1119
J . Phys. Chem. 1988, 92, 11 19-1 126
Equations A.6.b and A.6.c may be used to express the derivatives dF,/dO, and dF,/dO, in terms of spatial gradient information. Therefore, solving for these latter two quantities and substitution into eq A.6.a will finally lead to an expression for the sensitivity (dOn/daJ)in terms of the sensitivities of 0, and 0, and their various spatial gradients. This result is an exact analogue of eq 14. A similar statement for Green's functions would also follow in this case. (3) Two Dominant Dependent Variables with One Independent Coordinate. Under these conditions eq 10a takes on the form
The latter relation would imply, for example, that the velocity measured with respect to Ol is the same as that determined by 0, when x is the time t and y is a spatial coordinate. These various relations have been verified in a steady propagating combustion wave simulating a flame front moving through a combustible mediume9 Analogous relations may be derived for Green's functions. (2) Two Dominant Dependent Variables and Two Coordinates. This case is a direct extension of that discussed in item 1 above except now an additional dominant dependent variable 02(x,y,a) is assumed to exist. Recalling the discussion at the beginning of the appendix the two variables 0, and 0, are assumed to act independently of each other. Therefore, eq 10a is now replaced by the form
On(X,Y,a) E Fn(Ol(X,Y,a),O ~ ( X , Y P ) )
On(x,a) E F ~ ( O I ( X P ) , O ~ ( ~ P ) ) ('4.7) Differentiation of this equation with respect to ai and the coordinate x will lead to equations of exactly the same form as (A.6.a) and (A.6.b). However, in this case we no longer have t h e y coordinate to produce the remaining equation (A.6.c). A third independent equation of this type is necessary to again eliminate the gradients dF,/dOl and dFn/dO,. Such an equation can be found by differentiating eq A.7 with respect to a different parameter ak to produce the analogue of eq A.6.c. Following the same operations discussed above, a scaling relation will be found between the spatial gradients and sensitivities involving both parameters a, and &. The above brief treatment of multivariable systems only touches on a number of possibilities and even more complex relations might exist. Furthermore, we only considered scaling relation arguments and the development of self-similarity conditions has not been explored. As discussed in the conclusion, the basic remaining question concerns the derivation, or at least understanding, of the general conditions under which conjectues of the type in eq 10a are valid.
('4.5)
Simple differentiation of this equation will produce the following relationships:
(z)( (z)($) (z)($)
(2) 2)+ (7) ($( $)+ N
N
(A.6.b)
(A.6.c)
(9) Reuven, Y.; Smooke, M. D.; Rabitz, H., to be submitted for publica-
tion.
Rate Constants for the Reactions OH Products
+ HOC1
-
H,O
+ CIO and H + HOC1
-
C. A. Ennist and J. W. Birks* Department of Chemistry and Biochemistry and Cooperative Institute for Research in Environmental Sciences (CIRES). University of Colorado, Boulder, Colorado 80309 (Received: December 29, 1986; In Final Form: July 23, 1987)
A new laboratory source of gaseous hypochlorous acid (HOCl) has been used in two kinetics investigations in a mass spectrometry-resonance fluorescence discharge flow system. Two potential removal reactions of stratospheric HOCl were studied. The rate constant for the reaction OH + HOCl H 2 0 C10 (1) at 298 K was found to be lower than the NASA estimate by a factor of about 2-12; a value in the range (1.7-9.5) X lo-" cm3 molecule-' s-l for k l is reported here. The reaction of CI,O + OH interfered in the study of k , and was the subject of a preliminary investigation. Its rate constant was determined to be (9.4 f 1.0) X cm3 molecule-l s-l at 298 K. The rate constant for the reaction H + HOCl products (2) was determined to be (5.0 f 1.4) X cm3 molecule-' s-I at 298 K. Although branching ratios for three possible product channels could not be determined, OH was identified as a product. The results of this work imply that reactions 1 and 2 are not competitive with direct photolysis in the removal of HOCl from the stratosphere.
