Reaction of Monoenergetic Deuterium Atoms with Hydrogen and Monoenergetic Hydrogen Atoms with Per-Deutero Methane Citation Betts, Jeanette Asay (1971) Reaction of Monoenergetic Deuterium Atoms with Hydrogen and Monoenergetic Hydrogen Atoms with Per-Deutero Methane. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8E5X-D717. https://resolver.caltech.edu/CaltechTHESIS:02282018-135019156 Abstract Mixtures of DBr-H 2 , DI-H 2 and HBr-CD 4 were photolyzed with monochromatic light. Thirteen different wavelengths were used in the DBr-H 2 , DI-H 2 systems yielding deuterium atoms with initial laboratory energies ranging from 0.6 to 3.0 eV. We were able to obtain the integral reaction yield A H + D 2 = k 1 /k 1 + k 2 where k 1 and k 2 are effective bimolecular rate coefficients for the process: D* + H 2 → DH + H (1) D* + H 2 → D + H 2 (2) These processes describe rates of reaction and thermalization which accompany the injection of monoenergetic atoms into thermal H 2 gas. We were also able to obtain the integral reaction yield for the H + CD 4 system at five wavelengths with initial H atom laboratory energies ranging from 1.15 to 3.0 eV. For both the D + H 2 and H + CD 4 systems we were able to show that the integral reaction yield is a monotonically increasing function of energy over the energy ranges scanned. For D + H 2 a ranged from 0 at about 0.6 eV to 0.66 at 2.86 eV initial laboratory energy while for H + CD 4 A ranged from 0.015 at 1.15 eV to 0.040 at 3.0 eV initial laboratory energy. There is an order of magnitude difference between the integral reaction yields for H + CD 4 and either D + H 2 or H + D 2 . These differences were attributed to the greater probability of inelastic collisions occuring in the H + CD 4 system than in the D + H 2 or H + D 2 systems. Finally, we were able to show how reaction cross sections can be extracted from the experimental integral reaction yield using a steady state Boltzmann equation. We were also able to measure the abstraction fraction a for the reaction of H with DX (X = Br, I). The results were a(DBr) = 0.99 ± 0.03 and a (DI) = 0.97 ± 0.05. Finally, using the integral reaction yield versus energy plot for D + H 2 plus additional DI-H 2 , DI-He experiments we were able to determine the fraction f of iodine atoms produced in the excited 2 P 1/2 state in the photolysis of DI at 4 wavelengths. The results are f(2800Å) = -0.08 ± 0.27, f(2537Å) = 0.46 ± 0.05, f(2400Å) = 0.60 ± 0.07 and f(2138Å) = 0.33 ± 0.1. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Kuppermann, Aron Thesis Committee: Unknown, Unknown Defense Date: 24 September 1970 Funders: Funding Agency Grant Number National Defense Foundation UNSPECIFIED Record Number: CaltechTHESIS:02282018-135019156 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:02282018-135019156 DOI: 10.7907/8E5X-D717 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 10738 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 01 Mar 2018 18:20 Last Modified: 29 May 2024 23:49 Thesis Files Preview PDF - Final Version See Usage Policy. 86MB Repository Staff Only: item control page

REACTION OF MONOENERGETIC DEUTERIUM ATOMS WITH HYDROGEN AND MONOENERGETIC HYDROGEN ATOMS WITH PER-DEUTERO METHANE Thesis by Jeanette Asay Betts In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1971 (Submitted September 24, 1970) ii ACKNOWLEDGMENTS I wish to express my appreciation to Dr. Aron Kuppermann for suggesting the projects described in this thesis and for discussion and advice given throughout the course of this work. I wish to thank Dr. Donald R. Davis for the help and encouragement he gave me in starting this work and Dre Avigdor Persky for helpful discussions during the course of this work. Support in the form of a fellowship from the National Defense Foundation is appreciated. Finally, I wish to thank my husband Tim for the encouragement and support he has given me in the preparation of this thesis. iii ABSTRACT Mixtures of DBr-H , DI-H and HBr-CD were photolyzed 2 2 4 with monochromatic light. Thirteen different wavelengths were used in the DBr-H , DI-H systems yielding deuterium 2 2 atoms with initial laboratory energies ranging from 0.6 to 3.0 eV. We were able to obtain the integral reaction yield where k 1 and k 2 are effective bimolecular rate coefficients for the processes: - (l) DH + H (2) These processes describe rates of reaction and therrnalization. which accompany the injection of monoenergetic atoms into thermal H 2 gas. We were also able to obtain the integral reaction yield for the H + CD 4 system at five wavelengths with initial H atom laboratory energies ranging from 1.15 to 3.0 eV. For both ·the D + H and H + CD systems we were able 2 4 to show that the integral reaction yield is a monotonically increasing function of energy over the energy ranges scanned. For D + H A ranged from 0 at about 0.6 eV to 0.66 at 2.86 eV 2 initial laboratory energy while for H + CD 4 A ranged from 0.015 at 1.15 eV to 0.040 at 3.0 eV initial laboratory energy. iv There is an order of magnitude difference between the integral reaction yields for H + CD 4 and either D + H or H + D • 2 2 These differences were attributed to the greater probability of inelastic collisions occuring in the H + CD in the D + H or H + 2 4 system than n2 systems. Finally, we were able to show how reaction cross sections can be extracted from the experimental integral reaction yield using a steady state Boltzmann equation. We were also able to measure the abstraction fraction a for the reaction of H with DX (X a(DBr) = Br, I). The results were = 0.99 :!: 0.03 and a(DI) = 0.97 :!: 0.05. Finally, using the integral reaction yield versus energy plot for D + H plus additional DI-H , DI-He experiments we 2 2 were able to determine the fraction f of iodine atoms produced in the excited 2 state in the photolysis of DI P ; 1 2 = -0.08 :!: 0.27, f(2537~) = 0.46 :!: 0.05, f(24002) = 0.60 :!: 0.07 and f(21382) = at 4 wavelengths. 0.33 :!: 0.1. The results are: f(28002) v TABLE OF CONTENTS Page l. INTRODUCTION 2$ PAPER I. l Reaction of Monoenergetic Deuterium Atoms With Hydrogen Molecules 3 l. Introduction 3 2. Difficulties in Obtaining Reaction Cross Sections from Thermal Rate Constants and 3. 4. Crossed Molecular Beam Measurements 5 2.1. Thermal Rate Constants 5 2.2. Crossed Molecular Beam Measurements 9 Foundations of the Method 11 3.1. The Integral Reaction Yield 11 3.2. Hot and Cold Deuterium Atoms 13 3.3. Kinetic Analysis 14 22 Experimental 4.1. Apparatus 22 4.2. Reagents 30 4.3. Experimental Procedure 31 4.3.L . Preparation of Reaction Mixture 31 4.3.2. Photolyses 32 4.3.3. Analysis of Products 32 5. Results of ( [D ) /(HD) ) Measurements 0 2 34 60 Determination of Integral Reaction Yields 50 6.1. Initial Energy of Photochemically Produced Deuterium Atoms 50 vi Page 6.2. Mechanisms and Kinetic Analysis 6.2.1. The DX + H2 System 60 6.2.2. The DX + HX + H2 System 74 6.2.3. The DX + HX + He System 79 6.2.4. Exact Expression for the Integral Reaction yield 6.3. 82 6.3.l. Determination of HX Impurity in DX 6.3.2. Determination of the Abstraction Fraction of H + DX 6.3.3. 82 84 Results for the Integral Reaction Yield 85 89 Discussion 7.1. Shape of A(E(O» 1 7.2. Determination of Reaction Cross Sections 89 From Integral Reaction Yields 95 7.2.l. Boltzmann Equation 95 7.2.2. Relation Between A(v~) and the Reaction Cross Section 7~2.3. 98 Consequences of the Simplified Boltzmann Equation Appendix. 81 Determination of the Integral Reaction Yield 7. 60 100 Photolysis of DI Containing a Small Amount of HI Impurity 103 vii Page 3. 1. 5. PAPER 2. Reactions of H Atoms with DBr and DI 111 1. Introduction 111 2. Mechanism 112 3. Experimental 115 4. Results and Discussion 120 PAPER 3. Excited Iodine Atoms by Photolysis of DI 129 1. Introduction 129 2. Methods. 132 3. Experimental 136 4. Results and Discussion 137 5. References 149 PAPER 4. Reaction of Monoenergetic H Atoms With CD • 4 1. Introduction 150 2. Method 151 3. 2.1. Integral Reaction Yield 2.2. H~t 2.3. Kinetic Analysis and Thermal Hydrogen Atoms Experimental 151 152 153 154 3.1. Apparatus 154 3.2. Reagents 157 3.3. Procedure 157 pi 2 ) I [no) :!-leasurements 4. Results of 5. Determination of Integral Reaction Yields 5.1. Initial Energy of Photochemically 159 .163 viii Page 5.2. Produced Hydrogen Atoms 163 Mechanisms and Kinetic Analysis 165 5.2.l. List of Reactions in the HBr. CD 4 System 165 5.2.2. Consideration of CD H Impurity 5.2.3. Determination of the Integral 3 Reaction Yield 6. Discussion (0) Shape of A(E 6.2. Reaction Cross Section From Integral 1 ) 184 Reaction Yield 192 6.2.l. Boltzmann Equation 192 6.2.2. Relation of A(vH) and the Reaction Cross Section 6. 181 184 6.1. 6.3. 179 Summary 196 196 Appendix 197 References 201 · CONCLUSION 204 APPENDIX A. l~ 2. LIGHT SOURCES 208 Monochromators 208 1.1. Photolysis Monochromator 208 1.2. Monochromators for Testing and Calibrating 209 1.2.l. Jarrell Ash Monochromator 209 1.2.2. McPherson Monochromator 209 Light Sources 210 ix Page 2.1. 2500 watt Xenon Mercury Arc Lamp 210 2.2. 6500 watt Xenon Lamp 211 2.3. Mercury BH6 Lamp 211 2.4. Hanovia Low Pressure Mercury Lamp 216 2.5. Germicidal Lamp 219 2.6. Phillips Spectral Lamps 220 2.6.1. Zinz Lamp 221 2.6.2. Cadmium Lamp 221 2.6.3. Low Pressure Mercury Lamp 224 2.6.4. Thallium Lamp 224 2.6.5. Indium Lamp 224 2. 7. 3. Iodine Lamp 224 Comparison of High Intensity Continuous Lamps in the Wavelength Region From 2400R to 3660~. 227 4. Comparison of Low Pressure Mercury Lamps 228 5. Filters 232 5.1. Glass Filters 232 5.2. NiS0 -CoS0 Filter 4 4 232 5.3. cis-2-butene Gas Filter 236 Light Intensity Measuring Devices 236 6~ 7. 6.1. Eppley Thermopile 236 6.2. RCA 935 Phototube 238 Scattered Light in the Bausch and Lomb Monochromat or 242 x Page APPENDIX B. ADDITIONAL EXPERIMENTAL TECHNIQUES FOR 246 1. Reactant Mixing 246 2. Product Handling 246 3. Mass Spectral Analysis 248 APPENDIX C. ADDITIONAL EXPERIMENTAL TECHNIQUES FOR H + CD 250 4 1. Reactant Mixing 250 2 •. Product Handling 250 3. Mass Spectral Analysis 251 APPENDIX D. ADDITIONAL HESULTS FOR D + H 2 255 J• Photolyses at 1849~ 255 2. Photolyses at 2138R 259 Photolyses at 23002 259 4. Photolyses at 2446~ 268 s. Photolyses at 24832 273 6. Photolyses at 2500~ 273 7. Photolyses at 25372 282 8. Photolysis of DI at 2891A. 291 Photolysis of DI at 30302. 296 Photolysis of DI at 32612. 301 11. 0 Experiments to Determine the Fraction of Excited Iodine Atoms Produced in the Photolysis of DI 305 11.1. DI Photolysis at 2138~ 305 11.2. DI Photolysis at 2400~. 305 xi 11.3. APP~IHX 1. E. DI Photolysis at 28052 ADDITIONAL RESULTS FOR H + CD 310 4 Preliminary Experiments 314 314 1.1. Preliminary Experiments at 2138i 314 1.2. Preliminary Experiments at 2061~ 317 1.3. Preliminary Experiments at 2288~ 317 2. Photolysis at 2537~ 327 3. Photolysis at 21382 330 4. Photolysis at 2061~ 330 5. Photolysis at 18492 335 APPENDIX F. CALCULATION OF ROTATIONAL AND TRANSLATIONAL ENERGY SPREADS IN DBr AND DI 338 1. Rotational Energy Spread 338 2. Translational F..nergy Spread 338 1 1. INTRODUCTION The understanding of simple chemical reactions is a major area of interest in the field of chemical kinetics. It is profitable to study such systems experimentally since the results can be compared 'With detailed theoretical calculations leading to better understanding of detailed processes involved.. One qu.anti ty in particular that is interesting to study is the reaction cross section. This quantity is important in that it enables chemists. to gain greater insight into the molecular dynamics of chemical reactions. However, the amount of detailed information on this quantity, even on simple chemical systems, is small. The informa- tion available has been obtained by the elegant and complicated technique of molecular beams. However, this method has been used mainly in studies of reactions involving alkali atoms and/or halides, and even though it is now being extended to other systems, the energy dependence of total reaction cross sections for reactions with appreciable activation energy is not yet available. This study was undertaken to obtain cross section information on some elementary reactions by a relativezy simple photochemical technique. The two reactions reported here are the hydrogen isotope exchange reaction: - DH+ H and the reaction of hydrogen atoms 'With per-deutero methane~ H + cn 1ID + cn • 4 3 The thesis is comprised of (in addition to this introduction) 2 4 papers, a section of conclusions and 6 appendices. It should be mentioned that the first 3 papers were written in conj'l.Ulction with Drs. J. M. White, D. R. Davis and A. Kuppermann who contributed much to the work reported here. The first paper deals with the D + H reaction, the second with the abstraction :fraction for 2 the reaction H + DX (X = I, Br), the third with the fraction of iodine atoms produced in the excited 2p ; 2 state in the photolysis 1 of DI and the fourth with the H + CD4 system. The appendices expand on details of experimental techniques and results not included in the papers. 3 PAPER 1 1. INTRODUCTION The chemical reaction cross section is a very fundamental dynamical quantity which permits the formulation of bulk reaction properties in terms of the molecular level dynamics of reacting systems. 1 Furthermore, it contains information about the forces at play during reactive collisions of molecules. 2 Similar state- ments can be made about nuclear reaction cross sections, and indeed they have been extensively and profitably used by nuclear physicists in describing nuclear reactions and nuclear scattering processes and in developing a detailed understanding of these phenomena.3 However, until ten or fifteen years ago, very little was known about chemical reaction cross sections. The main reasons were that experimentally no good methods were available for their determination and, theoretically, the calculations involved could not be carried out analytically and were far too elaborate to be done 'With the computational equipment then available. The experimental difficulty was due to the fact that most measurements of reaction rates were made under thermal distribution conditions. For reasons described below, if the activation energy of the reaction is in excess of about 5 kcal/mole, such measurements do not contain information about the reaction cross section except relatively close to an effective threshold energye Even with the use of the elegant and powerful crossed-molecular 4 beam technique, 4 it is still very difficult to determine the energy dependence of the cross section of such reactions over an extended energy range. We will be concerned in this paper with the very important elementary process D+ ~ - DH+ H which, with its isotopic counterparts, has played a central role in the develoJ?lllent of the foundations of chemical kinetics. In recent years, using a classical approximation to the motion of the nuclei during reaction, 2 it has been :possible to calculate the energy dependence of the cross section of this reaction from first principles. In addition, theoretical formulations5 and numerical techniques are presently being developed which should permit quantum mechanical calculations of good accuracy in the near future. For these reasons, it is highly desirable to obtain a.s much experimental information as possible about the cross section of this reaction and of its isotopic counterparts over a wide energy range. Information of this type is also desirable for systems too complex to perform!: priori calculations, in order to test the validity of approximate models. In this paper we describe a photochemical technique designed to measure the energy dependence of' the integral reaction yield A [defined by Eq. (8)] of the D + H2 exchange reaction, a quantity closely related to the reaction cross section. Preliminary results concerning the phenomenological energy threshold of this reaction have been :previously described.6 5 In Section 2 we discuss the difficulties associated with obtaining reaction cross sections :from thermal rate constants and crossed molecular beam measurements. In Section 3 we describe the basis of the present met.hod, in Section 4 the experimental techniques, in Sections 5 and 6 the mode of analyzing the data and the results of the measurements of A for the relative energy range of 0.3 to 1.4 eV, and finally in Section 7 we discuss its relationship to reaction cross sections. 2. DITFICULTIES IN OBTAINING TOTAL REACTION CROSS SECTIONS FROM THERMAL RATE CONSTANTS AND CROSSED IDLECULAR BEAM MEASUREMENTS 2.1. Thermal Rate Constants Let us consider a homogeneous gas phase elementary bimolecular reaction between molecules A and B under conditions such that termolecu.la.r collisions are negligible. If' all molecules A were in internal quantum state i and all B in state j and if collisions between A and B occurred at relative energy E, then the bimolecular rate coefficient tor such a reaction would be (1) where v(E) is the relative translational velocity of the reagents at energy E and o-ij(E) the total reaction cross section for such collisions. For more realistic conditions under which the reac- tants posses wider distributions of internal and relative translational energies, the bimolecular rate coefficient is given by1 6 (2) where fij(E) is the normalized distribution function of relative translational energies of A in state i and B in state j and X~ are respectively the fraction of A and B molecules in and ~ j those states. The summation extends over all the states partici- pating in the reaction. For the case in which f and the X are given by Boltzmann distributions at temperature T, k becomes the bimolecular reaction rate constant at that temperature and is expressable as L exp [-(£A + EB )/kT] (l/rrµ.)l/2(2/k!r)3/2x i,j i j f O'"i}E)E e-E/k!r dE (3) Here ZA and ZB are the internal partition functions of A and B, and EB are the internal energies of A and B in states i and EA i j j respectively, µ. is the reduced mass of the A + B system and k the Boltzmann constant. For convenience in the discussion which follows, it is helpful to consider the hy:po:thetical case in which most of the contribution of k(T) comes from relatively few internal states i, j anda- 1 j(E) is almost independent of i, those states. j for This seems to be the case for the exchange reaction between hydrogen atoms and hydrogen molecules 2 and its isotopic counterparts (at temperatures below l000°K), considered in this paper. Under these conditions, Eq. (3) reduces approximately to (4) 7 It would seem at first glance that an experimental determination of k(T) followed by a numerical solution of the integral Eq. (4) should furnish o-(E). For reactions whose activation energy Ea is large compared to kT, as is usually the case for Ea > 5 kcal/mole 0 and T < 1000 K, this method results in complete failure, and is responsible for the central difficulty in obtaining reaction cross sections from rate constants. The nature of' this difficulty can be easily understood by considering a simple model for o-(E) for reactions of the type being considered. Such a model is the hard-sphere line of center one given by o-(E)= 2 7Tb (1 - EO] for E ~ E 1 E 0 o for E SE0 (5) This cross section rises from zero at threshold energy E0 and approaches 7Tb 2 at large energies. Its important feature is that its rate of rise with E is much slower than the rate of fall of E exp(-E/k.T) for E0 >> kT. Since, to within a few kT, Ea is approximately equal to E (this result can be easily derived from 0 Eqs. (4) and (5) and the usual definition of Ea as -kalnk(T)/o(l/T)) this la.st inequality is satisfied for reactions of the type being considered. If we consider a cross section with 77b 2 of' the order of lA2 and E0 of the order of 7 kcal/mole (-0.3 eV) and a temperao ture below 1000 K, a major fraction of the contribution to the integral in Eq. (4) will come from the relatively narrow energy range of 7 to 9 kcal/mole (-0.3 to o.4 eV).7 In other words, the Boltzmann distribution of translational energies samples effectively 8 a relatively small energy range beyond the threshold energy, insofar as contributions to the rate constant are concerned. conclusion is valid independently of the validity of Eq. Thia (6), as long as u(E) can be characterized in terms of an effective threshold energy E0 such that for E < E0 it is negligible [in terms of its contribution to k(T)] and for E > E0 uE increases with energy much more slowly than exp (E/'k!r). Under these conditions / after a short range of rise, o-E exp(-E/'k!r) decays with E at a rate essentially characterized by the Boltzmann factor exp(-E/'k!r). This is likely to be the case for most reactions satisfying Ea> > 'k!r. Therefore, for such reactions, even if Eq. ( 4) were accurate, i.e., if uij(E) were independent of i and j, it would be very difficult to obtain information aboutu(E) beyond a relatively narrow range (a few kT) of E around E0 • This :point is turther discussed elsewhere. 8 . The actual dependence of °ij(E) on i and j makes the situation worse, since several of these now contribute to k(T) in relative amounts which change with temperature. An attempt at increasing the energy range over which the reaction cross section is sampled by the Boltzmann distribution by substantially increasing the temperature and therefore shifting the tail of this distribution to higher energies brings with it an increase in the number of i, j states which may contribute significantly to k(T) and hence the number of significant and unknown "i_j(E). In many thermal experiments, in addition, as the temperature is substantially increased, processes of higher activation energy than the one of interest may start contributing 9 appreciably to the reaction mechanism, making it much more di:f:'ficult to measure rate constants for the individual steps involved. Also, the rate of the reaction may increase by orders of magnitude which further increases the di:f:'ficulties of accurate rate constant measurements. For all these reasons it has not been possible in the past to obtain much information from thermal experiments about the energy dependence of reaction cross sections with activation energy much greater than kT, and there is not much hope that such information can be gotten :rrom such experiments in the future, except perhaps within a few kT of threshold for sufficiently low T. However, to understand the molecular dynamical properties of bimolecular chemical reactions and to test approximate theoretical calculations, reaction cross sections over a much wider energy range are highly desirable. 2.2. Crossed Molecular Beam Measurements An alternative to thermal rate constant measurements for the determination of reaction cross sections is the elegant and powerf'ul technique of crossed molecular beams. 4 In such experiments, the relative energy of the reactants can be maintained within a narrow distribution by keeping one of the beams at room temperature and velocity-selecting the other one. The information of greatest importance which has been derived from this technique up to the present has been the measurement of the angular and energy distribution of the products and its interpretation in terms of molecular dynamical models. For technical reasons, most 10 measurements to date have been limited. to processes whose cross sections are greater than about 10~2 a:nd/or which have essentially no activation energy (less than 2 kcal/mole). Even for such reactions the determination of the total cross sections has been made difficult a:nd unreliable due to the necessity in many instances of including the contributions of large laboratory scattering angles, not always accessible to the detectors. In addition, if the beams are produced. by thermal e:f't'usion ovens, the accessible relative energy range is relatively low. For beams of highly reactive free radicals, such as H or D atoms, it is not possible to produce acceleration by hypersonic expansion at high pressures9 due to problems of radical recombination, and the lightness of such species precludes use of the seeding technique.9 Finally, many elementary bimolecular reactions have activation energies of 5 kcal/mole or greater and reaction cross sections around tbreshold, as suggested. by thermal rate constant measurements, of the order of il2 • In addition, the reactants cannot in these cases usually be detected by surface ionization techniques. As a result of these circumstances, the crossed molecular beam technique has not been very successful in studying such processes, even at thermal energies. A particular example are the hydrogen atom-hydrogen molecule isotope exchange reactions D + ~ - DH+ H H + D2 - IID + D Early attemptslO,ll to study these reactions by crossed. non-velo- city-selected molecular beams were strongly limited by low signal 11 to noise ratios. However, a modulated-crossed beam experiment on the reaction of D with ~ has been reported12 recently in which the angular distributions of product HD were measured. However, no energy dependence measurements were ma.de. In summary, essentially no experimental information is available about the energy dependence of the hydrogen exchange reactions above :from either thermal rate constant or crossed molecular beam studies, and furthermore there are no indications that such information, in the very important relative energy range :from threshold to about 70 kcal/mole (-0.3 eV to ....3 eV), is forthcoming from these techniques. We now describe a method capable of furnishing such information. 3. FOUNDATIONS OF THE METHOD 3.1. The Integral Reaction Yield It is well known 6' 13-16 that translationally 11hot 11 hydrogen atoms are formed in the photodissociation of HX (X = I,Br) and can be distinguished from thermal ones by their reaction properties (similar statements being also valid for the corresponding deuterium and tritium isotopes). Furthermore, if monochromatic radiation is used, these atoms are initially almost monoenergetic (there is a small spread associated to the thermal translation and rotation of the parent halide molecule), their average initial laboratory energy ElO) depending only on the wavelength A of the photodissociating light. The method of studying the D + ~ 12 exchange reaction consists in photolyzing mixtures of DX (X = I,Br) and ~ vi.th monochromatic light, and in determining the integral reaction yield (8) k1 (A) + k (}\) 2 as a :f'unction of Eio)~ Here k (A) and ~(A) are the effective 1 bimolecular rate coefficients for the elementary processes D* + H 2 DH+ H [l] D*+ ~ - D + H 2 [2] describing the rates of reaction and thermalization which accompany the injection of monochromatic deuterium atoms into a thermal H2 gas. The asterisk is used to denote translationally "hot" deuterium atoms, as defined in Section 3.2. (A more rigorous definition of A, which does not invoke the concept of hot D/ is given in Section 7.) These rate coefficients depend on the energy "With which the D* are initially formed and therefore on A. The integral reaction yield is a measure of the competition between reactive collisions and non-reactive ones, and its variation with A is related to the energy dependencies of the corresponding cross sections. If information is available about the differential non- reactive cross sections, from either theoretical calculations or independent experiments, the exchange reaction cross section O"(E), averaged over the distribution of rotational states of H2 at the temperature of the experiment, can be obtained from the experimental A(Eio)) according to methods to be described in a succeeding pa.per. 'rhe present one is limited to the experimental determination 13 (ElO) ) and to giving the formal rela.tions between it of A and the cross sections just mentioned.. 3.2. Hot and Cold Deuterium Atoms During photolysis of the DX plus H mixtures, a steady state 2 is expected. to prevail. Therefore, the deuterium atoms will be characterized. by a distribution function This steady state FE(o)(E1) 1 is considerably broadened towards lower energies compared to the one at formation, due to the non-reactive collisions the D atoms undergo with the H molecules. 2 These collisions are predominantly deactivating because in all our experiments ElO) >> kT, where T There is strong reason to is the temperature of the H2 gas. believe that FE(o)(E1) will be bimodal, with one peak at the initial energy E1 (O) and the other at an energy of the order of kT, because of the thermalization process. consider We may then conceptually FEfo)(E1) as the superposition of two distribution functions, one thermal at temperature T and the other having a :peak at the initial energy ElO). The deuterium atoms described. by these two distributions will be called respectively "cold" (or "thermal") and "hot", and in the mechanism below designated. by D and D*. This conceptual classification is not essential for a quanti-: tative analysis of the experiments. In Section 7, for ins~ce, we use a Boltzmann equation formalism which does not invoke it. Nevertheless1 it is a very use:f'ul classification for a physical 14 understanding of what is happening in the system. The steady state distribution function fE(O)(E) of relative energies E of D vi th respect to H 2 'Will have a hot component peaked approximately at E(O) = (l/2)E(o) (the factor 1/2 being the ratio of the reduced mass of the D + ~ system to that of the D atom), in ad.di tion to the thermal one, as indicated schematically in Fig. 1. The cross section cr(E) of reaction [l], for one internal quantum state of H , is also depicted. We can make this hot peak "scan" cr(E) by 2 varying the photolysis wavelength. This is the essential cbaracteristic of these experiments, which distinguishes them :f'rom thermal ones in which the hot peak is absent. Fundamentally, it is this peak which permits the determination of reaction cross sections :f'rom these experiments. 3.3. Kinetic Analysis The concept of hot and cold deuterium atoms as introduced above suggests a kinetic method of analyzing the experimental data.. The validation of this method of analysis :f'rom a Boltzmann equation formalism will be given in Section 7. Let us consider the cold D and hot D* as two chemically distinct species in that their reactive properties dif'fer due to dif'ferent energy distributions. To indicate how the integral reaction yield A can be obtained., let us assume that the following mechanism is a correct description of the :processes occurring in the DX + H system 2 15 Figure 1. Schematic representation of steady state distribution function fE(O)(E) of D atom energies E and of cross section O"(E) of relative to H 2 reaction D + H 2 - (a) "thermal" peak. (b) "hot" peak. DH + H. 16 .0 b -2w.~ --w II 0 w - .g 17 D* + x DX + hv D* + H 2 IT*+~ D* + DX D* + DX D + DX H + DX H +DX X+ X + M [O] - DH+ H - D+ H - - [l] [2] 2 D +X 2 D + DX [3] (4] D2 + X -:- HD + X - (5] [6] HX + D (7] ~ + M (8] where the third body M is either a species in the gas phase or a surface. Neglect of other possible steps is justified in detail i n Section 6.2.1. As shown in that section, there is strong rea- son to believe that the atomic product of [l] is translationally hot and should be denoted by H*, requiring that we consider its reactions in the mechanism. This complicates somewhat the resulting kinetic expressions but leaves the method of determination of the integral reaction yield A unchanged. For this reason we postpone inclusion of the H* reactions to that section. Assuming steady state concentrations of [D*], (D] and [HJ , a kinetic analysis of the mechanism above furnishes (9) where (10) 18 and a= _,__k_6_ (11) k6 + ~ Therefore, we should expect [D2 ]/[HD] to be a linear function of [DX]/[~] with positive intercept and slope, as found previously by Carter, Hamill and Williams 14 and by Martin and Willard.15. This turns out indeed to be the case also in our experiments (see Section 5) and can be justified theoretically from a more rigorous Boltzmann equation formalism as will be seen in Section 7. From Eqs. (8) and (ll) we obtain ([ED]/[D2 ]) A = 1 + a + a( [ED]/~D ] ) 2 0 (12) Under the simplifying conditions above, a determination of A requires the measurement of the quantity ([HD]/[D ]) , which is 2 0 the reciprocal of the intercept of Eq. (9), and of a. This latter quantity is the exchange fraction defined as the ratio of abstraction to abstraction plus exchange yields in H + DX collisions under the cond.i tions of our experiments. These H atoms, formed by reaction [l], undergo many collisions with H _before reacting 2 with DI, especially in the limit [DI]/[H2] - 0 used in determining ([D ]/[HD]) 0 • Therefore, they should have a thermal energy 2 distribution, and k6 and ~ should be thermal rate constants. Consequently, the exchange fraction can be determined from independent thermal experiments. Eq. (9) contains a paradox. We know that if DX is ma.de suf'f'iciently small, the rate of the thermal reaction [5] will 19 become negligible compared with the rate of the thermal reaction D + H 2 - [9] DH+ D this latter occurring due to the high-energy tail of the distribution of thermal D energies. This means that as [DX]/(H ] - O 2 o, in disagreement withEqns. (9) and we should have [D ]/[HD] 2 (10). The reason for this paradox is that Eq. (9) is not supposed to be valid for [D2 ]/[HD] too close to zero, exactly because of the exclusion of reaction [9] f'rom the mechanism. If that reaction is included, we get a generalization of Eq. (9) valid down to vanishingly small [DX]/[~]: J_I)~J_ D9 (13) The curve represented by Eq. (13) goes through the origin as expected. Under conditions such that (14) Eq. (13) represents a straight line which ~ not go through the origin; it has a slope equal to that of Eq. (9) and a :positive intercept ([D2 ]/[HD]) 0 which exceeds that of Eq. (9) by the amount a(k /k1 )(k /k ). In terms of the receprocal of this cor3 9 5 rected intercept, the integral reaction yield is given by A =____ ([_HD_]_/(_D_2]_).:-o-....--.,_,, a([HD]/(D2]) 0 . (1 - ~) k3 kl k5 (15) 20 which differs :f':rom Eq. (12) by the (k /k1 )(k /k ) term in the 9 5 3 denominator of the right hand side. We show in Section 6.2 that (16) and that, as soon as the laboratory D atom energy Elo) rises slightly above twice the relative threshold energy for reaction [l], (17) The meaning of Eqs. (16) and (17) is that DX is five orders of magnitude more efficient in scavenging thermal D atoms than ~ (because of the much smaller activation and threshold energies of reaction [5] compared to that of reaction [9], whereas for relative D + ~ energies in excess of the threshold for reaction [l], the energy advantage of [3] over reaction [l] disappears and DX and H2 become about equally eff'icient scavengers of D except perhaps very close to that threshold.) Physically, the non-vanishing intercept ([D ]/[HD]) 0 is due 2 to the sma.llness of k /k , so that even a relatively small amount 9 5 of DX suffices to scavenge the D atoms which were thermalized. before reacting while hot with ~· The positive slope of Eq. (9) is due to the competition between DX and H for hot deuterium 2 atoms; the intercept excludes this competition and is therefore a measure of the contribution of the D* with H only. 2 We show in Section 6.2 that Eq. (14) is equivalent to (DX] 1 k 9 ->>-[~] Ak 5 (18) 21 The smallest A in our experiments (see Table I) is about 0.02. In view of Eq. (16), a sufficient condition for the validity of the last inequality is that (19) Since the lowest [DX]/[~] value used in our experiments was 0.1, this condition is amply satisfied. validity of Eqs. As a result of this and the (16) and (17), Eqso (13) and (15) can be replaced by Eqs. (9) and (12) respectively, justifying the elimination of reaction [9] from the mechanism. From the straight line corres- ponding to Eq. (9) we therefore get ([D2]/[HD]) 0 quite independently of what the actual behavior of [D2]/[HD] is at values of (DX]/(~] very close to zero. It is interesting to note that for sufficiently small (DX]/ (H2] (much smaller than (l/A)(k /k )] Eq. (13) represents a 9 5 straight line going through the origin with slope [ (1 - a)k1 + ~] (k k ) 5 9 I ak 3 l-a+k2] k ----------- ~ [ (1 + a)(k + k2 ) 1 l+ a 1 A(k 5 /~) (20) The term in square brackets on the right hand side of Eq. (20) is equal to the slope of Eq. (9). Therefore, the slope of Eq. (13) at the origin is more that 2000 times greater than that of Eq. (9). This means that for conditions under which the mechanism being considered. is valid, as [DX]/[H2 ] increases from zero there is a sharp rise in the [D2 ]/[HD] ratio followed by a sharp bending over at [DX]/[H ] - (l/A)(k /k ). 2 9 5 Schematically, the full behaviour 22 of Eq. (13) is represented in Figure 2. One important detail was le:tt out in the mechanism considered. A certain amount of HX impurity (about Sf, for the iodide and l'/, for the bromide) was always present. In order to correct for this, we performed experiments of DX plus He or Ne (plus the unavoidable HX impurity) similar to tb.e DX plus H2 ones. The corresponding more general mechanisms and kinetic analysis are described in Section 6.2. In summary, the method for determining the integral reaction yield A defined by Eq. (8) consists in photolyzing mixtures of DX plus R with monochromatic light and measuring the resulting 2 [D2]/[BD] ratio as a function of the [DX]/[H2] one. From this, the intercept ([D2]/[BD]) 0 is determined and used to obtain A from a modified version of Eq. (12) which corrects for the effects of the HX impurity, as determined from similar DX plus rare gas experiments. Scanning of the photolysis wavelength furnishes the energy dependence of A. 4. EXPERIME:NTAL 4.1 Ao;paratus The equipment used in these experiments consisted of four parts: (1) a high vacuum line for preparing tb.e reactant mix- tures, (2) a photolysis system, (3) a high vacuum line for the removal of the products, and (4) an analysis system. 23 Figure 2. Schematic representation of Eq. (13). clarity, the slope of the line for For [in]/ [tt 2 ) = (l/A)(k /k ) has been greatly exagerated compared 9 5 to the slope of line passing through origin. 24 ! 