Recombination of Hydrogen Atoms in the Presence ofAtmospheric GasesBY F. S . LARKIN AND B. A. THRUSHDept. of Physical Chemistry, University of CambridgeReceived 23rd December, 1963A calorimetric technique has been used to determine the rate constants of the reactions :H+H+M = H2+M,H+02+M = H02+M,in discharge flow experiments. The mechanism of the decay of hydrogen and of oxygen atoms underconditions when [HI -g [0]< [02], [MI is discussed.The dominant spectrum of the night sky is the Meinel band emission 1 of OH,which is associated with the formation of vibrationally excited OH in the reaction,;!although some OH emission from lower vibrational levels may be associated withthe formation of vibrationally excited OH in other less exothermic reactions.This emission is believed 3 to originate mainly from altitudes around 80 km.In the centre of this region, the hydrogen atom concentration is believed4 to beabout 108 molecules cm-3 as compared with an oxygen atom concentration 5 of ca.5 x 1011 particles cm-3 with 0 2 = 1014 molecules cm-3 and N2 = 5 x 1014 mole-cules cm-3.Under these conditions, reactions (1) and (2) provide a catalytic pathO+OH = HS02, (2)for the decomposition of ozone which has the same stoichiometry as the reaction,0 + 0 3 = 0 2 4 - 0 2 , (3)with which it can compete 6 since kl N 1000 k3.also cause the removal of oxygen by reactions (3) and (4) :H-l-03 = OH+02, (1)Small amounts of hydrogen atomsO+02+M = O3+M. (4)The mechanism of this process was first suggested by Kaufman' to explainthe acceleration of oxygen-atom decay in discharge flow experiments when tracesof water were allowed to pass through the discharge :H+Oz+M = HOz+MO+HO2 = OH+02O+OH = H+02.Reaction (5) is the rate-determining step in the above scheme and this com-munication reports a new determination of the rate constant of this reaction andof the reactionH+ H+ M = H2 + M.(7)The kinetics of the decay of hydrogen and oxygen atoms are discussed for condi-tions where [HI 4 [O] < [02],[M], which occur in discharge-flow experimentsand in the region of the upper atmosphere from which the Meinel bands are emitted.11F. S. LARKIN AND B . A. THRUSH 113EXPERIMENTALHydrogen atoms were generated by passing pure hydrogen or an argon or heliumcarrier containing less than 10 % hydrogen through a 17 mc/sec 100 W electrodelessdischarge. Forced air cooling was used for the discharge, which was establishedin 8 mm int.diam. quartz tubing by means of external aluminium foil electrodes.The discharge products flowed through a light trap to a Pyrex glass reaction tube,2.5 cm int. diam. and 100 cm long, at the upstream end of which was a multipleinlet jet through which reactants could be introduced with rapid mixing. The surfaceof the flow tube was coated with Drifilm which gave a surface recombination efficiencyy not greater than 10-5.Hydrogen-atom concentrations were determined with a movable calorimetricprobe which was inserted through the downstream end of the flow line. A Tygonsleeve provided a sliding vacuum seal where the glass tube carrying the calorimeterleads and head entered the apparatus.Two calorimeters were used, each consistingof 50 cm of 34 s.w.g. 13 % rhodium/platinum wire wound in a spiral. These wereconnected to separate Wheatstone bridges and mounted in tandem about 3 cmapart so that the downstream calorimeter could determine the efficiency of recom-bination on the first spiral, which was always greater than 80 %. Experiments wereconducted at pressures between 1 mm and 6 mm Hg and with flow velocities of400-1200 cmlsec. Total pressures at each end of the flow tube were measured withsilicone oil manometers. Hydrogen-atom concentrations of up to 5 % were ob-tained. Allowance was made for errors due to diffusion effects, 8 , 9 but these weresmall in all cases.Cylinder argon, " mineral " helium and " high purity " hydrogen were obtainedfrom the British Oxygen Company.Hydrogen was purified at atmospheric pressureby passing it through a Deoxo unit and a packed trap at - 196°C. Argon and oxygenwere dried at atmospheric pressure by passing through at packed trap at -80°C.RESULTSH+H+MIn the absence of added oxygen the recombination of hydrogen atoms is givenby the equation-d[HJjdt = zk,,~[H]~[M]+k8[H].Values of k7 were determined by plotting d In [H]/dt against [HI, or by plotting1/[H] against time. The former procedure was used at lower pressures where thesurface recombination term kg made an appreciable contribution to the total rate.It was also necessary to use this procedure in experiments with helium where thepresence of an oxygen impurity ( N 0-5 %) made an appreciable contribution to therecombination which was