4750
J. Phys. Chem. 1984,88, 4150-4758
High-pressure Flow Kinetics. A Study of the OH
+ HCI Reactlon from 2 to 100 torr
Leon F, Keyser Molecular Physics and Chemistry Section, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91 109 (Received: January 31, 1984)
The discharge-flow resonance fluorescence technique has been used to obtain absolute rate data for the OH + HC1 reaction at total pressures from 2 to 100 torr of helium and 2 to 25 torr of 80% nitrogen plus 20% helium. At 295 K the rate constant is (7.9f 0.4) X cm3molecule-' s-l. The results are independent of the pressure, the carrier gas, the surface-to-volume ratio, and the source of HCl. The temperature dependence expressed in Arrhenius form is (2.1 f 0.4) X exp[(-285 A 40)/Tl for 258 5 T I 334 K. The error limits given are twice the standard deviation; overall experimental error is estimated to be f15%. The interaction of flow dynamics, diffusion, and chemical reaction is discussed. Procedures are given to correct rate data for axial and radial diffusion.
Introduction Isothermal flow reactors are widely used in the field of gas-phase chemical kinetics to obtain rate data over a large temperature range a t low pressures. The usual apparatus consists of a cylindrical tube through which reactive species are rapidly passed by means of an inert carrier gas such as helium, argon, or nitrogen. Detectors generally are fixed at the downstream end of the flow tube with either fixed or movable radical sources upstream. Conditions are such that laminar flow with a parabolic velocity profile is at least approximately established. Variations of this method have been used to study reactions of ground-state neutral, excited-state, and ionic species. Limitations imposed upon these systems by the interaction of flow dynamics, diffusion, and chemical reaction have been discussed by many a~th0rs.l-l~The minimum pressure which can be used is a few tenths of 1 torr and is determined by the size of the viscous pressure drop across the reaction region, axial diffusion, and wall losses of the reactive species. As the pressure is increased, diffusion rates decrease and the resulting radial concentration gradients and longer mixing times impose a high-pressure limit of about 10 torr on conventional flow system measurements. Recent studies have shown that rate coefficients for many apparently simple bimolecular reactions have negative temperature dependence^.'^ Reactions of this type include OH + H N 0 3 , OH + HO,, NO C10, NO HOz, and C10 + HOz. Moreover, rates of some of these same reactions may also depend on total pressure. These observations imply that the true reaction mechanism is more complicated than a simple two-body collision and may involve formation of an intermediate complex. These pressure and temperature dependencies require that rate data for such reactions not be extrapolated far from the conditions under which they were obtained. For modeling the upper atmosphere
+
+
(1) Kaufman, F. Prog. React. Kinet. 1961, 1, 1. (2) Walker, R. E. Phys. Fluids 1961, 4, 1211. (3) Mulcahy, M. F. R.; Pethard, M. R. Aust. J. Chem. 1963, 16, 527. (4) Huggins, R. W.; Cahn, J. H. J . Appl. Phys. 1967, 38, 180. (5) Ferguson, E. E.; Fehsenfeld, F. C.; Schmeltekopf, A. L. Adv. At. Mol. Phys. 1969, 5, 1. (6) Bolden, R. C.; Hemsworth, R. S.; Shaw, M. J.; Twiddy, N. D. J . Phys. B. 1970, 3, 45. (7) Farragher, A. L. Faraday SOC.Trans. 1970, 66, 1411. (8) Poirier, R. V.; Carr, R. W., Jr. J . Phys. Chem. 1971, 75, 1593. (9) Ogren, P. J. J. Phys. Chem. 1975, 79, 1749. (10) Hoyermann, K. H. In "Physical Chemistry, An Advanced Treatise"; Jost, W., Ed.; Academic Press: New York, 1975; Vol. VIB. (11) Brown, R. L. J . Res. Natl. Bur. Stand. (US.) 1978, 83, 1. (12) Howard, C. J. J. Phys. Chem. 1979,83, 3. (13) Fontijn, A.; Felder, W. In "Reactive Intermediates in the Gas Phase"; Setser, D. W., Ed.; Academic Press: New York, 1979. (14) Kolts, J. H.; Setser, D, W. In "Reactive Intermediates in the Gas Phase"; Setser, D. W., Ed.; Academic Press: New York, 1979. (15) DeMore, W. B.; Molina, M. J.; Watson, R. T.; Golden, D. M.; Hampson, R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R. JPL Publication 83-62; Jet Propulsion Laboratory, California Institute of Technology: Pasadena, CA, 1983.
0022-3654/84/2088-4750$01.50/0
from 15 to 50 km, rate coefficients for pressure- and temperature-sensitive reactions are needed from about 200 to 300 K and 0.5 to 100 torr. The purpose of the present study is to extend isothermal flow reactor measurements to pressures which are considerably higher than those previously used, for example, up to 100 torr of helium. This would allow use of this versatile experimental technique to obtain rate data for reactions under conditions which actually exist in the upper atmosphere. This pressure range also overlaps that of flash-photolysis measurements which generally have a lower limit around 10-20 torr and allows comparison of pressure-dependence studies using two entirely separate techniques. For the present study a specially designed flow tube was used in order to establish reactor conditions which closely approximate fully developed laminar flow. Numerical methods were used to correct the observed rate data for interaction of flow dynamics, diffusion, and chemical reaction. The bimolecular reaction of O H with HCl (eq l), which is known to be independent of pressure,'621 was used to test the validity of the method.
OH
+ HC1-
H20
+ C1
(1)
Experimental Section Flow Reactors. A schematic drawing of the flow reactors used in these experiments is shown in Figure 1. The reactors were constructed from precision-bore Pyrex tubing with internal diameters of 1.265 and 2.496 cm. All surfaces exposed to O H were coated with a halocarbon wax (series 15-00, Halocarbon Corp., Hackensack, NJ). The carrier gas was added through a multiholed Pyrex ring at one end of the tube. Approximately 3 cm downstream OH was produced by reacting excess NO, with H atoms generated in a 2.45-GHz discharge of H,in He. Excess reactant, in this case HC1, was added at a series of six addition ports located 10 cm apart at the downstream end of the tube. The 30-cm distance between carrier gas addition and the nearest reactant addition port ensured that, in most cases studied, laminar flow with a parabolic velocity profile was fully developed in the reaction zone. The reactant addition ports were designed to minimize disturbance of the viscous flow. At each of these ports six equally spaced 1 mm diameter holes were drilled along the circumference of the precision-bore reactor tube. These holes were enclosed by (16) Takacs, G. A.; Glass, G. P. J . Phys. Chem. 1973, 77, 1948. (17) Smith, I. W. M.; Zellner, R. J. Chem. SOC.,Faraday Trans. 2 1974, 70, 1045. (18) Zahniser, M. S.; Kaufman, F.; Anderson, J. G. Chem. Phys. Lett. 1974, 27, 507. (19) Ravishankara, A. R.; Smith, G.; Watson, R. T.; Davis, D. D. J . Phys. Chem. 1977,81, 2220. (20) Hack, W.; Mex, G.; Wagner, H. Gg. Ber. Bunsenges. 1977,81,677. (21) Husain, D.; Plane, J. M. C.; Slater, N. K. H. J. Chem. SOC.,Faraday Trans. 2 1981, 77, 1949.
