73
J. Phys. Chem. 1082, 8 6 , 73-81
reservoirs. Hence there is conduction of heat according to eq 1.1. If we denote by W the work output of the engine per cycle and by At the time spent in one cycle, the power output of the engine is P = W/At (IV.1) while the efficiency of the cycle is 9
= 1 - (T2/T,)
(IV.2)
For fixed and finite TC (aconstant) a relation between the temperature of the isotherm, Ti, the corresponding reservoir temperature, Tex,i,and the values of T~ and 7M which have been assigned, is provided by eq 11.7, while the adiabats are properly described by 71. = -rW When TM along the different branches of the cycle is finite and nonzero we have an irreversible cycle. It may be shown that the power output goes through a maximum - TeX,J],see Fig. 2a, and the efin the interval [0, (TeX,, ficiency, (IV.2), a t this maximum tends to4
(2) 112
I]
= 1-
(IV.3)
when the time spent on the adiabats is negligible compared to that spent on the isotherms. In the upper limit of the range [0,(Tex,, - Tex,z)], Figure 2a, the time scale 1 ~ ap-~ proaches m, which yields the classical quasistatic reversible Carnot cycle with zero power output. Let us now suppose that as (T,- T2)increases we also vary 7~ so that the heat transfer rates along the isotherms, qi = a(Texj- Ti),i = 1,2, are not zero. The power output versus (T, - T2)has a parabolic shape as shown in Fig. 2b. is reached The upper limit of the interval [O,(T,,,,- Tex,z)] when a 03 (rC 0), where, according to eq 11.7 and the assumption of nonzero heat flow, 1 ~ and ~ the 1 power output are finite and nonzero, while the efficiency attains the classical Carnot efficiency. In other words, we have a reversible cycle (AS = 0) which produces nonzero power output. However, as we have already mentioned, this case, although thermodynamically possible, is physically not attainable. Acknowledgment. We thank Professor William C. Reynolds for comments which led us to this study.
- -
(4)F. L. Curzon and B. Ahlborn, Am. J. Phys., 43, 22 (1975);D. Gutkowicz-Krusin,I. Procaccia, and J. Ross, J. Chem. Phys., 69,3898 (1978);M.H. Rubin, Phys. Rev., A19, 1272 (1979).
Rate Constants for the Gas-Phase Reaction between Hydroxyl and Hydrogen Sulfide over the Temperature Range 228-518 K Mlng-Taun Leu' and Roland H. Smltht Jet Propulsion Laboratory, Csllfornle Institute of Techno@& Pasadena, Callfornla 9 1109 (Received:March 16, 1981; In Flnel Form: September 18, 1981)
Discharge flow resonance fluorescence has been used to measure the rate constant for the reaction between hydroxyl and hydrogen sulfide over the temperature range 228-518 K while mass spectrometry was used to determine products and to measure stoichiometry. The reaction occurring is, as expected, OH + HzS HzO + HS (k2) with HS rapidly reacting with other substances. At 298 K k2 = (3.9 f 0.7) X cm3 s-l, where the error includes both statistical (4%) and systematic (13%) components. The temperature dependence can be described either by k2 = (5.9 X 10-l2)exp(-89/T) or by kz = (2.34 X 10-lg)P5exp{725/T]. These equations reproduce the experimental values to within 10% and 7%, respectively. The results are compared with other measurements.
-
Introduction Although there are quite significant natural and anthropogenic sources for atmospheric H2S,'4 ita steady-state concentration is quite low, because it is rapidly oxidized to SO2 and sulfate. The hydroxyl radical is believed to be a major oxidant of H2S,24 and hence, for reliable modeling of the atmosphere, accurate values are required for the rate constant for OH H2S over the atmospheric temperature range 200-300 K. The three previous room-temperature values for the rate constant for OH + H2Sranged from 3.1 f 0.5 obtained by Stuh13to 5.3 f 0.5 by Perry, Atkinson, and Pitts6 to 5.5 f 0.3 by Westenberg and de Haas! all values being in units of cm3 s-l. In the two temperature-dependent studies6I6the discrepancy is greater: Perry et al. obtained 5.3 X cm3 s-l a t 423.3 K at which temperature the (in-
+
+ On study leave from Macquarie University, North Ryde, New South Wales 2113, Australia.
terpolated) Westenberg and de Haas value is 8.2 X cm3s-l. The latter workers proposed an activation energy of 880 cal mol-' while the former group concluded that the rate constant is independent of temperature. All three studies wrote the reaction as OH + H2S H2O + HS (1) though no attempts were made at detecting products. To try to define the rate constant more precisely, particularly over the range of atmospheric temperature, we have undertaken an extensive kinetic study of the reaction by discharge flow resonance fluorescence and have used mass spectrometry to identify reaction products. These
-
(1)D. R. Hitchcock, J. Air Pollut. Control Assoc., 26, 210 (1976). (2)T.E.Graedel, Rev. Geophys. Space Phys., 15,421 (1977). (3)F. Stuhl, Ber. Bumenges. Phys. Chem., 78,231 (1974). (4)J. L.Sprung, Adv. Enuiron. Sci. Technol., 7 , 263 (1977). (5)R. A.Perry, R. Atkinson, and J. N. Pith, J. Chem. Phys., 64,3237 (1976). (6)A. A.Westenbergand N. de Haas, J. Chem. Phys., 59,6685(1973).
