Studies of Vibrationally Excited Nitrogen Using Mass Spectrometric and Calorimeter-Probe Techniques BY J. E. MORGAN, L. F. PHILLIPS AND H. I. SCHIFF Dept. of Chemistry, McGill University, Montreal, Canada Received 22nd January, 1962 Isothermal calorimeter-probe measurements showed that " active " nitrogen contains excited molecules with excitation energy corresponding to 6 kcal/mole of totaf gas. These molecules were deactivated mainly on the walls with an efficiency of 4-75 x 10-4. The collision efficiencies for the gas-phase deactivation by N20, C02, A and N2 are 1.38 X 10-4, 4.3 X 10-5, 1.5 x 10-6 and 3.3 x 10-8 respectively. This method was also used to show that the vibrationally-excited N$ molecules formed in the reaction N+NO+N;+O have an average energy of 21 5 5 kcal/mole.A mass-spectrometric method showed that 75f5 % of the NJ formed from this reaction have sufficient energy to decompose 0 3 . The rate of deactivation of N$ by unexcited N2 to vibrational levels below the fourth was found to be 3.5 x 10-16 cm3 molecule-1 sec-1 and by N20 to be 1.3 x 10-15 cm3 molecule-' sec-1. Convincing evidence has been obtained for the presence of energetic molecular species in " active " nitrogen. Kaufman and Kelso 1 found that the addition of N20 to a stream of discharged N2 resulted in a marked temperature rise in the neighbourhood of the mixing point. They were able to show that the energy release was not due to an acceleration of atom recombination and ascribed the effect to deactivation of vibrationally excited N2 by the N20.Although this experiment was largely qualitative, they estimated the energy release to be about 2 kcal/mole of total N2, and the lifetime of the excited molecules to be about 50 msec. Dressler 2 studied the ultra-violet absorption spectrum of discharged N2 and showed the presence of N2 in the first vibrational level of the ground state. From the space-average concentration of the excited molecules over the length of the flow tube, he was able to establish a lower limit of 10 msec for the half-life. In the present work it was possible to study the excited molecules by means of an isothermal calorimetric probe.3 This probe measures the total heat content of all the energetic species in the gas stream, i.e., both atoms and excited molecules. The heat content of the atoms can be calculated from the atom concentration and the dissociation energy of N2.It is therefore possible to determine, by subtraction, the heat content of the excited molecules. The N-atom concentration was determined by the NO-titration technique.4-6 The reaction (1) (2) (4) N+NO = N2+O k = 2.2 x 10-11 cm3 molecule-1 sec-1,7.8 k = 6 x 10-32 cm6 molecule-2 sec--1,9-11 k = 5 x 10-33 cm6 molecule-2 sec-1.13. 14 is much more rapid than the subsequent reactions : NO+O+M = NO2+M, NO + 0 = NO2 + Av, k = 3 x 1017 cm3 molecule-1 sec-1,12 (3) N + 0 + M = NO + M + hv, 118J . E. MORGAN, L . F. PHILLIPS AND H . I . SCHIFF 119 Reaction (3) produced chemiluminescence in the presence of excess NO and reaction (4) in the presence of excess N. The end-point is readily determined, since there is no chemiluminescence when reaction (1) is stoichiometric.Some evidence has been obtained 1 to indicate that part of this energy appears as vibrational excitation of the N2 produced. Two methods were used in the present work to study quan- titatively the Nl excited in this way. First, the heat content of the energetic species present in the gas stream after the titration could be compared with the calculated heat content of the 0-atoms produced by the reaction. (The titration also permits an evaluation of the number of 0-atoms produced.) Secondly, the NZ formed by reaction (1) was found to be sufficiently energetic to decompose 0 3 . This reaction was therefore investigated with a mass spectrometer. Reaction (1) is exothermic to the extent of 75 kcal/mole.EXPERIMENTAL ISOTHERMAL CALORIMETRIC-PROBE MEASUREMENTS Molecular nitrogen was dissociated to the extent of about 1 % in a flow system by a microwave discharge operated at 2450 Mc/sec. Descriptions may be found elsewhere of the movable probe,3 the titration techniques 15 and other experimental details.16 FIG. 1 .-Probe measurements on discharged nitrogen at p~~ = 4.10 mm Hg and (p& = 0-03 13 mm Hg. A, Hexpt. measured by cobalt plated probe ; B, Halc. from atom concentration at t = 0 and afterglow intensity ; c, In (Hexpt.