Kinetic Measurements Using Flow Tubes The Journal of Physical Chemistry, Vol. 83, No. 1, 1979 3 for diatomics substantial progress has been achieved, as bring experimenitalists and theorists together and to show evidenced by some of the present papers. that the field of thermal elementary reaction kinetics is Lastly, the symposium did achieve its major goal: to alive and well.

Kinetic Measurements Using Flow Tubes

Carleton J. Howard

Aeronomy Laboratory, NOAA Environmental Research Laboratory, Boulder, Colorado 80303 (Received October 6, 1978) Publication costs assisted by the NOAA Environmental Research Laboratory

This paper is a selective survey of the chemical kinetic literature involving flow tube measurements of elementary reaction rate constants. It describes the origins of the flow tube method, the experimental technique, the measurement of rate constants, and an analysis of the inherent errors. Emphasis is placed on the discussion of the strengths and limitations of the method as a source of kinetic data.

I. Introduction TABLE I: Comparison of Flow Tube and Flash-Photo- In recent years there has been an increasing demand for lysis Kinetic Tecliniques phase reaction rate data. Laser development,l at- flow tube flash photolysis mospheric chemi~try,~,~and combustion4 are examples of 200-600 K 100-600 K fields of application of elementary reaction studies. range Committees and organizations have been created to collect, 1-10 torr 5 torr-several evaluate, and disseminate kinetic information. In at- range atmospheres mospheric chemistry, for example, there are serious rate constant (1O-lo-lO-l ') cm3 (10~'o-10~'8)cm3 economic and social implications derived from the ap- range -' s-' molecule-' s-l detection excellent requires fast plication of kinetic data in computer models that assess versatility detector the impact of anthropogenic chemicals on stratospheric reactant excellent limited ozone. Thui;, increased concern for the accuracy of rate versatility constant measurements has developed concurrently with heterogeneous can be serious none the demand for more data. reactions The flow tube technique has been the most prolific expense low moderate source of kinetic data near 300 K. In evaluating the usefulness of this method for obtaining rate constant data work deals with reactions of metals and metal oxides in it is instructive to make a comparison with the flash- a special application of the flow tube technique and is photolysis technique. This comparison on the basis of described in detail elsewhere in this volume.1° seven different criteria is summarized in Table I. The B. Pressure Range. The flow tube technique is basically emphasis of this discussion is not to demonstrate the a low pressure technique as will be discussed later. Flash superiority of one method in all categories but rather to photolysis, on the other hand, can be used to very high show the complementary nature and strengths of both with the main limitation being the detection of methods. In making such a comparison it is necessary to reactants. If resonance fluorescence is used,for detection, make some generalizations that are not accurate for every some species such as OH are quenched by the buffer gas. study. In this respect the discussion is influenced by the In this case resonance absorption may be usedll to extend experiences we have had in the NOAA Aeronomy Labo- the pressure range. ratory using both techniques. C. Rate Constant Range. Both flow tube and flash- A. Ternpcrature Range. The useful temperature range photolysis techniques are used to measure fast reactions is nearly the same for both techniques. The upper with rates up to gas kinetic collision rates. The greater temperature limit is established by the onset of problems pressure range of the photolysis method also allows larger with the thermal stability of reactants and the selection reactant concentrations to be used and hence smaller rate of materials for fabricating the apparatus. At the low constants to be measured. Thus photolysis systems have temperature extreme the flow tube method is somewhat a significant advantage for studying slow reactions and more restricted than the flash-photolysis method because termolecular reactions at high pressures. of heterogeneous reactions. It is often observed that the D. Detector Versatility. One of the two major ad- rate of destruction of radicals such as C1, OH, and H02on vantages of the flow tube technique is the immense variety the reactor surface increases significantly at of methods that can be used to detect the reactants and below about 250 Ke5Nevertheless, there have been several products. This advantage is derived from the steady-state studies using flow itube techniques beyond these limits. nature of the flow system in which the progress of the For example, Trairior et aL6 have studied the recombi- reaction is frozen at any fixed observation point along the nation of atomic hydrogen down to 77 K, Westenberg and tube. Since the concentrations of the reactants are deHaas7s8 have routinely studied reactions of 0 and OH constant at that point, there are no constraints on the up to 1000 K, and Fontijn et ale9have developed a flow detector speed. A flash-photolysis experiment, on the reactor designed for operation up to 2000 K. The latter other hand, is studied in real time and requires a detector

This article not subject to US. Copyright. Published 1979 by the American Chemical Society 4 The Journal of Physical Chemistry, Vol. 83, No. 1, 1979 Carleton J. Howard