0022-3654/82/2086-0073~01.25/0 0 1982 American Chemical Society
1
74
The Journal of Physical Chemistty, Vol. 86, No. 1, 1982
Leu and Smith
latter experiments were also intended to provide information about the reactivity of HS, which would be helpful in interpreting the results obtained in parallel studies of the reactions of hydroxyl with OCS and CS2.7,8 Experimental Section The apparatus and techniques were the same as those described p r e v i o u ~ l y . ~ ~In~ Jsummary, ~ the 2.5-cm i.d. discharge flow tube had a fixed radical source (H + NO2), fixed detectors (fluorescence cell for OH just upstream of a pinhole leak to a mass spectrometer), and a movable H2S inlet, and it could be thermostated either by circulating liquid at temperaturea from 230 to 420 K or by an electrical tube furnace a t 520 K. Flow rates were measured by calibrated mass flowmeters. Linear flow velocities were generally in the range 10-40 m s-l with total pressure of 0.8-4.0 torr. Viscous pressure drop through the reaction zone (30-50 cm) rarely exceeded 6%. The pressure used in rate-constant calculations was the value at the midpoint of the reaction zone, and this was calculated from the measured pressure by Apll = 81ju/r2. To minimize wall removal of OH, we coated flow-tube and injector surfaces with phmphoric acid and conditioned them first by prolonged heating and evacuation and then by exposure to quite high OH concentrations for several hours before use for kinetic measurements. The wall constant was typically 5-15 s-’ as measured by adding NO2 through the movable inlet to an excess of H atoms and measuring the OH fluorescence signal as a function of the inlet distance from the detector. For a hydroxyl concentration of 10” ~ m - the ~ , fluorescence signal (measured by photon counting through an interference filter) was 4-5 times the signal from scattered light, which meant that we were able to use initial OH while concentrations in the range 0.6 X loll-4 X 10” following its decay for about 1order of magnitude. The proportionality constant relating fluorescence signal to OH concentration was determined by measuring the signal as a function of [NO,] when small flows of NO, were added through the movable inlet to much larger concentrations of H atoms with the inlet positioned to allow sufficient time for H NO2 OH + NO to go to virtual completion without any significant loss of OH by wall reaction so that [OH] = [NO,]. Such calibration plots were linear up to at least 2 x 1012or 3 x 1012~ m - ~ . The mass spectrometer was calibrated immediately after quantitative experiments by measuring the peak heights produced when known flows of the desired gas were added to the gas stream used in the experiments with all other conditions kept constant. Such calibrations of peak height vs. partial pressure were linear over the concentration ranges used. C.P. grade hydrogen sulfide (Matheson) of minimum purity 99.5%as checked by gas chromatography was used. Because of the high reactivity of H2S toward OH and the low reactivity of the most likely impurities, CS,, C02, OCS, and SO2,l1this gas was used as supplied.
+
-
Results Kinetics. Under conditions of [H2S] >> [OH],,, the concentration of hydroxyl was measured at the fluores- __ - -- _. (7)M. T. Leu and R. H.Smith, J. Phys. Chem., 85, 2570 (1981). (8)M.T.Leu and R. H.Smith, ‘Kinetics of OH + CS2”, J. Phys. Chem., in press. (9)M.T.Leu, J. Chem. Phys., 70, 1662 (1979). (10)M.T.Leu and W. B. DeMore, Chem. Phys. Lett., 41, 121 (1976). (11) ‘Matheson Gas Data Book”,4th ed., 1966,p 287. I
I
I
I
I
I
10
20
30
40
50
10
9 c1
I
9 c
8
7
0
DISTANCE, IN
60
70
CM FROM AN ARBITRARY ZERO
Flgure 1. Firstorder OH decays at 518 K with [H2S] = (a) 0, (b) 1.65, (c) 2.67, (d) 3.35, (e) 4.20, and (f) 5.12 ~ m - ~[OH] . is in arbitrary units. [OH], = 8 X 10” ~ m - Total ~ . pressure is 1.16 torr and How velocity is 3970 cm s-’.
cence cell as a function of the distance of the H2S inlet and absent, from this cell with H a both present, [OHIxH@, [OH],O; and, as has been shown elsewhere,12if the only removal processes for OH are first-order wall loss and reaction with added reactant, then k, (the pseudo-firstorder rate constant for removal of OH by H2S) is given by d In [OHIzHa d In [OH12 k1 = -U (2) dx dx where u is the average flow velocity and x the distance from inlet to fluorescence cell. The expression is independent of k,, the first-order rate constant for wall removal of OH. Since k, was typically 5-15 s-l in our phosphoric acid treated flow tube and since the movable inlet contributed only slightly to it, it proved convenient to perform experiments (a) by measuring as a function of x with constant [H2S]and then (b) by turning off the H2S flow and measuring [OH],O as a function of x. The contribution of the zero-H2S term to k, in eq 2 was usually 0-3 s-1. Sets of experiments were performed by setting up a constant flow of H2 and NO2 in helium carrier with a constant initial hydroxyl concentration, [OH],, and then by measuring OH decays for several different H2S concentrations (including zero). In this context [OH], is the concentrations at the most distant point from the fluorescence cell to which the H2S injector was withdrawn durin the set of experiments. [OH], was calculated from [OH],,,% the measured concentration of OH at the fluorescence cell with zero H2S flow, by using
-+’
[OHIO= [OHlze~exp(k,p/u) (3) The OH decay was fmt order for about 2-4 half-lives. The results from one typical set of experiments are shown in Figure 1. The pseudo-first-order rate constants from such experiments were plotted against [H2S],and the second(12)A. A.Westenberg and N. de Haas, J.Chem. Phys., 46,490 (1967).
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982 75
Gas-Phase Reaction between OH and H2S
01
0
I 1
I
2
I 3
I 4
I
I
I
I
I
I
0
I
2
3
4
5
I
I 5
6
[HpSI, c m 3
[H2S1,
F ure 2. Dependence of firstorder rate constant kl upon [H2S] at different temperatures. The origins have been displaced vertically by 40 s for 287 and 422 K, 80 s-' for 247 and 518 K, and 140 s-' for 228 K. Total pressures in torr were as follows: ( 0 )1.54 at 298 K, 0.75 at 228 K, 1.17 at 518 K; (A)2.07 at 298 K, 1.55 at 228 K, 1.83 at 518 K; (X) 4.01 at 298 K, 2.15 at 228 K, 2.20 at 518 K; (W) 3.22 at 518 K. For 0 and @ total pressures were in the range 0.75-4.01 torr.
