Mass-spectrometric Tracer and Photometric Studies of Catalysed Radical Recombination in Flames BY DAVID E. JENSEN" AND GEORGE A. JONES Rocket Propulsion Establishment, Westcott, Aylesbury, Buckinghamshire Received 31st May, 1974 Measurements of hydrogen atom concentrations in H2 + O2 + N2 flames with and without additives have been made by a mass-spectrometric tracer method dependent upon the reaction being balanced and by a well established photometric method dependent upon balance of the analogous reaction Results from the two methods agree well. Catalysis of flame radical recombination caused by addition of tin, molybdenum and tungsten is described. Mass-spectrometric results for tin are in good agreement with previous photometric measurements. Results for molybdenum and tungsten from both methods are quantitatively interpreted in terms of a cyclic homogeneous gas phase mechanism, with associated thermochemistry and reaction rate coefficients.Sr+ + H20 + SrOH+ + H, K = 47 exp( - 7 700 KIT), Li+ H20 + LiOH+H, K = 16 exp(- 10 O00 K/T). Recent work has shown that small quantities of various metal-containing additives can cause significant catalysis of recombination of the H, OH and 0 radicals generally present in above-equilibrium concentrations in H2 + 0, + N, flames. This work involved measurement of [HI by the well established Li/Na photometric m e t h ~ d . ~ In this method, known trace quantities (too small to perturb the flame properties significantly themselves) of lithium and sodium are added in turn to a flame and [Li] is measured via comparison of the Li first resonance doublet emission intensities or absorptions with those of the corresponding Na doublet.[HI is then calculated on the basis of the reasonable assumptions that the reaction is balanced,6* that lithium forms significant concentrations of Li and LiOH alone and that sodium exists largely as free atoms in the flame. (A reaction A+B + C + D is said to be " balanced " or " in equilibrium " when ([C][D])/([A][B]) is equal to the equilibrium constant for the reaction.) Under certain conditions, however (e.g. in fuel-lean flames where peroxide formation may occur,* in practical flames with interfering optical frequency radiation, or where additives form stable compounds with lithium and/or sodium) an alternative method is needed.Hayhurst and Kittel- son have suggested that a reaction analogous to (l), Sr+ + H20 + SrOH+ + H, Li + H 2 0 + LiOH + H (equilibrium constant K l ) (1) (2) balanced in a flame to which trace quantities of strontium are supplied, affords such an alternative if [SrOH+]/[Sr+] can be measured via mass-spectrometric sampling and K2 is known. The present paper describes application of both these methods to investigation of radical recombination catalysis in H2 + O2 + N2 flames caused by addition of tin, molybdenum and tungsten-containing compounds. The good agreement between results from the two methods supports the suggestion that the mass-spectrometric tracer method provides a useful means of studying radical 149150 RADICALS I N FLAMES recombination in flames and strengthens confidence in the quantitative data for the observed catalytic effects. The two methods of measuring [HI require knowledge of the equilibrium constants Kl and K2 as functions of temperature.On the basis of data from several sources, Kelly and Padley lo recommend a value for the standard zero-point enthalpy change AH; for Li(g)+OH(g) + LiOH(g) of 433 +8 kJ mol-l, in good agreement with another recommendation by Zeegers and A1kemade.l Vibration frequencies for the (assumed linear) LiOH molecule have been estimated lo as 66.5 (Li-0 stretch), 35.0 (bending mode) and 360.0 (0-H stretch) mm-l respectively, and the molecular moment of inertia ILioH estimated l2 to be 2 . 2 ~ kgm2. Together with other data, taken from the JANAF TabZes,13 this gives a recommended value Kl = 16 exp { - (10 OW_+ 1000 K ) / T ) for 1500 < T < 3000 K.K2 is less accurately known. If SrOH+ is assumed, by analogy with the iso- electronic RbOH,12 to be linear, having vibration frequencies v1 at 35.5 mm-’, v2 (doubly degenerate mode) at 31.0 mm-l and v3 at 360.0 mm-l and ISrOH+ = 1.35 x kg m2, the photometric measurements of Schofield and Sugden l4 may be interpreted to give AH;,2 = +74+40 kJ mol-l. The microwave measurements of Jensen,15 combined with Cotton and Jenkins’ value l6 for the bond energy of Sr-OH, lead to = + 52 35 kJ mol-I. After corrections for departures from equilibrium in the reaction 15* l7 Kelly and Padley’s electrostatic probe measurements l8 yield = + 38 f 35 kJ mol-l. Hayhurst and K i t t e l ~ o n , ~ ~ from mass-spectrometric experiments, find what is probably the most reliablevalue of = +40+ 10 kJ mol-l, although uncertainties caused by lack of knowledge concerning the chemical reactions occurring in the viscous flow field inside their sampling nozzle remain. A realistic best estimate of AH& would be +40+ 15 kJ mol-l, which, in combination withJANAFtabulations lS and the above data for SrOH+, yields K, = 47 exp(( - 7 700 5-2 000 K)/T).Sr + OH + SrOH+ + e-, (3) EXPERIMENTAL The burner, additive system and optical technique used were similar to those described previou~ly.~~~ 2o The flames were atmospheric-pressure, laminar, cylindrical, shielded, fuel-rich H2 + O2 + N2 flames in which distance downstream of the primary reaction zones was a measure of the reaction time available for recombination of the radicals produced in above-equilibrium amounts in these zones.Principal composition features, flow rates and temperatures are given in table 1. Tin was added to the flames as Sn(CH& and molybdenum and tungsten as hexacarbonyls, all in the form of vapours from an exponential decay reser- voir 21 at concentrations given by 5x 10l2 < [Melt < 5x 1014 molecule CM-~, where [Melt = ~i[Si] ; [Sj] is the concentration of the ith metal-containing species in the flame, which itself contains si atoms of metal per molecule. Lithium, sodium and strontium were added in known trace amounts (- 1 part in lo7) as salt solutions from a calibrated atomiser.lg Tests analogous to those described in ref. (19) confirmed the absence of significant quantities of condensed particles in the flames for all the additives.Hydroxyl radical concentrations were calculated from measured [HI on the assumption that the reaction is balanced. The mass spectrometer and sampling system used were similar to those described by Hayhurst, Mitchell and Telford.22 The ratio of mass spectrometer ion currents iSrOH+ /isr+ was measured with an ion multiplier, both currents being corrected for small proportions of ion h y d r a t i ~ n . ~ ~ 23 If the flame chemistry were unperturbed by the sampling process, one 1 1 H+H2O + OH+H2 (4)TABLE 1 .