J. Chem. SOC., Faraday Trans. I, 1982, 78, 1189-1 198 Threshold Energy and Excitation Function for the Reaction of Atomic Hydrogen with Cyclohexane BY DEREK GRIEF AND GEOFFREY A. OLDERSHAW* Department of Chemistry, University of Hull, Hull HU6 7RX Received 27th May, 1981 The reaction of photochemically generated hydrogen atoms with [aH,Jcyclohexane has been examined and the integral reaction probability of the abstraction reaction (1) determined at different translational (1) energies of H*: The phenomenological threshold energy of reaction (1) is 39 If: 4 kJ mol-l. Measurements of the moderating effect of xenon at different intial translational energies of H* have been combined with calculated collision densities to obtain the excitation function for reaction (1) in the energy range 30-200 kJ mol-l.The maximum reaction cross-section per D atom in this range is markedly less than that for the corresponding reaction of H* with the secondary D in n-C,D,,. H* + C6Dl, --* HD + C,D,,. Abstraction reactions of the hydrogen atom with alkanes have been examined by a variety of methods. In systems in which both reactants are essentially in thermal equilibrium with the surroundings, the Arrhenius parameters for several reactions have been determined from measurements of rate coefficients.l12 There is also literature concerning both the abstraction and substitution reactions of ‘hot’ tritium atoms, generated by nuclear recoil, with alkane^.^ Recoil tritium has initial energy far in excess of the maximum for chemical reaction and the reaction products result from the sampling of the excitation functions for different processes over the whole of their ranges.Only the most general information about reaction cross-sections can be obtained from such studies. Photodissociation provides an alternatiLe source of ‘hot’ H or D atoms which are reactive towards alkanes. The use of this method has the advantage that by varying the photolysis wavelength the initial translational energy of the atom can be selected in the range 0.3-4 eV. Following the original work on the reaction between D and H2,4 control of the initial energy has been exploited in several determinations of reaction Other work with alkanes has included the variation of reaction yields with initial energy of the atoms5* and examination of isotope effects.* However, the expectation that measurements of reaction yield as a function of initial energy would be used to obtain the energy-dependent form of the reaction cross-section (excitation function) has been fulfilled in only one instance, the reaction of H with butane.O The difficulty of calculating energy transfer in collisions between H and the polyatomic substrate was circumvented in that case by measuring the effect of initial energy on the moderating efficiency of xenon.The determination of the reaction cross-section then requires a knowledge of the collision density of H in xenon, which can be calculated from the H-Xe potential.1° We have now examined the reaction of photochemically generated H atoms with [2H,z]cyclohexane. Product yields for abstraction of D and the moderating efficiency of xenon have been measured for a series of initial atomic energies.Collision densities of H in Xe have been computed for each of the source energies and combined with 11891190 REACTION OF H* WITH [2H12]CYCLOHEXANE the experimental measurements to obtain the excitation function for the abstraction reaction. EXPERIMENTAL Gaseous mixtures of cyclo-C,D,, and HI or HBr were prepared in quartz vessels and irradiated with monochromatic light. In some experiments xenon was added to the reaction mixtures. Total pressures were in the range 20-500 Torr* and the temperature was ca. 293 K. H, and HD in the reaction products were determined mass-spectrometrically after condensing the reactants at 77 K. The mass spectrometer was calibrated with synthetic mixtures of H, and HD.For experiments with HBr the irradiation sources were a zinc resonance lamp, a cadmium resonance lamp and a super-pressure mercury lamp (Osram type HBO 200) with monochromator. The zinc lamp was used with a 100 mm filter of cis-but-2-ene