9
TABLE I: Second-Order Rate Constants for OH Helium as Carrier Gas temp, K
no. of expts
10-11. [OH] o , cm-3
518 422 364 298 267 247 228
29 19 21 22 8 23 17
0.8-1.1 0.8-2.5 1.3-3.2 0.6-4.2 1.9-2.9 0.8-4.2 0.5-1.5
+ H,S with 0.75-4.01 torr of Total Pressure and with 10"kZb 10'akza
5.5 f 4.7 f 4.3 f 3.9 f 3.9 k 4.4 k 4.3 f
0.13 0.20 0.19 0.08 0.23 0.20 0.24
( e s 6)
(eq i l j
5.62 4.62 4.21 3.96 4.00 4.09 4.28
5.0 4.8 4.6 4.4 4.2 4.1 4.0
interceptC
5 f 8 i 1oi 13 f 16 f 21 ?:
lo
3 4 4 3 4 4 +4
Units are cm3 s-' ; errors are one standard deviation of the slopes in Figure 2 and do not include systematic errors which were virtually constant for all temperatures. Values calculated from eq 6 and 11, respectively. Units are cm3 s-l. Of least-squares fit t o data in Figure 2; error is one standard deviation. a
order rate constant k2 was obtained from the slope. Similar sets of experiments were performed under different conditions to check the constancy or otherwise of k2. Providing [OH], I4 X 10" ~ m -it~was , found that k2 was independent of [OH],. At these low [OH], values, variation in [OH], of factors of 7 at 298 K, 3 at 420 K, and 5 at 246 K produced negligible change in k2. However, at higher [OH],, k2 increased in a manner indicative of interference by some secondary reaction consuming OH. For example, at 298 K the slope of the kl vs. 10-l2 [H2S] plot [OH], increased increased from 3.9 to 4.1 to 4.9 as from 5 4 to 7 f 2 to 15 f 5. A t these higher [OH], values curvature in the In [OH] vs. distance plots became noticeable in the direction of increasing kl with increasing reaction time. Only those experiments with [OH], I4 X 10" cm-3 were used to calculate k2 at each temperature. Results obtained at seven temperatures are shown in Figure 2. In each case the line of best fit was obtained by the method of least squares, and the values of k2 thus obtained are summarized in Table I.
To check whether k2 had any pressure dependence, we performed sets of experiments with total pressures of 1.54, 2.07, and 4.01 torr at 298 K, of 1.17, 1.83, 2.20, and 3.22 torr at 518 K, and of 0.75,1.55, and 2.15 torr at 228 K. No pressure dependence of k , was detectable (Figure 2). Although total pressure was varied only by a factor of 3, the precision of the measurements was such that this change should have been sufficient to reveal any pressure dependence of kz. Generally, experiments were performed with excess NO2 present, the ratio [N02]/[H], typically being in the range 10-50. The rate constant k2 was independent of this ratio. In addition, some experiments were performed with [NO2],, [HI, so that virtually no NO2 was present after formation of OH; again, k2 remained unchanged from its excess-NO2value. While the overall chemistry was dependent upon this ratio (see below), there was no significant effect upon k2 at least in the low [OH], region where secondary reactions did not interfere with kinetic measurements.
-
76
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982
Leu and Smith
two pieces of evidence tend to argue against this. First, the reproducibility (to withh 12%) of our measurements at 228 K after an interval of 2 months and with the flow tube cleaned and recoated tends to suggest the absence of extra wall effects. Secondly, in a concurrent study of this reaction by flash photolysis resonance fluorescence, Michael et al.13 observed a similar effect with similar values for k2; in their apparatus wall reactions are less likely (because the reaction and observation zone is remote from walls), and thus the agreement between the 228 K values suggests that our value is also predominantly homogeneous. The results were fitted to the equation k2 = B P exp(-E/RT) 1.1
1 1
1
I
I
2
3
4
-i 5
Flgure 3. Dependence of rate constant k 2 upon temperature. The dashed line is calculated from eq 8 and the dotted line from eq 11. Values from ref 13 are shown as A.
