Bimolecular rate coefficient

In a fourth step the cross section is related to a state-selected specific bimolecular rate coefficient... 

Instead of concentrating on the diffiisioii limit of reaction rates in liquid solution, it can be histnictive to consider die dependence of bimolecular rate coefficients of elementary chemical reactions on pressure over a wide solvent density range covering gas and liquid phase alike. Particularly amenable to such studies are atom recombination reactions whose rate coefficients can be easily hivestigated over a wide range of physical conditions from the dilute-gas phase to compressed liquid solution [3, 4]. 

The ions or cluster ions are thermalized by collisions with an inert carrier gas (usually helium), although often argon or even nitrogen is employed. Neutral reactant gas is added through a reactant gas inlet at an appropriate location downstream in the flow tube, and allowed to react with the injected ions. Rate coefficients, k, are determined by establishing pseudo-first-order reaction conditions in which the reactant ion concentration is small compared to the reactant neutral concentration. Bimolecular rate coefficients, k, are obtained from the slope of the natural logarithm of the measured signal intensity, /, of the reactant ion versus the flow rate (2b of reactant gas 45,48-50... 

Lenhardt et al. [30] conducted the first direct study of the reaction of butyl radicals with 02, reporting room-temperature rate coefficients for n-butyl, s-butyl, t-butyl, and 3-hydroxy s-butyl, where the radicals were prepared by broadband flash photolysis of the iodides. The bimolecular rate coefficients were independent of pressure over the range 1 to 4 torr, showing that these association reactions are in the high-pressure limit. The rate coefficients increased in the order n-butyl < s-butyl < f-butyl < 5-hydroxy s-butyl. On the other hand, the CH3 + 02 association has been shown to be well into the unimolecular falloff at pressures from 0.5 to 6 torr at room temperature [62]. Falloff behavior is not unexpected for the smaller CH3 radical, in contrast with C4H9 radicals. Methyl was generated by 193-nm photolysis of nitromethane. 

Figure 1. Energy-level diagram for excimer formation. Symbols represent hv, absorbed photon k emissive rate from the monomer species k, bimolecular rate coefficient for formation of the pyrene excimer k, unimolecular rate coefficient for dissociation of the excimer and k, emissive rate from the excimer species. Note no ground-state association is indicated.

Figure 9 shows the temperature dependence of the recovered kinetic rate coefficients for the formation (k bimolecular) and dissociation (k unimolecular) of pyrene excimers in supercritical CO2 at a reduced density of 1.17. Also, shown is the bimolecular rate coefficient expected based on a simple diffusion-controlled argument (11). The value for the theoretical rate constant was obtained through use of the Smoluchowski equation (26). As previously mentioned, the viscosities utilized in the equation were calculated using the Lucas and Reichenberg formulations (16). From these experiments we obtain two key results. First, the reverse rate, k, is very temperature sensitive and increases with temperature. Second, the forward rate, kDM, 1S diffusion controlled. Further discussion will be deferred until further experiments are performed nearer the critical point where we will investigate the rate parameters as a function of density. 

The last decade has witnessed an intense interest in the theory of radiative association rate coefficients because of the possible importance of the reactions in the interstellar medium and because of the difficulty of measuring these reactions in the laboratory. Several theories have been proposed these are all directed toward systems of at least three or four atoms and utilize statistical approximations to the exact quantum mechanical treatment. The utility of these treatments can be partially gauged by using them to calculate three body rate coefficients which can be compared with laboratory measurements. In order to explain these theories briefly, it would be helpful to write down equations for the mechanism of association reactions. Consider two species A+ and B that come together with bimolecular rate coefficient kj to form a complex AB+ which can then be stabilized radiatively with rate coefficient kr, be stabilized collisionally with helium with rate coefficient kcoll, or redissociate with rate coefficient k j ... 

We begin by returning to the question of the low-pressure third-order rate coefficient for association reactions. A steady-state treatment of reaction mechanism (2 ) leads to a bimolecular rate coefficient... 

These regularities combined with the approximation 9.25 allow the following order-of-magnitude estimates of ratios A , lk2 of bimolecular rate coefficients of two reaction steps 1 and 2 with enthalpies AH,° and AH2° to be stated ... 

From the slope of plots of lc2i versus pressure Kircher and Sander determined the termolecular rate coefficients and their temperature dependence for M = Ar and N2. The values of these are k(Ar) = 8.4 X 10- exp (1100 K) and k(N2) = 1.9 X lO " exp(980/T) in cm molecule" s . Thus the termolecular rate coefficient in N2 is about 5.1 X 10 at 298 K. The effect of one atmosphere of N2 is to increase the effective bimolecular rate coefficient from about 1.6X10 to about 2.9 X10 cm molecule s . If water vapor is present, a further enhancement about 70% is found with 10 torr H2O at 298 K. The recommended expression for modelling the HO2 + HO2 reaction in air at high pressures and in the presence of water vapor is given by the expression ... 