with a time resolution that is at least 1/10 the period of powerful kinetic tools, particularly through the use of laser the experiment, i.e., in the millisecond range. Low signal light sources. levels can be overcome using signal averaging Wood also discovered that certain materials became technique^'^,^^ but some detectors such as magnetic res- incandescent when exposed to the products of a hydrogen onance methods cannot be applied to flash-photolysis discharge.2fi He deduced that the glow was due to energy experiments. released by the surface-catalyzed recombination of radicals E. Reactant Versatility. The second major advantage produced in the discharge. This discovery was a primitive of the flow tube method is the great versatility it provides ancestor of catalytic probes used to measure atom con- for working with a wide variety of reactants. With the flow centrations in numerous flow tube kinetic st~dies.~~~~-~~ tube method it is possible to generate two different labile The first flow tube kinetic measurements were made in reactants in isolation and to study their reactions under the late 1920’s. In 1929 Smallw~od~~reported measure- carefully controlled conditions. For example, reactions ments of the rate of recombination of hydrogen atoms. He such as HOz + C10 - HOC1 + 02,140 + C10 - C1+ 02,15 employed a Wood-Bonhoeffer type discharge tube as a and N + OH - NO + HI6 have been studied in flow tubes. source of atomic hydrogen and a moveable catalytic probe Titration reactions, which will be described later, play an inspired by Wood’s “incandescent wire” experiment (both important role in the reactant versatility of the flow tube, Wood and Smallwood were at The Johns Hopkins since they make it possible to produce accurately known University). The atom concentration in the flow tube was concentrations of labile reactants. measured using a calorimeter attached to the outside of The flash-photolysis technique is limited by the re- the flow tube. Smallwood calculated both homogeneous quirement of photolytic generation of the radical reactant. and heterogeneous recombination rate constants using an This factor is a restriction on both reactants because some analysis similar to the modern method described later. such as NOz and O3 are also dissociated by the flash At about the same time in Germany, chemists following radiation and may produce unwanted reactive fragments. the leadership of BonhoeffeF were also making kinetic F. Heterogeneous Reactions. An important advantage measurements in discharge-flow systems. An important of the flash-photolysis experiment is that it can be con- step in this development was the invention of the Wre- ducted at the center of a larger reactor, far removed from de-Harteck gauge32 a simple device for measuring the the walls and the possibility of heterogeneous reactions. partial pressure of atoms in a discharged gas mixture. Heterogeneous chemistry is observed to interfere in the Harteck and Kops~h~~studied the reactions of atomic study of both bimolecular17 and termolecular18 reactions. oxygen with 22 different compounds including H2, CO, The reactor surface can also be an impediment to studying H2S, CSz, NH,, HC1, and numerous hydrocarbons. The reactions of vibrationally or electronically excited reactants atomic oxygen was produced by an ac discharge and its because of its high deactivation efficiency. Although concentration was estimated using a Wrede-Harteck gauge innovative studies of reactions of vibrationally excited and a hot platinum wire. The relative reactivities of the OH19 and metastable N(2D)20have been made in flow reactants were determined qualitatively by spectroscopic tubes, the photolysis technique is generally superior for measurements of chemiluminescent emissions from the this type of study. reaction zone and by trapping and analyzing the final G. Expense. Although this consideration is seldom products. examined, there can be a significant difference between In the late 1950’s and early 1960’s several important a flow tube system and a flash-photolysis system in initial advances were made in flow tube techniques and in- expenditure. A major component that contributes to this strumentation. Much of our present technology can be difference is the multichannel analyzer that is normally traced to these developments. used to do time-resolved signal averaging. By using a A paper by Ka~fman~~in 1958 made two major con- simple detection scheme such as chemiluminescence, a flow tributions to flow tube kinetics. He studied the kinetics tube kinetic system can be assembled relatively cheaply. of the air afterglow reaction 11. Origins and Development of the Flow Tube 0 + NO+ NO2 + h~ (1) Method and demonstrated that the intensity of the chemilu- The purpose of this section is to provide a brief history minescence is proportional to the concentrations of atomic of the flow tube with emphasis on the developments that oxygen and nitric oxide, Le., I a [O][NO]. This discovery have contributed most to its application as a kinetic tool. provided a sensitive quantitative detection method for The flow tube kinetic method has evolved from the early small concentrations of atomic oxygen. The second discharge tube studies of Wood and Bonhoeffer. A major contribution was the observation that the reaction discovery of these pioneers was that large concentrations 0 + NO2 -+ NO + 02 (2) of atoms and simple radicals were generated in low pressure gas discharges. Their goal was generally to was extremely fast and could be used as a gas phase ti- identify and characterize the sources of radiation that were tration to measure atomic oxygen concentrations in a flow emitted by the discharged gases but frequently the physics tube. The endpoint of the titration was indicated by the and chemistry of production and destruction of the extinction of the airglow emission. Kaufman applied these transient species were discussed. techniques to study some atomic oxygen reactions. Woodz1 was the epitome of the one man research in- Kaufman and co-workers also introduced two other stitutions that revolutionized experimental science in the important titration schemes