-FLAME TEMPERATURES AND COMPOSITIONS [HzOl/ [HzII LHlesl [HI3 om/ om/ reaction time flame unburned molecule cm-3 molecule cm-3 molecule cm-3 molecule cm-3 molecule cm-3 T/K (3 cm)/ms H2/N2/02 3.3/4.0/1 .O 5.0/3.0/1.0 4.5/3.5/1.0 4.0/4.0/1 .O 3.5/4.5 /I .O 3.2/4.8/1.0 3.0/5.0/1.0 4.0/5.0/1.0 3.5/6.0/1.0 9.3 x 1017 8 .9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 6 ~ 1017 8 . 6 ~ 1017 6.1 x 1017 9 . o ~ 1017 5 . 4 ~ 1017 4 . 5 ~ 1017 6 . 4 ~ 1017 1 . 4 ~ 10l8 1.1 x l0l8 6 . 8 ~ 1017 8 . 6 ~ 1017 6.1 x 1015 4 . 6 ~ 1015 4.1 x 1015 3.7 x 1015 3 . 2 ~ 1015 2 . 9 ~ 1015 2 . 6 ~ 1015 1 . 4 ~ 1015 5.8 x 1014 1.ox 10l6 1 . 6 ~ 10l6 1 . 4 ~ 10l6 1.2 x 10l6 1.ox 10l6 8 . 5 ~ 1015 7 . 4 ~ 1015 1.1 x 1OI6 1.ox 10l6 2 . 0 ~ 1015 1.1 x 1015 1.2 x 1015 1.3 x 1015 1 . 4 ~ 1015 1 . 5 ~ 1015 1 . 6 ~ 1015 9.1 x 1014 8 . 9 ~ 1014 2150 2035 2035 203 5 2035 2035 2035 1900 1800 1.09 1.05 1.05 1.05 1.05 1.05 1.05 1 .oo 1 .oo [H]es and [HI3 cm are hydrogen atom concentrations at equilibrium and at 3 cm downstream of the reaction zone, respectively.Na D-line reversal temperature of the burned gases. [HJ, [H,O] and [Nz] are essentially independent of distance downstream. T/K is the measured152 RADICALS IN FLAMES could calculate [HI from the relationship iSrOH+/iSr+ = 47 exp(-7 700 K / T ) [H,O]/[H], where T is the flame temperature. Because chemical reactions do occur in the sampling cone,23 however, a careful analysis of the viscous (Reynolds number R! 100) flow in this nozzle would be required to make the mass-spectrometric tracer method of measuring [HI accurate and independent of all calibrations. In the present work, where the main require- ment is accurate knowledge of relative [HI, is^^ + /isr + was simply used as a measure of this quantity for flames with and without additives.Results like those shown in fig. 1, where the current ratio is shown to vary linearly with [HI-' as measured by the photometric method in the absence of a catalysing additive, confirm the validity of this approach. I I I I I 2 4 6 8 10 I2 14 1017[H]-1/cm3 molecule-1 [[Sr], = 3 x 10l1 molecule ~ m - ~ . No catalyst present. [HI-' from photometricImeasurements. FIG. 1.-Variation of mass spectrometer ion current ratio (iSflH+/iSr+) with [Hl-l for flame 4. Overall, either the photometric or the mass-spectrometric tracer method yields relative [HI for a set of flames like that employed in this work accurate to within &lo %. The uncertainty in absolute [HI from the photometric method stems chiefly from uncertainties in Kl and is probably about +50 %, smaller than would be suggested by the stated error bounds on AH& because the latter take account of possible errors in statistical data used to derive AH$,l from the experimentally-measured K I .The uncertainty in absolute [HI from the mass-spectrometric method is probably about a factor of 2, smaller again than might be expected from the uncertainty bounds assigned to AH&2 because errors incurred when i S r O ~ + / i s r + for any flame are converted to absolute [HI are likely to compensate, at east in part, for those in K2. RESULTS AND DISCUSSION TIN Fig. 2 shows typical plots of [HI-', measured by the mass-spectrometric method, against time for flame 8 (1900 IS) with and without added tin.In the absence of additive, recombination of radicals proceeds via the relatively slow three-body reactions H+H+M + Hz+M ( 5 )D. E . JENSEN AND G . A. JONES 153 and where the collision partner M is usually H20, H2 or N2. The rate of decay of [HI when [HI is well above equilibrium is then given by where a = K4[H20]/[H2] and k5 and k6 are rate coefficients for composite M. The uncatalysed recombination rates in the flames of this work are nicely described by k5 = 2 x K/T and k6 = 1.6 x K/T cm6 s-', with K4 = 4.4 exp( - 7 530 K/T).I3 In the presence of tin, the decay of [HI with time in different flames for the range of values of [Sn], tried was found to fit the expression in agreement with the photometric observations of Bulewicz and Padley.2* Values of k , were obtained from plots like those of fig.2. The agreement between these and OH+H+M H,O+M, (6) - d[H]/dt = 2(k5 + ak6)( 1 + a)-'[M][HI2, (7) -d[H]/dt = 2(k,[M]+ak6[M] +k,[Sn],)(l +a)-'[HI2, (8) I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 timelms FIG. 2.-Catalysis of hydrogen atom decay by tin. [HI measured by the mass-spectrometric method. the photometric values,2* although the trend with temperature is opposite in the two cases, as illustrated in table 2, is reasonably encouraging in the light of the fact that the results become less reliable as the flame temperature increases and radical concentrations approach equilibrium levels. suggest the following reaction scheme to explain the essential features of the catalytic effect : Temperature = 1900 K.(A) no tin added ; (B) [Sn], = 2 x 1014 molecule ~ r n - ~ . Bulewicz and Padley 2* SnO( l2) + H(2S)( + M) + SnOH*(A)( + M) (9) SnOH*(A) -+ SnOH*(B) (10 ( 1 1) SnOH*(B) + H(2S) --+ SnO( 'Z) + H2(12).154 RADICALS I N FLAMES TABLE 2.-RATE COEFFICIENTS FOR THE EMPIRICAL REACTION H+ H+ SnO + H2 + SnO temperature/K 1800 1860 1900 2010 2035 21 50 21 80 2330 1028 x rate coefficient/cms molecule-2 s-1 ref. (2) present work They do not, however, attempt to assign thermochemical properties to SnOH*(A) and SnOH*(B) and to fit such a scheme quantitatively to the results. Their interpretation thus remains tentative, especially in view of the absence of quantitative thermo- chemical data for Sn(OH), (the dihydroxides of Ca, Sr, Ba and Fe appear to play important parts in catalysis effects for these metals l* 4, and the dangers attached to assuming that certain reactions in a cyclic mechanism are balanced whilst others remain ~nbalanced.