--Hcalc.). The N-atom concentration at one point was determined by NO titration. The NO flow was then stopped and the decrease in the atom concentration along the reaction tube was followed by photometer measurements of the " afterglow ", the intensity of which has been shown 17 to be proportional to m]2.The results of a typical experiment are shown in fig. 1. Curve A shows H, the rate of heat liberation to the probe, from the " active " nitrogen. as a function of t h e along the reaction tube. Curve B shows a plot of H120 STUDIES OF VIBRATIONALLY EXCITED NITROGEN calculated from the known N-atom flow rate, while the logarithm of the difference AH is shown as C. The half-life of the species responsible for this energy difference is 80msec. It seems reasonable to conclude that " active " nitrogen contains a relatively large fraction of excited N2 molecules, which will subsequently be denoted by N;. The degradation of the energy from N; to kinetic energy with subsequent loss to the wall can be represented as occurring in the gas phase by N; +M -+N, +M: and on the walls by N,*E%N,.The observed first-order rate constant k, obtained from the In (AH) against t plots, can be written as k = k5[M] + k g . The value of k was found to be independent of the nitrogen pressure within experimental error. It can, therefore, be concluded that k5 is close to zero when M = N2. From a series of such measurements, it was found that k6 = k = 8.7 f0.2 sec-1. 4 FIG. 2.-Probe measurements of discharged nitrogen at different linear flow rates (f.r.). 0 f.r. = 200 cmlsec, p~~ = 2.3 mm, ( p ~ ) o = 00188 mm; 0 f.r. = 165 cmlsec, p~~ = 2.95 mm, (pN)o = 0.0229 mm ; 0 f.r. = 126 cmlsec, p w = 4-10 mm, ( p p . ~ ) ~ = 0.0313 mm; 0 f.r. = 110 cmlsec, PN2 = 5.84 mm, (p& = 0-0405 mm.If the value of AH could be extrapolated to the discharge tube, it would be possible to calculate the energy of the excited molecules leaving the discharge. Unfortunately, the geometry of the tubing between the discharge and the reaction tube made such an extra- polation unreliable. The magnitude of AH at any position along the reaction tube will depend upon the elapsed time from the discharge and on the molar flow rate of N2, h2 For sets of experiments with different linear flow rates, plots of log (AH/&*) against time will have the same slope but will be displaced with respect to one another due to the differ- ence in elapsed time from the discharge to the point of measurement. However, if log (AH/fNJ is plotted against distance along the reaction tube for different linear flow rates, the slopes will also differ due to a change in time scale.Since the dis-J . E. MORGAN, L. F. PHILLIPS AND H. I . SCHIFF 121 charge is a fixed distance from the reaction tube, these plots should all intersect at the effective discharge position. Such plots are shown in fig. 2, where d = 0 is an arbitrary position in the reaction tube. The value of AH/fN2 at the intersection corresponds to a value of 6.03 kcal/mole. This can be taken as the average energy of the nitrogen molecules emerging from the discharge. This does not, however, preclude the possibility of other energetic species with lifetimes much shorter than the time required for the gas to flow from the discharge to the measuring region. In fact, Beale and Broida have recently shown 18 that under certain conditions a very energetic species may be formed with a lifetime of about 2 msec. The addition of about 10 % N20 to the gas stream after the discharge resulted in complete deactivation of N; within the 30msec time delay between the N20 inlet and the first measuring position.The agreement between the heat measured by the probe and that calculated for the atom recombination indicates that the probe quantitatively measured the contribution of the atoms to the heat content of the gas. Separate experiments, in which a second similar probe coil was placed in the reaction tube above the measuring probe, showed that no heat was liberated on the latter. This indicated that the probe measured the entire heat content of the gas and consequently was capable of giving quantitative values for the contribution of N;.I I I I 1 5 I I I I 1 50 100 150 200 msec FIG. 3.-Probe measurements of discharged nitrogen with Pyrex wool plug after the discharge tube ; p~~ = 2-00 m Hg. 0 heat measured by probe ; 0 heat calculated from atom concentration at t = 0, and afterglow intensity. Smaller amounts of N20 were added to the " active " nitrogen stream to determine the value of k5 in the presence of this gas. Similar experiments were performed with the addition of A and C02. The results are shown in table 1. TABLE 1 M kS collision k6 cm3 molecule-1 sec-1 efficiency 01 N2 8.7 sec-1 6 . 