110 -l<t Ci) ~~ "' ' ""' -------- 25 The high-vacuum line used to :Prepare the reactant mixture was entirely mercury free, because DX reacts rapidly with mercury and also to avoid mercury-photosensitized reactions in the photolysis system. Gas pressures were measured with the help of a Pace Electronics Co. (North Hollywood, California) model P7D-O.l differential pressure transducer as a null detector balanced against a mercury manometer. The IJhotolysis system, as depicted schematically in Fig. 3, consisted of a light source system (A), a reaction vessel (B), and a light detection system (c). Different light source systems were used for different wavelengths, as follows 17: (a) For experiments at wavelengths of 3340~, 3130~, 289J.)\, 248~ and 240~ a 2500 watt Hanovia medium pressure mercury- xenon lamp was used. The output was passed through a 2:1 nickel sulfate-cobalt sulfate filter solution (20g Niso .~, lOg 4 Coso .6H.~p 4 and 1 ml 16M sulfuric acid per liter of water in a 5 cm pat.hlength cell) to remove energy in the visible and infrared, and then through the entrance slit of a Bausch and Lomb model 33-86-0l monochromator. The bandpasses used varied depending on the wavelength and are listed in Table I. At 334o~ a 5 mm thick Corning Ol6o glass filter and at wavelengths 248Ji, 2~ and 289Jl a 2 mm thick Corning 7910 glass filter were placed at ,· the exit of the monochromator to remove shorter wavelength radiation. (b) For experiments at 326Ji a cadmium Phillips spectral lamp was used in conjunction with the 5 mm Corning Ol6o glass filter. 26 Figure 3. Schematic drawing of the photolysis system. A - light source system; A - lamp; A - filter 1 2 A - monochromator; A - filter; B - reaction 4 3 vessel; C - light detection system. 27 co 28 ( c) For experiments at 253~ and 1849R a Hanovia SC 2537 low pressure mercury lamp was used. To isolate the 25371l line a , 2 mm thick lithium fluoride window irradiated with a dose of one 60 million rad of eo gamma. rays was used to remove the 253~ radiation. The absorbance of the filter was always 2.5 or greater at 2537A and o.45 at 18495\. The lamp emitted lafo 18491l radiation, so approximately lafo of all light passing through the filter was 2537R. Since the extinction coefficient of DBr at 1849~ is over 100 times greater than at 2537A the correction for the 25371l light passing through the filter is less than o.1<f,. The window tended to fade during irradiation with 2537R light and was reirradiated with Co6o gamma rays if the absorbance at 2537~ fell below ~.o. (d) For photolyses at 2300R and 3250R a 6o0o watt Hanovia high pressure xenon lamp was used in conjunction with the nickel suli'ate-cobalt suli'ate filter described previously. A 2 IIm1 thick Corning 0160 glass :filter was placed at the exit of the monochromator in the 3250A experiment. (e) At 213811 a zinc Phillips spectral lamp was used with a ~-2-butene gas filter (100 torr pressure, 5 cm pathlength) to remove shorter wavelength radiation. The spectrum of the filter taken using the Cary spectrophotometer showed that its transmission was 60% at 21385\ and less than 0.02</o at 2050R. Several different reaction vessels were used in these experiments. They were all cylindrical in shape and made out of pyrex or fused silica. The windows at each end were of optical quality 29 pyrex or quartz. The length of the vessels was about 20 cm and the internal diameter 25mm. In some experiments a teflon tube of 22 mm internal diameter was inserted in a specially constructed vessel of larger internal diameter, in order to check for surface reactions. In all vessels, a high vacuum pyrex stopcock was attached to its side to permit the addition or removal of ·reactants and products. The light beam during most photolyses was not allowed to irradiate the inner cylindrical surfaces of the vessel. Light beams coming from the Bausch and I.omb monochromator had a rectangular cross section of approximate dimensions of 19 nnn by 2 mm. However, in the experiments at 2537R and 18491{. the light beam did irradiate the inner cylindrical surfaces of the vessel. Experiments described in Section 4 show that this introduced no error. The light intensity was measured by either an Eppley thermopile or a photocell calibrated by the thermopile. A Jarrell-Ash scanning monochromator with photomultiplier detector was used to measure the wavelength distribution of the light source system output and to carefully check for light of shorter wavelength than the one desired. The bandpasses ~A) listed in Table I were determined from the :f'ull width at half-height of the photomultiplier output. The shape of this output peak was approximately gaussian. The high vacuum line for removal of products included a mercury diffusion pump, a mercury toepler pump and a cell for thermally equilibrating mixtures of ~' HD, and D2 • This cell 30 included a platinum or chromel-A filament which could be heated by passage of an electric current. The analysis system was either an isotope ratio mass spectrometer18,l9 which accurately measured the ratio of the intensities of the peaks at m/e 3 and 2, or a Consolidated Electrodynamics Corporation M:>del 21-103C mass spectrometer. A more detailed description of the apparatus can be found elsewhere. 20 4.2 Reagents The deuterium iodide and bromide were supplied by Merck, Sharp and Dohme of Canada, Ltd. 9~ for DI and 9% for DBr. The stated isotopic purity was The actual isotopic purity, as measured in these experiments, was 97°/o for the DI and 98.Tf., for the DBr. Attempts to improve this purity for the iodide, by exchange vi th purer D2 over platinized asbestos at 550°K in a care:f'ully predeuterated line were unsuccessf'u1. 20 The DI and DBr were stored in black bulbs and purified prior to use as described below. Two kinds of hydrogen were used. One was Matheson Co. pre- purified grade with a reported minimum chemical purity of 99.gfo. The other was deuterium-depleted hydrogen, with a deuterium abundance about 100 times less th.an natural abund.ance. 21 Because of the lower HD background resulting from this n , more accurate 2 measurements of the experimental [D2 ]/[HD] ratios could be obtained. The Matheson hydrogen was further purified by passage through a 31 deoxocatalytic unit (Engelhardt Industries Inc., Ga.a Equipment Division, Ea.st Newark, N. J.) and the deuterium depleted hydrogen by passage through a liquid nitrogen trap. The helium and neon used were research grade obtained from the Linde Co., with a minimum purity of 99.9gf,. Mass spectro- metric analysis on the CEC-103C showed no detectable impurities in the m/e range 12 through 6o. 4.3 Experimental Procedure 4.3.1 Preparation of Reaction Mixture Using the mercury-free line, the DX is transferred from a storage bulb to a cold finger dipped in liquid nitrogen. It is then pumped to remove any residual D2 which could have been formed from some prior decomposition of the DX, and distilled from a dry ice-acetone bath (-78° C) into the reaction vessel. This step is to remove any x which may have been formed in that same decomp2 sition. The DX pressure is measured with the help of the differential pressure transducer plus mercury manometer and cathetometer. Pressures of DX ranged from 25 to 6o torr. Hydrogen or rare gas is then added, and the pressure of the mixture measured. From the two pressure measurements, the [DX)/[H2 ] or [DX]/[rare gas] ratios are determined. They range from about 0.2 to about 1.5. Blank experiments without photolysis showed no detectable D2 and no ED above that introduced by the H • . 2 The vacuum line and reaction vessel were deuterated prior to use by exposure to DX for approximately 24 hours. They were then 32 flushed several times with clean DX and were not :f'urther exposed to air to keep them in the same condition throughout a series of experiments for which the [HX]/[DX] was determined. Separate vacuum lines were used for the DI and DBr experiments since a small amount of DI in the DBr could drastically alter the results for the latter, because the DI has a much higher extinction coefficient than the DBr in the wavelength region used and produces D atoms of higher energy by photodissociation. 4.3.2 Photolyses The intensity of the photolysis light, as determined by the calibrated photocell, varied from about 2 x 1014 photons/sec to 16 photons/sec, depending on the light source used. about 10 During a given :photolysis it stayed constant to within about l<JI,, which is suff'icient for our purposes since the results were shown to be independent of light intensity over a much wider intensity range. The photolysis .times ranged from 15 minutes to 12 hours depending on the wavelength used and the extent of conversion of the DX desired. The latter varied from O.Oli to 2.li. 4.3.3 Analysis of Products After photolysis, one end of the reaction vessel is placed in liquid nitrogen for 15 minutes or more to freeze out the DX and IDC. The noncondensible gases are then transferred on a vacuum line into a glass sample bulb 'With the help of a. mercury toepler 33 pump. When the isotope ratio mass spectrometer was used, :pa.rt of this sample was transferred. to the equilibration cell mentioned. in Section 4.1, to convert all of the D into HD. The ratio of 2 intensities of the mass spectral peaks at m/e 3 and 2 was then determined. for the equilibrated and nonequilibrated samples, as well as for a sample of H2 used. in the experiment, and from these measurements, corrections for H contributions to m/e 3 and cali- 3 bration curves the [D2 ]/[HD] in the photolysis product was determined. After these e).."})eriments were completed, it was noticed that in the analysis of the products of the DX + He photolyses there was an unsuspected contribution from the He to the peak at m/e 3. Due to this, and to the availability of the deuterium- depleted hydrogen, use of the isotope ratio mass spectrometer was discontinued in favor of the CEC-l03C one. The results with . asterisks in Table I were obtained by this method and the helium interference was approximately corrected for~ ;posteriori. When the CEC-103C mass spectrometer was used, the entire product sample in the glass bulb was analyzed. As.· previously, corrections for the n contribution to m/e 3 were made, as well 3 as for the ED contribution from the H2 gas. Also, the instrument was calibrated With mixtures of known [D2 )/[HD] ratios whose composition was analogous to that of the photolysis samples. The resolution of th.is instrument of about 1/500 permitted ad.equate separation of the m/e peaks for He and D2 • 'Reproducibility of repeated analysis of the same sample was Within z./o. 34 Photolyses were done at thirteen different wavelengths. At- each wavelength a series of DX plus H2 and DX plus rare gas experiments were performed at [DX]/[ G] ratios ( G = H2 , rare gas) vary- _ ing in general between 0.3 and i.5. In some instances this ratio was as low as 0.2 and as high as 2.0. In each series of experi- ments the reaction vessel and vacuum line were soaked in DX between runs, without being exposed to air, to keep the deuterated condition of the internal surfaces unchanged. They were then evacuated to 10-6 torr for 1 hour prior to filling. At some wavelengths as many as four different series of experiments were done over the course of several years. For each series of experiments the plot of the [D2 ]/[ID)] ratio in the products against the [DX]/[G) ratio in the reactants was always a straight line of positive slope and intercept. These two quantities and their standard deviations were determined by a least mean square fit to the experimental points. H M The intercepts are labelled ([D2 ]/[ID)]) 02 and {(D2 ]/[HD]) 0 for the DX plus H and DX plus rare gas experiments respectively, 2 M standing for helium or neon. An important quantity to correct for the effect of HX impurity in the DX in the determination of the integral reaction yield A is i::l. = ([HD]/[D2])0H2 - ([ID)]/(D2])0M (24) where the quantities in the right hand side are the reciprocals of the corresponding intercepts defined above. If there were no 35 ID:: impurity present, ([HD]/[D 2 ])~ would vanish and A would be H2 equal to ([HDJ/[D2 ]) 0 • In particular, at the phenomenological reaction threshold both A and A should vanish. The effects of dark reactions, total pressure, light intensity, oxygen impurity, extent of DX conversion, temperature and nature of internal reaction vessel surfaces close to the photolysis volume were investigated, with the following results. (a) Effects of dark reactions. In blank experiments, for which the same experimental procedure of actual experiments was followed, except that the photolysis light was not turned on, no formation of D2 or HD was ever detected. This excludes the pre- sence of nonphotochemically initiated (i.e., "dark") thermal reactions. (b) Effect of total pressure. Two reaction vessels were filled at the same time with the same DI plus H2 mixture, but the pressure in one of them was decreased. by expansion into an evacuated volume. With total :pressures of 64.9 and 36.0 torr, photolysis at 3030R :f'urnished the same [D2 ]/[HD] product ratio to within l'/,, indicating no total pressure effects over an approximate two-fold variation in pressure. (c) Effect of light intensity. Two reaction vessels were filled at the same time with the same DI plus H2 mixture and photolyzed for the same length of time at 303oi with light intensities of about 2.5 x io14 and 1.2 x io15 photons/sec respectively. The resulting [D2 ]/[HD] ratios agreed to within 'i!f,, indicating the absence of significant light intensity effects over 36 a five-fold range. (d) Effect of oxygen impurity. filled as follows. Two reaction vessels were One of them, in clean condition, was filled with a certain DI plus H2 mixture. The other was filled with 20 torr of oxygen for 6 hours and evacuated to approximately lo-4 torr. The stopcock of the first vessel was then opened for about 2 seconds allowing expansion into the second vessel. Both cells were then photolyzed under the same conditions at 303aft and the resulting [D2 ]/[HD] ratios agreed to within 3%, indicating a small m·..7gen effect. Since in our experiments no .such exposure to oxygen or air was allowed, this shows that no oxygen effects were present in them. (e) Effect of extent of DX conversion. mixtures were photolyzed at 3030R. Several DI plus H2 For eight of them the extent of DI conversion was allowed to reach 0.55%, for another six 1.2'% and a final set of six 2.11;(,. . H2 The corresponding ([D2 )/[HD]) 0 values were 3.00 +- 0.1a1 3.20 +- 0.15 and 2.·a1 +- 0.1a respectively. A similar study was performed with 3340.ft light at o.45% and o.gf, conversions furnishing intercepts equal to 2. 78 ! 0.19 and 2.62 ! 0.15 respectively. Finally photolyses of DBr at 2537ft at 0.5% and 1% conversion furnished intercepts equal to 2.70 ! 0.07 and 2.70 +- 0.03 respectively. The differences within each set of intercepts are within experimental error and show no systematic trend with extent of conversion. All our experiments were per- formed at extents of DX conversion ranging from 0.15 to 2.1%, with most of them between 0.2 and 0.7°/o, as shown in Table I. 37 Under these conditions the results are not significantly dependent on the extent of conversion. (f) Effect of temperature. Temperature dependence studies were performed for DI plus H2 mixutres at 303oft and 2537~ as follows. Two identical vessels were filled with DI plus H mix2 tures having the same [DI]/[~] ratio of 0.50 and photolyzed with 303oft light at room ( 20°c) and at dry ice (-78°c) temperatures respectively. The corresponding [D2 ]/[HD] ratios were 2.78 and 2.69. The difference between these results is within experimental accuracy. At 2537R a series of experiments with varying [DI]/(H ] 2 ratios were performed. at dry ice and at room temperature. The corresponding straight lines of [D2 ] /[BD] versus [DI]/[H2 ] had intercepts of 1.38 ! 0.15 and 1.45 ! 0.07 and slopes of i.76 ! 0.09 and 1.57 ! 0.06 respectively. experimental error. The intercepts are equal within We conclude that no temperature effects on ([D2 ]/[HD] )~ are detectable in the -78°c to 20°c range. We also conclude that it is unnecessary to keep the reaction vessel thermostated at room temperature, since small temperature variations :from day to day or during an experiment should not, within our experimental accuracy, alter the results. (g) Effect of teflon lining and nature of the reaction vessel. It is conceivable that some of the species generated in the light beam region could diffuse to nearby walls and undergo heterogeneous reactions. To test for such effects, we compared the results obtained for reaction vessels lined with a teflon tube insert with those for unlined vessels and also the results obtained. 38 with both quartz and silica reaction vessels. Since using differ- ent reaction vessels may a.:f:fect the amount of HX impurity formed as a result of exchange of the DX with the surfaces to which it was exposed, the quantity 11, defined by Eq. (18) above, is the important one to consider. The values of ([HD)/[D ])~2 and He ([HD]/[D2 )) 0 for photolysis of DI and H2 mixtures at 3030~ were 0.364 ! 0.013 and 0.100 :!: 0.003 for a lined pyrex vessel and 2 O. 420 :!: O. 032 and O.150 :!: O. 006 for an unlined one leading to /), values of 0.26 :!: 0.01 and 0.27 :!: 0.03 respectively. Experiments were done a year earlier comparing lined pyrex and silica vessels. T'ne A values were 0.22 :!: 0.02 for the pyrex vessel and 0.20 :!: 0.01 for the silica one. At 3340~, which is close to the phenomenolog- ical threshold for A and A, the A values were 0.053 :!: 0.014 for a lined pyrex vessel and 0.10 :!: 0.03 for an unlined one. At 2537~ DI-H2 photolyses were done comparing lined and unlined silica vessels. The A values were o.64 :!: 0.02 for the lined silica vessel and 0.67 :!: 0.02 for the unlined one. The results for DBr- H2 photolyses show less scatter than those for DI-H2 indicating that the nature of surface is less important for DBr. Hence we conclude that a small surface effect may exist near threshold, but that at higher energies it should not significantly alter the value of A. (h) Effect of irradiating the sides of the reaction vessel. Photolyses of DBr-R:2 mixtures with (DBr]/[~] = 1.46 were done using 3 low pressure mercury lamps with different geometries. The first lamp was the Ha.nivia SC 2537 lamp which sent out a 39 divergent beam of light initially l inch in diameter which irradiated the windows and also some of the inner cylindrical surface of the reaction vessel. The second lamp was a General Electric germicidal lamp which was placed so it irradiated the sides of the vessel. The third lamp was a low pressure mercury Phillips spectral lamp with a light area approximately l inch high and 1/2 inch across which irradiated only the windows of the vessel. The (HD]/[D2 ] ratios obtained were 0.240, 0.245 and 0.250 respectively. This is within the experimental error of the experiments indicating that light hitting the inner cylindrical surfaces of the reaction does not alter the results. Illustrative examples of lines of [D2 ]/(HD] versus [DX]/[G] are given in Figs. 4 and 5. The ones in Fig. 4 correspond to photolysis of DI mixtures at 3340R and :furnish A =0.053 ! 0.015. The ones in Fig. 5 correspond to photolysis of DBr mixtures at 213~ and furnish A= 1.32 :!: 0.05. The results of all experiments together with the experimental conditions are summarized in Table I. Column 1 gives the central photolysis wavelength, column 2 the wavelength range (full width at half maximum), column 3 the substance photolyzed, columns 4, 5 and 6 the initial laboratory velocity, initial laboratory energy with associated spread and initial energy relative to stationary H2 of the D atoms produced in the photodissociation (calculated as described in Section 6.1), column 7 the extent of the DX conversion, column 8 the ratio of molar extenction coefficients of HX and DX as described in Section 6.3 and column 9 specifies the nature of the reaction vessel. 40 Figure 4. Plot of [D2 ] / [ HD] versus [DI]/[G] at A = 3340~. He line: intercept= 3.34 ! 0.12; slope = 0.90 ! 0.20 H line: 2 intercept= 2. 83 ! 0.06; slope = 0.69 ! 0.07. 41 Cl) C\I :c :c o e 0 e . \ ,........., ~ (.9 '---' \ ' ,........., ..__. 0 0 '---' LO 0 42 Figure 5. Plot of [D2] /[HD] versus [DBr]/[G] at A =. 2138~. He line: intercept= 29.1 : 0 .2; slope = 2.8 ,: 0.2 H2 line: intercept = O. 74 :!: 0.03; slope = 0.91 :!: 0.03 43 o He @H 2 32 31 i..-------- ~ f/fJ_. -. A-e-------@•- - e---...- ~ 1.5 0.5 (DBr]/(GJ 1.0 44 TABLE I. AX. >..(){) (R) Summary of ResuJ.ts for D + H 2 Substance Photolyzed Initial La.boratory Velocity (105cm/sec) Initial laboratory Energy (eV) Initial Relative Energy (ev) 4.5a 3340 ~~a DI 7.72 0.622 :t 0.023 0.311 3261 le le DI 8.27 o. 714 :!:: 0.018 0.357 3251 3oa DI 8.33 o. 724 :t 0.053 0.362 3130 16a 16a 32b DI 9.u o.866 :!: 0.038 o.866 :!: 0.038 o.866 :t 0.058 o.433 3030 l0.3a 10b3a 32 io.3a DI 9.79 1.000 = 0.031 1.000 :!: 0.031 1.000 :!: 0.058 1.000 :!: 0.031 0.500 2891 lla DI 10.66 1.182 ± 0.038 0.591 2537 le le DBr 10.19 1.084 ± 0.024 0.542 2500 33a DBr 10.52 1.154 ± 0.087 0.577 2483 24a DBr 10.66 1.186 ± 0.072 0.593 2446 34a DBr 10.99 1.260 ±. 0.090 0.630 2300 . 22a DBr 12.36 1.594 ± 0.081 o.8<J7 2138 le DBr 13.75 1.973 ± 0.024 0.986 1849 le DBr 16.54 2.856 ± 0.024 1.428 width at half' height of peak band.pass of monochromator c. line source - no monochromator a. b. 45 TABLE I (continued) Reciprocal Intercept H A,(A) (~) x=DX Nature of Reaction Vessel 3340 0.15 - 0.56 o.45 + 0.9 0.02 12 :!: l lined pyrex 0.353 ± 0.008 0.355 ± 0.014 0.362 ± O.Oll 3261 0.18 + 0.36 7.4 :!: 0.3 0.27 - o.49 lined pyrex 0.353 ± 0.019 0.292 ± 0.026 Extent DX d Conversion 0 RX ([HD]/(H2])02 3251 o.46 7.0 :!: 0.08 lined pyrex 0.326 :!: 0.021 3130 0.39 - 1.9 0.38 0.10 3.85 :!: 0.07 lined pyrex 0.279 ± 0.012 o.zro = 0.008 0.280 ± 0.004 3030 1.0 - 3.0 0.61 0.2 0.55 + 1.2 2.54 :!: 0.07 lined pyrex 0.303 ± 0.012 0.364 ± 0.012 0.325 ± 0.012 0.326 ;!; 0.012 2891 0.5 i.72 ;!; 0.03 unlined silica o.420 ± o.oo6 2537 0.7 0.50 + 1.0 6.7 ± 0.3 unlined silica o.423 ± 0.00'7 0.370 ;!: 0.005 2500 0.25 5.4 ± 0.1 unlined silica 0.399 ± 0.009 2483 0.35 4.9 ;!; 0.1 unlined silica o.476 ± 0.014 2446 o.40 4.19 :!: o.o8 unlined silica o.485 ± o.o66 2300 0.20 2.39 :!: o.o4 unlined silica 0.896 :t o.o64 2138 0.50 1.47 :!: 0.02 unlined silica 1.36 ± 0.13 1849 o.4o 0.78 :!: 0.01 unlined silica 3.22 ± 0.13 d. If' A - B means variable conversion between limits If A + B means conversion study at conversions listed. 46 TABLE I (continued) Slope of DX-H2 Experiments Reciprocal Intercept a= [HX] ([HD]/[R2))~e Slope of DX-He Experiments 3340 0.74 :!: 0.06 0.69 :!: 0.074 1.03 :!: 0.05 0.300 ± 0.011 0.308 ;t 0.011 o.296e 1.1 ± 0.2 0.9 ± 0.2 1.8 :!: 0.2 0.020 0.018 0.023 3261 1.4 ! 0.3 1.5 :!: 0.3 0.299 ± 0.012 0.187 :!: 0.013 o.8 ± 0.3 o.6 ± 0.3 0.023 0.021 3251 1.0 :!: 0.2 0.197 +- o.oo6f 1.0 ± 0.2 0.021 0.135 :!: o.008 0.130 ± 0.006 o.15oe 1.0 ::!: 0.7 3130 1.3 :!: 0.2 1.5 ::!: 0.2 1.5 :!: 0.1 1.3 :!: 0.5 4.1 :!: 0.2 0.020 0.023 0.021 3030 1.30 ± 0.10 2.00 ± 0.07 1.56 ± 0.05 1.44 ± 0.11 0.092 :!: 0.003 0.100 :!: 0.003 o.151e 0.107 ;t 0.003 2.4 ::!: 0.5 3.0 ± 0.5 3.4 :!: 0.5 o.4 ± 0.5 0.021 0.019 0.023 0.023 2891 1.87 ;t 0.03 + 0.072 - 0.004 2.0 ± o.8 0.019 2537 1.32 ± 0.05 1.25 ± 0.05 0.098 ± 0.001 0.074 ± 0.002 2.0 ! 0.1 1.1 ;!; 0.5 0.012 0.012 2500 o.88± o.08 0.062 ± 0.001 1.5 ± 0.5 0.012 2483 1.45 ± 0.07 0.075 ± 0.0003 2.2 ± o.6 0.013 2446 1..18 ± o.o4 0.061 ± 0.001 2.9 ± o.6 0.013 2300 1.09 ± 0.08 o.0402 ± o.0004 2.1 ± o.4 0.012 2138 0.91 :!; 0.03 0.034 ± 0.0006 2.8 :!; 0.2 0.013 1849 o. 73 ± 0.02 0.025 ± 0.0004 0.1 ± 1.0 0.013 A.(~) e. f. [DXj · Isotope ratio mass spectrometer measurements approximately corrected for He interference {see text). Ne used as rare gas. 47 TABLE I (continued) A A (a. = 0.96 :!: 0.04) (a = 0.93 :!: 0.03) A(i) f:,. A 3340 0.053 :t; 0.015 o.o42 ± 0.015 o.o66 ± 0.015 0.025 ± 0.007 0.020 ± 0.007 3261 0.054 ± 0.022 0.105 ± 0.028 0.025 ± 0.010 o_.050 ± 0.013 3251 0.129 ± 0.025 0.060 ± 0.011 3130 0.149 ± 0.013 0.135 ± O.Oll 0.130 ± 0.010 0.070 ± 0.006 0.064 ± 0.005 o.o62 ± 0.005 3030 0.210 ± 0.01 0.264 ± 0.01 0.174 :!: 0.01 0.219 ± 0.01 0.098 ± 0.005 0.120 ± 0.005 0.080 ± 0.005 0.101 ± 0.006 2891 0.345 ± 0.007 0.154 ± 0.006 2537 0.325 :!: 0.007 0.295: 0.006 0.133 : o.oo4g 0.123 :!: o.005g 0.135 ± o.oo4 0.137 ! o.oo4 0.125 ± 0.005 0.127 ± 0.005 2500 0.337 ! 0.010 0.140 ± o.005g 0.143 :t 0.005 0.145 :t 0.005 2483 o.401 :!: 0.015 0.161 :!: o.oo6g 0.164 :!: 0.006 0.167 :!: 0.007 2446 o.425 :!: 0.006 0.170 ± o.oo4g o.i73 2300 0.29 ± O.Olg 0.30 ± 0.01 0.31 ± 0.01 2138 - o.o4 + 0.05 1.32 - 0.39 ± O.Olg o.4o :t 0.01 o.41 ± 0.01 1849 3.2 :!: 0.1 0.61 ± o.02g 0.63 ± 0.02 0.65 ± 0.02 g. 0.85 + A(a = 0.99 :!: 0.03) ;!; 0.005 0.177 ± 0.005 48 Columns 10 through 13 give the reciprocal of' the intercepts and the slopes of the [D2 ]/[RD] versus [DX]/[G] lines, column 14 the impurity ratio [HX]/[DX] determined as described in Section 6.3, column 15 the A value def'ined by Eq. (8) and finally columns 16 through 18 the values of A calculated as described in Section The results of the DBr plus H2 experiments at 1849A can be compared with those of Martin and Willard. 15 They correct for the BBr impurity by a slightly different technique than ours (i.e., by subtracting [RD]/[D2] determined from 11 pure 11 DBr photolysis as compared. to our DBr plus rare gas mixtures), but this correction is of the order of a few percent only both in their and in our experiments, and therefore a comparison is meaningful. Their corrected ([HD]/[D2 ] )0 is 3.2 ! 0.1 whereas our (i.e.,~) is 3.2 ! 0 0.1 • This excellent agreement is very gratifying. 3 Inspection of the columns of Table I giving ([HD]/[D ])~, 2 M ((HD]/[D ]) andA shows that the effect of the HX, even though 2 0 this impurity amounts to only a few percent of the DX, is a major one in the case of DI. The reason is that in the wavelength region used, the ratio of molar extinction coefficients EHI/e DI is greater than unity, tending to favor the absorption of light by the HI. The reason for this is discussed in Section 6.1. If we take 3340~ as an extreme example, even though the [HI]/[DI] ratio may be only 0.03, its product by EHI/EDI is 0.36, i.e., about 26.5% of the light absorbed is absorbed by the 3% HI impurity. A second magnifying factor is that at such a. long wavelength (i.e., low 49 initial D atom energy) a relatively small fraction of the D* atoms is expected to react with~ to form HD, whereas a large fraction (of the order of unity) of the H* atom formed by the photodissociation of the HI is expected to react with DI after thermalization giving ED. A combination of these two effects is res:ponsible for the relatively large ((HD]/[D2 ]) M values in spite of the 0 relatively small (HX]/[DX] ones, indicating that care must be ta.ken to correct for this effect appropriately. How this is done is described in Section 6.2. The errors in some of the slopes of the plots of [D2 ]/[HD] versus [DX]/[G] are large, as indicated in columns 12 and 14 of Table I. This is particularly true in the DX-He experiments. However, the scatter which leads to the large error in these slopes does not lead to a corres:ponding large error in the intercepts in which we are interested. For instance, in the case of DBr-He at 1849R which is the worst case the [D2]/[HD] ratios were of the order of 40. Hence a large error (r..1ooo],) in the slope led to only a 2.5'fo error in the intercept. Also as the wavelength decreases, the intercept of the helium experiments contributes less to fl. Hence a large error in the intercept of the helium experiments can occur without leading to large errors in fl • 50 6. 6.1 DETERMINATION OF INTEGRAL REACTION YIELDS Initial Energy of Photochemically Produced Deuterium Atoms Because of its central role in these experiments, we will discuss the basis for knowledge of the initial laboratory translational energy of the D a toms in some detail. The absorption spectra of the hydrogen halides have been measured by several workers. 22 Measurements of HBr, DBr, HI and DI were repeated in this laboratory23 and used to obtain the ratios of molar extinction coefficients (21) x = [IIX]/(DX] listed in Table I. Mulliken24 has made a theoretical analysis of the lower lying electronic states in the hydrogen halides. He concludes that the only three important transitions from the 1 'Z+ ground state are to the 3I!i_, 1Ir, and n0 states. He designates these states as N, 3Q.1 , ~ and Q , respectively. The :potential energy 0 curves that he deduced for DI (or HI) are shown in Figure 6. The curves for DBr should be analogous. The Q0 state 2 . . dissociatesto give ground state D and excited P ; iodine atoms. 1 2 At wavelengths longer than 307cfA in DI and 271cit in DBr, it is energetically :possible to form only ground state 2 P ; halogen 3 2 atoms. At shorter wavelengths both ground state and excited halogen atoms can be formed. The first excited state of the deuterium atom is at 10.2 eV. and cannot be' produced with the wavelengths used in these experiments. 51 Figure 6. Potential energy curves for HI. 52 80 70 60 - '°I0 x I 50 40 E ~ 30 > 20 10 53 The initial kinetic energy of the deuterium atom can be calculated if the final electronic states of the atoms formed by the dissociation of DX are known. If only grotmd state atoms a.re :formed, the energy available for products is Et = Ev - Dg (22) where Ev is the energy of a photon of frequency v and Dg is the dissociation energy of the grotmd vibrational state of DX. The fraction of this energy which goes to the deuterium in the center of mass system of DX is mxf~x· When we add the small contribu- tions due to rotation and translation of the DX, the following expression for the average initial laboratory energy Elo_) o:f' the D atoms is obtained: (o) El = m.._ ( ) ~ !:.£ - n° ~x A. o + m L Innx (E rot ) + m _p_ Ir ) ~x \"-DX (23) where (~x) and (Erot) are the average room temperature laboratory translational and rotational energy of the DX molecules. Over the wavelength range of these experiments, the first term in the right hand side of Eq. (23) varies 1'rom o.60 eV to 1.16 eV :for DI and 1.06 eV to 2.84 eV for DBr. The second term is 0.020 eV :for DI and 0.025 eV for DBr and third one is correspondingly 0.0006 eV and 0.0010 ev. Since the photolysis light used is not completely monochromatic, and since the translational and rotational energies of the DX have thermal spreads, the D atoms formed with average energy (o) E1 · are characterized by a distribution :function which can be calculated :from the wavelength distribution in the photolysis 54 light, the wavelength dependence of the DX absorption coefficient and the Boltzmann distribution of its translational and rotational energies. However, a qualitative description of this distribution is contained in the spread 6ElO) defined as the root mean square of the spreads of the three terms in the right hand side of Eq. (23), each one of these being associated to an interval containing 7Cf!f, of the corresponding molecules. For DI, the spreads in the second and third terms in the right hand side of Eq. (23) are 0.018 eV and 0.00045 eV, respectively, whereas for DBr they are 0.025 and 0.0007 eV. In column 5 of Table I are given the values of (o) (o) E1 + t:.E 1 , these intervals including approximately 7C/fo of the initial D atoms. At wavelengths shorter than 307o1t in DI and 271oR in DBr photolyses the formation of electronically excited 2P / halogen 1 2 atoms is allowed energetically and we may expect D atoms of two different initial energies to be formed; one given by Eq. (23) and the second by a similar equation obtained by replacing by (D~ + E( 2P ; )). 1 2 2 of the P1; 2 state. Dg E( 2P / ) is the electronic excitation energy 1 2 For all but two wavelengths used to disso- ciate DI the 2P1; 2 state of I is not accessible. However, in the case of DBr it is energetically possible to form Br( 2P / ) at 1 2 every wavelength used. Satisfying the energy criterion is a necessary but not sufficient condition for the formation of excited halogen atoms. In principle the oscillator strengths of the various transitions and the details of the dissociation process (for example, the influence 55 of curve crossing) must be known in order to properly evaluate the extent of the excited halogen atom formation. We sunnnarize here what is known about the oscillator strengths. Little is known about the influence o:f the curve crossings shown in Fig. 6. Figure 7 shows plots of the molar extinction coefficient ratios EDI/EHI and EDBr/EHBr versus wavenumber. There is some structure in the plot o:f EDI/~HI while there is none in the case of the bromides. The structure is attributed to the presence o'f the ~ - N transition, in ad.di tion to the 3Q1 - N one. The absence of structure for the bromides suggests that a second transition is at most very weak. Mullikan24 predicts theoretically that the %- N transition will be 15 to 20 times less intense in HBr than in HI, and that consequently the number of excited bromine atoms formed will be small. Donovan and Husain 25 have used flash photolysis of HI and RBr in the ultraviolet and vacuum ultraviolet to determine the :fraction of iodine or bromine atoms formed in the excited state. Using a continuous source they observed approximately 2C11/o excited iodine atoms in the flash photolysis of HI at wavelengths longer than 2oooR. They observed no excited bromine atoms in the flash photolysis of RBr when wavelengths greater than 200~ were used but saw a weak spectrum of excited bromine atoms when the wavelengths extended down to 185~. From the above observations and arguments we conclude that only ground state deuterium and bromine atoms are important dissociation products of DBr except at wavelengths shorter than 2000R where small amounts of excited Br atoms may be formed. In ad.di tion, 56 Figure 7. Molar extinction coefficient ratio as a function of wavenumber. 57 0 00 0 "- ........ CD II 0 0 0 II xx ® 0 0 00 0 @ 0 0 0 0 0 0 0 00 0 0 0 0 'Q" 0 0 0 'E (.) rt) I 0 x I~ -0 . co d <D d -xx :c -0 \U \U "'d 58 since for the iodides the structure in Fig. 7 is very small for 1 less than 34600 cm- , we conclude that between 3070<;.. and 2890~ the amount of excited iodine atoms from the photodissociation of DI is unimportant. The 11 = 0 state of DX has been assumed as the absorbing state in the El.ab calculations. Absorption by the 11 = 1 state of DI would :furnish D atoms with 0.20 eV more energy than given in Table I. The 11 = 1 state will be most significant at long wave- lengths (3340A) where it makes the largest relative contribution to the total absorption and to the initial laboratory energy of the resulting D atom. We show below that under all our experi- mental conditions absorption by this state can be neglected. The population ratio N ll=l/N :v=o is 4 x lo- 4 at 20° C for the vibrational energy level spacing of 1630 cm- 1 • Simple theore- tical calculations described below indicate that the ratio of extinction coefficients for these two states at 334oli is about 12. Hence the ratio of absorption by molecules in the first excited state and in the ground state is approximately 5 x io-3. There- fore, at this most unfavorable wavelength, about 99.5% of the D atoms are formed with a lab energy around 0.62 eV and about o.5<fo with a lab energy around 0.82 eV. The effect of the latter may be ignored in view of the results of Fig. 8, to be described and discussed in Section 6.5. The calculated extinction coefficient ratio e 1/c 0 = 12 for the two vibrational states is approximately equal to the ratio of lo/Ji/lo/I~ of the square of the absolute values of the harmonic oscillator wavefunctions evaluated at the 59 internuclear distances which result in absorption of 3340A light. This ratio is an approximation to a more exact expression which includes also the wavefunctions of the photo-produced repulsive upper state. The approximation is discussed by Coolidge, James and Presa.1t26 and by Herzberg27 and has been used by Goodeve and Taylor22a to analyze the spectra of HI and BBr. Using harmonic oscillator wave functions it leads to 2 2 2 2ay1 exp[a(y0 - y1 )] (24) 2 where a= µ.w 0 /n = 96.51( and y = r 1 - r 0 is the displacement of 1 ~1 ;~ 0 = the internuclear distance r. for state i (i = 0,1) from the equilJ. ibrium value, corresponding to absorption of photons of the frequency ll for which ,; /t: 0 is being obtained. To calculate 1 y1 (v) it is necessary to have expressions for the lower and upper electronic state potential energy functions. For the former we took a quadratic potential corresponding to the observed vibrational spectrum of HI and for the later an exponential function of the -GX form 21 = DO • 0 + Ee The parameters E and G were determined by fitting the calculated DI absorption spectrum to the observed one we observed, yielding 13, 400 cm -1 and 3.1 Ao-1 , respectively. For 334o1l this resulted in y0 = o.32J.i, y1 = 0.126.R and E 1 /e 0 = 11. 7. A similar calculation using a linear function for the upper state potential gives ~ 1 / E 0 = 17. 28 In summary, in the totality of experiments here reported, electronically excited I or Br atoms are either completely absent or present in negligible amounts, and the effect of light absorption 60 by vibrationally excited DX molecules is also negligible. Equa- tion (23) furnishes the average laboratory energy of the D atoms at formation, given in Table I, column 5 together with its spread. 6.2 Mechanisms and Kinetic Analysis In Section 3.3 we have already considered a simplified mech- anism for the :photolysis of DX + H2 mixtures. In this section we justify the neglect of certain other conceivable elementary steps a.nd extend the kinetic analysis to the DX + HX + H and 2 DX + HX + rare gas systems made necessary by the unavoidable presence of small amounts of RX impurity. 