early 1900’s. He experimented with resonance fluorescence N + NO + 0 + N2j (3) in metal atoms22,23and used the expressions resonance fluorescence and photoluminescence to describe the and process of excitation and re-emission of resonant radia- H + NO2 + OH + (4) tionz4 Wood applied the method only to spectroscopic problems. In 1967 Braun and LenziZ6were the first to The importance of the titration methods cannot be ov- adapt resonance fluorescence to a flash-photolysis kinetic eremphasized because they provide the foundation for experiment. It has subsequently become one of the most nearly all kinetic measurements in flow systems. They are Kinetic Measurements Using Flow Tubes The Journal of Physical Chemistry, Vol. 83, No. 1, 1979 5 fast stoichiometric reactions that provide cleanly quan- AIOrn *, titative methods of preparing labile species. The concept aC,ro# D.dilOl of gas phase titrations has now been extended to many soYn' i : n hb".ou different atomic and simple radical species. Clyne has been m*,mn, 8Mll :; Goa&- :: instrumental in developing numerous useful titration :: - schemes and recently reviewed many of them.37J8 , I, 11 ,-I - The use of chemiluminescence as a flow tube reaction codel con rate diagnostic has also been widely extended. For ex- Figure 1. Schematic of flow tube apparatus. ample, Clyne and developed a UV detector for atomic oxygen using CO and Setser and co-w~rkers'~ ond-order reactions and secondary chemistry becomes reported an IR chemiluminescent detector for studying negligible. The suppression of secondary reactions of hydrogen abstraction reactions of atomic fluorine. products and intermediates eliminates a major source of There were two major developments in instrumentation error in kinetic measurements. that helped to estahlish the early dominance of the flow In conclusion, we now have an assortment of methods tube method in the field of gas kinetics. These were mass for producing accurately measured concentrations of spectrometry" and electron paramagnetic resonance reactants and for detecting low concentrations of atoms (EPR)" or electron spin resonance (ESR). Foner and and radicals. The next section reviews the measurement Hud~on'~,'~and Phillips and Schiff45were the first to and analysis procedures used to determine the rate con- combine mass spectrometer detectors with flow tubes for stants. kinetic measurements. Subsequently, this combination has 111. Technique and Analysis been successfully exploited in a wide variety of kinetic application^."^^ The mass spectrometer has potential as A schematic of a flow tube reactor is shown in Figure a universal detector but lacks in selectivity due to the 1. The major component is a glass tube usually about 2.5 fragmentation and ionization of all gases present in the ion cm i.d. and 1 m long. The section of the reactor on the source. This problem has been significantly reduced by right is the reaction zone and is surrounded by a tem- two innovations: photoionization ion sources and magnetic perature regulated jacket that allows a constant tem- deflection of neutrals. Jones and and Gutman perature to be maintained anywhere from about 200 to 600 and co-worker~~~J'were among the first to apply pho- K. toionization to gas kinetics. Kaufman and co-w~rkers~~.~~The carrier gas (M) enters the flow tube at the left. This have used an inhomogeneous magnetic field to separate gas is the major component in the flow tube and thus the paramagnetic species (radicals) from the diamagnetic serves to define the physical properties of the gas stream, background gas and to selectively deflect the paramagnetic e.g., pressure, flow velocity, heat capacity, thermal con- species into a mass spectrometer. The sensitivity of mass ductivity, viscosity, etc. It also acts as a heat bath to spectrometers varies greatly for different systems and maintain the reactants at the temperature of the walls of different hut concentrations down to about lo9 the reactor, controls , and serves as a third body molecules cm-3 can he detected. in termolecular reactions. Helium is a common choice as a carrier gas because of its inertness, high thermal con- EPR can he used to detect only paramagnetic species, ductivity, and excellent diffusion coefficients. hut fortunately that encompasses most atoms and simple Atomic reactants are usually generated in electrodeless radicals. The first kinetic measurement with EPR was microwave discharges or by thermal dissociation. The reported by Krongelh and Strandhergs7 in a study of microwave discharge system is the more common method atomic oxygen recombination. Westenherg and deHaa~%,~~since the development of simple and compact cavities!' have been leaders in its application to flow tube gas ki- Langm~ir~~developed an apparatus for producing atoms netics and have reported studies on a wide variety of by thermal dissociation which is a very clean method, hut species including H, 0, N, C1, and OH. Several other is seldom used in flow sy~tems.6.