Rate constant for unimolecular dissociation

The rate constants for unimolecular dissociation of the intermediate ions suggested earlier indicate that all ions containing seven or more carbon atoms arise from reactions of the dissociation products of Steps 9, 13, and 17 when pressures are of the order of a few torr and of Step 20 and its analogues at pressures in excess of a few hundred torr. The product ions are generally quite complex, and the simple exothermicity rule given earlier will not apply. Thus, we may well expect that there will be inefficient ion-molecule reactions in the sequences originating with these ions as well. 

The rate constants for unimolecular dissociation reactions were adjusted to tne high pressure of the supercritical water system by using high pressure rate constants, k, where applicable. For dissociations still in the low pressure... 

The rate constant ) for unimolecular dissociation defines the resulting El mass spectra [26]. Ions with dissociation rate constants A (E) < 10 s" can reach the detector as molecular ions since the total time in mass spectrometers 10 s. Those with rate constants )> 10 s are unstable ions and fragment in the ion source, while the intermediate situation (10 s >A(E)> 10 s" ) represents metastable ions (see below) that fragment between the ion source and the detector. Figure 2.2 illustrates the relative portions of stable, metastable, and unstable ions in an internal energy distribution curve. 

What we want to compute is HE), the rate constant for unimolecular dissociation at the total energy E. The quickest route to this result is to use detailed balance. We equate the rate of association of the products to the rate of dissociation into products when both the energy-rich molecule and the products are at equilibrium. Let k E) be the rate constant for crossing the barrier from the products valley into the well. k(J ) is known to us from transition state theory, Eq. (6.5), k(E) = N (E — ), where/0p( ) is the density of states of the... 

Rate coefficients for recombination reactions are related to those for dissociation via the equilibrium constant, which can generally be calculated from thermodynamical information with a high degree of precision, although the accuracy depends on the quality of the thermodynamic data. The rate coefficients are pressure dependent and the theoretical framework of unimolecular reactions can therefore be used to describe them. Because there is little or no activation energy for the recombination process, rates of radical association reactions can be measured over a wide range of temperatures and can be used, in combination with thermodynamic information, to calculate rate coefficients for unimolecular dissociations. The availability of data for a number of radical recombination reactions over a wide range of pressures and temperatures makes these reactions excellent test beds for theoretical models of pressure dependent reactions. 

In this scheme, kq is the rate constant for unimolecular decay of the excited state, kM and k tf are diffusion-controlled rate constants, k = ka is the unimolecular rate constant for electron transfer, k a is the rate constant for the backward reaction of rate constant ka, kr is the rate constant for reverse electron transfer to ground-state reactants, and kp is the rate constant for radical ion dissociation or trapping reactions in the presence of scavengers. Applying a steady-state treatment to the various intermediates in Eq. (3.11) one can evaluate kq (Eq. 

Pesiherbe G H and Hase W L 1996 Statistical anharmonic unimolecular rate constants for the dissociation of fluxional molecules. Application to aluminum clusters J, Chem. Rhys. 105 7432-47... 

Song K and Hase W L 1998 Role of state specificity in the temperature- and pressure-dependent unimolecular rate constants for H02->H+02 dissociation J. Phys. Chem. A 102 1292-6... 

The first indication that A-acyloxy-A-alkoxyamidcs reacted by an acid-catalysed process came from preliminary H NMR investigations in a homogeneous D20/ CD3CN mixture, which indicated that A-acetoxy-A-butoxybenzamide 25c reacted slowly in aqueous acetonitrile by an autocatalytic process according to Scheme 4 (.k is the unimolecular or pseudo unimolecular rate constant, K the dissociation constant of acetic acid and K the pre-equilibrium constant for protonation of 25c).38... 

In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2lT"], shows that. 

Figure 19. Dependence of the unimolecular dissociation rate constant for H2O loss from the cluster ion, (H20)4H% on pressure of CH4 in the FTICR cell.

Again the radiative association kinetics described above allow a direct comparison for some realistic values of k and k. For most chemically activated systems at the threshold for unimolecular dissociation, the observed radiative rate constants are of the order of 10-100 s and hence are much below the values expected for k of about 10 s . Therefore, the first limit is most likely to be valid, with the interesting conclusion that the observed unimolecular dissociation rate constant will depend only on the photon density and the absorption cross section (rate constant) at a given wavelength. 

Rapid Equilibrium Case. In the absence of significant amounts of product (i.e., initial rate conditions thus, [P] 0), the rate expression for the rapid equilibrium random Bi Uni mechanism is v = Uniax[A][B]/(i iai b + i b[A] + i a[B] + [A][B]) where is the dissociation constant for the EA complex, and T b are the dissociation constants for the EAB complex with regard to ligands A and B, respectively, and Umax = 9[Etotai] where kg is the forward unimolecular rate constant for the conversion of EAB to EP. Double-reciprocal plots (1/v v. 1/[A] at different constant concentrations of B and 1/v v. 1/[B] at different constant concentrations of A) will be intersecting lines. Slope and intercept replots will provide values for the kinetic parameters. 

