ABSTRACT CARBON-13 KINETIC ISOTOPE EFFECT IN THE THERMAL ISOMERIZATION OF METHYL ISOCYANIDE by John Frederick Wettaw The carbon-13 kinetic isotope effect in the thermal unimolecular isomerization of methyl isocyanide to aceto- nitrile was investigated from 1 atmOSphenato 1 centimeter pressure at 243.4, 226.0, and 213°C. Methyl isocyanide was prepared from silver cyanide and methyl iodides. Purified methyl isocyanide (labeled with natural abundance 13C in both carbon prositions) was isomer- ized and the remaining unreacted methyl isocyanide separated by gas chromatography from the product acetonitrile. The fraction of reaction was determined from the ratio of the areas on the chromatogram, and the separated products were trapped and retained for analysis. The products were oxidized over copper oxide at 600°C and the carbon dioxide separated from the water and nitro- gen products and purified by vacuum sublimation. The 13C02/12C02 molar ratio R was determined on the carbon- ‘ dioxide derived from oxidation of methyl isocyanide (RNC) and acetonitrile (RC§)obtained at fraction f of reaction. and f define a C-13 kinetic The three data R R NC' CN' isotope effect I = k/k', which is an average of the iso- tope effects r1 = k/k1 arising from labeling in the methyl carbon position and r2 = k/kz arising from label- ing at the isonitrile carbon. John Frederick Wettaw At high pressures the average isotope effect r is given by r00 = 0.998 exp(20 i 5/RT) . At lower pressures, the effect declines as expected for a unimolecular reactions, the values at 1 atmOSphere and at 1 centimeter being 1.0185 and 1.0115, respectively, at 226°C. An expression relating the observed average isotope effect r to the isotope effects r1 and r2 was de- rived, and used to compare the experimental results with theoretical values of r1 and r2 derived from the RRKM theorylofunimolecular reactions for various models of the activated complex. Good agreement between theory and ex- periment was obtained for a complex model in which one of the degenerate CNC linear bending vibrational modes of methyl isocyanide becomes the reaction coordinate leading to a ring structure as proposed by Rabinovitch and co- workers. The calculated results are quite sensitive to the vibrational frequency pattern of the complex, and it has been possible to define the complex frequencies within rather narrow limits from an examination of all of the ex- perimental results on methyl isocyanide. The carbon-13 iso- tOpe effect suggests that the major changes in frequency pattern in going from the molecule to the complex involves lowering the C-N and NEC stretching frequencies, in agree- ment with the results of Rabinovitch, §£_§l, on the fall-off John Frederick Wettaw of the rate constant for isomerization and the deuterium isotope effects. The results indicate substantially larger carbon-13 isotOpe effect associated with labeling at iso- nitrile position than with that arising from labeling at the methyl carbon. CARBON-13 KINETIC ISOTOPE EFFECT IN THE THERMAL ISOMERIZATION OF METHYL ISOCYANIDE BY John Frederick Wettaw A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1967 QHSWaQ '3 o- a 3w" t; 3’3. To My Parents ACKNOWLEDGMENTS The author wishes to extend his sincere appreciation to Dr. L. B. Sims for his inSpiration and guidance during the course of this investigation. Appreciation is extended to Dr. P. E. Yankwich of the University of Illinois who made available the Isotope- Ratio Mass Spectrometer. In addition thanks is extended to Mr. Thomas Huang of the University of Illinois for his assistance in helping the author with the operation of the Isotope—Ratio Mass Spectometer. The author wishes to acknowledge two fellow students Mr. Hans P. E. Sachse and Mr. Richard C. Benson who contri- buted both knowledge and personality during this investiga- tion. iii TABLE OF CONTENTS CHAPTER I INTRODUCTION . . . . . . . . . . . . . . II HISTORICAL . . . . . . . . . . . . . . . . . III EXPERIMENTAL . . . . . . . . . . . . . . . A. Materials . . . . . . . . . . . . . . . B. Apparatus . . . . . . . . . C. Procedure . . . . . . . . . . . . . . IV RESULTS . . . . . . . . . . . . . . . . . . A. Kinetics . . . . . . . . . . . . . . . . B. -Kinetic ISotOpe Effects . . . . . . . . V DISCUSSION . . . . . . . . . . . . . . . . A. Relation of the Average Isotope Effect to Labeling at the Methyl and Isonitrile Position . . . . . . . . . . . . . . B. Calculation of the Carbon-13 Isotope Effect using the RRKM Theory . . . . . C. Comparison of Experiment and RRKM Theory BIBLIOGRAPHY . . . . . . . . . . . . . . . . APPENDIX . . . . . . . . . . . . . . . . . iv Page 23 23 25 42 50 50 51 64 64 73 86 103 106 LIST OF TABLES Summary of kinetic data . . . . . . . . . . Summary of isotOpe effect data . . . . . Potential constants for methyl isocyanide . Observed and calculated frequencies and principal moments of inertia of isotopic methyl isocyanide molecules . . . . . Construction of the complex models . . . . . Frequencies and moments of inertia of isotopic molecules and complexes of methyl isocyanide Input data for calculation of RRKM rate data Comparison of limiting high pressure rate constant . . . . . . . . . . . . . . Calculated values of r1, IQ, and average r at 226.0°C . . . . . . . . . . . . . . . . Page 52 61 76 78 88 91 96 101 Figure 10 11 LIST OF FIGURES Schematic of Furnace Assembly . . . . Schematic of Furnace Inlet System . . . . . Schematic for the Gas Chromatographic Analysis and Collection SyStem. Schematic of the Gas Chromatographic Detector BlOck . . . . . . . . . . . Schematic of Bridge Circuit for Gas Chromatograph . . . . . . . . . . . . Schematic of Gas Analysis and Handling System . . . . . . . . . . . . . . . . . Experimental Rate Constants versus Pressure at 243.40c, 226.0°C, 213.00c . . . . . Experimental Rate Constants versus Pressure ,at 243,40c, 226.0°C . . . . . . . . . . . Relative Error in the Approximate IsotOpe Ratio Calculation versus Fraction of Reaction . . . . . . . . . . . . . . . . . Comparison of EXperimental Rate Constant with RRKM Calculation . . . . . . . . . . . Comparison of Experimental Isotope Effect with 8/30 and 10/40 Model RRKM Calculations Page 27 32 35 38 41 44 54 63 69 93 98 I. INTRODUCTION A gas—phase reaction is described as a unimolecular kinetic process if the formally—defined first-order rate constant exhibits certain characteristics: at high pres- sures, the rate constant appnnmmes a limiting constant value; as the reactant pressure decreased, the rate constant begins to decline or "fall-off" from the limiting value; and at sufficiently low pressures, the rate constant be- comes proportional to reactant concentration, so that the kinetics may be described by a second-order rate law. Early experiments on unimolecular reactions were limited to the high pressure first—order region. The first-order rate constants were strongly dependent on the temperature, suggesting that the molecule must contain a certain mini- mum energy approximately equal to the observed activation energy for reaction. The existence of first-order kinetics, however, seems inconsistent with a collisional activation process, since collisional activation is a second—order process. Perrin1 suggested that dissociation followed ab- sorption of radiation whose frequency was proportional to the activation energy per molecule. The radiation theory was shown to be inconsistent with other aspects of these reactions and was replaced by the‘Lindemann2 hypothesis that collisional activation could lead to an observed first-order rate law at high pressures, if the mean lifetime of a high 1 2 energy (active) molecule were long compared to the time be- tween collisions. Under these conditions, an effective steady concentration of active molecules would be maintained by collisional activation--deactivation processes, the actual concentration of active molecules (to which the rate is directly proportional) being limited by the concentration of reactant molecules. At sufficiently low pressures, the time between collisions would necessarily be long relative to the lifetime of an active molecule, so that every active molecule would react. The rate in this case would be limited by the collisional activation reaction, a second-order process. The quantitative explanation of the decline of the first-order rate constant with decreasing pressure requires an extension of the Lindemann hypothesis. The pressure range of the fall-off will depend on the relative magnitudes of the rate of collisional deactivation and spontaneous de- composition of active molecules. All of the theories of uni- molecular reactions have incorporated the strong collision assumption3 of deactivation at every collision, and the rate of collisional deactivation is equated to the kinetic theory collision frequency. The rate of spontaneous decomposition, however, depends on the molecular model for the active mole- cule and on the criterion for reaction, which are treated dif- ferently in the various theories of unimolecular reactions. Classical theories of unimolecular reactions have been 3 developed principally by Hinshelwood‘, Rice and Rampsberger5, Kassela, (referred to collectively as the RRK theory) and more recently by Slater. Quantum theories have been developed by Kassela, Slater 1, and by Marcus and Rice":8 (referred to as the RRKM theory). I The development of these theories requires certain basic assumptions that should be tested in accordance with available experimental information. Because of the numerous technical difficulties encountered in the observation of gaseous unimolecular reactions, reliable experimental data have been lacking until fairly recently. A number of gase- ous reactions which once were believed to be unimolecular have now been shown to have complex mechanisms. The mechan— isms of certain complex reactions, such as the decomposition of N205,'9.1° may include a unimolecular elementary step whose rate can be determined under special conditions. De- spite the uncertainty as to the proper characterization of many reactions, there are a number of reactions which have been studied in sufficient detail to determine unambiguously that the reaction occurs as a unimolecular process. In addition to the decomposition of N205, the best-documented.11 examples of gas-phase unimolecular reactions include the structural isomerization of cyclopropane,12I13 cyclobutane,14 and many other substituted