~~The advantage of laboratories have also recently made major contrihutions thermal dissociation is that the method is much more to this field.46,60,61The detection limit for EPR is about discriminating than an electrical discharge. While a 10" molecules cm-'. discharge will fragment nearly any type of molecule,66a Resonance absorption has been employed in both the thermal source tends to break only the weakest bonds. UV and vacuum UV wavelength regions as a detection Thus small impurities of H20, N,, and 0, can be tolerated method in flow tube kinetic studies. This technique is in a thermal source hut will give a mixture of atomic sensitive and very selective. Kaufman used UV resonance products in a discharge source. Thermal sources are useful absorption in the first flow tube study of the kinetic for generating hydrogen and halogen atoms. sources and chemistry of OH radicals.36 Later work in his Atoms from the discharge or thermal source can he used laboratory used vacuum UV ahsorption to study atomic directly or can he converted to a different atomic or radical species in flow tubes.20 There ai-e a few examples of studies species by a titration rea~tion.~~-~~It is important to where resonance absorption is still superior to other de- employ different radical sources when possible to test for tection methods (such as in the study of atomic fluorine interference from excited states or secondary reactions. but resonance fluorescence to a great extent The radical reactant enters the flow tube at a port has supplanted this technique. Resonance fluorescence downstream from the carrier gas entrance. A small flow is routinely used to detect atoms and radicals at con- of He or Ar is added to flush the gas through the radical centrations as low as lo9 molecules cmd in flow tuhe source. The flow tube is often treated with a wall coating st~dies.''J~~~~ or poison to inhibit the removal of radicals on the tube A new era in flow tube kinetics has been introduced by ~urface.6~Phosphoric acid, boric acid, sulfuric acid, and the application of sensitive detection techniques such as various dry polymeric materials68 have been used effec- mass spectrometry, resonance fluorescence, and laser tively. Wall coatings are a black art and most laboratories magnetic res0nance.6~ With these detection methods, have their own magic elixir. measurements are made at low radical concentrations The pressure port is located at the center of the reaction (

gradient in the flow tube. Care must be taken that the cm3 s-l), I' is the. temperature (K),PT is the total pressure pressure port is smooth and oriented at right angles to the (torr), and R is the flow tube radius (cm). gas flow in order to measure only the static pressure in the With most radical reactants there is a significant flow tube. first-order loss at the reactor wall. The fraction of wall Flow tube kinetic measurements usually are made by collisions that remove the radicals is y. The number of varying the reaction zone length (z), that is the distance radical destroying wall collisions per unit area is given by to the detector from the point at which the two reactants gas kinetic theory: 1/4yoc, where w is the average mo- are mixed. This can be accomplished by changing the lecular speed. Thus the rate of removal of radicals by wall position of the detector or the reactant inlet. Moveable collisions is given by detectors were used in some st~dies~~~~~~~as were moveable discharge sources. Most flow tube systems now employ (7) either a series of fixed, valved ports along the flow tube69 or a moveable injector70 as shown in Figure 1. The fixed where S/ V is the surface-to-volume ratio of the cylindrical inlets are short and therefore have an advantage if the reactor = 2/R. This rate defines the first-order rate added reactant is very reactive and destroyed by wall constant h, collisions or by gas recombination. The moveable inlet on the other hand requires fewer connections through the flow k," = yo/(2R) s-l (8) tube temperature jacket and allows greater flexibility in Clyne and and Westenberg and deHaas70 have varying the reaction zone length. Both methods have been demonstrated the advantage of the variable reaction zone used to add reactive species such as 0, N, H, HQz,and C10. length method of analysis by showing that the rate con- The exit orifice on the moveable inlet consists of a series stants derived by this method are not affected by wall of small holes around the diameter of the tube. The reactions. The radical concentration at the detector a fixed purpose of this configuration is to provide rapid mixing distance 1 from the radical source is c = co exp(-k,l/u), of the added gas with the carrier stream. The added where co is the initial radical concentration. When reactant reactant is assumed to be thoroughly mixed with the A is added at a distance z from the detector, the detected carrier gas. radical concentration is A great variety of detectors can be used with the flow c = co exp(-k,l/u) exp(-kz/ul tube. The most important requirement of the detector is (9) that it be sensitive. For best results the concentration of Thus the wall reaction term is constant and independent the radical species, c, should be less than about 10" of the z-dependent reaction term if y is unchanged in the molecules cm-3 when radical-molecule reactions are presence of added reactant. A plot of In c vs. z will have studied. The concentration of the added reactant, A, is a slope, d In c/dz = -k/v. much larger, typically in the range 1012-1016molecules Westenberg and deHaasS0also demonstrated in their Thus the reaction becomes pseudo-first order in c analysis that the detector may be outside the tempera- and the rate equation is ture-controlled region. This is equivalent lo having a dc/dt = -kc (5) poorly defined absolute reaction length, e.g., as results from a change in flow tube diameter at the intersection with the The first-order rate constant k(s-') = k"A, where k" is the detector. Since the rate constant is derived from the slope, second-order rate constant (cm3 molecule-' s-l) and A is it can be shown that