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4751
High-pressure Flow Kinetics
TABLE I: Summary of Flow Conditions expt press., temp, no. torr K 1 2 3 4 5 6 7
2.08 4.19 8.14 16.1 32.3 50.9 99.7
294 294 294 294 294 294 295
8 9 10 11 12
2.04 4.13 8.15 16.1 24.8
295 295 294 295 295
13 14 15 16 17 18
2.02 4.02 4.03 4.02 4.03 4.01
295 295 294 334 279 258
19 20 21
3.99 7.96 15.8
296 294 293
Reynolds entrance cm s-l IO~APIP no. length, cm Tube Radius = 0.6325 cm; Carrier Gas = 100% Helium 8,
957 1905 1920 1967 1473 1160 1006
2.6 4.1 2.1 1 .o 0.4 0.3 0.0
2.8 11 22 44 67 83 141
Tube Radius = 0.6325 cm; Carrier Gas = 80% Nitrogen 986 2.4 18 1441 1942 1975 1979
2.8 1.9 1 .o 0.6
0.2 0.8 1.6 3.2 4.9 6.0 10.3
+ 20% Helium 1.3 3.8
52 138 277 428
10.0 20.2 31.1
D,,b
cmz s-I
tmix:
ms
35 1 174 89.7 45.3 22.6 14.3 7.32
0.3 0.6 1.1 2.2 4.4 7.0 13.6
130 64.0 32.4 16.4 10.7
0.9 1.8 3.6 7.2 11.1
Tube Radius = 1.248 cm; Carrier Gas = 100% Helium 992 1495 1464 1505 1498 1500
0.7 0.8 0.8 0.9 0.9 0.8
5.5 17 16 14 18 20
Tube Radius = 1.248 cm; Carrier Gas = 80% Nitrogen 0.8 0.4 0.2
1494 1493 990
“Viscous pressure drop over observed pressure; correction factor is (1 time for HCl in carrier gas (eq 6). PRESSURE H p He
2.45 GHz HCL t He
Figure 1. Schematic diagram of the discharge-flow reactor. The addition ports are located at IO-cm intervals from the downstream end of the reactor tube.
a Pyrex sleeve which was sealed to the precision-bore tubing by means of 0 rings and conical stainless steel flanges. Glass vacuum valves with Teflon plugs were used to control the flow of reactants to each of the addition ports. The maximum flow rate through the ports was kept less than 5% of the total flow rate used in a given experiment. OH was monitored by using resonance fluorescence near 308 nm. Details have been given earlier.2z Although absolute concentrations of OH were not required for the present measurements, approximate concentrations were determined in order to assess the importance of secondary reactions. Calibrations were carried out by adding known amounts of NOz through one of the addition ports to an excess of H atoms (eq 2). Small corrections were H + NO2 OH + NO (2) +
applied for wall loss between the addition port and the detector. Typical signals at 4 torr of helium were 4500 counts s-l at [OH] = 1 X 10” cm-3 with background signals, comprised of scatter plus dark noise, about 700 counts s-l. The background was determined by using two methods: (1) the discharge producing atomic hydrogen was turned off while maintaining all flows at (22) Keyser, L. F. J . Phys. Chem. 1980, 84, 1659.
102 205 27 1
0.8 2.4 2.3 2.0 2.6 2.9
+ 20% Helium 14.6 29.4 38.9
361 182 181 219 166 150 66.3 33.2 16.7
1.1 2.1 2.2 1.8 2.3 2.6
7.0 13.9 27.6
+ AP/P).bDiffusioncoefficient for OH radicals in carrier gas.
CMixing
the same levels and (2)with the atomic hydrogen discharge on, a large excess of propylene was added to remove all OH. No significant difference in background levels was observed by using these methods. Calibrated capacitance manometers with full-scale sensitivities of 10 and 100 torr were used to measure the flow-tube pressures. The pressure measurement port was located immediately downstream of the OH fluorescence cell. Flows of HCl in helium mixtures were measured by determining the rate of pressure rise in a known volume. All other flows were measured by using calibrated mass flowmeters. The temperature was controlled by passing a heat-exchange fluid through an insulated brass jacket which completely surrounded the flow tube and addition ports. At 295 K most experiments were carried out with no fluid circulating; the jacket was filled with air. Several runs at 295 K were carried out with either water or 1,1,2-trichlorotrifluoroethane(Freon 113) as the heat-exchange fluid. The results were identical with those with air in the jacket. At 334 K water was used, and at 279 K Freon 1 1 3. At lower temperatures both Freon 113 and methanol were found to be unsuitable due to small leaks possibly at the O-ring seals. This was evidenced by pressure fluctuations and nonlinear pseudo-first-order decays. No leaks were observed when cold nitrogen gas was circulated at 258 K. However, larger temperature variations along the flow reactor were observed with the nitrogen. Temperatures were measured by using chromel-constantan thermocouples firmly attached to the outside of the flow tube. A thermocouple probe placed inside the reactor agreed within 2 K with temperatures measured at the outside wall. Errors in the temperature measurements are estimated to be f2 K except at 258 K, where they are f4 K. Wall loss of OH in the reactor was measured daily before or after each series of rate constant determinations. The reaction of H atoms with NOz (eq 2) was used to generate OH. Both excess H atoms and excess NOz were used. Losses were less than 10 s-l at temperatures between 258 and 334 K. Generally, losses observed in excess H atoms were slightly greater than in excess NO*. Flow Conditions. The carrier gas was in very large excess over the reactants and so determined the nature of the flow. Table I gives several parameters which may be used to characterize the
4152 The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 flow conditions. Over the pressure range used, the ratio of the mean free path to the reactor radius (Knudsen number) was less than 0.01. Thus, molecular flow may be ignored and the carrier gas may be treated as a continuum fluid with no slip at the wall (zero flow velocity at the wall). Since the ratio of flow velocity to the local acoustic velocity (Mach number) was less than 0.1, compressibility also was not important. Axial pressure gradients and the resulting velocity gradients were small under the present conditions. Observed pressures were corrected for the viscous pressure drop (determined in separate experiments) between the measurement port and the midpoint of the reaction zone. The relative pressure drops given in column 5 of Table I are less than 5%. Above 8 torr the corrections were less than 1% and may be ignored. Equation 3 defines the dimensionless Reynolds number Re = 2a0p/p (3) where a is the tube radius in centimeters, 0 the average flow velocity in cm 8,p the gas density in g ~ m - and ~ , p the absolute viscosity in poise. The Reynolds numbers given in column six are less than 500. This shows that the experimental flows were essentially laminar without appreciable turbulence which begins at nubmers greater than about 2000. The entrance length or the distance required for the flow to develop a parabolic velocity profile may be estimated by using eq 4,23which gives the