Where (H20) is the first order rate constant for the uncatalyzed reaction at a given water concentration, k3 = A2/[H20], A2 = Ac/[C1 ], kc = ki (catalyzed) + kx (uncatalyzed), and [Cl-] is the concentration of chloride ion from neutral salts. They again oppose the Swain mechanism on the basis a) that the unimolecular dissociation of the pentacovalent complex should be subject to electrophylic catalysis, b) that the steric effects are too great, c) that symmetrical chloride exchange is... 

The RRKM theory of unimolecular reactions predicts that the rate constant for dissociation will be given by eq. (5-3). The probability of populating a state with energy Ev restricted into the chromophore vibrations is proportional to the ratio of the density of van der Waals states at E — Ev to that at ... 

The dynamics near the TS have been the subject of many theoretical [52-66] and experimental [24,25] investigations. The experiments of Lovejoy and co-workers [24,25] see the TS via the photofragment excitation spectra for unimolecular dissociation of excited ketene. They have shown that, in the vicinity of the barrier, the reaction rate is controlled by the flux through quantized thresholds. The observability of quantized thresholds in the TS was first discussed by Chatfield et al. [23]. Marcus pointed out that this indicates that the transverse vibrational quantum numbers might indeed be approximate constants of the motion in the saddle region [60]. 

Fig. 2.21. (a) Time-resolved LIF decay profiles for two closely spaced rotational levels of vibrationally excited CH3O (X). The solid line is an exponential fit for the decay convoluted with the dump laser pulse shape function, (b) Measured state specific unimolecular dissociation rate constants for CH3O (X) compared to calculated k E, J) curves without and with tunneling corrections. 

From the measurement of the time of flight of the cations their dissociation rates can be calculated and, using statistical theory, it was possible to conclude that the unimolecular rate constant for dissociation (of the order of 10 s " at / = 10-10.5 eV) was too small by a factor of 10 for the possibility that the bicyclobutane cation itself could be the immediate precursor of the fragments. The results were suggestive that a complete isomerization to the cation of 1,3-butadiene occurs before dissociation. 

The specific rate constants of interest to the ECD and NIMS are dissociative and nondissociative electron attachment, electron detachment, unimolecular anion dissociation, and electron and ion recombination. The reactions that have been studied most frequently are electron attachment and electron and ion recombination. To measure recombination coefficients, the electron concentration is measured as a function of time. The values are dependent on the nature of the positive and negative ions and most important on the total pressure in the system. Thus far few experiments have been carried out under the conditions of the NIMS and ECD. However, the values obtained under other conditions suggest that there is a limit to the bimolecular rate constant, just as there is a limit to the value of the rate constant for electron attachment. The bimolecular rate constants for recombination are generally large, on the order of 10 7 to 10-6 cc/molecule-s or 1014 to 1015 1/mole-s at about 1 atm pressure. Since the pseudo-first-order rate constants are approximately 100 to 1,000 s 1, the positive-ion concentrations in the ECD and NIMS are about 109 ions/cc. 

The PES calculated at the G2M (CC2)//PW91PW91/6-311-i-G(3df) level is shown in Fig. 11. The key structures of species involved in this reaction are shown in Fig. 12. TSl is the transition state for the OCIO ClOO isomerization reaction with a barrier of 63.3 kcal/mol, whereas TS2 is that for the CIO O C10 0 isomerization with a barrier of 61.5 kcal/mol. Predicted rate constants for the production of O + CIO and Cl + O2 resulted directly from the unimolecular decomposition processes with no contributions from the isomerization reactions. Comparison of the predicted ClOO decomposition rate with experimentally available values is shown in Fig. 13. The low- and high-pressure rate constants for OCIO and ClOO dissociations can be expressed by ... 

Rate constants for three distinct competing processes were separately determined solvolysis k, unimolecular k, and bimolecular k2. The Hammett equation with cross-terms was applied to the effects of substituents X in the nucleophile and Z in the leaving group on the analysed rate constants, but in most cases the pxz term was negligible. The Hammett equation with cross-terms has also been applied to the reactions of Z-substituted benzyl X-benzenesulfonates with Y-substituted thiobenzamides in acetone at 45 The findings pz < 0 and pyz > Pxz indicate that this reaction proceeds by a dissociative 5ivr2 mechanism. 

Figure A3.12.3. Harmonic RRKM unimolecular rate constants for C2HJ—>H+C2H4 dissociation classical...

The classical anharmonic RRKM rate constant for a fluxional molecule may be calculated from classical trajectories by following the initial decay of a microcanonical ensemble of states for the unimolecular reactant, as given by equation 1A3.12.41. Such a calculation has been performed for dissociation of the Alg and A1j3 clusters using a model analytic potential energy function written as a sum of Lennard-Jones and Axelrod-Teller potentials [30]. Stmctures of some of the Alg minima, for the potential function, are shown in figure A3.12.6. The deepest potential minimum has... 

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