cyclopropanes and cyclobutanes, and more recently the isomerization of methyl isocyanide.15.16 Kinetic isotope effects have recently been used ex- tensively to study details of the mechanisms of unimolecular 5 comparison of theory with experiment are simple and more meaningful. Useful information concerning the validity of the strong collision assumption, relative collisional ef- ficiences for energy exchange, and other assumptions of the theories may be obtained from such comparisons if the reac- tion mechanism is sufficiently well-characterized. The detailed fall—off behavior15 of the rate constant, and the deuterium isotope effect 16 in the isomerization of methyl isocyanide have been investigated by Schneider and Rabinovitch. Good agreement of the RRKM calculated results with experiment have been obtained21 for a complex model in which one of the degenerate CNC bending modes becomes the reaction coordinate. The C-N and NEC molecule frequencies were lowered in the complex to improve agreement with ex- periment, and other molecule frequencies were assumed un- changed in the complexes. However, the calculated fall-off behavior and the deuterium isotope effect are not very sensitive to the details of the complex vibrational frequency pattern, especially since the deuterium isotope effect is a secondary isotope effect in this reaction. More direct and detailed information on the vibrational frequency pat- tern of the complex might be obtainable from the carbon-13 isotope effect. At least the carbon—13 isotope effect would be excellent confirmatory evidence for the suggested detailed mechanism. II. HISTORICAL A. THEORIES OF UNIMOLECULAR REACTIONS 1. Generalized Formulation of the Apparent First- Order Rate Constant The development of the theory of reaction rates has its beginning in the proposal by Arrhenius22 that the very strong temperature dependence of the rate constant for the inver- sion of sucrose was given by the equation: k = A exp(—Ea/RT) (1) where the constants A and Ea are the pre-exponential factor and the experimental acthntion energy, respectively. This temperature dependence was interpreted to mean that molecules can react only from certain special states charac- terized by high energy. Molecules in these special states lying above a minimum citical energy EC necessary for re— action are termed "active”. The temperature dependence of most rate constants is given adequately by an Arrhenius ex- pression. Let i = 1,2,3, ----- be an enumeration of these states. These states may be continuous or, quantized and may be specified by one or more parameters but a different notation for classical and quantum models is not necessary to the present development. If a fraction fi of molecules are in state i, from which the probability of reaction is ci per unit time,the observed first-order rate constant is 6 k = E Cifi (2) where the summation is over all states i of the active molecules. The distribution function fi may differ markedly depending upon the method of excitation used. Experimental techniques other than collisional activation or "thermal" methods include chemical activation, photosensitization and electron impact. The specific decomposition rate of active molecules ci depends only upon the properties of the ac- tive molecules once formed. 2. Distribution Function for Active Molecules in a Thermal System. The Lindemann Mechanism. The Lindemann hypothesis 2 Y of a time lag between the collision-energization and the dissociation of active mole- cules is represented for a thermal reaction k A Products v by the following collision mechanism23 a. A+M 1 >A§+M * bi Ai+M 2A +M (3) C. * J. A. > Products where A represents the reacting species, M, being any * species with which A can collide and exchange energy, Ai a molecule of Species A which has been activated to level 8 i, ai, bi' ci the rate constants for collisional activa— tion, collisional deactivation, and spontaneous decomposi- tion of the active molecule in level i, respectively, and k is the observed overall rate constant. At high pressures, the molecular distribution among the allowed energy levels will be essentially the statistical equilibrium distribution of a non-reacting gas. At lower pressures, the concentration of active molecules will be reduced by reaction and the fraction of molecules in any level i can be found by application of the steady-state approximation to the concentration of the species AE: - g; a o = ai(A)(M) — bi(A:)(M) — ciA: which leads to * a.(A)(M) (Ai) = c: + b;(M) The fraction of molecules in state i is therefore W : (ai/bi) bi(M) (5) bi(M) + ci * _i i A. H where ai/bi is the equilibrium fraction, Fi’ of active molecules A: in a non—reacting gas. Invoking the strong collision assumption 1 , that collisional deactivation efficiency is unity for all levels i, leads to the expression bi(M) = ZP = w (6) where w is the kinetic theory collision frequency at 9 pressure P, 2 being the collision probability per unit time per unit pressure. The observed overall rate constant k thus may be expressed in the following form k =ZZ—i—‘i <7> The fraction of active molecules A: in a non-reacting gas, Fi’ can be calculated from the Boltzman equation24 and the molecular model The rate constant for spontaneous decomposition of A1, Ci’ likewise depends on the molecular model and, in addition, on the assumed criterion for reac- tion, both of which are treated differently in the various theories of unimolecular reactions. 3. Early Classical Theories Lindemann's hypothesis was first developed mathematically by Hinshelwood in 1926.4 The theory is based on the as— sumption that the rate constant for spontaneous decomposi- tion is independent of the amount of energy in excess of the critical minimum; i323, c1 = c for all i, where c is an average specific decomposition rate. Comparison of the Hinshelwood theory with experimental data results in very poor agreement. Clearly the assumption that active molecules have the same rate constant for spon— taneous decomposition from all levels i is an over-simpli- fication. A more reasonable assumption, that the lifetime 10 of an active molecule is a function of the energy in excess of the critical minimum, has been incorporated into more recent theories of unimolecular reactions, both classical and quantum mechanical. The classical theories of Kassel6 and of Rice and Rampsberger 5 are essentially identical, in that the model of the reactant molecule is that of a set of lightly coupled classical harmonic oscillators. The molecule reacts when- ever the requisite amount of energy , Ei' greater than Ec' accumulates in an critical oscillator. The rate constant for spontaneous decomposition is as— sumed from statistical arguments to be of the form c. = 0 for E. :_E where A is identified with the high pressure pre-exponen- tial Arrhenius factors and s is the number of effective oscillators (those which contribute their vibrational energy to the observed activation energy) of the molecule. The value of s is chosen to give the best agreement between calculated and experimental decline of the fall-off of the rate constant with pressure. The basic assumption of clas- sical harmonic oscillators for representation of molecular vibrations and the fact that s has the status of an ad- justable curve-fitting parameter, which must be allowed to assume physically unreasonable non-integral values in order 11 to obtain agreement between theory and experiment, are the most serious short comings of the theory. In addition the oscillators are not clearly defined. 4. The Slater Theory Classical Slater 25 takes as the model for the reacting mole- cule, a vibrating system of n non-interacting classical oscillators at all energies. The oscillators change energy content only during a collision with other molecules. The oscillators are identified in Slater theory with the clas- sical normal mode oscillators of vibration theory. The internal displacement coordinates qi, of the molecule are then linear combinations of the normal displacement coordin- ates Qj' Reaction is assumed to occur when a "critical" internal distance (coordinate) attains a critical exten— sion in the direction necessary for reaction. This will occur whenever the normal modes of vibration come suffici- ently into phase. The rate constant for spontaneous decomposition then E-EC C.“ T" where E is total vibrational energy, distributed in all has the form: 1/2n possible ways among the various oscillators; n, the number of non-degenerate frequencies, determined by the symmetry properties of the molecule; and v, a weighted average of the n vibrational frequencies. 12 While the Slater theory is more appealing because there are no parameters which are not determined by properties of the reacting active molecule, comparisons with experiment indicate gross errors, particularly with regard to the as- sumption of uncoupled oscillators, which precludes intra- molecular energy transfer between collisions?5'27:33:29 5. The Quantum Statistical Theory of Unimolecular Reactions (RRKM Theory) The quantum versions of the theories of Kassel and Slater both assume an unrealistic molecular model consisting of harmonic oscillators with degenerate or commensurable frequencies. The RRKM theory 3:9 allows for distinct frequencies of the oscillators. Since the present work is mainly concerned with the RRKM formulation, it will be dis- cussed in more detail than the other theories described. As was the case in the previous theories, the active molecule is assumed to be harmonic at all energies, but now any or all vibrational degrees of freedom and/or internal rotations may be described as "active", 332,, they contribute their energy to the reaction coordinate. Overall rotations are assumed to be "adiabatic", in the sense that they re- main in the same quantum state throughout the reaction, and contribute only centrifugal energy to the reaction. In addition to the minimum energy requirement for reaction, the RRKM theory requires the formation of some specific internal configuration, and is in this respect similar to the transi— tion state theory .30 The collisional Lindemann mechanism is 13 modified as follows: a' * A+MbJJ>Ai+M (kt A’f—i—sA‘.