6.2.1 The DX + H0 System -r:- The kinetic analysis given in Section 3.3 has shown that in the mechanism given by reactions (l] through (9), the thermal reaction (9) can be neglected as long as relations (16) and (17) can be justified a.nd (18) shown to be a sUfficient condition for the validity of (14). Let us now show that this is indeed the case. (a) Validity of Eq. (16). decomposition of DI + r 2 constant of the reaction From studies of the thermal mixtures, Sullivan29 determined the ·rate I + D2 - DI + D (10] to be 1.9 x 103 cm.3 •mole -1 .sec -1 • From this value and a simple statistical thermodynamic calculation of the equilibrium constant 61 betw"een the two sides of this equation, we determine the value of the rate constant of the reverse reaction D + DI - D + I 2 to be 1.4 x 1013 cm3.mole-1 .sec-1 • (11] Sullivan30 has also shown that the activation energy for the reaction R + HI - [12] H + I 2 is zero and inferred that the activation energy for reaction (11] should also be zero or very close to zero. Therefore, we conclude that 297°K k (which is the same as k for X =I) should be 11 5 13 1 3 1.4 x io cm .mole- .sec-l also. From the data of Ridley, Schulz and LeRoy,3 1 the value of k at 297°K is 2.08 x 108 cm3.mole-l.sec-1 , whereas from that of 9 Westenberg and de Haas 32 it is 1. 61 x 108 cm3 .mole -l. sec -l. The value of the k /k ratio at 297°K, for X = I, is therefore of the 5 9 order of 105, as given by Eq. (16). (b) Validity of Eq. (13)e Previous information about the hot atom reaction D* +DI - is not available. (13] D2 +I However, we may infer something about its cross section from the lack of temperature dependence of the rate constant of its thermal counterpart, reaction (11]. This implies that the cross section for this reaction has a threshold energy smaller than kT (which at 700°K is 0.06 eV), and it may even be zero. It also implies that over the energy range sampled by a thermal Boltzmann distribution, it does not depend strongly on energy. If, for example, it were inversely proportional to 62 relative energy and independent of the internal DI states partici:pating in the reaction, i.e., if v(E) = u . . (E) = C (25) 1J with C a constant independent of E, i and j, Eqs. (1) and (2) would furnish k =c (26) for any distribution functions f including thermal ones. This means that Eq. (26) predicts a thermal rate constant rigorously independent of temperature. If, on the other hand, uij , were equal to a constant u(ll) independent of energy and of the internal states of the participating DI, Eq. (3) would fUrnish k11 (T) = u(ll) (~) 1/2 which has a T 1/2 µ. temperature dependence, but which (27) in an Arrhenius plot over a temperature range of a few hundred degrees absolute would furnish an activation energy indistinguisable from zero within experimental accuracy. Since assuming u(l3) (E) to be constant will furnish a larger ~ 3 than assuming u(l3)(E)v(E) to be constant, and since according to Eq. (17) we are interested. in establishing an upper limit for k /k , we will use the former 13 1 assumption and Eq. (27) to estimate k • Replacement of uij(E) 13 3 by the constant u(l ) into Eqs. (1) and (2) furnishes k13 = o-(13) (v) (28) where (v) is the relative velocity averaged over the distribution function of relative hot atom energies. Since, as discussed in Section 3.2, the distribution function of laboratory D energies should peak at the initial laboratory energy Eio), and since 63 (~/~I) << l, we have k ,... 13 CT ( 11) ( 2E ( 0 ) ) l/2 1 (29) Inn In order to estimate k , we may use the c:r(E) values obtained from 1 ) the trajectory calculations of t.he type reported by Karplus, Porter and Sharma. 2 The cross section c:r(l) for reaction (l], averaged over the distribution of' ~ rotational states at 300°K, sbows33 a threshold relative energy of about 2.29 eV, and values of about 0.1, 1.0 and 1.7 ~ at energies of 0.31, o.6 and 1.2 eV, respec2 tively. From Eqs. (1) and (2) we may write (30) where u(l) is the rotationally averaged cross section just described and (v(l)) is t.he relative velocity of D wit.h respect to H2 averaged over the hot atom distribution function of relative energies. As for the D + DI case we write (l) (v [ 2Elo) ) "" ( 1/2)~ ] 1/2 (31) From Eqs. (29) through (31) we get kl 0"(1) -kl3 ,... h o-\13 -rz-;;) (32) Because of the assumed energy independence of o-(l3) it is equal to cr(ll). From Eq. (27) and the value of k we get o-(l3) = 0.5 11.2 • (700°K) given above 11 However, if the cross section of reaction [13] increased from 0.511.2 at thermal energies ~0.05 eV) to a few times that value at energies of the order of l eV, this would 64 probably not change the values of the experimental k11 (T). The important point, however, is that in view of the absence of long range forces between D and DI, there is no reason why O"(l3) should ever exceed a few ~2 • On the other hand, as mentioned above, O"(l) varies :from 0.1 to 1. 7 .R2 as the D atom energy relative to ~ varies from 0.02 eV above threshold to 1.2 eV, corresponding to laboratory energies of 0.62 to 2.4 eV approximately. Therefore, in this energy range k /k exceeds 0.28 if we use the 0.5 R2 for 1 13 O"(l3); if we use instead a very conservative upper limit of 5 ~2 , k 1/k 13 is larger than 0.028 which justifies Eq. (17) for X = I. The important point is that in the energy range of interest the cross section for reactions [l] and ( 13] should not differ by more than about one or (closer to the threshold of [l]) two orders of magnitude, and therefore k1 and k than that. (c) 3 can also not differ by more A similar arguments holds for X =Br. Validity of Eq. (18). The condition (14) of Eq. (13) to represent a straight line with a positive intercept can be written as [DX] [~] >> l k9 Ak 5 l ~~~~~~~-- l - (k4/k1 )(k /k5 ) 9 (33) This is equivalent to Eq. (18) if (34) That this inequality is indeed satisfied results :from the following facts: l) k4/k2 is smaller than unity since D* atoms are therma- lized much more efficiently by H2 molecules than DI ones because 65 of the better matching of' collision partner masses; 2) throughout our experiments A exceeds 0.02 (qee Table I) and therefore, as a result of Eq. (8), k2 /k is smaller than 50; 3) from Eq. (16) 1 k /k ,.... io-5. As a result, the left hand side of Eq. (34) is 9 5 smaller than 5 x io- 4 and this inequality is satisfied, making (18) valid for X = I. Similar arguments hold for X = Br. We have now completed the justification of the neglect of reaction [9). Since halogen atoms are formed in the initial photodissociation of the halides as well as in reactions [3], [5] and (6], consideration must be given to steps involving these atoms: - X + H 2 X +DX X* + H 2 (14] HX + H - (15) - [16] x2 + D X* + DX - [17] Reaction (14] has an activation energy of 33 Kcal/mole3 4 and 19 Kcal/mole35 for I and Br, respectively. The X + HX counter- part of reaction [15] has an activation energy of 36.5 Kcal/mole3 6 and 41.7 Kcal/mo1e 35 for I and Br, respectively. these reactions is therefore [14] for X = Br. its rate with that of reaction [8]. The fastest of We must compare The lifetime of Br atoms with respect to reaction (14] is (k14 [H ])-1 , which is about 25 2 hours for 100 torr of R2 and ~ = 2 x io-3 liter.mole-1 sec-l. 4 This is several orders of magnitude in excess of the lifetime with respect to reaction [8] under our experimental conditions. Indeed, the ratio of the rates of reactions [8] and [14] is about 66 1/2 (k /k14 )(I0 Enx/AN) 8 1/2 ([DX]/[H2 ]) 1/2 as can be seen by estimating the steady state concentration of X atoms from reactions [O), [5] and [8] and talcing M to be [H2 ]. In the preceding expression, I 0 is the intensity of the photolysis light beam, A its cross-sectional area, EDX the molar extinction coefficient of DX and N Avof!jJ.d:ro 's number. Assuming k8 to be of the order of 1010 liter.mole-2.aec-1 ,32 4 that ratio exceeds 10 under all of our experimental conditions. Therefore, we are justified in neglecting reactions [14] and (15] in our mechanism. We also calculate that reaction [8] itself occurs partly in the gas phase and partly on wall surfaces. This is in agreement with the experimental finding that in the DI experiments vi.th teflon-lined vessels, if after a few tens of hours of photolysis a cross-sectional cut is made through the cylindrical teflon sleeve, a purple ring, attributed to iodine, appears near the inner surface. In reactions [16] and (17] the asterisk denoted translational excitation, since as pointed out in Section 6.1 electronically excited X atoms from reaction [O] are unimportant under our experimental conditions. The fraction of the excess of the photon energy Ev over the DX bond dissociation energy ng which is given to the X atom (in the DX center of mass system) is Innlinnx• For a stationary DX and ~ this leads to a X + H relative energy of 2 2 (ID:o/~X) (Ev - D~), which ranges from about 1.4 x lo-4 eV to about 1.6 x io-3 eV in our experiments. These values are small compared With average room temperature thermal energies of 3.9 x 10-2 eV, and we can therefore neglect reaction [ 16]. For X + DX collisions 67 the corresponding energies range :from 0.46 x lo- 2 eV to 3.3 x io-2 eV, which are not negligible compared to average thermal energies. For the highest energy, the total average relative energy due to the thermal motion of the DX and the translational hotness of the Xis then about 7.2 x lo-2 eV. A thermal distribution of relative energies having this average value would correspond to a temperature of about 550°K. The rate coefficient for reaction [17) will therefore not exceed that of reaction (15) taken at 550°K, since .· it is tb.e high energy tail of tb.e distribution fU.nction of rela·tive energies that contributes to the rate coefficients, and the one for reaction [15] at 550°K should be much more important than that for energy. [17] with hot X of equal total average relative Since the activation energy of [15] exceeds · 33 Kcal/mole, we conclude that k 17 is less than 7 x 1010 times k (300°K). 15 The activation energy of reaction [14] for X = Br is less th.an that of reaction (15] by at least 14 Kcal/mole and therefore Br o 10 o Br ~4 (300 K) > 1.6 x 10 k (300 K). As a result, k17 < k14 15 (300°K) and since, as shown in the previous paragraph, k14/ka is less th.an 10-4 under all our experimental conditions, k is 17 negligible compared to k8 , and we may therefore also eliminate reaction (17) from our mechanism. We next consider reactions D + ~ - DX+ X (18) H+ ~ - HX+ X (19) The ratios of their rates to those of reactions (5) and [6] are respectively 68 ~= ~ [X~J r k5 [DX] 5 (35) rl9 = klQ [X2] r 6 (36) k6 [DX] The halogen molecules are in general much better scavengers for The k18/k and 5 k /k are approximately equal to each other and independent of hydrogen atoms than the corresponding halides. 9 6 temperature and have values of 22. 737 for X = Br and 12 to 1738 for X = I. In order to minimuze the scavenging of H and D atoms by halogen molecules, we kept the :fractional conversion c of the DX into products as low as possible. The [~)/[DX] ratio at the end of an experiment is c/2 if adsorption of ~ on walls is ignored, and its average value throughout an experiment is c/4. The r 1 8/r and r /r ratios for small conversions are then approximately 19 6 5.5 c for X = Br and 3.5 c for X = I. As seen from Table I, c had values ranging from O.z:/:, to lc/o for X 2.1% for X = I. = Br, and from 0.15% to Therefore, these ratios ranged from 0.01 to 0.05 for X = Br and from 0.005 to 0.07 for X = I but were about 0.02 for most of the iodide experiments. As seen in Section 5, the values of ([D ]/[HD])~2 were independent of c within the experi- 2 mental accuracy, even at the higher values of 2.1%. The reason seems to be that the small amount of ~ scavenges both H and D atoms, showing therefore a demagnified effect of the [D2 ]/[HD] ratio. Therefore, under our eJ..'l'erimental conditions, we can neglect reactions [18] and (19] with respect to (5] and (6], respectively, alt.hough at somewhat higher conversions than those 5 69 ve used this might not have been the case. Finally, as mentioned in Section 3.3, ve must consider the efiect of t.ranslationally hot H atoms. is reaction [l]. The source of such atoms As t.ranslationally hot D atoms 'W'ith a relative translational energy in excess of the :potential barrier height of the D + H2 system react 'W'ith lI:2i the excess energy must appear in internal or translational degrees of freedom of the DH H products. Let us consider, for simplicity, the case in vhich the ~ reagent is stationary in the laboratory system of reference. In this case, conservation of linear momentum guarantees than even if the rel.ative energy of the products is zero, the laboratory energy ~ of the H atom produced in the reaction must be equal to one quarter of the relative energy Erel of the reactants. If the relative energy of the products is not zero, EH depends in addition on the scattering angle and on the difference E between the internal energies of the reagent ~ and product HD. For the H + H2 system and the relative energies typical of our experiments, there are theoretical indications 39 that the diatomic reaction product is :predominantly back-scattered in the center of mass system. Assuming the same to hold true in the D + ~ system, a simple kinematic analysis shows that for E - O ~would be about twice re 1 whereas for E - 0.5 eV (corresponding to HD being formed vibrationally excited), ~would again be about one quarter of E ~el. The final conclusion is that we expect the H atoms produced. by reaction (l] to have laboratory energies considerable in excess cf thermal. 70 In addition accurate quantum mechanical calculations for an electronically adiabatic, collinear model of the H H system, 2 40 using a parameterized energy surf'ace yield the following results. For relative energies of 0.2 to o.6 eV reaction occurs with no vibrational excitation with probability of about 1.0. For relative energies in the range o.6 to 0.85 eV reaction still proceeds with no vibrational excitation with a probability of about 0.55, while reaction with vibrational excitation occurs with a :probability of about 0.45. Threshold for vibrational excitation occurs at a relative energy of approximately 0.52 eV. However, the probability of excitation does not become significant until a relative energy of approximately o.6 eV is reached. The 0.1 eV difference is much greater than the energy of thermal H and thus, the contribution of thermal H from the H + H2 reaction is insignificant in comparison with the non-thermal H from the same reaction. Therefore, if we extra:polate these results to the D + H system, 2 we would expect that the majority of the H product of this reaction would come off with energies in excess of thermal as was indicated by the arguments above. The H* atom reactions which must be added to the mechanism are: H* + H2 H* + DX H* + DX H-l<· + DX - - - H+ H 2 [20] HD+ x [21] HX + D* [22] H + DX [23] Process [20] includes both non-reactive and reactive collisions. 71 In reaction [22] the atomic product should come out translationally hot for reasons similar to those invoked for reaction [l]. Consideration of reactions [O] - [8] and [20] - [23] yields the following steady state expression for the ratio of rates of production of D2 to HD: b- ge c - ~ f d[D 2 J/dt = [D2 J = ~((DX)) + _ _f_+ d(HD]/dt [HD] f (H2] (b - fge) (37) f([DX])+ e (H2] f where: (38) (39) (40) e =1 + a (41) f = 2k21 + k22 + k23(1 + a) (42) k20 This equation is linear in [DX]/(~] if [DX] e -<<[H2] (43) f i.e. (44) In order to show that the above inequality is satisfied under the conditions of our experiments we first note that a has been shown elsewhere 41 to between 0.90 and l.O. For the purposes of this discussion we will assume t.ha.t a = 1. Using a.= 0.9 makes the 72 right hand side of Eq. (44) less than when a= 1. With a= 1 the right hand side of Eq. (44) becomes: o 2k_ ..,..,..._ _(1 ,.._..+_ a)k __,____,I'"':'-' 20 ____ ,..., ...,......_ ___,, 2 _...,,..,,... 2~1 + lt:22 + ~3 ( 1 + a) - ~l + ~2 + ~3 ~o - k21 + 1/2 k22 + k23 > k21 + k2o k22 + k23 (45) We now note that k is the total rate coefficient (reactive plus 20 nonreactive) of H* + H whereas (k21 + k22 + k ) is the equiva2 23 lent rate coefficient for H* + DX. It is reasonable to assume that (46) because ~O is dominated by its elastic part which is large whereas the elastic pa.rt o'f (~ 1 + ~ 2 + ~ ) is small, and although 3 the reactive one is large it should not be as large as the elastic one of ~o· Therefore, Eq. (46) coupled with Eq. (45) yields (1 + a)k20 [D11 - - - - - - - - - >> 1 > 2k21 + ~2 + ~3(1 + a) - [H ] 2 (47) since (DX]/[H2] is always less than or equal to 1 in our experiments. Therefore Eq. (44) is satisfied and Eqn. (37) becomes: where (49) The intercept of this equation ((D ]/[HD]) 0 is the same as 2 arrived. at in Section 3.3, Eq. (10). However, the slope differs from the one derived. in that section by an amount 73 - (k3 + kii:\ [ 8- kl k21 + k22 + k23 l J 2k21 + k22 + ( l + a )k23 - l + a ] {50) The quantity {k + k + k )/[2k + k 22 + {l + a)~ ] varies 21 21 22 23 3 from 1/2 to a maximum of 1 as the fraction k varies :from 1 to 0. use a = i.o. 21 / (k 21 + k 22 +k 23 ) In order to maximize the difference we will Therefore, 8 ranges i'rom 0 to o.5[(k + k )/k ]. 4 1 3 We can obtain a crude estimate of (k + k )/k :f."rom the slopes 4 1 3 of the [D2 ]/[HD] versus [DX]/[H2] lines by neglecting BX impurity and assuming that Eqs. (9) and (48) a.re valid descriptions of the slopes. Since the experimental slopes va:t:'J :from O. 7 to 1.5 (see Table I), we find that (k 3.0. 3 + k )/k can be anywhere between 0.7 and 4 1 Hence the change in the slope 8 could be as much as 1.5 which is not negligible. This indicates that the H* reactions [20] - (23] should be included in the overall mechanism, even though they don't contribute to the intercept. This inclusion is required if information is to be obtained from the slopes of these lines. The reactions D* + x2 - DX+ X [24] H~- + X 2 BX + X [25] - must also be consid~red since they can compete effectively with reactions (3] and [21] for hot deuterium or hydrogen atoms.. The ratios of the rates of these reactions to those of [3] and [21] are respectively: r24 k24 [X2] -[DX) r3 = k 3 (51) 74 (52) The k24/k and k /k21 are approximately equal to each other and 25 3 independent of temperature and wavelength. They have values of 3.5 for X = Br 42 and 3.8 to 4.4 for X = I. 43 The [X ]/[DX] 2 ratio at the end of an experiment is c/2 (where c is the :f'ractional conversion) if absorption of x on the walls is ignored, and its 2 average value throughout an experiment is about c/4. The r 24/r 3 /r ratios are then approximately 0.9 c for X = Br and 25 21 1.1 c for X = I. As seen from Table I, c bad values ranging from and r 0.2$ to 1% for X= Br and from 0.15% to 2.1% for X =I. Therefore, these ratios ranged f'rom 0.0018 to 0.009 for X = Br and from 0.0016 to 0.02 for X = I. Consequently, at the [X2]/[DX] ratios attained in our experiments reactions [24] and [25] are not expected. to contribute significantly to the mechanism. This is verified experimentally as seen in Section 5 since no conversion effect was observed. 6.2.2. The DX + RX + H System 2 In the presence of HX impurity, the following reactions must be added to the mechanism: RX+ h11 D* + RX D* + RX D+ RX D+ HX - - - H* + x [26] DX+ H* [27] HD+ x [28] DX+ H [29] HD+ x [30] 75 These reactions, along with reactions (O] - [8] and (20] - (23] give rise to the following steady state expression for the rate of formation of D2 divided by the rate of formation of IID: k _l u + E + E(l-a) H(u) [D2] = [RD] k2 h + a~~7 u + G + [~~ u + a + G(l-a) ]H(u) (53) where k3 + a~7 + a.k:2s ax ( · H(u)= k 2 l+ k:2s u + a~ u + ax(l + h) + h (54) ~ ( 1 + k 22 (1 + ax)~ u k20 and u= [DX]/(~] a= k6 k6 + ~ (55) (56) a= (IIXJ/[DX] (57) E= (58) 1 l+ G= a(c + aD) a~c + aD~ 1 + a(c + an) (59) c = k3o/k5 (60) D= k29/k5 (61) x= ~E/Enx (62) h= k1/k2 (63) 76 As discussed :further in Section 6.3.2, the quantity a has been determined experimentaJ..ly and the quantities C and D have been estimated, so that E and G can be evaJ..uated if a is known. If' we take an a of 0.020 as observed for the DI-He experiments {see Section 6.3.1 for a discussion of how this is obtained), E and G can be evaluated for DI to be 0.97 :!: 0.04 and 0.05 :!: 0.01 respectively. The ratios ~ 2 /k 21 , ~7 /k28 and k 27 /k3 are estimated in /k = 1. 9 :!: 0. 3 and k /k = O. 8 28 3 27 28 Using these values Eq. (53) can be reduced to an equation the appendix to be k22 /k21 = k :!: 0.2. 3 containing only k1/k2 , k /~ and k /k • The ratio k1 /k can 21 20 2 be calculated 'from the values of A listed in Table I. If we fUrther make the assumption that k /k2 = k /k , the values of 21 20 3 (D2 ]/[ED] as calculated from Eq. (53) as a function of [DX]/[H ] 2 and k /k can be compared with experimental data. At 3030~ 3 2 experiments were done with [DI]/[H ] ratios ranging from 0.3 to 2 3.2. Hence there is a wide range over which to compare theory and experiment. The best fit to the experimental data occurs for k /k = 0.25. A plot of' the experimental and theoretical values 3 2 is shown in Fig. 8. This gives a straight line for [DX)/(H ] 2 values i"rom 0.3 to 1.5 which then curves ov~r at higher [DX]/[H2 ] ratios. Hence the above mechanism can explain the experimentally observed straight line behavior of a :plot of [D )/[HD] versus 2 [DX) /[R ]. A similar fit vra.s performed for DI-H :photolyses 2 2 at 2537~ yielding the best fit for values of k /k between 1.1 3 2 and 1.4. Hence, some approximate information about the hot atom rate constant ratio k /k 3 2 can be extracted from the :plot of 77 Figure 8. 78 0. 0 ~ I l ., 0 II II . .::::.C\I ~ 0.. ....... !() ~ ~ C\J 0 x w \ \ \ LO (\1 ' !() ~ 0 . I") \ \ \ \ \ ~\ ,--.., \ ~ \ CJ :c \ \ \ \ \ a \ \ \ ~ \ \ ....... ,--..., . C\I 0 \ \ \ \ .\ , ~\ \\ '\\\ -. 0 79 (D ]/[ED] versus [DX] / [H ]. 2 2 In the limit of zero [DX] / [H ] the reciprocal of Eq. (53) 2 reduces to: ( aD) + [l+ a(c + aD)] [hl++ (1-a)[ax(h a[a.x(h + 1) + h) ]( 64 ) ] = a c+ + 1) + h] ([D[HD])~ 2 0 where a, c, D, a , x and h are defined by Eqns. (56) and (60) - (63) Eq. (64) will be used in Section 6.2.4 to derive an respectively. expression for the integral reaction yield A in terms of the above quantities. 6.2.3. The DX+ HX +He System For photolysis of DX with a small amount of HX impurity;, the mechanism to be considered includes reactions [OJ, (3] - [8] and [21] - [28]. In addition, the reactions: D*+ M - D + M [31] H* + M - H+ M (32] where M is rare gas must be included.· Using this mechanism, the following steady state expression for the rate of formation of D 2 divided by the rate of formation of HD is obtained~ (~+~E + ~ Y + (l-a)E(~ y + l) Z(y) [D] [~J = 11:28 31 y (2:4 + l\ G +311:21 y+ ~23 y3: l] [a+ (1-a)G]lZ(y) (65) + . where a, E, G and 31 I 32 lk32 a have been defined by Eqs. (56), (58), (59) and (57), y = [DX]/[Re] and 80 ~~l a:xy - 3 z(y) = ( k27 k28) 31 31 k21 + k22) . k + a:k + a:k 32 + (66) k22 y + l+ ax k 32 y As mentioned in Section 6.2.2, good estimates of a, E, G and a are available. If we again assume that ~ 2 /k 21 = 1. 9 /k = o. s and likewise that k /k = k 21/k32 , Eq. (65) can be 26 3 3 31 reduced to an equation containing only k /k • This equation can 3 31 be fit to the experimental slopes. A plot of [D2]/[HD] versus k [DX] /[He] from Eq. (65) shows this plot is a,pproximately linear over the range 0 S [DX] /[He] ::; 1.5 but shows decreasing slope as [DX]/[He] increases. The best fit to the experimental at 303olt comes for k /k = o.4 ! 0.1. The large experimental error in the 3 29 slope (due to fluctuations in a during a series of experiments) :precludes more accurate fitting of theory to experiment. If the [D2]/[HD] ratios were lmown very accurately (to 6 or 8 significant figures) more information could be extracted from Eq. (65) with the help of computers. In the limit as y - ~ o, the reciprocal of Eq. (65) becomes: [ -[HD])He = ClC+aD+ax [~J 0 (1 + a(c + 1+a~ aD))] (67) Note that since the mechanism for the helium experiments is the same as for the hydrogen experiments with the exception of reactions [l) and [2] , it would seem intuitive that replacing ([HD]/(D2] )0 by the dif:f'erence between the reciprocal of the intercepts of plots of [D2] /[HD] versus [DX]/[G] for G = H and 2 He respectively, should give a good value for the integral 81 reaction yield corrected. for RX impurity. In the next section we give the exact formula for the integral reaction yield and show its dependence on (68) 6.2.4. Exact expression for the integral reaction yield An exact expression for the integral reaction yield can be arrived at by subtracting Eq. (67) from Eq. (64) to obtain an expression for A and then solving this expression for A. When this is done the following equation is obtained for the integral reaction yield: A= A(l + aBx) 1 + a(l + A)+ a(l + aBx)- 1 [xa2 + (C ( + aD)(a + l + ax)] 69 ) If we perform an expansion in a power series in a and drop the terms of order a2 and higher (this is justified since the maximum value of a is 0.03, the coefficient in a is less than 3 and the coefficient in a2 ranges from 0.07 to 1. At most only a 11i error results from dropping the terms of order a 2 and higher.) the following expression for A is obtained: _ A - l + l (1 a(l +A) 1 a A + + 2 a(l + A )]Bx - [xa - (c + aD)(a + l)] (1 + a(l + A )] l( 70) Note that the quantity preceding the parenthesis is the result obtained in Eq. (12) when pure DX was considered with A replacing H ([HD]/[D2]) 2. The quantity in parenthesis varies from 0~92 to 0 0.99 depending on wavelength which shows the utility of A in determining the integral reaction yield. 82 6.3. Determination of the integral reaction yield In order to use Eq. (69) to obtain the integral reaction yield, values of a and a must be known. In the following subsection we will describe how these values were determined and will show how the errors in these and other factors a.ff'ect the calculated value of A. 6.3.1. Determination of HX impurity in DX We obtained the quantity a. = [HX]/[DX], which is a measure of the a.mount of HX impurity present in the DX, from the reciprocal of the intercepts of the appropriate plots of the helium runs. Eq. (67) gives the explicit steady state solution for ([HD]/[D2J)ge. This equation is a. quadratic equation in a. and can be solved to obtain: -p :!: a= v{,2 + 4aI(C + aD) (71) 2a.( c + aD) where p = C + aD - (72) ax - xI(l - a) and (73) + For the DI experiments the resulting a was 0.03 - 0.004 while for DBr it was 0.013 ~ 0.001. The estimation of the ratios C = k /k4 and D = ka/k4 which 9 are needed to determine both a and A is discussed in another pa.per. 41 These ratios.were estimated from experimental data of Timmons and WeGton 44 and Sullivan2 9 using transition state theory. Independent experiments in these laboratories 45 were also used to conf'irm these estimates. The results of these estimates are, for DI, C = 1.45 :!: 0.15 and D = 1.2 ! O.l and for DBr, C = 2.0 :!: 0.2 and + D = 1.35 - 0.14. It will be shown in Section 6.3.2 that these ratios are not needed with a high degree of accuracy for the final determination of the integral reaction yield. 6.3.2. Determination of the abstraction fraction of H + DX The abstraction fraction a = k 6/(k 6 + additional helium experiments. 17) was determined by The basis of the method is variable wavelength photolysis of 3-&fo HX in DX mixtures in helium. The extinction coefficient ratio EHX/EDX is strongly wavelength dependent, 23 and a plot of the ((HD]/[D2 ])~e values versus EFIX/EDX is linear and allows calculation of a. Further details are contained in a separate paper. 41 The resulting values are a(DI) = 0.97 :!: 0.05 and a(DBr) = 0.99 :: 0.03. However, other experiments 45 based on the photolysis of mixtures of DX and FIX in the concentration ratio of about 1 to 4 give a(DI) = 0.95 + 0.03 and a(DBr) = 0.93-+ 0.03. The agreement is well within experimental error ·in the case of the iodides and barely so in the case of the bromides. Since there is no basis for concluding which measure- ment is most accurate, we list values of the integral reaction yield for the bromide experiments based on each of the values of a(DBr) and also on their average, i.e., 0.93 ! 0.03, 0.99 :!: 0.03 and 0.96 :!: O.o4, respectively. 85 6.3.3. Results for the integral reaction yield. The integral reaction yield A(A) was calculated :t'rom the experimental 6.•s listed in Table I using Eq. (69) and values of a. and a calculated as described above. The results for A(A) at each wavelength are listed in Table I. A plot of A versus Eio) is shown in Fig. 9. The contributing errors in A were determined by taking its derivatives with respect to the five independent variables A, a, a, C and D and multiplying each derivative by the absolute standard error of the variable considered. The total error was taken as the square root of the sum of the squares of these errors. The associated confidence is 7(Jfo. The uncertainty in A is usually dominated by the uncertainty in a single one of the variables on which it depends. A, the error in bi. dominates. in a contribute equally. dominates. For small At about A= 0.1 the errors in A and For larger A, the error in a(DBr) Therefore, a more accurate value for a(DBr) would permit us to reduce the uncertainties in A > 0.1. the uncertainty in a, C or D important. In no case is At worst an error of l(Jfo in one of them causes an error of 0.04% in A. In order to check the seli'-consistency of the values of A(Elo)) it is important to have the initial energy range spanned by the D atoms from DI overlap the range of initial energies spanned by the D from DBr. The experiment at 289J.i with DI is important in this connection. This was the shortest wavelength used with DI to avoid the formation of electronically excited iodine atoms. The 86 Figure 9. = k 1/(k 1 + k 2 ) versus laboratory Values of a(DBr) = 0.96 and Plot of A energy. a(DI) = 0.97 were used in computing A. 87 . LO C\J 0. -> . Ci) 1() - -. 0 LO o·.~~~-JLco~--~~<.0~.~~----~~~----~-C\JJ.~-------l.100 - 0 0 0 0 o_ w 88 fact that this point lies on a smooth curve going through the DBr points is a manifestation of the consistency of the interpretation. As stated in Section 6.1, it is energetically possible to form excited bromine atoms in the DBr photolysis, but the best theoretical and experimental evidence available indicates that the fraction of the Br atoms which are excited is negligible. Nevertheless, if such excited Br atoms were present in significant amounts, the experimental A values would correspond to lower energies than those used for Fig. 9. T'nerefore, the A's reported in this paper for DBr photolyses are lower limits and are correct only if the assumption of no excited bromine atoms is correct. evidence is needed to confirm this assumption. Further experimental Any direct measurements of the fraction of bromine atoms produced in DBr photolysis as a function of wavelength could be used to correct our values of A. For example, if it were found that at 2138Jl lo{o of the Br atoms were excited, but th.at at 246oR none were, the corrected A value corresponding to no excited Br at 213ffil (E~O) = l.973ev) would be 0.44 compared to the present value of o.41, indicating that we would have made an error of 7fo. An additional complication which could result as a result of formation of the 2p ; excited Br atoms is that these atoms 1 2 could react with either R2 or DBr, thus complicating the mechanism. However, Donovan and Husain46 observed no excited bromine atom reactions except quenching and 3-body recombination in their study 89 of excited bromine a toms. Therefore, excited bromine a toms would not be expected to cause further complications. 7. DISCUSSION Our experiments show tha.t the integral reaction yield is a monotonically increasing :f\mction of the laboratory energy over the range o.48 eV to 3.0 ev. It has a value of o.66 at 2.86 eV dropping to near zero at o.48 ev. A region of interest in the A versus Eio) plot is near A= O. The experimental value where A first eg_uals zero occurs approximately at a laboratory energy of 0.48 eV corresponding to a relative D + H2 energy of 0.24 eV for stationary R • This is however not 2 the energy at which the reaction cross section goes to zero. The reason for this can be seen by considering the behavior of k1 near threshold. This behavior is a good approximation to the behavior of the integral reaction yield A = k1/ (k + k ) since k1 is 1 2 changing rapidly near the threshold whereas k (which depends on 2 the non-reactive cross section) is a slowly increasing function of Elo) in this region and hence can be considered a constant with respect to k 1 • The rate constant k 1 (Ei0 )) is related to the reaction cross section by the expression: (74) 90 where S (E) is the reactive cross section, v(E) is the relative R velocity of D and H and f (o)(E) is the steady state distribution 2 El function of relative energies E for D atoms with an initial laboratory energy Ei0). In the following, approximations will be made to ~(E) and fE(O) in order to obtain a qualitative description of 1 the behavior of kr For this purpose5R(E) will be assumed to be the simple line of centers ha.rd sphere cross section1 : = S (E) R l o for E ~ E 0 (75) 7l"b 2[1 - E0/E] for E > E0 ·where b is the distance between the centers of the hard spheres at contact, i.e., the sum of their radii, and E0 is the minimum energy along the line of centers for reaction to occur and is therefore the threshold energy Ethrs for this cross section. approximation to As an (o)(E) we will consider the relative energy El distribution of D vTi th respect to ~ before any collision takes f place for D atoms with a sharply defined laboratory velocity '1;• The distribution function cp(v~) of the laboratory velocity vH 2 of the ~ molecules will be assumed to be a Boltzmann distribution at temperature T: (76) where m2 is the mass of H2 and k is the Boltzmann factor~ The resulting distribution f'unction of relative energies described above is: 91 eJ..'}) -&r (1) v) 2'l - [m + I dE (77) where v is the relative velocity, p,is the reduced mass and ~ and v are considered. to be functions of Eio) and Erel according to: EiO) = 1/2 IDnv~2 (78) (79) This distribution function has been shown to have a width o.f+7 (80) Hence its energy spread is 0.22 eV a.t a relative energy of 0.3 eV which is close to the threshold energy. The above expression for fEfO)(E) should be a good approximation for calculations in the region near threshold since it should differ from the real distribution involving multiple collisions mainly in the low energy side, (i.e., for E < (ri./~) Elo) = 1/2 Ei0 »leaving the high energy tail, which contributes most to the integral in Eq. (74) for ElO) < 2Ethr basically unchanged. k1 (EiO)) was evaluated from Eq. (74) using Eqs. (75) and (77). The integrals involving exp[-(m /2k.T)·(vn + v) 2] contribute negligibly to Eq. (74) and may 2 be dropped (Their contribution is less than io·l5 of the one resulting from the exp[-(m~/21d')•(l) .. v) 2] term)~ expression is: The resulting k (E(o)) = b2 1 1 v~ 92 l ~ (~s 1 2.fiisl/2 + (v-£ + vo) exp[-s(vo - ~)2] '1)2 - v;) er:rc[s1/ 2 (v0 - vtlll (81) 2 where s = ~/2kT and v0 = 2F. fµ.. Er:f'c is the complementary 0 error function. 48 Since the above 'equation increases linearly with vn at large V-£ a more SUi table function is k 1/vD Which 1 approaches asymptotically to the maximum value 71'b2. The expression for k (Elo)) was evaluated at 300°K and E = 0.3 eV. 1 0 The results of this calculation are shown in Fig. 10 as well as a plot of the line of centers cross section used in the calculation. Note that the two curves nearly coincide except at low energies where k1 /1) goes asymptotically -"co zero and SR (E) bas a sharp cutof'f'. This low velocity tail in ~/v; comes ?rom the Boltzmann spread of the velocities of' the H2 target; and makes it difficult to estimate the threshold velocity v E of 3R (E). 0 0 and corresponding threshold energy If we define a phenomenological threshold as the energy at which (k1 /v;) becomes a certain fraction ~ of its maximum value, then for Crespectively equal to 0.01, 0.03 and 0.10 the corresponding phenomenological threshold energies are equal to · 0.17 eV, 0.21 eV and 0.294 eV respectively compared to the correct assumed val.ue of 0.30 eV. Therefore, we may expect significant errors to occur if we try to estimate the reaction cross section threshold energy from the energy at which A vanishes. This calculation points out the need for a more rigorous analysis than the one carried out above in order to obtain the 93 Figure 10. Plot of calculated k /vD and the line of 1 centers cross section used in its versus relative energy. cal~ulation 94 I I I >o ........ --w C'\J lo.. ~ ? en I -> - tJI I (i) Q) t... L&J . 0 - 00 (!) d 0 ~ 0 . (.\J 0 95 threshold energy of the cross section for the reaction of D with H • 2 Calculations are also required to extract the reaction cross section f'rom the experimental data. An outline of the method used to obtain cross sections and threshold energies from experimental data is given in the next section. A more detailed description and the associated results will be given in a forthcoming paper. 7.2. Determination of reaction cross sections from integral reaction yields 7 .2.1. Boltzmann Equation The behavior of the DX-R photolysis system can be described 2 by a steady-state :Boltzmann equation. The details of this derivation are given elsewhere47 and the results will be suzmnarized here. Let R be the rate of initial D atom production due to photolysis 0 andcpvf, (vD)' the normalized initial distribution fUnction of D atom laboratory velocities. at vD. This is a narrow function centered Let Gv:n<vn) dvD be the concentration of D atoms under steady state :photolysis conditions in the laboratory velocity range vD to vD + dvD" It satisfies the :fol.lo'Wing steady-state Boltzmann equation: In the above K.c(vD) is defined as: K t = i(l2 + "IfX (83) 96 02 = 1'R~ + I~2 (84) i(JX = 1<RDX + ~X (85) ~ H2 = [H2 ) frl..'t'TR2 (vD,v) v SRH2{v) dv (86) ~~ = ~ gi~ ~~,i {87) ~~ = [H2] fc/>T~(vD,v) v ~~(v) dv {88) ~ g.