5 ~ 10-18 3.3 x 10-8 CO2 8.7 ,9 7 . 5 ~ 10-15 4.3 x 10-5 NZO 8.7 ,Y 2 4 x 10-14 1 . 3 8 ~ 10-4 A 8.7 ,¶ 2.5 x 10-16 1 .5 ~ 10-6 u ~ I G A 0.02 1 29 92122 STUDIES OF VIBRATIONALLY EXCITED NITROGEN As mentioned above, the value of k5 for M = N2 was zero within experimental error. The value given in table 1 represents an upper limit only based on the uncertainty in the measurement of k. The value of kg will be seen to be unaffected by the addition of other gases. The wall- deactivation coefficient, calculated from kg, the radius of the tube and the molecular velocity, was 4.75~ 10-4. The corresponding efficiency of the wall to nitrogen atom recombination is 2x 10-5.199 20 Thus, it should be possible to remove N; preferentially by increasing the surface area. It was found that the insertion of a loose plug of Pyrex wool into the tube after the discharge removed all the N$, but reduced the atom concentration by only 25 %.Fig. 3 shows the agreement between the measured heat content (open circles) and that calculated from the 0-atom concentration (closed circles). msec FIG. 4.-Probe measurement of " filtered " discharged nitrogen titrated by NO. PN = 2.6 mm Hg ; po = 00219 ~llm Hg. A, Hexpt. measured by cobalt plated probe ; B, Hcdc. from titration value of [O] and known decay rate of 0-atoms ; c, In (Hexpt. - Hcalc.). Such a " filtered " system was used to study the @ produced by reaction (1). Curve A in fig. 4 shows a plot of the measured H for the gas as a function of time after the titration. Curve B shows a plot of H due to the 0-atoms, calculated from the titration value of the atom concentration, the known recombination rate and the heat of dissociation of 02.The difference shown in curve C can be ascribed to the NI formed by reaction (1). It should be pointed out that the accuracy of such an experiment is low since (a) AH repre- sents a rather small difference between two relatively large quantities, and (b) the " noise " level of the probe amounts to about 1-2 mcal/sec which is an appreciable fraction of AH. A number of such experiments indicated that the average value of the energy of @ is 21 f5 kcal/mole. MASS-SPECTROMETRIC MEASUREMENTS The flow system and mass spectrometer used to study the reaction NJ+ o,+N,+ O,+O (7) has been described previously.8 Nitrogen atoms were titrated by addition of NO through a fixed inlet to form O-atoms+N$ The end-point of the titration was determined massJ .E. MORGAN, L . F . PHILLIPS AND H. I . SCHIFF 123 spectrometrically. Ozone was added through a movable inlet located between the NO- inlet and the mass-spectrometer “leak”. The distance between the NO-inlet and the movable 03-inlet could be related to the decay time of the NZ formed by reaction (l), while the distance between the movable 03-inlet and the ‘‘ leak ” could be related to the time available for the reaction of N$ with the 0 3 . When the discharge was off, 0 3 was consumed by the reaction, NO+ 0 3 = NO2+ 0 2 , k = 2-5 x 10-14 cm3 molecule-1 sec-1. When the discharge was excited, 0 3 was consumed by the reaction, O+ 0 3 = 202, k = 2.1 x 10-14 cm3 molecule-1 sec-1, and by reaction (7). I I 15 30 45 t, mec FIG. 5.-Change in 0 3 consumption when discharge is excited.0 p~~ = 0.56 111111, (p0,)o = 2.2 x 10-2 mm, PNO = 1.31 x 10-2 rtl~; (D P N ~ = 0.40 mm, (po3)o = 2.5 X 10-2 mm, p NO= 1.08 x 10-2 mrn ; 0 p~~ = 0.35 fll~ PO,)^ = 1-7 X 10-2 111111, p ~ o = 6.2 X 10-3 111111 ; (> p~~ = 0.31 mm (po3)o = 1.45 x 10-2 mm, NO = 5-5 x 10-3 mm. Note:pNo is the amount of NO required for stoichiometry of reaction (1). The rate constants of reactions (8) and (9) are almost identical. Thus, if reaction (7) did not occur, the 0 3 concentration at any time t would, as a first approximation, be the same whether the discharge was on or off. Any additional consumption of 0 3 when the discharge is excited can then be attributed to reaction (7). Fig. 5 shows a series of curves, at different partial pressures of N2, of the decrease in the 0 3 concentration upon excitation of the discharge, as a function of time from the 0 3 - inlet to the “ leak ”.Each curve tends to a plateau value of [AOJ which corresponds to1 24 75 f 5 % of the NJ formed by reaction (1). This figure can be interpreted as the