‘ l 3 A; '£2§£-> Products where A: and A; represent the active molecule and the "activated complex" with internal energies E: and E; and ki represents the probability for formation of a reaction complex from an active molecule at the same total energy in excess of the zero point vibrational energy. The observed first-order specific rate constant k for the overall reaction IA >P is obtained by application of the steady state approximation to A: and A; in the reaction sequence 8 , which leads to f. = i p (9) The resulting expression for k (see equation 2 ) is then (ai/bi) kl k :2: k1. — <10) 1 1 + BZTEV where i represents all energy states of the active molecule. 14 Development of a final expression for k in terms of molec- ular parameters, depends upon whether the activated complex is "rigid" (if only vibrational degrees of freedom are considered active), or "loose" (if internal rotations are also active). In the present work only rigid complexes are considered. The summation in equation 11) is appropriate for a quantized model, but may be replaced by an integral over internal energy for thermal systems for the following reasons: In the case of the active molecule at energies in excess of the critical energy (several Kcal/mole), the vibrational energy states are extremely dense, so that a continuous density function may be used with confidence; in the forma- tion of the complex, one of the real vibrational degrees of freedom of the active molecule becomes an internal translational degree of freedom along the reaction coordin- ate. The quantized nature of the complex vibrations is quite apparent at the relatively low energies (relative to the zero-point vibrational energy of the complex) involved, and cannot be treated as continuous; however, as any distribu— tion of the internal energy of the complex between real vibrational modes and the internal translational mode is possible, so long as consistent with the quantized nature of the vibrations, the energy E+ of the complex will be continuous. The term ai/bi in equation 10 then becomes F(E*)dE*, the equilibrium fraction of active molecules at energy E* 15 to E* + dE*, given by 24 F(E*)dE* = N*(E*) e:p(-E*/kT)dE* I (11) V where N*(E*) is the density of active energy states at E*, and Q; is the vibrational partition function for the active molecule. The term bi(M) in equation 10 is set equal to the collision frequency ZP at all energies (strong collision assumption). The specific decomposition rate ki becomes kE the decomposition probability for active molecules at energy E*. kE represents the probability of forming an activated complex from an active molecule at constant energy; thus kE will be proportional to the ratio of the number of energy states of the complex at energy E+ to the number of active vibrational energy states at E*. The final ex- pression i333 2; P(E 3+ ...E+ Ir V (12) kE = a TT' N*(E*) +) where II is the inertial ratio, or the ratio of rotational partition functions for the complex to that of the active molecule (this term corrects for the contribution of centri- fugal energy of the adiabatic rotations), P(E$) is the vibrational degeneracy at energy E3, and the summation recognizes that any fraction of the total energy E+ of the complex may be in vibrational degrees of freedom as E3, 16 (consistent with the quantized nature of the vibrations), the rest being in the internal translational degree of free- dom. a is the reaction path multiplicity, a correction fac- tor to account for the possibility that more than one unique path for reaction may exist due to symmetry properties of the molecule. The correct prescription for a will be given in the discussion section. The final expression for the unimolecular rate constant k for the case of "rigid" complexes becomes:3: + -E /RT 00 z P(E ) e +< + 3 V k- 511 eIEC/RT EV—E am (13) ‘ a 11 r kE RT 1 + -—— E+=0 ZP At high pressures, equation 13 becomes + 3. =a‘i-‘91 3y. eEc/RT (14) CD h, r 0* ’ v identical with the transition state expression.3° At low pressures, the limiting second order rate constant is given by: (I) .. * k0 =-3¢ f N*(E*) e E (RT dE* (15) Qv E c since E* = EC + E+. At low pressures, all dependence on the activated complex disappears. The critical energy EC (the difference in zero-point energies of the complex and active molecules) can be re- lated to the experimental activation energy by requiring 17 the high pressure rate constant (equation 14 ) to have the experimental temperature dependence. This results in7'31 EC = Ea + < E; > - < E: > - RT (16) where < Ev > represents average vibrational energy. 6. Kinetic Isotope Effects and Quantum Statistical Effects. (RRKM Theory) The reaction rates for isotopic molecules, 2:23: mole- cules differing only in the substitution of one or more atoms by isotopes, will generally differ, the effect being re- ferred to as kinetic isotope effect. The fact that the potential energy surfaces of isotopic molecules are very nearly identical30 , infers that any mechanistic isotope effect will result largely from the mass effect on the vi- brational patterns of the isotopic molecules and complexes. Kinetic isotope effects may be described as primary or secondary, depending upon the proximity of the isot0pic sub- stitution site to the reaction site. If the atom is inti- mately involved in the reaction coordinate, the effect is termed primary, while an atom situated at a position rela— tively removed from the site of the reaction will produce a secondary effect due to the dependence of the reaction coordinate on all of the normal coordinates. The RRKM theory predicts a decrease in the magnitude of the isotope effect from the high to low pressure region. 32 as do the classical theories. This mechanistic effect results because of the insensitivity of the rate-determining 18 collisional energization reaction in the low pressure region to isotopic substitution. In addition, the RRKM theory admits of the possibility of other non-mechanistic effects (quantum statistical effects). Consider the ezperssions for the limiting high and low pressure isotope effects: + I Q Q*' ]< r)(r v v ~22, = —-,- —— —-—- exp (AE /RT) (17) k 00 II Q'+ Q; c V CD N* (E* )e><13>(-E*/R'1‘)9‘-§1 k z E ' Q" f.- O = E.- ° (13) ooN*(E*)exp(-E*/RT)%g;77 so V where the prime represents the heavier molecule. In the product of the first three terms is generally only slightly smaller than unity, whereas AEC §(Eé - Ec) may be as large as one-two kilocalories, the exponential term always outweighs the first three terms with the result that the isotope effect is normal ($323. klight/kheavy >1). In 18 , it can be seen that the isotope effect will be strongly dependent upon the ratio of the density of energy states of the two isotopic molecules. This density is much larger for the heavier isotopic molecule at all energies due to the closer spacing of energy levels for a harmonic oscillator of larger mass. Thus an inverse iso- tope effect should be observed at low pressures. Statistical 19 weight inverse isotope effects have been observed for both the structural isomerization of cyclopropane3-3'3‘9 and the thermal isomerization of methyl isocyanide.15'16 3. The Unimolecular Isomerization of Methyl Isocyanide Molecules The first investigation of the isomerization of the isocyanides was that reported by Ogg.34 The work was in- complete, but preliminary data on methyl and ethyl iso- cyanides indicated activation energies of approximately 40 kcal/mole and frequency factor > 1013 sec-1. Such data were interpreted as indicating that the reactions were probably unimolecular. In an exploratory study, an examination of the thermal isomerization of pftolyl isocyanide was made by Kohlmaier 1 for and Rabinovitch.35 Frequency factors of 101307 sec- solution studies and 1013'5 for gas phase studies were observed, a value y ~’1013 sec-1 is characteristic of uni- molecular processes. Activation energies of 36.9 kcal/mole and 33.8 kcal/mole for solution and gas phase reactions, respectively, were determined. The structure of the isocyanides has been shown to involve a linear C-NEC: submolecule. The degenerate bend- ing motions increase the importance of the valence bond structure C~N~. , and the isomerization can formally be ‘\C: considered as due to bending of the CNC linear portion of the molecule to form an activated complex in which the carbon 20 [attached to the isonitrile group and the isonitrile carbon can approach one another, facilitating the isomerization to the CCN nitrile structure. In the pftolyl case, acti- vated complex models involving (a) free rotation about the C-N bond in the complex, and (b) a rigid ring structure, were considered, and it was shown that the ring structure was more consistent with the fairly large entropy of activation (-4.8 e.u.) observed. The thermal unimolecular isomerization of methyl iso- cyanide to acetonitrile has been investigated by Schneider and Rabinovitchl5 as part of a thorough investigation of this reaction type. Results show the reaction to be a first- order homogeneous reaction in the temperature range 200— 260°C. "Fall-off" was studied over a pressure range from several atmospheres to about 0.02 mm, well into the "second-order" region. The activation energy was found to: decline with pressure by about two kilocalories between the high-pressure and low-pressure regions. At high pressures, the temperature dependence of the rate constant is given by 10910 k = 13.6 - 38,350/2.303RT. The RRKM theory was used to calculate the rate constant at a function of pressure, assuming a ring structure for the activated complex, with one of the degenerate CNC modes representing the reaction coordinate. Several vibrational frequency patterns for the complex were considered, but only two gave results reasonably in accord with experiment. In 21 both, one of the CNC bending frequencies of the molecule was considered to become internal translational motion in the complex, and was removed. In the 300 model of Schneider and Rabinovitch, the C-N and NEC stretching frequencies were lowered slightly, and all other molecule frequencies were considered as unchanged in the complex. In the 700 model, in addition the frequency changes in the 300 model, the second CNC molecule bending frequency was assumed to in- crease from 300 to 700 cm-1 in going to the complex. The agreement with experiment was slightly better for the 300 model, but the calculated results were fairly insensitive to changes in the vibfimfional frequency pattern of the com- plex. The deuterium kinetic isotope effect (k(CH3NC)/k(CD3/NC) or kH/kD) has also been investigated by Schneider and -Rabinovitch. A large statistical weight inverse isotope effect ((kH/kD)o = 0.28) was observed at low pressures, as predicted by the RRKM theory. The deuterium isotope effect is a secondary isotOpe effect in the isomerization, as reflected by the small limiting high pressure value ob- served, (kH/kD)CD = 1.07. The calculated RRKM values using the 300 model are 0.38 and 1.35, respectively, in fair agree— ment with experiment. Better agreement has recently been obtained by Rabinovitch and co-workers 21 using a 300-type model in which the lowering of the molecule C-N and CEN stretching frequencies were smaller in going to the complex than in the original 300 model, and an improved frequency 22 assignment for the molecule was used. The RRKM calculated values for the improved model are reported as (kH/kD)°= 0.315 and (kH/kD)GD = 1121, in better agreement with ex- periment. The relative efficiencies for collisional energy exhange were determined for a large number of unreactive gases added to the low pressure region in order to assess the validity of the strong collision assumption. The re- sults indicate that the assumption is excellent except for very small molecules (diatomics and triatomics,h where it is still a reasonably good approximation), and monatomic gases such as the rare gases. III. EXPERIMENTAL A. MATERIALS 1. Helium (Matheson Co., High Purity) was used without purification as the carrier gas in all gas chroma- togrpahy work. Ethane (Matheson Co., C. P. Grade) was passed di- rectly from a cylinder, through a dry-ice-alcohol trap, into a storage bulb on the vacuum system. Further purification was effected by numerous trap-trap vacuum distillations before being used in inert-gas runs. Acetonitrile (Fisher Certified Reagent) was puri- fied by distillation in vacuum before use in gas chromatography studies. Methyl Isocyanide was prepared by the method de- scribed by Schneideraq which is a modification of a widely-used method due to Gautieraz This method was found to give good yields and a product which did not require extensive purification. In a typical preparation 0.16 mole of powdered AgCN (Fisher Purified used without further purification) were placed in a cylinderical Pyrex reaction vessel (3.8 cm id. and 10 cm long) which had a seal-off attached to one end. This reaction vessel was attached to vacuum line via 10/30 23 24 standard taper joined to the seal-off end of the vessel. The vessel was evacuated and 0.08 mole (5.0 cc) of CH31 (Baker white label, used without further purification) were distilled on top of the AgCN. The vessel was sealed off and the mixture of CH31 and AgCN allowed to warm to room temperature. The vessel was clampled to the arm of an electric shaker which extended into a water bath whose temperature was maintained between 55 and 60°C. At this temperature the pressure of CH3I in the reaction vessel approaches two atmospheres so the bath and shaker were shielded with a glass window. After about an hour and a half the contents of the reaction vessel turned a light yellow color. Termination of the reaction at this point prevented the formation of hard brown polymer products which cut down the yield considerably. The sealed tube was broken, the contents of which were then powdered and poured into a 100 cc round bottom flask fitted with a 24/40 standard taper joint. After addition of 50 cc of a concentrated KCN solution, (prepared from Baker analyzed KCN) the flask was attached to a vacuum line by use of a 24/40 -10/30 standard taper adapter. The solu- tion was quickly cooled to liquid nitrogen temperature and evacuated. All air was removed by the pump-freeze-melt technique. The mixture was allowed to warm up to 0°C and the CH3NC which was present as an oily layer was vacuum distilled into a sample bulb. Five trap to trap distillations from an ice- salt bath at -20°C removed all traces of water. 25 The resulting sample was checked on a carbowaX' 20M gas chromotagraphic column for impurities. The only im— purity found was CH3I, and that in very small amounts never exceeding 0.3 mole %. B. APPARATUS 1. Furnace The furnace consisted of two concentric heating ele- ments as shown in the schematic of the furnace assembly Figure 1. The inner heating element consisted of three heater sections wound on a steel cylinder (4130 grade alloy steel, five inches in diameter, twenty inches in length, closed on bottom with a 1/4 inch bolt—on steel plate). Five layers of asbestos paper, then three thirty-foot sections of Chromel-A heating wire (B & S #22 gauge, 0.997 ohms/foot), were wound around the inner cylinder. The in- ner heating element was completed by covering the heating wire as well as the bottom plate with ten layers of asbestos paper. The three.heater sections were powered by three manually-controlled 7.5 amp Variacs capable of dissipating 400 watts power each at 110 volts. The outer heating element consisted of two heater sec- tions wound on a steel cylinder (4130 grade Alloy steel, seven inches in diameter, twenty-six inches in length, closed on the bottom With a 1/4 inch bolt-on steel plate). Each of these two heater sections consisted of parallel windings of two sixty-foot lengths of Chromel-A heating wire (B & S 26 Figure 1. Schematic of Furnace Assembly 27 Thanh:m.-.~3m.r.j._a:#£w.41-1::__H_E.... ::meH.3uth..: --H~H~_HF:JHH~::HHAqfiuu—: F1 - S O l .11 S .1 t6 0 0 CS t r C aS S e 66 e p +. DAV. kg 3 a M. H . ... .. .. .t . .... ..,. _ .. ..._ ...o....... A... .q......... __: __:fia_:_ nmld - - Hh~:h~u::~p-:u 1 A K31. . u - n l 1 IL I r 3 i < 3 kilfi 1.. 1 I no on. c ll. 0 Bl. 1 ¢ s.n B n nvnfi s I LL! 0 u. SH t l e] S . b.u e .1 uFannnuuuh-HH fihnjh—FF..-~_.71m_.-_.~H~mFF. ST. b .. -. . . q . - . - Al 8 1:.” ll; A -1 —:::. . m. p l S u em I 0 e .m. m tm r S 1n m 38 8.1 I Sd 81 e an ty h Ii SC T Bl Y C llLJIlll—TII‘LIJJILIUJIIIIIIIIIIIIIIIIII[Ill[ILLIIITllllllleIIIT'III—jI v fittm:.ipw::::a~3_:~::~_:1 inunfinhndnnnHHfidh ’ Figure 1. 28 #22 gauge, 0.403 ohm/foot). The outer heating element was then completed by covering the heating wires as well as the bottom plate with ten layers of asbestos paper. These two sections, which comprised the main heater, were capable of dissipating 1000 watts each at 100 volts, and were powered by 15 amp manually-controlled Variacs. The furnace was assembled by placing the inner cylin- drical heating element on asbestos blocks inside the outer cylindrical heating element, which in turn was set on as- bestos blocks inside a fifty-five gallon steel drum. Both heating elements were closed at the top with 1/4 inch bolt— on steel plates, each of which had two one-inch slots at 90° to each other cut radially nearly to the center to allow thermocouples, reaction flask neck, etc., to extend from the furnace. The space between the steel drum and the outer heater was filled with Vermiculite (mica) insulation. The reaction vessel rested on an asbestos-covered section of five inch brass tubing placed inside the inner heater, so that the reaction vessel occupied the central third of the vertical space, and its neck was then connected to the vacu- um system by means of a 6 mm stopcock directly above the assembled furnace. The thermocouple leads and the leads to the section heaters were brought out through the upper steel plates, and the top of the assembly was covered with Vermiculite insulation. When the furnace assembly was complete the layer of Vermiculite surrounding the outer heating element was about three inches thick. 29 2. Temperature Regulation System The reaction vessel was heated by radiation from the inner wall of the inner heating element, which was about one-half inch from the surface of the vessel. The main source of heat was the outer heating element, approximately three inches from the reaction vessel. The temperature was maintained to within 10 - 20°C of the desired reaction tem- perature by manually adjusting the two 15 amp Variacs to the main heater. A Stabiline 3 KVA line voltage regulator was interposed between the 100 V source and the Variacs. Fine adjustment to attain the required reaction temperature was made by adjustment of the three 7.5 amp Variacs which powered the three inner heating elements. Since these Variacs were normally set to a small percentage of their voltage output, changes in the line voltage did not change the temperature of the reaction vessel appreciably. The regulation system provided a temperature constant and uniform over the entire extent of the reaction vessel to i 0.1°C for a period of several hours at the reaction temperatures used. 3. Reaction Vessel The reactor was a cylindrical vessel, 23.9 cm in length and 8 cm inside diameter, (1020 cc) constructed of Pyrex medium-wall tubing. Five Chromel-Alumel and one Platinum— Platinum, 10% Rhodium thermocouples were tied at various positions on the surface of the reactor with asbestos twine. 30 The neck of the reaction vessel was 10 mm Pyrex medium- wall tubing and was connected to the vacuum system via 6 mm high-pressure stopcock (a solid-bore vacuum stopcock fitted with a Universal stOpcock-adapter (Sargent, S-77353). High-pressure stopcocks will be referred to in later section by use of the Symbol PS; high-vacuum stopcocks are indicated by the symbol S). 4. The Furnace Inlet System The manifold was of conventional design, consisting of a large (20 mm) glass tube MA, Figure 2 to which other sections were attached by means of high-vacuum stopcocks. The manifold was evacuated by a fore pump, FP (Cenco Hy-Vac 14), connected to the manifold via a 15 mm 3eway stop- cock Sl and a liquid-nitrogen cooled trap T1.. An oil dif- fusion pump, D (Consolidated Vacuum Corporation, Model VMF-ZO), could be introduced between trap T1 and the fore pump FP by means of stopcocks SI and 82. The pressure in the manifold was monitored with a thermocouple ionization vacuum gauge, TG1 (Consolidated Vacuum Corporation, Model GIG-110A). Under normal operating conditions, the fore pump was found to be capable of pro— ducing a vacuum of at least 0.5 microns. Use of the oil diffusion pump resulted in an ultimate vacuum of better than 0.01 microns in the manifold. 31 Figure 2. Schematic of the Furnace Inlet System. 32 EVl 89 $6 '1 $5 ‘ EF51 T1 Figure 2. 