The temperature dependence of k2 as shown in Table I and Figure 3 shows that k2 appears to pass through a minimum in the range 298-266 K. The possibility that some systematic error had caused this effect was investigated by writing the equations used for calculating k 2 in the forms (760 torr)FbaT u=
~ ~ ( 2 K)P,, 9 3
FHaPa,(9.662
X
lo'* cm3 K-'
torr-')
[HzSl =
FbaT 12, = -(u/[H,S])(d In [OH])/dx
where u is the average linear flow velocity, F, and FH s are the total flow rate and the flow rate of Ha,respectivefy (expressed in volume of gas at 293 K and 760 torr per unit time), r is the radius of the flow tube, P,, is the pressure a t the midpoint of the reaction zone over which d In [OH]/dx was measured (and was calculated from the pressure measured near the fluorescence cell by using Poiseuille's formula), and T is the temperature of the experiment. Hence aFba2P d In [OH] k2 = (4) r2Pa2FHfidx where a incorporates all of the numerical constants. Measurement of k2 thus involves determination of flow rates (by mass flowmeters regularly calibrated and always operated at 293 K regardless of the temperature of the flow tube), temperature, pressure, and the experimental slope. A careful examination of these factors eliminated the possibility of a large inadvertent systematic error creeping in at low or high temperatures to produce the unexpected temperature dependence. Experimental conditions such as flow velocity, total pressure, k,, and kl were always in the ranges in which diffusional errors were negligible and pressure-drop corrections small and accurately allowed for so that it is unlikely that any transport problems could have inadvertently produced this unusual temperature effect. There is the possibility that an additional surface reaction (apart from the normal OH wall loss) was increasing the rate of OH removal at lower temperatures. However,
(5)
because, of all of the equations commonly used to describe the temperature dependence of rate constants, this is the only one capable of yielding a rate minimum. The best fit to the results is k , = (2.27 X 10-19)P.5exp(725/T) cm3 s-l
(6)
where the precision in n is f0.5. Equation 6 reproduces the experimental k2 to within 7% (3% if the 247 K value is omitted), as shown in Table I. This equation is the dashed curve in Figure 3. The error bars on the experimental points represent one standard deviation. Use of a fixed radical source, a fixed detector, and a movable inlet for the other reactant under pseudo-firstorder conditions eliminates any contribution of wall reaction to k,, as shown in eq 2, provided that the wall constant k , remains the same both with and without added reactant. Plots of kl vs. [H2S] should therefore pass through the origin. However, positive intercepts were obtained at all temperatures (Figure 2 and Table I), though it is debatable whether they are significant at the higher temperatures. Interference from secondary reactions at low [H2S](i.e., low [H2S]/[OH], ratios) could produce this effect, but both our kinetic evidence and stoichiometric evidence (below) seem to eliminate this possibility. Care was taken to avoid excessively high reaction rates which could exceed the capabilities of the equipment and lead to low kl values at high [H2S]and hence produce positive intercepts. Another possibility is that, in the presence of H2S, the value of k , is increased (i.e., the surface for removal of OH is sensitized by H2S though the removal process is still independent of [H2S]and merely first order in [OH]). This possibility seems to be eliminated by the stoichiometricevidence presented below. Another possible explanation is that there is a wall reaction between OH and H2S which is independent of [H,S]; we were unable to find evidence for or against this possibility. Because of the linearity of the plots in Figure 2, we prefer to calculate k 2 from the slopes of these lines rather than from individual experiments by using k 2 = k,/[H,S]. It should be noted that similar intercepts have been observed prealso without adequate explanation. vi0us1y~~J~ Use of one standard deviation of the slopes of the linear in Figure 2 probably underestimates the uncertainty in k2 because of the occurrence of finite intercepts. However, use of the difference between k2 from the slope and k2 from the average of Izl/[H2S] is probably too extreme because, in the rather unlikely possibility that there is some heterogeneous component in k,, it would cause our estimate (13)J. V. Michael, D. F. Nava, W. Brobst, R. P. Borkowski, and L. J. Stief, J. Phys. Chem., following paper in this issue. (14) U. C. Sridharan,B. Reinmann, and F. Kaufman, J . Chem. Phys., 73, 1286 (1980). (15)L.F.Keyser, J . Phys. Chem., 84,1659 (1980).
Gas-Phase Reaction between OH and H,S
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982 77
of k2 to be high and use of this average would extend our limit even higher still. We therefore assess the error in k2 values as two standard deviations of the slope plus a systematic error resulting from use of eq 4 and from use of the "plug-flow" approximation for actual behavior in our flow tube. Errors of 0.5% in r, 0.5% in Pa,, 1% in T , and 1% in both Fbd and F H awith eq 4 lead to a systematic error of 7%. To estimate the error resulting from use of the plug-flow approximation, we can use the equation obtained by integrating the mass-conservation equation which accounts for viscous pressure drop as well as chemical reaction. This equation for a pseudo-fit-order reaction can be written as shown by MulcahyI6 in the form
where y = p/po the total pressure at the position at which [OH], was measured and p the total pressure at distance x: downstream where the concentration was [OH]. The plug-flow formula can be written as
Use of pav= (Po + p)/2 which is only approximately true, and rearrangement give kuwr, - (1 - Y W + y) -(1 - Y4)
(i
1
In ([OHIO/[OHI) lny This ratio will deviate most markedly from unity for a small extent of reaction ([OH],/[OH] small) over a large pressure drop 0, significantly less than 1). Although the equation for kl(cor)is not strictly applicable to this study in that it applies to a fixed radical source, a fixed H a inlet, and a movable detector and in that it is only a "two-point" formula, it is adequate for estimating errors. The extreme values used in this study were y = 0.85 with [OH],/[OH] = 4 and they lead to kl(wr)/kl(lug) = 0.95. More typically with y = 0.90 and [OH],/[OEf] > 4, the ratio was >0.97. Averaged over all experiments, use of a plug-flow formula should introduce an error of no more than 3%. Although not considered in the above analysis, radial diffusion is necessary to flatten out the parabolic concentration profile produced by viscous flow in order to approximate plug flow. It can be shown" that provided D/klr2 I1.0 (or since D a l/p, for helium carrier gas 690/pa,,k1? 2 1.0) then radial diffusion is sufficiently fast to produce plug flow and negligible error results. In all but a couple of our experiments this condition was met. Again it can be shown that errors due to axial diffusion will be less than 1% providing klD/u2 < 0.01 (or for helium carrier gas, 690kl/pavv2< 0.011, and again this condition held for all but a few of our experiments. Nevertheless, it would probably be cautious to assume errors in k2 of 1% from each of these diffusional effects. Possible impurities (almost certainly unreactive) in H2S could account for a further 0.5% error in FHzs. The total systematic error associated with our measurement of k2 is thus 7 + 3 + l + l + 0.5 N 13%. Combined with two standard deviations in the slopes as discussed above, this leads to our final estimate of (3.9 f 0.7) X lo-', cm3s-l for k2 at 298 K with the error in 1012k2 at each of the other temperatures being h l . 0 cm3 s-l. kl(Plug)
+
(16) M. F. R.Mulcahy, "Gas Kinetics", Nelson, London, 1973, p 60. (17) M. F. R. Mulcahy, "Gas Kinetics",Nelson, London, 1973, p 145.