accurate measurements are required the concentration of the added reactant (molecule ~m-~). only of the relative radical concentration, of the Az in- When all of the processes affecting c are first order, only crements, and of absolute reactant concentration (A). relative concentrations of c need to be measured. It is useful to estimate the precision expected in mea- The basic assumption of the flow tube analysis is that surements of rate constants using eq 6. This requires the radical reactant is mixed homogeneously with the estimates of the precision in the measurement of each of carrier gas and that there are no concentration gradients. the variables in the calculation and a standard propagation Then the carrier gas flow velocity, v (typically 300-2000 of errors analysis of the equation.71 The result is cm s-l), is the transport velocity of the radicals. With this assumption the reaction time in the flow tube, t = z/u, is A!?! = [ (2 ) + (23+ ( 2 ) + the time that the radicals and reactants are in contact from kI1 2 the point of addition of the reactant to the point of de- tection. Thus, reaction time and distance are equivalent (10) in the flow system. (2!5) + (2$!)? + ( *)2]1'2slope A rate constant measurement is made by measuring the radical concentration with the moveable inlet at several The last term is the estimated precision in determining different positions, typically at 10-cm intervals between the slope d (In c)/dz. Reasonable estimates of the precision z = 10 and 50 while the reactant flow rate is held constant. (95% confidence limits) of each of the variables are These data are plotted In c vs. z and the slope is used to SFT/FT = 0.03, AT/T = 0.01, mA/FA = 0.03, APT/PT = calculate the pseudo-first-order rate constant 0.01, AR/R = 0.01, and A slope/slope = 0.02. The re- d (In c) sultant precision in measurement of k'' is hk1'/k" = 8%. k=-u---- Rate constant measurements generally have a corre- dz sponding precision in the range 5-207' The bimolecular rate constant is This analysis ignores two important factors: (1) the contribution of errors due to the temperature dependence of k" and (2) the contributions of systematic errors. Cvetanovic et aL71 and Fontijn and FelderlO give analyses d (In c) of the effect of the temperature dependence of the rate

-_I cm3 molecule-I s-l (6) constant on the error analysis. The magnitude of the dz contribution depends on the activation energy and will not where FT and .FA are the total and reactant flow rates (STP be discussed here. Systematic errors are very difficult to Kinetic Measurements Using Flow Tubes The Journal of Physical Chemistry, Vol. 83, No. 1, 1979 7 evaluate but are important because they determine the is the corrected rate constant and k is the measured value, accuracy. Consideration of possible systematic errors in the correction for axial diffusion is (u + ud)/u, and calibrations and measurements gives an estimated accuracy in the range of 10-1 5%, k, = h(1 + hD/u2) (15) IV. Limitations of Flow Tube Reactors This result is identical with that obtained earlier73s79by integrating the 'one-dimensional continuity equationso One of the first dtetailed discussions of the limitations of flow tube reactors was given by Ka~fman~~in 1961. He dc . d2c U- = D- - kc enumerated the basic problems arising from viscous flow dz dz2 and diffusion. Although these factors are important, they are frequently ignored. The most common error is to This correction will be largest at low pressures (since D neglect the effects of concentration gradients. This section 1/P) and slow velocities. For example, when k = 100 will describe the origins of the limitations and methods s-l, D = 500 cm2 s-l, and u = 800 cm s-l, the correction is to minimize and correct for errors. 8%. One normally operates under conditions that min- The flow through the reactor is fully developed viscous imize the corrections for axial diffusion. When these The forces moving the gas develop a pressure corrections are riot negligible, one must also allow for the gradient along the length of the tube. Under conditions effects of other first-order reactions that contribute to the of high flow velocities this gradient can be significant in axial concentration gradient such as wall reactions. The small tubes73 appropriate correction for rate constants measured by varying the reaction zone length is AI3/& = 5.9 x ~O-~~U/R~torr cm-l (11) 7 is the gas viscosity (g cm-' s-l), u is the flow velocity, and R is the tube radius. Since gas viscosities increase with temperature, the gradients will be larger at high tem- peratures. The gas maintains a parabolic velocity profile The flow tube analysis assumes that there are no radial concentration gradients. There are two factors that act u(r) = 241 - r2/R2) (12) to reduce the concentration of radicals near the wall. The first is the wall reaction. The second factor is the slow where r is the radial parameter. Since the gas velocity is speed of the gas near the walls gives the reactants in that maximum at the center of the tube, the moveable inlet region a longer residence time than the fast moving radicals seriously disrupts the velocity profile. The pressure at the center. Under ideal (low pressure) conditions, gradient is nearly twice the value obtained by eq 11 when diffusion will maintain a uniform radial profile. However, a 3-mm 0.d. injector is present in a 25-mm i.d. flow tube.75 as the pressure is increased and diffusion becomes less The pressure gradient produces corresponding velocity and effective the radical concentration will develop a parabolic concentration gradients. These effects are normally profile. Rate coinstants measured under this condition will negligible when the pressure is measured at the center of be in error if the average transport velocity for the radical the reaction zone. is assumed to be the gas flow velocity. When the radial Since the viscosity has a positive temperature coefficient, concentration profile is a known function of r, c(r), and the velocity profile is also disrupted when the gas enters is constant along the length of the reaction zone, the a heated or cooled region. However, this effect is small correct average transport velocity, uT, can be calculated compared to the time required for the reactants to become eq~ilibrated.