~ Until further work, probably on fuel-lean flames, clarifies the picture, effects of tin on free radical concentrations in fuel-rich flames may be adequately described in terms of the empirical reaction with k12 w 4 x H+H+SnO -P H2+Sn0, (12) cm6 molecule-2 s-l, where [SnO] w [Sn], for these flames., MOLYBDENUM The catalytic effect of molybdenum on free radical recombination is illustrated in fig.3, where [H]-l measured by both the mass-spectrometric tracer and the photo- metric method is shown as a function of time for flames 1 and 8. Lines 1 and 3 in this figure correspond to a total mole fraction of added molybdenum of approxi- mately whilst lines 2 and 4 represent results obtained in the absence of molybdenum.Agreement between results from the two methods is again good. In all the flames of table 1, the rate of catalysed recombination was found to be directly proportional to [Mo],, a feature consistent with homogeneous catalysis. Because the observed decreases in [HI and [OH] caused by addition of molybdenum are generally much greater than [Mo],, any interpretation of the effects of molybdenum on radical recombination must be based on a cyclic reaction sequence involving the regeneration of participating Mo-containing species. Calculations based on thermo- chemical data given in ref. (13) suggest that [MOO,] and [H2Mo04] contribute significantly to [Mo], but that other molybdenum-containing species for which data are available are present in concentrations too low for them to play significant parts in a catalytic cycle. It is therefore necessary to invoke the participation in the cycle of a molecule for which thermochemical data are currently unavailable.By analogy with the species involved in catalytic cycles based on such other metals as calcium [CaO, CaOH, Ca(OH),] and iron [FeO, FeOH and Fe(OH),], it is reasonable to suggest as a working hypothesis that HMoO, should participate, together with MOO, and H,Mo04, in a cycle for molybdenum. A likely catalytic cycle would then consist of the reactions HMoO, + H + MOO, + H2, (1 3) MOO, +H20 4 H2Mo0, (14)D. E . JENSEN AND G. A . JONES 155 and H2Mo0, + H + HMoO, + HzO.(1 5 ) To test this hypothesis, estimated data for HMoO, are required. By analogy with JANAF data,' the following set of vibration frequencies (as wavenumbers) seems reasonable: 80.0, 100.0, 95.0, 30.0, 35.0, 25.0, 150.0, 60.0 and 10.0mm-l. So also does a value of 7.5 x kg3 m6 for the product of the three principal molecular moments of inertia. With a symmetry number for HMoO, of 3, an electronic partition function for this molecule taken to be the same as that for MOO, and an energy for the HO-Mo0,H bond of 456 kJ rnol-l, these give a value for KI3 of 0.04 exp(l9 600 K/T) and a corresponding value for K15 of 0.24 exp(83 50 K/T). These values are consistent with the recent data of Farber and S r i v a s t a ~ a , ~ ~ obtained from mass-spectrometer studies on oxygen-rich flames containing molybdenum, inasmuch as they imply that HMoO, would be present in such flames in quantities too low to be detected.I I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 timelms FIG. 3.-Catalysis of hydrogen atom decay by molybdenum. Points represent experimental measurements made between 7.5 and 40 min above reaction zones. Open points, photometric method ; filled points, mass-spectrometric method. (1) Temperature = 2150 K, [Molt = 4.2 x 1013 molecule ~ m - ~ ; (2) T = 2150 K, [Molt = 0 ; (3) T = 1900 K, [Molt = 4.0 x loi3 molecule ~ r n - ~ ; (4) T = 1900 K, [MO]~ = 0 ; lines drawn are computed plots. With the method of ref. (4) and the computer program of ref. (25), it was found that the cycle consisting of reactions (13)-(15) provides computed lines giving an excellent fit to the experimental observations of temperature (fig.3) and composition (fig. 4) dependences when kI3 = 1.1 x exp(- 1 400 KIT), k14 = 1 x lo-', and k , , = 1.4 x lo-" exp( -300 K/T) cm3 molecule-1 s-l. All these rate coefficients appear reasonable. A number of alternative cycles involving HMoO, and HMoO,156 RADICALS IN FLAMES (observations of HMoO;; in flames similar to those of the present work 26 suggest that the radical HMoO, might be present in significant concentrations) was developed along the lines described in ref. (4), and attempts were made to fit these to the experi- mental measurements. No alternative cycle could be fitted to the data without an unreasonably high rate coefficient being assigned to at least one of the reactions involved.It is reasonable to rule out cycles including reactions of 0 and O2 on the basis that such reactions are likely to be too slow to contribute significantly at the low concentrations of these species in the fuel-rich flames. The interpretation based on reactions (13)-(15) is thus the only one found to account adequately for the experimental results. h I I I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 4.-Composition dependence (flames 2-7) for molybdenum catalysis. [MO]~ = 4.1 x 1013 molecule ~ m - ~ . Points represent experimental (photometric) measurements made between 10 and 40 mm above reaction zones. Lines drawn are computed plots. Typical rates of reactions (1 3)-( 15) under experimental conditions are given in table 3.Reaction (13) is seen to be the reaction furthest from equilibrium in the sense that ([Mo03][H,])/([HMo03][H]K13) is far from unity, but neither reaction (14) nor reaction (15) is quite balanced. It is difficult to assign probable uncertainty bounds to the rate coefficients given, partly because of the uncertainties in absolute [HI of about +50 % mentioned above and partly as a result of the uncertainties in the estimated thermochemical data for HMoO,. A series of calculations in which individual rate coefficients for reactions in the cycle were varied, separately and together, showed that changing k I 3 by a factor of 2 from the values of table 3 causedTABLE 3 .-MOLYBDENUM REACTION MECHANISM, RATE COEFFICIENTS AND RATES reaction rate coefficient rate difference reverse forward reverse forward 5.H+H+M + H2+M 2 x 10-30 K/T 2.8 x exp( - 52 650 K/T) 5.07 x 1017 8.75 x 1015 4.98 x 1017 6. H+OH+M +H2O+M 1.6 x K/T 9.6 x exp( - 60 180 K/T) 3.39 x 1OI8 5.63 x 10l6 3.34 x 10" 4. H20+H + H2+0H 1 . 6 ~ 10-'oexp(-10 130K/T) 3 . 6 ~ 10-l' exp(-2600K/T) 7.38 x lo2' 7.38 x 1021 2.31 x loi8 13. HMoO,+H + MOO,+H, 1.1 x 10-10exp(-1400K/T) 3 x 10-9exp(-21 000K/T) 3 . 9 0 ~ 10I8 1 . 0 2 ~ 1 0 ~ ~ 3 . 8 0 ~ 1 0 ~ ~ 14. MOO3+H20 + H2M004 1 x 10-l1 2.3 x 1011 exp(-24 700 K/T) 1 . 9 2 ~ lOI9 1 . 5 4 ~ loi9 3 . 7 9 ~ 10l8 15. H2Mo04+H + HMo0,+H20 1 . 4 ~ 10-lo exp(-300 K/T) 6 x 10-lo exp( - 8650 K/T) 4.02 x 1019 3.64 x 1019 3.75 x 1018 Rate coefficients and rates in cm3-molecule-s units. Rates computed for flame 8 (1900 K) at 0.5 ms with initial concentrations (molecule ~ r n - ~ ) of H2M004, 4.7 x 10l2 ; Moo3, 3.1 x 1013 ; HMo03, 3.8 x 10l2 ; H20, 8.6 x 1017 ; H, 2.8 x 10l6 ; OH, 2.3 x 1015 ; H2, 8.6 x 1017 ; M, 3.9 x lo1*.The results are insensitive to the precise values of initial concentrations for the Mo-containing species. react ion TABLE 4.-TUNGSTEN REACTION MECHANISM, RATE COEFFICIENTS AND RATES rate coefficient rate forward reverse reverse difference forward 5. H+H+M +H2+M 2 x 10-30 KIT 2.8 x lo-' exp( - 52 650 K/T) 7.48 x 1017 8.74 x lo1' 7.40 x l O I 7 6. H+OH+M +H2O+M 1.6 x K/T 9.6 x exp( -60 180 K/T) 5.02 x 10I8 5.62 x 10l6 4.96 x 10l8 4. H20+H + OHfH2 1.6 x lo-'' exp(- 10 130 K/T) 3.6 x lo-" exp( -2600 K/T) 8.97 x lo2' 8.97 x 10'' 3.92 x 10I8 16. HW03 + H + W03 I- H2 1.1 x lO-'O exp(-lOOO K/T) 3 x lo-' exp( - 10 040 K/T) 2.25 x 10l8 3.54 x 1017 1.90 x 10l8 17.WOJ+H~O + H2W04 1 x 10-'O 5 x 10l2 exp(-38 600 K / T ) 2.08 x 10l8 1.83 x lo1' 1 . 