The present data at three temperatures are plotted together with those of Hamilton and Lii6 (-298 K, 2 atm of Hz),Hochanadel et aL4 (298 K, 1 atm of H2), and Paukert and Johnston3 (-300 K, 1atm of He). The agreement between the H 2 0 dependence observed by us and by Hamilton is certainly
2566
R. A. Cox and J. P. Burrows
The Journal of Physical Chemistry, Vol. 83, No. 20, 7979
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t 3,L9(-1(
t
3'0
0'1
10
10
100
However, it will be seen that H 2 0 suppressed @(H202) at least under conditions where k1 was affected. Mechanism of the Disproportionation of HOz. It is clear from the results described above that the disproportionation of HOPdoes not proceed by an elementary bimolecular H-atom stripping reaction as suggested by Hochanadel et al.4 Such a mechanism would be inconsistent with the observed negative temperature dependence and the pressure effect on kl. The results are suggestive of a mechanism involving association to form H z 0 4 molecules, of more or less stability, the fate of which can be influenced by collisional energy transfer. A possible scheme may be formulated as follows:
T
H02+ H02 H204*+ M Tar 1298K)
5 0
10
15
16 32 48 Water Vapour CoKentration molecules ~ m - ~ r 1 0 "
20 6L
Flgure 6. Water vapor dependence of k,: Plot of k,lo(230.5 nm) against [H,O]; (filled points) data from present wok; (X) data of Hamilton and Lii;' (V)Paukert and J~hnston;~ (0) Hochanadel et all at -300 K.
good to within the experimental error of the measurements and seems to reconcile the result of Hochanadel et al. with that of Paukert and Johnston. The pronounced temperature effect on the H 2 0 dependence as well as on the H20-freevalue of k l a t 760 torr is readily apparent. We could not reproduce the rate constant data of Hamilton a t higher [H,O] and 298 K, since the model second-order behavior was not observed at H 2 0 pressures above 12 torr in our system. The quantum yields for Hz02formation in the presence of H20are also shown in Table I. Measurements of optical density changes with H 2 0 present were less accurate due to increased noise and drift in the monitoring beam.
-
+
H204t (+ M)
ka
Hz04*
6-a
H204f+ M
(b)
2H02
(4 (4
-+
H204t -,H202 + 0 2
Here it is proposed that collisions between two HOz radicals form a short-lived association complex H204* which can spontaneously dissociate back to two H 0 2 in reaction -a unless energy is removed by collisions with other molecules to form a vibrationally relaxed H20dt species. This molecule may also dissociate, either to two H 0 2 or H 2 0 2+ O2 but the former route is envisaged as being much slower than reaction -a and may even require collisional purturbation, reaction c. The postulated H2O4 species has been previously identified as a product in discharged water vapor/ oxygen mixtures by observation of its IR spectrum with the matrix isolation technique.23 Analysis by using the steady-state approximation for [H204*]and [H204t]gives the following expression for the overall reaction rate:
Disproportionation of HOz in the Gas Phase
The Journal of Physical Chemistry, Vol. 83,No. 20, 1979 2567
This model indicates that the overall second-order rate constant is composed of two parts, one of which will decrease with a fall in pressure when kb[M] 5 k-, and a second which may increase with falling pressure depending on the magnitudes and pressure dependence of k, and k& Since the falloff of kl did not occur until the pressure was reduced to less than 25 torr, it is probable that, at 760 torr, kb[M] >> k-, and the value of kl is given by kl = k,kd/(kc + kd). On the basis of recently measured rate constants for H 0 2 + radical reactions16J7a value of about 5 X can be ascribed to k,; thus the observed value of kl = 2.3 X 10-l2 cm3 molecule-l s-l at 298 K and 760 torr implies kc/kd = 20, and therefore kl = k,kd/kc. The temperature dependence of k, is expected to be close to zero and the observed negative temperature dependence of kl must arise from that of kd and k,, Le., El = E d -E, = -10.4 kJ mol-'. A small difference in activation energy in this sense is not unreasonable for these reactions, considering the nature of the two dissociation processes. Although the model requires k, = 20kd, A d may be several powers of 10 less than A, since elimination of Oz i s envisaged as occurring via a 4-center transition state, e.g., I or 11. The H