at 100 Torr and the principal absorbed line was at 213.9 nm. The cadmium lamp was used with a 20 mm filter of toluene (1.0 x mol dm-3) in hexane; in this case the principal absorbed lines were at 228.8 and 226.5 nm with relative intensities of cu. 17: 1, giving an effective mean absorbed output wavelength of 228.7 nm. The mercury lamp was used with a monochromator setting to give a mean output wavelength of 248.4nm. For experiments with HI, the mercury lamp and monochromator were used to obtain mean output wavelengths of 312.4, 333.4 and 352.0 nm.In order to eliminate, at the higher wavelengths used, small quantities of low-wavelength radiation which would be preferentially absorbed, plate-glass filters of thickness 4 and 12 mm were used at the wavelengths 333.4 and 352.0nm, respectively. The half-width of the monochromator output was between 3 and 6 nm for the various wavelength settings. For irradiation at the highest wavelength, a combination of the super-pressure lamp, an interference filter and a 25 mm plate-glass filter was used to obtain an output wavelength of 365+3 nm. [ZH,Jcyclohexane (99%) was from Fluorochem, xenon from B.O.C. and Air Products, and HD (98%) used for calibration from Merck, Sharpe and Dohme. RESULTS AND DISCUSSION Photolysis of mixtures of HI and cyclo-C,D,,, or HBr and cyclo-C,D12, yielded products which included H, and HD. In the reaction system, H atoms with high translational energy are generated by photolysis of HX and may abstract D from cyclo-C,D,, to generate HD.Energy loss in non-reactive collisions also occurs and those atoms with energy below the threshold for reaction with cyclo-C,D,, are scavenged by HX to yield H,. Product ratios for various photolysis wavelengths are shown in fig. 1-3. For runs in which no xenon was present in the reaction mixture the ratio [H,]/[HD] was found to be a linear function of the reactant ratio [HX]/[C,D,,], with a positive intercept. As in other systems of this type5* the results are interpreted using the following reaction mechanism : H*+HX+H+HX (4) H*+Xe+H+Xe ( 5 ) H+HX+H2+X X+X+M +X2+M.* 1 Tom = (101 325/760)Pa.D. GRIEF AND G. A. OLDERSHAW 1191 I 1 I I I I 1 0 0.2 0.4 0.6 0.8 1.0 1.2 FIG. 1.-Product ratios in the photolysis of mixtures of HBr and cyclo-CeDl, at 229 nm. tHBr1 /tC,Di,] 0 0.2 0.4 0.6 0.8 1.0 1.2 FIG. 2.-Product ratios in the photolysis of mixtures of HBr and cyclo-CeDl, at 248 nm (0) and of mixtures of HI and Cyclo-CeD,, at 3 12 nm (a). [HXl/[CciDnI 80 - 60 - 5 - 40 z - n N Y 20 - I 1 1 1 I I 1 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 FIG. 3.-Product ratios in the photolysis of mixtures of HI and Cyclo-CeD,, at 333 (0) and 352 (0) nm. [HII/[C,D,,l1192 REACTION OF H* WITH [2Hl,]CYCLOHEXANE H* respresents an atom with energy above the threshold for reaction (1) and H represents one with less than this energy.Steps (2), (4) and (5) are moderation processes and (4) includes both non-reactive collisions and moderation through the exchange reaction.ll9 l2 Abstraction by X of D from C,D12 or X from HX is excluded on energetic grounds. The hot substitution reaction (8) H* + C,D1, 3 C,DllH + D (8) has a threshold of ca. 1.5 eV139 l4 and is expected to be much less important than the abstraction (1) even at the highest energy (2.0 V) used in the present work. Thus for small extents of reaction the ratio of products is and in the absence of xenon [H,]/[HD] is a linear function of [HX]/[C,D,,]. The coefficients k, to k, depend on the initial energy of H* as reflected in the slopes and intercepts of fig. 1-3. Reaction of thermalised H atoms with accumulated X, from reaction (7) competes with reaction (6) as the photolysis proceeds.For runs with HI the consequent reduction in [H,]/[HD] was in the region of 2% and was ignored, but for runs with HBr the observed product ratios were increased by between 3 and 10% to correct for scavenging by Br,.15 INTEGRAL REACTION PROBABILITIES AND THRESHOLD FOR D ABSTRACTION The integral reaction probability (net probability of reaction) for a hydrogen atom of specified initial energy is P = kl/(kl + k2). Values of P obtained from the intercepts k 2 / k , of plots of [H2]/[HD] against [HX]/[C,D,,] are given in table 1. Experiments at 365 nm enabled an upper limit of 0.003 to be set on the fraction of HD in the reaction products for an initial energy of 35 kJ mol-l.The initial laboratory energy of the H atom EL was ca1culatedls*l7 using values of the dissociation energy Do of TABLE INTEGRAL REACTION PROBABILITY AND kl/k5 FOR DIFFERENT INITIAL ENERGIES OF THE HYDROGEN ATOM EL (initial) /kJ mol-l P k l / k 5 197 0.205 k 0.006 4.93 & 0.07 161 0.200 k 0.008 4.15 & 0.07 120 0.193 k 0.005 2.83 k 0.07 90 0.155 & 0.008 2.00 & 0.09 66 0.086 & 0.009 1.22 0.08 47 0.024k 0.003 - 35 - - HBr and HI of 362.5 and 294.7 kJ mol-l, respectively. Fig. 4 shows the variation of the integral probability of reaction (1) with the initial laboratory energy of the hydrogen atom. The phenomenological threshold obtained by linear extrapolation of the lowest points is EL = 39 f 4 kJ mol-l. As pointed out else~here,~~ l5 this does not represent the true threshold for reaction.Conversion to relative energy requires aD. GRIEF AND G. A. OLDERSHAW 0.05 1193 - / I & I I 1 0 50 100 150 200 EL/kJ mol-’ FIG. 4.-Integral reaction probability for reaction (1) at various initial laboratory energies of H. reduction of only 1 %, but model calculations using an assumed ‘line-of-centres’ excitation function shows that linear extrapolation of yields gives an apparent threshold substantially above the true value. Few other thresholds for abstraction of D by H are available for comparison. Gann et al.9 have determined the true threshold for abstraction of the secondary D in [2Hl,]butane as 34 & 2 kJ mol-1 and the phenomenological threshold determined by direct extrapolation of their data is ca.37 kJ mol-l. Since the secondary CH bonds in butane and cyclohexane have approximately the same strength1* the similarity of the thresholds for secondary D abstraction is not unexpected; for the stronger primary bond in CD,CH,CH,CD, Gann et aL9 give the apparent threshold for D abstraction as 48 f 5 kJ mol-l. Fink and coworkers have determined thresholds for abstraction by D of H from a number of alkanes.s* 19-21 In comparing their results with the present work it should be noted that the translational energies of D appear to be based on a value for the dissociation energy for HI slightly higher than that adopted here. For the purposes of comparison with the present work the thresholds given by Fink and coworkers should be raised by ca. 3 kJ mol-1 to bring the results onto a common basis.Allowing for this adjustment, the threshold reported21 for the abstraction by D of H from cyclohexane is equal to that found here for the isotopically reversed process. This is surprising in view of the difference in the CH and CD bond strengths, but the expected difference in thresholds is within the combined experimental error. MODERATING EFFECT OF XENON Addition of inert gases to the reaction mixtures reduced the yield of hot product HD by removing energy from the hot atoms in non-reactive collisions. A detailed study of the moderating effect of xenon was carried out principally to provide information for use in the evaluation of the excitation function, as discussed more fully below. If a comparison of the ratio [H,]/[HD] is made for two reaction mixtures, each having the same ratio [HX]/[C,D12], one with and the other without xenon moderator, then eqn (9) shows that the increase in [H,]/[HD] caused by the presence of xenon is1194 REACTION OF H* WITH [2H12]CYCLOHEXANE 0 10 20 30 40 50 60 FIG.6.-Moderating effect of xenon at 229 nm. [XeI/[C,D,21 0 10 20 30 40 FIG. 7.-Moderating effect of xenon at 248 nm. W e 1 /[C6D121 Experiments on the moderating effect of Xe were carried out using a number of different initial energies of the hydrogen atom. In each case measurements of ([H2]/[HD])mod were combined with values of ([H,]/[HD]),,,,, for the appropriate ratios [HX]/[C,D,,] obtained from fig. 1-3. The resulting values of A([H,J/[HD]) for the photolysis wavelengths used are shown in fig.5-8 and are proportional toD. GRIEF AND G. A. OLDERSHAW 1195 0 10 20 30 LO [Xel/[C$,,l FIG. 8.