9 0 ~ 10l8 18. HzW04+H + HW03+HzO 5.82 x lo1' 5.63 x lo1' 1.88 x 10l8 3 x 10-Io exp( - lo00 K/T) 6 x 10-lo exp( - 6010 K/T) 0 5 v1 Rate coefficients and rates in cm3-molecule-s units. Rates computed for flame 8 (1900 K) at 0.5 ms with initial concentrations (molecule ~ r n - ~ ) of H2W04, W03, HWO3, 9 x 10l2 ; H20, 8.6 x 1017 ; H, 2.8 x 10I6 ; OH, 2.3 x 1015 ; H2, 8 . 6 ~ 1017 ; M, 3.9 x 10l8. The results are insensitive to the precise values of initial concentretions for the W-containing species.158 RADICALS IN FLAMES significant discrepancy between computations and experiment, whatever efforts were made to compensate by changing other rate coefficients.Similarly, changing kI4 and k15 by a factor of 5 resulted in significant discrepancies. Overall, it is reasonable to assign to k13, k14 and k15 rough uncertainty factors of 5, 10 and 10 respectively. TUNGSTEN Mass-spectrometric tracer and photometric values of [Hl-l are shown as functions of time for flames 1 and 8 with and without added tungsten in fig. 5. The significant catalytic effect of tungsten on radical recombination is apparent in this figure, even for a mole fraction of added metal as low as In a manner entirely analogous to that described above for molybdenum, the computer program 2 5 was used to show that the experimental results could be fitted to the catalytic cycle consisting of the reactions HW03 +H -+ W03 +H2, (16) W03 +H20 -+ H2W04 (17) and H2W04+H + HWO,+H,O (18) when k16 = 1.1 x 10-lo exp(- 1000 K/T), kl, = 1 x 10-lo and k18 = 3 x 10-lo exp( - 1000 K/T) cm3 molecule-I s-l.All these values appear reasonable. They rest again upon estimates of thermochemical data for the intermediate radical HW03, which in conjunction with JANAF data l 3 for H, H2, H20, W03 and H2W04 give rise to K16 = 0.04 exp(9 000 K / T ) and K18 = 0.5 exp(5 000 K/T). No other cycle (for HW03 or HWO,) was found that fitted the experimental temperature and 16 14 12 I0 8 6 I I I I I 1 I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 5.-Catalysis of hydrogen atom decay by tungsten. Points represent experimental measure- ments made between 7.5 and 40 mm above reaction zones.Open points, photometric method ; filled points, mass-spectrometric method. (1) T = 2150 K, [WIG = 2.9 x l O I 3 molecule ~ r n - ~ ; (2) T = 2150K, [WJc = 0; (3) T = 1900K, [WJc = 2 . 7 ~ 1013 molecule ~ m - ~ ; (4) T = 1900K, Iw], = 0. Lines drawn are computed plots.D. E. JENSEN AND G. A. JONES 159 composition dependences of the catalytic effect with reasonable rate coefficients for reactions included. Examples of how well the cycle consisting of reactions (1 6)-( 18) fits the experimental data are shown in fig. 5 (temperature dependence) and fig. 6 (composition dependence). 2 0 "i 2i 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 6.-Composition dependence (flames 2-7) for tungsten catalysis. [W], = 2.8 x loi3 molecule ~ r n - ~ . Points represent experimental (photometric) measurements made between 10 and 40 mm above the reaction zones.Lines drawn are computed plots. Typical rates of the reactions (1 6)-( 18) under experimental conditions are given in table 4. Reaction (17), as well as reaction (16), is well away from equilibrium, although reaction (18) is not far from balance. There is thus a significant kinetic difference between tungsten and molybdenum mechanisms which manifests itself in different composition dependences of catalytic effect for the two metals. An analysis of the effects of varying kI6, kI7 and kI8 upon computed [H]/time profiles, similar to that described for molybdenum above, suggests that rough uncertainty factors of 5 , 5 and 10 respectively may reasonably be assigned to these rate coefficients.CONCLUSIONS The good agreement between sets of results obtained by the two methods of determining [HI supports the suggestion that the mass-spectrometric tracer method provides a valuable quantitative means of studying radical reactions in flames. The results show that no significant compound formation between e.g. lithium and160 RADICALS IN FLAMES molybdenum or tungsten occurs for the values of [Mo], and [w, of this work. By analogy with corresponding potassium + molybdenum and potassium + tungsten 26* 27 such compound formation would be expected to occur at higher [MO]~ and [W],, under which circumstances the mass-spectrometric method could still be used straightforwardly but the photometric method could not. The catalytic mechanisms for tin, molybdenum and tungsten account quantita- tively for the effects of these metals on radical recombination.In the absence of reliable thermochemical data for such species as SnOH*(A), SnOH*(B), Sn(OH),, HMoO,, HW03, HMoO, and HW04, however, these mechanisms remain somewhat speculative. The mechanisms for molybdenum and tungsten are formally similar to those proposed for the alkaline earth metals and iron,4 although inspection of the rates of individual reactions in the catalytic cycles involved reveals differences in degree of departure from equilibrium for corresponding reactions which give rise to different composition-dependences of the catalytic effects. D. H. Cotton and D. R. Jenkins, Truns. Furuduy SOC., 1971,67,730, E. M. Bulewicz and P. J. Padley, 13th Int.Symp. Combustion (Combustion Institute, Pitts- burgh, 1971), p. 73. E. M. Bulewicz and P. J. Padley, Trans. Furuduy SOC., 1971, 67, 2337. D. E. Jensen and G. A. Jones, J. Chem. Phys., 1974, 60, 3421. ' E. M. Bulewicz, C. G. James and T. M. Sugden, Proc. Roy. SOC. A, 1956,235,89. T. M. Sugden, Truns. Furuduy SOC., 1956,52,1465. ' D. E. Jensen, Combustion and Flume, 1972, 18, 217. M. J. McEwan and L. F. Phillips, Combustion and Flume, 1967, 11, 63. A. N. Hayhurst and D. B. Kittelson, Nature Phys. Sci., 1972, 235, 136. P. J. Th. Zeegers and C. Th. J. Alkemade, Combustion and Flame, 1970, 15, 193. JANAF ThermochemicuE Tables (National Standard Reference Data System, National Bureau of Standards, Washington D.C., 1971), No. 37. 14K. Schofield and T. M. Sugden, 10th Int.Symp. Combustion. (The Combustion Institute, Pittsburgh, 1965), p. 589. D. E. Jensen, Combustion and Flume, 1968, 12,261. lo R. Kelly and P. J. Padley, Truns. Furuday SOC., 1971, 67, 740. I2 D. E. Jensen, J. Phys. Chem., 1970, 74, 207. l6 D. H. Cotton and D. R. Jenkins, Trans. Furuday SOC., 1968,64,2988. l7 A. N. Hayhurst and D. B. Kittelson, Combustion and Flume, 1972, 19, 306. l 8 R. Kelly and P. J. Padley, Trans. Faraduy SOC., 1971, 67, 1384. l 9 D. E. Jensen and G. A. Jones, J.C.S. Furuduy I, 1972,68,259. 