percentage of N$ formed initially by the reaction with u>4, Le., with energy equal to, or greater than the 24 kcal/mole required to dissociate 0 3 . In this set of experiments, the flow rates were too fast to detect any decay of NZ along the reaction tube, in the absence of 0 3 . To study the deactivation of N;, a number of experiments were performed in which the linear flows were reduced by “ throttling ” the pump. A large excess of 0 3 was added through the movable inlet, so that reactions (7) and (9) went to completion before the “ leak ”.This procedure essentially titrated the NZ, with ~2-4, remaining at various times after its initial production. STUDIES OF VIBRATIONALLY EXCITED NITROGEN log A03 t, msec FIG. 6.-Decay of N$ measured by 03-decomposition. 0 pN2 = 0.60 m; 0 P N ~ = 0-69 mm, p ~ ~ o = 0 1 1 mm; @ pN2 = 0.62 mm, pN20 = 0.23 IWll. Some plots of log w2], determined in this manner, as a function of time after its formation, are shown in fig. 6. The lower two curves show the more rapid decay when small amounts of N20 were added to the system. The decay can be represented in the simplest terms, by the processes : NI + M+N; + M”, (11) where Ng and M” have energies less than 24 kcal/mole. The observed first-order rate con- stant ko can then be represented by ko = kllCMI+kl29 and a plot of the slopes of the log mi] against f curves against [MI should be a straight line.Such a plot is shown in fig. 7, where M = N2. It yields a value of k12 which cor- responds to a wall-recombination coefficient of 1 . 9 ~ 10-4 and a value for kll of 3.5 x 10-16 c m 3 molecule-1 sec-1. The value of kll when M = N20 was found to be about 1-3 x 10-15 cm3 molecule-1 sec-1. The rate constant for reaction (7) was found-to be 54x 10-13 cm3 molecule-1 sec-1.J . E. MORGAN, L. F. PHILLIPS AND H. I . SCHIFF 125 DISCUSSION An attempt may now be made to compare the results obtained by the two techniques. The probe method showed that the Nl produced in reaction (1) has an average energy of 21 rt5 kcal/mole, while the 03-decomposition methcd indicated that 75 f5 % are formed initially with excess energy equal to, or greater than, 24 kcal/mole.From these results some deductions may be made about the energy distribution among the approximately evenly-spaced, vibrational levels of Ni. Let us first consider whether a Boltmann distribution is possible. The upper limit of 26 kcal/mole for the average energy would then correspond to a temperature of 13,000"K. Since the vibrational spacing E is close to 6 kcal/mole, the fraction of NI with energy equal to or greater than 24 kcal/mole is e-4n = 0-40, where x = E/RT. I I I I I 't 1 PN2, mm FIG. 7.-Slopes of In";] against t plots as a function of N2 pressure. If it is further assumed that Ni molecules with excess energy248 kcal/mole and those with excess energy 272 kcal/mole can decompose 2 and 3 molecules of 0 3 respectively, the fraction of the NJ capable of decomposing 0 3 would be e-4s+e-8x+e-12x - 0.62, compared with the observed value of 0.75f0-05.This observed value may, however, be somewhat too high. The NJ was formed in these experiments by NO-titration of " unfil- tered ", discharged nitrogen. The probe experiments indicated that the discharged nitrogen would contain about 3 kcal/mole of excess energy at the titration point. If this energy is also in a Boltzmann distribution, calculations show that about 3 % of the observed 0 3 decomposition may be attributed to the discharged nitrogen. This leaves 72*5 as the percentage of the N$ formed by reaction (1) capable of decomposing 0 3 .The difference between the observed and the calculated figures suggests that the dis- tribution is not Boltzmann, unless the magnitude of the experimental errors are greater than indicated. Thus, it would only be necessary to raise the average excitation energy to 28 kcal/mole to obtain a calculated value of 72 % 03-decomposition. Alternately, and perhaps more likely, the N l molecules are not formed with a Boltzmann energy dis- tribution, but have a relatively higher population at, or sIightly above, u = 4.126 STUDIES OF VIBRATIONALLY EXCITED NITROGEN DEACTIVATION OF N; AND Ni The wall-deactivation coefficient of N; measured by the probe method agrees, within a factor of 2, with the wall deactivation of NI measured by the 03-decomposition method.This agreement can be considered satisfactory in view of the difference in apparatus and experimental conditions used. It also suggests