TABLE 11: Conditions for Experiments in Figures 4 and 5 10'". [OHIO, curve a
10-12.
,
[H$I
cm-3
cm-3
7.3 14.6
e f
7.6 7.6 7.6 9.0 12.3 11.0
g
11.0
b C
d
5.1 5.3 5.3 5.5 5.5
[NO,I,/ [HI, 0.6 0.6 6.1 0.7 1.5 0.9 4.0
Product Analysis. The expected product HS was detected mass spectrometrically at m / e 33 by using a sufficiently low electron energy (15 eV) so that H a made only a small contribution to the peak. However, the profile of peak height vs. reaction time (typical ones in Figure 4) was that of a reaction intermediate rather than of a final product in that it passed through a maximum. The time at which this maximum occurred varied from considerably greater than the half-life for OH decay in the absence of excess NO, (i.e., [NO,], < [HI,) to somewhat less than the hydroxyl half-life when [NO21 > [HIP To quantify the amount of HS detected, we monitored the m / e 33 peak in the reaction of excess H,S with H atoms (performed by simply turning off the NO, flow in an OH + H2S experiment). The concentration of HS was calculated from the scheme H
+ H2S
H
+ HS
-
H2 + HS
(7)
H2 + S
(8)
+
with k, = 7.2 X (ref 18) and k8 = 2.5 X lo-" cm3 s-l (ref 19) by using known [HI,, [H2S],, and reaction times (which were short compared with the half-life of the reaction). Comparison of these peak heights with those observed in OH + H2S experiments performed under similar conditions just before and after these sensitivity measurements showed that the maximum HS concentrations in the OH + H2S experiments were of the order of one-third of the initial OH concentrations when [HI,> [NO,], and much less when [NO,], >> [HI,. These observations imply that there are some fairly fast procesm removing HS. Certainly HS + HS H2S + S with k 3 1.2 X 10-l' (ref 19) on its own would not be fast enough. Other product peaks were detected at m l e 48,49, and 64. A set of typical profiles is shown in Figure 5 with experimental conditions given in Table 11. It was not possible to convert these peak heights into concentrations, except that, if m / e 64 is solely SO2, then its rate of production is relatively slow (compared with removal of OH) and is of the right order of magnitude for production via SO + NO2 SO, + NO with k = 1.36 X lo-" cm3 s-'.~ However, the possibility of some contribution from SO + OH SO,+ H with k = 8.4 X cm3s-' (ref 21) cannot be eliminated. The curves in Figure 5 would correspond at the longest reaction times to about a 2550% conversion of reacted H2Sto SO2. Again, if the m / e 64 peak is solely SO,, then, the basis of our measured cracking pattern, there is some species other than SO2 making a major contribution to the peak at m / e 48. This is presumably
-
-
-
(18) M. J. Kurylo, N. C. Peterson, and W. Braun, J. Chem. Phys., 54, 943 (1971). (19) R.F.Hampson and D. Garvin, NBS Spec. h b l . , No.513 (1978). (20) M. A. A. Clyne and A. J. MacRobert,Znt.J.Chem. Kinet., 12,79 (1980). (21) J. L. Jourdain, G. LeBras, and J. Combourieu, Int. J. Chem. Kinet., 11, 569 (1979).
78
Leu and Smith
The Journal of Physical Chemistry, Vol. 86, No. I, 1982 I
I
I
I
I
I
I
I
I 50
I 10
I 20
30
I
I
1
I
10
20
33
40
TIME, msec
I
TIME, msec
Flgure 4. Dependence of [OH] (by resonance fluorescence) and [HS](by mass spectrometry at m l e 33) upon time at 296 K for conditions given in Table 11.
SO. However, because a significant m / e 64 peak is observed even when [NO,], < [HIo,we are inclined to believe that the peak is not solely SO,; there is probably some S2 produced at least in the absence of excess NOz. The peak at m / e 49 is observed only when [NO,], > [HI, and is probably due to HSO formed by HS + NOz HSO + NO. However, the m / e 48 peak appears both with and without excess NOz, which implies that there is a pathway to SO other than through HSO. With [HI, > [NO,], residual concentrations of NOz were so low (of the order of 5 X 1O1O~ m - that ~ ) the reaction S + NOz SO NO with k = 6.7 X lo-" (ref 22) could contribute only slightly to SO production in the required time scale. The reaction sequence H2S + OH HzO, HS + OH HzO + S, S + OH SO + H would hardly seem fast enough to contribute significantly before HzS had removed virtually all OH. The reaction S Oz SO 0 with k = 2.2 X 10-l2 cm3 s-l (ref 23) should also be only a minor participant since Oz concentrations in our system were typically of the order of 1Ol2cm-3 or less. The possibility that SO is being formed by S or SH scavenging oxygen from material adsorbed on the walls of the flow tube cannot be eliminated and, in the absence of other oxidants, seems a likely explanation. When [NO,], > [HI,, the m / e 46 peak showed a slow decrease as reaction time increased, corresponding to
Scheme I HO
-
-
-
+
-
-
(22) M. A. A. Clyne and P. D. Whitefield, J. Chem. SOC.,Faraday Trans. 2, 75, 1329 (1979). (23) D. D. Davis, R. B. Klemm, and M. Pilling, Int. J. Chem. Kinet., 4, 367 (1972).