2o D. E. Jensen and G. A. Jones, J.C.S. Faraduy I, 1973, 69, 1448. 21 D. E. Jensen, Trans. Furuduy SOC., 1969, 65,2123. " A. N. Hayhurst, F. R. G. Mitchell and N. R. Telford, Int. J. Mass Spectr. Ion Phys., 1971, 7, 177. 23 A. N. Hayhurst and N. R.Telford, Proc. Roy. SOC. A , 1971,322,483. 24 M. Farber and R. D. Srivastava, Combustion and Flame, 1973,20,33. 25 K. Allen and D. E. Jensen, Rocket Propulsion Establishment Tech. Rep. 73/1 (1973). 26 D. E. Jensen and W. J. Miller, 13th Int. Symp. Combustion (Combustion Institute, Pittsburgh, 27 D. E. Jensen and W. J. Miller, J. Chem. Phys., 1970,53, 3287. 1971), p. 363. Mass-spectrometric Tracer and Photometric Studies of Catalysed Radical Recombination in Flames BY DAVID E. JENSEN" AND GEORGE A. JONES Rocket Propulsion Establishment, Westcott, Aylesbury, Buckinghamshire Received 31st May, 1974 Measurements of hydrogen atom concentrations in H2 + O2 + N2 flames with and without additives have been made by a mass-spectrometric tracer method dependent upon the reaction being balanced and by a well established photometric method dependent upon balance of the analogous reaction Results from the two methods agree well.Catalysis of flame radical recombination caused by addition of tin, molybdenum and tungsten is described. Mass-spectrometric results for tin are in good agreement with previous photometric measurements. Results for molybdenum and tungsten from both methods are quantitatively interpreted in terms of a cyclic homogeneous gas phase mechanism, with associated thermochemistry and reaction rate coefficients. Sr+ + H20 + SrOH+ + H, K = 47 exp( - 7 700 KIT), Li+ H20 + LiOH+H, K = 16 exp(- 10 O00 K/T). Recent work has shown that small quantities of various metal-containing additives can cause significant catalysis of recombination of the H, OH and 0 radicals generally present in above-equilibrium concentrations in H2 + 0, + N, flames.This work involved measurement of [HI by the well established Li/Na photometric m e t h ~ d . ~ In this method, known trace quantities (too small to perturb the flame properties significantly themselves) of lithium and sodium are added in turn to a flame and [Li] is measured via comparison of the Li first resonance doublet emission intensities or absorptions with those of the corresponding Na doublet. [HI is then calculated on the basis of the reasonable assumptions that the reaction is balanced,6* that lithium forms significant concentrations of Li and LiOH alone and that sodium exists largely as free atoms in the flame. (A reaction A+B + C + D is said to be " balanced " or " in equilibrium " when ([C][D])/([A][B]) is equal to the equilibrium constant for the reaction.) Under certain conditions, however (e.g. in fuel-lean flames where peroxide formation may occur,* in practical flames with interfering optical frequency radiation, or where additives form stable compounds with lithium and/or sodium) an alternative method is needed.Hayhurst and Kittel- son have suggested that a reaction analogous to (l), Sr+ + H20 + SrOH+ + H, Li + H 2 0 + LiOH + H (equilibrium constant K l ) (1) (2) balanced in a flame to which trace quantities of strontium are supplied, affords such an alternative if [SrOH+]/[Sr+] can be measured via mass-spectrometric sampling and K2 is known. The present paper describes application of both these methods to investigation of radical recombination catalysis in H2 + O2 + N2 flames caused by addition of tin, molybdenum and tungsten-containing compounds.The good agreement between results from the two methods supports the suggestion that the mass-spectrometric tracer method provides a useful means of studying radical 149150 RADICALS I N FLAMES recombination in flames and strengthens confidence in the quantitative data for the observed catalytic effects. The two methods of measuring [HI require knowledge of the equilibrium constants Kl and K2 as functions of temperature. On the basis of data from several sources, Kelly and Padley lo recommend a value for the standard zero-point enthalpy change AH; for Li(g)+OH(g) + LiOH(g) of 433 +8 kJ mol-l, in good agreement with another recommendation by Zeegers and A1kemade.l Vibration frequencies for the (assumed linear) LiOH molecule have been estimated lo as 66.5 (Li-0 stretch), 35.0 (bending mode) and 360.0 (0-H stretch) mm-l respectively, and the molecular moment of inertia ILioH estimated l2 to be 2 .2 ~ kgm2. Together with other data, taken from the JANAF TabZes,13 this gives a recommended value Kl = 16 exp { - (10 OW_+ 1000 K ) / T ) for 1500 < T < 3000 K. K2 is less accurately known. If SrOH+ is assumed, by analogy with the iso- electronic RbOH,12 to be linear, having vibration frequencies v1 at 35.5 mm-’, v2 (doubly degenerate mode) at 31.0 mm-l and v3 at 360.0 mm-l and ISrOH+ = 1.35 x kg m2, the photometric measurements of Schofield and Sugden l4 may be interpreted to give AH;,2 = +74+40 kJ mol-l.The microwave measurements of Jensen,15 combined with Cotton and Jenkins’ value l6 for the bond energy of Sr-OH, lead to = + 52 35 kJ mol-I. After corrections for departures from equilibrium in the reaction 15* l7 Kelly and Padley’s electrostatic probe measurements l8 yield = + 38 f 35 kJ mol-l. Hayhurst and K i t t e l ~ o n , ~ ~ from mass-spectrometric experiments, find what is probably the most reliablevalue of = +40+ 10 kJ mol-l, although uncertainties caused by lack of knowledge concerning the chemical reactions occurring in the viscous flow field inside their sampling nozzle remain. A realistic best estimate of AH& would be +40+ 15 kJ mol-l, which, in combination withJANAFtabulations lS and the above data for SrOH+, yields K, = 47 exp(( - 7 700 5-2 000 K)/T).Sr + OH + SrOH+ + e-, (3) EXPERIMENTAL The burner, additive system and optical technique used were similar to those described previou~ly.~~~ 2o The flames were atmospheric-pressure, laminar, cylindrical, shielded, fuel-rich H2 + O2 + N2 flames in which distance downstream of the primary reaction zones was a measure of the reaction time available for recombination of the radicals produced in above-equilibrium amounts in these zones. Principal composition features, flow rates and temperatures are given in table 1. Tin was added to the flames as Sn(CH& and molybdenum and tungsten as hexacarbonyls, all in the form of vapours from an exponential decay reser- voir 21 at concentrations given by 5x 10l2 < [Melt < 5x 1014 molecule CM-~, where [Melt = ~i[Si] ; [Sj] is the concentration of the ith metal-containing species in the flame, which itself contains si atoms of metal per molecule.Lithium, sodium and strontium were added in known trace amounts (- 1 part in lo7) as salt solutions from a calibrated atomiser.lg Tests analogous to those described in ref. (19) confirmed the absence of significant quantities of condensed particles in the flames for all the additives. Hydroxyl radical concentrations were calculated from measured [HI on the assumption that the reaction is balanced. The mass spectrometer and sampling system used were similar to those described by Hayhurst, Mitchell and Telford.22 The ratio of mass spectrometer ion currents iSrOH+ /isr+ was measured with an ion multiplier, both currents being corrected for small proportions of ion h y d r a t i ~ n .