distance for 1 = 0.115aRe (4) the central velocity to attain 99% of its final value. Entrance lengths obtained in this way are given in column 7 of Table I. These estimates show that to a good approximation the velocity profile was parabolic in the reaction zone used for the present measurements. Diffusion coefficients for OH in helium and nitrogen (column 8) were calculated by using experimental values for atomic 0xygen.2~ A correction factor of (16/17)1/2was used to account for the difference in molecular weight. A temperature dependence of was used. At 295 K the resulting values of the pressure-independent diffusion coefficients, pD,, are 730 torr cm2 s-l for O H in helium and 228 torr cm2 s-l for O H in nitrogen. A similar procedure based on experimental values for argon in helium and argon in nitrogen was used to estimate diffusion coefficients for HCI. At 295 K the results are 585 torr cm2 s-l for HC1 in helium and 152 torr cm2 s-l for HC1 in nitrogen. Diffusion coefficients for OH or HCl in nitrogen-helium mixtures were obtained by using eq 525 where x(N2)and x(He) are the mole fractions of nitrogen and helium in the carrier gas mixture, and D,(N2) and Dc(He) are the pressure-dependent diffusion coefficients for O H or HCl in the pure gases, nitrogen and helium, respectively. Mixing times for HCl in the carrier gas (column 9) were estimated by using eq 6,26which gives the relaxation time required for diffusion to tmix = a2/5Dc
(6) reduce a radial concentration inhomogeneity to 5% of its initial value. For most cases studied, estimated mixing times were small compared to the mean reaction time given by 30/8. Reagents. Gases used were chromatographic-grade helium (99.9999%), Matheson-purity nitrogen (99.995%), research-grade hydrogen (99.9995%), ultrahigh-purity oxygen (99.95%), nitric oxide (99.0%), and research-purity propylene. The preparation and purification of NO2 have been described earlier.27 Both helium and nitrogen were passed through molecular seive traps (Linde 3A) a t 77 K. To prevent condensation, the trap in the nitrogen line was on the low-pressure side of the flow-metering valve. Two sources of HCl were used in these measurements. Matheson electronic grade (99.99%) was purified by vacuum (23) Langhaar, H. L. Am. SOC.Mech. Eng. Trans. 1942, 64, A55. (24) Marrero, T. R.; Mason, E. A. J. Phys. Chem. Rex Data 1972, I , 3. (25) Walker, R. E.; de Haas, N.; Westenberg, A. A. J. Chem. Phys. 1960, 32, 1314. (26) Taylor, G. Proc. R. SOC.London, Ser. A 1953, 219, 186. (27) Keyser, L. F. J . Phys. Chem. 1981, 85, 3667.
Keyser distillation at -1 18 OC; the middle fraction was retained and stored at 77 K. HCl was also prepared from NaCl and 96% H2S04,both Baker analyzed reagent grade. The HCl was passed through a -78 OC trap and collected at 77 K. The same vacuum distillation procedure was then used to purify the product. Interaction of Flow, Diffusion, and Chemical Reaction Plug Flow. As a first approach to the analysis of flow-reactor data, the effects of laminar flow and molecular diffusion are ignored. In this case the flow velocity, directed along the tube axis, is assumed to be independent of both radial and axial position. It is given by eq 7 (7) where F is the total flow rate in standard atm cm3 s-l, a is the reactor radius in centimeters, P is the total pressure in torr, and T i s the temperature in kelvin. Rate data are obtained by following concentrations as a function of axial distance, z. Under this plug-flow approximation, the axial distance is easily converted to reaction time, t = z / 0 . The loss of labile species, C, by a first-order reaction may be written B(dC/dz) = -kC
(8) Plots of In C vs. z are used to determine the rate constant, k. When laminar flow and diffusion are included, this simple analysis can no longer be used. In the discussion which follows, the effects on observed rate data due to the interaction of flow, diffusion, and reaction are outlined. First, the equation of continuity is presented. Next, solutions expected in various regions of the reactor are described. Finally, procedures are given to correct experimental data for the effects of laminar flow and diffusion. Continuity Equation and Its Solution. From a consideration of the continuity equation under steady-state conditions, eq 9 may
be written to describe the interaction of laminar flow, molecular diffusion, and a first-order gas-phase reaction. The wall loss gives the boundary condition where r and z are the cylindrical coordinates (azimuthal symmetry is assumed), 0 is the average flow velocity in cm s-l, a is the flow-tube radius in centimeters, Cis the concentration of the labile ~ ,is the diffusion coefficient of the species in molecules ~ m - Dc labile species in cm2 s-l, and k is the first-order rate constant for the gas-phase chemical reaction in units of 8. The first-order rate constant, k,, for loss of the labile species at the reactor wall in units of s-l is given by' k, = y a / 2 a
(1 1)
where y is the collision efficiency for wall loss and w is the molecular velocity of the labile species. For OH, Q = 6.6 X lo4 cm s-l at 295 K and y < 4 X for reactor surfaces used in the present study. Various approaches have been used to solve eq 9. For flowing afterglow studies of neutral metastabile and ionic species where y = 1 and = 0, Ferguson et al.5 used numerical methods while Huggins and Cahn? Farragher? and Bolden et aL6 obtained an approximate analytical solution, eq 12, by ignoring axial diffusion.
(ar-,
C(r,z) = f ( r ) exp[-(3.67Dc/a2
+ 0.629k)z/O]
(12)
For the case of current interest where y < 1 and the boundary condition of eq 10 applies, several methods have been used to obtain solutions of eq 9.2,8,9,11An approach which offers considerable insight into the problem was first developed by Walker2 and later extended by Brown." For a more complete description of this method, these papers should be consulted. The notation
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4753
High-pressure Flow Kinetics ADDlTlONOf Of HCL
PARABOLIC
c l W l PADIAL PRMILECONSTANT
-
on LOST B Y EACllMi
WITH HCLAND DlFiUSlON TO WALL
-,
I
OH LOST BY DIFFUSIONTOWALL
Figure 2. Flow-reactor regions in a typical kinetics experiment. The excess species (HC1) is added to the labile species (OH) under fully developed laminar flow conditions.
used in the present discussion is that used by Brown. When one defines the dimensionless parameters R = r i a , Z = z / a , D = DC/2aB, K = ak/& and K, = ak,/20, eq 9 and 10 become
lOOxK
Figure 3. K* vs. K for experiment 12, pressure = 24.8 torr of nitrogen plus helium, temperature = 295 K, 0 = 1979 cm s-', flow tube radius = 0.6325 cm.