Kinetic isotopic effect studies of this kind permit a test of the mass dependence predicted by transition state theory or other theories of bimolecular rate coefficients. A qualitative test of various potential energy surfaces can also be made using such data. Using the theory of Bigeleisen and Wolfsberg of kinetic isotopic effects and several methods of constructing potential energy surfaces (Wheeler et al, Sato, Johnston and Parr ) Timmons and Weston ° found no surface which predicted rates to within better than 40 % of the measured values taken as a whole. 

Deisen ° using a shock tube with time-of-flight mass spectrometry detection has investigated the kinetics of the F2-N2F4, system in the range 1100-1600 °K. From an analysis of the variation of NFj with time at different temperatures a bimolecular rate coefficient of 4.8 x lO exp (—14,400/RT) l.mole . sec was obtained for the reaction... 

Pseudo-first-order rate coefficients are obtained from the gradient of a plot of ln[OH], vs t, e.g., Fig. 2.4. If the pseudo-first-order rate coefficient is determined for a number of different ethane concentrations, then the bimolecular rate coefficient for reaction (10) will be the gradient of a plot of k vs [C2H6]. 

Each time the photolysis laser fires a complete profile of the OH decay is obtained and recorded. A number of such decays are stored and averaged to reduce the signal to noise and bimolecular rate coefficients are obtained at a number of different temperatures by the procedures outlined above. 

The reaction cell could be heated and bimolecular rate coefficients were... 

Fig. 2.12. Schematic diagram of a 2-D potential energy curve for a unimolecular reaction. k and are the bimolecular rate coefficients for activation and deactivation respectively by a bath gas M. k, is the rate coefficient for the unimolecular reaction of an energized molecule, A, to give product, P.

There seems little doubt that in radiation induced polymerizations the reactive entity is a free cation (vinyl ethers are not susceptible to free radical or anionic polymerization). The dielectric constant of bulk isobutyl vinyl ether is low (<4) and very little solvation of cations is likely. Under these circumstances, therefore, the charge density of the active centre is likely to be a maximum and hence, also, the bimolecular rate coefficient for reaction with monomer. These data can, therefore, be regarded as a measure of the reactivity of a non-solvated or naked free ion and bear out the high reactivity predicted some years ago [110, 111]. The experimental results from initiation by stable carbonium ion salts are approximately one order of magnitude lower than those from 7-ray studies, but nevertheless still represent extremely high reactivity. In the latter work the dielectric constant of the solvent is much higher (CHjClj, e 10, 0°C) and considerable solvation of the active centre must be anticipated. As a result the charge density of the free cation will be reduced, and hence the lower value of fep represents the reactivity of a solvated free ion rather than a naked one. Confirmation of the apparent free ion nature of these polymerizations is afforded by the data on the ion pair dissociation constant,, of the salts used for initiation, and, more importantly, the invariance, within experimental error, of ftp with the counter-ion used (SbCl or BF4). Overall effects of solvent polarity will be considered shortly in more detail. 

When comparing this relaxation to its condensed phase counterpart one should note a technical difference between the ways relaxation rates are defined in the two phases. In contrast to the bimolecular rate coefficient Argas, in condensed environments the density is high and is not easily controlled, so the relaxation rate is conventionally defined in terms of a unimolecular rate coefficient Acond, defined from dC ldt = —AcondC = — This difference between the two... 

In order to obtain an expression of the bimolecular rate coefficient associated... 

Fig. 2-4. Bimolecular rate coefficient for the reaction OH + N02-> HN03 in nitrogen as a function of number density and temperature. Points indicate measurements of Anastasi and Smith (1976) solid curves were calculated with k0 = 2.6 x 10 30(3 00/ T)29 and / = 1.5x 10 1 (300/ T)13 using the approximation formula of Zellner (1978).

Table 2-3. Effective Bimolecular Rate Coefficients (cm3/ molecule s)a for Several Recombination Reactions as a Function of Altitude in the Atmosphere (Zellner, 1978)... 

Further information on the rate coefficients for the reactions in Eqs. 2a and 2b is given in some recent papers. Gutman and Nelson (1983) used laser-induced fluorescence to study the addition reactions of the (32H3O radical with O2 and NO. The bimolecular rate coefficients for the reaction with NO were observed over the major portion of the transition region from the low- to high-pressure limits and give at room temperature hP = (2.36 0.31) X 10 ilf -sec with N2 as a chaperone and k" = (1.51 0.18) x 10 ° A/ -sec . However the C2H3O radical has two resonance forms. 

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