~ ~ 23 If the flame chemistry were unperturbed by the sampling process, one 1 1 H+H2O + OH+H2 (4)TABLE 1 .-FLAME TEMPERATURES AND COMPOSITIONS [HzOl/ [HzII LHlesl [HI3 om/ om/ reaction time flame unburned molecule cm-3 molecule cm-3 molecule cm-3 molecule cm-3 molecule cm-3 T/K (3 cm)/ms H2/N2/02 3.3/4.0/1 .O 5.0/3.0/1.0 4.5/3.5/1.0 4.0/4.0/1 .O 3.5/4.5 /I .O 3.2/4.8/1.0 3.0/5.0/1.0 4.0/5.0/1.0 3.5/6.0/1.0 9.3 x 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 9 ~ 1017 8 . 6 ~ 1017 8 . 6 ~ 1017 6.1 x 1017 9 . o ~ 1017 5 . 4 ~ 1017 4 . 5 ~ 1017 6 . 4 ~ 1017 1 . 4 ~ 10l8 1.1 x l0l8 6 . 8 ~ 1017 8 . 6 ~ 1017 6.1 x 1015 4 .6 ~ 1015 4.1 x 1015 3.7 x 1015 3 . 2 ~ 1015 2 . 9 ~ 1015 2 . 6 ~ 1015 1 . 4 ~ 1015 5.8 x 1014 1.ox 10l6 1 . 6 ~ 10l6 1 . 4 ~ 10l6 1.2 x 10l6 1.ox 10l6 8 . 5 ~ 1015 7 . 4 ~ 1015 1.1 x 1OI6 1.ox 10l6 2 . 0 ~ 1015 1.1 x 1015 1.2 x 1015 1.3 x 1015 1 . 4 ~ 1015 1 . 5 ~ 1015 1 . 6 ~ 1015 9.1 x 1014 8 . 9 ~ 1014 2150 2035 2035 203 5 2035 2035 2035 1900 1800 1.09 1.05 1.05 1.05 1.05 1.05 1.05 1 .oo 1 .oo [H]es and [HI3 cm are hydrogen atom concentrations at equilibrium and at 3 cm downstream of the reaction zone, respectively. Na D-line reversal temperature of the burned gases. [HJ, [H,O] and [Nz] are essentially independent of distance downstream. T/K is the measured152 RADICALS IN FLAMES could calculate [HI from the relationship iSrOH+/iSr+ = 47 exp(-7 700 K / T ) [H,O]/[H], where T is the flame temperature.Because chemical reactions do occur in the sampling cone,23 however, a careful analysis of the viscous (Reynolds number R! 100) flow in this nozzle would be required to make the mass-spectrometric tracer method of measuring [HI accurate and independent of all calibrations. In the present work, where the main require- ment is accurate knowledge of relative [HI, is^^ + /isr + was simply used as a measure of this quantity for flames with and without additives. Results like those shown in fig. 1, where the current ratio is shown to vary linearly with [HI-' as measured by the photometric method in the absence of a catalysing additive, confirm the validity of this approach. I I I I I 2 4 6 8 10 I2 14 1017[H]-1/cm3 molecule-1 [[Sr], = 3 x 10l1 molecule ~ m - ~ .No catalyst present. [HI-' from photometricImeasurements. FIG. 1.-Variation of mass spectrometer ion current ratio (iSflH+/iSr+) with [Hl-l for flame 4. Overall, either the photometric or the mass-spectrometric tracer method yields relative [HI for a set of flames like that employed in this work accurate to within &lo %. The uncertainty in absolute [HI from the photometric method stems chiefly from uncertainties in Kl and is probably about +50 %, smaller than would be suggested by the stated error bounds on AH& because the latter take account of possible errors in statistical data used to derive AH$,l from the experimentally-measured K I . The uncertainty in absolute [HI from the mass-spectrometric method is probably about a factor of 2, smaller again than might be expected from the uncertainty bounds assigned to AH&2 because errors incurred when i S r O ~ + / i s r + for any flame are converted to absolute [HI are likely to compensate, at east in part, for those in K2.RESULTS AND DISCUSSION TIN Fig. 2 shows typical plots of [HI-', measured by the mass-spectrometric method, against time for flame 8 (1900 IS) with and without added tin. In the absence of additive, recombination of radicals proceeds via the relatively slow three-body reactions H+H+M + Hz+M ( 5 )D. E . JENSEN AND G . A. JONES 153 and where the collision partner M is usually H20, H2 or N2. The rate of decay of [HI when [HI is well above equilibrium is then given by where a = K4[H20]/[H2] and k5 and k6 are rate coefficients for composite M.The uncatalysed recombination rates in the flames of this work are nicely described by k5 = 2 x K/T and k6 = 1.6 x K/T cm6 s-', with K4 = 4.4 exp( - 7 530 K/T).I3 In the presence of tin, the decay of [HI with time in different flames for the range of values of [Sn], tried was found to fit the expression in agreement with the photometric observations of Bulewicz and Padley.2* Values of k , were obtained from plots like those of fig. 2. The agreement between these and OH+H+M H,O+M, (6) - d[H]/dt = 2(k5 + ak6)( 1 + a)-'[M][HI2, (7) -d[H]/dt = 2(k,[M]+ak6[M] +k,[Sn],)(l +a)-'[HI2, (8) I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 timelms FIG. 2.-Catalysis of hydrogen atom decay by tin. [HI measured by the mass-spectrometric method. the photometric values,2* although the trend with temperature is opposite in the two cases, as illustrated in table 2, is reasonably encouraging in the light of the fact that the results become less reliable as the flame temperature increases and radical concentrations approach equilibrium levels.suggest the following reaction scheme to explain the essential features of the catalytic effect : Temperature = 1900 K. (A) no tin added ; (B) [Sn], = 2 x 1014 molecule ~ r n - ~ . Bulewicz and Padley 2* SnO( l2) + H(2S)( + M) + SnOH*(A)( + M) (9) SnOH*(A) -+ SnOH*(B) (10 ( 1 1) SnOH*(B) + H(2S) --+ SnO( 'Z) + H2(12).154 RADICALS I N FLAMES TABLE 2.-RATE COEFFICIENTS FOR THE EMPIRICAL REACTION H+ H+ SnO + H2 + SnO temperature/K 1800 1860 1900 2010 2035 21 50 21 80 2330 1028 x rate coefficient/cms molecule-2 s-1 ref.(2) present work They do not, however, attempt to assign thermochemical properties to SnOH*(A) and SnOH*(B) and to fit such a scheme quantitatively to the results. Their interpretation thus remains tentative, especially in view of the absence of quantitative thermo- chemical data for Sn(OH), (the dihydroxides of Ca, Sr, Ba and Fe appear to play important parts in catalysis effects for these metals l* 4, and the dangers attached to assuming that certain reactions in a cyclic mechanism are balanced whilst others remain ~nbalanced.