D(aC/aR)R=l = -(Kw/2)(C)R=l
(14)
Note that the definition of k, used in this discussion, eq 1 1 , is that most frequently used in kinetics studies. It differs from the definition used by Brown and others by the factor, 2/a, the surface-to-volume ratio of a cylinder. Types of Solutions. It is useful to consider the types of solutions to be expected in various regions of the flow reactor (see Figure 2). Upstream of the point at which excess reactant is added, the parabolic velocity profile develops and the labile species is lost only by diffusion to the walls where it is destroyed with collision efficiency y. Beyond the entrance length eq 13 and 14 with K = 0 describe this region and the solutions may be written C=
5 A,g,(R) exp(-K,*Z)
r=1
(15)
where the K,* are dimensionless parameters which describe the experimentally observed decay. Generally K, * is much smaller than K,* (i 2 2), and a short distance downstream of the entrance region the solution may be equated to the first term in eq 15. That is, the solution quickly decays to a single exponential, the lowest diffusion mode. Here the radial concentration profile of the labile species is constant, independent of the axial distance. After addition of the excess reactant, K # 0 and the solution is also given by eq 15 but with different parameters, A, and K,*, and different radial functions, g,(R). Immediately downstream of the addition point, there exists a mixing zone in which the radial concentration profile of the excess reactant becomes uniform. It will be shown below that the lowest order decay parameter, K1*, is again much smaller than K,* for i 1 2, and sufficiently far downstream of the mixing zone the solution becomes
C = Algl(R) exp(-Kl*Z) (16) The reactor region over which eq 16 holds is of practical importance for kinetics experiments since it is here that the decay of the labile species may be written in terms of a single exponential. Here also the radial profile of the labile species is independent of axial distance and, as a consequence, its observed decay will be independent of the radial averaging specific to the detection method used. Relation between the Observed Decay and the True Rate Constant. In a kinetics experiment, the observed decay parameter, K1*, is obtained from the slope of a In (C) vs. z plot. Under conditions where diffusion and laminar flow may be ignored, the one-dimensional solution of eq 13 is obtained by averaging over the radial coordinateZ and K1* = (k + k,)a/B (17) which is just the solution for the plug-flow approximation with an added wall-loss term. For the general case when diffusion and laminar flow are considered and the wall loss is nonzero, the
relation between the observed decay and the true rate constant must be determined by solving eq 13 numerically. Since the method has been discussed it will only be summarized here. Solutions are given by eq 15 where for each i, the radial function, gi(R), is expanded in an even power series of R, eq 18. Substitution into eq 13 leads to a recursion formula for m
the coefficients, B,, which are functions of Ki* K, and D. The boundary condition at the wall leads to eq 19. The relationship m
2 (2n + Kw/2D)Bn(Kl*,K,D) = 0
n=O
(19)
between the observed decay parameter, Kl*, and the true rate constant is determined by finding the lowest root of eq 19 for given values of K, D, and K,. In addition to the observed pseudofirst-order rate constant, the required experimental quantities are a, the flow tube radius; 6, the average flow velocity calculated by using eq 7; D,, the diffusion coefficient of the labile species in the carrier gas; and k,, the observed first-order rate constant for the wall reaction. Equation 19 is solved for K* over a range of K while K, and D are held constant. Results of this procedure are shown in Figure 3, which gives K* vs. K for experiment 12. Here K* refers to the lowest root of eq 19, the subscript 1 being understood. Plots such as this may be used to correct experimental data by reading the value of K which corresponds to an experimentally observed decay parameter K*. These results may be developed further by writing K* in terms of its wall and gas-phase components, eq 20 K* = K,* Kg* (20)
+
where Kw*is the dimensionless wall loss observed in the absence of a gas-phase reaction (K = 0) and Kg* is the added loss due to the gas-phase reaction (K # 0). Defining Oo aBKw*/Dcand 0, Kg*/K and changing to dimensional variables, eq 16 becomes C(r,z) = g(r/a) exp[-(OoD,/a2
+ Olk)z/B]
(21)
Equation 21 has the same form as the solution (eq 12) obtained earlier for the flowing afterglow experiment^.^-^ The first term in the exponential is related to the wall loss of the labile species, while Qlk is the observed first-order rate constant for the gas-phase reaction. Equation 21 describes the loss of a labile species for the case of a movable source and fixed detector. For the present measurements where kinetics runs were carried out by using a fixed source and fixed detector, the reaction length for the wall loss is constant. Thus, the first term in the exponential becomes a constant factor. Only the second term in the exponential is actually observed as the addition point, z, of the excess species is varied.