~ SNR~,i J. J. DX ~ DX = [DxJjcpT DX 8R - L DX 8R f DX 1Sm = [DX] cj>T DX = L SNR i gi DX (90) DX,i i gi DX DX (vD,v') v' 8R {v') dv' (91) DX (vn,v') v' Srm (v') dv' (92) DX,i (93) 8NR where v is the relative velocity of D with respect to H and v• 2 is the relative velocity of D with respect to DX. cJ>T~{vD,v) is the distribution function of D + H relative velocities for D atoms 2 with a laboratory velocity vD and ~ molecules 'With a Boltzmann distribution of laboratory velocities andcpTDX(vn,v') is a similar distribution for D + DX. sRR2(v) is the reactive cross section for D + ~ averaged over the internal states of H at temperature T 2 and ~2(v) is the corresponding total non-reactive cross section DX DX . averaged over these internal states. 8R and Siffi. are similarly the reactive and non-reactive cross sections for D + DX and g.~ J. and g DX are mole fractions of an initial internal state i of 1 97 either H2 or DX. It is assumed that thermalization of D by DX is negligible compared to thermalization by H2 and hence ~X is set equal to zero when applying Eq. (82). This is valid since the masses of D and H2 are equal and hence exchange energy very efficiently compared to D and DX where the difference in mass is greater. · The quantity H(vD,vD) is defined as follows: sinX dv~ d)( d'T] [DX] +- 2 (94) In the above v' and v' are the laboratory velociti'es of H and 2 DX DX respectively before collision, vif is the magnitude of the H2 relative velocity vector of D with respect to either H or DX, 2 X and 7] are scattering angles which define the directions of these vectors after collision and Y. f is the angle between between v' and D i v' H2 or vn' before collision. . X H The quantity O" 2 (v!f,-X.'7]) is the i-f J. differential non-reactive cross section for the collision of a D atom with a ~ molecule in internal state i to give a D atom and a H molecule in internal state f. O"~_:f is a similarly defined 2 quantity defined for D +DX. cp~2(v~) is the Maxwell Boltzmann distribution function of H velocities in laboratory coordinates 2 while ¢TDX(vDX) is a similar distribution for DX velocities. ~ 98 is the distribution :function for initial internal states of H2 or DX. If inelastic collsions a.re unimportant, tb.e summation over f in Eq. (94) may be dropped.. Again, since thermalization of D by DX is negligible compared to thermalization by H , rfJX(v•,v) is 2 D D set equal to zero. The :physical interpretation of Eq. (82) is very sim:ple despite the complexities of some of its terms. The first term represents the rate of formation of D atoms in the velocity range vD + dvD directly from the photolysis source. The second represents their rate of removal from the same velocity range by all collisions ·wi. th H and reactive collisions with DX. 2 Finally, the third term represents the rate of production of D atoms in the velocity range vD + dvD due to all non-reactive collisions of D atoms at all other velocities with H and DX. The net rate of production of D 2 atoms in BilY given velocity rfmge must vanish under steady state conditions and hence the sum of terms in Eq. (82) is set equal to zero. 7 .2.2. Relation between A(v:[p aud..,. the reaction cross section The integral reaction yield A( v~) is related ' to the above quantities by the expression: A(v~) = ~ !KaH2(vD) Gvn(vD) dvD . where \ H 0 2(vD) is defined by Eq. (86). The Boltzmann equation given by Eq. (82) can be reexpressed in terins of A(~) as 4 9 (95) 99 (96) In the limit of dilute [DX] which corresponds to the intercept of a plot of [D2]/(HD] versus [DX] / [H ] we have 2 (97) Using this relation in Eq. (96) and rearranging, the following expression is obtained for ~~: Therefore, if the differential non-reactive scattering cross sections a-(f(v:i_f,x;17) are known, they can be used to determine ~~(vD). To a first approximation we may in t12 use the term coming from the elastic process only, since it usually predominates In this case only ~l (v' ~x_,7]) is needed over the inelastic ones. H to calculate H 2(vD,vD). Once ~ H2(vD) is known, Eq. (86) is an integral equation in which the total internal-state~averaged reaction cross section SR~(v) is the only unknown. One way to solve it is to tt-ansform it into an equivalent partial differential equation with the help of Fourier tt-ansforms. The result49 is th.at if u(v,v') is the solution of the differential equation ou -- (99) oT' subject to the initial condition u(v o) = ...:!_.. K ~(v) ' (H ] ~ ~ 2 (100) 100 H then ~ 2(v) is given by H S R 2 (v) = ~ v (101) where T is the H temperature at which the m-..-periment was conducted 2 and u(v,T) is obtained by solving Eq. (99) numerically subject to Eq. (100). Therefore, a knowledge of CTe~ ( v' ,X,'1')) and the experimentally known A(vD) furnishes the SR~(v). o-e~(v' ,x;ry) has been calculated 50 by Kar:plus and Tang in a central field approximation. Hence all pertinent inf'ormation is available to calculate 8R~(v) from the present experiments. The results of this calculation will appear in the near fUture. 7.2.3. Consequences of the simplified Boltzmann equation. In sections 3.2 and 3.3 it was stated that the Boltzmann equation leads to a steady-state distribution :f'unction of D atom energies which is bi-modal, having a "hot" atom peak, as indicated in Fig. 1, and that the variation of [D2]/[BD) with [DX]/[~] was as depicted in Fig. 2. In order to validate these statements let us consider a simplified model. Assume that the ~ and DX are stationary (i.e., that the experiment is conducted at T = o°K but that the system is still gaseous), that the energy dependence of the cross sections of reactions [l] and [3] are independent of the molecular reagents and that the contribution of non-reactive collisions of D* v:ri th DI to thermalization of the D* is negligible compared to the contribution of the D* + ~ collisions and that 101 the latter are dominated by elastic collisions having a differential cross section ue~2 independent of internal state and orientation of the ~· Under these conditions, Eq. (82) becomes, using the laboratory energy E1 of the D atoms instead of their velocities as the independent variable: where the K's and H aquire the simplified forms H H2 DX Kt(El) = Kfil{2(El) + ~ (El) + ~ (El) (103) ~2 (E1 ) = [~] VD SNRii:2(vD) (lo4) KRH2(El) = [~] VD Sp_~(vD) (105) DX ~ DX (El)= [DX] VD Sp. (vn) H(Ei,E1 ) = [H2] 2 VD CTNR~(Ei,E1) (106) (107) In these expressions, the laboratory velocity vD becomes equal to the velocity v relative to either H or DX and is related to the 2 laboratory energy E by 1 VD = [2El/~]l/2 (108) In addition, the S are the internal-state-independent total cross sections, and CTNR~(Ei,E ) (where E is the D laboratory energy 1 before collision and Ei is that after collision) is related to· the 1 differential elastic cross section ~~(v' ,X) by 102 H2 O"NR E ) ,J!;l' l - ( .,..,. I 2 H2 ET O"el ( v iX. I ) (109) 1 where v • is the relative velocity before collision and X is the s cattering angle. The total non-reactive cross section is related to the differential one by (llO) M:>del calculations with :particular but reasonably realistic choices of the cross sections SR~(v), SRDX(v) and o-;2(v',X) 4 have been performed and are described elsewhere. 9 The results are indeed that GEf0 ) (E1 ) and therefore the distribution function fE(o ){E) are bimodal and that the behavior of [D2]/[HD] Versus l [DI]/[~] is the one depicted in Fig. 2. 103 APPENDIX Photolysis of DI Containing a Small Amount of HI Impurity In sections 6.2.2 and 6.2.3 we needed crude estimates of k 22 /~1 1 k27 /k23 and k23/k3 in order to evaluate the slopes of plots of [D2]/[HD] versus [DX]/[H2] and [D2]/[HD] versus [DX]/[He] to test whether the mechanism given in that section could be f'it to the experimental data. To obtain such estimates, we performed a series of ex:periments in which "pure" DI (except i"or the small amount of HI impurity) was photolyzed. The resulting [D2] /[HD] ratio depended on the previous history of the reaction vessel, presumably due to various states of deuteration of its surface and the consequent variation of HI impurity. However, the ratio of (ED]/[D ] at two 2 wavelengths obtained in consecutive experiments was reproducible. In a series of pairs of consecutive experiments at 3030~ and 2537~, in the same reaction vessel, the lowest [HD]/[D2 ] obtained. were 0.0397 and 0.0337 respectively and correspond therefore to the smallest a. In view of the results in Table I we w:LJ.l assume this a to be 0.020. From these results, we may estimate the rate constant ratios mentioned. above as follows. The mechanism characterizing these experiments is the same as for the DX-HX-He system excluding reactions [31] and (32]. The corresponding steady state expression for the ratio of the rate o'f formation of [HD] to that of [D2] is 104 ct ~8 k:23 • x[i·a~(l·~)j ·~ (ill) 1 + ~ 2 ( 1 + CI X) k21 In this expression, not only x but also the ratios of rate coefficients should be functions of wavelength, the latter via. the initial energy of the D and H aJcoms. However, since k28/k 3 represents the isotope effect of the abstraction reaction, it is reasonable to assume that it is approximatly energy independent. The k 22 /k ratio represents the ratio of exchange to abstraction 21 and we should allow it to be energy dependent. However, it is reasonable to make it equal to k /1{ at the energies used, 27 28 since this represents an isotope effect on the exchange to abstrac- tion ratio. Calculations of the energy dependence of the ratio of the probabilities of exchange to abstraction in single H + DI collisions were performed using the statistical theory. 51 They show that this ratio increases by 24% as the relative collision energy increases f'rom 0.570 eV to 1.00 eV. In our experiments, the initial energy of H with respect to DX is 0.500 eV at 3030R and 0.89 eV. at 2537R (for DI dissociating into ground state iodine atoms). The ~ 2 /~ 1 ratio is not equal to the monoenergetic probability ratio since they involve averages over the distribution ftm.ctions characteristic of our experiments. Therefore, on the basis of these statistical theory results, we would expect this rate constant ratio to change by less than 2Cl/o. Let 8 be 105 the :f'ractional increase just mentioned in ~ 2 /k21 1n going from 303o5l to 253~: a= (k22/~1)2537~ - C~2/k21)3030~ (112) (~/k21)3030~ If vre apply Eq. (lll) at these 2 wavelengths, use the assumptions above and consider 8 to be known, we get a system of 2 equations 28 /k3 and (~2 /~) 303 cli, since the extinction coef:ficient ratio x is known f'rom independent experiin the two unknowns k ments described elsewhere. 23 Solving them :f'urnishes the restilts given in Table II. The reproducibility of the quantities ([ED]/[D 2])A /([ED]/[D2))A 1 for pairs of consecutive experiments mentioned in the beginning of this appendix can be understood by assuming a to be unchanged in these experiments. Using (lll) at wavelengths Al and~ and dividing the resulting expressions elim:ina.tes the ma.in dependence on a. The remaining dependence is negligible as can be verified by direct substitution into this expression of the value of a and of the rate coef:ficients of Table II. Table II shows also that the effect of 8 on the rate coefficient ratios over the energy range of interest is not excessively pronounced. Although they represent crude estimates, these ratios should be adequate for the purposes for which they were used in Sections 6.2.2 and 6.2.3. 2 106 TABLE II Estimates of k28/k , k 22 /k and k27/k28 21 3 e= o.o e= 0.24 >,.(lt) 3030 2537 3030 2537 k28/k3 0.82 0.82 0.80 o.80 k22/k21 1.9 2.3 2.3 2.8 k28/k27 1.9 2.3 2.3 2.8 107 REFERENCES 1. M. A. Eliason and J. O. Hirschf'elder, J. Chem. Phys., _lQ, 1426 (1959). 2. M. Karplus, R. N. Porter and R. D. Sharma, J. Chem. Phys., ~, 3259 (1965). 3. J. M. Blatt and V. F. Weisskopf, Phil. Mag., 44, 356 (1953). 4. For reviews see: (a) D. Herschbach, Adv. Chem. Phys., 10, 319, (1966); (b) H. Pauly and J. P. Toennies, Methods of Experimental Physics, 1, 227 (1968). 5. M. Karplus, personal communication to A. Kuppermann. · 6. J. M. White and A. Kupperm.ann, J. Chem. Phys., !t!±, 4352 (1966). 7. A. Kuppermann, Nobel Symposium 5, Stig Claes son, ed. (Interscience Publishers, New York, 1967) pp. 131-140. 8. L. Melton and A. Kuppermann, to be published. 9. J. B. Anderson, R. P. Andres and J. B. Fenn, Adv. Chem. Phys., 10, 275 (1966). 10. s. Datz and E. H. Taylor, J. Chem. Phys., .,22, 1896 (1963). 11. W. L. Fite and R. T. Brackm.ann, (a) Atomic Collision Processes, M. R. C. McDowell, ed. (North-Holland Publishing Company, Amsterdam, 1964) PP• 955-963; (b) J. Chem. Phys., 42, 4o57 (1965). 12. J. Geddes, H. F. Krause and W. L. Fite, J. Chem. Phys., zg, 3296 (1970) • 13· (a) R. A. Ogg, Jr. and R. R. Williams, Jr., J. Chem. Phys., 13, 586 (1945); (b) R. R. Williams, Jr. and R. A. Ogg, Jr., J. Chem. Phys., 12,, 691 (1947). 108 14. (a) H. H. Schwarz, R. R. Williams, Jr. and W. H. Hamill, J. Am. Chem. Soc., 74, 6007 (1952); (b) R. J. Carter, W. H. Hamill and R. R. Williams, Jr., J. Am. Chem. Soc., Tf., 6457 (1955). 15· R. M. Martin and J. E. Willard, J. Chem. Phys., 40, 3007 (1964). 16. (a) c. C. Chou and F. s. Rowland, J. Am. Chem. Soc., 88, 1612 (1966); (b) c. C. Chou and F. S. Rowland, J. Chem. Phys., !!:£, 812 (1967); (c) C. C. Chou and F. S. Rowland, J. Chem. Phys. 50 2763 (1969). _, 17. D. R. Davis and J. A. Betts, forthcoming. (The main details tha:t will a:ppear are in Appendix A of this thesis). · 18. Instrument in geochemistry department of California Institue of Technology and made available by Professor Samuel Epstein of that department. 19. A. o. Nier, Rev. Sci. Instr., 1§., 398 (1947). 20. J. M. White, Ph.D. Thesis, University of Illinois, Urbana, Illinois (1966), P• Bo. 21. natural abundance ED supplied by Dan Quinn, High Energy , Physics Laboratory, Stanford University. 220 (a) C. F. Goodeve and A. W. C. Taylor, Proc. Roy. Soc. (London) · 154A, 181 (1936); (b) B. J. Huebert and R. M. Martin, J. PhyS• Chem., E_, 3046 (1968); (c) J.P. Bates, J. o. Halford · and · L. C. Anderson, J. Chem. Phys., .J., 415 (1935); (d) J. Roma.nd, Ann. de Phys., ,!t, 527 (1948); (e) A. A. Gordus, D. A. Caughey, and T. R. Wilcox, personal communication to J. M. White and - A. Kuppermann.. 109 23. J. A. Betts, D. R. Davis, J. M. White and A. Kup:permann, to be published. 24. (a) R. S. Vrulliken, J. Chem. Phys., 8, 382 (1940); (b) R. S~ Mu.l.liken, Phys. Rev., 51, 310 (1937). 25. (a) R. J. Donovan and D. Husain, Trans. Faraday Soc., 62, 1050 (1966); (b) R. J. Donovan and D. Husain, ~., §.g, 2643, 2987 ( 1966) • 26. A. s. Coolidge, H. M. James and R. D. Present, J. Chem. Phys., ~, 27. 193 (1936). G. Herzberg, Spectra of Diatomic Molecules, (D. van Nostrand Co., Inc., Princeton, New Jersey, 1950) pp. 199-201, 392-3. 28. J. M. White, Ph.D. T'nesis, University of Illinois, Urbana, Illinois ( 1966) • 29. J. H. Sullivan, J. Chem. Phys., l2_, 3001 (1963). 30. J. H. Sullivan, J. Chem. Phys., 1§, 1925 (1962). 31. B. A. Ridley, W. R. Schulz and D. J. Le Roy, J. Chem. Phys., ~, 3344 ( 1966) • 32. A. A. Westenberg and N. de Ha.as, J. Chem. Phys., !7,, 1393 (1967). 33. M. Karplus, private communication to A. K. 34. J. A. Sullivan, J. Chem. Phys., .:2Q, 1292 (1959). 35. A. F. Trotman-Dickenson and G. S. Milne, National Standard Reference Data Series - National Bureau of Standards 9, p. 22 (1967). 36. J. A. Sullivan, J. Chem. Phys., 36, 1925 (1962). 37. R. A. Fass, J. Phys. Chem., J!±., 984 (1970). llO 38. A. F. Trotman-Dickenson and G. S. V.ilne, National Standard. Reference Data Series - National Bureau of Standards 9, P• 39. 12 (1967). (a) M. Karplus, R. N. Porter and R. D. Sharma., J. Chem. Phys., 43, 3254 (1965); (b) N. C. Blais and D. L. Bunker, J. Chem. Phys., 41, 2377 (1964). 40. D. G. Truhlar and A. Kupperma.nn, J. Chem. Phys., 2,g, 3841 (1970). 41. D. R. Davis, J. A. Betts, J. M. White and A. Kuppermarin, forthcoming (this is Paper 2 in this thesis). 42. R. A. Fass, J. Phys. Chem., ~' 984 (1970). 43. R. D. Penzhorn and B. deB. Darwen~c, J. Phys. Chem. , E, 1639, (1968). 44. R. B. Timmons and R. E. Weston, J. Chem. Phys., 41, 1654 (1964). 45. A. Persky and A. Kuppermann, forthcoming. 46. R. J. Donovan and D. Husain, Trans. Faraday Soc., .§g, 2987 (1966). 47. A. Kuppermann, J. Stevensen and P. 0 Keefe, Disc. Faraday Soc., 44, 46 (1967). 48. M. Abramowitz and L. A. Stegun, National Bureau of Standards Applied Mathematics Series 55, 1964, P• 295. 49. A. Kuppermann and R. N. Porter, forthcoming. 50. M. Karplus and K. T. Tang, Disc. Faraday Soc., ~' 56 (1967). Also, M. Karplus, personal communication to A. Kuppermrum. 51. D. G. Truh1ar and A. Kuppermann, J. Phys. Chem., ,U_, 1722 (1969). 111 PAPER 2 REACTIONS OF H ATOMS WITH DBr AND DI INTRODUCTION The reaction of thermal hydrogen atoms with deuterium iodide or bromide may resuJ.t in either of the two processes, H +DX - ED+ X [l] H +DX - RX+ D [2] We have measured the ratio k /(k + k2 ) for the iodide a.nd 1 1 0 bromide reactions at 300 K. These results are needed for the interpretation of hot atom experiments 1-3 in which DX serves as a.n H-atom scavenger and for adjusting para.meters in theoretical treatments of these reactions. 4-5 The method is an indirect one based on photodissociation of HX-DX mixtures with essentially monochromatic light. Over the range of wavelengths utilized, the extinction coefficient ratio EHX/~DX varies by about a factor of 10. This ratio must be known as well as certain other rate constant ratios in order to evaluate k1/(k1 + ~). The photoproduced atoms are born with o.6 to 3 eV kinetic energy depending on the photolysis wavelength, but in the presence of increasing a.mounts of added helium, the average energy of the atoms at the time of reaction is shifted toward thermal energies. Our results are extrapolated to infinite dilution in He, which gives ordinary thermal rate constants characteristic of the teill]?erature of the helium. 112 MECHANISM The following mechanism is used to interpret the extrapolated results. me + hv - H* + X [3l DX + h'V D* + x (4] HD + X [l] + D [2] ED + x ['5] DX + H [6] H +DX H +DX - me - D + HX D + HX - - D2 + x - H2 + x X + X M - x2 D +DX [7] H +RX [8] + + M The la.st reaction occurs both on the walls and by a termolecula.r mechanism in the gas. The ratio a= [HX]/[DX] is kept small (0.02- 0.06) to minimize the importance of reactions [5] a.nd (6] and to permit neglect of reaction (8) in the mechanism. The effect of · including reaction [8] is discussed in a later section. Neglect of several other reactions is justified elsewhere. 2 The quantum yields of [3] and (4] are one, 6-8 so the ratio of photoproduced H and D is simply £rrJ~nx· If one knows this ratio and the auxilliary rate constant ratios involving reactions [5], [6] and [7], then a. single measurement of the extrapolated product ratio [HD]/[D2 ] suffices to determine k /(ki + k2 ). But accurate 1 direct knowledge of a is difficult to obtain, and one can instead va:ry the wavelength (and hence ~nJcDX) with a constant. Then 113 k /(k + k ) and a. can be calculated. from measurements of the 2 1 1 product ratio, the auxilliary ratios and the wavelength dependence of EdEnx· The mechanism neglecting reaction [ 8] ·~ti th a. steady state assumption for the H and D concentrations yields for the extrapolated product ratio, [RD] )He _ [ ax[l+ a(C + a.D)]l - Ol. c + aD y - - - _ , . . . . - - - , - ([D2] 0 l+ a(l - a)x (1) where a = k 1/(l\ + k 2 ) k /k 1 c = k5/k7 2 Ol = a/ ( 1 - a) = [RX] / [ DX] D = k /k 6 7 The complete mechanism which accounts for the positive slope of a plot of [D2]/[ED] versus [DX] /[Re] has been discussed elsewhere. 2 There it was shmm that very little information content could be extracted from the slope unless it was lmown to within 6 to 8 signif'ica.."lt figureso However, the intercept value given by Eq. (1) is sui'ficient to give the needed information on a and a. On the basis of Eq. (1) it is expected that a plot of' the extrapolated :product ratio versus x/[1 +CL (1-a)x] will be linear with slope s = a.a[l + a(C + aD}] (2) = a(c + aD) (3) intercept i From this it follows that a= C + K s [i ( i + l 1) + sK j (4) 114 a = i (i + 1) + sK (5) (1 + i)(C + K) where K = (k /k ). (k /~) has been introduced because 1t is 6 2 1 more readily estimated by theory than the related D = k 6/~. The term (1 - a) occur-ring in the expression for ([HD]/[D2) )~e is obtained by first assuming a = 1 and calculating a and a from He a. plot of ([HD]/[D ] ) 2 0 versus x. These calculated values of a and a are then used to make a new plot of ([HD]/(D2 ])~e versus x/[l + a(l-a)x], the slope and intercept of which are used to calculate new values of a and a. This process is repeated until the xesults converge, w'.aich usually takes 3 or 4 iterations. Calculation of the ratios C and K will be discussed later. If reaction [8] is added. to the mechanism, the expression for the extrapolated product ratio becomes (HD] He= [D2 ] 0 afC + L aD + aX [ 1 + 1+aG a(c + an[a~g : ml aaG + 1 + ax(l - a) J (6 ) where G = k /k • Then a plot of ([HD]/[D ] )~e versus 2 8 1 x/[aa.G + 1 +a.x(l - a)] is expected to be linear with slope s = aa j1 a(c + intercept i = + a[c + an/aG + ~ )] l \aaG + 1 J (7) aD ) 1 +aG Solving for a in Eq. (8) and using this in Eq. (7) one obtains a 5th order equation in a which can be solved using Newton's root method.9 In the worst case in our experiments corresponding to the largest value of a of 0 .. 06 in DBr, we find 115 tha. t a = 0. 99 when reaction [ 8] is neglected and a = 1. 00 when reaction [8] is included in the mechanism. This is within exper~ imenta.J. error and justifies neglecting reaction [8]. EXPERDIBNTAL Preparation, :photolysis and analysis of the mixtures was carried out by techniques described elsewhere. 2110 DBr and DI were obtained from Merck, Sharp and Dohme of Canada. Ltd. The DI, after transfer to the photolysis vessel, contained ?Jfo of RI and was used in that form. Under similar conditions the DBr contained less HBr impurity and we added HBr to it. helium was obtained from Matheson. Separate vacuum lines and photolysis cells were used for DI and DBr. are given in Table I. Ultra high purity The wavelengths used Great care was takenlO to insure that the light was sufficiently monochromatic to avoid significant error. Conversion of halide ranged from 0.2 to 2fo in about 1 hour for most experiments. At each wavelength the product ratio [D2]/[HD] was plotted versus [DX]/[He] for about 5 to 15 photolysis mixtures with [DX]/[He] ranging from about 0.1 to 2. Such plots a.re linea.r2 '3 and a linear least squares fit gave the desired extrapolated intercept and a measure of its uncertainty due to rand.om errors (mostly caused by lack of constancy of a). in Figs. 1 and 2. The plots are shown 116 Figure 1. Plots of photolysis results for DBr-He mixtures 117 -. LO ~ ! j \ 6 0 . © l I \ e .......... I>- CD 0 LO 0 ¢ (\JI o QI C\I 118 Figure 2. Plots of photolysis results for DI-He mixtures. 119 E:a 33 4 0 A 3251 @ 3130 0 3029 12 II 10 9 D _g HD e @ 8 0 7 6 5 4 ~. . 3..._~~~~~--'---~~~~~__..~~~~~~,__J 0 0.5 1.0 DI/He 1.5 120 RESULTS AND DISCUSSION Results of the variable ·wavelength :photolyses of HX-DX mixtures in helium are presented in Table I. Plots of extrapolated [HD]/[D2] ratios versus x/(l + a(l-a)x + aaG] are shown in Fig. 3. The values and stand.a.rd errors of the resulting slopes (s) and intercepts (i) were obtained from a least squares fit which took into account errors in both the ordinate and abcissa11 of each point. values of a and a. a.re shown :for each series. Finally, The standard error shown is the square root of the sum of squares of individual errors. The later were obtained from products of derivatives of Eqs. (1) and (4) with the appropriate estimated standard errors for each variable. In order to evaluate the expressions for a(DX) and Cl. from Eqs. (4) and (5), one must have the rate constant ratios C = k5 /~ and K = (k6/k2 )(k1/k.;) or, if the ef'fect of reaction [8] is to be included and Eqs. (7) and (8) used, we need G = k8/ki_ in addition. The ratio k /k2 is estimated by equilibrium statistical 6 mechanics to be 4.2 for the bromides and 3.5 for the iodides. · We can estimate k /~ and k8/k from transition state theory or 5 1 make an independent measurement of these quantities. Timmons and Weston12 give force constants and internuclear distances for the H-H-Br activated complex. assumed. to be isotope independent. These parameters are Thus, the following :formulas can be used to calculate the needed frequencies: Table I. Summary of results of photolysis of DX in He. least squares standard. errors. HalidE >.. - X=~ -· I ([IID])He Standard. error s are calculated. as described. in the text. -- [D2J 0 3029 2.50 ± 0.07 8 0.094 ± 0.005 3130 3.68 ± 0.08 8 0.133 ± 0.006 6.8 ± 0.3 11 0.197 ± 0.01 3340 11.0 ± 1.0 5 0.300 ± 0.01 2138 1.42 ± 0.02 5 0.198 ± 0.002 2400 3.25 ± 0.09 5 0.317 ± 0.006 3252 Br DX No. of Pbotolyses The indicated uncertainties are the s 0.024 ± 0 . 001 i a 0.038 ± o.oo6 0.023 ± 0.002 a o. 97 ± 0.05 ..... [\.) ..... 2483 4.99 ± 0.14 5 o.410 ± o.oo4 2537 6.78± 0.29 5 0.512 ± 0.003 0.065 ± 0. 002 0.120 ± o.008 0.059 ± 0.005 0.99 ± 0.03 122 Fig. 3. Plots of ([HD]/[D2 ]) wavelengths. He ratios measured at different 0 123 -- 0 co - <!> <l: I'- 0 tj + x <.O + -x <l: I ,..._ ~ l{) ~ N ,,_ CD ...... 0 0 0 Q <.O I.() 0 0 ~ 0 C\J 0 0 ...- 1:24 # :;6 >)_ + x3 = ~ +µ.y)fy;f + {µy_ +Ji-z)fyz - 2JY'int >;s = (fy;ffyz - f~ntHJ4xf'y + }1-y}Jz + }Ly}Jz > 'f = 2 where 'A~ = (9) fa [ RXYRyz (10) RXY~ + Ryzfkx + (~ + ~)2Ji-y] Ryz RXY (11) RXYRyz 47lv[ 2 and vf is the vibrational f'requency of the activated complex, 'VF is the bending frequency of the activated complex and '1/~is the imaginary frequency corresponding to motion along the reaction coordinate at the saddle point of the potential energy surface. The fij's are force constants corresponding to a linear J:fZ type molecule, the Rij's are the internuclear distances and Jl-i = l/m1 where the m1 's are the masses of the atoms. The 5 ratio k /~ can be expressed in terms of the above calculated frequencies as (12) where v DX and'VBX are the vibrational frequencies· of DX and BX, (~ - ~X) is the difference in zero point energy and u = hC'J//k!r. The vibrational :frequencies of HBr and DBr are 1650 cm-1 and 1898 cm-1 respectively. 13 The zero point energy difference is 376 cm-1 • The ratio k /k is calculated by the same expression with DHX 8 1 replaced by HHX and DDX replaced by HDX. Likewise · 125 sinh(l/2 ulDDX) sinh(l/2 ullIDX) sinh(l/2 u2DDX) 2 sinh(l/2 ~x) (l3 ) Using sets A and C of force constants and internuclear distances given by Timmons and Weston, we obtain k /~ 5 = 2.2, k1/17 =1.2 4 and k /k = 2.2. Experiments done in this laborator? , indicate 8 1 that k5/17 = 2.0 : 0.2, kl/17 = 1.35 : 0.14, and ka/11_ = 2.0 ! 0.2. These latter experimental values were used in interpreting the data. For the iodides the only work on isotope effects is by = 1.75 '! 0.15 from his frequencies. 8 7 Then, experiments done in this la.boratory14 used this number to Sullivan. + We calculate k /k 0.15. The extinction coef'f'icients for HBr, DBr, HI and DI have been measured in this laboratory. 1 5 These values were used to obtain the x 's listed in Table I. With the above values for /17, /17 k1 and k /k1 the abstraction fraction a is O.<JT :!: 0.05 8 5 for DI and 0.99 :!: 0.03 for DBr as shown in Table I. k 5 Our major sources of error are due to uncertainty in k /~, the slope and the intercept. The ratio k /~ contributes 2.&{o 5 error to a(DBr) and 2. 5% error to a(DI). errors of l.\f/; to a(DBr) and 2.1% to a(DI) while the intercept error is l.'7% in DBr and 4.5% in DI. negligible. errors. The slope contributes There error due to K is The errors reported in this paper are standard 126 A systematic error in the extinction coefficients could alter the results. For example for the iodides a decrease of' x(3340A) to 9.6 f'rom 11.0 and o:f x(3250A) to 6.25 :trom 6.77 would increase a(DI) to 1.00. LeRoy et al. 16 A flow system such as that used by in the study of hydrogen isotope reactions is being set up by one of us (D. R. Davis) to achieve a more direct measurement of a. 4 The abstraction :traction has been studied theoretically using a statistical phase space theory of chemical kinetics. This theory contains no adjustable parameters and gives values of a(DI) = 0.98 and a(DBr) = 0.97 at 300°K. As can be seen from Table I, these values are in good agreement with the experimental values of' a(DI) = 0.97 :!: 0.05 and a(DBr) = 0.98::: 0.03. The reason the theory predicts abstraction :fractions near 1 is that the exchange reaction leading to HX and D is endothermic and hence is statistically less likely to occur. The theory also predicts that the abstraction :fraction will decrease with increasing temperatures as the endothermicity of reaction [2] is overcome. However, the temperature dependence of the abstraction fraction was not measured. 127 REFERENCES 1. A. Kuppermann and J. M. White, J. Chem. Phys. , 44, 4352 ( 1966). 2. J. M. White, D. R. Davis, J. A. Betts and A. Kuppermann, forthcoming (this is Paper I in this thesis). 3. R. M. Martin and J. E. Willard, J. Chem. Phys., 40, 3007 (1964). 4. D. G. Truhla.r and A. Kup:permann, J. Phys. Chem. , 1l1 1722 (1969). 5. c. A. Parr, Ph.D. Thesis, California Institute of Technology, 1968. 6. E. Warburg, Sitzb. Preuss. Akad., 300 (1918). 7. A. Bodenstein and C. Lieneweg, Zeit. Phys. Chem., 119, 123 . (1926). 8. B. Lewis, Proc. Natl. Acad. Sci., 13, 720 (1927). 9. M. Abramowitz and L. A. Stegun, National Bureau of Standards Applied Ma.thematics Series 55, 1964, :p. 18. 10. D. R. Davis and J. A. Betts, forthcoming (this is Appendix A of this thesis). ll. W. E. Deming, Statistical Adjustment of' Data (John Wiley and Sons, Inc., New York, 1943). 12. R. B. Timmons and R. E. Weston, Jr., J. Chem. Phys., 41, 1654 ( 1964) • 13. G. Herzberg, :Violecular Spectra and Molecular Structure, II, Spectra of Diatomic Molecules (D. Van Nostrand Co., Inc., New York, 1950). pp. 534-540. 14. A. Persky and A. Kupperma.nn, forthcoming. 128 15. J. A. Betts, D. R. Davis, J. M. White and A. Kuppermann, forthcoming. 16. B. A. Ridley, W. R. Schulz and D. J. LeRoy, J. Chem. Phys., .1,i, 3344 (1966). 129 PAPER 3 EXCITED IODINE ATOMS BY PHOTOLYSIS OF DI INTRODUCTION Deuterium iodide has a broad, continuous absorption which extends from the near ultraviolet to the vacuum ultraviolet, reaching a maximum around 22255{. Only three excited states ( 371"~ J,,, 37!') can contribute to this absorption. 1 ' 2 All three o' , are repulsive and lead to dissociation of the iodide. The disso- ciation of the 37'o and 1 -rr states leads to ground state iodine atoms, 2P 312 , while that of the 371'+states leads to an excited iodine 0 atom, 2P , which is 0.942 eV above the ground state. This is 112 depicted in Fig. 1. Therefore, at a given wavelength :photodissocia- tion of DI can occur into two channels: DI+ hv DI+ hJI - - 2 < P3/2) [l] D + I*(2pl/2) [2] D + I We have measured the fraction f(>..) = k2/(kl + k2) (1) of iodine atoms produced in excited states by photolysis of' DI as a function of' ""7a.velength. This fraction f is zero unless the :photon absorbed has sufficient energy both to break the D-I bond and to excite the iodine. The critical wavelength corresponding to this energy in DI is 307o1l. Cadman, Polanyi and Smith3 measured the sum of f in HI at 130 Figure l. Potential Energy Curves for HI. 131 70 60 - 50 I"> I 0 x I 40 E -> <..> 20 10 132 2537~ and the fraction of iodine atoms which are produced excited in the reactions: H + HI H +HI - H2 + I (2P3/2) [3] H2 + I*(2pl/2) [4] They reported C = k /(k + k ) + k4/(k + k ) to be 1.5 + 0.4. 2 1 4 2 3 In a later paper Cadman and Polanyi4 used a new experimental measurement of the Einstein transition probability to reinterpret their data to give C = 0.55 ! 0.25. They also estimated k4/(k4 + k ) 3 to be 0.02 ! 0.015 indicating that f = 0.53 ! 0.25. Donovan and Husain5 used flash photolysis of HI in the ultraviolet to determine the fraction of' iodine atoms formed in the excited state. Using a continuous source, theyobserved an average f 'of approximately 0.2 for wavelengths longer than 2000~. Compton and Martin6 used a method similar to ours to obtain f's in HI of 0.93 ! 0.15, 0.81 ! 0.15 and 1.00 ! 0.15 at wavelengths of 2537~1 22~ and 1849R, respectively. METHODS Our measurement of f'(A.) follows f'rom the fact that the deuterium atom produced in process [l] has nearly 1 eV more kinetic energy (in the laboratory system) than that produced in (2]. In other work f'rom this laboratory7 we have shown the yield of HD from the reaction D*+H 2 - IID+H [5] is a sensitive function of the initial kinetic energy (denoted by the asterisk) of the deuterium atom. 133 Figure 2 presents the fraction A of D* atoms which undergo reaction [5 ] in ~ as a f'unction of the initial laboratory energy at 300°K. A is called the integral reaction yield of D* with H • 2 The quantity (1 - A) is the fraction of those atoms which are thermalized by elastic collisions with H and are removed by 2 thermal reaction with a scavenger, in our case DI or DBr. The f'unction A(Elab) can be used as a calibrated "energy measuring device" for deuterium atoms in the photolysis of DI in the presence of H • 2 This calibration is based on measurements of A for D* produced by photolysis of DI and DBr with monochromatic radiation for which Elab is kno"Wn (i.e., for which f is zero or very small). Photolysis of DI at wavelength A greater than 307cil yields l)-K having an average laboratory energy of E _ ~ (he lab - 1I1:DI ~ - Do) + mI h . ) + IDn ;~) O unI \rot unr \'-DI (2) If the DI is at 3000 K, this gives ~ E = ~I (!1..£ lab A. n°) + 0 026ev + O.OOleV O • (3) In the above D~ is the bond dissociation energy of DI, (Erot) is the average rotational energy of DI and (Ei;I) is the average laboratory translational energy of DI molecules. wavelength iodine is produced in both the 2 P ; 3 2 If at a given and 2 P ; states, 1 2 D atoms of two different energies are formed; one is given by Eq. (2) when ng is replaced by [Dg + E( 2 P ; )]. E( 2P ; ) is the 1 2 1 2 2 electronic excitation energy of the P ; state and is 0.9426 eV 1 2 134 Figure 2. The fraction of D atoms having laboratory energy Elab which react with pure H to form HD 2 (T = :300°K). 135 .------------~----..----~~---~----_,,.--______ o "> 0 (\.! -> . w ® o_ - lO -. 0 . I.() o~.---------ioo~.-------w...1:-.-------~~~-.-------~~.~------w 0 - 0 0 0 0 0 - 136 for iodine atoms. (Erot) , (EJ)I) and Elab have distribution functions associated with them due to thermal spreads and the fact that the photolysis light is not completely monochromatic. The spreads in the second and third terms have been shown to be 0.018 eV and o.ooo45 ev respectively.7 The spreads due to the photolysis light are less than 0.02.eV in these experiments so the D* atoms are produced in a nearly monoenergetic distribution. The quantity f can be determined from a measurement of the average A for D atoms produced in H by photolysis of DI at the 2 desired wavelength, and :from interpolated values of A(E1 ) and A(E ) 2 :from Fig. 2. Of the D* atoms produced, a :f'raction f have 2 Elab = E1 and a f'raction (1 - f) have Ela.b = E2 + E1 - E( P1; 2 ). Thus the fraction of all D* atoms which yield HD is A(.A) = f • A(E1 ) + (1 - f) • A(E2 ) where A(.A) is the observed average. f (4) Solving, we get = A(E 2 ) - A(A) A(E2 ) - A(E1 ) (5) EXPERrMENTAL DI-~ and DI-He mixtures were prepared using a mercury-free vacuum line. The cylindrical reaction vessel was 50 mm in diameter and 75 mm long and was made of fused silica vi th high optical quality windows. A Ha.novia SC 2537 low pressure mercury lamp with a 2 mm Corning 7910 filter to remove the 18491l line was used for photolysis 137 at 2537~. A Ha.."'lovia 2500 watt medium pressure mercury lamp was used for photolysis at 2800~ and 24oolt. The light was passed through a Bausch and Lomb model 33-86-01 monochromator with a 2 mm thick Corning 7910 filter at the exit to remove short wavelength radiation (transmission lo{o at 2240~, l'/o at 2175~). A zinc Phillips spectral lamp with a ~-2-butene gas filter (100 torr pressure, 5 cm pathlength) was used for photolysis at 2138~ (transmission &:!fo at 21381l, less than 0.01'/o at 2050~). The light intensities were of the order 5 x iol5 photons/sec at all wavelengths. At all wavelengths about lc:/o of the DI was decomposed. Ai'ter photolysis, the DI was frozen in liquid nitrogen and the volatile gases transferred to an ana~ J.ysis bulb via a toepler pump. The products were analyzed for HD and D on a calibrated CEC-21-103C 2 mass spectrometer. Unirradiated blanks showed no products. The hydrogen used was depleted in deuterium atoms with respect to their natural abundance and contained. only 5 ppm HD and cor-.L"ections for this HD amounted to less than 1</o. Further details are given elsewhere.7 RESULTS AND DI SCUSSION At each waveleng""vh a series of DI-H and DI-He experiments 2 were performed at (DI] / [ G] (G stands for H or He) ratios varying · 2 from 0.3 to 1.5. · The product rati o [D2] /(1ID] was then plotted against the reactant ratio [DI] /[G] . These plots were linear for 138 both hydrogen and rare gas runs. A typical plot is shown in Fig. 3. A linear least squares analysis gave the intercepts ([D ]/[HD])~2 2 He and ([D 2 ]/[HD]) and their standard deviations. The intercepts 0 He ([D ]/[HD]) are needed to correct the results for HI impurity 2 0 in the DI; they would be inf'ini te if' there were no impurity. The ·· quantity A(DI,A) is derived. elsewhere7 and is A (l + a.Bx) A(>.) = 1 1 + a(l+ A) + a(l + aBxf [xa2 + (C where a= [ RI] x (Dfj' (6) + aD)(a + 1 + a.x)] = ~BI ~DI where the rate constants above correspond to the thermal reactions: D + DI H + DI H+ DI D + HI D + HI - - D + I 2 HD +I [6] +D [7] DI + H [8] BD + I [9] HI - c We used a(DI) = 0.97 : o.04, = 1.45 ! 0.15 and D [5] = 0.14 ! 0.02; the determination of these rate constant ratios is discussed elsewhere, 8 as is the determination of a and the measurement of x. We used a(DBr) = 0.96 ! 0.04 to calculate the upper portion of' the curve in Fig. 2. This value could be either 0.93 or 0.99 as discussed in reference 7. The effect of' changing this 139 Fig. 3 Plots of product ratio [D2 ]/[lfD] versus reactant ratios [DI]/[H2 ] or [DI]/[He] for photolysis of DI-H and DI-He mixtures at 2537R. Linear least-squares intercepts are 1.48 ! 