-
Introduction Hypochlorous acid (HOC1) began to attract attention in 1976 when an atmospheric modeling study suggested that HOCl may serve as a temporary reservoir for chlorine atoms in the stratosphere.' Evaluation of this possibility requires values of the rate constants for all reactions that form and destroy HOCl to a significant extent. In earlier work our group has reported on several such reactions.2-5 Here, we present rate constant measurements for two previously unstudied reactions of HOCI. The primary focus of our study is the reaction OH + HOC1 H,O + CIO (1)
-
Present address: National Center for Atmospheric Research, Boulder, CO 80307. *
0022-3654/88/2092-1119$01.50/0
+
-
Using a low-pressure, mass spectrometry-resonance fluorescence discharge flow system, we have measured the rate constant of reaction 1 ( k , ) at 298 K. Additionally, we have found that the reaction H + HOCl products (2)
-
(1) Prasad, S. S. Planet. Space Sci. 1976, 24, 1187. (2) Leck, T. J.; Cook, J. L.; Birks, J. W. J. Chem. Phys. 1980, 72, 2364. (3) (a) Cook, J. L.; Ennis, C. A.; Leck, T. J.; Birks, J. W. J. Chem. Phys. 1981, 74, 545. (b) Cook,J. L.; Ennis, C. A,; Leck, T. J.; Birks, J. W. J. Chem. Phys. 1981, 75, 497. (4) (a) Ennis, C. A,; Birks, J. W. J. Phys. Chem. 1985.89, 186. (b) Ennis, C. A. Ph.D. Thesis, University of Colorado, Boulder, CO, 1985. (5) Mishalanie, E. A,; Rutkowski, C. J.; Hutte, R. S.; Birks, J. W. J. Phys. Chem. 1986, 90, 5578.
0 1988 American Chemical Society
1120 The Journal of Physical Chemistry, Vol. 92, No. 5, 1988
Ennis and Birks
c-----a perature-regulated fluids may be circulated. In this way, reaction
,,,ET
-1.
MlCROWAVE
TITRATION PORT\,,
m
f
WMP
Figure 1. Schematic of the discharge flow system, with laser-induced fluorescence and mass spectrometry for detection. Details of the construction of the jacketed flow tube and double injector are omitted in the interest of clarity.
occurs readily under laboratory conditions, and we report a measurement of its room temperature rate constant. Previous kinetics studies of HOCl have investigated the HOCl formation reactionzyb* ultraviolet absorption s p e c t r ~ m , ~ *and ~-'~ reaction with chlorine atomse3g4To date, the reactions HOz + CIO HOCl 0 2 (3) HOC1 hv O H + C1 (4) have emerged as the most likely dominant formation and destruction mechanisms of stratospheric HOCl. In an attempt to explain the recently discovered antarctic ozone hole, the heterogeneous reaction CIONOz HzO HOCl + H N 0 3 (5)
+
+
+
-+
-
has been proposed as a source of HOC1.I6 Because of the difficulty of measuring the UV absorption spectrum and the lack of kinetics measurements for chemical reactions of HOCl with OH, 0, and H, the destruction pathway has been the most uncertain component in the current picture of HOC1 stratospheric photochemistry. Considering both the stratospheric abundances of 0, H, and O H radicals and the estimates of the OH HOC1 and 0 HOCl rate constants," the OH HOCl reaction would be expected to be the most important of the chemical removal processes. Our measurements of the OH HOCl and H + HOC1 rate constants make use of a new laboratory source of gaseous HOCI, described earlier.4 Compared to the conventional static preparation of HOC1 by C1zO-HzO-HOC1 equilibration, the new source is dynamic and has a substantially lower ClzO impurity level. The source enabled us to make measurements, reported here and in earlier papers,"*5which otherwise would have been impossible due to large interferences from C1,O.
+
+
-
-
WMP
PRESSURE PORT
+
rates can be measured over a range of temperatures. The injector used in this work is a double injector, designed specifically for production of OH radicals but equally useful for producing H atoms. The injector consists of an outer tube of 12 mm i.d. surrounding a coaxial and shorter tube of -4 mm i.d. Gases flowing down the inner tube and outer tube do not mix until a point 10 dm from the end of the injector. Gases exit the tip of the injector via five radially directed, 1-"-diameter orifices and rapidly mix with the flow tube gas stream. Inner surfaces of the injector are coated with phosphoric acid to reduce heterogeneous loss of radicals on the walls. For the same reason, a thin Teflon liner is inserted into the flow tube. Wall loss constants of 10 s-l or less are achieved for O H radicals in the Teflon flow tube. Differential pumping is used to admit a sample of the flow tube gases into the ion source of a UTI Model 1OOC-02 quadrupole mass spectrometer, so that a typical flow tube pressure of 2 Torr Torr in the mass spectrometer produces a pressure of 5 X chamber. Sample ionization by impact of moderate energy (70 eV) electrons is followed by extraction and focusing of positive ions onto the first dynode of a 14-stage Cu-Be electron multiplier. The mass spectrometer