4754
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984
Keyser
-
TABLE II: Kinetic Data for the Reaction OH + HCI H20+ CI 10-I4[HC1] Qlk,b 10-14[HC1],’ Qlk: s-I QIC cm-’ s-1 QIC Experiment 1, k, = 1.6 s-l Experiment 6. k, = 1 s-l 0.388 27:3 0.988 0.788 58.9 0.962 0.576 46.8 0.980 1.04 80.4 0.950 0.819 57.7 0.976 1.35 102 0.938 1.20 97.7 0.960 1.71 126 0.924 1.30 85.7 0.965 2.05 144 0.915 1.61 113 0.955 2.39 172 0.900 135 0.947 2.03 Experiment 7, k, = 1 s-l Experiment 2, k, = 5.8 5-l 0.396 29.8 0.960 0.426 32.9 0.995 0.514 39.8 0.949 0.599 44.9 0.994 0.582 42.1 0.946 0.813 63.6 0.992 0.814 59.6 0.927 1.02 74.0 0.991 0.999 74.9 0.911 1.17 79.0 0.907 1.05 80.0 0.990 1.06 83.2 0.990 Experiment 8, k, = 1 s-I 1.48 118 0.987 0.28 1 24.3 0.994 1.99 160 0.983 0.472 40.8 0.991 2.02 157 0.983 0.630 46.7 0.990 2.04 163 0.982 0.720 58.0 0.988 2.40 182 0.981 0.839 68.8 0.986 2.61 202 0.979 0.895 76.9 0.984 2.94 229 0.976 1.03 82.3 0.983 3.05 226 0.976 1.34 112 0.978 3.09 239 0.975 1.50 116 0.977 3.11 238 0.975 Experiment 9, k, = 3.2 s-’ Experiment 3, k, = 1 s-l 0.392 31.6 0.992 0.420 32.8 0.996 0.594 47.3 0.990 0.654 50.0 0.994 0.879 63.2 0.987 0.817 59.2 0.992 0.970 75.2 0.985 1.01 73.1 0.991 1.41 109 0.980 1.33 101 0.988 1.67 128 0.977 1.75 137 0.983 2.14 161 0.972 2.04 151 0.982 2.20 157 0.972 0.246 177 0.979 2.84 212 0.975 Experiment 10, k, = 3.1 s-l 3.12 233 0.973 0.408 37.9 0.985 0.565 47.2 0.983 Experiment 4, k, = 1 s-l 0.807 61.0 0.979 0.320 24.3 0.994 1.02 80.5 0.974 0.549 40.8 0.991 1.36 107 0.967 0.769 56.9 0.988 1.80 153 0.955 1.oo 74.3 0.984 2.05 150 0.956 1.26 96.6 0.980 2.61 180 0.948 1.73 135 0.973 1.95 141 0.972 Experiment 11, k, = 4.2 s-I 2.50 186 0.963 0.339 26.1 0.974 2.87 197 0.961 0.629 44.6 0.965 2.95 214 0.958 0.806 60.7 0.957 1.05 88.8 0.943 Experiment 5, k, = 5.8 s-I 1.33 103 0.936 0.368 28.2 0.977 1.45 113 0.932 0.620 42.5 0.971 1.69 132 0.923 0.806 64.0 0.963 2.07 154 0.912 1.03 75.1 0.959 2.46 185 0.898 1.31 95.3 0.952 2.80 190 0.896 1.67 115 0.945 2.00 156 0.930 2.41 186 0.920 2.64 194 0.917 2.99 203 0.914
10-14[HCl],” cni3 Experiment 0.408 0.580 0.790 0.920 1.06 1.30 1.60 1.60 2.08 2.44
Qlk,b s-I QIC 12, k, = 8.2 s-I 31.8 0.939 49.9 9.926 50.6 0.925 67.1 0.914 71.6 0.910 90.3 0.897 103 0.889 124 0.876 134 0.870 187 0.838
Experiment 13, k, = 3.9 SKI 0.348 28.8 0.982 0.716 56.1 0.970 0.968 76.5 0.962 1.21 93.2 0.955 1.35 99.1 0,952 1.62 133 0.938 Experiment 0.747 0.782 0.815 1.13 1.15 1.24 1.79 1.86 1.88 2.33 2.34 2.48
14, k, = 2.0 s-l 57.8 0.983 60.4 0.982 62.6 0.982 86.5 0.975 88.5 0.975 93.3 0.974 136 0.963 139 0.962 139 0.962 177 0.953 180 0.952 181 0.952
Experiment 15: k, = 1.9 S-1
0.394 0.609 0.760 0.944 1.18 1.24 1.49 1.50 1.76 1.87 2.17 2.24 2.42
31.4 45.3 59.8 71.9 86.6 90.9 107 111 140 145 161 171 176
0.989 0.986 0.982 0.979 0.975 0.974 0.970 0.969 0.961 0.960 0.956 0.954 0.953
Experiment 16,” k, = 2.7 S-1
0.353 0.797 0.925 1.24 1.44 1.69 1.95 2.05 2.16 2.65
31.0 70.2 80.7 109 128 137 170 167 200 216
Qlk,”
10-I4[HC1],’ c~n-~ Experiment 0.393 0.766 0.993 1.15 1.48 1.78 1.98 2.31 2.74 2.89
s-I Q1” 17, k, = 1.5 s-l 28.8 0.990 55.2 0.983 72.4 0.979 83.3 0.976 110 0.969 127 0.965 139 0.962 160 0.956 185 0.950 210 0.944
Experiment 0.695 1.19 1.53 1.78 1.90 2.27 2.54 2.90
18, k, = 1.2 s d 46.0 0.985 83.6 0.975 102 0.970 122 0.964 129 0.963 152 0.956 174 0.951 184 0.948
Experiment 0.397 0.532 0.683 0.776 0.959 1.03 1.18 1.19
19, k, = 1 s-l 30.1 0.982 41.4 0.976 52.7 0.970 59.8 0.966 73.4 0.960 77.8 0.957 91.4 0.951 85.9 0.953
Experiment 20, k, = 1 s-I 0.402 33.4 0.962 0.783 62.3 0.934 0.847 65.8 0.931 1.22 85.7 0.913 1.44 108 0.893 1.77 115 0.888 2.19 147 0.862 2.43 161 0.851 2.94 184 0.834 Experiment 0.358 1.oo 1.20 1.46 1.84 2.07 2.31 2.61
21, k, = 1 s-l 26.4 0.938 60.7 0.879 76.1 0.855 84.6 0.842 108 0.811 110 0.808 138 0.777 136 0.779
0.990 0.980 0.978 0.971 0.967 0.964 0.957 0.958 0.950 0.946
”HC1 is Matheson electronic grade (99.99%) unless stated otherwise. bPseudo-first-order rate constant from slope of In (I,,/I) vs. z plots. cFrom numerical solution of eq 9. “HCl from H2S04+ NaCI.
Results and Discussion The present experiments were carried out by using concentrations of HC1 in the range 0.28 1014-3.2 1014 cm-3 with initial OH concentrations less than 3.5 1011 cm-3, Under these conditions the loss of OH is pseudo first order, when one substitutes fluorescence intensities for concentrations, 21 becomes In (Zo/Z) = Q,kz/ii
Qlk, were obtained from the slopes of In (Zo/Z) vs. z plots such as those shown in Figure 4. The results are presented in Table 11, which lists the HCI concentrations, the observed rate constants, and the correction factors, a,, which were obtained from plots similar to Figure XZ8 Corrected pseudo-first-order rate constants, kwr9were obtained by dividing the observed values by ai. Bimolecular rate constants were calculated from k,,,/[HCl] and
(22)
where Z and Zo are respectively the OH fluorescence signals with and without added HCl. The observed first-order rate constants,
(28) The correction factors, R,, may also be obtained by finding the roots, K,of eq 19 starting with values for K+,D, and K,. See ref 11 for details.