HS
+
HS
HS
+
OH
HS
+H 2s
S
+
OH or 02 or
h
+ - + - +
H2S
S
HSO
+
SO
+
H2S
S (minor)
H20
S (minor)
+S
homo- or
s2
g,nro"r
I
- + - + - + -
wall
NO2 or 02 or wall NO2
HS
H20
-HZ
+ NO2 SO + OH HS + NO2
+
+
+
when
[HI0
'
[NO210
SO
SO
SO2
HSO
-
N O (minor) H (minor)
1
NO
SO or SOz when[N02]0 > [ H I 0
SO2
+ NO
consumption of a further 4040% of the amount consumed initially to form OH. This is consistent with the above suggestions that NOz oxidizes HS and that it forms SOz (remembering that these latter processes were not followed to completion). Figure 5 implies that HSO is fairly rapidly removed, presumably by conversion to SO and/or SO,. No evidence could be found for the nature of this process which is probably due to reaction with NOz, Oz, and/or wall-adsorbed species. The possibility that H (and hence OH) is produced in this process cannot be eliminated, but the amount would have to be relatively small since predominantly linear first-order decay curves were observed for OH. No peaks could be found at m / e 51 (corresponding
Gas-Phase Reaction between OH and H2S
The Journal of Physical Chemistry, Vol. 86, No. 1, 1982 70
TABLE 111: Stoichiometric Measurements at 296 K * 5 a Z l
1
A1 A2 A3 A4 A5 B1 B2 B3 B4
10.0
c1 D1 D2 El F1 F2 F3 F4 F5
G1
0
10
20
30
40
50
60
70
TIME, msec Flgure 5. Time dependence at 296 K of [OH] (by resonance fluorescence) and of mass spectrometer peaks at m l e 48, 49, and 64 for conditions given in Table 11. Peak heights were converted to " t r a t b n s by assuning that the m l e 64 peak was solely SO2 and by using the same conversion factor for the m l e 48 and 49 peaks, which means that for these curves absolute concentrations are only semiquantitative.
to an initial adduct H2SOH),at m / e 47 (HN02),or at m / e 65 (HS02). The proposed mechanism can be summarized by Scheme I. In view of the complexity of the reactions occurring in time scales similar to those in which OH decays were measured, it was essential to establish as conclusively as possible that the measured OH decay rates were indeed the rates of the initial reaction of OH with H2S. While the usual kinetic techniques for testing for the elimination of secondary reactions was used, namely, reduction of [OHIO to lower and lower values until constant k2 values were obtained, a further test was undertaken by measuring the stoichiometric ratio. Stoichiometric Measurements. In a significant number of kinetic experiments, the stoichiometric ratio, A[OH]Ha/A[H2S],the number of OH radicals consumed by HzS (as distinct from wall loss) per H2S molecule consumed, was measured. This was done with the H2S injector at the position of longest reaction time by measuring [OHIO,,, the concentration of OH at the fluorescence cell with zero H2S flow, then by adding H2S and measuring [OH]," (fluorescence) and h34(mass spectrometry), and finally by turning off the discharge producing H atoms and remeasuring hW The difference in h34peaks combined with a calibration factor determined under identical conditions gave A[H2S]. Periodic calibration of the resonance fluorescence signal allowed conversion of measured signals into actual OH concentrations. If the kinetic scheme is written as OH + wall OH removal (k,) qOH + H2S products (k2) with -d[OHl/dt = (k, + qk2[H2SI)[OHl
--
H1 J1 52 53
1.8
2.7
3.1
6.5
4.0 2.1
11.2 11.0
1.5 1.4
12 18
0.9 0.7 0.5
11.2 8.5 4.8
7.8 11.4 18.6 24.6 35.0 4.1 9.3 14.2 18.5 4.7 4.4 11.3 4.4 1.6 2.3 3.0 4.9 7.1 4.7 6.2 6.4 17.4 25.5
1.0 0.95 1.2 0.70 1.07 1.4 1.2 0.9 1.1 1.2 1.4 1.5 1.9 1.8 1.6 1.5 1.3 1.3 1.5 2.0 1.3 1.16 1.0
The total amount of OH consumed between injector and fluorescence cell with H2S present is A[OHI,tal = [OHIO - [OHIcell and [OHIHB,the amount of OH consumed by reaction With H2S (as distinct from wall loss) is
qk2[H2S]is the pseudo-first-order rate constant obtained from resonance fluorescence decay measurements. Hence, the stoichiometric ratio q can be calculated: q = A[oHlH$3/A[H2s]
The results from these experiments are shown in Table 111. Because A[H2S]was calculated from the small difference between two quite large peaks, the overall accuracy in q was approximately fO.l. Sets A and B show that, with [NO,], > [HI, at comparatively low [OH],, providing that [H2SlO/[OH], is greater than about 8-15, q is approximately unity so that under these conditions (which correspond to those used for the majority of kinetic measurements) the measured rate constant, qk2, is in fact k2, the rate constant for the initial step. Comparison of sets A, D, and F indicate that q depends not only upon [H2S],/[OH], (as would tend to be the case for two simple consecutive OH reactions) but also upon [OH],: the higher [OH], the greater is q. Experiments C1, D1,and E l show that increasing amounts of NO2 tend to lower q toward unity. These observations are consistent with the above mechanism because, if [NO2] is great enough for NOz reactions to dominate over the comparable OH reactions, q would be 1. Set J shows that, when [HI, > [NOzlo, a somewhat higher ratio of [H,S],/[OH], (viz., about 20) is needed to reduce q to 1. This is consistent with the proposed H2S + S mechanism in that dominance of HS + HS over HS OH H20 + S does not reduce q downward toward 1: it is necessary for HS to react with something else (e.g., H) to produce q = 1. Experiments G1, H1, and J1 suggest that again q depends upon [OH], and not just upon [H,S],/[OH],. Values of q are quite high when the
+
-
-
80
Leu and Smith
The Journal of Physical Chemlstty, Vol. 86, No. 1, 1982