33 5. The Gas Chromatographic Sampling and Collection System The products of the reaction, acetonitrile and unreacted methyl isocyanide, were separated by gas chromatography. A schematic of the vacuum system is shown in Figure 3 . Sample was introduced from a storage bulb through port P1 into a small (5 cc) trap, T2. Generally about 10 cm pressure, as indicated on the capillary manometer M1, was introduced. Helium from a cylinder, HE, was used as the carrier gas. The helium stream was plit at x, part being diverted through a reference column RC to the reference side of the detector cell (DC). The remainder of the helium stream either by passed trap T2 containing the sample and flowed directly through the separative column SC, or passed through stopcocks P55 and P56, sweeping the sample through SC, the - detector cell, the sample collection traps (T3 for methyl isocyanide and T4 for acetonitrile, both cooled to liquid nitrogen temperatures) and finally into the atmOSphere through a calibrated ball-type flowmeter, FM, A flow rate of 100 cc/minute generally was used. Usually the products from five sample introductions were combined for mass spectral analysis. 6. The Gas Chromatograph The design of the gas Chromatograph is a modification of that described by L. B. Sims38. :Full scale deflection of the recorder was produced with less than 10.5 mole of 34 .Emummm mEmfiom How can mmo one oanmmumoumfiounu ¢ . mammamc 00 new . cofluowaa .m wusmflm 35 .m magmas HE 36 sample on the most sensitive scale, sufficient to detect impurities of the order of 0.1 mole per cent in the samples. The chromatograph consisted essentially of four sections: the column, the detector cell, the bridge circuit, and the recorder. b. The column was 15 ft x 1/4 inch i.d. stainless steel fitted with brass Swagelock connectors and packed with 15% carbowax 20M on 60/80 chromosorb W (Wilkens Instrument Company). ghg detector cell was a thermal-conductivity cell machined from brass Figure 44. The sens- ing elements were matched thermistors (Victory Engineering Corporation, type A33), fitted on a Teflon washer on a seat in the detector block, and held in place by means of a threaded brass washer assembly, as shown in Figure 4. The detector block was connected to the column assemblies suspended in a constant- temperature air furnace beneath by means of Swagelock metal-glass connectors fitted with »Teflon ferrules. The sample was swept with helium from the sampling inlet system, through the collection system where the sample was re- moved from the helium stream. The helium then passed through the flowmeter and issued into the atmOSphere. 37 Figure 4. Schematic for Gas Chromatographic Detector Block 38 5/8'I—18 SAE Screw Caps 3/8" diameter 1/8" pipe 5 an. T/ I. I 7 7% E / 1/'2., \ -_—_ Z drill B¢¢¢¢é¢7 section BB 2" thEn fill / Ag Solder _ / /A / 11/32" diameter ;T\\\\ 1/8" diameter ' symmetrical about AA ' A 3/8" diameter Figure 4. 1/8" Pipe thread Screw Caps 1/8" diameter 39 c. A Wheatstone bridge circuit was used to convert the change in resistance of the sensing therm- istor, when the gas stream consisted of a "peak" of different thermal-conductivity from the carrier gas, to a change in voltage which was then fed to a recorder. The circuit is shown in Figure 5. A six-volt P6 sbtorage cell was used as the battern in the circuit. The potential applied to the bridge circuit was set at four volts by the 500 ohm variable resistor R5. The at— tenuator was set to give nearly full scale de- flection (1 mV) on the recorder. The peak areas corresponding to methyl isocyanide and aceto- nitrile on the chromatograph were measured with a compensating polar planimeter. The ratio of areas methyl isocyanide/acetonitrile was used to determine the fraction f of reaction. d. The recorder was a Sargent Model SR, variable range. The most sensitive range, 1 millivolt, was used both when analyzing a sample of methyl isocyanide for impurities or when separating acetonitrile. 7. The Gas Analysis and HandlingiSystem .The intermolecular carbon—13 isotope effect was deter- mined as a function of temperature and pressure by comparing 40 Figure 5. Schematic of Bridge Circuit for Gas Chromatograph 41 ‘* recorder " Attenuator R11 R10 R9 R8 R7 R6 1/32 1/16 1/8 1/4 1/2 T1 T2(:) *_ Ill! M34 {qummthH ”$573W$021w3023 WUCNHmCOU mgmm HMHCQEflHQMWM .b wusmflm 54 .8 musmflm AEEV enummwnm . «UH — A m mow UOMVN fl .n .mmmv em omm4wml em OOH H 0mm.mml I [D H I O N g + X OIEOT 55 where the prime refers to the heavier isotopic molecule, the kinetic isotOpe effect 6 is defined as the deviation from unity of the isotopic rate constant ratio k/k': _ k e - l? - 1| (21) It has become somewhat conventional to refer to the isotopic rate constant ratio. r = k/k' itself as the kinetic isotope effect, and this convention will be adopted in the remaining discussion. The experimental ratio r of isotopic rate constants can be determined from any three of the four data (where A, B refer to moles of A and B respectively): f B + B. = the fraction of reaction AO+A5 R (E R ) = the initial molar ratio“ (A'/A)o A0 Boo RA = the molar ratio (A'/A)t obtaining at f (22) t RB = the molar ratio (B'/B)t obtaining at f. t Exact expressions for r in terms of any three of the four data have been given by Yankwich and Tong 40. The expression involving R R , and ,f At' Bt - R In 1 _ f RBt At 1 - f 1 - f RB + 1 — _ t .- r - F RB". " RA 1 (23) ln 1 + f t t 1 - f 1 - f RB + 1 _ t _ 56 has the advantage that the relative error in r is extremely insensitive to the error in f, the least precisely known (1 1%; the corresponding error generated in r is less than 0.1 %) datum. The molar ratios can be determined to at least i 0.001% by isotope-ratio mass spectrometry. An expression appropriate for tracer levels of A' and B', for which f may be approximated by 1. E. f _. A0 is ;1n(1 - f) H II (24) t f ln R (1 _ f) + 1 At This equation will be derived in the following chapter. The results from equation 24 are in excellent agreement with those calculated from equation 23 for the case of natural abundance 13C. Equation 24 greatly simplifies the analysis of the results in this study. Methyl isocyanide contains two non-equivalent carbon atoms, either of which may be labeled, so that three iso- tOpic reactions CH3NC k > CH3CN k 13CH3NC 1 > 13CH3CN k CH3N13C 2 > CH313CN need to be considered (the probability of double labeling, 13CH3N13C, is negligible at the tracer level), and two 57 kinetic isotope effects arise: k/k1 and k/kz. The experimental procedure used in this study involved deter- mining (see Chapter III) the 13C02/12C02 ratio R for carbon dioxide derived from oxidation of unreacted methyl isocyanide (RA) and acetonitrile (RB) accumulated to time t. The 13C02/12C02 molar ratio was taken as the 45/44 mass spectral peak ratio, corrected as follows: (1) Contribution of the species 12C16017O to the 45 peak was made by subtracting 0.0008 from each ratio.a (2) The inability of the instrument to resolve completely the large 44 peak and the 45 peak was made by sub- tracting 0.0002 from each ratio.a (3) Instrumental response fluctuations were negated by subtracting from or adding to each sample ratio the difference between the 45/44 ratio of a standard sample of C02 and its accepted value. The standard was run at least once each four-hour period. As an example of how a corrected ratio was determined, consider the following at 243.4°C and 343 mm pressure for the carbon dioxide from the combustion of methyl isocyanide. m/e(45/44) = 0.0121341 tank 002: m/e(45/44) = 0.0127142 Accepted tank value= 0.0127000 0.0000142 aCorrections previously established in the Mass Spectrometry Laboratory of the University of Illinois. 58 0.0121341 —0.0000142 tank correction 0.0121199 -0.0008 12C15017O correction 0.0113199 -0.0002 resolution correction 0.0111199 < corrected ratio These ratios are related to the molar ratios of iso- topic methyl isocyanide and/or acetonitrile by the conbus- tion reactions: CH3NC > 2C02 13CH3NC > 13c02 + coz CH3N13C > 13002 + co2 whence, the molar ratio 13CH3NC + CH3N13C A 2 13CH3NC + CH3N13C + 2CH3NC . or fix- = 1 + 2 13CH3NC + CH3N13C (26) 1 2 __ = 1 + __ RA Rue A corresponding equation relates RB and R The CN' molar ratios 13CH3NC and CH3N13C needed to determine separately k/k1 and k/k2 from either equation 23 or equation 24 cannot be obtained separately from natural abundance studies. However, the ratio RNC or R can CN be used in either equation 23 or equation 24 to calculate 59 an "average" isotope effect k/k' . If equation 24 is used a relation between the average isotope effect k/k' and the individual isotope effects k/k1 and k/kz can be derived (Chapter V). Information concerning the individual isotope effects k/kl and k/kz, arising from labeling the methyl and isonitrile carbons, respectively,nay thus be ob- tained from the experimental average isotope effect k/k'. Alternatively, studies involving methyl isocyanide enriched in either the methyl or isonitrile position can be used to- gether with the natural abundance results to obtain directly k/k1 and k/kz. Attempts were made to label the methyl position and obtain the separate effects k/k1 and k/kz directly, but difficulties were encountered. These attempts are described in the Appendix. The isotope effect results are given in Table 2 , , and in Figure 8 . Most effort was directed toward the experiments performed at 226°C; the results for this tempera- ture represent the average of a large number of separate experiments at each pressure. The results at the other temperatures (243.4 and 213°C) represent single experiments at each pressure, or in some cases duplicates. The results at these temperatures are not of the same quality as those at 226°C, and were carried out mainly to determine the dif- ference in critical energies for the isotopic molecules. It is often found that, at high pressures, the temperature dependence of the isotope effect is of the Arrhenius form: (k/k')oo = Ar exp(AEo/RT) 60 where AEO = E6 - E0 . and the critical energy E0 is related to the observed activation energy by E0 = 8:0 + (EV*> - <8V+> - RT where represents the average vibrational energy , and *3 and + refer to active molecule and activated complex, respectively. The temperature dependence of the average 13c isotope effect k/k' for methyl isocyanide isomerization was found to be (k/k')CD = 0.998 exp(20 1 5/RT) . Since the temperature dependence is small, and subject to considerable experimental error, the detailed pressure "fall-off" of the isotope effect at a given temperature is more important for comparisons with theory than results of lesser quality at several temperatures. Table 2. Summary of isotOpe effect data. Presa a b c k/k' sure f R R Calc by Calc by (mm) A B Eq. 24 Eq. 23 T = 243.4°C 525‘ 0.461 0.0110900 0.0108450 1.01703 1.01702 438 0.294 0.0110749 0.0108861 1.01482 1.01481 343 0.474 0.0111199 0.0108778 1.01659 1.01659 271 0.696 0.0111835 0.0109260 1.01391 1.01391 242 0.468 0.0111004 0.0108912 1.01439 1.01439 33 0.590 0.0110877 0.1093360 1.00943 1.00943 12.5 0.588 0.0111168 0.0109918 1.00762 1.00762 T = 226.0°C 880 0.483 0.0111016 0.0108289 1.01863 1.01863 475 0.443 0.0111055 0.0108740 1.01629 1.01629 369 0.397 0.0111009 0.0108680 1.01700 1.01700 74.0 0.511 0.0111032 0.0108797 1.01483 1.01482 46.0 0.479 0.0111251 0.0108985 1.01544 1.01545 32.0 0.411 0.0110972 0.0109026 1.01401 1.01400 17.0 0.602 0.0111175 0.0109167 1.01214 1.01214 11.5 0.533 0.0110897 0.0108997 1.01233 1.01233 T é'213.0°c 88.0 0 594 0.0111473 0.0108850 1.01604 1.01604 46.0 0.515 0.0111784 0.0109171 1.01721 1.01723 16.0 0 680 0.0111900 0.0109275 1.01448 1 0144s a I 0 Fraction of reaction. b 13002/12002 from combustion of unreacted methyl isocyanide. C 13C02/12C02 from combustion of the product, acetonitrile. 