~~The solution to this problem is to allow 2rJRc(r)u(r)r dr adequate time (distance) for the reactants to enter the temperature-regulated section before mixing. About 15-20 UT = - R (18) ms (15-20 cm) is sufficient in a 2.5-cm i.d. reactor operating 2r-L c(r)r dr in the usual temperature range. At low pressures (<1torr) the velocity profile may be The flowing afterglow is an interesting example of a system modified by slip, Le., molecular The condition for with an analysis of this type. Here the reactive species are this effect tlo be negligible is X << R (A is the mean free ions which are destroyed by every collision with the reactor path). Slip causes the flow velocity to be greater than zero wall (y = 1). The resultant ion transport velocity has been at the wall and thereby flattens the parabolic profile. calculated using a variety of different method~~l-~~to Fortunately, the velocity profile is not a factor in the obtain the radi,sl profile. UT = 1.6~under low pressure, analysis when there are no radical concentration gradients. diffusion-controlled conditions. Rajottes4has used optical In the preceding (analysis we assumed that there are no methods to mealsure the radial profile of metastable neon concentration gradiients and that the flow velocity is the atoms (y = 1) at pressures from 0.1 to 5 torr. He observes transport velocity of the reactants. Whenever reaction the expected transition from a zero order Bessel type occurs, this assumption is violated. This can be seen from distribution at low pressures to a Gaussian type distri- the equation bution at higher pressures. dc/dz = -kc/u (13) Ka~frnan~~derived a formula for calculating the ap- proximate radial concentration gradient for y << 1. His This axial concentration gradient will cause the radicals result is to be transported down the tube with an additional velocity component ud given by Fick's first law dc J = -D- = u dz (14) where ea, cw, and c are the axial, wall, and average radical concentrations, respectively. Thus, the concentration where J is the flus (molecules cm-2 sl)and D is the gradient is inversely dependent on the diffusion coefficient diffusion coefficient (cm2 Thus ud = Dk/u and the and directly proportional to the square of the tube radius. correct transport velocity for the radicals is u + ud. If h, Both the homogeneous reaction and the wall reaction are 8 The Journal of Physical Chemistry, Vol. 83, No. 1, 1979 Carleton J. Howard TABLE 11: Errors in Flow Tube Kinetic Measurements of the flow tube method indicates that an overall accuracy source typical range of 10-15% is possible. In conclusion, it is interesting to see how "state of the flow parameters i- (5-1 0%) art" kinetic measurements compare to this estimated pressure gradient 515% axial concentration -( 1-20%) accuracy limit. Watson88has recently reviewed kinetic gradient data for reactions involving chlorine. Because of the radial concentration -( < 100%) importance of these reactions in stratospheric chemistry gradient many laboratories have studied the same reactions using reactant purity t different kinetic techniques. Three reactions from Watson's compilation have been studied recently by four important but the wall loss is more critical. Equation 19 or more laboratories: (1) OH + HC1,4 labs, h N 3.0 X is useful to estimate the pressure regime where radial exp(-425/7') cm3 molecule-1 s-l, (2) C1 + CH4, 6 labs, h N gradients become significant. 7.3 X exp(-1260/T); and (3) C1 + Os,5 labs, h N 2.7 There have been numerous papers that evaluate the x exp(-257/T). At least half of the measurements effects of diffusion and kinetics in a flow reactor. The were made using flow tubes. The rate constants for each usual starting point is the continuity equation reaction were averaged and the standard errors were calculated at 298 and 240 K. At both temperatures the agreement is superb. At 298 K the ratio of the standard error to the mean is 4, 8, and 10% for reactions 1-3, re- spectively. The data for 240 K give ratios of 14 and 12% for reactions 2 and 3. There are only three measurements of reaction 1at 240 K and all are within 15% of the mean. The first term is for flow or convective transport, the It is not surprising that the low temperature data do not second term is for radial diffusion, the third term is for agree as well as the room temperature data since the axial diffusion, and the final term is for reaction. Poirier measurements are near the limit of the temperature range and Cad5 have presented an interesting numerical and represent fewer data points. If this comparison can analysis of the high pressure regime under conditions be taken as a fair evaluation of present kinetic data, it where axial diffusion may be neglected. They solve the indicates that flow tube measurements are within the continuity equation for first- and second-order homoge- estimated 10-15% accuracy range and that there are no neous reactions and first-order wall reaction coupled with significant systematic differences between data obtained radial diffusion. They derive correction factors for the using flow tubes and that obtained with other methods. transport velocity for a variety of different conditions including detection geometry. They demonstrate that References and Notes detectors that sample on axis, average along a diameter, (1) E R. Mosburg, Jr., EEJ. Quantum Nectron , QE9, 843 (1973). or average across the flow tube cross section give different (2) P. J. Crutzen, I S. A Isaksen, and J. R McAfee, J Geophys Res , 83. 