0.06 and 11.1 ! o.6. 2 140 -. LO 0.. - Cl IQ 0 QI (;) @ 141 value will be shown later. The results of all the experiments are shown in Table I. The main sources of error are the random error in the experiments, errors in the values of a(DI) used to calculate A(obs) and a(DBr) used to obtain the upper portion of the curve in Fig. 1, and errors in interpolating the values of A(Ei). For the latter we have used errors the size of the error bars in Fig. 2. The stand.a.rd errors listed for the A(obs) take into account errors in all the quantities that go into determining A. This is discussed in detail elsewhere. 7 T'.ae errors in A(A.) are important in all experiments. The experiments at 2800)1 include only 4 points so the random error contributes al.most the entire total error listed. At 2537~ and 2400~ A(A.) and A(E2 ) contribute almost equally to the error while at 21385( the major source of error comes from A(E2 ). Since A(E ) is dependent mainly on a(DBr), changes in this quantity 2 greatly affect the reported f. For example, if a (DBr) = 0.91, f(213ffi() = o.41, while if a(DBr) change of almost 5Cf/o. =0.99, f(213~) = 0.24, a , The results at other wavelengths are not as dependent on a(DBr). We have used the interpolated values of A(E2 ) with the assumption that the observed A values are not strongly biased by production of excited bromine atoms in DBr photolysis. Although there is no reason to believe that a significant fraction of these bromine atoms are excited, 1121 7 our values of f'(DI, A.) would have to be revised if f(DBr,A.) were found non-zero. For example, if TABLE I. A(R) B2 Su:rnmary of Results 28oo 2537 24oo 2138 slope 2.0 ± o.4 i.64 ± o.o8 1.65 ± 0.07 i.36 ± 0.02 intercept i.4 ± o.4 1.48 ± 0.06 1.25 ± 0.07 o.45 ± 0.02 slope o.4 ± o.66 ± O.ll 3.4 ± 0.9 ± 0.1 intercept ll.l ± 0.9 10.8 ± o.8 12.1 ± 0.2 9.4 b. 0.62 ± 0.2 0.58 ± 0.02 0.72 ± 0.05 2.10 ± 0.09 A(A) 0.229 ± 0.05 0.218 ± o.008 0.257 ± 0.014 0.505 ± 0.02 E1 {eV) E2 (ev) o.402 0.854 1.128 i.736 i.326 1.780 2.056 2.682 A(E1 ) o.o ± o.o65 ± 0.005 0.143 ± 0.03 0.336 ± 0.03 A(E2) 0.212 ± 0.02 0.35 ± 0.02 o.427 ± 0.03 0.590 ± 0.03 f -o.o8 ± 0.27 o.46 ± 0.05 o.6o ± 0.07 0.33 ± 0.1 He 0.1 0.001 0.2 ± o.8 '~ """ N 143 f(DBr, 2250~) = 0.05 then f(DI, 2537~) would increase by 0.019. We can compare our DI results with the HI results of Cadman and Polanyi and Compton and Martin. Cadman and Polanyi obtain f(HI, 2537R) = 0.53 ! 0.25, while we obtain f(DI, 2537R) = o.46 + 0.05. Compton and Martin obtain f(HI, 2537R) = 0.07 ! 0.15. Further experiments are needed to establish f(HI) and to show whether there is a measurable real difference between f(HI) and f(DI). It is difficult to compare our results with those of Donovan and Husain since they measured an average f over a continuum of wavelengths. Our results agree qualitatively with theirs. The isotope effect to be expected in going from DI to HI can be estimated using the following approximate theory. First, we assume that the extinction coefficient to the i th electronic state is: E(v,i) = vK(i) \f10 In the above \fl, 0 2 2 (7) is the square of the normalized ground state ' vibrational wavef'unction, vis the wavenumber and .K(i) is related to the integral over the electronic wavefunctions and is assumed to be constant. This approximation is further discussed by Coolidge, James and Present9 and by HerzberglO and has been used by Goodeve and Taylor11 in analyzing their HI and HBr spectra. The total extinction coefficient at each wavelength is just E = LE ( 11, i ) j ( 8) Secondly we assume that the upper electronic state :potential curves are given by the expression: (9) 144 where p =r - r e and r e is the equilibrium distance of the oscilla- tor, the D (i)'s are dissociation energies for each excited state 0 and the E(i)'s and F(i)'s are isotope independent parameters to be fitted to the experimental data. included in \jl and the D0 (i)'s. 0 10 and D(2) = 32,263 cm-1 • The isotope dependency is For DI, D(l) = D(3) = 24,66o cm- 1 In the following discussion we have assumed the t:round , state vibrational wave:function to be a Morse wavefunction l)(2b)2b (2b) 1 12 of the form: exp[2b(-ap - e-ap) + ap1 (10) 'J In the above, a = 0.12177 we~ where we is the vibrational frequency equal to 2309. 5 cm-1 :for HI and 1640 cm-1 for DI, 10 De is the dissociation energy from the bottom of the potential and -1 equals 25,804.7 cm -:for both HI and DI andµ. is the reduced mass and b = 2De/we. An attempt was made to fit the parameters K(i), E(i) and F(i) to the experimental data illustrated in Fig. 4. These attempts were largely unsuccessf'u.l in providing precise agreement with our data although qualitative agreement could be obtained. This analysis is sufficient to determine the magnitude of the isotope effect to be expected in going from DI to HI. For example for our best fit with K( l ) = 1.2 x 10-4 1. mole -1 , E( 1 ) =13370 cm-1 , F(l ) = 3.1 cm-1 , K( 2 ) = 7.0 x 10-4 1. mole -1, E(2 ) = 11772 cm-1 , ~ cm-1 F ( 2 ) = 6 .o cm-1, K( 3 ) = 6 .o x 10-4 1. mole -1 , E ( 3 ) = 29j70 1 and F(3) = 1.5 cm- , we obtain f(DI, 255ci() = 0.76 and f(HI, 255mt) = 0.82. Changing the above parameters changes the predicted 145 percent isotope effect only slightly. This predicted isotope effect is consistant with that observed by comparing our results for DI and Cadman and Polanyi's results for HI. However, it is not consistent if we compare our results with those of Compton and Martin for HI. In the above analysis we did not take into account the possibility than an absorption to the 377 state could cross to the 3.,, + state producing an excited. iodine atom. Such 0 intersystem crossing has been observed in other systems (see for instance Herzberg13 ). If this intersystem crossing were much more efficient in DI than in HI it could explain the differences in our results and those of Compton and ltiartin. One value of the experiments is to determine to what extent each of the three possible transitions to excited states contribute to the total extinction coefficient of DI. According to 1 2 Mullikan ' at low energies the extinction coefficient would be due to transitions to the 3Tr0 state. At energies above about O. 6 eV transition to the 37To+ state contributes. At even greater energies come contributions from transitions to the 17T state. Since only the 377 + state leads to an excited iodine atom, 0 we have assumed that the quantity f which we measured is equal to the fractional contribution o:f' this state to the total extinction coefficient. as there In this analysis we will neglect intersystem crossing is no criterion for deciding how much it would contribute. I f we assume that all excited iodine atoms :produced come from a transition to the 371"+ state, the fraction f multiplied by the 0 146 total extinction coefficient gives the contribution of this state to the extinction coefficient at each wavelength measured. Fig. 4 shows the resulting breakdown of the extinction coefficient of DI versus wavelength into component parts. The extinction coefficients used were measured in this laboratory. Our analysis indicates that there is a maximum in the curve showing absorption to the 3,, + state at approximately 2300R. 0 No attempt was made to determine the contribution from transitions to tb.e 1 71' state. 147 Figure 4. Contribution of the DI excited states to the total extinction coefficient as a function of wavelength. The upper line is the measured extinction coefficient from reference 8 while the lower slashed lines are the contributions of each state. 148 0 0 11 ~ II II I // I I I I/ ,'l'I ;/ 0 0 <O C\l :x: I; I- 1' I C!> , I z ,/I I I II1 1 0 0 I ~- C\J I 11 A \0 ~ I \ e 0 0 f;; ~\ C\J C\J '~ \,\ \ \ ' \ '-,, 0 '-------1------1------'-----~------'-------'0 0 0 ro 0 LO C\J 0 0 0 LO (\J ( w~ 1- 0 0 a1ow sJa+!I) IQ.ii> 1- w _J w > <t 3: /1 I - O........ <! 0 LO 00 C\J 149 REFERENCES 1. R. s. Mulliken, J. Chem. Phys., 8, 382 (1940). 2. R. S. Mulliken, Phys. Rev., ,21, 310 (1937). 3. P. Cadman, J. C. Pola.nyi and I. W. M. Smith, J. Chim. Phys., §!, i l l (1967). 4. P. Cadman and J. C. Polanyi, J. Phys. Chem., 72, 3715 (1968). 5. R. J. Donovan and D. Husain, Trans. Faraday Soc., 62, 1050 (1966). 6. L. E. CoIDIJton and R. M. ~.artin, J. Phys. Chem., 11, 3474 (1969). 7. J. M. White, D. R. Davis, J. A. Betts, and A. Kupperma.n, forthcoming (this is Paper I in this thesis). 8. D. R. Davis, J. A. Betts, J. M. White and A. Kuppermann, forthcoming (this is Paper II in this thesis). 9. A. s. Coolidge, H. M. James and R. D. Present, J. Chem. Phys., ~, 193 (1936). 10. G. Herzberg, Spectra of Diatomic Molecules, (D. Van Nostrand · Co., Inc., Princeton, New Jersey, 1950) pp. 199-201, 392-3. 11. C. F. Goodeve and A. W. C. Taylor, Proc. Roy. Soc., Al52, 221 (1935). 12. P. H. Morse, Phys. Rev., 34, 57 (1929). 13. G. Herzberg, Spectra of Diatomic Molecules, (D. Van Nostrand Co., Inc., Princeton, New Jersey, 1967) pp. 359, 368. 150 PAPER 4 1. INTRODUCTION The chemical reaction cross section is a very fundamental dynamical quantity which permits the formulation of bulk reaction properties in terms of the molecular level dynamics of reacting systems. 1 In a previous paper2 (designated here as I) the impor- tance of chemical reaction cross sections and the experimental difficulties in obtaining them were discussed. A photochemical technique was presented which gives the energy dependence of the integral reaction yield A for the reaction: D*+R2 - [ 1 '] HD+H where A is defined as the fraction of the hot D·* atoms (produced monoenergetically) which react accordi..."1g to [ 1'] rather than with a dilute scavenger of thermalized D atoms. It describes the com:peti tion between reaction [ 1 '] and the thermalization process: [2'] and was shown to be closely related to the cross sections for these collision processes. In this paper we extend the technique to obtain the integral reaction yield of the reaction: H* + cn 4 - HD + CD 3 (1) as a :f'unction of energy. In (I) we discussed the many experimental difficulties associated with obtaining the c1•oss sections of reaction [l'] and its isotopic counterparts. Neither thermal rate constant 151 measurements nor molecular beam experiments are able at present to f'Urnish the cross sections for these reactions in the energy range from O to 3 eV. As explained in (I), such in:formation would be extremely useful for comparison with either !: ;priori or more approximate model calculations. This information can be obtained using our teclmig,ue. In this pa.per we discuss the details pertinent to the H + CD4 system. In section 2 we outline the basis of the present method and in section 3 the experimental techniques employed. In sec- tions 4 and 5 we discuss the results of the experiments and the manner of analyzing these results to obtain the integral reaction yield. In section 6 we discuss the relation of the integral reaction yield to the reaction cross section. 2. METHOD 2.1 Integral reaction yield The method consists of photolyzing mixtures of HBr and cn4 with monochromatic radiation to produce translationally "hot" monoenergetic hydrogen atoms. therma.lized in the system. These either react "hot" or are The integral reaction yield: (1) is measured as a :f'uncti on of the initial laboratory energy EiO) of the hydrogen atoms produced when the H.Br. is photolyzed with ligllt of wavelength A • In the above, k (A.) and k2 (X.) are the 1 152 effective bimolecular rate coefficients for the elementary :processes: RD + CD 3 [1] [2] describing the rates of reaction and thermalization which accompany the injection of' monochromatic hydrogen atoms into thermal CD gas. 4 The asterisk denotes translationa.J.ly hot hydrogen atoms which are defined in section 2.2. The rate coefficients k1 and k depend on the energy with 2 which the hydrogen atoms are initially formed. The integral reaction yield ia a measure of the competition between reactive collisions and non-reactive ones, and its variation with wavelength is related to the energy dependencies of the corresponding cross sections. If information is available about the differen- tial non-reactive cross sections i'rom either theoretical calcul.ations or independent experiments, the exchange reaction cross section, averaged over the appropriate internal states of the C}\, (0) can be obtained from the experimental A(E 1 ) by methods which will be described. later. 2.2 Hot and thermal hydrogen atoms As in (I), the steady state distribution function of laboratory energies of hydrogen atoms is e.A.")?ected 'to be bimodal with one (o) : :peak at the initial energy E1 and the other at an energy o~ the order of kT where T is Jche temperature of the reaction mixture. This distribution may, for descriptive purposes, be considered as 153 the superposition of t\."'O distribution :runctions, the hydrogen atoms described by the one peaked at El being called "hot" and O) denoted. as H*, and the hydrogen atoms described. by the one peaked at kT being called "thermal" and denoted as H. 2.3 Kinetic analysis In the following kinetic analysis we consider the thermal H and hot H* as two chemically distinct species since their reactive properties differ due to their dif:f'erent energy distributions. If the cn 3H impurity in the cn is neglected, the following mech4 anism is expected for the HBr-cD system: 4 4 4 HBr HBr - HBr + h:v H·l." +Br (O] H·* + CD CD + ED (1) H* + CD H + CD4 [2] H* + H + Br 2 (31 H + EBr [4] H + HBr H + Br 2 [5] CD CD H + Br [6] + M (7] w~· + 3 + HBr Br+ Br+ M - 3 3 Br 2 where the third body M is either a species in the gas phase or a surface. Neglect of other possible steps is justified in section Assuming steady state concentrations of (H*], (H] and (CD3), a kinetic analysis of the above mechanism gives: (2) 154 Therefore we should expect a plot of [H ) / [IID] versus 2 (IIDr]/[CD4] to be linear with positive slope and intercept as found previously by Carter, Hamill and Williams 3 and by Martin and Willard. 4 This turns out to be the case in our experiments. From equation (1) we can see that: l where ([IID] / [~] ) (3) 0 is the reciprocal of the intercept of the above st.:caigb.t line.. A determination of A requires therefore only the measurement of ( [HD] / [H2] ) • Small corrections a.re made 0 for competing reactions as discussed in section 5. In summary, the method for determining the integral reaction yield A consists in :photolyzing mixtures of RBr and CD with mono4 cbroma.tic light and measuring the resulting [H2] /[HD] product ratios as a function of the reactant ratios [EBr] / [cD4]. This provides a linear plot, the intercept ([~)/[HD]) 0 of which is used to determine A. 3. EXPERIMENTAL 3.1 Apparatus A mercury free vacuum line with an oil diffusion pump was used in preparing reactant mixtures. Pressures were measured wit.h a mercury manometer and cathetometer using a Pace differen- tial transducer as a null device. The reaction vessel was ma.de 155 of fused silica with optical quality quartz windows. It was cylindrical in shape being 6 inches long and 1 1/2 inches in diameter and had a stopcock attached for addition and removal of gases. The vindows were fused onto its ends. The photolysis apparatus consisted of an optical bench on which the light sources, filters and reaction vessel were mounted. The light sources used were as follows: 1849~ - An Hanovia low pressure mercury lamp which draws 110 ma current at 28o volts was used for photolysis at this wavelength. A 2 mm thick 60co gamma-irradiated lithium flouride wind.ow was placed in front of the lamp to remove ·the 2537R radiation. The absorbance of the filter was always 2.5 or greater at 2537R and approximately 0.5 at 1849Jl. The lamp emitted lC/fo 18491l radiation, so approximately lcr/o of all light passing through the filter was 2537R. Since the absorption coefficient of HBr at 1849~ is over 100 times greater than that at 2537~, the correction for the 2537R light passing through the filter is less than 0.1~ • . The intensity of the lamp with the lithium flouride filter was approximately 9 x io13 photons/sec. 206:Ut - An iodine lamp5 powered by a microwave source was used for photolysis at this wavelength. There were impurity lines at approximately 18201l, 183cil and 186oft which were less than 0.5<{, of the peak at 206:Ut. These lines were removed by the quartz window of the reaction vessel and by an additional thickness of quartz :placed in :front of the window. The intensity of the lamp was approximately 1.8 x io16 photons/sec. 156 2138ft - A zinc Phillips spectral lamp with a ~-2-butene filter (100 torr pressure, 5 cm pathleng'"vh) was used for photolysis at this wavelength. The transmission of the filter was 6Cff, at 2138ll and less than o.ozt, at 2050R. The la.mp had impurity lines at 2025Jt and 2062ft, each of which was 14i of the peak at 2138ft. Less than o.o~ of all light passing through the filter was 2025ft or 2062R radiation. The intensity of the lamp was approximately 6.7 x 1015 photons/sec. 2288R - A cadmium Phillips spectral lamp was used for photolysis at this wavelength. A small peak at 2145R was removed with a cis-2-butene filter (650 torr pressure, 5 cm pathlength). 'I'he transmission of the filter was 35% at 2288R and O.li at 2145~. There was also a peak at 2266Yl which was lCJ/o of the peak at 2288R. The resulting data were corrected for the presence of this peak as described in section 6. The intensity of the lamp was approx- imately 8 x 1015 photons/sec. 2537ft - A General Electric germicidal la.mp was used for photolysis at this wavelength. A Corning 7910 glass filter was placed in front of the lamp to remove any 1849~ radiation. A McPherson Model 235 fifty centimeter vacuum ultraviolet scanning monochromator with a grating blazed for 3000~ was used to scan the output of the light sources to check for unwanted lines. A RCA 935 phototube was used to measure light intensities during a photolysis. Products were handled on a mercury vacuum line. This line contained a dewar cooled by pumped liquid nitrogen (to produce 157 temperatures of about -212° C), a 1 1/2 liter toepler pump and analysis bulbs. A CEC-l03C mass spectrometer was used to analyze the reaction products. 3.2 Reagents The HBr was obtained in lecture bottles from the Matheson Company. It was frozen in liquid nitrogen and pumped to remove any hydrogen impurity and then distilled from a dry ice-acetone bath at -78°c to remove any bromine. It was stored in black 1-liter bulbs after purification and was repurified prior to a photolysis. Ltd. T'.ae CD4 was f:rom Merck, Sharp and Dohme of Canada It had a minimum stated isotopic purity of 9% D atoms. Our mass spectrometric analysis showed 0.9 atom percent H atoms. There was also o.4,% nitrogen and O.l&/o oxygen impurity present. 3.3 Procedure Prior to use the RBr was again frozen in liquid nitrogen in a cold finger and pumped and then distilled into the reaction vessel from a dry ice-acetone bath. The :pressure of the HBr was measured and found to range from 30 to 45 torr. The CD4 was then added to the reaction vessel and the pressure of the mixture measured. From the two pressure measurements, the pressure of the CD4 was determined. Pressures o'f CD4 ranged from 30 to 150 torr and [HBr] /[cD4] ratios ranged from 0.25 to 1.3. The reaction vessel was then moved to an optical bench 158 where the contents were photolyzed by one of the light sources described above. Blank experiments were also per.formed. as described in section 4. Mter photolysis one end of the reaction vessel was placed in liquid nitrogen for 15 minutes or longer to remove the HBr and some of the cn 4 • The contents v."ere then passed with the help of a toepler pump through a trap cooled to -212°c or less (as measured. by a copper-constantan thermocouple inserted. in the dewar) by pumped liquid nii:;rogen and were then transferred. to a glass bulb for analysis. With one such pass we were able to increase the ratio of ([ED]+ [~]) / [CD4] from a value of the order of a few times 10-3 to at least 0.098. The HD and ~ were measured. on the CEC mass spectrometer. Corrections were ma.de 'for the contributions of the remaining CD4 to the m/e 2 peak and the CD H to the m/ e 3 peak. 3 In no case did the correction to the m/e 2 peak exceed 5CY/o and it was usually of the order of 20-30% of this peak's height. The correction to the m/e 3 peak was al'W8.ys less than lo% of its measured. height. Calibration mll."tures with composition analogous to photolysis mixtures were prepared. These were then passed through the trap cooled to -212°c and analyzed.. This served to calibrate the mass spectrometer and also to check the efficiency of the trap. Reproducibility for a given sample ~ro.s 2!f, or better. 159 4. RESULTS OF (~]/[HD] MEASUREMENTS A series of photolyses was carried out at each of five different wavelengths. For each series the [HBr]/[cD4] ratios varied from 0.25 to i.3. The product ratio [~]/[HD] was then plotted against the reactant ratio [HBr]/[cD ]. 4 linear with positive slopes and intercepts. The plots were These slopes and intercepts and their standard deviations were determined by a The plots of [H2]/(HD] versus linear least squares analysis. [HBr]/[cD4J at all 5 wavelengths are shown in Figure 1, together with the root mean sq_uare fitted straight lines. T"ne effects of dark reactions, light intensity and extent of conversion wel'"e investiga"ced. The extent of each of these effects is as follows: (a) Dark reactions - Blank experiments were run at inter- vals in which the same experimen"~ procedure as other experiments was followed except for the actual photolysis. No products were observed in these experiments indicating that dark reactions do not contribute to the mechanism. (b) Light intensity - Two e:>...-periments with the same [HBr]/ [CD4] ratio were :photolyzed for the same length of time at 2288.R with light intensities of' about 1.2 x io16 and 6.0 x 1015 photons/ sec respectively. The results agreed to 'Within the zf, experi- mental reproducibility indicating there uas no detectable effect of intensity over this range of intensities. (c) Conversion - Two series of experiments with [HBr]/[CD4] 160 Figure 1. Variation of [H2]/[HD] with [HBr]/[CD4] at several photolysis wavelengths. ¢ 1849~ e 206Ji 0 213~ A 2288Jt 02537~ The straight lines are root mean square fits to the points at each "W"a.velength. 16 Db 120 110 100 90 80 70 60 50 40 30 20"--~~~~_._~~~~-'-~~~~--... 0 0.5 1.0 [Hsr J/[co4] 1.5 161 ratios ranging f'rom 0.25 to 1.0 were done at 2288R at different EBr conversions. Since the conversion is approximately equal to: [112]) ((HD] + 2[~]) = ~( (He] l+ 2 (~ [HBr] (4) [HBr]/[He]- the conversion could be measured by adding a known amount of helium to the reaction vessel after a photolysis and analyzing for helium as well as H2 and .IID. Only one experiment of this kind was performed at each wavelength and the intensity of the lamp and the photolysis time were kept constant for the remaining experiments. One series was done at o.45% conversion and the other at o,.9c:;fi conversion. The intercepts were 37. 7 ::: 0.9 and 37.1 ! 0.8 and the slopes i;rere 49.1 ! 1.8 and 49.3 ! 1.2 respectively. These agree within experimental error. However, experi- ments wlth [HBr] / [cD4] ratios ranging from 0.03 to 0.12 showed a marked conversion effect. The reason for this will be dis- cussed in section 5. T'.ae results of all experiments along with experimental conditions are given in Table I. Column 1 gives the photolysis wavelength and columns 2, 3 and 4 the initial laboratory velocity, initial laboratory energy a:nd initial energy relative to stationa:ry CD4 of the hydrogen atoms produced in: the photodissociation. Column 5 gives the extent of BBr conversion and columns 6 and 7 give the reciprocal of the intercepts and the slopes of the (H2]/[1ID] versus [EBr]/[cn4] least mean square straight line :plots. Finally column 8 gives the values of the reaction fraction ,~_,~,--· . TABLE I. Summary of Experiments - >..(~) vi0 )(106 cm/sec) E(o)(ev) 1 ~el{ev) conversion ([H2]/[HDJ)o slope A 2537 1.481 1.143 1.098 1.~ 61.8 ± 0.7 63.8 ± 1.0 0.0155 ± 0.0002 2288 1.797 1..684 1.609 0 . 52~1. ohfo 37 .8 ± 0. 5 48.7 ± 0.9 0.0251 ± 0.0003 ~ O'l 2138 i.980 2.o43 1.941 o.8% 30.3 ± o.8 50.5 ± 1.1 0.0311 ± o. ooo8 2061 2.081 2.257 2.154 o.5&fo 27 . 8 ± o.4 53.0 ± o.6 0.0338 ± 0.0005 1849 2.374 2.938 2.850 o.W/o 24.6 ± 1.0 56.5 :t 1. 5 0.0381 ± 0.0015 N 163 A calculated as described in section 5. The results of the HBr plus cn4 experiments at 1849ft can be , compared i;nth those of Martin and Willard. 4 We obtained a value ' of 24.6 :!: 1.0 for the intercept while they obtained a value o:f 15. This large discrepancy can be explained by the :fact that Martin and Willard did experiments at [EBr]/[cD4] ratios ranging from 0.02 to 0.1 at high conversions (-lo%). The discussion in section 5 shows that this discrepancy is to be expected due to the different experimental conditions and that our procedure and values are the correct ones to use to obtain information about processes [l] and [2]. 5. DE'I'ERMINATION' OF INTEGRAL REACTION YIELDS 5.1 Initial Energy of Photochemically Produced Hydrogen Atoms A detailed discussion of the factors involved in determining the initial laboratory translational energy in the photolysis of DBr is included in (I). Since the same discussion applies for lil3r, only a summary o:f the conclusions will be given here. Mull.ikan6 has concluded that the only important transitions from the 1 2:+ ground state of HBr to excited states are to the 3rr11 1 rr and 3n 0 states. He designates the ground state and excited states as N, 3Ql' ~ and % respectively. The 3Q.1 and lQ states dissociate to give hydrogen and bromine atoms in their ground states, 1s and 2P ; 2 respectively. 3 The Q0 state dissociates to give ground state hydrogen and excited 2P1 ; 2 bromine atoms. At 164 the wavelengths used in these experiments it is energetically possible to form bromine atoms in both these states. However, theoretical argumen"'.:;s and experimental evidence as :presented in (I) indicate that only ground state 3p / 2 bromine atoms are 3 formed. in the photolysis of B:Br at these wavelengths. The first excited state of the hydrogen atoms is at 10.2 eV and cannot be produced 'With the wavelengths used in these experiments. The initial kinetic energy of the hydrogen atoms is calculated assuming a lmowledge of the final electronic states in the dissociation of Iffir. For only ground state atoms the photon energy available to :products is E t = Ev - n°o (5) ·w·here Ev is the energy of a i:ihoton of frequency v and ng is the dissociation energy of the ground vibrational state of IIBr. The traction of this energy which goes to the hydrogen in the center of mass system of HBr is mBr/~r· When we add the small contri- butions due to rotation and translation of the I:IBr, the following .· expression for the average initial laboratory energy ElO) of . the .. D atoms is obtained: E(O) = mBr 1 mHBr (he _ DO) + mBr (E ) A 0 mHBr rot (6) Here (~r) and (Erot) are the average room temperature labora~ tory translational and rotational energies of the HBr molecules • . Over the wavelength range of these experiments the first term in the right hand side o:f: Eq. (6) varies from 1.12 to 2.91 eV, the second term is 0.024 eV and the third term is 0.0005 eV. 165 In (I) we showed that the contribution of excited vibrational states of DBr to the light absorption is negligible. The same arguments hold in the case of ID3r. In summary, we conclude that electronically excited bromine atoms are present in negligible amounts and that the absorption by vibrationally excited HBr molecules is also negligible. Eq. (6) gives the laboratory energy of hydrogen atoms at formation. 5.2 Mechanisms and Kinetic Analysis A mechanism for the photolysis of EBr-CD4 mixtures has already been considered in section 2.3. In this section we will justify the neglect of other reactions and include reactions involving the cn H impurity in the cn4 • 3 5.2.1 List of reactions in the HBr-cn 4 system (in the absence of CD H impurity) 3 Contributions of the following processes should be considered: HBr + hv H*+ Br (O] H*+ CD 4 CD3 +HD [l] H·* + CD4 CD4 + H [2] . H + Br 2 [3] H + BEr [4] H + Br 2 (5] CD H + Br (6] Br + M (7] HBr + Br [8] H* + HBr H* + HBr H + HBr - - CD + HBr 3 Br+ Br+ M - - 3 2 166 + CD 3 DBr + CD3 (10] Br2 + H (11] EBr + Br [12] CD H + D 3 (13] D+ HBr HD +Br (14] D+ EBr H + DBr (15] H + CD4 Br+ CD 4 Br+ EBr H* + Br 2 Ho)(·+ CD 4 Br*+ CD4 Br*+ EBr (9] ED - - DBr + CD3 (16] [17] Br2 + H In the following we 'Will show that reactions [8] through [17] may be neglected in the kinetic analysis of this system. (a) Reaction [9] If reaction [9] is incl uded i n the mechanism together with reactions [l] through [7] , the following expression for (~]/[HD] results: (7) .· The above expression goes through the origin as one would expect if experiments were done in the limit of zero [EBr]/[CD4]. How- ever, if the lowest [HBr] /[cD ] ratio considered satisfies the 4 relation: (8) the plot from this [HBr]/[cD4] ratio u:pwa.rds is a straight line 167 plot with a non-zero intercept. This intercept is greater than the one given by Eq. (2) by (k /k ).(k /k ). As shown in (I) for 3 1 9 5 the DBr-H system, condition (8) is equivalent to: 2 (9) :provided that: (10) One can show that the above app1--oximations are correct by the following arguments. First, the measurements of LeRoy et.al. 7 extrapolated to 25°c yield k :;: 5 x 103 M- 1 sec- 1 • Similar extrapolations to 25°c 9 from the measurements of Skinner and Ringrose8 and Steiner9 yield k :;: 5 x 108 M-1 sec -1 • Hence: 5 k /k 9 5 e: io-5 (ll) · Secondly, k4/~ < 1 since H* atoms are thermalized more 4 than by HBr. This is true because the masses are more similar than those of H and EBr. efficiently by cn of H and cn 4 Finally, ~/k1 < 65 since in our experiments A always exceeds 0.015. Thus we can conclude that: (12) and therefore that Eq. (10) is satisfied. In view o:r the above arguments, a sufficient condition :f'or the validity of Eq. (9) is that: 168 f~:f > > 7 x io- 4 (13) Since the lowest [HBr]/[cD4] ratio used in our experiments was 0.25, this condition is satisfied. We must also show that (14) in order that Eq. (7) reduce to Eq. (2). (I) we were able to show that k than two orders of magnitude. HBr-CD4 system. 3 and k 1 For the DBr-H system 2 should not differ by more A similar argument holds for the Further confirmation comes from the fact that the slope of a plot of [~] /[ED] versus [EBr] /[cD4] (see table I) is never greater than 65. Noting from Eq. (7) that this slope is equal to (k /~ + kL/k1 ) we necessarily conclude that: 3 k3/k1 < 65 (15) On the other hand, from Eq. (12) k2 _ l - A k A 1 (16) and therefore ~/~ is a decreasing i\mction of A. Since the largest value of A is, from Table I, 0.038, k2/k always exceeds 1 25 in the energy range of these experiments. Collecting the above estimates together we can write: (17) which again validates Eq. (12). This reasoning is apparently circular since the experimental determination of A already assumes 169 that relation (14) is valid, and •re then use the resulting A to prove the validity of ( 13). The process is however self-consis- tent and valid and is essentially an iterative approach in which the value of A determined assuming the validity of (14) corresponds to a first iteration and the second iteration is shown to agree with the first one. A :further discussion of the effects of reaction (9] near the intercept is given in (I). (b) Reaction [ 8] Since bromine is a much better scavenger of hydrogen atoms than EBr (k8/k = 22.7 at 27°c10 ), the srn.all amount of bromine 5 formed during a photolysis could appreciably reduce the [~]/[IID] ratio by effectively competing with RBr for hydrogen atoms. amount of Br 2 The . formed should increase with the extent of conversion of HBr, and therefore, the [~]/(HD] ratio should decrease concomitantly. As discussed in section 4, experiments with [HBr]/ [cn4 ] ratios ranging from 0.25 to 1.0 were done at two different conversions. The slopes and intercepts of the straight line plots for these experiments agreed ·within experimental error indicating that eff'ects due to bromine molecule reactions are negligible at these conversions. However, experiments with [HBr]/ [cD4] ratios ranging from 0.03 to 0.1 showed a marked conversion e:ffect. To illustrate this, the photolysis time, experimental conversion and experimental (~] / [HD] are tabulated. in Table II for a fixed [HBr] /[cn ] ratio of 0.075 for 2288A radiation. 4 The above [~] /[ED] is plotted versus photolysis time and %conversion in Fig. 2. The value of [132] / [IID] extrapolated to zero 170 Figure 2. Variation of [H2] / [HD] with time for [EBr] / [CD4] 0.075. = 47.8, k4/ kl = 1.0 k3/ kl = 1.0, k4/k l = 47.8 k3/ kl 171 0 ro ..-.. c - E 0 C\l © cr- en U> ->-0 ~ 0 .s:: c. 0 0 172 conversion fits nicely on the plot of [~]/[HD] versus [HBr]/[CD4] for [HBr]/[cD ] ratios ranging from 0.3 to 1.0 (zero conversion 4 value is 41.5, value f'rom least squares fit of' straight line of' Fig. l is 41.4). Likewise, ~.;o series of eA1?er1ments with [HBr]/ (CD ] ratios ranging f'rom 0.03 to O.l were done at the two con-_ 4 versions o.&f, and l.z;/o. Plots of [~]/[HD] versus [HBr]/[CD4] were linear with intercepts of 34.7 and 31.9 respectively. These intercepts were then linearly extrapolated . to zero conversion. The extrapolated intercept of 37.5 is within experimental error equal to the intercept of 37 .8 ~ Oe8 of Fig. 1 obtained at 2288A in the experiments with [HBr]/(cD4 ] ratios ranging from 0.3 to 1.0. Hence it appears that the extent of reaction of H atoms with bromine must depend on the [EBr] /(cD4] ratio. A theoretical justification of the above behavior is obtained by calculating the bromine concentration as a function of conver- sion and CD4 concentration from the assumed mechanism. If reac-· tions [l] through [7] are included. we find: [18] where [EBr]t=o is the initial concentration of HBr, EHBr is the EBr molar extinction coefficient, I 0 is the incident photon intensity in photons/sec, N is Avogadro's number and A is the light beam cross sectional area. [Br2] 1 . In terms of [Br2 ]/[HBr] this is: TB:Br] = 2 [exp(2 ~HBrI0 t/NA) for I 0 ~ HBr t/NA << 1. EHBrio t 1] =: NA (19] Note that there is no dependence on CD4 173 concentration. If reaction [8] is included the following two simultaneous first order dif'ferentia.l equations are obtained: E I ~ = - ~~ 0 [HBr] (20) and. d[Br2] dt _! d[BBr] = - 2 dt (21) These equations were solved numerically to obtain "che concentrations of Br 2 and IIBr as a fUnction of photolysis time (conversion) q concentration. The value of = EHBrI /NA was chosen 4 0 so the theoretical conversion matched the experimental one. At and cn 2288A .:HB is 30 i.rlcm·1 , A is 8 cm2 and I ranged :f'rom 1. 7 x r o 15 1 10 5 photons/sec to 1.9 x io photons/sec. This gives a q ranging from 0.00065 to 0.00070. The initial concentration of HBr was ta.ken as 1.626 x 10-3 M {30 torr pressure at· 23°c) and the initial concentration of cD ranged :from 1.626 x io-3 M to 5.42 x 4 2 io- M depending on the [HBr] / [cD4] ratio desired. Values of ~/k1 , k /k1 and k4/k axe also needed for the above calculations. 1 3 These values were obtained as follows. From Eq. (2) and the :plot of [~]/[HD] versus [RBr]/[CD4] at 2288A shown in Fig. 1, we obtain ~/k1 = 39.0 and 174 (22) The values of k /k and k /11J_ were then adjusted within the 4 3 1 limits of the restraint given by Eq. (22). The effect of' varying these ratios will be shown below. Dii"ferential equations for [H ] and [HD] were also solved 2 numerically (these are given in the append.ix) so the theory could be compared with experimental values of [H ] /[ED]. 2 Results of the calculation at 2288A for [H2]/ [HD] versus time for a fixed [RBr]/[CD ] ratio of 0.075 are shown in Table II and in Fig. 2 4 where they are compared with experiment. corresponds to k /k = 47 e8 and k 4/ k 3 1 1 The top line in Fig. 2 = 1. 0 while the lower line corresponds to k /k1 = l.O and k 4/k = 47 .8. Hence the values 1 3 chosen for k /~ and k4/k cannot be determined by fitting the 3 1 theory to the experimental data. However, the excellent fit to the experimental date. indicates that the proposed mechanism is correct. The independence of the conversion to the ratio u = (23) k4/k1 + k}k1 can be further illustrated as follows. Eqn. (20) can be 'Written in terms of the extent conversion x by making the substitutions: [HBr] = [HBr] 0 (1 - x) (24) and (25) The following differential equation in x then results: 175 dx = q(l-x) 1 + dt = q(l-x) [l+(l-u)aw(l-x)][ 1-x+~x] +[ b+uaw{l-x)][ 1-x-~x] [ l+b+aw( 1-x)] [1-x+~x] (1 + ~:) (26) where q = €HBrI0 /NA, a= k /k + k4/k , b = k /~, c = ka/k 2 5 3 1 1 and w = [HBr] 0/[cD ]. By substituting the known values of a, b, 4 c and w in the above equation, assuming a conversion of 11' we find that A' can be vritten as A• = 39.8 - o.83u (27) Note that in A' is the only place where u appears in the above equation. Hence varying u within its limits of from 0 to l pro- duces at most only a 2% change i n A 1 ~ D' can be evaluated to be 48.5 indicating that A'/D' is appr oximately equal to 0.82. Hence varying u within its limits only produces a zip change in dx/dt. The calculated [Br ], [Br 2]/[HBr] and [H ]/[HD] (using 2 2 equations (20) and (21)) for various [HBr]/[cD4] ratios are given in Table III and compared with those calculated using Eqns. (18) and (19). Note that at the end or a. 10 minute experiment there is 7.2$ less bromine in experiments with an [HBr]/[CD4] ratio of 0.03 than would be the case if reaction [8] did pot contribute and 3.4% less bromine in experiments with an [RBr]/[cD4] ratio of 1.0. This corresponds in changes in [~]/[HD] from time 0 of 6.ff/o and 3.5% respectively. This indicates that the effect of reaction [8] is greatest at low [BBr]/[cD4] ratios. We also note that for an (HBr]/[cD4] ratio of l.O, the [H ]/[ED] ratio would 2 decrease from its value f'or zero RBr conversion at t = 0 by 1. 