62 .Uoo.mNN .0 v.mvm um musmmmum mflmuw> ..¥\x mOHumm unmumcoo mumm Hmucmfimnmmxm .w mudmflm 63 «OH .w muswflm «OH AEEV mndmmmnm OH db 055.6mm Dov.mvm n. O ~3- -- boo.H n.moo.H IIHHO.H l CO H O H I In H O H .bHo.H L.mHo.H V. DISCUSSION .A. RELATION OF THE AVERAGE ISOTOPE EFFECT TO LABELING AT THE METHYL AND ISONITRILE POSITION The experimental method used in this study involved determination of the 13C02/12C02 ratio R on samples of carbon dioxide derived from oxidation of unreacted methyl isocyanide (RA) and acetonitrile (RB) accumulated to time t or fraction f of reaction. As discussed in the last chapter, RA and RB can simply be related to the molar ratios of isotopic methyl isocyanides and acetonitriles, 13CH3NC + CH3N13C RNC = CH3NC (R respectively. The ratios RNC and RCN and f can CN ). then be used to calculate an isotOpe effect k/k' which is an "average" of the position isotope effects arising from labeling the methyl (k/ki) and the isonitrile (k/kz) car- bons, by the use of the exact expression of Yankwich and TongJU3 The exact relationship between k/k‘ and the individual position isotope effects k/k1 and k/kz» can be derived by use of an approximation which has high valid— ity for the case of tracer (natural abundance 13C) labeling, as discussed earlier. The approximate equation can be de- rived simply as follows: Consider the competitive first— order reactions of isotopic molecules A and A', with rate constants k and k', respectively: A k > B 64 65 A' k > B' . where the prime refers to the heavier isotopic molecule. The isotope effect will be defined as r = k/k'. Follow- ing Yankwich and Tong4° the fraction of heavy isotopic molecules remaining at t can be written: g=—r=e (27) = e = e = g (28) The isotopic ratios of molecules of A remaining (RAt) and of product B accumulated (RBt)V to t are then _ A' R0 RAt — (X—Qt r—l (29) g I R 1 _ RBt = (g—) " 0( 1:9) (30) t 1 - g Al Bl where R = -—- '—- 31 O (A )0 (B )CX) ( ) the fraction of reaction f is f _ B + B' _ (A0 + A6) .',. (A + A‘) = (1-qr) + RA(1-g) (32) — AO+A5 — A0 + A; 1 + R0. Elimination of g from equations 29 , 30, and 31 leads to the exact expression for r: 66 In [1) + (1—ff) (it .4123.) ]” Bt . _ (33) RAt Rat . 1nl:(11- f) (1 - ff) R R + 1)] At( Bt The approximate expression is derived by realizing that for tracer level labeling A'/A << 1 at all times, and hence =A._0__:_A=1_L=1—gr (34) m IQ Elimination of g from 29 . 30 and 34 , and rearrangement yields H II —" Hi1; ”f . (35) ln Pf; i—Z—f q ' An error analysis of equation 35 results in the fol- lowing expression for the relative error in r: (Ar 2 (>27 -1[:(-f(ln-(1-f)i| (9‘32 ”(Ta 24332 (36) where the relative error in f, égn was taken to be 1%, and the relative errors in RA and RB’ %, were both taken as 0.01%. A representative value of 1.02 was assumed for the isotopic rate constant ratio r. This represents the limiting maximum value observed for the C-13 isotope effect in this study. The variation of Q%- with fraction of reaction is shown in Figure 9 . An expression similar to equation 33 but employing input data R0, RBt' and f, has been 67 derived by Bigelisen and Allen41 , using the same approxi- mation to f as described here. The error analysis on their equation shows that the relative error in r is much larger at all fractions of reaction for the same parameters assumed above. Exact expressions requiring as input data R0, RBt’ f; R0, RAt, f; R0, RAt, RBt and the relative errors obtaining in r have been discussed by Yankvich and Tong4O , and show that the equation requiring RAt, R f, are much less sensitive to errors in f than the Bt’ other three cases. Values of RNC and RCN were used in place of RBt and RAt in equation 35; resulting values of r have been presented in Table 2. Comparison of the values shows that equation 35 is an excellent approximation to the exact expression 33 for natural abundance 13C levels. The reactions of the isotopic methyl isocyanides can be written A k > B A1 k1 > Bi A2 k2 > B2 where A s CH3NC . A1 2 13CH3NC A2 a CH3N13C and B, B1, B2 refer to the correSponding isotopic aceto- nitriles. 68 .COHflUmmm MO COHHUMHM mfimHmb. mCOHumasono oflumm maouomH mumEonumm¢ may CH Honum 0>Humamm .m wusmflm -r d- 0 O 3. .m wnswflm w coeuumwm mo GOHDUMHE r m“ o m.o . . . )- H (o 69 [TON 70 (Let RA = Al/A , 'RBI = 81/8 (37) RA2 = Az/A , RB2 = 82/8 and R0 = (Al/A)o = (Az/A)0v assuming both the methyl and isonitrile carbons are labeled to.natural abundance in the starting material (confirmation of this assumption comes from the fact that the 13COz/IZCOZ ratio for samples of completely oxidized methyl isocyanide were observed to be twice the natural 13C abundance). The ratio RNC/RCN defined for the average isotope effect is then simply related to R . R , R . R by , A1 A2 Bl B2 + RNC = RA1 RE; RCN RB1 + BB2 which can be rearranged to -1 —1 R '1 R R R (.911) = 434 52.1...41 .55.,5a-R_A2 (38) c RA2 RAZ RA2 A1 RA2 A1 The ratios --. . can be derived as follows: Define fractions of A1 and A2 remaining at time t by: g = = e'klt 1 A10 (39) 92 A20 I and the isotope effects r1 = k/k1 71 r2 = k/kz The fraction of A remaining at t is then r r A/Ao = 911 = 922 = 1 ‘ f . (40) employing the same approximation for f as in the deriva- tion of equation 34. Then R0 R0 R - ° R ‘ A r -1 ' A r -1 1 9.11 2 9,22 (41) 3 R0(1 ‘ 91) R0(1 ' 92) R = o R = Bl _ r]. I B2 _ r2 1 91 1 92 Combining equations 40 and 41: 1/r 511:1”? 1411/5: RA1 f (1 f) 1 RB2 = 1 - f 1 - (1 - f) /r2 2 (42) RA2 f (1 f)1/r2 R ' /r2 .5. = (1 fl RA1 (1 f)1 r1 Equations 41 are valid for any value of. f. Since most of the experiments in this study were’ of complex and active molecules by31 80 EC = Ea + - — RT (46) * and + referring to the active molecule and activated complex, respectively. The average vibrational energy is given by hv. exp(—hv./kT) ' = :E:: 11- exP(-h:i/kT) ‘47) The critical energy EC is the difference between the lowest transitional rotational vibrational state of the complex and the active molecule. For two isotopic molecules A and 'A' with rate constant k and k', reSpectively, the tempera- ture dependence of the high-pressure isotope effect (k/k') a) can often be expressed by an Arrhenius equation: (k/k )oo = Ar exp(AEa/RT) (48) where AEa = E; - Ea' the difference in experimental activa— tion energies for the isotOpic molecules. The high-pressure limit of the RRKM rate constant ex- pression (Equation 25) leads to an expression for the high— pressure isotope effect: * + I Q' Q . RRKM = .r. .11 ._r (k/k )CO I; Qv Q; exp (ABC/RT). (49) where AEC = Eé - EC , the difference in critical energies for the isotopic molecules. From the physical significance of EC , it must be temperature-independent. However, equa— tion 46, (which gives an approximate value of Ec by 81 forcing the high—pressure RRKM rate constant to have an Arrhenius temperature dependence) yields a value of EC which is very slightly temperature dependent, since and RT are temperature dependent. Typical values of EC are 40-60 kcal/mole, and a change of 20-50 cal/mole for a temperature interval of 50°C near 500°C may result for these reactions. This is a small temperature dependence, but if both EC and E; are evaluated using equation 46 an error comparable to the total magnitude of ABC ( 20 cal/ mole for C-13 isotOpe effects) may well result, and large errors in k/k' may be introduced. This difficulty may be avoided by realizing that ABC = (E - Eé)* - (E z - Egg)+ (50) Z (See Figure) Therefore, the following procedure was adopted in the calculations; for the light isotopic molecule, Ec was calculated from equation 46. ABC was then evaluated using equation 50 , and the critical energy for the heavy isotopic molecule calculated from 82 7. The Collision Frequency w = ZP The strong collision assumption was used in all calcu- lations. The assumption affects the positioning of the isotope effect is. pressure curves (isotope fall-off curves) but not the fall-off shape. The net effect of the assump- tion is to replace the actual pressure P by an effective pressure 1P, where A is a coefficient for collisional deactivation efficienty. In comparisons with theory, the shape of the isotope fall—off curve, rather than the posi- tioning of the curve along the pressure axis, is of impor- tance. Very little is known of the quantitative validity of the strong collision assumption, but avlues of 0.1.: 1.: 1 are usually sufficient to correct the positioning of the isotope fall-off curve. Values of A = 1 were assumed in the calculations. The kinetic theory collision frequency was calculated from the expression 51: 1/2 _ £2. 2 E_. ‘1 Z -¢4 n1 0 RT sec mm -1 (5;) where N = Avogadro's number, and R = gas constant in —1 -1 cc mole deg . +) 8. The Calculation of Z P(EV The vibrational degeneracy was calculated using direct + . count method38 for E+.: 0.5 Ez , the zero-p01nt energy of 83 the complex, and by an approximate equation due to Whitten and Rabinovitch 52 for higher energies. The contribution to the overall rate of molecules in which E+.: 0.5 E: is very small, so that an almost negligible error is intro— duced by using an approximate expression for ZP(E:) at these energies; however, the direct count method is onerous at these energies even for methyl isocyanide and the com- puter time required for evaluation of ZP(E:) was reduced from about 5 min per run to about 1 min per run by use of the approximate expression. 