-Moderating effect of xenon at 312 (0) and 333 (0) nm. ~e]/[C,D,,] as required by eqn (10). Values of kl/k5 derived from the plots are listed in table 1. EVALUATION OF REACTION CROSS-SECTION The procedure is that suggested by Gann et aL99 l6 The reactivity of H* with some particular initial (source) distribution of kinetic energies (designated by subscript a) expressed relative to moderation by xenon is given by where Erepresents the relative translational energy of H and C8DI2, E, is the threshold (relative energy) for reaction (l), EL is the laboratory translational energy of H and SR ( E ) is the cross-section for reaction (1). S(E,),, is the average total scattering cross-section of xenon for a hydrogen atom of energy EL and n, (EL)Xe is the collision density in pure xenon of H atoms with initial E,-distribution a.G(EL,E) is the normalised distribution function of laboratory translational energies corresponding to a particular value of the relative translational energy E between H and C&2, the latter having a Maxwellian velocity di~tributi0n.l~ Values of kl/k5 are determined experimentally for different initial energies of the hydrogen atom by measuring the moderating effect of xenon, as described in the last section. By comparing the kl/k5 values for two different initial H atom energy distributions, a and b, the average reaction cross-section over the intermediate energy range can be obtained from where In addition to the experimental values of kl/k6, the collision densities of H in xenon are required and are computed from the H-Xe interaction potential.1196 REACTION OF H* WITH [2H12]CYCLOHEXANE COLLISION DENSITY OF H IN Xe Collision densities of the hydrogen atom in a thermal xenon medium were calculated using random selection of the dynamical variables in a manner similar to that outlined by Rebick and Dubrin.lo Hydrogen atoms of initial energy corresponding to that generated in the photolysis are imagined to make successive collisions with xenon atoms in thermal equilibrium at the experimental temperature.The collision density is obtained by computing the average number of collisions occurring in each energy interval. The computations are conveniently carried out using a H-Xe interaction potential of the form V(r) = drd and the Born-Mayer potential given by Bickes et aZ.22 was fitted to this form at 0.35 and 2.0eV to yield S = 9 and d = 0.329 J mol-1 nm9.In each collision between the hydrogen atom and the xenon atom the energy of the hydrogen atom after collision, EL, was calculated from that before collision, E L usingl5? 23 ,u EL = EL - [2EL - m,, vXe2 +(mXe-mH) (2EL/mH)avXecosyl -cOsx) +,u ( 2 ~ ~ / m ~ ) ~ v , , s i n y s i n ~ c o s q (14) where M = mH +mxe, ,u is the reduced mass of H and Xe, vXe is the xenon speed, y is the angle between the H and Xe velocity vectors and x (deflection angle) and q (azimuthal angle) are the scattering angles [as shown in ref. (lo)]. Taking the vXe distribution to be Maxwellian at the experimental temperature, vXe, y and q were chosen randomly from suitably weighted distributions.l0? l5 For the inverse power repulsive potential x is a function of yo = b (E/8d)1/6,24 where b is the impact parameter, and the relationship between x and yo was computed for S = 9.15 x was determined by a random choice of yo, i.e.yo = yomaX&, where R is a random number between 0 and 1. To avoid counting collisions with very large impact parameters which involve small deflections and energy losses, an arbitrary constant value of yomax of 1.1 was employed over the whole energy range. This excluded collisions with energy losses less than ca. 1 % of the maximum. As a consequence of this procedure, the total scattering cross-section varied as E-&; In selecting the initial energy of the hot atoms a distribution appropriate to each photofysis wavelength was used.This took into account the monochromator band pass, the translational motion of HX and the distribution of HX among rotational states. For energies below ca. 93% of the source energy an asymptotic formulalo* 24 appropriate to the functional form of S(E),, adopted here was used to calculate the collision density : 4,uA(1)(9) (EL - 3kT/2)-' where A 9 9 ) = 0.327.24 DERIVED EXCITATION FUNCTION Int (a), Int (b), . . .were computed for each of the source energies from the collision densities na(EL)xe, nb(EL)Xe,. . .and used in eqn (12) with (kl/k5)a, (kl/k5)b,. . . to obtain the average reaction cross-section forD. GRIEF A N D G. A. OLDERSHAW 1197 141 12 / I I I I I 0 50 100 150 200 ElkJ mol-I FIG.9.