345 (1978). results at high pressures. (3) J. A. Logan, M. J. Prather, S. C. Wofsy, and M. B. McEiroy, Phil. Trans. OgrerP has also developed an analysis that considers R. SOC.,290, 187 (1978). both homogeneous and heterogeneous first-order reactions (4) H. B. Palmer and D. J. Seery, Annu. Rev. Phys. Chem., 24, 235 (1973). with radial concentration gradients. He gives a method (5) The mechanism for the increase in wall removal of radicals at low for correcting rate data. temperatures has not been explained. Limitations from this effect Since the correction factor for radial concentration on a study of chlorine atom reactions below 200 K were described by M. S. Zahniser, B. M. Berquist, and F. Kaufman, Int. J. Chem. gradients depends upon the radial concentration profile, Kinet., 10, 15 (1978). it is not possible to reduce the problem to a simple general (6) D. W. Trainor, D. 0. Ham, and F. Kaufman, J. Chem. Phys., 58, solution. The largest possible correction arises when all 4599 (1973). radicals are concentrated on the reactor axis, in which case, (7) A. A. Westenberg and N. deHaas, J. Chem. Phys., 46, 490 (1967). (8) A. A. Westenberg and N. deHaas, J. Chem. Phys., 58, 4061 (1973). UT = 2u. Therefore the correction factor is always between (9) A. Fontijn, S.C. Kurzius, J. J. Houghton, and J. A. Emerson, Rev. 1 and 2. Although methods have been derived for cor- Sci. Instrum., 43, 726 (1972); A. Fontijn, W. Felder, and J. J. Houghton, recting high pressure data, there has been no serious effort Fifteenth Symp. (Int.) Combust,, [Proc.], 15fh, 775 (1975). (10) A. Fontijn and W. Feider, J. Phys. Chem., this issue. to apply these corrections. (11) C. Anastasi and I. W. M. Smith, J. Chem. Soc., Faraday Trans. Westbrook et alas7have developed a technique for 2, 72, 1459 (1976). studying kinetics in a turbulent flow reactor and report (12) D. D. Davis, R. E. Huie, J. T. Herron, M. J. Kuryio, and W. Braun, J. Chem. Phys., 56, 4868 (1972). results for studies of high temperature combustion pro- (13) R. B. Kiemm and L. J. Stief, J. Chem. Phys., 61, 4900 (1974). cesses. Their work may provide a new direction for flow (14) B. Reimann and F. Kaufman, J. Chem. Phys., 69, 2925 (1978). tube studies in which high flow velocities are employed to (15) P. P. Bemand, M. A. A. Ciyne, and R. T. Watson, J. Chem. SOC., Faraday Trans. 1, 69, 1356 (1973). give turbulent mixing, thus eliminating difficulties due to (16) I. M. Campbell and B. A. Thrush, Trans. Faraday SOC.,64, 1265 diffusion. In principle this method can also be employed (1968). to extend the pressure range of low temperature kinetic (17) C. J. Howard and K. M. Evenson, J. Chem. Phys., 84, 4303 (1976). (18) J. G. Anderson, J. J. Margitan, and F. Kaufman, J. Chem. Phys., studies, but it remains to be seen whether it can be applied 60, 3310 (1974). to the direct measurement of elementary reaction rate (19) J. E. Spencer and G. P. Glass, Chem. Phys., 15, 35 (1976). constants. (20) C.-L. Lin and F, Kaufman, J, Chem. Phys., 55, 3760 (1971). (21) A brief summary of the career of R. W. Wood and a list of his The various sources of errors are summarized in Table publications is given by G. H. Dieke, "Biographical Memoirs of Feiiows 11. The sign indicates the direction in which the rate of the Royal Society", Vol. 2, Royal Society, London, 1956, p 327. constant is in error. Inaccuracies in the measurement of (22) R. W. Wood, Phil. Mag., 6, 513 (1905). flow parameters cannot be eliminated, but those from (23) R. W. Wood and F. L. Mohier, Phys. Rev., 11, 70 (1918). (24) A. C. G. Mitchell and M. W. Zemansky, "Resonance Radiation and pressure and concentration gradients can be reduced to Excited Atoms," Cambridge University Press, New York, 1971, p 31. less than 2 or 3%. Impurities in the reactant gas can cause (25) W. Braun and M. Lenzi, Discuss. Faraday SOC.,44, 252 (1967). errors if they are much more reactive than the reactant (26) R. W. Wood, Proc. R. SOC.,London, Ser. A, 102, 1 (1922). (27) E. L. Toilefson and D. J. LeRoy, J. Chem. Phys., 16, 1057 (1948). itself. This error must be eliminated through careful (28) L. Eiias, E. A. Ogryzio, and H. I. Schiff, Can. J. Chem., 37, 1680 purification and analysis of reactants. A complete analysis (1959). Kinetic Measurements Using Flow Tubes The Journal of Physical Chemistry, Vol. 83, No. I, 1979 9

(29) R. V. Poirier and R. W. Carr, Jr., Rev. Sci. Instrum., 43, 354 (1972). L. Singleton, and G. Paraskevopoulos, J. fhys. Chem., this issue. (30) H. M. Smallwood, S. Am. Chem. Soc., 51, 1985 (1929). (72) C. J. Howard and K. M. Evenson, J. Chem. fhys., 64, 197 (1976); (31) K. F. Bonhoeffer, Z. fhys. Chem., 113, 199 (1924); R. Boehrn and 65, 4771 (1976). K. F. Bonhoeffer, ihid., 119, 385 (1925); K. F. Bonhoeffer and P. (73) F. Kaufman, F'rog. React. Kinet. 1, 3-39 (1961). Harteck, bid., A139, 64 (1928). (74) S. Dushman and J. M. Lafferty, "Scientific Foundations of Vacuum (32) E. Wrede, 2. Phys., 54, 53 (1929); P. Harteck. Z. fhys. Chem., Technique", Wiley, New York, N.Y., 1962, p 82. A139, 98 (1928). (75) J. G. Anderson (private communication) derived a correction term (33) P. Hartecic and U. Kopsch, Z. fhys. Chem., 812, 327 (1931). to the Poiseuille equation to describe the effect of an inlet tube of (34) F. Kauman, froc. R. SOC. London, Ser. A, 247, 123 (1958). 