9. The Density of Active Energy States N*(E*) Since N*(E*) is the number of vibrational quantum states of the active molecule per unit energy, it is related to the Vibrational degeneracy P(E;) by N*(E*) = (52) At the high energies E* involved for the active . . . . 52. molecule, the express1on of Whitten and RabinOV1tch 1S an excellent approximation to ZP(E:). This expression may be used to evaluate N*(E*) as follows: The approximate expression for ZP(E§) is loglo ZP(E;) = s log10(EI — 1 + 5m) + C (53) where s = number of active vibrational degrees of freedom E' = E*/E; where E; is the zero—point energy of the active molecule. 84 S is a frequency dispersion parameter given by _ s - 1 v2 fl — s v where is the mean square frequency and (v) is the mean frequency of the active molecule, and w is an empirical parameter given by the relations 10910 (L) = "1.0506 (E')o°25 for 1.0 _: EI ._<.. 8.0 (1)-1 = 5E' + 2.73 (E')°'5° + 3.5100 for 0.1 :E' 2 1.0 and the constant C is given by C = s loglo E; — loglo st - E loglo (hvi) To evaluate N*(E*) we write a ZP(E;) E)* a 1an( E*) (54) mm) = BE* = P( E>v 63* but from equation 52 danP(E* _ S 5 E* ‘ E;(E' + 1 - 690V and hence (55) N*(E*) = E;(E' +51 _ 667 P(E:) 10. Evaluation of the RRKM Integral RRKM contains a semi—definite integral (i.e., one of the integration limits is infinity) IRRKM; however, examination shows the integrand has an appreciable Equation 43 for k 85 magnitude only at small values of the integration variable E+ and decreases nearly exponentially at high energies. The contribution to the integral at high energies is very small, with the result that the integral can be approximated closely by a definite integral in which the upper integra— tion limit is chosen to assure a small error. Simpson's rule53 was used for numerical integration of I It was shown to fit an analytical test expression, RRKM. having the same general characteristics as the IRRKM integrand, to better than 6 decimal places. In addition since it is known that the limit of high pressures of the RRKM integral is the vibrational partition of the complex + Qv , which can be calculated exactly from complex frequencies. - + 1”“ (IRRKM ‘ Qv P -—*> 00 (56) The integration limit Emax was chosen so that the error in the integrated partition function was less than 0.1% Bfi. c. COMPARISON OF EXPERIMENT AND RRKM THEORY 1. Activated Complex Models The geometry and bond orders assumed for all of the complex models have been described in Section B of this chapter. Several different complex models, differing only in the vibrational frequency were constructed and the re- sults were examined by comparison with the experimental "average" isotope effect, as described previously. For the calculation of r1 and r2 (isotOpe effects arising from labeling at the methyl and isonitrile position, re- spectively), vibrational frequency patterns for the com- plexes (CH3NC+), (13CH3NC)¢, and (CH3N13C)+ are required The prescription for constructing the two "types“ of com- plexes (i,§,, two different complex vibrational frequency patterns, referred to as the 8/30 and 10/40 complexes). giving the best overall agreement with experiment was as follows. One of the degenerate CNC bending modes of methyl isocyanide was considered to become internal translational motion along the reaction coordinate in going to the com— plex, and the frequency was removed from the set of complex frequencies, as required in transition state and RRKM theories. The C-N and NEC stretching frequencies of methyl isocyanide Were lowered 30 or 40% and 8~10% correSponding to the 8/30 or 10/40 complex model, respectively. In ad- dition the degenerate (Species E) C-H stretching frequencies of methyl isocyanide were lowered 0.2% (the frequencies for 87 methyl isocyanide are 3014 (2) cm-l, and for acetonitrile 3009 c:m"1)‘8 . For the 8/30 model, the remaining cnc bend—y ing frequency was raised 10% (respective molecule frequencies are: CNC bend, 270 cm-1, methyl isocyanide; 361 cm-1 acetonitrile). All other molecule frequencies were assumed not to change in going to the complex. -These changes are summarized in Table 5. The complex frequencies determined by these rules for the isotopic molecules A1 ~and H2 (13CH3NC and CH3N13C, respectively) were adjusted slightly in the final frequency pattern in order to (1) satisfy the Teller-Redlich product rule j, and to insure the correct ABC between the isotopic moleCule A1 or A2 and unlabeled- methyl isocyanide, A. The observed experimental activation energy difference for the average isotope effect r was AEa = 20 i 5 cal/mole. The temperature dependences (ex- pressed as AEC) of the isotope effects ‘r1 and r2 ‘are not known precisely, but from comparison with the results fromother systems , would not be expected to be very dif- ferent from one another nor from the value 20 cal/mole; consequently, AEC for both r1 and r2 was assumed to be 20 cal/mole, and the vibrational frequency pattern of the isotopic molecules A1 or A2 were adjusted as described in Section B in order to insure this value. This did not require adjustment by more than 2 or 3 cm"1 in any frequ- ency from the values determined using the prescription of Table 5. In the case Of 13CH3NC this value of‘AEc could not be Obtained by small adjustments unless the C-H and Table 5. Construction of the complex models. 38 fl,— Molecule Frequency ‘Complex Frequency 8/30 10/40 Species A1 CéH stretch unchanged unchanged ¥C stretch lowered 8% lowered 10% CH3 deformation unchanged unchanged C-N stretch Species E C-H stretch CH3 deformation CH3 rook CNC linear bending lowered 30% lowered 0.2% unchanged unchanged one deleted, one raised 10% lowered 40%_ lowered.0.2% unchanged unchanged one deleted, one unchanged 89 CNC frequencies were assumed to change as shown in Table 5. The prescription in Table 5 corresponds rather closely, to that given by Schneider and Rabinovitch15 (for the 10/40 model) and more recently by Rabinovitch, 33 £1.21 for the 8/30 model, except that the C-H and remaining CNC bending frequencies were assumed not to change by these workers. However, since the isomerization rate constant fall-off and deuterium isotope effect are fairly insensitive to mod— est changes in these frequencbsijmy give substantially the same agreement for these quantities as those of Rabinovitch and co—workers. Table 6 gives the final frequencies for the isotopic complexes. For comparison, the corresponding molecule frequencies are also included. 2. Isomerization Rate Constant and Fall-off The complex models described in the preceding section were used to calculate the rate constant k for isomeriza- tion of CH3NC as a function of pressure at each of the three temperatures of the investigations from the RRKM expression (Equation 43, p. 73). Input data for the calcu- lation are: The reaction path multiplicity, a = 3 (pp 81-83); the moments of inertia of the molecule (Table 4, p. 78) and of the complex (Table 6, p. 90); frequencies of Table 7 give a summary of the input data for the calculations. FORTRAN programs for calculating the vibrational degeneracy of the complex, the density of energy states for the active . I p . I O . n 0 no ww 1 +H no ww I +H on nw u +H . n m . n m . n m on on I +H we on n +H wo an 1 +H . I< . I4 . I4 we on 1 +H ow on 1 +H ow on 1 +H nen non Anvnon wen Hon Anvwnn wen Hon Anvwen %. own How non won one now own eno oeo Anveooe Anveeoe Anveeoe Anvwooe Anvwooe Anvwooe Anvenoe Anveeoe Anveeoe HwnH mee Hwne onne onne onme nwmn nwme nwne Anvomwe Anvonwe Anvonwn Anvnewe Anvnowe Anvmown Anvomwe Anyonwe Anvomwe name. ,.onoe moon anon «one wnen enoe none wnen oeon oeon ooon moon moon moon coon ooon oeon Anvneom Anvenon Anvoeon Anvnoon Anvnoon Anvwoon Anveeon Anvenon Anveeon ixmamsoo memEOO memEOU, Xmamfioo xoameoo xmameoo owxoe onxn manomeoz ow\on om\n manomeoz ow\oH anxn oeoooeoz - . Ooezomo OzhmOoH Ozomo mpflsmmoomfl Hmnugfif. mo mmxmamfioo pom mOHDOOHoE owmouomfl mo OHHHOGH mo mummEOE can mmflocmsvmum .o magma 91 Table 7. Input data for calculation of RRKM rate constant Quantity and Symbol Value Reference Reaction path Muliplicity, a 3 Principal moments of molecule see inertia, 1*, I reference complex Frequencies of CH3NC molecule and complex v*, v High-pressure activation energy, Ea Kinetic Theory collision diameter, 0 Molecular weight, CH3NC. M Collisional deactivation probability A Temperature T see reference 38.35 Kcal/mole 4.5 R 41.02655 g/mole 1.0 pp. 77-81 Table 4, p. 78 Table 6, p. 90 Table 6, p. 90 p. 54 p. 82, Ref. 36 92 molecule, and for evaluation of the RRKM rate integral by Simpson's rule were written and tested using hand calcula- tions (carried to 8 decimal figures), and analytical functions designed to have a form similar to the RRKM rate integrand, respectively. Calculations were carried out on the M.S.U. Control Data 3600 digital computer. Integra- tion steps of 5 cm—1 were used for most of the calculations, and the integration was carried to an energy sufficiently high that the value of the high~pressure integral gave the complex vibrational partition function to better than 0.1%; an upper integration limit of 10,000 cm"1 was generally sufficient for the purpose. Several comparisons with experiments can be made, the most important being the shape and positioning of the fall— off curve, log k/kOD 33. log P, as shown in Figure 10 at 226°C. Open circles represent the results of this study. Data of Schneider at 230.4°Caxe included for a comparison (solid points). The agreement at the other temperatures is comparable. Our data is not as extensive as those of Schneider, the main purpose of this investigation being the determination of the Carbon-13 isotOpe effect. The agree- ment between the present results and those of Schneider are considered satisfactory. The RRKM calculated fall—off curves for both the 8/30 and 10/40 model are practically identical and are both represented by the solid line in Figure 10. The agreement with experiment is not as good as claimed by Schneider36, but is considered satisfactory. 93 Figure 10. Comparison of Experimental Rate Constant with RRKM Calculation. 94 0.61 0.2“- . 230.4°C(Ref. 36) 0 226°C 0.15 .,- . 1 J, 1'0 102 163 Pressure (mm) Figure 10. 