amount of exces H is small (Gl, Hl), which is consistent when HS + H competing with HS HS and HS + OH. This system is so complex that it is not possible to make other than qualitative conclusions about the mechanism, and even then some are rather speculative. Despite this, both by stoichiometric and by kinetic means, it has been possible to demonstrate that the rate constant measured from OH decay rates is in fact the rate constant of the initial step, providing [OH], is leas than about 4 X 10" cmS and [H2S],/[OH], is greater than about 10-20. These stoichiometric results can also be used to further information about the unexplained intercepts in Figure 2 discussed above. If these intercepts are due (a) to some experimental artifact or (b) to the occurrence of a wall reaction of HzS with OH which is independent of HzS concentration,then the above analysis of the stoichiometric measurements is valid. If, however, the intercept is due to an additional wall removal of OH sensitized by H2S but independent of H2S concentration, then, instead of eq 9, we should write
CH,). Association reactions (OH + NOz + M,n OH + SOz + M,28OH + C2H4 + MB) are usually fitted by eq 5 with n = 0 and negative E , this being interpreted in terms of a composite rate constant which represents both reaction and collisional stabilization of an excited adduct first formed. A third group of reactions (e.g., OH + CO, OH + OHN)shows very little temperature dependence around room temperature but significantly greater dependence at higher temperature, and these have been fitted by equations such as it = exp(a + b T ) or k = AT'. The reaction 0 + OH which displays a negative temperature dependence% but none of the other features of association reactions seems to fit into none of these categories. While a negative E was found for OH + CH3SCH3,3, it was sufficiently small to be attributed to a temperature-dependent preexponential factor. In view of this diversity of temperature dependences of OH reactions, the unusual behavior displayed in Figure 3 is perhaps not so surprising. For hydrogen abstraction we would expect the transition state for reaction 1 to be
where k'is the intercept and k'+ qk2[H&3]is the measured pseudo-first-order rate contant for the prevailing value of [H,SI. If this expression is used to calculate q, then, for 19 of the 23 experiments in Table 111, q is significantly less than unity (typically 0.6-0.8) and in the other 4 it is approximately unity. Since it is hard to envisage a mechanism which would lead to q less than unity, we conclude that the intercepts in Figure 2 are not due to mere additional wall loss of OH.
Because the rotational and vibrational partition functions of this transition state are extremely sensitive to the OS internuclear distance and to the frequencies of the OHS bending vibrations, respectively, and because there are no stable compounds of similar geometry to allow us to argue by analogy, transition-state calculations involve great uncertainties but even so seem unable to rationalize a negative AH* value. On a few occasions previously, similarly shaped Arrhenius plots have been reported, for example, for Br + H131and F HBr and F DBr.32 These were interpreted in terms of two parallel mechanisms (one with a positive, the other a negative temperature dependence). Although our results could probably be interpreted analogously, we can find no convincing support for such an explanation. Alternatively, if we attribute the apparent rate minimum to some unaccounted experimental artifact (not particularly likely in view of the thorough investigation of possible sources of error), the results can be fitted to a simple Arrhenius expression to yield k , = (5.9 X 10-l2) exp(-89/T) cm3 s-l (11)
+
Discussion The unusual temperature dependence in Figure 3 can be rationalized by proposing that the enthalpy and entropy of activation, AH* and AS*, both have significant temperature dependence. If ACp* is defined by AC,' = ( d A H * / d V p , then
AH' = AH', + TAC,* AS' = AS*,
+ ACp In T
Hence, the usual transition-state equation k (kT/h)eG*/Re-m*/RT becomes, after taking logarithms and substituting I n k = In B + n l n T + E/T (10) where In B = In k / h + AS*,/R - ACp'/R, n = 1 + ACp'/R, and E = -AHSo/R. Equation 10 is of the same form as the experimental equation 6. Comparison of terms yields ACp'/R = 1.5 and AH*,= -6.0 kJ mol-'. The finding of a negative enthalpy of activation for what appears to be a simple hydrogen abstraction reaction is surprising. However, it should be noted that a great variety of temperature dependences has been observed for OH reactions. Most hydrogen abstraction reactions (OH + Hz, OH + alkane^^^-^^) follow eq 5 with positive E and with n = 0 over small temperature ranges and n around 1.5-2.5 for large temperature ranges (notably OH + H2, OH + (24)R.Zellner, J. Phys. Chem., 83,18 (1979). (25)F. P. Tully and A. R. Ravishankara, J. Phys. Chem., 84, 3126 (1980). (26)R.Atkinson, K.R. Darnall, A. C. Lloyd, A. M. Winer, and J. N. Pitts, Adu. Photochem., 11, 375 (1979).
+
+
and this equation reproduces the experimental values to within 10% over the full temperature range (dotted line in Figure 3). Transition-state theory predicts for the A factor a value of the same order of magnitude as that in eq 11. When our results are compared with those of previous workers, the worst discrepancy occurs between ours and those of Westenberg and de H a a ~ In . ~ view of the limited number of experiments performed by them and of the higher [OH], used, it seems likely that they did not adequately eliminate secondary reactions which consume OH, and hence their values are probably high. Our value is in fair agreement with the room-temperature value of StuhP when estimated errors of both studies are considered. The discrepancy between our results and those of Perry et aL5 (27)P. H.Wine, N. M. Kreutter, and A. R. Ravishankara,J. Phys. Chem., 83,3191 (1979). (28)G.W. Harris,R. Atkinson,and J. N. Pitta, Chem. Phys. Lett., 69, 378 (1980). (29)R. S.Lewis and R. T. Wataon, J . Phys. Chem., 84,3495(1980). (30)R.Atkinson, R.A. Perry, and J. N. Pitta, Chem. Phys. Lett., 64, 14 (1978). (31)C . C. Mei and C. B. Moore, J. Chem. Phys., 70, 1759 (1979). (32)E.Wunberg and P. L. Houston,J. Chem. Phys., 72,5915(1980).