~ Until further work, probably on fuel-lean flames, clarifies the picture, effects of tin on free radical concentrations in fuel-rich flames may be adequately described in terms of the empirical reaction with k12 w 4 x H+H+SnO -P H2+Sn0, (12) cm6 molecule-2 s-l, where [SnO] w [Sn], for these flames., MOLYBDENUM The catalytic effect of molybdenum on free radical recombination is illustrated in fig.3, where [H]-l measured by both the mass-spectrometric tracer and the photo- metric method is shown as a function of time for flames 1 and 8. Lines 1 and 3 in this figure correspond to a total mole fraction of added molybdenum of approxi- mately whilst lines 2 and 4 represent results obtained in the absence of molybdenum. Agreement between results from the two methods is again good. In all the flames of table 1, the rate of catalysed recombination was found to be directly proportional to [Mo],, a feature consistent with homogeneous catalysis. Because the observed decreases in [HI and [OH] caused by addition of molybdenum are generally much greater than [Mo],, any interpretation of the effects of molybdenum on radical recombination must be based on a cyclic reaction sequence involving the regeneration of participating Mo-containing species.Calculations based on thermo- chemical data given in ref. (13) suggest that [MOO,] and [H2Mo04] contribute significantly to [Mo], but that other molybdenum-containing species for which data are available are present in concentrations too low for them to play significant parts in a catalytic cycle. It is therefore necessary to invoke the participation in the cycle of a molecule for which thermochemical data are currently unavailable. By analogy with the species involved in catalytic cycles based on such other metals as calcium [CaO, CaOH, Ca(OH),] and iron [FeO, FeOH and Fe(OH),], it is reasonable to suggest as a working hypothesis that HMoO, should participate, together with MOO, and H,Mo04, in a cycle for molybdenum.A likely catalytic cycle would then consist of the reactions HMoO, + H + MOO, + H2, (1 3) MOO, +H20 4 H2Mo0, (14)D. E . JENSEN AND G. A . JONES 155 and H2Mo0, + H + HMoO, + HzO. (1 5 ) To test this hypothesis, estimated data for HMoO, are required. By analogy with JANAF data,' the following set of vibration frequencies (as wavenumbers) seems reasonable: 80.0, 100.0, 95.0, 30.0, 35.0, 25.0, 150.0, 60.0 and 10.0mm-l. So also does a value of 7.5 x kg3 m6 for the product of the three principal molecular moments of inertia.With a symmetry number for HMoO, of 3, an electronic partition function for this molecule taken to be the same as that for MOO, and an energy for the HO-Mo0,H bond of 456 kJ rnol-l, these give a value for KI3 of 0.04 exp(l9 600 K/T) and a corresponding value for K15 of 0.24 exp(83 50 K/T). These values are consistent with the recent data of Farber and S r i v a s t a ~ a , ~ ~ obtained from mass-spectrometer studies on oxygen-rich flames containing molybdenum, inasmuch as they imply that HMoO, would be present in such flames in quantities too low to be detected. I I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 timelms FIG. 3.-Catalysis of hydrogen atom decay by molybdenum. Points represent experimental measurements made between 7.5 and 40 min above reaction zones. Open points, photometric method ; filled points, mass-spectrometric method. (1) Temperature = 2150 K, [Molt = 4.2 x 1013 molecule ~ m - ~ ; (2) T = 2150 K, [Molt = 0 ; (3) T = 1900 K, [Molt = 4.0 x loi3 molecule ~ r n - ~ ; (4) T = 1900 K, [MO]~ = 0 ; lines drawn are computed plots.With the method of ref. (4) and the computer program of ref. (25), it was found that the cycle consisting of reactions (13)-(15) provides computed lines giving an excellent fit to the experimental observations of temperature (fig. 3) and composition (fig. 4) dependences when kI3 = 1.1 x exp(- 1 400 KIT), k14 = 1 x lo-', and k , , = 1.4 x lo-" exp( -300 K/T) cm3 molecule-1 s-l. All these rate coefficients appear reasonable. A number of alternative cycles involving HMoO, and HMoO,156 RADICALS IN FLAMES (observations of HMoO;; in flames similar to those of the present work 26 suggest that the radical HMoO, might be present in significant concentrations) was developed along the lines described in ref.(4), and attempts were made to fit these to the experi- mental measurements. No alternative cycle could be fitted to the data without an unreasonably high rate coefficient being assigned to at least one of the reactions involved. It is reasonable to rule out cycles including reactions of 0 and O2 on the basis that such reactions are likely to be too slow to contribute significantly at the low concentrations of these species in the fuel-rich flames. The interpretation based on reactions (13)-(15) is thus the only one found to account adequately for the experimental results.h I I I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 4.-Composition dependence (flames 2-7) for molybdenum catalysis. [MO]~ = 4.1 x 1013 molecule ~ m - ~ . Points represent experimental (photometric) measurements made between 10 and 40 mm above reaction zones. Lines drawn are computed plots. Typical rates of reactions (1 3)-( 15) under experimental conditions are given in table 3. Reaction (13) is seen to be the reaction furthest from equilibrium in the sense that ([Mo03][H,])/([HMo03][H]K13) is far from unity, but neither reaction (14) nor reaction (15) is quite balanced. It is difficult to assign probable uncertainty bounds to the rate coefficients given, partly because of the uncertainties in absolute [HI of about +50 % mentioned above and partly as a result of the uncertainties in the estimated thermochemical data for HMoO,.A series of calculations in which individual rate coefficients for reactions in the cycle were varied, separately and together, showed that changing k I 3 by a factor of 2 from the values of table 3 causedTABLE 3 .-MOLYBDENUM REACTION MECHANISM, RATE COEFFICIENTS AND RATES reaction rate coefficient rate difference reverse forward reverse forward 5. H+H+M + H2+M 2 x 10-30 K/T 2.8 x exp( - 52 650 K/T) 5.07 x 1017 8.75 x 1015 4.98 x 1017 6. H+OH+M +H2O+M 1.6 x K/T 9.6 x exp( - 60 180 K/T) 3.39 x 1OI8 5.63 x 10l6 3.34 x 10" 4. H20+H + H2+0H 1 . 6 ~ 10-'oexp(-10 130K/T) 3 . 6 ~ 10-l' exp(-2600K/T) 7.38 x lo2' 7.38 x 1021 2.31 x loi8 13. HMoO,+H + MOO,+H, 1.1 x 10-10exp(-1400K/T) 3 x 10-9exp(-21 000K/T) 3 .9 0 ~ 10I8 1 . 0 2 ~ 1 0 ~ ~ 3 . 8 0 ~ 1 0 ~ ~ 14. MOO3+H20 + H2M004 1 x 10-l1 2.3 x 1011 exp(-24 700 K/T) 1 . 9 2 ~ lOI9 1 . 5 4 ~ loi9 3 . 7 9 ~ 10l8 15. H2Mo04+H + HMo0,+H20 1 . 4 ~ 10-lo exp(-300 K/T) 6 x 10-lo exp( - 8650 K/T) 4.02 x 1019 3.64 x 1019 3.75 x 1018 Rate coefficients and rates in cm3-molecule-s units. Rates computed for flame 8 (1900 K) at 0.5 ms with initial concentrations (molecule ~ r n - ~ ) of H2M004, 4.7 x 10l2 ; Moo3, 3.1 x 1013 ; HMo03, 3.8 x 10l2 ; H20, 8.6 x 1017 ; H, 2.8 x 10l6 ; OH, 2.3 x 1015 ; H2, 8.6 x 1017 ; M, 3.9 x lo1*. The results are insensitive to the precise values of initial concentrations for the Mo-containing species. react ion TABLE 4.