that N; and NI are basically similar species which differ only in the extent of their vibrational excitation. On the other hand, there are considerable differences between the homogeneous de- activations of the two species. Thus the value of k5 for N; is at least 50 times lower than kl1 for NJ when M = N2. The reason for this djfference may be understood if consideration is given to the processes measured by the two methods. The calorimeter-probe technique measured the total excitation energy of the gas and, therefore, will not detect any exchange of vibrational energy between molecules. It can only follow the rate at which vibrational energy is lost from the system, i.e., by an exchange from vibrational to kinetic energy which is subsequently lost to the walls.Because of the close matching of vibrational levels, an unexcited nitrogen molecule should be a very efficient collision partner for vibrational exchange, and therefore a poor one for transferring vibrational to kinetic energy. The 03-decomposition method measures the rate at which the energy of the N$ molecules are degraded to vibrational levels below the fourth. Such a system has been examined theoretically by Shuler 21 who showed that the rate of energy loss from a small number of excited oscillators in, effectively, a constant temperature bath of unexcited molecules, will be exponential regardless of the initial distribution. This loss may occur either by vibrational-vibrational or vibrational-kinetic energy transfer to the heat-bath molecules.Normal nitrogen should, by vibrational exchange, be very effective in lowering the excitation of N$ below the fourth level. When M = N20 the value of k5 for N; was found to be 20 times higher than kll for NI. The value for kll was calculated from the rate equation The rate of change of 0 3 decomposition will also be equal to the rate at which the NS molecules cross the fourth vibrational level. If vibrational energy is lost principally by single quantum jumps, the rate can also be expressed as -d[AO,]/dt = k'[N!(v = 4)], where k' is the rate constant for loss of a single vibrational quantum. Equating the two rate expressions gives Thus, the observed rate constant will be less than that for a single quantum jump by the ratio of the number of molecules in the fourth level to the sum of those in the fourth and higher levels.For a Boltzmann distribution at 13,000°K, this ratio is approximately 1/5. The rate constant k5 represents the degradation of one vibrational quantum to kinetic energy, whereas k' represents the transfer of one vibrational quantum either to kinetic or to vibrational energy. Therefore, in this case, k5 could be, at most, higher than kll by a factor of 5, compared with the observed factor of 20. This again suggests that there is a higher proportion of NJ near = 5 than is given by a Boltzmann distribution. Acknowledgements are gratefully made to the Defence Research Board of Canada, and to the U.S.A.F. Cambridge Research Laboratories for financial assis- tance, and to the National Research Council of Canada for two Fellowship awards to J. E. M.J . E. MORGAN, L . F . PHILLIPS A N D H. I . SCHIFF 127 1 Kaufman and Kelso, J. Chem. Physics, 1958, 28, 510. 2 Dressler, J. Chern. Physics, 1959, 30, 1621. 3 Elias, Ogryzlo and Schiff, Can. J. Chem., 1959, 37, 1680. 4 Kistiakowsky and Volpi, J. Chem. Physics, 1957, 27, 1141. 5 Kaufman and Kelso, J. Chem. Physics, 1957,27, 1209. 6 Harteck, Reeves and Mannela, J. Chem. Physics, 1958, 29, 608. 7 Herron, J. Res. Nat. Bur. Stand.lA, 1961, 65, 411. 8 Phillips and Schiff, J. Chem. Physics, 1962, 36, 000. 9 Kaufman, J. Chem. Physics, 1958, 28, 352. 10 Harteck, Reeves and Mannela, J. Chem. Physics, 1957, 26, 1333. 11 Ogryzlo and Schiff, Can. J. Chem., 1959, 37, 1690. 12 Fontijn and Schiff, Chemical Reactions in the Lower and Upper Atmosphere (Interscience, 1962), 13 Barth, Chemical Reactions in the Lower and Upper Atmosphere (Interscience, 1962), p. 303. 14 Mavroyannis and Winkler, Can. J. Chem., 1961, 39, 1601. 15 Morgan, Elias and Schiff, J. Chem. Physics, 1960, 33, 930. 16 Morgan and Schiff, J. Chem. Physics, in press. 17 Berkowitz, Chupka and Kistiakowsky, J. Chem. Physics, 1956, 25,457. 18 Beale and Broida, J. Chem. Physics, 1959, 31, 1030. 19 Herron, Franklin, Bradt and Dibeler, J. Chem. Physics, 1959, 29, 230. 20 Wentink, Sullivan and Wray, J. Chem. Physics, 1959, 29, 231. 21 Shuler, J. Chem. Physics, 1957, 26, 454. p. 239.