J. phys. Chem. 1982, 86,81-84
is only just outside the quoted errors. However, in their experiments inadvertent photolysis of H2S by the flash woould probably have produced significant amounts of HS which via the rapid reaction HS + OH could lead to high values for k2; if this latter reaction had a near-zero temperature dependence, it would lead to those workers observing an erroneously low temperature dependence for kp. However, the observed independence of k2 upon flash energy tends to argue against this explanation. When quoted errors are taken into account, our values agree with those of Michael et al.13 at all three temperatures used by them. Although their larger random errors did not allow them to place any significance upon the apparent dependence of k2 upon temperature, we note that they appear to have obtained the same qualitative tem-
81
perature dependence that we observed. Note Added in Proof. Very recently Wine et al. [ J . Phys. Chem., 81,2660 (198l)l reported kz = (6.4 f 1.3) X W2exp[(-55 f 58)/T]cm3 s-' which is in good agreement with the present result. Acknowledgment. R.H.S.thanks Macquarie University for a grant of study leave and thanks the Jet Propulsion Laboratory and W. B. DeMore in particular for hospitality andd partial financial support. We are grateful to L. J. Stief for disclosure of unpublished results from his laboratory. This paper represents the results of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under NASA Contract No. NAS7-100.
Temperature Dependence of the Absolute Rate Constant for the Reaction of Hydroxyl Radical with Hydrogen Sulfide J. V. Michael,+ D. F. Nava, W. D. Brobst, R. P. Borkowskl,t and L. J. Stlef's Asfrochembfry Bnlnch, Laboratory for Exfraterrestrlel R~plcs,oodderd Space N@ht Center, Qtwnben, Maryland 20771 (Recelvd: March 1, 1981; I n Finel Form: September 18, 1981)
Absolute rate constants for the reaction of hydroxyl radical with hydrogen sulfide were measured at 228,298, and 437 K by using the flash photolysis-resonance fluorescence method. Hydroxyl radicals were produced by the photolysis of water, and resonance fluorescence from OH was measured by multiscaling techniques. The results at 228, 298, and 437 K were found to be (5.11 f 0.39) X 10-l2,(4.42 f 0.36) X 10-l2,and (5.57 f 0.48) X respectively, all in units of cm3molecule-' s-l. The average value measured was (5.01 f 0.55) X cm3molecule-' s-l, where the uncertainty cited is one standard deviation. The results are discussed theoretically and compared to previous determinations.
Introduction The oxidation of hydrogen sulfide is of interest in such phenomena as the chemistry of combustion processes, the atmosphere of Venus, and the troposphere and the stratosphere of the earth. The reaction
OH
+ H2S
-+
H2O + SH
(1)
is significant in all of these instances and is probably the major loss process for H2S in the troposphere and the stratosphere.'P2 Knowledge of the rate constant for reaction 1at atmospheric temperatures is therefore useful in order to estimate the chemical lifetime of atmospheric H2S. Conversely, the accuracy of removal coefficients for H2S determined from atmospheric measurements can be checked by calculating the mean concentration of OH required to produce this observed removal rate and comparing such [OH] estimates with observational data. Again, this requires knowledge of the rate constant kl. Such a comparison was very recently made by Jaeschke et al.? but they used a value2 for kl of (3.1 f 0.5) X cm3molecule-' s-' which is nearly a factor of 2 lower than three other determinations* of this rate constant. 'Viiting Professor of Chemistry, Catholic University of America, Washington, DC 20061. NASA/ASEE Summer Faculty Fellow, 1980; Chemistry Department, King's College, Wilkes-Barre, PA 18711. 'Adjunct Professor of Chemistry, Catholic University of America, Washington, DC 20084.
*
The rate constant kl has been measured by several different investigators using a variety of technique^.^^^^ The room-temperature values of the rate constant obtained by three of these studies agree very well. The values reported by Westenberg and de Ham4 using discharge flow with electron spin resonance detection, by Perry et ala6 using flash photolysis-resonance fluorescence, and by Cox and Sheppards using a competitive rate method were (5.5 f 0.3) X W2,(5.25 f 0.53) X 10-l2,and (5.0 f 0.3) X 10-l2 cm3 molecule-' s-l, respectively. In contrast to this apparently good agreement, however, the temperature dependence of the rate constant remains unsettled. Westenberg and de Haas4 report k = 2.3 X lo-'' exp(-880/RT) cms molecule-' s-' over the temperature range 298-885 K. Perry et aL6 find the rate constant to be invariant with temperature over the range 297-424 K and quote an avcm3molecule-' s-'. At erage value of (5.25 f 0.53) X 424 K, the Perry et alS5value is -55% lower than that calculated from the data of Westenberg and de Haas.4 In addition, if the data reported by Westenberg and de Haaa4 were extrapolated to lower temperatures and the temperature invariance noted by Perry et al.s were assumed (1)T.E.Graedel, Rev. Geophys. Space Phys., 15,421 (1977). (2)F.Stuhl, Ber. Bunsenges. Phys. Chem., 78, 230 (1974). (3)W.Jaeschke, H. Claude, and J. Herrmann, J. Geophys. Res., 85, 5639 (1980). (4)A. A. Westenberg and N. de Haas, J. Chem. Phys., 59,6685(1973). ( 5 ) R. A. Perry, R. Atkinson, and J. N. Pitb, Jr., J.Chem. Phys., 64, 3237 (1976). (6)R. A. Cox and D. Sheppard, Nature (London), 284,330 (1980).
This article not subject to US. Copyright. Published 1982 by the American Chemical Society