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4755
High-pressure Flow Kinetics TABLE III: Bimolecular Rate Constants for the Reaction OH
expt no.“
press., torr
1 2 3 4 5 6 7
2.08 4.19 8.14 16.1 32.3 50.9 99.7
8 9 10 11 12
2.04 4.13 8.15 16.1 24.8
13 14 159 16s 17 18
2.02 4.02 4.03 4.02 4.03 4.01
19 20 21h
3.99 7.96 15.8
+ HCI
-
H20
+ CI
iOi3k,,ccm3 molecule-’ s-’ temp! K avdSe slopee,’ Tube Radius = 0.6325 cm; Carrier Gas = 100% Helium 294 294 294 294 294 294 295
7.48 f 0.65 7.84 f 0.23 7.60 f 0.22 7.59 f 0.24 7.79 f 0.47 7.93 f 0.18 7.87 f 0.30 av = 7.73 f 0.17
6.96 f 0.52 7.89 f 0.11 7.65 f 0.12 7.42 f 0.18 7.93 f 0.32 7.82 f 0.23 7.58 f 0.46
intercept:’
s-l
5 f 6 Of2 -1 f 2 2 f 3 -1 f 6 1 f 4 2 f 4
Tube Radius = 0.6325 cm; Carrier Gas = 80% Nitrogen + 20% Helium 29 5 295 294 295 295
8.30 7.76 8.22 8.12 8.04 av = 8.09
i 0.42 f 0.31 f 0.70 f 0.47 f 0.84 f 0.21
8.14 f 0.32 7.48 f 0.21 7.33 f 0.46 7.94 f 0.30 8.58 f 0.65
l 3 9 3 -6
f f f f
3 3 7 5 f9
8.46 7.87 7.88 8.84 7.38 6.88
-2 f 6 Of2 -1 f 3 I f 6 Of3 2 f 5
Tube Radius = 2.248 cm; Carrier Gas = 100% Helium 295 295 294 334 279 258
8.21 f 0.36 7.84 f 0.12 7.78 f 0.28 8.93 f 0.38 7.41 f 0.19 6.98 f 0.20 av (295 K) = 7.94 f 0.23
f 0.55 f 0.13 f
0.19
f 0.39
f 0.19 f 0.23
Tube Radius = 1.248 cm; Carrier Gas = 80% Nitrogen + 20% Helium 296 294 293
7.90 8.01 7.16 av = 7.96
f 0.18
0.47 f 0.47 f 0.08 f
7.86 f 0.26 7.35 f 0.20 6.89 f 0.44
Of2 8 f 3 3 1 8
“HCl is Matheson electronic grade (99.99%) unless stated otherwise. *Estimated error in temperature is f 2 K except at 258 K, where it is f 4 K. CCorrectedfor viscous pressure drop, axial and radial diffusion. “Average of k,/[HCI] values. ‘Errors are one standard deviation. ’From linear least-squares fit of k,, vs. [HCl]. sHCl from H2S04+ NaC1. *Not included in average because of incomplete mixing, see text. averaging 17 individual experiments (column 4 of Table 111) is cm3 molecyle-’ s-’. Experiment 21 has been (7.9 f 0.4) X excluded because of incomplete HCl mixing; see below. The temperature dependence expressed in Arrhenius form is
5.0
40
kl (cm3 molecule-’ 8) = (2.1 f 0.4) X lo-’* exg[(-285 f 40)/T]
- 3.0 P
3
2.0
1.0
‘0
10
20
30
40
50 60 0 10 20 REACTION LENGTH, ZlCM
30
40
50
60
Figure 4. Pseudo-first-orderplots of In &/I) vs. the reaction length, z .
Lines through the data pints are linear least-squares fits. Concentrations of HCl are given in units of IOL4 molecules ~ m - ~(a). Experiment 17, pressure = 4.03 torr of helium, temperature = 279 K, fi = 1498 cm s-’, flow-tuberadius = 1.248 cm. (b) Experiment 6, pressure = 50.9 torr of helium, temperature = 294 K, fi = 1160 cm s-’, flow-tube radius = 0.6325 cm. from the slopes of k , vs. [HCl] plots, The results are summarized in Table 111. Corrections to the bimolecular rate constants due to the viscous pressure drops (column 5 of Table I) are less than 10% with typical values less than 5%. Corrections due to axial and radial diffusion are less than 30% (al 1 0.777) with typical values less than 10% (a, 1 0.909). Pressure and Temperature Dependence. After the corrections described above are made, kl is found to be independent of pressure from 2 to 100 tom of helium and from 2 to 25 tom of 80% nitrogen and 20% helium. In addition, no dependence on the nature of the carrier gas is observed. At 295 f 2 K the result obtained by
for 258 I T I 334 K. The errors given are two standard deviations obtained from a linear least-squares analysis of the data. Overall experimental error is estimated to be f15%. Absolute HC1 Concentrations. Helium and HC1 mixtures of known composition were prepared in 5-L glass flasks by pressure measurements. Mole fractions of HCl between 0.15 and 0.40 were used. Concentrations of HCl in the flow reactor were calculated from the flow rates of these mixtures, the total flow rate, the reactor temperature, and pressure. Compositions of the mixtures were also determined by photometric analysis at 190 nm using an absorption cross section of 1.45 X cm2 molecule-’.29 The results averaged only 3% below the Pressure m % ~ ~ r e m e n t To s. check the actual HCl concentrations in the flow reactor, samples of the reaction mixture (without added OH) were analyzed photometrically. These samples were taken by passing the reaction mixture into a previously evacuated calibrated volume. The HCl was trapped in a 77 K U-tube attached to an absorption cell and analyzed at room temperature. Concentrations of HC1 obtained from the sampling experiments were 2 . 4 4 0 % higher than those calculated from the flow m e a s ~ e m e n t sand show that no Significant decomposition occurred in the vacuum lines between the HC1 storage flasks and the flow reactor. Two entirely different sources of HCl were used to check for impurities. Comparison of experiments 14 and 15 (Table 111) shows that the rate constant is independent of the HCl source. Blank experiments were carried out to check for possible impurities in the vacuum lines. These experiments were identical in every (29) Inn, E. C.Y.Armos. Sci. 1975, 32, 2375.