7% after 5 minutes and by 3.5% after 10 minutes. This predicted 176 i.7% change in the [H2] / (HD] due to conversion is of the order of our experimental er.car and hence was not observed experimentally. However, our experiments do show the predicted decrease of [H2]/ [HD] with decreasing [HBr]/[CD4] at low [EBr]/[CD4] ratios. Since our experimental results where the [HBr]/[cD4] ratios vary from 6.3 to 1.0 agree so well with those at lower (HBr]/[CD4] ratios extrapolated to zero conversion, we conclude that the above corrections due to bromine molecule reactions are not impertaut for [EBr] /[cD ] ratios from 0.3 to 1.0. 4 The difference between our results and those of' !Ji'.artin and Willa.rd4 can be explained by a similar calculation. Their net decomposition of HBr was approximately 10%. 4,ll We find that with this conversion the theory predicts that their [~]/[HD] ratio would be 17.0 at an [HBr]/[cD4] ratio of 0.03 compared. to their experimental value of 17.2 (determined from their least squares fit to their plot of [~]/[HD] versus [HBr]/(cD4]. The value of [~]/[HD] extrapolated to zero conversion would be 26.3 compared to our experimental value of 26.4 (determined from our least squa.l"es fit to our data). Thus we conclude that the discrepancies between our results and those of .V.artin and Willard is due to their not having taken into account the EBr conversion effect at low [HBr]/[CD4] ratios. c) Reaction [ 13] If' reaction [13] is included in the mechanism the following steady state expression for [H ]/(HD] is obtained: 2 177 (28) where In order to justify neglect of this reaction we must show that: (30) 12 For the reaction of T-* with cn4 , Chou and Rowland found that k13/ki is a monotonically increasing function of energy with a value of less than 0.01 at 2288A increasing to 0.065 at 1849A. We vill use the largest of these values for our analysis. On the basis of transition state theory we expect k 13/k1 to be similar for both the T* + CD and Hi<· + CD systems. ,: This is 4 4 because the transition states leading to abstraction and exchange are the same and hence ratios betv1een T* + cn4 and H* + cn4 would be the same for both abstrac~cion and exchange. Also, recent theoretical calculationsl3 indicate that k /k1 should decrease 13 as the mass of the attacking atom decreases. The fraction (31) has been determined in our laboratories by independent experi- ments14 and is o. 80 +- 0.05. From Eq. (29) and these considerations we obtain, at l849A: ( (H2 ] ) VID1 0 = k 2 /k 1 + O.OJ2 i.05 (32) 178 Using this expression and Eg,. (1) to determine A produces a value that differs by 5% f'rom the one obtained from Eq. (3). This correction becomes less than 1% at 2288A. Since as mentioned above k 13 / k 1 is expected to be smaller for the H* + CD4 system than for the T* + cn4 system, no correction has been applied for the contribution of reaction [13]. d) Reactions [10], (ll], [16] and [17] The above reactions were considered in (I) where cn replaced by ~· is 4 For both H2 and cn4 consideration of activation energies indicates that [10] is faster than [11]. For the case of Br + H2 k 10 eq_uals 2 :x 10-3 M-1 sec -1 whereas for Br + CD4 it equals 3.8 x io- 3 ?>r-1 sec-1 • 1 5 By similar agruments to those used 4 in (I) we can show that ~/k > 10 under all experimental con- 10 ditions. Thus reactions [10] and (ll] can be neglected In reactions [16] and [17] the asterisk denotes translational excitation. As shown in (I) the Br + CD4 relative energy is (mH/mHBr) 2 (E - D~) which ranges from 2.02 x lo- 4 to 4.2 x lo- 4 eV in our experiments. These values are small compared with average room temperature thermal energies of 3.9 x 10-2 eV and hence reaction (16] can be neglected with respect to [10]. Reaction [17] for DBr was considered in (I). There it was shown that reaction [17] is negligible compared to reaction [8]. The same arguments hold for HBr. Hence all bromine atom reactions except 3-body recombination can be neglected. 179 e) Reaction [12] Fass io found k12I k to be 5.3 -+ 0.04 independent of tempera3 ture and wavelength for temperatures from 300°K to 523°K and T'.ae [Br ]/[HBr] ratio at the 2 end of an ex:periment vTi th conversion c is approximately c/2 for wavelengths from 1849A to 248oA. small c; the average [Br2] /[HBr] ratio during the experiment is therefore approximately c/4. Taking into account the above rate constant ratio, the average ratio of H* reacting vrith Br2 compared. to H·X- reacting with HBr is l.4c. Since c ranges from 0.005 to 0.01, reaction of H* -vTith Br a.mounts to only o.&fo to 1.4')0. This 2 effect is negligible within the accuracy o:f our experiments since varying c produced no significant change in the [H2 ]/[HD] ratio. 5.2.2 Consideration of CD H impurity 3 Since the cn used in these experiments contained about 3.&fa 4 CD H impurity, reactions involving cn H must be considered in 3 3 interpreting the experiments. The additional ;processes to be considered are as follows: H* + cn H 3 H* + CD H 3 R* + CD H 3 CD~ + HBr - - HD + CD H 2 (18] ~ + CD3 (19] H + CD H 3 CD2~ +Br [20] [21] We have shown in the last section that reactions [8] through (17] can be neglected. Similar arguments bold for reactions similar to [9], (10], [13] and [16] where cn4 is replaced by cn n. 3 Consideration of reactions [O] - (7] and (18] - [21] gives rise 180 to the following steady state expression: 1 [k.2 + [CD3H] h_9 + k2o\ + pre Jfk3 k4)1l 3-~..,,..Jk-1--.8 1<i t CD4] \ - kl I t CD:l\~ + k1 ] ( 33) .,__t.,,_C-D l+ 4.. 1 Again we expect a linear plot of [~]/[HD] versus [BBr]/[CD4] with positive slope and intercept. From the intercept of this plot we can see that the integral reaction yield A is: (34) A= To evaluate this expression we need values for k15/k1 , k 19/ k1 , 0 ~ /k1 and [CD B]/[CD1) . .Arguments based on probability consider3 ations and neglect of isotope effects would lead one to expect k 18 /k = 0.75 and k /k1 = 0.25. These are at least upper limits 1 19 to the true values since statistical mechanical calculations for thermal reactions :predicts k /k to be even smaller than the 19 1 above. Likewise we expect k20 /~ to be close to k2 /k1 since ~ 0 /k2 should be c:ose to unity and k20 /k1 = (~0/~).(k2/~). The impurity ratio [CD H]/[CD4] measured on the mass spectrometer 3 was 0.038. Using values o:f' the rate constants listed above and Eq. (34) we find that neglect of the cD3H impurity contributes less than 1% error at all wavelengths. 181 5.2.3 Determination of the Integral Reaction Yield The integral reaction yield A was calculated from the experimental ([BD] /(~]) A are listed in Table I. 0 using equation (3). The results for A plot of A versus EiO) is shown in Fig. 3. The error in A due to ((ED]/(H ]) 0 was determined by ta.king 2 the derivative of A with respect to ([HD]/(H ]) 0 and multiplying 2 it by the standard experimental error of ([HD]/[H ]) 0• Other 2 corrections were neglected. As mentioned in section 5.1 it is energetically possible to form excited bromine atoms in JGhe HBr photolysis. If' excited bromine atoms are important, the measured A values would cor-respond at each wavelength, to contributions of two different initial laboratory energies, one being the value assumed in this pa.per and the other a value smaller than it by 0.45 eV due to the 0.457 eV spacing between the 2P3; 2 and 2P1; 2 levels. Due to the monotoni- cally increasing nature of A versus initial laboratory energy, the A's reported in this pa.per for HBr photolysis are at t.he very least lower limits to the idealized values. Further experiments could either confirm or indicate the slight corrections due to the neglect of excited Br atoms. More extensive measurements on the fraction of such atoms as a fUnction of wavelength could be used to refine our values of A. 182 Figure 3. Plot of A = k /(k + k ) versus initial 1 2 1 laboratory energy. 183 \l ~ \ \ ~ .q ~ C\J_ 0 . I{) q ! ¢ q rt) q C\I q 'co>l 3) \:J 0 . 0 184 6. DISCUSSION 6.1 Shape of A(E(o)) 1 The integral reaction yield A is a monotonically increasing function of the laboratory energy from 1.1 to 2.9 eV. Its slope is greater at low energies and appears to be leveling off at high energies. The results for the H + CD 4 system can be compared qualita- tively with those for the H + D one. 16 The values of A for 2 B + cn are about an order of magnitude lower than those for 4 R + D2 at corresponding relative energies. This difference can be explained on the basis of the following arguments. First, since the masses of H and D are closer than those of 2 H and cn we expect a relatively more effective thermalization, 4 due to elastic collisions, of H by D than by cn4• This would 2 tend to make A smaller in the D2 system than in the CD4 system, the opposite of what is observed. However, as we will show in what follows, inelastic collisions are much more probable in the H + CD4 system than in the H + n2 one and this can account for the difference in the respective va'iues of the integral reaction yields. We will first consider inelastic collisions involving transfer of translational energy of the H atom to rotational energy of either the D or cn4 • Since rotational relaxation times are 2 in general much shorter than vibrational ones 17 rotational energy transfer is expected to be important compared to vibrational 185 transfer. There are no accurate theories to date covering the case where a large number of rotational levels are excited in a collision. However, approximate theories 18 indicate ~t if an interaction potential of the form exp(-aR) is assumed, then the larger a's lead to larger transition probabilities between rotational states in collisions. In the above R is the internuclear distance and ct is defined by : (35) where M is the reduced mass of the molecule, k is the oscillator force constant which is determined from spectroscopic data and ~ and me are the individual masses of the two atoms of the harmonic· oscillator respectively. Hence, Jche larger the a the harder the collision between the atom and molecule. For the purpose of this discussion we will consider cn to be a diatom D-CD with the H 4 3 atom colliding collinea.rly with the D. We may assume that the L's for D and cn a.re both o.~. 1 9 This calculation leads to aD = 0.26 4 2 2 and<I = 0.44. This indicates that CD undergoes harder collisions 4 CD4 with an H atom than does D2 and therefore that its rotational transition probability should be greater. Also, the spacing of the rotational levels is related to translational rotational energy transfer; the closer the spacing, the more likely a tra.nsition. 18 Since cn has more closely spaced rotational levels (Be = 2.05 4 cm-l 20 ) available than D (Be= 30.43 cm-1 21 ) it should undergo 2 more efficient rotational energy transfer. Finally, experimental relaxation times for D2 and cn4 determined by accoustical methods 186 verify the above asslllllptions. For D2 the rotational relaxation . ha s been measur ed. as 2.0 x 10-8 sec 22 at 273OK while . time for cn : 4 this relaxation time is of the order of 1 x 10-9 sec 23 at 314°K. These relaxation times lead to energy transfer collision numbers Zrot of 210 for D2 and 14-17 for cn4 • Ca.re is needed in applying the above argument since we are comparing D2 + D2 collisions with cn4 + cn4 ones and not H + D2 collisions with H + cn4 ones. However, it appears from the combined arguments above that the probability of inelastic collisions involving rotational energy tra."lsfer is greater for an H atom colliding with cn than with 4 n2 by more than an order of magnitude. To treat inelastic collisions involving transfer of translational energy of the H atom to vibrational energy of either the D or cD4 an approximate theory of Secrest and Jobnson 24 can be 2 used in which they consider only collinear collisions of the type A+ BC where A, B and C are atoms. They assume an interaction potential between A and the harmonic o.s cillator BC of the form V(x-y) = A0 exp[-a(x-y)]. Here x and y are reduced coordinates where x is the distance between an atom of mass m = mAmC/m_g(mA+m_s+mc) and the equilibrium position of the oscillator and y is the distance of a harmonic oscillator of unit mass from its equilibrium position. mA' m_s and me are the masses of the colliding atom and the individual masses ?f the two atoms of the harmonic oscillator respectively, A0 is a constant having no effect on the results and a is as defined by Eq. (35) in the discussion of translational to rotational energy transfer above. Again, we will consider CD4 to be a diatom 187 D-CD with the H atom colliding collinearly with the D. 3 The m's for D and CD are 0.20 and 0.43 respectively and the a•s have 4 2 been calculated above to be ~ = 0.26 and aCD = 0.44. 2 4 Transition probabilities were calculated for each experimental energy using the method of Secrest and Johnson. 25 The probabilities that the molecule in question (either D2 or cn 4 ) will be excited to a higher vibrational state are shown in Table IV. As can be seen, for an H atom colliding with CD4 the probability of excitation is almost unity at all relative energies except 1.1 eV while for an H atom colliding with D2 the probabilities range from 0.12 at 1.1 eV relative energy to 0.96 at 2.9 eV relative energy. Hence the probability of inelastic collisions involving vibrational energy transfer is greater for an H atom with a given initial energy colliding with cn4 than with D2 • The above arguments indicate that inelastic collisions a;r.e_ more important in cD 4 than in D and that they may :provide an 2 e:A']?lanation for the order of magni tu.de difference in the integral reaction yields for the two systems. 26 In support of the above assumptions, Rosenberg and Wolfgang and Root and Rowland,27 using experimental results interpreted by the Estrup-Wolfga.ng kinetic theory, have deduced that inelastic collisions are important in the overall mechanism for tritium recoil reactions with cn • Also, Biordi, Rous eau and :V..a.ins28 4 have argued that in the :flc..sh photolysis of HI in the presence of deuterated hydrocarbons, collisions between hot hydrogen atoms 188 in the energy range :from o.8 to 2.2 eV. An additional comparison of interest is that between the integral reaction yields of t.he present H + cn system and those 4 of the D + CH system investigated by Martin and Willard4 at 1849i. 4 These authors list their intercept value for a :plot of [D ]/[HD] 2 versus [DBr] / [cD ] as 5.0. From this we can calculate an integral 4 reaction yield of 0.166. Our result at the same relative energy in the H + cn system is Oe0381 which is 4.3 times smaller than 4 their value. A small isotope effect in this direction is expected but not as great a.s that observed. For example, the integral reaction yield for D + H at a relative energy of 1.4 eV is 1.4 2 times greater than the integral reaction yield for H + D at the 2 1116 same relative energy. Martin and Willard did their DBr-CH4 :photolyses at high DBr conversions (5-10%). In section 5.2 we showed that their RBr-cD4 results done at high conversions were in error and hence it is :possible that their DBr-CD a similar error. 4 results have If such an error exists it would lower the integral reaction yield ma...'ldng it more compatible with the H + cn4 one. However, since their experiments were done at [HBr] / [cD4] ratios f'rom 0.3 to 1.5 we do not expect the error for DBr-cH4 to be as great as in the HBr-CD experiments done at [HBr] / [CD ] 4 ratios from 0.03 to 0.1. 4 Nevertheless, it would be worthwhile to repeat their experiments taking into a.cco\.lllt the conversion effect and to determine how large an error is involved. If their experimental error is assumed to be small, an explanation of the difference in the integral reaction yields of 189 H + CD 4 and D + CH is needed. 4 To provide this explanation we will first con.sider the effects of elastic collisions. The average energy lost by a moving sphere in an elastic collision with a sphere initially at rest is f 2mAIIJ:B =---- (36) (mA + m.a)2 Therefore, for the elastic collisions between H + cn4 and D + CH , 4 the f's are 0.0913 and 0.197 respectively. Hence we expect a more effective thermalization, due to elastic collisions, of D by CHl~ than of H by cn 4• This would tend to make A smaller in the D + CH4 system, opposite to what is observed. Secondly, the effect of inelastic collisions in the D + CH4 system can be examined as was For D + CH the a, calculated 4 from Eq. (35) assuming L = o.Z\, is 0.52 compared to o.44 for done in the B'. + CD4 and H + D2 ones. H + CD4. This indicates that CH4 should undergo harder collisions with a D atom than cn4 undergoes with an H atom. However, this effect is compensated for by the closer spacing of vibrational levels in cn4 than in cH leading to greater probability of 4 translational to vibrational energy transfer in H + cn4 collisions than in D + CH ones. However, Cottrell and Matheson29 have 4 measured vibrational relaxation times in CD4 and CH4 by the ultrasonic method and found that 'en / TCR = 1. 9 at 298°K. This 4 4 indicates that energy transfer is more eff'icient in CH4 + CH4 collisions than in cn 4 + cn4 ones. They explained this on the basis of translational to rotational energy transfer. They argue that since CD4 has a greater moment of inertia than CH4 190 (ICD /IcH = 1.98) it ·w'ill undergo less efficient translational 4 4 to rotational energy transfer than will CH4. They conclude that the process they observe is the relaxation vibration - rotationtranslation and that the second process is slower for CD4 than for CH4 making the overall relaxation time longer. If this trend holds for H + cn and D + CH4 collisions it could lead to more 4 inelastic collisions in D + CH4 making A smaller in this system. This is again opposite to what is observed. Hence, on the basis of these arguments and observations it does not seem likely that the observed differences in integral reaction yields between H + cn4 and D + CR4 are due to a more ef'fective therma.lization of the atoms in the former tha.'1 in the latter. Finally, we must consider whether these differences can be due to differences in the reactive cross sections of these systems. We can make a comparison with the H + D and D + H2 2 results to get an idea of the isotope effect to be expected. The cross section for the D + H2 system is approximately 2.5 times greater at the same relative energy (0.7 to 1.1 eV) the,n for H + D230 whereas the ratio of the corresponding integral reaction yields is about 1.4. Hence, this difference, although in the right direction, does not seem sufficient to explain the difference in integral reaction yields in the H + CD4 and D + CH4 systems. Hence, we are unable to adequately explain the differences in integral :reaction yields of H + cn of these arguments. 4 and D + CH4 on the basis However, further experiments on D + CH4 are needed before any definite statement as to discrepancies between 191 the H + cD 4 a..11d D + CH4 systems can be made. It was not experimentally :possible because of low HD yields to determine the laboratory energy at which the integral reaction However, it is still interesting to compare yield goes to zero. the initial relative energy distribution function for H + CD4 with D + ~ to see what effect the different :pairs of masses has on the width of this function. As in (I) the relative energy distribution function is given by m f(E) = _1.,.. ( _.'...3. ~rl where "frY:£ )1/2 [ ex-9( ... __g_ m 2 m 2] (v-:x· - v) ] - exp[- _?_(v:* + v) ] (37) kl' 1 kT r is the reduced. mass Of the colliding system, of the target molecule, ~ 1 is the mass vr is the initial laboratory velocity of the atoms, v is the relative velocity of the atom ·with respect to the molecule, k is the Boltzmann constant and T is the absolute temperThe corresponding width as derived in (I) is: ature. where E* is the initial laboratory energy of the atoms. l Note that the product of the masses of the atom and molecule appears in the denominator. Hence as the mass of the molecule becomes larger the width of the relative energy distribution becomes narrower for a given initial laboratory velocity. For example, for a laboratory energy E-* = 1.5 ev, E equals 0.39 eV for the H + n2 system and 0.20 eV for the H + cn4 system, and it is o.48 eV for the D + H2 1 system. This narrower distribution for H + cn4 should make the determination of the threshold energy for this system easier than for D + H and also helps in simplifying the extraction of reaction 2 192 cross sections f'rom e:>.--perimental integral reaction yield data as is discussed in the next; section. 6.2 Reaction cross section f'rom integral reaction yield In this section we discuss how the cross section of reaction [l] is related to the measured integral reaction yields. 6.2.1. Boltzmann E~uation For the RBr-cD 4 system the behavior of the entire photolysis system can be described by a steady-state Boltzmann equation. In analogy to -'che DBr-H 2 system described in (I) we can vr.cite this equation as: R0cf>"fr(vH) - 1S;(vH)Gvjj(vH) + ~~ H(vH,vH)G"Ji(vH) dvH = O (39) In the above R is the rate of initial H atom production due to 0 :photolysis. ¢v.x·(vH) is the normalized initial distribution H function of> H atom laboratory velocities. This is a narrow function peaked at vii as indicated by our notation. is the concentration of H atoms under steady-state photolysis conditions in the laboratory velocity range vH to vH + dvH. Kt(vH) is defined as: = KCD4 + KHBr (40) KCD4 = KR CD4 + ~4 (41) K ~r NR (42) K t . lffir r =1~ RBr + 193 KRCD4 = (CD4Jj cpTCD~· (vH,v) v ~CD4(v) dv (43) (44) (45) (46) HBr v' SR (v') dv' RBr KR L = i 8i HBr ~ (47) HBr,i (48) (49) S EBr NR L = i gi BBr,i In the above equations v is the relative velocity of H and cD (50) 4 and v ' the relative velocity of H and EBr. cpTCD4 is the distribution function of H-CD4 relative velocities for H atoms with a laboratory velocity vH and cn4 molecules with a Boltzmann distribution of laboratory velocities andcpTBBr is a similar distribution function for H-HBr. SRCD4(v) is the reactive cross section for H-cD4 averaged over internal states at temperature T and SNRCD4(v) is the non-reactive cross section averaged over internal states. SR HBr HBr and ~R are similarly the reactive and non-reactive cross sections for H-HBr averaged over the internal states of HBr. The g.CD4 and FZ..HBr are the distribution functions for the internal 1 -i . states of cn a...'1.d HBr respectively. In applying Eq. (41) the 4 assumption is made that thermalization of H by EBr is negligible with respect to the other processes and hence I<NRHBr is set equal 194 This is valid because the masses of H and cn4 are to zero. closer than those of H and HBr. Finally: (51) is the laboratory velocity of cn before collision, 4 4 v;_f is the relative velocity vector of H and CD4, X and 7] are where vCD direction angles of this vector after collision and y f is the 1 angle between and vCn before collision. The quantity vH CD 4 1 71 ) is the differential non-reactive cross section for eri 4(v X f if'' :; •t the reaction in which the inter.a.al state of the two particle system changes from i to f, <PTCD4 ( v' CD4 · ) is the Maxwell Boltzmann distribution function of cD velocities in laboratory coordinates and g1 is 4 the probability of an initial internal state i of CD . 4 The inde- pendent variables in the above expression are vCD , X , 7] , vH and l~ .!lEif' the change in internal energy of the CD • . The relative 4 velocity v' and the angle ydepend on these variables and hence on the initial and final states of the cn4 molecule. The physical interpretation of Eq. (39) can be explained very sim:pl:y. The first term gives the rate of :production of H atoms in the velocity range vH to vH + dvH directly :from the :photolysis source. The second repr esents their rate of removal from that 195 velocity range due to all collisions with cn and reactive colli- 4 sions with RBr. The third term represents the rate of production of H atoms in the velocity range vll to vH + dvH as a result of nonreactive collisions of H atoms at all other velocities vH with cn4 molecules. Under steady-state conditions, the net rate of produc- tion of H atoms in any given velocity range must vanish. 6.2.2. Relation of A(v'H) and the reaction cross section In terms of the above quantities we can write A(vtf ) as: A(ir<·) = H ~ f~CD4(vff.) Gv*( vH) dvH H o where K.RCD4 is defined by Eq. (52) (43). It can be shown that the Boltzmann equation given above can be reexpressed in terms of A(vfi) as31 In the limit of dilut e [EBr] Kt(vR) = KRCD4 + ~D4 Hence from equation (53) -vre obtain KRCD4 as ~ cn4 (v ) = K:'4A(vif) - fn(vH,vJr) A(vJr) dvH 1 - A(vR) H ( 8RCD4(v) can then be evaluated from a knowledge of theO"'~D4 (which su:ff'ices to determine both ~D4(vH) and H(vH,vH) in the above expression). Indeed it has been shown3 1 that a correct :procedure to use is as follows. The fUnction 54 ) 196 CD 2 CD4 u 4(v,T) = v SR (v) (55) satisfies the dif:t'usion equation: (56) with the initial condition: (57) Therefore, integrating Eq. (56) numerically furnishes u(v,T) and therefore ~ ( v) • 'I'hus &... _H CD4(v) is completely determined by a knowledge of CDLJ. o-NR · and the experimentally known A(vH). Tbe o-NR are not known but may be estimated from approximate model calculations or independent experiments. 6.3. Summary In summary, a :photochemical method was used to obtain the integral reaction yield A(E (O)) for the H + cn system. It was 4 1 found that A(Eio)) is a monotonically increasing function of laboratory energy in the range from 1.1 to 3 eV. The A(Elo))'s for the H + cn4 system are an order of magnitude lower than for the H + n system for corresponding energies. This di:t'ference was 2 attributed to the greater :probability of inelastic collisions occuring in the H + CD4 system than in the H + D one. Finally, 2 the rela-tion of the ·integral reaction yield to the cross section was given and a method indicated of how in principle one can be 197 calculated :from the other. APPENDIX The dif'f'erential equations to be solved to obtain [H ] and 2 [HD] as a function of time a.re as follows: d[~] = dt d [ lID] dt (58) I HBr o = NA (EBr] E (59) whei.. e the symbols are as defined in the text. These equations were solved numerically in conjunction with Eg_ns. (19) and (20) in the text to obtain the theoretical [H ]/[IID] ratios listed in 2 Table III. TABLE II. Comparison of Theor y and Experiment for a Fixed. [HBr]/[CD4] Ratio of 0.075 • ......._...~,-= k"37k; ~~~ k4/k1 = Photolysis time _Jmin.) [~] Experimental Conver si on LBD] ~ • 1.0 H2 theoretical - ,, __ L .t~2J conversion [fib] conversion tYfi5J i) _ ____£,<:-]-£.!.'""" <JI. calc. theoretical ._ _',., y d• L1 .L..--, -·l ...L IH5J ca.le. -1 5 0.62 39.8 0.62 40.3 0.62 40.2 0 .62 40.2 10 1.2 38.8 lo2 39.2 1.2 39.1 ~ 39.0 15 1.7 37.6 2.7 38.2 1.7 38.1 _L 4' l 37.9 20 2.3 37.2 2.3 37.3 2 .. 3 37.1 2.3 36. 9 25 2.8 36.1 2.8 36.4 2.8 36.2 2.8 36. 0 30 3.3 35.5 3.3 35 . 6 3.3 35.4 3.3 35.2 ~ ;o ____..~--..-...,..~ j:~ :Z::.,~~~.o;;-~f } J :- "1 # g:;;::;m t =: e F t =x:t i f '& ___,.;;::;:: g : J -:0?'$ I-' r..':' G: TABLE III. Results of Calculations of Bromine Concent;rat i on as a Fu.n.ction of Conversion a.11d [lIBr]/[cD4 ] ::!::51 ., Photolysis Extent HBr Time (min .. ) Conversion (~) ~~----= Eq. (17) [Br2 ] (x 10- 4 M) ~ r-1 = r ~=t:::t::z:z::r-"""=?': ~'~: [ HBr] /[CD4J Eq. (18) .c ~r?l ll' C:OOC>Oil .0:.£3 [ IIB:r] 0.1 0. 3 [Br ] (x io-4 ~2 1.6 -- ~"-= 0 o.oo 0 . 0000 0 . 00000 0. 0000 0 . 0000 0.0000 0 . 0000 l 0.14 0.0387 0 .00070 0 . 0380 o .. 038o 0 . 0382 o.038L, 2 0.28 0 .0775 0 . 00140 0 . 0756 0 . 0760 o . 076o 0 . 0766 3 o.lt.2 0.116 0 . 00211 O.ll2 0 .113 0.113 0 .111.,i 4 0 . 56 0 .155 0 . 00281 0 .1!1.9 0 .149 0.150 0 .152 5 0 . 70 0 .191~ 0.00351 0.184 0.184 0 .186 0.188 6 o.84 0 . 232 0.00422 0.219 0.221 0 . 223 0 . 225 7 0.98 0 . 269 0.00493 0 . 255 0.256 0 . 258 0.261 8 1.1 0.308 0.00563 0 . 289 0.291 0.293 0 . 298 9 1.2 0.345 0 . 00634 0. 322 0.325 0.328 0.336 10 1.4 0.384 0.00705 0. 356 o.36o 0.363 0 .370 ..... <D <D TABLE III (continued) ......... _ -- ~ Photolysis Time {min.) 0.03 ~ . . . > , :- e (B.Br]/[cD4) i.o 0.03 -~=~r-z==- --0 :-3- 0.1 [Br ]/[HBr] 2 t? es=-- 1=*:¥ ;=>CO · -~~ 0.1 ·~~ = .::.... ~ 0.3 1.0 (~]/[HD] -~~- 0 0.00000 0.00000 0.00000 0. 00000 39e4 42.8 52.6 86.7 1 0.00069 0.00069 0.00069 0.00069 39.1 42.6 52.3 86.3 2 0.00137 0.00137 0.00138 0.00139 38.9 42.3 52.0 86.3 OQ00207 38.6 ~-2.0 51.7 85.7 0.00276 38.3 41.7 51.4 85.4 f\) 3 0.00204 o.002o4 0.00206 4 0.00271 0.00271 0.00273 - - 5 0000335 0.00335 0.0034.o 0000342 38.1 41.4 51.1 85.1 6 o.oo4o1 0.00402 0.00406 0.00412 37.8 41.2 50.9 81~. 7 7 q.00465 0.00467 0.00471 0.00479 37.5 40.9 50.6 84.5 8 0.00529 0.00531 0.00537 0.00546 37.3 40.7 50.3 84.2 9 0.00591 0.00594 0.00601 0.00607 37.1 4o.4 50.1 83.9 10 0.00654 0.00657 0.00665 0. 00680 36.8 40.2 49.8 83.6 -- - -- . - -~ -~ 0 0 201 REFERENCES 1. M. A. Eliason and J. O. Hirshfelder, J. Chem. Phys., 30, 1426 (1959). 2. J. M. White, D. R. Davis, J. A. Betts and A. Kuppermann, forthcoming (Paper I in this thesis). 3. R. J. Carter, W. H. Ham.ill and R. R. Williams, Jr., J. Am. Chem. Soc., 71, 6457 (1955). 4. R. M. Martin and J. E. Willard, J. Chem. Phys., 40, 3007 (1964). 5. This lamp was built by William B. De:Vi0re at the Jet ?.repulsion Laboratory in Pasadena9 We wish to thank him for permitting us to use it. 6. R. S. Mullikan, J. C'nem. Phys., ~' 382 (1940). 7. (a) D. J. LeRoy, Disc. Faraday Soc., 14, 120 (1953); (b) M. R. Berlie and D. J. LeRoy, Can. J. Chem., ~' 650 (1954). 8. G. B. Skinner and G. H. Ringrose, J. Chem. Phys., ~' 4129 (1965). 9. J. B. Steiner, Proc. Roy. Soc., 173A, 531 (1939). 10. R. A. Fass, J. Phys. Chem., 74, 984 (1970 ). ll. R. M. Martin, Ph.D. Thesis, University of Wisconsin, 1964. 12. C. C. Chou and F. 13. P. J. Kuntz, E. M. Nemeth, J. C. Pola.nyi and W. H. Wong, s. Rowland, J. Chem. Phys., .2.Q, 2763 (1969). J. Chem. Phys., 52, 4654 (1970). 14. (a) G. B. Kistiakowsky and E. R. Van Artsdalan, J. Chem. Phys., E_, 469 (191~4); (b) G. C. Fettis, J. H. Knox and A. F. Trotman-Dickenson, J. Chem. Soc. , 4177 (1960).· 202 15. A. Persky and A. Kupperma.nn, forthcoming (Paper I). 16. A. Persky and A. Kupperma.nn, forthcoming (Paper II). 17. T. L. Cottrell and J. C. Mccoubrey, Molecular Energy Transfer in Gases, (Butter-worths, London, 1961) J?P• 74-124. 18. K. Ta.kanyanagi, Prog. Theoret. Phys. (Kyoto) Supple., _gz, 1 (1963). 19. K. F. Herzfeld and T. A. Litovitz, Absorption and Dispersion of Ultrasonic Waves (Academic Press Inc., New York, 1959). 20. G. Herzberg, Infrared and Raman Spectra, (D. Van Nostrand Co., Inco, New York, 1945) J?• 306. 21. G. Herzberg, I>blecular Spectra and V.ole cula.r Structure, I Spectra of Diatomic Mo lecules (D. Van Nostrand Co., Inc., New York, 1950) p. 534 . 22. E. S. Steward and J. L. Steward., J. Acoust. Soc • .Amer. ~, 194 (1952). 23. B. T. Kelley, J. Acoust. Soc • .Amer., 32, 1005 (1957). 24. D. Secrest and B. R. Johnson, J. Chem. Phys., 45, 4556 (1966). 25. We wish to thank Albert F. Wagner for performing this calculation. 26. A. H. Rosenberg and R. Woli'gang, J. Cb.em. Phys., l~l, 2159 (1964). 27. J. W. Root and F. s. Rowland, J. C"nem. Phys., ~' 2030 (1963). 28. J. C. Biodi, Y. Rouseau and G. J. Ma.ins, J. Chem. Phys., !t2 2642 ( 1968) • 29. F. L. Cottrell and A. J. Matheson, Trans. Faraday Soc., 58, 2336 (1962). 30. A. Kuppermann, f'orJlcoming. 203 31· A. Kupperma.nn and R. N. Porter, f'orthcoming. 204 60 CONCLUSION Mixtures of DBr-H , DI-H and EBr-cD4 were :photolyzed with 2 2 monochromatic light. Thirteen different wavelengths were used in the DBr-H , DI-H systems yielding deuterium atoms with initial 2 2 laboratory energies ranging from 0.6 to 3.0 eV. By :photolyzing analogous DX-Ile mixtures (where X = I or Br) we were able to obtain the integral reaction yield for the processes: D* + li 2 - DE + H [1] H 2 - D + H 2 [2] j}l(· + These processes describe rates of reaction and thermalization which accompany the injection of monoenergetic atoms into thermal ~ gas. We were able to show that resu,J.ts obtained using DBr as the source of' monoenergetic atoms were consistent with those obtained using DI. For the HBr-CD4 system, photolyses were performed at 5 wavelengths giving H atoms with laboratory energies ranging from 1.15 to 3.0 eV. By analyzing the results of these :photolyses we were able to calculate the integral reaction yield 205 where kj_ ().. ) i k2 (>..) correspond t :. ·:,n.e processes: cn4 - HD + CD (l'] H* + CD4 - H + CD4 (2'] H-l<· + 3 For both the D + H and H + cD systems we were able to show 4 2 that the integral reaction yield is a monotonically increasing function of energy over the energy ranges scanned. For D + H 2 A ranged from O at about o.6 eV to o.66 at 2.86 eV initial laboratory energy while for R + cn A ranged from 0.015 at 1.15 eV to 4 o.ou,.o at 3.0 eV initial laboratory energy. If we assume, in a first approximation, that the H and cn 2 4 targets are stationary, the corresponding ranges of initial relative energies are 0.3 eV to 1.L~3 eV for D + ~ and 1.15 eV to 3.0 eV for H + cn4 • These results show that there is almost an order of magnitude difference between the integral reaction yields for these two reactions at the same initial relative energies. We were also able to com:pa.:re the H + cn results with some for H + D where there was likewise 2 4 an order of magnitude difference favoring the latter. This difference was attributed to the greater probability of inelastic collisions occuring in the H + C1\ system than in the H + D2 one. The relative initial velocity distribution functions between the atoms (D or H) and the molecules (~ or CD4) were examined. The relative velocities were found to follow a distribution tunction of the form: f ., (E )dE V':[ 1 ~ =µvx·1 (277i?1 ) 1/2 [ m exp - _s_ (v.1* - v) 2kT where m is the mass of' the molecule, 2 2 m . 2la 1 ] - exp - _g_( v* + v} 2 dE vy is the initial laboratory 206 velocity with which the atom is :formed, v is the relative velocity, k is the Boltzmann constant and T is the absolute temperature. Thia distribution 1\mction has a width of the order o:f' where µ.is the reduced mass, E1 is the laboratory energy of the atom and~ is the mass of the atom. This distribution flmction is narrower when the mass of the molecule is large compared to that of the atom which facilitates interpretation of the H + CD4 results relative to the D + H ones. We were able to show that 2 the initial nominal phenomenological relative energy at which the experimental integral reaction yield for the D + H system went 2 to zero could differ by as much as 0.1 eV from the equivalent phenomenological threshold relative energy for the reactive cross section because of this spread. Finally we were able to show bow reaction cross sections can be extracted from the experimental integral reaction yield using a steady state Boltzmann equation. This determination depends on a knowledge of the differential non-reactive cross sections. Obtaining these non-reactive cross sections theoretically is easier for D + ~ than for H + CD4 and therefore a complete analysis of the D + H system will be completed sooner than the one for H + CD4. 2 In the course.of the D + H2 experiments additional information to that described above was obtained. From ad.di tional DX-IDC-He experiments we were able to measure the abstraction :fraction a defined as: 2 0 '? where k 6 and k correspond to the processes: 7 H +DX - HD+ X (6) H + DX - RX+ D (7) The results were a(DI) = 0.97 :!: 0.05 and a(DEr) = 0.99 :!: 0.03. In the course of doing these experiments, accurate extinction coefficients were measured for DI and HI in the wavelength range from 2900~ - 3400~ and for DBr and HBr in the wavelength region :r-~om 2100~ - 26oo~. Finally, using the integ):'al reaction yield versus energy plot for D + H2 plus additional DI-H2 , DI-He experiments we were able to determine the fraction f of iodine a.toms produced in the 2 excited P / state in the photolysis of DI at 4 wavelengths. 1 2 The results are: f(280~) = -0.08 :!: 0.27, f(2537~) = o.46 : 0.05 f(240~) = o.60 :!: 0.07 and f(213~) = 0.33 :!: 0.1. 2 C3 APPEND :;:~: A LIGHT SOUHC ~2 S 1. Mono ch~ omators 1.1 Photolysis monochromator A Bausch and lomb high intensity monochromator with a model 33-86-01 ultraviolet grating and quartz optics was used to select a narrow band of radiation from continuous spectra lamps for a photolysis experiment. The grating is plane with 2700 groves/mm and is blazed for 2500A; the instrument blaze efficiency is approximately 3ofo. The dispersion of the monochromator is 32 Angstroms per millimeter at the exit slit. The monochromator had adjustable slits at both its entrance and exit allowing for band0 0 passes from lA to 190A. The instrument without final collimator had an r/3.5 divergent exit beam. It was found that a factor of 2 more intensity could be obtained for a given monochromator setting if a 1-inch diameter, 2-inch focal length quartz lens was used to replace the Bausch and lomb Model 33-80-51 achromatic condenser lens. The 1-inch lens was mounted so that it could be adjusted to• give maximum intensity for a given monochromator setting. After about 2 years continuous use the amount of scattered light in the monochromator had increased by approximately 10 times its original amount . At this point the monochromator was returned to Bausch and lomb to be renewed, which involved replacing the grating and blackening the inside of the housing. 20 ~ The w<lvelength dial of the roo:no chromator was :calibrated using a low 1rressure mercury lamp. 1.2 Jvkn..ochromators for Testing and Calibrating 1.2.l Jarrell Ash Scanning Monochromator A Jarrell Ash 1/2 meter Ebert high resolution scanning monochromator with photomultiplier detector was used to scan the output of the light sources. 0 a resolution of o.5A. 0 It has a grating blazed for 5000A and It used a RCA IP28 phototube which had a gain of 1.25 x 106 at 1.00 Kv. The photocathode of the tube is S5 (Cs-Sb) and its spectral response is shown in Figure 8. The monochromator wavelength scale was calibrated using a low pressure mercury lamp. The output of the Bausch and Lomb monochromator was scanned with the Jarrell Ash monochromator to calibrate the peak wavelength, to determine the width of the peak at half height and to check for scattered light coming through the monochromator. The Jarrell Ash instrument was used in preference to the McPherson described in the next section because it was more portable and also had a greater range of sensitivity. Its resolution is higher than that of the Bausch and Lomb one and could conveniently be used for the purposes above. 