first order in [HI.At higher pressures identical valuesof k7 were obtained from the two methods. These are given in table 1 for a tem-perature of 293°K. The value for M t H2 agrees well with earlier data on therecombination reaction,lop 11 although no acceleration due to a high value 11 of k7for M = H could be detected at the highest hydrogen-atom concentrations used ( 5 %) .MTABLE 1MH2 0.68 f0.1 2.0 f0-3Ar 0-45 f0.08 1-3 f0.210-16 k7 (cm6 mole-2 sec-1) 1032 k, (cm6 molecules-2 sec-1114 RECOMBINATION OF HYDROGEN ATOMSH+02+MIn these experiments about 1 % of molecular oxygen was added to the productsof a discharge through hydrogen in an argon carrier.The hydrogen-atom con-centrations used were below 0.7 % to reduce the contribution from reaction (7).The molecular hydrogen concentration was low enough that OH radicals formedin the reaction H + HO2 gave negligible hydrogen-atom regeneration by the reaction 12OH + €32 = H20 + H. (9)3.0-2 . 0 -1.0- slope = 2.1 x 1016 c m 6 mole-2 sec-1I0 2-0 3.0107 [MI, mole cm-3 assuming kH, = 5 k ~ ,FIG. 1.0, determination by calorimetry ; 0, determination by HNO emission.and thatwhereClyne and Thrush 13 have shown that under these conditions, the reaction pro-ceeds by the mechanismH+02+M = HOz+M ( 5 )H+H02 = H2+02 (104= OH+OH (lob)= H20+O (10c)OH+OH = H20+O (1 1)O+OH = H+02 (2F.S . LARKIN AND B. A. THRUSH 115Excellent first-order decays of hydrogen atoms were observed in experimentswith added oxygen. Fig. 1 is a plot of - against pressure of argon plus1 0 2 1 dtfive times the pressure of hydrogen. This is chosen since data on the hydrogen + oxygensecond explosion limit 143 15 have shown that the ratio k5 (MrH2)lks (M EZ Ar) is 5.Our experiments which necessarily cover a very limited range of hydrogen con-centrations indicate a value of 6+2 for this quantity at room temperature.The data of Clyne and Thrush 13 who used HNO emission to follow the reactionis also shown in fig. 1. There is good agreement between the two sets of data.The calorimetric points lie on a straight line passing through the origin, showingthat surface reactions between H and 0 2 are negligible in this system.1 dlog[H]Using the value of x given above, the line drawn in fig.1 corresponds tok5 = 1.35 x 1016 cm6 mole-2 sec-1 at 293°K (M = Ar)= 3.7 x 10-32 cm6 molecule-2 sec-1 at 293°K (M 3 Ar).DISCUSSIONThe rate constants reported here have been mainly determined for argon orhydrogen as third bodies. Data on the H+02 reaction at the second explosionlimit 149 15 and on bromine and iodine atom recombination 169 17 give rate con-stants for M s N2 or 0 2 close to twice those for argon as third body. In the follow-ing discussion which applies to the upper atmosphere and to discharge flow experi-ments where the predominant third bodies are oxygen and nitrogen, values of k5and k7 twice those for M = Ar will be used.In the upper atmosphere where [H]<[0]<[02], "21 the half-life of reaction(7) will be very much longer than that of reaction (5).For the following concentra-tions in particles cm-3 corresponding to an altitude of about 80 km, [HI = 108,[O] = 5 x 1011, [02] = 1014, "21 = 5 x 1014, the half-lives would be 105 h and 5 minrespectively.The effective rate of removal of hydrogen atoms by reaction (5) is much lowerthan this since hydrogen atoms are regenerated in subsequent reactions :O+HO2 = OH+02 (6)H+ HO2 = H2 + 0 2 ( 104= OH+OH (lob)= H20+O (1 0 4OH+OH = H20+O (11)O+OH = H+02OH+H = O+Hz.The rate constants of reactions (6) and (10) are not known, but there is evidence 13particularly from Foner and Hudson's mass-spectrometric work 18 that both re-actions are very rapid.At 300"K, k2 = 4 x 10-11 cm3 molecule-1 sec-1,129 19kll = 5 x 10-12 cm3 molecule-1 sec-1,12 and a value of k12 = 4 x 10-17 cm3 molecule-1sec-1 can be calculated data on the reverse reaction 19 knowing the equilibriumconstant.12.20 It can be seen thatReactions (1 1) and (12) make a negligible contribution to the removal of OH radical116 RECOMBINATION OF HYDROGEN ATOMSand hence of hydrogen atoms. The dominance of reaction (2) determines thathydrogen atoms are removed only by reactions (1Oa) and (10c).Evidence 21 indicates that the rate constant of the reactionO+H+M = OH+M (1 3)is less than 5 x 10-32 cm6 molecule-2 sec-1. Since [O]< [02] its contribution to theoverall kinetics can be neglected.A steady-state analysis of the hydrogen and oxygen atom decays in a systemwhere [H]<[O]<[02], [MI in which the initial steps are reactions (4) and (9, inwhich ozone is removed by reactions (3) and (1) + (2), and where HO2 is removedby reactions (6) and (10) followed by (2), yields(9 -- dL-Hl - - 2ak 5 k 1 0 [HI c 0 2 1 CM3dt k6Wlandwhere- dL-Ol/dt = 2(k,COI 4- ~,[HI)CO2IL-MI (ii)a = kloa+klocklOll+ klOb+ kloc'In deriving these equations, it has been assumed that k~[0]9k~o[H].This isjustified providing [0]9[H], since k6 and klo will be shown to have similar mag-nitudes. Eqn. (i) and (ii) yield a first-order differential equation in [H]/[O]. Ifthis equation is integrated and then substituted in eqn.