95 The absolute positioning of the fall-off curve is de- pendent on the assumption of strong collisions, and ex- tremely sensitive to the value of koa’ whidlis Obtained experimentally by extrapolating a plot of k.1 XE: p_1/2 to p = 0, and is subject to considerable experimental error unless much more extensive high—pressure data are obtained. The high-pressure rate constants obtained in this study, by Schneider36, and the RRKM calculated values for both models are compared in Table 8. The agreement between the present work and that of Schneider is good. Both models give similar results in good agreement with experi- ment, although the agreement with the 8/30 model is somewhat better. 3. Carbon-13 Kinetic Isotope Effect The rate constants for the isomerization of 13CH3NC (k1) and CH3N13C (kg) were calculated as a function of pressure by RRKM in the same manner as just described for CH3NC (k) by simply changing the input data in Table 7, p. 91 appropriate for the molecule in question. The isotOpe effects r1 = k/k1 and r2 = k/k2 were then calculated as a ratio of the apprOpriate rate constants at each pres- sure, and an "average" isotOpe effect r determined as described in Section A of this chapter. The RRKM eXpression for an isotOpe effect k/k' at high pressures reduces to 96 Table 8. Comparison of limiting high-pressure rate constant 1 105 k sec” RRKM Calculated This Study Schneider36 8/30 10/40 213°C 25.0 --- 23.0 28.4 226°C 75.0 92.5(230.40C) 64.6 80.0 243.4°C 267 --- 238 294 Arrhenius Parameter Ea(Kcal/mole) 38.35 38.35 38.363 38.376 A (sec—1) 13.65 13.61 13.61 13.70 97 * + ' (k/k ) H —-II. -Q‘" --QV ( / ) ." ' .? , . exp AE RT , 00; Ir. Qv Qv c where the symbols have been previously defined. The IrQ*Q+ term is always close to unity for carbon-13 iso- tope effects, and the magnitude of the calculated isotope effect is nearly determined by the value of AEC. The calculated isotope effects r1 and r2 are thus depend- ent upon the assumption discussed earlier that ABC ~'AEa for both effects. However, as the value for C-13 isotope effects in unimolecular reactions is very close to 20 cal/ mole observed for AEa in this study, the assumption seems reasonable. Furthermore, changes in vibrational frequency pattern required to change AEC also changes the IrQ*Q+ ratio, so that the adjustment is not completely arbitrary. In all of the model calculations in this work, the pre- scriptions and limitations were adhered to rigidly and con- sistently, and changes made in the complex model for one molecule were carried through as corresponding changes for the other molecules. Thus, modest adjustments: of this nature on the final frequency patterns would not effect the isotope fall-off or the magnitude of the effect un- realistically. -Nevertheless, the calculated isotope effect is much more sensitive to details of the complex frequency patterns. The comparison of the calculated average isotOpe effect r = k/k' with experiment is shown in Figure 11 at 226°C. Comparable agreement is obtained at 243.4°C, and 98 .mcoflumasoamo Exam Hwooz ov\oa pom om\w £DH3 Doomwm OQODOmH Housmaflnmmxm mo somHHmQEoo .HH musmflm 99 .HH mesons AEEV OHSmmmum we «be «an on o.H . . a . n1 5 en moo.H . Ooomm . zxmm Umumadoamo III Ilwoo H HmucmEHHmmxm O ow\0H Itouo.H o 0 11E x o --wno.e 0 ll \\3 O 1- mac. H on? o I I)» 2V9 .uwHo.H I) .O 100 though only a few low-pressure results were obtained at 213°C, the present model is consistent with those results. The agreement generally is quite satisfactory over the pres- sure range studied. Plotting hhe data on a larger scale indicates clearly, however, that the 8/30 model fits slightly better than the 10/40 model. The main difference in the results of the two models, however, is between the high and extremely low pressure regions, where the 8/30 model pre- dicts a smaller Spread of extrenum values than does the 10/40 model. More data in these regions would be invalu- able for refinement of the complex model. The values of r1,r2, and the calculated average iso- tope effect r are compared at several pressures in Table 9. As can be seen from the results, the isotOpe effect aris— ing from labeling the isonitrile carbon is subStantially larger than that arising from labeling the methyl position. This effect was found in all of the models investigated; in fact, attempts to reverse this trend of changing the frequency patterns in the indicated direction as far as physicalhrreasonable were unsuccessful. This differential effect is not entirely unexpected, since the vibrational analysis revealed that labeling the methyl carbon had a much less pronounced effect on the frequencies associated with the linear CNC submolecule than did isotOpe substi— tution at the isonitrile carbon. The results substantiate the mechanism proposed by Rabinovitch and co—workers on the basis of the isomerization 101 Table 9. Calculated values of r1, r2, and average r at 226°C. r1 r2 r P(mm) 8/30 10/40 8/30 10/40 8/30 10/40 00 1.01701 1.01610 1.01962 1.02105 1.018315 1.01857 104 1.01698 1.01606 1.01961 1.02104 1.01830 1.01855 103 1.01674 1.01577 1.01947 1.02088 1.018105 1.01833 103 1.01495 1.01361 1.01841 1.01968 1.01668 1.01665 10 1.00725 1.00627 1.01425 1.01482 1.01075 1.01055 102 rate constant fall-off and the deuterium isotope effect. The calculated carbon-13 isotope effect is more sensitive to the details of the complex frequency pattern than either of the other results, and the results indicate an increased "tightening" of the complex structure to that proposed pre- viously; in particular, the results indicate that CNC bending frequency remaining as a "ring deformation" fre- ’quency of the complex is raised substantially from that in the molecule, a result to which the rate constant fall-off and deuterium isotope effect are insensitive. Confirmation of the new details of the complex vibrational frequency pattern will depend upon extending the range of investiga- tion to both higher and lower pressures, and in particular to determining r1 and/or r2 separately in order to check the assumptions in the "averaging" process employed in this study. It is not expected that the temperature dependences of r1 and r2 will be found to be very different from one another, so that the results of this study should be valid at least in direction and approximately in magnitude. 1. 10. 11. 12. 13. 14. 15. 16. 17. N. F. R. BIBLIOGRAPHY B. Slater, "Theory of Unimolecular Reactions", Ithaca, New York, Cornell Univ. Press, 1959. A. Lindemann, Trans. Faraday Soc., 11, 598 (1922). . S. Johnston, "Gas Phase Reaction Rate Theory", The Ronald Press Company, New York, 1966. . N Hinshelwood, "The Kinetics of Chemical Change". Oxford Univ. Press, 1940. K. Rice, and H. C. Ramsperger, J. Am. Chem. Soc., 42, 1617 (1927). S. 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Chem., To be published. 20. L. B. Sims and P. E. Yankwich, In preparation. 21. F. J. Fletcher, B. S. Rabinovitch, K.,W. Watkins, and D. J. Locker,-J. Phys. Chem., 25, 2823 (1966). 22. s. Arrhenius, z. physik, Chem., 3, 226 (1889).. 23. H. S. Johnston, J. Chem. Phys., 55, 1103 (1952). 24. T. L. Hill, "Introduction to Statistical Thermodynamics", Reading, Mass., Addison-Wesley Publ. Co., Inc., 1960. 25. N. B. Slater, Phil. Trans. Roy. Soc., (London), A246, 57 (1953). 26. N. C. Hung and.D. J. Wilson, J. Chem. Phys., 55, 828 (1963). 27. E. Thiele and D. J. Wilson, J. Chem. Phys., 55, 1256 (1961). 28. S. W. Benson, J. Chem. Phys., 55, 521 (1961). 29. O. K. Rice, J. Chem. Phys., 55, 1588 (1961). 30. S. Glasstone, K. J. Laidler, and H. Eyring, “The Theory of Rate Processes", New York, McGraw-Hill Book Co., 1941. 31. G. M, Wieder, Ph.D. Thesis, Polytechnic Institute of Brooklyn, 1960. 32. R. B. Bernstein, J. Phys. Chem., 55, 893 (1952). 33. B. S. Rabinovitch, D. W. Setser, and F. W. 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APPENDIX Studies Involving Labeled Methyl Isocyanide 13CH3NC Labeled methyl isocyanide (13CH3NC) was prepared from labeled barium carbonate Ba13CO3, 55 atom percent in a four step reaction sequence as follows54: Step I. Preparation of 13c02: Ba13co3 + 2HClO4 -—-————> Ba(ClO4)2 + H20 + 13co2 Twelve and one-half milliliters of 70% HClO4 was slowly added to a frozen mixture of 3.25 grams of Ba13CO3 in 6 ml of H20. The mixture was allowed tOVfimm.slow1y and the re- sulting C02 was collected in a trap. (The CO; was separated from the water and other products and purified by standard vacuum techniques. Step II. Preparation of 13CH3OH: ROH a) 4 13cc2 + 3 LiAlH4 > LiA1(O13CH3)4 + 2 1.111102 where ROH = diethylcarbitol(diethylene glycol di- ethyl ether). b) L1A1(013CH3)4 + 4R'OH ——> LiA1(0R')4 + 13CH30H where R'OH = butyl carbitol(diethylene glycol, mono butyl ether). The 13C02 obtained in Step I was slowly added to a frozen mixture of 1.8 grams of LiAlH4 dissolved in 190 ml of diethyl carbitol. After all the C02 was adsorbed the mixture was allowed to come to room temperature and 30 grams 106 107 of butyl carbitol added slowly. After refluxing at 70°C for 2 hours, the 13CH3OH was distilled into a trap at -196°C. °Impurities were removed by vacuum distillation from a salt bath at -20°C. Step III. Preparation of 13CH3I: 13CH30H + HI -——————e 13CH3I + H20 The 13CH30H obtained from Step II was transferred to a heavy wall glass reactor and cooled with liquid N2. Twenty-five milliliters of HI (density = 1.7 g/ml) was added and the mixture heated to 90° for 2 hours. The product was purified by passage through a drying train of soda lime and P205 and collected in a sample bulb at -196°C. Step IV. Preparation of 13CH3NC: a) 13CH31 + 2AgCN -—> 13CH3Nc-AgCN + AgI b) 13 . ‘ + ‘ CH3NC AgCN + KCN ——e CH3NC + Ag(CN)2 + K + I Labeled methyl isocyanide (13CH3NC) was prepared as described in Chapter III. The 13CH3NC (55.8% label in methyl position was mixed with normal CH3NC (natural abundance label in both positions) so that the final labeling in methyl position was about 3% since isotOpe-ratio mass spectrometer used in this study is limited to a maximum 13C02/C02 ratio of 10%, the signal/ noise ratio increases rapidly with isotopic content of the) carbon dioxide introduced. The labeled methyl isocyanide was reacted, analyzed, 108 combusted, and the resulting COz prepared for mass spectro- metric analysis exactly as described for normal methyl isocyanide in Chapter III. The mass Spectrometric results were, however, of such poor quality for the runs with labeled reactant that no useful results were obtained. No explanation of the poor Operation of the mass Spectometer for these samples is evident; however, similar difficulties have been encountered with enriched materials before by the mass spectrometer laboratory at the University of Illinois. ”'7I’III))I)))(I))))I[)[)I1))))I))IIs