1.2.2 McPherson Scanning Monochromator A McPherson Model 235 ultraviolet scanning monochromator was .· also used to scan some of our light sources. This instrumen~ 0 0 proved most useful in the wavelength region from 1800A to 2200A where the sensitivity of the phototube on the Jarrell Ash 2 10 monochromator began to drop. 2. Light Sources Several light sources were used and are described below. 2.1 2500 watt Xenon Mercury Arc Lamp This is a lamp manuf'actured by Hanovia (#929-Bl). It is housed in a universal lamp housing model C-60-80 manuf'actured by Orion Optics Co. The housing contained a 3- inch diameter spheri- cal mirror behind the lamp and a 2-inch diameter, 3- inch focal length collimating lens. intensity. These were adjusted to give maximum The power supply for the lamp was built by Hughes Electronics (Model #5000R41T). It was originally intended to power an Orion 6500 watt xenon lamp but was adaptable to the 2500 watt xenon-mercury lamp. The lifetime of the lamp is rated at 1000 hours by the manufacturer. After 400 hours the intensity was down by 2Cf/o of its original value and the lamp had begun to darken on the top . It was replaced after 600 hours running time when the intensity was down by 4CP/o and the lamp envelope was very dark. The output of the collimating lens was passed through a nickel sulfate-cobalt sulfate filter (see section 5 . 2) to remove the intense undesired radiation in the visible and infrared . The radiation was then passed through the Bausch and Lomb monochromator. The output of the monochromator was mon itored using an Eppley thermopile (see section 6 . 1). A spectrum of the lamp with 211 intensity plotted versus wavelength is shown in Figure 1. The lamp had. been running for l hour ut 24 1jO wutta when tld.o spec ·trum waa taken. 0 The monochromator was set tor an 8A bandpass and the Bausch and li:>mb collimator was used at the exit of the monochromator. Comparison of this lamp with other high intensity conti- nuum sources is given in section 3. 2.2 6500 watt Xenon La.mp This lamp was built by Osram Optical Co. .It was hous,ed in . the same housing as the 2500 watt xenon mercury lamp and powered by the same supply. The lifetime of the lamp is rated by the manufacturer at 1000 hours. However, it exploded during cool- down after 300 hours running time, extensively damaging the · inside of the lamp housing. No specific reason could be found for the lamp failure. The output of this lamp was passed through the NiS04-Coso filter and then through the Bausch and li:>mb monochromator. 4 The output of the monochromator was monitored by the Eppley thermopile. A spectrum of the lamp with intensity plotted versus wave- length is shown in Figure 2. When this spectrum was taken, the lamp was running at 5000 watts and the monochromator was set for 0 a 16A bandpass. For the measurement, the Niso 4-coso 4 filter was removed to give the true intensity of the lamp. 2.3 Mercury BH6 Lamp A 1000 watt General Electric BH6 lamp was tested and 212 Figure 1. Spectrum of 2500 watt Hanovia xenon mercury arc lamp. Bausch and Lomb monochromator set for a bandpass of 8 ~. 2 13 II w 10 9 - 8 ~ (.) Q) (/) (/') c 0 -<0 7 .c a. ' 1, '• 6 tj"' 0 -...... ~ ..., >- 5 !- 11. (f) z w 4 •) !- z 3 (\1) 11 i\ )f.'•1 2 2000 2500 3000 3500 0 WAVE LENGTH , A 214 Figure 2. Spectrum of 6500 watt xenon lamp. Bausch and 0 Lomb monochromator set for a bandpass of 16A. 215 0 0 lO i'O 0 0 I{) N 0 (oes I suoio4d Ol)AllSN3.LNI vi 216 compared with several other high pressure mercury sources (see section 3). These are air-cooled capillary lamps with an effec- tive illuminated area of 25mm by l.5mm. The lamps were run in the vertical position in our tests although the manufacturer recommends that they be run horizontally. The mercury frequently had to be redistributed between electrodes when run in this position. The power supply f or the lamp was General Electr ic Cata- logue No. Al4262. The aver age lifetime of a lamp was 30 hours. The intensity of the lamp decreased 201/o during this period. The lamps are inexpensive so this is not a limiting factor. A lens system consist ing of a 2-inch diameter, 3-inch focal length quartz lens f ollowed by a 2-inch diameter, 10-inch focal length lens was used to f ocus the light from the lamp into the monochromator. With this lens system, the maximum intensity was obtained with the lamp 23 cm from the monochromator. The output of the monochromator was monitored with the Eppley thermopile. A spectrum of the lamp is shown in Figure 3. For these measure0 ments the bandpass of the monochromator was set a t 20A. The 1-inch diameter, 2-inch focal length lens was used at the exit of the monochromat or to f ocus the light into the thermopile. 2.4 Hanovia Low Pressure Mercury Lamp A SC 2537 low pressure mercury lamp built by Engelhard, 0 0 Hanovia, Inc. was used for photol yses at 2537A and 1849A. lamp draws 110 ma current at 280 volts. The It consists of a tube 21 . 5 cm long and 2.5 cm in diameter with a supr asil quartz window 217 Figure 3. Spectrum of General Electric BH6 lamp. Bausch and Lomb monochromator set for a bandpass of 20~. 218 0 0 I() I') -::~ 0 0 0 i'C') I f~ z w .....I w > <t 3: 0 0 I() C\I 0 ......~~~-'-~~~~~-'-~~~~~~...._~~~~~-'-~~~~~--10 o~ ( oe~ I ~uo~o4d SI 01) AJ.ISN 3J.N I 219 attached at one end . to the main tube. The electrodes are contained in legs attached A scan of the spectrum of this lamp with the 0 McPherson monochromator showed that 92% of its light was 2537A 0 radiation, the remaining &/o being 1849A radiation. This lamp was also used as a microwave discharge lamp by A 2450 MHz. using a microwave antenna to stimulate the lamp. Raytheon microwave generator, model KV-104, was used to drive the discharge. The nominal relative output power applied to the antenna cable is read from a meter on the microwave generator. On this meter, lOcY/o corresponds to 85 watts of radiative power. A study was made with t he McPherson monochromator of the effect 0 of the power applied on the relative amount of 1849A radiation generated . 0 It was found that lOCP/o power gave 3.&;o 1849A radiao 0 tion , 8CP/o gave 7.g1/J 1849A radiation and 5o% gave 2.&/o 1849A radiation. Hence, the Raytheon unit was run at 8afo power when 0 0 1849A radiation was desired and at lOCJ'/o when 2537A radiation was needed. The intensity of the lamp increased approximately an order of magnitude when it was run in this manner as compared with the DC supply . The intensity of the lamp run both by elec- trode discharge and microwave discharge is compared with the 0 intensities of other 2537A lamps in section 4. 2.5 Germicidal La.mp A General Electric germicidal lamp (#G4T4-1) was tested in 0 an effort to obtain more intensity at 2537A. and approximately 10 cm in length. T'ne lamp is U-shaped The lamp was used lengthwise 220 so the radiation was incident on the cylindrical surface of the reaction vessel. Approximately 9&/o of the output of this lamp is 0 0 2537A radiation, 'C'/o being 1849A radiation . A scan of the lamp with the McPherson monochromator showed the only other line 0 0 appearing up to 3200 A to be a doublet at 3130A. This lamp is compared in intensity to other low pressure mercury lamps in section 4. 2.6 Phillips Spectral Lamps Zinc, cadmium, low pressure mercury, indium and thallium Phillips spectral lamps were tested in the course of this research . The lamps are manufactured by Phillips in Holland and distributed by the Ealing Corporation in the United States . All of them draw 0.9 amperes current and dissipate from 15 to 25 watts power. They require an initial striking voltage of approximately 470 volts. The power supply for these lamps was also manufactured by Phillips (Cat. No . 26-295) . side diameter of 3 cm. They are all 17 cm high with an out- Their radiation is emitted from a cylin- der approximately 10 mm in diameter and 25 mm long whose center is 11 cm from the tip of the basecap . A 2- inch diameter, 3-inch focal length quartz lens followed by a 2-inch diameter, 10-inch focal length lens was used to collect and collimate the output of the lamps . The lenses were adjusted for maximum intensity of radiation as measured by the RCA pbototube. 221 2.6.1 Zinc Lamp The spectrum of the zinc Phillips spectral lamp was scanned using the Jarrell Ash monochromator. The wavelengths at which the spectral lines occur as well as their relative intensities 0 are given in Table I. 0 The spectral lines at 2025A and 2062A can be removed by a cis-2-butene gas filter (100 torr, 5 cm pathlength, 0 see section 5 for its spectrum) which renders the line at 2138A photochemically useful. The intensity of this line for our lamp was 6.7 x 101 5 photons/sec when the lamp was new. This dropped by 5CP/o when the lamp had been run 250 hours at which time a new lamp was installed. 2.6.2 Cadmium Lamp The spectrum of the Phillips cadmium lamp was scanned with the Jarrell Ash monochromator. The wavelengths at which spectral lines occur along with their relative intensities are given in Table II. istry. 0 0 The lines at 2288A and 3260A are useful for photochemo The 3260A line can be isolated from the shorter wavelength lines by use of a 5 mm thick Corning0160 glass filter (see section 5 for spectrum). The intensity of this line was approximately 16 1 x 10 photons/sec. The lines at 2288A and 22651 could not be separated from one another. 0 When using the 2288A one, a correco tion can be made to account for the 2265A one. 0 The line at 2145A . can be removed by a cis-2-butene gas filter (5 cm pathlength, 630 torr pressure). 0 The combined intensity of the lines at 2288A 222 Table I. Spectral Distribution of Zinc Phillips Spectral La.mp ( ) relative intensity 2025 0.200 2062 0.186 2138 1.00 3072 o.419 3282 0.110 3303 0.273 3345 0.294 wavel!ngth . 223 Table II. Spectral Distribution of Cadmium Phillips Spectral La.mp (~) relative intensity 2145 0.025 2265 0.118 2288 0.869 3261 . 1.00 3404 0.062 3467 0.091 3611 0.091 wav~ length 224 0 and 2265A was 8 x 10 15 photons/sec. The intensity gradually decreased as the lamp was used, dropping to about 5CP~ of its original value after 300 hours use. The lamp was run for 8 hours at a time. 2.6.3 Low Pressure Mercury La.mp The major line of the low pressure mercury Phillips spectral lamp is at 2537%. The intensity of this line was 1.5 x 101 6 photons/sec when the lamp was new. 0 0 1849A was about Z1/o of the 2537A one. The intensity of the line at This lamp is compared with other low pressure mercury lamps in section 4. 2.6.4 Thallium Lamp The spectrum of the thallium Phillips spectral lamp was 0 0 taken in the wavelength region from 2000A to 5500A with the Jarrel Ash monochromator. 0 The major line of this lamp was 5350A which is at too low an energy to be useful for our work. The other lines are not intense enough for photochemistry. The total intensity of the lamp was greater than 101 6 photons/sec. 2.6.5 Indium La.mp The spectrum of the indium Phillips spectral lamp was 0 0 taken in the wavelength region from 2000A to 4700A with the Jarrel Ash monochromator. The lines at 410~ and 451J5t are likely candidates for photochemical experiments although they are at too low an energy for our work. The wavelengths at which the spectral 225 Table III. Spectral Distribution of Thallium Phillips Spectral I.amp (A) relative intensity 3229 0.17 3519 4.o 3529 1.3 3776 14.15 5350 27.7 waveJ-ength 226 Table DI. Spectral Distribution of Indium P'.oillips Spectral Lamp wav(i)ngth relative intensity 3039 0.7 3256 5.2 3259 2.3 4102 17.5 4511 19.1 227 lines occur along with the relative intensities of the lines are given in Table TV. 2.7 Iodine la.mp An iodine lamp built by William B. DeMore at the Jet Propulsion Laboratories following the specifications given in a paper by Harteck, Reeves and Thompson 1 was tested and used in this research. It was designed to be run by an electrode discharge but was operated as a microwave discharge lamp in these tests because of the greater intensity emitted under this mode. The microwave source used to stimulate the lamp was described in section 2.4. Its output spectrum was scanned with the McPherson monochromator. 0 The major line occurred at 2061A. 0 0 There were 0 also lines at 1820A, 1830A and 1860A which were less than 0.5~ of 0 the 2061A one. These lines were removed by a 5 mm thickness of quartz placed in front of the reaction vessel. The intensity of 16 the line at 206ift. was 1.8 x 10 photons/sec measured using EBr as an actinometer. 2 3. Comparison of High Intensity Continuum Lamps in the Wavelength 0 0 Region from 2400A to 3660A The intensities of several high intensity continuum lamps were compared over a range of wavelengths. The output of each lamp was passed through the Bausch and L::lmb monochromator with a 0 bandpass set for 16A. and the intensity was measured with the Eppley thermopile. The lamps considered are: (1) a 200 watt 228 Hanovia super pressure mercury lamp3, (2) a 2500 watt Hanovia xenon mercury lamp, (3) a 6500 watt Osram xenon lamp and (4) a 1000 watt Genera l Electric BH6 super pressure mercury lamp. These were run under the conditions described .in section 2. Table V gives the absolute intensity of each lamp after passing the output through the Bausch and Lomb monochromator at 9 different wavelengths. Most of the wavelengths chosen for comparison correspond to the maxima of the high pressure mercury lamps. The 2500 watt xenon mercury lamp is the most intense of the lamps considered at these peak wavelengths. However, both the 200 watt super pressure mercury and the 1000 watt BH6 lamp have enough intensity for photochemical purposes and are less expensive than the 2500 watt xenon mercury one. The 6500 watt xenon lamp is useful at wavelengths where the high pressure mercury lamps have 0 little intensity (such as 3250A). Table V, along with the inten- sity versus wavelength plots in section 2, is useful in chosing which lamp to use for given photolysis conditions. 4. Comparison of Low Pressure Mercury Lamps The lamps compared here are the Hanovia SC 2537 lamp (run by both electrode and mocrowave discharge), the Phillips low pressure mercury spectral lamp, and the General Electric germicidal lamp. The relative intensities were measured by photolyzing DBr with each lamp and measuring the rate of conversion of DBr per hour. Since DBr has a quantum yield of D2 of 1, the absolute intensities could be calculated for all lamps except .the germicidal lamp 229 Table v. waveiength ( ) Comparision of High Intensity Continuum Lamps 200 watt mercury 2500 watt 6500 watt Xe-Hg xenon 1000 watt BH6 (101 photons/sec) 24oo 2.2 6.3 1.8 0.52 2483 4.2 10.8 2.5 1.4 2700 0.1 7.1 5.5 2.6 2800 2.3 16.8 7.1 4.2 2891 2.6 14.5 8.4 6.4 3030 3.3 37.8 9.1 13.4 3130 11.7 40.5 11.0 20.4 3340 3.5 20.6 13.2 14.4 3660 20.0 47.5 12.0 35.6 230 where the geometry used did not permit an accurate determination of the pathlength. The output of all lamps was passed through a 0 2-rnm Corning 7910 glass filter to remove any 1849A radiation. The Hanovia lamp was used with no lenses. The Phillips lamp had a 2-inch diameter, 3-inch focal length lens followed by a 2-inch diameter, 10-inch focal length lens to collect the light from the lamp. For both these lamps the light was directed through the quartz window of the reaction vessel containing the DBr. For the General Electric germicidal lamp the light was directed through the fused silica sides of the cylindrical reaction vessel to use the maximum amount of radiation. The results in terms of conver- sion of DBr and absolute intensity are shown in Table VI. The SC 2537 lamp run as a microwave discharge lamp was the most intense source. The main disadvantage of running the lamp in this manner was the large quantity of heat generated by the discharge. A cooling coil had to be wrapped around the reaction vessel to keep it at room temperature. Of the lamps operating on an electrode discharge, the germicidal lamp was best. This may have been because of the large area irradiated by the lamp. If the position of the lamp with respect to the reaction vessel is unimportant for the photolysis experiment being done, the germicidal lamps are the most economical high intensity low pressure mercury lamps available. The SC 2537 lamp and the Phillips lamp are about equal in performance. The Phillips lamp has the advantage that its light can be focused into a smaller area. 23 1 Table VI. Comparison of Low Pressure Mercury Lamps at 253~ Extent DBr Conversion (°/o per hour) Absolute 5ntensity (101 photons/ sec) SC 2537 electrode 0.057 1.12 SC 2537 microwave 0.51 10.0 Phillips Spectral Lamp 0.065 1.28 Germicidal 0.16 Lamp Lamp 232 5. Filters 5.1 Glass Filters High energy cut off filters were used with several of the light sources to remove unwanted lines and at the exit of the Bausch and Lomb monochromator to remove undesired high energy radiation. Corning 7910 (2 mm thick) and 0160 (2 mm and 5 mm thick) glass filters were used in the course of this work and their transmission characteristics are shown in Figure 4. 0 The 0 7910 filter was used when wavelengths from 2400A to 2537A were desired. The 5 mm 0160 filter was used with the cadmium Phillips 0 spectral lamp to isolate the 3261A line and also at the output 0 0 of the monochromator for wavelengths from 3250A to 3400A. Also shown are the transmission characteristics of a 2 mm thick piece of quartz similar to the quartz windows of the reaction vessel. All spectra were taken with a Cary 14 spectrophotometer. 5.2 NiS0 -coso 4 Filter 4 A filter solution containing lOg of Coso .7H o, 20g of 4 2 NiS04.6H 20 and 1 ml of l&~ sulfuric acid per liter of water was used to remove much of the visible and infrared radiation from the 2500 watt xenon mercury lamp and the 6500 watt xenon lamp. The transmission characteristics of the filter for a 5 cm pathlength are shown in Figure 6. A temperature dependence study was made on this filter at 25°c, 50°c and 65°c. Little if any temper- ature effect was observed. A 5 cm long stainless steel cell with 4 cm diameter quartz 100~~~~-~~~~~~~~~~~~-.--~~~-.--~~~ 80 z 0 ~ 60 -2 CJ) z ~ 40 ~~ ?/!. 20v I 11 /-7910 (2rnrn) 0160(5rnml -t 0160-¢ (2mm) I 0'--~~___.,"--~~~-'--~~~.._,_~~~~~~~-'--~~--i 1800 2200 2600 3000 3400 WAVELENGTH (A) Figure 4. Transmission curves of glass filters. 3800 4200 [\) VI CA 100 ---. 80 z 0 ~ (!) Cf) 60 ~ :2: (f) ~ 4ol I I \ \ J~ ~ I=0 (}' 20 0 2000 I 3000 4000 5000 WAVELENGTH(%\) Figure 5. Transmissi on of NiS0 4 - CoS0 4 filter (5 cm pathlength). 6000 1001801_ ·-· I ,- - - - - - -- - - - -. ::£ 0 ~ 60 ""'· en Cl) -= <:(':~ c~ ~~ CJ) z 40 ~-------- <! ~ I= ~ 0 20 ~ Q 1800 2000 2200 ., 2400 = · • ·· ~ 2600 ViAVE LENGTH (2.\ ) Figure 6. Transmission of co 60 gamma-i r radia t ed lithium flou r ide filter. I 2800 236 windows sealed on with General Electric RTV-108 silicone rubber adhesive was used to contain the filter solution. This container was water cooled by a coil of copper tubing soldered around the circumference. Some difficulty was encountered in finding a suitable cell because of the high reactivity of the solution. A Pyrex cell was insufficiently heat conductive. Brass ruined the optical properties of the filter solution, and we could not get a nickle plate to ad.here sufficiently well. Neither Varian's Torr Seal nor Fuller's Resiweld adhesives could long withstand the warm solution. 5.3 cis-2-butene Gas Filter A cis-2-butene gas filter at 100 torr pressure, 5 cm patho length was used to isolate the 2138A line of the zinc Phillips spectral lamp . The transmission of this filter is plotted as a function of wavelength in Figure 7. A 5 cm long, 5 cm diameter A similar filter a t 630 quartz cell was used to contain the gas. 0 torr pressure was used to remove the 2145A line of the Cadmium Phillips spectral lamp . Figure 7. Its transmission curve is also shown in A Cary 14 spectrophotometer was used to measure ' these spectra . 6. Light Intensity Measuring Devices 6.1 Eppley Thermopile An Eppley thermopile (serial number 5823) was used to measure the light intensity in some of our experiments. It is a surface 237 80 7 0 60 U) 01 ~ .=. 40L U") -c;;;.z:._ <( u: 20 i0~ 2~00 Figure 7. 2200 2400 WAVELENGTH (A) Transmission of cis-2-butene gas filters. 2600 238 type thermopile with 12 bismuth silver junctions. It was con- tained in an aluminum housing with an aperature 3 mm wide and 10 mm high. It was calibrated by Eppley with an NBS standard lamp and was found to develop an emf of 0.056 microvolts when a radiant flux of 1.00 microwatts per square centimeter was incident upon it. A Keithley Model 150 microvolt-ammeter was used to measure the voltage developed by the thermopile. 6.2 RCA 935 Phototube An RCA 935 phototube was frequently substituted for the Eppley thermopile. The photo tube was housed in a housing made of.· anodized aluminum. The aperature to the phototube was 2.5 cm high and 1.25 cm across. A power supply-ammeter was built by our electronics shop to supply 250 VDC to the photocell and to measure currents from 0 to 50 microamps. A battery could probably be found that would take the place of the power supply . The phototube has an S-5 response. RCA's data for the rela- tive S-5 response (per energy interval) is shown in Figure 8. The photocell was also calibrated against the Eppley thermopile. The photocell sensitivity as a function of wavelength is given in Table VII . The photon flux is obtained from the output of the phototube in microamps by the formula I = output sens. x 1014 where I is the photon flux in units of photons/sec, the output is in microamps and the sensitivity is in units of microamps/ 239 Table VII. RCA 935 Photocell Sensitivity sensitivity (amp/1014 photons/sec) 2000 0.05 2100 1.8 2200 2.0 2300 2.2 2400 2.4 2500 2.5 2600 2.6 2700 2.6 2800 2.5 2900 2.5 3000 2.5 3100 2.6 3200 2.6 3300 2.6 3400 2.6 3500 2.6 3600 2.5 3700 2.4 3800 2.3 3900 2.2 4000 2.1 240 Figure 8. Relative S-5 response (per energy). 241 0 0 0 lO 0 0 0 v -- ~ :c f- (.!) z w _J w > <l ~ 0 0 0 fO ' ..... .......... ..... __ ---- .... -- --- ... 2 0 0 0 ro d © d 3SNOdS3~ ~ 0 ~ d 3/\Ll V113Cl 0 242 1014 photons/sec. The phototube was found to be more useful than the thermopile because of its wider aperature. 7. Scattered Light in the Bausch and Lomb Monochromator The amount of scattered light was checked by scanning the output of the Bausch and Lomb monochromator with the Jarrell Ash monochromator described in section 1. In a system such as ours in which the extinction coefficient of the substance being photolyzed increases rapidly with decreasing wavelength, a small amount of scattered light of short wavelength could lead to drastically wrong results for a given wavelength setting. Figure 9 shows a plot of the output of the monochromator as a function of wavelength for the Xe-Hg lamp when the dial on the 0 Bausch and Lomb instrument was set for 2480A and the bandpass of 0 the monochromator was set for 24A. The width at half-height 0 of the peak is 22A in good agreement with the bandpass settings. 0 Note that the peak at 2400A has been completely removed by the monochromator and that the tail of the peak drops rapidly to zero at short wavelengths. A 2 mm Corning 7910 glass filter was placed at the exit of the monochromator at this wavelength to remove any short wavelength light present. From a scan of this type we could discover if scattered light was coming through the monochromator and could decide if a filter was needed to remove excessive short wavelength light. These considerations became increasingly important for long wavelengths since the extinction 243 coefficients became very small. The peak absorbed wavelength could be found by making a plot of intensity times extinction coefficient versus wavelength. The peak of this plot sometimes differed from the peak intensity by 2 to 3 Angstroms. REFERENCE 1. P. Harteck, R.R. Reeves, Jr., and B. A. Thompson, z. Naturforschg., 19a, 2 (1964). 244 Figure 9. Output of Bausch and Lomb monochromator as a function of wavelength for the Xe-Hg lamp with the dial of the monochromator set at 248 02 and 0 the bandpass set for 24A. 245 10 9 s>- I- 7 ({) z w !z w -> 6 5 I- <: _J w a:: 4 3 2 2400 2500 VvAVELENGTH ctl) 2600 246 APPENDIX B ADDITIONAL EXPERIMENTAL TECHNIQUES FOR D + H2 1. Reactant Mixing A mercury free vacuum line utilizing an oil diffusion pump was used for mixing reactants. The vacuum line is essentially the same as described in J.M. White's thesis 1 with the addition of a separate section to handle DBr. This section was added in order to avoid contamination of the DBr by the DI or vice versa. A schematic sketch of the vacuum line is shown in Figure Bl. Section I is the pumping section and utilizes the same mechanical and diffusion pumps as described in J. M. White's thesis. Section II is the section of the line for handling DI and section III is the section of the line for handling DBr. These two sections are separated by a cold trap C to prevent mixing of DI and DBr . . Hydrogen and helium were added directly to the line from high pressure gas tanks through cold traps. The technique for filling the reaction vessels is as described in J. M. White's thesis. 2. P-~oduct Handling The vacuum line for product handling was the same as described in J.M. White's thesis. One end of the reaction vessel was . placed in liquid nitrogen for 15 minutes to remove the DBr or DI and the remaining gases were transferred via a toepler pump to a glass bulb for analysis. r ' I I , I section ,------,I Section 11 @ ,_~-+-r(\) .... "1 I I _ _ _ _ _ _ _ _J L_ I A. Mechanical Pump B. Pump Diffusion ·E. Transduc er C. Cold Trap F. Cold D. Gauge G. Reaction Ion Figure Bl. Fing er Vessel Schematic sketch of vacuum line. 248 3. Mass Spectral Analysis A CEC-103C mass spectrometer was used for product analysis. The spectra were recorded photographically on an oscillograph recorder built into the mass spectrometer. The slowest automatic scan rate (1/6 octave/min) was used in analyzing the samples. A rigid time schedule was adhered to in these analyses so the same peaks were in register at a given time after the sample was introduced. For samples containing HD, D2 and H2 , the m/e = 3 peak was scanned 3 times at 10 second intervals. Five seconds we allowed to adjust the ion accelerating voltage to the peak at m/3 = 4 and this peak was scanned 3 times at 10 second intervals. Five seconds were then allowed to adjust the ion accelerating voltage to the m/e = 2 peak and this peak was scanned 3 times at 10 second intervals. Hence there was 100 seconds elapsed time from the time the sample was introduced until the analysis was completed with m/e = 3 peaks at 5, 15 and 25 seconds elapsed time, m/e = 4 peaks at 40, 50 and 60 seconds elapsed time and m/e = 2 peaks at 75, 85 and 95 seconds elapsed time. For the samples + containing H2 a correction had to be made for the H contributing 3 to the peak at m/e = 3. This was done by running a given sample at 4 different inlet pressures and extrapolating the measured [HD]/[H2 ] and [HD]/[D 2 ] ratios to zero pressure where the H+3 contribution to the m/e = 3 peak vanishes. The correction for the HD originally in the H2 was made by the expression: [I:ID]) - ([ED]\ ID2J photolysis - TD2f} total ( [ED]) (TD2l tank 1 -(Uffil) ID2J total 249 where the ratios ([HD]/[D 2 ])total and ([HD]/[H2 J)total are from the observed peak ratios extrapolated to zero inlet pressure and ([HD]/[H2 J)tank is the ratio of the HD and H2 peaks in the tank hydrogen used in the photolyses. For samples containing HD, D2 and He, the same time schedule was followed with the exception of not scanning the m/e = 2 peak. It was also not necessary to extrapolate the results to zero pressure. The m/e peaks for He and D2 were separated enough so analysis of D was possible. 2 Even though the He peak was as much as 100 times larger than the D2 peak, the contribution of the He peak to the D2 peak was always less than 2!{o of the latter. Carefully prepared calibration mixtures of HD, D2 and H2 and HD, D2 and Re with compositions analogous to photolysis mixtures were analyzed using the procedures described above to calibrate the mass spectrometer. The deviations of the peak height ratios of these mixtures from the known concentration ratios was always less than Jfo. Reproducibility for a given sample was always 'c/o or less. REFERENCE l. J. M. White, Ph.D. Thesis, University of Illinois, Urbana Illinois (1966). 250 APPENDIX C ADDITIONAL EXPERIMENTAL ~'ECENIQUES FOR H + CD4 1. Reactant :Vdxing The vacuum line used was the same as that used for D + H2 as described in Appendix B with bulbs of EBr and CD4 attached in place of those of DBr and ~ respectively. The :procedure for preparing reactant mixtures was identical to the DBr-~ case described in detail in J. M. White's thesis, Paper I and Appendix B. 2. Product Handling A new glass vacuum line using a mercury diffusion pump was constructed to process reaction :products. The vacuum pumps are as described for D + ~ in J. M. White 1 s thesis and Appendix B. In order to remove most of the unreacted CD4 f'rom the products H and HD, (because of its contributions to m/e 2 = 2 from the D+ :fragment and m/e = 3 from the "IID+ :fragment of the cD H impurity) · 3 a dewar for pumping on liquid nitrogen was constructed. A schematic drawing of the dewar and toepler pump is shown in Figure Cl. The reaction vessel A is placed on the standard ta.per joint at the top of the trap B and the trap is evacuated. One end of the reaction vessel is placed in liquid nitrogen to remove the EBr and some of the CDii. before the remaining contents a.re passed through the trap. dewar through C. Liquid nitrogen is then added to the Mter nitrogen has been added, the opening C is closed with a ground glass joint. This joint b.a.s a small 251 diameter tube sealed into it in which a thermocouple is placed to measure the temperature in the dewar. The nitrogen is then pumped on through D with a Cenco Megavac Pump (pumping speed liters/min) until the temperature of the nitrogen reaches -212°c or lower as measured by the thermocouple. from 15 to 20 minutes. This usually takes The contents of the reaction vessel are then passed through the trap with the aid of a 1 1/2 liter toepler pump. One sweep of the toepler pump collects about 75°/o of the sample and reduces the [cD4 ] /( [HD] + [~] ) ratio by at least 98.5%. Mixtures of HD, H2 and CD4 of known compo sition analogous to photolysis mixtures were :prepared, passed through the dewar and analyzed to check for fractionation of H2 and ED and to measure the efficiency of the dewar. The measured [H2 ] / [HD] ratios agreed with the known ones within l°/o. After passing through the dewar, the sample was transferred to a sample bulb and then analyzed by the CEC mass spectrometer. 3. Mass Spectral Analysis T'ne products H2 and HD were analyzed on the CEC-103C mass spectrometer. T'.ae spectrum of' peaks was scanned automatically with the slowest automatic scan rate (1/6 octave/min) of the mass spect'..cometer. The output was measured with a strip-chart recorder connected to the amplifier jack of the mass spectrometer. This enabled us to obtain at least 3 times more sensitivity (when the instrument noise level was low) than with the oscillograph recorder used for the D + R analysis as described in Appendix B. 2 A B f\.) C.11 f\.) Figure Cl. Schematic drawing of pumped liquid nitrogen dewar and toepler pump. 253 Each peak at m/e 3, 2 and 20 was scanned five times in succession and an average ta.ken. To correct for peak heights decreasing with time, the peaks were scanned at reproducible times from when the sample was introduced. The peak at m/e 3 was scanned 5 times at 10 second intervals, 5 seconds were then allowed to adjust the accelerating voltage f or the peak at m/e 2 and this peak was scanned 5 times at 10 second intervals. One minute was then allowed to adjust the accelerating voltage for the peak at m/e 20 since the magnet current range had to be changed to get this peak into register. intervals. This peak was then scanned 5 times at 10 second The same time schedule was used on all samples and calibration mixtures, allevi ating the need to extrapolate the measured peak heights to zero time. In order to correct for the contributions of the CD4 to the m/e 2 peak and the c:n H impurity to the m/e 3 peak, samples of 3 "pure" CD4 were analyzed and the ratios of .the peaks at m/e 2 and m/e 3 to the peak at m/e 20 were determined. These were then used to correct for CD4 in the sample by the formula: [H2 J ) [H2]obs - [CD4 ]obs.CH2 ( [HD] _phot olysi s - [ED ]obs - [ CD4 ]obs•CHD In the above [H2 ] / [HD] is the true experimental value and [H2l obs' [HD ] 0 bs and [ CD4 ]obs are the observed peak heights at m/e 2, 3 and 20 respectively. CH2 and CED are ratios of peak heights of masses 2 and 3 to mass 20 in "pure" CD4 • The second term in the numerator was usually 20-3Cfio of the measured peak .[ ~ ]obs and the second term in the denominator was less than lCY/o of [HD] 0 bs • 254 Calibration mL~tures whose composition was analogous to photolysis mixtures were analyzed by the same procedure and a correction was applied if necessary. Corrections varied slightly from day to day but never exceeded J/o. Reproducibility for a given sample was within Z{o. 255 APPE.NDIX D ADDITIONAL RESULTS FOR D + H 2 1. 0 Photolyses at 18~-9A Photolyses of DBr-H2 and DBr-He mixtures were carried out at this wavelength using the experimental techniques described in Paper 1 and Appendix B. A 6-inch long l 1/2-inch diameter f'used. silica reaction vessel with optical quality quartz windows was used in this and all following experiments except where specifically stated otherwise. The Hanovia SC 2537 lamp described in Appendix A was used with the 60co gamma-irradiated filter. The intensity of this lamp at 1849A was approximately 9 x io13 photons/sec. Photolysis times f or DBr-~ ranged from 1-2 hours with DBr conversions of from 0.2!fo to 0.5°/o while for DBr-He, photolysis times were 3 hours with conversions of approximately o.fl%. The results of the DBr-H2 experiments are given in Table DI while those of the DBr-He experiments are given in Table DII. The results of' both sets are plotted in Figure Dl. DBr-H 2 . For the system, least squares analysis of the photolysis data + gives a slope of 0.73 - 0.02 and an intercept of 0.31 ! 0.01. For the DBr-He system the least squares slope and intercept are 0.1 ! 1.0 and 39.3 ! 0.7 respectively. 256 0 2 Photolyses at 1849.A Table DI. Results of DBr-H Ex-pt. PDBr (torr) 1 [DBr] [H2] [Dz] (torr) Photolysi s Time(hrs.) [HD] conv. (%) 42.0 47.7 1.0 o.88o 0.965 0.30 2 51.7 173.7 loO Oo298 0.523 0.25 3 6o.2 64o l 1.0 0.938 0~990 0.21 4 55.3 166.8 L5 0d31 0.549 0.39 5 50.0 1~9.5 L6 1.01 1.079 o.43 6 53.2 105.2 1.8 0.506 0.663 o.42 7 40.7 90.2 i.5 o.451 0.653 o.48 8 61.1 93.6 2.3 0.652 o.452 0.57 9 54.9 121.3 1.5 o.452 0.657 0.35 10 57.5 47.8 1.0 1.202 1.167 0.23 PH2 257 0 Table Dll. Results of DBr-He Photolyses at 1849A PDBr (torr) Photolysis (torr) Time(hrs.) (DB~ ~- (D~. conv. [Hg (%) 1 29.1 92.6 5 0.314 39.2 1.25 2 35.3 45.9 3 1/2 0.771 40.4 0.85 3 32.0 68.8 4 1/ 3 o.465 40.0 1.16 4 32.0 61.3 4 0.522 39.3 1.06 5 41.0 36.2 3 1.132 38.3 0.80 6 37.2 84.8 4 o.439 38.8 1.00 7 32.6 99.8 4 0.326 40.4 0.98 8 41.0 41.6 3 1/2 0.985 40.7 o.86 9 29.7 55.4 4 0.536 38.1 1.01 Expt. PHe 258 40 0 39 ~ 38 [HD] 37 D He 3 2 0.5 1.0 [DBr] I [G] Figure Dl. Results of DBr-H 2 0 and DBr-He photolyses at 1849A. 259 2. 0 Photolyses at 2138A Photolyses of DBr-~ and DBr-He mixtures were performed at this wavelength using the zinc Phillips spectral lamp with the cis-2-butene filter described in Appendix A. The intensity of the lamp was approximately 2 x 1015 photons/sec with the filter. T'.ae same experimental procedure as described previously was used. Photolyses lasted an average of 15 minutes resulting in conversions of approximately 0.45%. The results of the DBr-H2 photolyses are given in Table DIII and are plotted in figure D2. Least squares analysis of these data gives a slope of 0.91 :: 0.03 and an intercept of 0.735 ! 0.026. T'a.e results of' the DBr-He photolyses are given in Table DIV and are plotted in figure D2. Least squares analysis gives a slope of 2.8 ! 0.2 and an intercept of 29.1 ! 0.2 . 3. 0 Photolyses at 2300A 0 Photolyses of DBr-H2 and DBr-He mixtures were done at 2300A using a 6500 watt Orion xenon lamp with the Bausch and lomb 0 monochromator set for a 24A band.pass. The width at half height 0 of the peak was 22.A as measured by the Jarrell Ash monochromator. The 2:1 NiS0 4-coso4 filter used to cut out visible and infra.red radiation became clouded as photolyses preceded and was changed periodically. This caused the intensity exiting from the mono- chroma.tor to vary by as much as 2c:PP during a photolysis. The intensity at the beginning of a photolysis was usually about 1 x 1015 :photons/sec. Photolyses lasted 2 1/2 hours and 260 Table DIII. 0 Results o':f DBr-~ Photolyses at 2138A PDBr (torr) PH2 (torr) Photolysis [DBr] Time(min.) l. 41.2 47.0 2 44.2 3 Ex:pt. [~] ~2]) conv. (i) 60 0.876 l..480 2.12 138.7 15 0.319 1.022 0.695 L,9.2 39.0 15 1.261 1.952 o.403 L, l{.3.8 97.5 15 o.449 1.138 o.45 5 53.7 55.0 20 0.976 l..640 o.465 6 45.7 70.3 15 0. 651 i.323 o.429 7 43.1 143.2 20 0.301 1.037 0.636 8 43.5 48.8 17 0.891 1.548 o.45 9 58.5 44.5 18 1.315 1.910 o.46 10 58.3 43.7 15 1.334 1.934 o.44 261 0 Table DIV. Results of DBr-He Photolyses at 2138A Expt. Poor PH2 Photolysis [DBr] [D2] conv. (torr) (torr) Time(min.) [ ~] [RD] (%) 1 58 . 5 58 . 2 15 1.005 32.1 o.42 2 53.4 171.4 15 0.311 30.2 o.J.~o 3 35.4 9L4 15 0.388 29.8 o.43 4 54.2 40.1 15 1.350 32.9 o.43 5 38 .. 1 145.8 20 0.261 30.0 o.48 6 60.5 44.5 15 1.360 32.8 o.41 262 Figure D2. Results of DBr-H 2 and DBr-He photolyses at 21382. :..!63 o He ~H 2 -----e e----,_____ <9_"'__.o-.:;;0 1.5 264 0 Table DV. Results of DBr-H P'notolyses at 2300A Expt . PDBr (torr) PH2 (torr) Photolysis [DBr] Time(hrs.) 1 58.0 94.4 2 51.5 3 2 conv. r~1- [D2] [HD] 1. 