-TUNGSTEN REACTION MECHANISM, RATE COEFFICIENTS AND RATES rate coefficient rate forward reverse reverse difference forward 5.H+H+M +H2+M 2 x 10-30 KIT 2.8 x lo-' exp( - 52 650 K/T) 7.48 x 1017 8.74 x lo1' 7.40 x l O I 7 6. H+OH+M +H2O+M 1.6 x K/T 9.6 x exp( -60 180 K/T) 5.02 x 10I8 5.62 x 10l6 4.96 x 10l8 4. H20+H + OHfH2 1.6 x lo-'' exp(- 10 130 K/T) 3.6 x lo-" exp( -2600 K/T) 8.97 x lo2' 8.97 x 10'' 3.92 x 10I8 16. HW03 + H + W03 I- H2 1.1 x lO-'O exp(-lOOO K/T) 3 x lo-' exp( - 10 040 K/T) 2.25 x 10l8 3.54 x 1017 1.90 x 10l8 17. WOJ+H~O + H2W04 1 x 10-'O 5 x 10l2 exp(-38 600 K / T ) 2.08 x 10l8 1.83 x lo1' 1 . 9 0 ~ 10l8 18. HzW04+H + HW03+HzO 5.82 x lo1' 5.63 x lo1' 1.88 x 10l8 3 x 10-Io exp( - lo00 K/T) 6 x 10-lo exp( - 6010 K/T) 0 5 v1 Rate coefficients and rates in cm3-molecule-s units. Rates computed for flame 8 (1900 K) at 0.5 ms with initial concentrations (molecule ~ r n - ~ ) of H2W04, W03, HWO3, 9 x 10l2 ; H20, 8.6 x 1017 ; H, 2.8 x 10I6 ; OH, 2.3 x 1015 ; H2, 8 .6 ~ 1017 ; M, 3.9 x 10l8. The results are insensitive to the precise values of initial concentretions for the W-containing species.158 RADICALS IN FLAMES significant discrepancy between computations and experiment, whatever efforts were made to compensate by changing other rate coefficients. Similarly, changing kI4 and k15 by a factor of 5 resulted in significant discrepancies. Overall, it is reasonable to assign to k13, k14 and k15 rough uncertainty factors of 5, 10 and 10 respectively. TUNGSTEN Mass-spectrometric tracer and photometric values of [Hl-l are shown as functions of time for flames 1 and 8 with and without added tungsten in fig.5. The significant catalytic effect of tungsten on radical recombination is apparent in this figure, even for a mole fraction of added metal as low as In a manner entirely analogous to that described above for molybdenum, the computer program 2 5 was used to show that the experimental results could be fitted to the catalytic cycle consisting of the reactions HW03 +H -+ W03 +H2, (16) W03 +H20 -+ H2W04 (17) and H2W04+H + HWO,+H,O (18) when k16 = 1.1 x 10-lo exp(- 1000 K/T), kl, = 1 x 10-lo and k18 = 3 x 10-lo exp( - 1000 K/T) cm3 molecule-I s-l. All these values appear reasonable. They rest again upon estimates of thermochemical data for the intermediate radical HW03, which in conjunction with JANAF data l 3 for H, H2, H20, W03 and H2W04 give rise to K16 = 0.04 exp(9 000 K / T ) and K18 = 0.5 exp(5 000 K/T).No other cycle (for HW03 or HWO,) was found that fitted the experimental temperature and 16 14 12 I0 8 6 I I I I I 1 I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 5.-Catalysis of hydrogen atom decay by tungsten. Points represent experimental measure- ments made between 7.5 and 40 mm above reaction zones. Open points, photometric method ; filled points, mass-spectrometric method. (1) T = 2150 K, [WIG = 2.9 x l O I 3 molecule ~ r n - ~ ; (2) T = 2150K, [WJc = 0; (3) T = 1900K, [WJc = 2 . 7 ~ 1013 molecule ~ m - ~ ; (4) T = 1900K, Iw], = 0. Lines drawn are computed plots.D. E. JENSEN AND G. A. JONES 159 composition dependences of the catalytic effect with reasonable rate coefficients for reactions included.Examples of how well the cycle consisting of reactions (1 6)-( 18) fits the experimental data are shown in fig. 5 (temperature dependence) and fig. 6 (composition dependence). 2 0 "i 2i 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 time/ms FIG. 6.-Composition dependence (flames 2-7) for tungsten catalysis. [W], = 2.8 x loi3 molecule ~ r n - ~ . Points represent experimental (photometric) measurements made between 10 and 40 mm above the reaction zones. Lines drawn are computed plots. Typical rates of the reactions (1 6)-( 18) under experimental conditions are given in table 4. Reaction (17), as well as reaction (16), is well away from equilibrium, although reaction (18) is not far from balance. There is thus a significant kinetic difference between tungsten and molybdenum mechanisms which manifests itself in different composition dependences of catalytic effect for the two metals.An analysis of the effects of varying kI6, kI7 and kI8 upon computed [H]/time profiles, similar to that described for molybdenum above, suggests that rough uncertainty factors of 5 , 5 and 10 respectively may reasonably be assigned to these rate coefficients. CONCLUSIONS The good agreement between sets of results obtained by the two methods of determining [HI supports the suggestion that the mass-spectrometric tracer method provides a valuable quantitative means of studying radical reactions in flames. The results show that no significant compound formation between e.g. lithium and160 RADICALS IN FLAMES molybdenum or tungsten occurs for the values of [Mo], and [w, of this work.By analogy with corresponding potassium + molybdenum and potassium + tungsten 26* 27 such compound formation would be expected to occur at higher [MO]~ and [W],, under which circumstances the mass-spectrometric method could still be used straightforwardly but the photometric method could not. The catalytic mechanisms for tin, molybdenum and tungsten account quantita- tively for the effects of these metals on radical recombination. In the absence of reliable thermochemical data for such species as SnOH*(A), SnOH*(B), Sn(OH),, HMoO,, HW03, HMoO, and HW04, however, these mechanisms remain somewhat speculative. The mechanisms for molybdenum and tungsten are formally similar to those proposed for the alkaline earth metals and iron,4 although inspection of the rates of individual reactions in the catalytic cycles involved reveals differences in degree of departure from equilibrium for corresponding reactions which give rise to different composition-dependences of the catalytic effects. D. H. Cotton and D. R. Jenkins, Truns. Furuduy SOC., 1971,67,730, E. M. Bulewicz and P. J. Padley, 13th Int. Symp. Combustion (Combustion Institute, Pitts- burgh, 1971), p. 73. E. M. Bulewicz and P. J. Padley, Trans. Furuduy SOC., 1971, 67, 2337. D. E. Jensen and G. A. Jones, J. Chem. Phys., 1974, 60, 3421. ' E. M. Bulewicz, C. G. James and T. M. Sugden, Proc. Roy. SOC. A, 1956,235,89. T. M. Sugden, Truns. Furuduy SOC., 1956,52,1465. ' D. E. Jensen, Combustion and Flume, 1972, 18, 217. M. J. McEwan and L. F. Phillips, Combustion and Flume, 1967, 11, 63. A. N. Hayhurst and D. B. Kittelson, Nature Phys. 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