4756 The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 TABLE I V Summary of k lMeasurements lo%, cm3 molecile-' s-1 (295 f 5)Ka 250 Kb press., torr 7.9 f 1.2 6.7 2-100 8.5 f 0.4 6.7 f 0.5 6.6 f 1.7 6.7 f 0.4 6.7 f 1.0 6.9 f 1.0 6.4 f 1.5
6.2 5.0 5.7 4.9
750 24 1.7-3.8 20-50 2-6 10-20 0.5-1.5
Keyser
methodc DF-RF
Arrhenius expression, cm3 molecule-' s-I (2.1 h 0.4) X exp[(-285 i 4 0 ) / q
FP-RF FP-RF DF-ESR FP-RF DF-RF FP-RA DF-ESR
(4.6 f 0.3) X
temp range, K 258-334
exp[(-500 f 6 0 ) / q
240-295
(3.3 f 0.3) X exp[(-472 f 20)/77 (2.0 f 0.1) X lo-'* exp[(-312 f l O ) / q (4.1 f 2.0) X exp[(-530 f 25)/7'l
250-402 224-460 220-480
ref present results 31 21 20 19 18 17 16
'Measured. *Calculated from the Arrhenius expression. 'DF = discharge flow; R F = resonance fluorescence; FP = flash photolysis; ESR = electron spin resonance; RA = resonance absorption.
respect to measurement runs except that HCl was not added to the helium in the storage flasks. Observed first-order OH losses in the blank experiments were less than 1 s-l. Secondary Reactions. Under the pseudo-first-order conditions used for the present study, secondary reactions are not expected to interfere. This is confirmed by the absence of curvature in the OH decay plots (Figure 4) and by the lack of any significant variation in k l over a wide range of initial concentrations. Computer simulations which include reactions among OH, HCl, 0, H, H2, NO2,and C1 show that secondary chemistry does not interfere over the entire pressure range studied. To test for possible interference from vibrationally excited species produced in the microwave discharge of H2 in He or as the result of O H production from reaction 2, a large excess of NO2was added to the reaction mixtures in experiment 13. A rate constant of 1.3 X lo-" cm3 molecule-] s-l has been reported for vibrational quenching of OH by N02.30 For this test NOz concentrations were about 1.6 X 10" ~ m - typical ~; concentrations . used in the other experiments were about 2.5 X 10l2~ m - ~No significant difference in kl was observed when high concentrations of NO2 were present. Surface Reactions. Wall loss of OH radicals determined in the absence of HCl was less than 10 s-' in all cases studied. This is equivalent to a collision efficiency, y, less than 4 X Intercepts of k,, vs. [HCl] plots were less than 10 s-] and typically were not significantly different from zero. This demonstrates that no large change in the first-order wall loss occurred when HCl was added. Since the results were also independent of the surface-to-volume ratio (flow-tube radius), no appreciable secondorder surface reaction occurred in these systems. Thus, wall reactions of OH should not interfere with the present measurements. Comparison with Previous Results. Table IV summarizes recent measurements of k l . Over the temperature range studied, the present results agree within * l o % with the recent flashphotolysis measurement of Molina et aL31and are 1520% above the discharge-flow results of Zahniser et a1.18 At 295 K the study of Molina et al. and the present results are about 20-25% above the earlier measurements. These differences lie within the combined experimental errors and may not be significant. However, at 250 K, a temperature characteristic of the upper stratosphere near 40 km, the two earlier flash-photolysis studiesI7J9lie 35% below the present result. The reason for this difference is not clear a t the present time. Correction Factors, 0,.Rate data were corrected for axial and radial diffusion by using the factors, Q , , obtained from the numerical solution of eq 13. When wall losses are low and diffusion is rapid compared with reaction, an approximate analytical exThe first pression (eq 23) may be used to estimate Q1 = [ l + K*(2D 1/96D)]-' (23) Q1.3-11*26*32333
+ ~
~
(30) Jaffer, D. H.; Smith, I. W. M. J . Chem. SOC.,Faraday Discuss. 1979, 67,212. (31) Molina, M. J.; Molina, L. T.; Smith, C. A. Inr. J . Chem. Kine?.,in press. (32) Taylor, G. Proc. R. SOC.London, Ser. A 1954, 225, 473.
TABLE V Calculated Decay Parameters and Coefficients for Eq 15' i
1 2 3 4 5
Kt* expt 7 expt 12 0.0860 (+1.39) 0.0831 (+1.43) 0.250 (-0.546) 0.213 (-0.621) 0.582 (+0.228) 0.464 (+0.279) 1.09 (-0.132) 0.848 (-0.166) 1.78 (+0.0687) 1.36 (+0.0866)
(4) expt 2Ob expt 2OC 0.166 (+1.46) 0.120 (+1.69) 0.430 (-0.659) 0.482 (-1.14) 0.939 (+0.295) 1.04 (+0.740) 1.71 (-0.173) 1.81 (-0.529) 2.72 (+0.0892) 2.82 (+0.293)
"Unless specified otherwise, K is uniform and equal to 0.1. b K = 0.2. c K = 3kR2 and k = 0.2
term (2DK* = kobsdD,/B2) in eq 23 may be identified with the axial diffusion correction.' The second term ( K * / 9 6 D = koMa2/48Dc) may then be considered as an added correction due to radial diffusion. Equation 23 shows that Ql should be a maximum at D = 0.072. At this point the corrections required for axial and radial diffusion are equal and the observed rate constant deviates least from the true value. For D > 0.072 corrections due to axial diffusion dominate and for D C 0.072 radial diffusion corrections dominate. Figure 5 compares Q1, obtained from the numerical solution of eq 13, with values obtained from eq 23 for K* I0.25, K,* 5 0.02, and 0.004 ID I0.6. In the axial diffusion region ( D > 0.072), eq 23 gives Q l within &5% for all cases studied. In the radial diffusion region ( D < 0.072), eq 23 may be used to estimate Q1 within h5% for Kw* = 0 and D over the entire range investigated, for K,* = 0.005 and D 1 0.008, for K,* = 0.01 and D 1 0 . 0 1 5 , and for Kw* = 0.02 and D 1 0.03. Higher Order Decay Parameters. The correction factors discussed above were obtained by assuming that in the reaction zone only the lowest decay parameter, K 1 * ,makes a significant contribution to the loss of O H (eq 16). To test this assumption, higher order decay parameters, Ki*, and the corresponding coefficients, Ai,in eq 15 were calculated for several cases which simulate the experimental conditions of this study. The Ki*were calculated by finding the higher roots of eq 19 for given K , K,, and D. The A coefficients were then determined by requiring the radial concentration profile at the point of HC1 addition to match the profile for wall loss only. This is similar to the method described by Pirkle and S i g i l l i t ~ . The ~ ~ results are summarized in Table V. For all of the cases studied, the lowest decay parameter is well separated from the higher order parameters. Moreover, the corresponding higher order coefficients are the same magnitude or less than the lowest order coefficient. Relative OH concentrations calculated by using only the lowest mode were compared with those calculated by using the first five modes. The slopes of In [OH] vs. z plots agree within 2% if z > 10 cm. Thus, a short distance downstream of the HC1 addition point, the higher order modes make a negligible contribution to the observed OH decay. For these calculations the [OH] profile was averaged over the tube radius. (33) A!is,
R. Proc. R. SOC.London, Ser. A 1956, 235, 61. (34) Pirkle, J. C., Jr.; Sigillito, V. G. In?. J . Eng. Sci. 1972, 10, 553.