(ii),--= din [O] 2[02][M]{k4+E[exp (-at)-dtwhere a = 2k4[02][M].The initial rate of oxygen atom decay corresponds to an apparent value of(k4+k5[H]0/[0]0) for the rate constant of reaction (4). The term within the squarebrackets can be expanded to give a factorin the denominator of the term in k5[H]o/[O]o. The effect of hydrogen atoms inaccelerating the oxygen-atom decay will change with time unless the second termin expression (iv) remains much less than unity.The most reliable value 22 of k4 appears to be 2.7 x 1014 cm6 mole-2 sec-1for M = 0 2 at 293°K. Thus k 5 ~ 100 k4 and enough hydrogen atoms to causesignificant acceleration will be present in discharge flow experiments unless stringentprecautions are taken to dry the oxygen used.No author has reported the de-parture from first-order kinetics at longer times predicted by eqn. (iii) in experi-ments in which moisture was accidentally or intentionally present in the oxygenused. Kretschmer and Petersen23 report that addition of water to the oxygensupply increases - d In [O]/dt but that this quantity stays constant over the decay.For this reason they suggest that reaction (6) is rate-determining and deduce avalue of k6 = 5 x 109 cm3 mole-1 sec-1. There is good evidence 18 that reaction (6)is much more rapid than this but their rate-constant is consistent with reaction (5)being rate determining. Dickens, Gould, Linnett and Richmond 8 obtained thF. S. LARKIN AND B . A. THRUSH 117high value of k4 = 6 x 1014 cm6 mole-2 sec-1 using oxygen which contained somewater vapour.Their published first-order decay plots are linear for up to threehalf-lives, although it is difficult to detect curvature in such cases. We concludethat, for oxygen atom decays in which hydrogen atom catalysis predominates, ifthen0*5>2[OJ[M] [ k4+ ( 1-- a::") ks- ; 3 1 > - 1 ;.. 1.5 > aklo/k, > 0.75 iA kinetic study of the H + 0 2 reaction 13 has shown thatkloa/(klOb+ kloc) = 0.5 kO.2 and 2k10b) klo,.From these data,0.78 & 0.03 > a > 0.33 & 0.08,and hence that the ratio k1&6 lies between unity and six. The assumption in eqn.(i) and (ii) that the term klo[H] could be neglected by comparison with k6[O] for[O]>[H] is therefore justified.The ratios of the rate constants for the reactions ofhydrogen and oxygen atoms with nitrogen dioxide is N 10, whereas the correspondingratio for ozone k7/k3 N 1000 at normal temperatures.Substitution of relationship (v) in eqn. (i) shows that the presence of excessoxygen atoms reduces the rate of removal of hydrogen atoms in reaction (5) to givea rate approximately 2[H]/[0] times that of the initial reaction. For the conditionsquoted at an altitude of 80 km, this corresponds to a decrease in the rate of hydrogenatom removal by a factor of a thousand. We therefore conclude that the rate ofchemical removal of small concentrations of hydrogen atoms is very low indeed inthe upper atmosphere, and that diffusive escape 4 is the dominant removal process.The authors thank the D.S.I.R.for a special research grant and for a main-tenance award to F. s. L.1 Meinel, Astrophys. J., 1953, 111, 207.2 McKinley, Garvin and Boudart, J. Chem. Physics, 1955,23,784.3Packer, Ann. Geophys., 1961, 17, 67.5 Nicolet, J. Geophys. Res., 1959, 64, 2092.6 Clyne, Thrush and Wayne, Nature, 1963,199, 1057.7 Kaufman, Proc. Roy. SOC. A, 1958,247, 123.8 Dickens, Gould, Linnett and Richmond, Nature, 1960, 187, 686.9 Wise and Ablow, J. Chem. Physics, 1961, 35, 10.10 Amdur, J. Amer. Chem. SOC., 1938, 60,2347.11 Steiner, Trans. Faraday SOC., 1935,31, 623.12 Kaufman and Del Greco, 9th Symp. Combustion (Academic Press, 1963), p. 659.13 Clyne and Thrush, Proc. Roy. SOC. A., 1963,275, 559.14 Lewis and von Elbe, J. Chem. Physics, 1942, 10, 366.15 Hinshelwood and Willbourn, Proc. Roy. SOC. A, 1946, 185, 353.16 Rabinowitch, Trans. Faraday SOC., 1937, 33, 283.17 Russell and Simons, Proc. Roy. SOC. A , 1953, 217, 271.18 Foner and Hudson, J. Chem. Physics, 1962,36,2676,2681.19 Clyne and Thrush, Proc. Roy. SOC. A, 1963,275, 544.20 JANAF Thermodynamical Tables (Dow Chemical Co., 1960).21 Harteck and Reeves, Chemical Reactions in the Lower and Upper Atmosphere (Interscience,22 Kaufman and Kelso, this Discussion.23 Kretschmer and Petersen, J. Chem. Physics, 1960, 33, 948.4Nicolet, Bull. SOC. Chem. Be&., 1962, 71, 665.1961), p. 219