H
'O***d
I
0-0
H-0
I
H-0
\i 0-0 I I1
I
observation of a deuterium isotope effect of klH/klD= 2.8 at high pressure6 suggests that I1 may represent the major reaction pathway. This is also consistent with the observation that disproportionation of H 0 2via reaction 1in aqueous solution proceeds only very slowly, kl = 1.26 X 10-l5 cm3 molecule-l s-l.18 Collisional relaxation to form HZO4should be efficient in solution but H bonding to surrounding solvent molecules could prevent the formation of a cyclic transition state involving H. In hydrocarbon solvents, disproportionation of H 0 2 is much more rapid than in a polar medium.lg Because the rate constants of reactions a-d and the M dependence of reaction c are not known with any certainty, a quantitative analysis of the pressure dependence of kl is not justified. However, the mechanism involving HzO4 offers a plausible interpretation of the unusual effects of water vapor. Hamilton5 suggested that the effect of H 2 0 arises from the formation of a 1:l hydrogen-bonded complex of H 0 2with HzO. Further support for this comes from his observation of a similar effect of ammonia and also from ab initio calculations of the stability of such complexes.20 He invokes establishment of the equilibrium HOz + H2O e HZO-HOZ (8) Kg* = ks/k-g followed by a rapid reaction with a second HOz molecule, and suggests that this latter reaction proceeds at the gas cm3molecule-l s-l, kinetic collision frequency, 3.5 X to yield H202+ 02.An alternative explanation is that the reaction of the H20-H02 complex with H 0 2 provides an efficient route for the formation of vibrationally relaxed H2O4+molecules: HzO-H02 + H02 H204++ HzO (9) -+
The expression for the overall second-order removal of H02 at a given total pressure and temperature is then given by 1d[HOZl - -2
therefore
dt
-
(kA + kB[H201)[Ho212 (1 + K3*[HzOI)
kl =
+ ~B[H@I) (1 + K,*[HzOI) @A
where kA = kl in the absence of HzO and kB = k9K8*' ((k,/kd) + 1)-l.This equation predicts the observed linear dependence of k1 on [HzO]for the limiting condition that K8*[HzO]> 1,EB Eg 4- (AHo),+ E, - E d and, as Egis probably close to zero, we estimate (AHo)8 = -37.6 f 10 kJ mol-l. This compares reasonably well with the calculated valuez0 of -31.0 kJ mol-l (relative to a standard state of 1 mol L-l). Thus the observed temperature dependence of the HzO effect can be accounted for in terms of the calculated thermodynamic properties of the 1:l H20-H02 complex. H202Quantum Yields. The above mechanism does not offer any explanation of the consistently low quantum yield for HzOzformation, as measured from the optical density at 220 nm. The discrepancy was too large to be accounted for by uncertainty in the absorption cross section for H202 at the monitoring wavelength and must be due to loss of C1 or H 0 2by processes other than reaction 3 or the overall reaction 1, respectively. Loss of H atoms or HCO radicals by processes other than reactions 4 and 6 seems highly unlikely at the O2 pressures employed. The rate constant for the reaction of C1 atoms with H2 is now well knownz1and the lifetime of C1 with respect to reaction 3 can be calculated; at the lowest temperature and lowest [H,] it was 0.4 ms. In the HCHO experiments it was at least a factor of 100 lower due to the very rapid rate of reaction 5. Even with very efficient removal of C1 atoms at the surface, a major wall loss of C1 seems unlikely, since diffusion from the bulk of the gas phase is relatively slow, especially at pressures near 1 atm. Removal of both C1 and HOz can occur in the gas-phase reaction C1+ HOz ---* HC1+ 02 (10) We have shown previously' that the observed falloff in @(H20z)at low [H,] can be satisfactorily accounted for by this process. A recent direct determination of klo = 4 X cm3 molecule-l s-l l5 allows the role of this reaction to be assessed quantitatively for the present conditions. The removal of C1 and HOz by reaction 10 was always