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4757
High-pressure Flow Kinetics
--
m
m
Kw*=0.00
m m
0.4
Kw*=0.0 1
/ 0*6 / 0.8
m. m
/I0
,
m. N
0
, ,,
I
/
I
r
,I0
c
I
’
-
/ 1.0
I I
I r
H
1.5
I
2.0 -
v
2.0
X
m
!? v)
-
4.0 7.2
?
4.0 7.2
(d)
(a)
A
1 0 0 x K*
1 0 0 x K* ul m
Kw*=0.02 0.8 1 .a 1.5 2.0 3.0 4.0 7.2
(e)
3
5
%
10
1 0 0 x K*
15 100 x
20
30
25
K*
m
1
m.
-
1
Nl
Kw*=0.005 m
I i //
Kw*=0.02
/
m.
4 0 ‘.
n
ln.
m
m N
m
50.
I
07
-
30.
I +
20.
10.
(f)
15
20
25
1 0 0 x K*
5
10
15
20
25
30
1 0 0 x K*
Figure 5. Plots of the factor, a,, obtained by solving eq 13 numerically, vs. the dimensionless observed rate constant, K * , for several values of the dimensionless observed wall loss, Kw*, and the dimensionless diffusion coefficient, D. The observed first-order rate constant for the gas-phase reaction and the observed first-order wall loss, both in units of S-I, are converted to the dimensionless quantities by using the factor a/O where a is the tube radius and ~7is the average flow velocity. The numbers given at the end of each curve are lOOD where D = D,/2aB and D, is the diffusion coefficient of the labile species in cmz SKI.The solid lines indicate that Q, obtained from eq 23 agrees within *5% with the numerical solution. Note that for a given observed wall loss, the corresponding true wall loss depends on the value of the diffusion coefficient, D. For Kw* = 0.02,0.0102 5 K , 5 0.0143; for K,* = 0.01, 0.00505 IK , I 0.00623; and for Kw* = 0.005, 0.00251 IK , I0.00283 over the range of D studied. The true wall loss in units of s-I is equal to 20Kw/a.
HC1 Mixing. For most of the present measurements, estimated HC1 mixing times are less than 10 ms (see Table I, column 9). Thus, nonuniform HC1 concentration profiles should not seriously interfere. To investigate the effect of incomplete HCl mixing, several calculations were done by using a nonuniform decay parameter K = 3KR2where K is the average of K over the tube radius. This is the simplest R dependence of K which simulates conditions in the mixing zone for HCl addition at the reactor walls ( K maximum at R = 1). The proportionality factor, 3K, is de-
termined by the requirement that K averaged over the tube radius be the same for uniform and nonuniform distributions. This is equivalent to requiring that the total amount of HC1 be the same for both cases. For the purposes of this simulation, K is the value that K attains when HCl becomes completely mixed. The effect of incomplete mixing on the observed decay parameter can be seen by comparing the results of calculations using K = 0.2 (Table V, column 4)with results using K = 0.6RZ(Table V, column 5). The calculations show that, in the mixing zone, the observed O H decay
4758 The Journal of Physical Chemistry, Vol. 88, No. 20, 1984
would be less than in the completely mixed region. This result depends of course on the geometry of HCl addition. In the present study HCl was added at the reactor walls. Before mixing occurs, this tends to concentrate unreacted OH at the center of the flow tube where the velocity is highest and leads to a lower observed OH decay. Except for experiment 21, mixing times were sufficiently rapid that this effect of nonuniform HCl was not observed. The results of experiment 21 are not included in the average reported for kl at 295 K. Comparison with the Results of Poirier and Carr. Since they have been widely used to estimate the effect of radial diffusion on observed rate data, the solutions obtained by Poirier and Carr’ (PC) will be discussed briefly. Ignoring axial diffusion, they solved eq 9 numerically. To simulate various detector geometries, four methods were used to average the labile species concentration over the radial coordinate. For each of these averaging methods, they gave plots of In (C) vs. an axial coordinate parameter, A = kz/2D, and several values of a radial diffusion parameter, a = Dc/ka2. Actual kinetics experiments generally are carried out in a flowreactor region over which the labile species decay can be written as a single exponential. In this region the radial concentration profile of the labile species is independent of the axial distance; see eq 16. Therefore, the observed decay must be independent of the averaging method used. PC’s Figures 1-4 for a first-order reaction show that when a > 0.1 and X > 0.4, the slopes of the In (C) vs. X plots are independent of the averaging. These limits can be used to obtain rough estimates of the range of conditions under which practical flow-tube kinetics measurements can be carried out. The results obtained by PC in the single-exponential region may be used to correct observed rate constants for radial diffusion. The correction factor is the ratio of d In C/dX calculated at the experimental value of a to d In C/dX calculated at infinitely fast diffusion (a = a). Correction factors obtained from the present study may be compared with those obtained from PC’s results only for D < 0.072 since PC did not include axial diffusion. For D = 0.005 and K* = 0.1, a = 2D/K* = 0.1 and Q,,obtained from Figure 5 of the present study, is 0.82. The ratio of slopes obtained from Figure 4 of PC is 0.81. Atmospheric Chemistry. In the stratosphere, reaction 1 initiates a catalytic cycle (eq 24 and 25) which recombines odd oxygen. c1+ 0 3 c10 + 02 (24) 0 c 1 0 c1+ 0 2 (25) net: 0 + O3 202
+
--
-
Keyser Since reaction 25 is the rate-limiting step, C10 concentrations give a measure of the importance of this cycle. Stratospheric concentrations of C10 are proportional to the value of k1.35 At 40 km near the peak of the chlorine catalytic cycle, the present results give kl about 30% higher than the average of the earlier temperature-dependent measurement^.^^-'^ Thus, the present results are expected to have a significant effect on model calculations of stratospheric chlorine chemistry. Conclusion The present results show that under the proper conditions isothermal flow reactors can be used to obtain reliable rate data over a much wider pressure range than previously studied. The reactor configuration and the experimental conditions were chosen to minimize effects on the observed rate constants due to the viscous pressure drop, axial and radial diffusion, mixing of reactants, and perturbation of laminar flow. Using the OH + HC1 reaction to test the method, we have obtained rate data at pressures from 2 to 100 torr of helium and 2 to 25 torr of 80% nitrogen plus 20% helium. After correction of the observed rate data for axial and radial diffusion, the average rate constant, kl, at 295 K is (7.9 f 0.4) X cm3 molecule-’ s-l, independent of the pressure and the nature of the carrier gas. The variation of kl over the entire pressure range studied is