2 0.615 1.78 0.24 179.8 1.2 0.286 1.39 o.42 54.1 45.5 1.5 1.189 2.43 0.15 4 54.8 131.4 1 o.417 l.67 0.23 5 67.6 74.4 2 0.908 2.20 0.15 6 47.1 87.5 2 0.538 l . 65 0.16 7 55 . 6 270.4 1.7 0.205 1.40 0.55 8 47.8 63.9 3 0.749 1.87 0.32 ("/o) 265 0 Table DVI. Results of DBr-He Pbotolyses at 2300A Expt. PDBr ( t-orr) Photol ys is Time (brso) (DBr ] , 2 ) t torr 1 4-1.4 73.7 2 75 .0 3 4 ---:.... [ ~] [ D2] [ HD] conv. (%) 2.5 0$561 25.9 0.34 74. 2 2.5 1.0ll 26.9 o.41 48.6 153-0 3 0.317 25.5 o.45 48.9 71.4 3 0.685 26.5 0.50 PH 266 Figure D3. Results of DBr-H 2 and DBr-He photolyses at 2300~. 267 e; He E:J H2 27 26 J .3 2 0.5 [osr]/[G] LO 268 resulted in conversions ranging from 0.15 to o.3a{o. T'ne results of the DBr-B photolyses are given in Table DV 2 and are plotted in figure D3. Least squares analysis of these data gives a slope of 1.09 : 0.08 and an intercept of 1.13 : 0.05. The results of the DBr-He photolyses are given in Table DVI and are plotted in figure D3. Least squares analysis of these data gives a slope of 2.1 :!: o.4 and an intercept of 24.8 ! 0.2. 0 4. Photolyses at 2446A Photolyses of both DBr-~ and DBr-He mixtures were performed. at this wavelength using the procedures described previously. The BH6 lamp was used in conjunction with the Bausch and Lomb 0 monochromator set for a 32A bandpass. The width of the peak at 0 hali' height exiting from the monochromator was 34A. vas approximately 5 x io1 4 photons/ sec. The intensity Photolyses lasted an average of 3 hours with conversions of 0.35%. Results of the DBr-H2 experiments are listed in Table DVII and plotted in figure D4. Least squares analysis of these data gives a slope of 1.18 :!: 0.04 and an intercept of 2.06 :!: 0.02. Results of the DBr-He e:A.'Periments are listed in Table DVIII and are plotted in figure D4. Least squares analysis of these data gives a slope of 2.9 :!: o.6 and an intercept of 16.4 ! o.4. 269 'I'able DVII. 0 Results of DBr-~ Photolyses at 2446A conv. [~] 021 [HD] 2.8 0.822 3.01 0.345 176.5 3 0.288 2.38 0.351 50.6 57.5 3 0.877 . 3.14. 0.352 ~- 49.0 133.0 3 0.368 2.~.9 0.349 5 46.3 43.6 2.5 1.061 3.28 0.344 6 31.5 68.7 3 o.459 2.64 0.353 7 47.8 164.1 3 0.291 2.38 0.351 8 46.1 77.5 3 0.595 2.75 0.34.8 9 38.7 60.9 3 0.635 2.83 0.349 Photolysis [DBr] ( tor-.c) Time(hrs.) 49.1 59.7 2 50.9 3 Expt. PDBr (torr) l PH2 (%) 270 0 Table DVIII. Results o'f DBr-He Photolyses at 24l!-6A PDBr (torr) P~- Photolysis [DBr ] (torr) Time(hrs.) 1 42.9 140.9 2 50.2 3 4 Expt. conv. (He] ( D2] [RD] l~ 0.304 17.l o.45 52.3 2.9 o.96o 19.1 0.37 41.5 79.5 4 0.512 18.2 o.46 37.6 61.5 4 0.611 18.3 o.47 rt2 (~) 271 Figure D4. Results of DBr-H 0 2 and DBr-He photolyses at 2446A. 272 o He 0H 2 19 18 ~7 - [o~ [HD] 16 if'" 2 0.5 (DBr]/[G] LO 273 5. 0 Photolyses at 2483A Photolyses at this wavelength were carried out using the Ranovia. 2500 watt mercury-xenon lamp. It was used in conjunction 0 with the Bausch and Lomb monochromator with a bandpass of 24A. A 7910 Corning glass filter was placed at the exit of the monochromator to remove any short wavelength radiation. T'.o.e intensity of the lamp was approximately 3 x 101 5 photons/sec. Photolyses lasted an average of 1 hour which resulted in conversions of o.35i. The results of the DBr-H photolyses are given in Table DIX 2 and Figure D5. Least squares analysis of these data gives a slope of 1.45 :'.: 0.07 and an intercept of 2.10 :: 0.06. The results of the DBr-Ee photolyses are given in Table DX and Figure D5. Least squares analysis of the data gives a slope of 2.2 :!: 0.06 and an intercept of 13-3 ~ o.6. 6. 0 Photolyses at 2500A Photolyses of both DBr-H2 and DBr-He mixtures were carried out using the BH6 lamp with the Bausch and l.Dmb monochromator. 0 The monochromator was set for a 32A bandpass. The width of the 0 peak at hall-height was 30A as measured with the Jarrell Ash monochromator. A 2mm thick Corning 7910 glass filter was placed at the exit of the monochromator to remove shorter wavelength radiation. The total intensity passing into the reaction vessel was 5.7 x 10i4 photons I sec. Photolysis times ranged from 3.8 to 6 hours with conversions varying from 0. 15% to 0.2&/o. Tb.e results for DBr-H2 photolyses are given in Table 274 o: Table DIX. Results of DBr-H2 Photolyses at 2483A PDBr (torr) PH2 (torr) Photolysis Time(brs.) [DBr] l 77.3 55 .1 1.2 2 31.7 110-3 3 41.9 4 ~ [D ] [RD] conv. {%) l.~-02 4.16 o.4o 1.1 0.288 . 2.56 o.43 71.8 1.0 0 ~ 582 2.84 0.33 49.0 66.o 1.0 0.742 3.24 0.35 5 54.8 47.9 1.0 1.142 3.73 0.36 6 56.7 179.7 1.0 0.316 2.45 0.33 7 48.5 37.3 1.0 1.301 3.97 0.34 8 32.7 83.2 1.0 0.393 2.79 0.37 Ex}_)t. [~] 275 0 Table DX. Results of D13r-He P'.aotolyses at 2Lr83A Expt. PDBr PH2 (torr) l (torr) P'.aotolysis Time(brs) [DBr] [B'.e] [ D2] [BD] conv. (%) 36.9 53.9 2.0 0.685 14.6 0.65 2 1+7.2 51.1 1.9 0.923 15.0 0.61 3 6lol 47.3 1.6 1.29 16.6 0.57 4 47.2 155·7 2.0 0.303 14.3 o.64 276 Figure D5. Results of DBr- H and DBr-He photolyses at 24832. 2 277 o He EJ 16~ i3 lj [D2] r [HD) 43 H2 278 Table DXI . 0 Results of DBr-R2 Photolyses at 2500A (DBr] (H2] ---""-- [IID] (%) 4 O.L~lO 2.97 0. 26 ' 31.2 4 i.310 3. 61 0.19 33.4 34.5 3.8 0.969 3.44 0.15 4 22.2 rr.6 4. 5 0.286 2.70 0.18 5 30.3 46.3 5.0 0.655 3.11 0.23 6 32.1 91.2 6.o 0.352 2.80 0.28 7 44.5 77.5 5. 5 0.575 2.93 0.23 E.xpt. PDBr (torr) PH2 Photo l ysis (torr) Time (hrs.) 1 34.1 83.3 2 40.9 3 [D2] conv. 279 Table mar. 0 Results of DBr-He Photolyses at 2500A Photolysis [DBr] Time(b.rs.) conv. [He] [D2] [ED] l.i, 0 . 299 16.55 0.21 44.6 .... :J o. 961r 18.12 0.16 28.8 97.1 3 0.296 16.65 0.13 4 35.9 69.1 3 0.519 17-13 0.17 5 40.7 4-o.8 "":> 1.00 17.36 0.19 6 34.4 44.9 3 0.765 17.12 0.18 Expt. PDBr (torr) PH2 (torr) l 27. 3 91.L~ 2 43. 0 3 (%) 280 Figure D6. Results of DBr-H 2 and DBr-He pho t o lyses at 2500~. 281 ®He B H2 i8 - 4 2 0.5 [DBrj/[G] LO 282 DXI and Figure D6. Least squares analysis of the data gives a slope of 0.88 :!: 0.08 and an intercept of 2.51 ! 0.06. The results for the DBr-He photolyses are given in Table XII and Figure 6. Least squares analysis of the data gives a slope of 1.5 +- 0.5 and an intercept of 16.2 ! o.4. 0 7. Photolyses at 2537A 0 Two different series of photolyses were done at 2537A. One used. the I:Ianovia SC 2537 low pressure mercury lamp with the 2mm Corning 7910 glass filter while the other used the same SC 2537 lamp at one end of the reaction vessel and the low pressure mercury Fnillips spectral lamp at the other end. Intensities of both lamps were approximately l x 1016 photons I sec.. were done at intervals 3 months apart. The two series The second series was also a study of the effect of DBr conversion on the experiments. For the first set of experiments photolysis times ranged from 8 to 11 hours resulting in DBr conversions of from 0.57% to 0.86%. In the second set of experiments, one group of experiments had photolysis times of 4 hours resulting in 0.53% conversion and another group had photolysis times of 10 hours resulting in 1.02% conversion. The results for the first series of DBr-H2 and DBr-He experiments are given in Tables DXIII and DXIV respectively, and both are plotted in Figure D7. Least squares analysis of the data gives a slo:pe of 1.32 ! 0.05 and an intercept of 2.36 :!: 0.04 for the DBr-~ experiments and a slo:pe of 2.0 ! 0.1 and an 283 0 Table DXIII. Results of D:Sr-H2 Photolyses at 2537A, Set I PDBr (torr) Photolysis [DBr] (ton) Time(hrs.) 1 50.3 176.3 2 44.3 3 Expt. [ ~] [D2] [HD] conv. (%) 8.o 0.285 2.70 0.70 140.6 10.5 0.315 2.73 0.76 50.4 64.8 7.5 0.778 3.40 0.57 4 42.5 37.7 7.1 1.128 3.95 0.56 5 37.3 122.6 9.75 0.304 2.84 0.75 6 36.0 67.7 8.o 0.531 3.01 0.62 7 32.1 83.5 11.0 0.384 2.91 o.86 8 50.8 32.6 9.7 1.57 4.39 0.699 PH2 284 Table DXIVo Expt. 0 Results of DBr-He Photolyses at 2537A, Set I PDBr (torr) PE2 Photolysis (torr) 1 40.4 2 [ D2] Time(b.rs.) [DBr] [Be] [RD] conv. (%) 101 .0 9.9 0.399 l0.91 0.70 58.9 48.4 8.0 1.219 12.68 0.61 3 27.7 95.0 l0.5 0.292 10.87 0.77 4 34.6 75.6 ll.O o.458 ll..10 0.85 285 Figure D7. Results of photolyses at 2537~, Set I. 286 I- ~ ----~~~~~~~-- Q) OJ :c :c CD f] l() -- 0 - l() 0 287 Table DX:V. Results of Variable C~nversion DBr-~ Photolyses at 2537 Expt. [ DBr] [H2) [D2] conv. [HD] (%) (torr) (to~) Photolysis Time(hrs.) l 78.1 78.8 4.o 0.991 3.96 0.53 2 55.7 176.3 t~.o 0.316 3.08 0.54 3 52.9 112.8 10.0 o.lic69 3.24 1.02 4 60.7 i~o.6 10.0 1.492 l;..55 l.02 5 73°5 49.6 4.o l.482 4.56 0.54 6 51.9 176.5 10.0 0.294 3.04 1.02 7 66.4 212.5 4.o 0.312 2.98 0.52 8 77.0 72.5 10.0 1.062 3.98 1.03 9 52.3 76.4 4.o 0.685 3.51 0.55 10 56.9 73.0 10.0 O.Tf9 3.70 1.01 ll 53.0 88.o 4.o 0.602 3.62 0.51 12 55 . 6 182.8 10.0 0.304 3.12 l.05 13 45.0 107.2 4.o o.419 3.31 0.51 PDBr PH 288 Table DXVI. 0 Results of DBr-He Photolyses at 2537A, set II PDBr (torr) PH2 (torr) Photolysis Time(hrs.) [DBr] [D2] conv. [He] (RD] (~) 1 62 .0 39.9 b,."5 1. 554 15.4 0.57 2 45.7 161.0 4.o 0.284 14.l.l 0.54 3 56c 3 55.9 4.o 1.026 14.3 0.53 4 43. 5 151.6 10.2 0.287 14.1 1.04 5 47.1 194.7 5.0 0..241 23.0 0.61 6 50.5 71.6 4.1 0.705 13.7 0.56 Expt. 289 Figure D8. Results of variable conversion photolyses at 2537i, Set II. 2 90 c: 0 ~ (/) I- Cl) © > :.:: 0 u e ~ Q r<) L() 0 (!.3 ::!: 0 c 0 - > c 0 u 0~ C\l 0 LO ... C\J C\J 0 <j :r: :c 0 LO d rI If'>. v 291 intercept of 10.18 ~ 0.09 f or the DBr-He experiments. The results for the second series of DBr-H2 and DBr-He experiments are tabulated in Tables DXV and DVI respectively and plotted in Figure D8. Least squares analysis of all DBr-~ data gives a slope of 1.25 ::: 0.05 and an intercept of 2. 70 :!: 0.04. The slope and intercept from the data of experiments at 0.53% conversion are 1.27 ! 0.09 . and 2.70 ! 0.04 while those from the experiments at 1.02% conversion are 1.23 ! O.o4 and 2. 70 ! 0.03. Hence we are able to con- elude that the extent of conversion of DBr has no effect on the results for conversions less than 1%. Least squares analysis of the DBr-He eA'Jleriments gives a slope of 1.1 :!: 0.5 and an intercept of 13.4 : 0. 4. The descrepancies between data sets I and II can be most plausibly ex-plained by a change in the condition of the internal surfaces of the reaction vessel over the period of 3 months. An average of the two sets of data were used in the results given in Paper 1. 8. 0 Photolysis of DI at 2891A Photolyses at this wavelength were done using the Ha.novia 2500 watt mercury-xenon la.mp in conjunction with the Bausch and Lomb monochromator. The monochromator was set f or a l~ bandpass. The width at half height of the peak at 289lA was l:& as measured with the Jar..cell Ash monochromator. A 2 mm thick pyrex filter 0 (transmission 201'p at 289oj 1% at 2700A) was placed at the exit of the monochromator to cut out any short wavelength radiation. intensity of light exiting through the monochromator with the The 292 Table DXVII. 0 Results of DI-~ Photolyses at 2891A [DI) [DC?]_ (~] [RD] conv. (%) 2.0 0.752 3.76 0.51 30.2 2.0 1.035 4.32 0.52 .o 48.6 1.5 00966 4.22 o.46 4 50.6 32.0 2.0 1. 584- 5.35 0.50 5 64.o 37.9 2.0 l.689 5.57 0.51 6 46.2 156.3 2.0 0.295 2.90 0.51 7 28.9 101.5 2.1 0.284 . 3.00 0.53 Expt. PDI (torr) Photol,YSiS PH2 (torr) Time(hrs.) 1 27.8 37.0 2 31.2 3 ~~1 293 Table DXVIII. 0 Results of DI-He Photolyses a"c 289lA PDI PHe Photolysis [DI] [D?] (torr) (torr) Tirne (brs .) [Ee] [HD] conv. (%) 1 47.1 145.6 2.5 0.323 JA.o 0.56 2 41.0 123.6 2.5 0.332 15.0 0.56 3 52.6 4-4.7 3.0 1.176 J..6.1 0.62 4 34.6 46 .. 2 3.0 0.750 15.6 o.62 5 44.3 48.1 3.0 0.920 15-7 0.62 E..xpt. 294 Figure D9. Results of DI-H 2 and DI-He photolyses at 28912. 295 © C\I :c :c 0 0 0 LO 0 296 :filter wa s 2.8 x 1015 photons I sec. A 3-inch long, 2-inch diameter fused silica reaction vessel with optical quality quartz windows was used for the pbotolyses. Photolysis times were two hours which resulted in a conversion of 0.61%. The results for the DI-H and DI-He experiments a.re tabulated 2 in Tables DXVII and DXVIII respectively and plotted in Figure D9. Least squares analysis of the DI-~ photolysis data gives a slope of 1.87 :!: 0.03 and an intercept of 2.40 :!: 0.03. Least squares analysis of the DI-He :photolysis data gives a slope of 2.0 : and an intercept of 13.9 : 9. o.8 o.6. 0 Photolysis of DI at 3030A - Study of DI Conversion 0 Photolyses were performed at 3030A to determine the effect of extent DI conversion on the experiments. The Hanovia 2500 watt xenon-mercuxy lamp was used for :photolysis in conjunction 0 with the Bausch and Lomb monochromator set for a bandpass of 24A. The width of the peak at half-height as measured with the Jarrell Ash monochromator was 20.i. The intensity coming through the reaction vessel was approximately 6 x 101 5 photons/sec. Photoly- ses lasted 30 minutes, 1 hour and 2 hours resulting in conversions of 0.55%, 1.2'% and 2.1% respectively. Results of the DI-H experiments are tabulated in Table max 2 and plotted in Figure DlO. Least squares analysis of all data gives a slope of 1.44 ! O.ll and a.~ intercept of 3.06 :!: 0.10. For the o.55'fo conversion experiments the slope is 1.46 :!: 0.21 and the intercept is 3.00 ! 0.18, for the 1.::$ conversion runs 297 Table DXIX. 0 ResuJ..ts of DI-~ Photolyses at 3030A PDI (torr) PH2 Photolysis [DI] [Dz] (torr) T:ime(hrs) [~] (HD] conv. (%) l 39.9 40.8 2.0 0.976 4.23 2.1 2 36.4 113.8 2.0 0.320 3.33 2.1 3 32.3 19.4 2.0 1.074 4.71 2.1 4 32.0 29.8 2.0 1.074 4.71 2.1 5 29.9 51.8 2.0 0.576 4.. oo 2.1 6 36.8 26.9 1.0 i.368 4.95 1.2 7 38.4 76.•7 1.0 0.501 3.79 1.2 8 33.8 96.4 1.0 0.351 3.62 1.2 9 51.4 171.6 1.0 0.299 3.68 1.2 10 29.4 26.6 0.5 1.106 4.54 0.55 " 11 35.0 60.1 0.5 0.582 3.95 0.55 12 36.3 22.8 0.5 l.590 5.46 0.55 13 30.8 93.1 0.5 0.331 3.44 0.55 14 37.6 134.8 o.45 0.279 3.57 0.55 15 36.1 30.9 0.5 i.169 4.65 0.55 16 35.7 116.o 0.5 0.308 3.27 0.55 17 40.8 54.4 0.55 0.750 4.00 0.56 fu.-pt. 298 Table mac. 0 Results of DI-He Photolyses at 3030A [DI] [ D2] [He] [RD] conv. (%) 1. 5 0~304 8.95 1.7 25.7 1.5 1.342 9$74 1.7 38.0 43.4 1.5 0.875 9.94 1.7 37.6 128.3 1.5 0.293 9.81 1.7 PDI (torr) Fnotolysis PHe (torr) Time(brs) l 35. 0 115. 0 2 3~·.5 3 4 Expt. 299 Figure DlO. Results of DI-H 0 2 and DI-He photolyses at 3030A. 300 0 c c c (/) (/) (/) I(!) L- I... (j) Ci) > > c 0 0 > c: u (.) 0~ I.{) I.{) ~ 0~ 0 C\J 0 C\l 0 0 0 c 0 0 0 .. c\J c\J C\J :c :c :c :c © 0 0 <3 0 . l() 301 the slope is 1.29 ~ 0.23 and the intercept is 3.2 ! 0.1, and for the 2.1% conversion experiments the slope is 1.6 ! 0.1 and the intercept is 2.9: 0.2. These results show no trend with DI conversion and lead to the conclusion that the amount of DI decomposition is not important if' conversions are kept below zip. The results for the DI-He experiments are tabulated in Table DXX. The conversion was not varied in these experiments since even a. large error in the intercept would lead to a small error in the integral reaction yield in which we are interested. Least squares analysis of the + o.4. and an intercept of 9.3 - 10. data. gives a. slope of 0.42 :!: 0.55 0 Photolysis of DI-H2 and DI-He tl.i.xtures at 3261A EA.-periments at this wavelength were performed using the cadmium Phillips spectral lamp with a 5 mm Corning Ol6o glass filter to eliminate the short wavelength lines. A 16 cm long, 2.5 cm diameter pyrex reaction vessel with a 3.2 cm inside diameter teflon sleeve was used. The intensity of the lamp with the filter was approximately 5 x 1015 J;lhotons/sec. Phot.olyses lasted f'rom 7 to 22 hours resulting in conversions ranging from Results for the DI-H :photolyses are tabulated in Table DXXI 2 and plotted in Figure Dll. Least squares analysis of the data gives a slope of 1.5 :!: 0.3 and an intercept of 3.4 : 0.3. Results of t.b.e DI-He photolyses ere tabulated in Table DXXII and plotted in Figure Dll. Least squares analysis of this data gives a 302 0 (torr) 2 Photolyses at 3261A p.,., Photolysis [DI] n2 (torr ) Time(b.rs.) [II2] 1 28.1 32.5 9.0 0.863 l~.25 0.36 2 38.8 26.7 8.8 1.454 5.94 0.36 3 25.3 89.0 22.0 0.284 3.78 0.78 4 31.8 52.9 10.6 o.6o1 4.67 o.4o 5 27.9 26.0 14.. 5 1.073 4.73 0.32 6 25.2 24.5 8.o 1.029 4.95 0.27 7 22.8 51.0 13.5 o.447 4.29 o.49 Table XXI. Results of DI-H Ex:pt. PDI [D2] conv. [ ED] (°/o) 303 Table DXXII. 0 Results of DI-He Photolyses at 3261A Photolysis [DI ] (torr) PH 2 ( t01~.c) Time(hrs.) 1 29.6 109.1 2 25.4 3 Exp+. ,. conv • [Re] (D::;i] [RD] 7~9 0.272 5.10 0.27 22.6 9.0 1.122 5.80 0.38 38.2 24.3 7.1 i.572 6.15 0.23 4 30.3 45.7 6.9 0.663 6.oo 0.22 5 27.0 70.7 12.9 0.382 5.75 o.48 6 28.8 29.8 8.2 0.968 6.30 0.28 PDI (%) 7 .--~~~~~~v--~~~~~~.-~~~~~-.~~~ 6 ~ 0 t . G 0 ® . 0 0 [HD) 4t= ~ ©He I c,.i 0 I rn H2 I 3 2 0 -' 1.0 0.5 L 1.5 [DI] [G] Figure Dll. Results of DI-H 2 and DI-He photolyses at 3261X. -- *" 305 slope of 0.59! 0.31 and an intercept of 5.4 + 0.3. 11. Experiments to Determine the Fraction of Excited Iodine Atoms Produced in the Photolysis of DI. 11.l 0 DI Photolysis at 2138A. Several experiments were :per.formed at 213si to determine the rraction of i odine atoms produced in the excited 2p1; 2 state in the :photolysis of DL 'I'he analysis of this and the following experiments is found in Paper 3. The zinc P'.nillips spectral lamp 1<."'i th the cj.s-2-butene filter was used f or photolysis. The intensity of the lamp wi. th the filter was approximately 2 x 1015 photons/sec. The 3-inch long, 2-inch diameter fused silica reaction vessel was used. Photolysis times ranged from 10-15 minutes with conversions of 0.5%. The results of these e:i-..-periments are given in Table DXXIII and plotted in Figure Dl2. Least squares analysis of the DI-~ data gives a slope of l.35 ::!: 0.02 and an intercep~c o:f o.45 :!: 0.02. The intercept of the helium experiments is taken as 9.4: 0.5. 0 ll.2 DI Photolysis at 2400A The experiments at this wavelength were done using the General Electric BR6 lamp in conjunction with the Bausch and Lomb 0 monochromator with a bandpass set for 32A. The 3-inch long, 2-inch diameter fused silica reaction vessel was used. sity of the lamp was 3.7 x io14 :photons/sec. The inten- Photolyses lasted 306 Table DXXIII. &.--:pt. Gas 0 Results of DI experiments at 2138A PDI (torr) P:s:2 Photolysis [DI] (torr) Time(min.) [gas] IE.tl [ED] conv. (%) 1 112 41.4 135·9 10 0.304 o.847 0.76 2 H2 LrO. 7 40.1 15 i.·010 1.820 0.82 3 R 38.3 130.4 15 0.294 0.872 0.83 4 ~ 36.3 27.7 15 1.301 2.20 0.82 5 He 40.4 140.8 20 0.287 9.63 0.89 6 lie 34.7 26.6 15 1.304 10.47 0.81 2 --. 11 t 10 9 ------------- I I r---- - .o 0 . (D2J [F-1 DJ I 21- [J --------- I []----- O He o H2 00 0.5 1.0 1.5 [QJJ [G] Figure Dl2. Results _of DI-H 2 and DI -He photolyses at 21382 . 0l 0 -...] 308 0 Table DJOO::V. Results of DI Experiments at 2400A Expt. Gas PDI PH2 Photolysis [DI] (torr) (torr) Time(min.) [gas] [D2] [HD] conv. · (%) 1 E2 28.4 95.2 60 0.299 1. 68 1.03 2 H 2 35.6 32.6 30 i.092 2 . 98 0.51 3 R2 53.5 36.5 30 1.465 3.69 0.50 4 ~ 50.2 153-0 30 0.328 i.87 0.51 5 ~ 32.9 29.0 30 1.135 3.16 0.52 6 He 36.5 114.1 30 0.320 13.2 0.51 7 He 45.5 33.4 30 i.362 16.7 0.50 8 Be 37.2 43.4 30 0.858 14.8 0.51 16 14 [b2] 12·[HDJ 1' (,.! 0 c.o 4 ~fl !il~ ..... 3 ~ k:J ® He 2 ~ H2 'o 0.5 1.0 1.5 [D!] I [G] Figure Dl3 . Results of DI~H 2 and DI~He photolyses at 2400.2. 310 30 minutes with a conversion of o.&jo. The results of these experiments are tabulated in Table DXXIV a.'1d plotted in Figure Dl3. Least sq_uares analysis for the DI-H data gives a slope of 1.65 :!: 0.07 and an intercept of 1.25 2 -+ 0.07. Least squares analysis for the DI-He data gives a slope of 3.5 ! 0.2 and an intercept of 12.l ! 0.2. 0 11.3 DI Photolysis at 2805A The Eanovia 2500 watt xenon-mercury lamp in conjunction with 0 the Bausch and Lomb monochromator with a bandpass of 20A was used for photolysis at this wavelength. A 2 mm thick Corning 7910 glass filter was placed at the exit of the monochromator to · remove any shorter wavelength radiation. The 3-inch long, 2-inch diameter fused silica reaction vessel was used. The intensity exiting from the monochromator was 1.8 x 101 5 photons/sec. Photolyses lasted f"~om 15 to 45 minutes with conversions ranging f'rom 0.4 to o.%. Results of both the DI-H and DI-He experiments are tabulated 2 in Table DXXV and plotted in Figure Dl4. Linear least squares analysis of the DI-H2 data gives a slope of 2.0 :!: 0.4 and an intercept of 1.4 ! 0.4. The intercept of the DI-Re experiments was taken as 11.2 ! 0.5 on the basis of the three experiments which were done. 311 Table DX1.'V. Expt. Gas 0 Results of DI EA'Jleriments at 28o5A (torr) PH Photolysis 2 (torr) Time(min) PDI [DI] .EP_d [gas] [RD] conv. (%) 1 H2 23.2 77.9 15 0.298 1.79 0.56 2 ~ 45.6 37.4 15 1.221 4.oo 0.57 3 H2 30.0 29.3 15 1. 023 3.28 0.58 4 ~ 39.8 81.5 15 o.488 2.76 0.56 5 lie 33.2 137-2 15 0.319 11.25 <?·58 6 He 29.2 34.6 20 o.844 11.30 0.58 7 He 32.8 46.9 15 0.700 11.40 0.57 312 Figure Dl4. Results of DI- H and DI-He photolyses at 28052~ 2 313 © N 0 Cl :c :c - lO. 0 no. 0 """" i....; (' ! (\j -~ I "1i,_ I rt) :0 N)D., I ~ . r ~ 0 314 APPENDIX E ADDITIONAL EXPERIMENTAL RESULTS FOR H + CD4 l. Preliminary Experiments 0 Preliminary experiments were run at wavelengths of 2138A, 0 0 206lA and 2288A. The 1 1/2-inch diameter, 6-inch long f'used silica reaction vessel described in Paper 4 was used for all e).'})eriments. The experimental procedure was the same as that; described in Paper 4 and Appendix C. The first experiments were done with HBr/cD4 ratios ranging from 0.03 to 0.15 in accordance 'With the ratios used by Martin and Willard 1 and by Carter, Hamill and Williams 2 for the same system. 0 1.1 Preliminary experiments at 2138A T'ne photolyses at this wavelength were done using the zinc Phillips spectral lamp with the cis-2-butene filter. The photoly- ses lasted 3 hours resulting in approximately 1.5% conversion. The results of the first series of experiments performed at 0 2138A are shown in Table EI and in the lower curve of Figure El. They had a slope of 10.6: 6.o and an intercept of 17.4: o.6. About 2 months later, a second series of experiments was per:formed at this wavelength to check for internal consistency of the results. These were done under the same experimental conditions with the exception that the conversion was 0.5%. The results of these experiments a.re shmm in Table EII and the upper line in Figure El. They had a slope of 105 ~ 6 and an intercept of 315 Table El. 0 Results of RBr-CD4 Photolyses at 2138A With [HBr]/[CD4] Ratios from 0.03 to 0.1. Conversion 1.5% PRBr (torr ) PcD4 (torr) Photolysis [RBr] [H2] Time{hrs.) (CD~J [HD] 1 10.5~- 2 30~7 3o0 o.o456 23 .4 2 10.52 26L2 3.0 0.0403 22.0 3 11.71 l(f{.2 3.0 0.109 28.9 4 11.76 152.4 3.0 0.0771 26.0 5 11.37 333.6 3.0 0.0342 20.2 6 8.63 345.6 3.0 0.0250 19.0 7 9.80 123.9 3.0 0.0792 26.1 8 9.79 80.6 3.0 0.121 29.0 9 11.49 i50.7 3.0 0.0762 26.2 10 . 10.22 174.9 3.0 0.0585 23.2 11 10.11 100.l 3.0 0.101 29.1 Expt .. 316 4oir-~~~~~.--~~~~~..--~-r~~~-- J 361 321 H2 HD 28- 24 0.05 O.i 0 .15 HBr CDiV• . Figure El. Results of preliminary photolyses at 21382. 317 27 .2: o.8 . T'ne intercept was 40% higher than the intercept of' the first series of experiments. 'I'hese two series of experiments suggested a conversion effect in experiments with [EBr]/[CD4] ratios ranging f'rom 0.03 to 0.15 and motivated the conversion eA'"Periments described in Section 1.3. 0 1.2 Preliminary Experiments at 206lA 0 Preliminary experiments at 206lA were done using an iodine lamp powered by a microwave source. The intensity of' the lam:p was not constant for these experiments, varying by as much as a factor of 2 during a photolyses. as much as 15i scatter. 'I'he experimental results showed A plot of [H2 ] / [ED] versus [HBr] / [cD4] yielded an average intercept of 21 : 2. T'nis intercept is higher 0 than the intercept of the :first series of experiments run at 2138.A.. This behavior was not expected since the D + H and H + D systems 2 2 always showed a decrease in intercept with decreasing ·wavelength. This led us to perform further experiments to check the consistency of the method. 0 1.3 Preliminary experiments at 2288A A cadmium Phillips spectral lamp 'With the cis-2-butene filter described in Paper 4 and Appendix A was used for these experiments. 0 T'.ne two sets o'f experiments at 2138A indicated that a conversion effect might be causing the irreproducibilities observed in the early eA'"Periments. Hence a set of experiments was per- formed at 2288A in which the [HBr] /[cn 4 ] ratio and the intensity 318 Table E2. Results of I:IBr-CD1~ P'.aotolyses at 2138~ with [HBr]/[CD4] Ratios From 0.03 to 0.15 . Expt. p Conversion 0.5°/o Pbotolysis f. IIBr ) ( I:I ] __2._ (torr) ·cD4 ( tor.c ) Ti me(b:rs. ) ( CD~J [ ED] 1 10.71 160.2 1 0.0669 34..2 2 l0.91 272.1 l o.o401 31.5 3 12.87 228.9 1 0.0563 32.8 4 10.80 103.9 1 0 .. 0969 36.3 5 11.11 323.9 l 0.0291 29.6 PHBr 319 were kept constant and the time (and hence the conversion) varied. 'l'his wavelength was chosen for these experiments because of the shorter photolysis times required. The results of the above experiments is given in Table EIII and in Figure E2. There is a considerable 'variation of [H2]/[HD] with time indicating a conversion effect at this [BBr]/[cD ] ratio. 4 These data are further analyzed in Paper 4.. Also two sets of experiments with :phot.olysis times of 10 minutes and 5 minutes respectively were performed with [IIBr] /[CD~_] ratios vru.7ing from 0.03 to 0.12. 'Tue results of these experiments a.re given in Table EIV and are plotted in Figure E3. For the experiments with 10 minute photolysis times the slope was + + 67 .2 - 2.9 and the intercept was 31.9 - 0.2. For the eXJ>eriments with 5 minutes :photolysis time the slope was 67.8 ! 2.2 and the intercept was 34.5 :!: 0.3. Photolysis e:i..-periments of Compton and M"artin3 on the HBrC4D10 system indicated. that a conversion effect observed at ratios were greater than 0.3. .Hence we did two series of experi- ments at [HBr]/(CD4] ratios ranging from 0.3 to 1.2 with conversions of o.45% and o.gfo to see if Compton and Martin's observa- · tions -w-rere true :f.'or our system. 'l,,.ae results o"f these experiments are tabulated in Table EV and plotted in Figure E4. For the experiments at o.45% conversion, least squares analysis of the photolysis data gh-es a slope of 49.1 ::!: 1.8 and an in·eercep·c of 37.7 ::!: 0.9. For the experiments at O.gfo conversion the least 320 sq_uares slope and intercept were 49.3::: 1.2 and 37 .1 :!: 0.8 respectively. a Least sg_uares analysis o-r the combined data gives slope of 48.7 :!: 0.9 and an intercept of 37.8 :!: 0.5. Hence the slopes and intercepts of two series of experiments done at two different conversions agree within experimental error and indicate that no conversion effect is present at [HBr]/[CD4] ratios ranging :t'".rom O. 3 to 1. 2. The results in Table EIII where [HBr]/[CD4] equals 0.77 and the time is varied extrapolate to zero time to give an [~]/[HD] ratio of ~-lo5• The least squares f i t of the e:iqleriments with [IIBr]/ [CD4] ranging from 0.3 to lo2 gives [H2]/[ED] eg_ual to 41.4 a•c [EBr] / [ cD4] eg_ual to 0.()(75. ment. Renee the two are in good agree- Also the intercepts in Figure E3 extrapolate to zero conver- sion to give a zero conversion intercept of 37.5 which is in experimental agreement 'With the 37.8 above. Hence, the above eA-peri ments lead to the conclusion that the extent of RBr conversion is unimportant if [RBr]/[CD4] ratios are greater than 0.2. 321 Table EIII. 0 Results of Variable Conversion Experiments at 2288A With [BBr]/[cD4] Ratios Approximately Constant PHBr (torr) Photolysis [liB:r] [II ] _a_ (torr) Time(min.) (CD1] [ED] conv. (%) l 10.29 131.5 10 0.0783 38.9 1.23 2 33.8 ~-26.5 10 0.0792 38.6 1.24 3 10.48 139·3 15 0.0751 37.6 1.77 4 10.37 137·7 30 O.<J(52 35.6 3.34 5 io.57 145.4 30 0.0727 35.4 3.35 6 9.70 126.3 5 0.0768 39.8 0.62 7 l0.36 136.6 5 0.0758 39.7 0.65 8 10.05 131.3 20 0.0765 37.2 2.28 9 10.40 138.8 25 0.0~(69 36.1 2.81 Exp'ci. PCDl.~ ' I 40·- r---1 r---J ' 0 -rC\11 '---' ::i:: ~ c,J [\.) 1\:1 35 ·~ . 30 J. 5 10 15 20 25 30 35 Time (mi n) Figure E2. Results of photolyses at 2 2 882 wi t h variable photolysis times. 323 Table E4. 0 Results of Variable Conversion EA-periments at 2288A With [IIBr]/[cD4] Ratios From 0.03 to 0.12 Expt. ~ PRBr (torr) Pcnu. (torr) Photolysis [B.Er] Time(min.) [CD4] l 10.ll 81.9 10 0.1236 40.3 2 10.51 i13.3 10 0.0928 38.0 3 10.l.}6 14b,.6 10 0.0723 37.0 4 10.12 185.3 10 0.0546 35.4 5 10 .. 00 307.1 10 0.0326 34.2 6 10 .. 13 350.4 5 0.0289 36.6 7 10.10 307.8 5 0.0328 36.6 8 10.16 134.9 5 0.0753 39.5 9 10.13 13L8 5 0.0769 39.9 [ED] 32 4 40 o t == 5 min. en t == iOman. HBr co~ ....... Figure E3. Results of preliminary experiments at 22882. 325 Table EV. 0 Results of Variable Conversion Ex'periments at 2288A With [EBr]/[cD4] Ratios From 0.25 to l.O ~ (BD] conv. (%) 0.385 55.5 1.21 10 0.534 63.9 1.20 35.9 5 0.788 7602 0.61 28.7 209.5 5 0.262 50.6 0.62 5 26.5 63.5 5 o.417 57.5 0.61 6 61.2 58.2 10 i.052 89.4 1.21 7 43.8 56.3 10 O.'"n8 7l~.5 1.20 8 46.6 69.8 5 o.668 71.7 0.62 9 ~~3.1 87.1 5 o.495 61.5 0.61 10 37.8 150.9 10 0.251 49.8 1.22 ll 36.5 142.0 5 0.257 51.1 0.61 .· [EBr] (torr) Photolysis Time(min.) 27.8 72.2 10 2 24.4 45. 6 3 28.3 4 &.'J)t. PHBr PCD4 (torr) 1 [ CDL~] 326 ra 5 minutes o IOminutes 40 Figure E4. Results of HBr -CD 4 photolyses at 22882. 327 0 2. Photolysis at 2537A A General Electric germicidal lamp was used in conjunction with a 2 mm thick Corning 7910 glass filter for photolyses at this wavelength. One side of the reaction vessel was irradiated. instead of the window as in other experiments. To verify tila,(; this geometry gave consistant results, a. photolysis was done with the Hanovia. SC 2537 low pressure mercury lamp where only the window of the reaction vessel was irradiated. At an [RBr]/[cD4] ratio of 0.388, the [H2] / [BD] ratio ·was 87 .5 with the Hanovia lamp while at an [RBr] / [CDi.) ratio of 0.378, the [H2 ] / [RD] ratio was 86.9 ·with the ge:t."!nicidal lampQ ei~.cor This is within experimental and shows "'Ghat the geometry or the :photolysis system is unimportant. Photolyses in all experiments lasted 20 mi."lutes. T'ne conversion vras measured in only the first experiment of each series at a given wavelength by' adding a knovr.a amount of He to the reaction vessel after the :photolysis, measuring [IID] /[He] on the mass spectrometer and then obtaining the conversion from the formula: r (1 + lfilll _g_c_~2l)/ EJ3:ri c = I~.l (He] [Re] The measured conversion in the first experiment vras l.Cf/o. The results of these experiments are listed. in Table EIV and a plot of [H2 ] / [RD] versus [B'.Br] /[ CD4] is shovm in Figure E5. Least squares analysis of the data gives a slope of 63.8 ~ 1.1 and an intercept of 61.8 :!: o. 7. 328 0 Table EVI. Results of Experiments at 2537A - Conversion l.CJI, Expt. [HBr] [CD4] ru (torr) c~oorr) Photolysis Tiwe(min.) l 49.2 129.9 20 0.378 86.9 2 53.7 78.0 20 o.688 io6.o :;; •") 36.3 166.2 23 0.218 74.6 4 61.i•• ::>-. 64.6 20 0.995 124.8 5 49.8 70.2 20 0.710 108.o 6 51.8 102.1 20 0 .. 507 94.6 7 50.4 173·3 20 0.291 79.8 8 41.0 42 .. 0 22 0.978 123.5 PBBr PCD4 [ED] 329 1"'"'0 1..:> 120[ 110 H2 100 -HD I I f3 90 0 80 60 50L-~~~~~~~L-~~~~~~--L----' 0 0.5 1.0 HBr CD4 Figure E5. Results of HBr-CDA photolyses at 25372. " 330 3. 0 Photolyses at 2138A Experiments at this wavelength were peri'ormed using the zinc Phillips spectral la.mp with the cis-2-butene filter described in Appendix A. P'notolyses lasted 1 1/2 hours which resulted in an HBr conversion for the first ex})eriment performed of o.&;o. The results of these experiments a.re given in Table EVII and a plot of [H ]/ [HD] versus [HBr]/[CD ] is shown in Figure E6. 4 2 L.east squares analysis of the data gives a slope of 50.5 :!: 1.1 and an intercept of 30.3 ! o.8. 0 4. Photolyses at 2061A Experiments at this wavelength were carried out using an iodine lamp powered by a. micro-wave source. Since a large amount of heat was generated by the lamp, a cooling coil was wrapped around the reaction vessel t o keep it at room temperature. The remainder of the experimental procedure was as described previously. Photolyses lasted. 30 minutes for all ex:periments. The measured conversion for the first experiment -was o.5f;fo. The results of these experiments a.re given in Table .EVIII and a plot of [E:2]/[1ID] versus [RBr] / [cD ] is shown in Figure E7. 4 Least squares analysis of the data gives a slope of' 53.0::; o.6 and an intercept of 27 .8 :: o.l.~a 331 Table EVII. Expt. 0 Results of Experiments at 2138A - Conversion o.f:fP PHBr (torr) PCDL· P'notolysi s [HB:r] (tor;) Time(hrs.) [ CDi.iJ [H2] [HD] 1 49.8 67)t- L5 o.74o 68.5 2 66.1 55.7 L5 l.188 89.5 3 47.6 151.6 1.5 0.314 46.5 4 48.o 92.1 1.5 0.521 55.5 5 38.2 155.2 1.5 0.246 42.2 0 / 66.2 69.8 1.5 0.948 79.5 . 7 52.2 103.6 1.5 0.503 56.5 8 68.o 7(.2 1..5 0.881 74.o 332 90 80 70 I-'j2 HD 60- I i>:;Qi- :J / (J 30 Figure E6 • . Results of HBr -CD 4 experiments at 2138~. 333 . Table EVIII. 0 Results of Experiments at 206JA - Conversion 0.5&/o ~ Photolysis Time(min.) [1IBr] (torr) PCDt~ (torr) [CD4] [ED] 1 40o0 86.4 30 0.1:-03 52.7 2 49.6 135·7 30 0.356 46. 5 3 52~4 55. 3 30 0.947 78.5 4 4~.• 2 71 .. 3 30 0.620 60.3 5 47.5 160.8 30 0.295 43.1 6 40.0 63.9 30 0.627 60.9 7 49.9 60.0 30 0.832 71.5 8 37.5 105.8 30 0.355 47.4 9 49.5 54.5 . 30 0.909 76.0 Ex:pte PHBr 334 90 80- 70 60 1.0 0.5 HB L1" CD..et•. Figure E7. Results of HBr-CD 0 4 experiments at 2061A. 335 5. 0 Photolyses at 1849A The photolyses at this wavelength were done with the Ha.novia SC 2537 lamp with the 60co gamma-irradiated. filter. This lamp was powered by the microwave source as described in Appendix A to give greater intensities. A cooling coil was wrapped around the cell to keep it at room temperature. T'.o.e remainder of the procedure was as described previously. Photolyses lasted 30 min- utes for each experiment. The measured. HBr conversion for the The results of these experiments are given in Table EIX and a plot of [H ]/[ED] versus [HBr] / [ CD4] is shown in Figure ES. 2 Least squares analysis of the data gives a slope of 56.5 :!: 1.5 and an intercept of 24.6 :!: 1.1. REFERENCES 1. R. M. Martin and J. E. Willard, J. Chem. Phys., 4 0, 3007 (1964). 2. R. J. Carter, W. H. Hamill and R. R. Williams 9 Jr., J. Am. Chem. Soc.~ z.z, 6457 (1955). 336 0 Table EIX. Results of Experiments at 1849A - Conva~sion - Oo6f::f/p E."\."']?t .. "'P p (torr) 1 Photolysis ( B::ar] (tori) Time (min. ) [CD~J [!2_] [ BD] 4o.o 65.6 30 0.610 5~r 2 42.0 112.6 30 0.376 46.o 3 54.o 56.7 30 0.953 79.2 4 53.6 95.2 30 0.563 55.9 5 34.6 127.1 30 0.272 40.6 6 39.5 ~-8.1 30 0.821 69.1 7 65.9 5~-.8 20 1.202 93.5 8 43.5 102.0 20 o.450 51.4 - Jffir CDti. .7 337 90 80 60 ' 50 40 3020.___________________________________..___________ 0 1.0 0.5 HBr . CD.o.. Figure ES. Results of HBr-CD 0 4 photo l ys.e s at l849A. 338 APPEJ\l])IX F CALCULA.TION OF ROTATIONAL .AlW TRANSLATIONAL ENERGY SPREADS IN DBr PJ\iD DI 1. Rotational Energy Spread The relative rotational populations for DBr and DI at 298°K are listed in Tab+e Fl and plotted as a f'unction of J(J+l) in figures Fl and F2. The average rotational energy of DBr is 0.025 These energies correspond to eV while for DI it is 0 .020 eV. average values of J(J+l) of 23.8 and 48.8 respectively. As a measu:re of the energy spread we use an interval, symmetric about the average J(J+l), which contains approximately 70% of the molecules. T'nis was done by a method of trial and err or . Table FII shows the fraction of the total population present in various J(J+l) intervals for DBr. For DBr the chosen interval contains J(.J+ 1) values from 0 to 47 which corres:pOnds to an energy spread of 0.025 eV on either side of the average and includes 71% of the molecules. For DI the chosen interval includes J(J+l) values from 7 to 90 which corresponds to an energy spread of 0.018 eV on either side of the average and includes 73% of the molecules. 2. Translational Energy Spread The translational energies of DBr and DI follow a Boltz- mann distribution f'u.nction of the form: 339 Q 3/ g(E£x ) a.EDx = 47i ~) (_g-) lab 2 lab 2-nKT 1/2 ( lab) l/2 ~x lab exp(-E/kT) dEDx ;'1DX lab 1/2 1 ab lab A plot of EDx exp(-EDx /1.."T) as a function of Enx /irr is shown in figure F3. Table FIII shows the approximate percentage of DX molecules contained in each energy interval. Again, an interval is selected which is synm1etric about the average energy of 3/2 kT (1. 5 in figure F3) and contains 7afo of the molecules. lab The chosen interval was for values of ~X /'Kr from o.4 to 2.6 which contains 71% of the population. 'I'his interval corresponds to a translational energy spread in DX of 0.57 eV. 340 Table FI. Relative Rotational Populations for DBr and DI DBr J J(J+l) NJ/N x 102 DI NJ/N x 102 0 0 4.oo 1.60 1 2 11.09 4.64 2 6 25.69 7.25 3 12 17.23 9.22 ~~ 20 16.02 10.40 5 30 13.12 10.87 0 42 9.47 10.61 7 56 6.18 9.79 8 72 3.67 8.59 9 90 1.98 7.08 10 110 0.98 5.76 11 132 o.43 4.45 12 166 0.11 3.31 13 182 0.07 2.35 14 210 1.62 15 240 1.09 16 272 0.69 ,.. 341 Table FIL Fraction of Population in Various Rotational Energy Intervals in DBr J(J+l) Interval 0 to Fraction (in percent) 5 5 to 10 10 to 15 10.23 15 to 20 9.94 20 to 23 5.63 23 to 25 3.56 25 to 30 8.30 30 to 40 13.82 40 to 50 10.07 50 to 70 13.18 70 to 90 6.70 90 to 110 3.1.1 110 to 130 1.43 342 Table FIII. Fraction of Population in Various ~~anslational Energy Intervals E/0.026 Fraction (in ;percent) o.o - 0.2 4.27 0.2 - O.l+ 9.25 o. 4 - o.6 9.82 o.6 - o.8 9.52 o.8 - i.o 8.90 1.0 - 1.4 15.35 1.4 - 1. 5 o.46 1.5 - 2.0 16.39 2.0 - 3.0 15.30 3.0 - ~~.o 6.76 4.o - 5.0 2.49 5.0 - 6.o 1.42 20r -.- r 15 C\.J 0 10 (,.J ~ C..l x z ......... z-:> 5 (J(J-.'= I))= 2 2.8 O' 0 I 20 _ __,_______ - I I 40 60 80 100 120 J(J+ I) Figure Fl. Population of rotational ene rgy levels of DBr at room temperature. 140 -------·- .---· ---·~--- . -"~·-~,.,_.-~-------·~ (\J 0 x z ...... ~ z (,.! >!::> ~ orr ,... (J{J+ I)) =48.8 00 50 100 150 J(J+ I) Figure F2. Population of rotational energy lev els of DI at ro om temperature. 200 8r-- .__,_- · --~ -1--"· 6 I~ ' ..0 0 ~ wI (i) (.\j -- ....... 4 II I ~ ..Q 0 lr.J ..._, 2"'" 00 I 1.0 I I "' Jl~~~~~__JI----~~~-=' 2.0 3.0 4 .0 Ela bI kT Figure F3. Boltzmann distributio n of tra ns lational energies at 300°K. (,1 "" (.!1