-Excitation function for reaction (1). over the interval between each adjacent pair of source energies. The derived excitation function is shown in fig. 9. The lowest point shown was calculated from the experimental kl/k5 at EL = 66 kJ mol-1 and a value of EL = 47 kJ mol-1 obtained by extrapolation of a plot of k1/k5 against EL. Extrapolation to a lower energy was avoided because of the unknown shape of the kl/k5 against EL curve near the threshold. Owing to the fact that the lowest initial energy for which kl/k5 was determined (66 kJ mol-l) is much higher than the threshold, the value of the true threshold energy and the shape of the excitation function below 60 kJ mol-1 are difficult to establish. The function drawn in fig.9 in this region is of the ‘line-of-centres’ form, &(E) cc (1 - Eo/E),withEo = 30 kJ mol-’,butasteeperfunctionwithhigherthreshold is also compatible with the results. Taking into account both the values of kJk5 and the values of P listed in table 1, the true threshold lies in the range 28-38 kJ mol-l. The observations are of course insufficient to reveal details of the shape of the excitation function in the immediate region of the threshold. In the case of abstraction by H of secondary D from n-C4Dlo (16) Gann et al. found9 that the best fit to their results was obtained with an excitation function rising from the threshold significantly steeper than the line-of-centres function, but pointed out the uncertainties surrounding the shape of the function in the threshold region.The other principal feature of the excitation function determined for reaction (1 6)9 was the presence of a maximum in the cross-section at ca. 116 kJ mol-l. In the present case, the results obtained for abstraction by H of D from cyclo-C,D,,, reaction (l), allow the possibility of a maximum around 150 kJ mol-1 but do not establish one conclusively. In any event, the sharp decline in the excitation function over the range 100-180 kJ mol-l found for reaction (16) is not observed for reaction (1). The curve drawn in fig. 9 is of the line-of-centres form up to 140 kJ mol-1 and falls slightly below this function at higher energies. On the assumption that a maximum in the cross-section for reaction (1) exists below H* + n-C4Dlo + s-C,D, + HD1198 REACTION OF H* WITH [2H12]CYCLOHEXANE 200 kJ mol-l, it is substantially smaller, when allowance is made for the number of D atoms, than the maximum cross-section found for reaction (16).In the case of reaction (1) the maximum cross-section is (1 1.8 _+ 2.0) x 1 0-3 nm2, or (0.98k0.17) x nm2 per D. By using a number of different H-Xe potential functions Gann et aL9 obtained a maximum cross-section for reaction (16) of (3.5 f 1.5) x nm2. Treatment of their experimental data using the 9th power potential employed in this work yields a maximum cross-section of (6.3 f 1.2) x nm2, or (1.58 k0.30) x nm2 per D. Thus the strengths of the bonds broken, and the threshold energies, for reactions (1) and (16) are similar, but the excitation functions in the region below 200 kJ mol-l differ significantly.The rate coefficient of the related reaction D +CyC10-C6H12 + HD +~yclo-C~H,, has been measured as a function of temperatu~e.~~ In general, the activation energy is expected to be higher than the true threshold energy, which is itself lower than the phenomenological threshold. The activation energy reported for reaction (1 7), 16.7 & 1.3 kJ mol-l, is substantially lower than that expected from the observed threshold of reaction (17)21 or that of reaction (1). D.G. thanks the S.R.C. for a research studentship for the period when this work was carried out. W. E. Jones, S. D. MacKnight and L. Teng, Chem. Rev., 1973,73,407. R. R. 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