0.d. R, inside a flow tube of i.d. R. It is (1 - (R,/R)4- (1 - R,*/R*)/in (35) F. Kaufman and J. R. Kelso, Symp. (Int.)Combustion., [froc.], 7th, (R/Ri)I, 53 (1958). (76) M. Gilbert, Combust. Name, 2, 149 (1958). (36) F. Kaufman and F. P. Del Greco, Discuss. Faraday SOC.,33, 128 (77) G. P. Brown, A. DiNardo, G. K. Cheng, and T. K. Sherwood, J. Appl. (1962). fhys., 17, 802 (1946). (37) M. A. A. Ciyne, "Physical Chemistry of Fast Reactions", Vol. 1, 6. (78) Data for diffudon coefficients are found in T. R. Marrero and E. A. P. Levitt, Ed., Plenum Press, New York, N.Y., 1973, pp 245-330. Mason, J. fhys. Chem. Ref. Data, 1, 3 (1972). (38) E. H. Appelman and M. A. A. Ciyne, ACS Symp, Ser., No. 66, 3-25 (79) P. G. Dickens, R. D. Gouid, J. W. Linnett, and A. Richmond, Nature (1978). (London), 187, 686 (1960). (39) M. A. A. Clvne and B. A. Thrush, Roc. R. SOC.London. Ser. A. (80) W. Jost, "Diffusion in Solids, Liquids, and Gases", Academic Press, 269, 404 (i962). New York, N.Y., 1952, p 58. D. J. Bogan, D. W. Setser, and J. P. Sung, J. fhys. Chem., 81, 888 (81) R. W. Huggins and J. H. Cahn, J. Appl. fhys., 38, 180 (1967). (1977); D. J. Smith, D. W. Setser, K. C. Kim, and D. J. Bogan, J. (82) E. E. Ferguson, F. C. Fehsenfeld, and A. L. Schmeltekopf, Adv. At. fhys. Chem., 81, 898 (1977). Mol. fhys., 5, 1 (1969). Mass spectrometry with electron impact ionization originates with (83) R. C. Bolden, i3. S. Hemsworth, M. J. Shaw, and N. 0. Twiddy, J. J. A. Hipple and D. P. Stevenson, fhys. Rev., 63, 121 (1943). fhys. B, 3, 4!5 (1970). EPR was invented by Beringer and co-workers: R. Beringer and J. (84) R. J. Rajotte, Can. J. Spectrosc., 19, 178 (1974). G. Castle, Jr., fhys. Rev., 75, 1963 (1949); E. 6. Rawson and R. (85) R. V. Poirier and R. W. Carr, Jr., J. fhys. Chem., 75, 1593 (1971). Beringer, fhys. Rev., 88, 677 (1952). (86) P. J. Ogren, J. fhys. Chern., 79, 1749 (1975). S. N. Foner and R. L. Hudson, J. Chem. fhys., 36, 2681 (1962). (87) C. K. Westbrook, J. Creighton, C. Lund, and F. L. Dryer, J. fhys. S. N. Foner and R. L. Hudson, Adv. Chem. Ser., 36, 34 (1962). Chem., 81, 2542 (1977). L. F. Phillips and H. I. Schiff, J. Chem. fhys., 36, 1509 (1962). (88) R. T. Watson, J. fhys. Chem. Ref. Data, 6, 871 (1977). E. A. Aibers, K. Hoyermann, H. Gg. Wagner, and J. Wolfrum, Symp. (Int.) Combust., [/'roc.], lath, 313 (1969). E. E. Daby, H. Niki, and B. Weinstock, Symp. (Int.)Combust., proc.], 72th. 277 (1969). M. A,' A. Clyne and R. T. Watson, J. Chem. SOC.,Faraday Trans. 7, 70, 1109 (1974'1. Discussion J. W, Birks, B. Shoemaker, T. J. Leck, and D.M. Henton, J. Chem. fhys., 65, 5181 (1977). GEORGEBCRNS. The principal differences between these two G. Poulet, G. LeBra:;, and J. Cornbourieu, J. Chem. fhys., 69, 767 techniques are (1)the methods of initiation of reaction and (2) (1978). detection methods of reaction products. In principle, most of the I. T. N. Jones and IC. D. Bayes, Chem. fhys. Left., 11, 163 (1971). fast gas phase reactions can be studied over a wide temperature I. T. N. Jones and K. D. Bayes, Symp. (Int.)Combust., [froc.], 14th, 277 (1973). range using both of these techniques. In practice, however, one J. R. Kanofskv and D. Gutman. Chem. fhvs. Left.. 15. 236 (19721. technique will prove to be more appropriate for studying a J. R. Kanofsiy, D. I-ucas, and D. Gutman: Symp. (Int.) Combust:, particular reaction than the other. For example, halogen re- [froc.], 14th, 285 (1973). combination-dissociation can be studied more easily by flash C. E. Kolb and M. I

(19591.\ important in disclharge flow reactions and are, generally, insig- A. A. Westenberg and N. deHaas, J. Chem. fhys., 50, 707 (1969), nificant in flash photolysis reactions. On the other hand, re- and earlier references noted therein. combination of hydrogen atoms can be best studied by the A. A. Westenberg, Science, 164, 381 (1969). flow-discharge technique, because H2absorbs only in vacuum UV. G. A. Takacs and G. P. Glass, J. fhys. Chem., 77, 1060 (1973). C.-N. Wei and R. B. Timmons, J. Chem. fhys., 62, 3240 (1975). In this connection the study of H atom recombination down to P. P. Bemand and M. A. A. Clyne, J. Chem. SOC.,Faraday Trans. 4 K by the flow-discharge technique would be particularly 2, 72, 191 (1976). important both from the experimental and theoretical uiew- C. J. Howard and K. M. Evenson, J. Chem. fhys., 61, 1943 (1974). points. The problem, then, is to determine which technique is F. C. Fehsenfeld, K. M. Evenson, and H. P. Broida, Rev. Sci. Instrum., 36, 294 (1965). most advantageous in studying a particular reaction. C. G. Suits, Ed., "The Collected Works of Irving Langmuir", Voi. 1, Pergamon Press, New York, N.Y., 1960, p 103; I. Langmuir and G. DANIELW. TRAINOR.You indicate that wall reactions con- M. J. Mackay, J. Am. Chem. SOC.,36, 1708 (1914). tribute to the low temperature limit attainable in such mea- F. Kaufrnan, Adv. Chem. Ser., 80, 29 (1969). surements. Would you comment on the magnitude of the wall E. A. Ogryzlo, Can. J. Chem., 39, 2556 (1961). loss as a function of temperature? R. 6. Badnchhape, P. Kamarchik, A. P. Conroy, G. P. Glass, and J, L. Margrave, Int. J. Chem. Kinet., 8. 23 (1976). M. A. A. Clyne and 6. A. Thrush, Proc. R. Soc. London, Ser. A, CARLETONJ. HOWARD.Of course this function depends on the 275, 544 (1963). radical and the wall coating. We have not analyzed the de- A. A. Weatenberg and N. deHaas, J. Chem. fhys., 46, 490 (1967). pendence but typical results H02in a 2.54-cm id. H3P04coated R. J. Cvetanovic, R,. P. Overend, and G. Paraskevopouios, Int. J. tube are 296 K, k,,, = 1- 3 s-l; 250 K, k, = 5-7 and 230 K, k, Chem. Kinet., Syrrrp. 7, 249 (1975); see also R. J. Cvetanovic, D. = 15-20 s-',