serves as a general detector for many flow tube species, such as HOCl, ClZO,Cl,, and NO2 in this study. Through selected-ion monitoring of the parent peaks, detection limits (S/N = 2) are 2 X 10" molecules cm-3 for CI, at m / e 70, 1 X 10" molecules cm-3 for ClzO at m / e 86, and 4 X 1O1O molecules cm-3 for NO2at m / e 46. HOC1 is detected at its parent peak at m / e 52.4 The detection limit for HOC1 is 1 X lo9 molecules ~ m - ~ . Absolute calibration of the HOCl signal is referenced to the NO2 calibration. A brief description of the HOCl calibration will be given here; details have been described previously! A three-step scheme is used. In the first step, the ratio of the mass specis determined trometer's sensitivities to O3and HOCl (So,/SHml) by reacting a supply of chlorine atoms alternately with either an excess of O3or an excess of HOC1. Under the conditions of the experiment, the amount of O3 consumed can be equated to the is calculated. In the amount of HOCl consumed, and So,/SHoa second step, the ratio of the mass spectrometer's sensitivities to NOz and O3 (SNo2/So3) is determined by equating the amount of O3consumed with the amount of NOz produced in the reaction NO O3 NOz + 02. In the final step of the scheme, the desired ratio of sensitivities, S N 0 2 / S H O C I , is calculated by multiplication of the ratios found in steps one and two. The presence of large residual water peaks at m / e 18 (HzO+) and m / e 17 (OH') precludes the use of the mass spectrometer to detect O H radicals in the flow system. For this reason, the optical technique of resonance fluorescence is employed as a specific detection scheme for OH radicals and supplements the more general detection capabilities of the mass spectrometer. The two detection schemes are used simultaneously, with the flow tube species first crossing the region of OH detection and then entering the sampling orifices and mass spectrometer chamber (Figure 1). Hydroxyl radicals are detected by exciting the O H X211 A2Z+ transition (0,Ovibrational band) at 309 nm and observing the fluorescence from the A X transition, resonant at 309 nm. Excitation is achieved using the frequency-doubled, 6 18-nm fundamental of a flashlamp-pumped dye laser (Chromatix Model CMX-4). A typical pulse rate of 5 H z is used to excite a dye solution consisting of R590 rhodamine perchlorate (Exciton, Inc.) dissolved in a 1:l volume mixture of methanol-water. O H fluorescence radiation is detected with a UV-sensitive bialkali photomultiplier tube (Hamamatsu Model R269P), mounted on the flow tube housing at right angle to the excitation beam. A 307-nm narrow band-pass filter (Melles Griot No. 03FlR001, fwhm = 10 f 2 nm, 20% transmission at peak wavelength) precedes the photocathode. Photon counting electronics are gated to the laser pulse. For a typical integration time of 30 s, the OH detection limit is -3 X 10" molecules cm-'. B. Reactant Generation and Calibration. Cylinder gases used in this work were helium (U.H.P., 99.999%), chlorine (H.P ,
+
+
Experimental Section A . Flow Tube Apparatus. Experiments were performed using a low-pressure discharge flow system (Figure 1). Some details of the system have been described earlier: Briefly, reactants enter the system by way of either the 2.6-cm-i.d. Pyrex flow tube or a coaxial 1.2-cm4.d. Pyrex injector. Surrounding the flow tube's inner region of gas flow is an outer jacket, through which tem(6) Reimann, B.; Kaufman, F. J . Chem. Phys. 1978, 69, 2925. (7) Stimpfle, R. M.; Perry, R. A.; Howard, C. J. J . Chem. Phys. 1979,71, 5183. ( 8 ) Burrows, J. P.; Cox, R. A. J . Chem. SOC.,Faraday Trans. 1 1981, 77,
(11) Jaffe, R. L.; Langhoff, S. R. J . Chem. Phys. 1978,68, 1638. (12) Molina, L. T.;Molina, M. J. J . Phys. Chem. 1978, 82, 2410. (13) Spence, J. W.; Edney, E. 0.; Hanst, P. L. J . Air Pollut. Control Assoc. 1980, 30, 5 1 . (14) Knauth, H.-D.; Alberti, H.; Clausen, H . J . Phys. Chem. 1979, 83, 1604. (15) Molina, M. J.; Ishiwata, T.;Molina, L. T.J . Phys. Chem. 1980, 84, 821. (16) McElroy. M. B.;Salawitch, R. J.; Wofsy, S. C.; Logan, J. A. Nature 1986, 321, 7 5 9 . (17) "Chemical Kinetic and Photochemical Data for Use in Stratospheric Modeling"; Evaluation Number 7, NASA Panel for Data Evaluation, JPL Publication 85-37, Pasadena, CA, 1985.
-
+
-
-
+
The Journal of Physical Chemistry, Vol. 92, No. 5, 1988 1121
Reactions of HOCl with H and OH 99.5%), nitric oxide (C.P., 99%), and a commercially prepared mixture of 0.13% H2 in helium. HOCl was prepared by using the dynamic source, described earlier." HOC1 is formed by continuously bubbling a dilute C12/He mixture through a saturated aqueous C a C 0 3 solution. The resultant gas stream is introduced directly into the flow tube and contains a mixture of water vapor, C 0 2 , HOCl, unreacted C12, and C1,O. The C120 impurity is typically
