Collision rate constants

Gilbert R G, Luther K and Troe J 1983 Theory of thermal unimolecular reactions in the fall-off range. II. Weak collision rate constants Ber. Bunsenges. Phys. Chem. 87 169-77... 

Bhowmik P K and Su T 1986 Tra]ectory calculations of ion-quadrupolar molecule collision rate constants J. Chem. Phys. 84 1432-4... 

Troe J 1977 Theory of thermal unimolecular reactions at low pressures. II. Strong collision rate constants. Applications J. Chem. Phys. 66 4758... 

Effects of particle size on collision rate constants for agglomeration. Left di = 1 pm right d,=10pm. 

Because the collisions between ions and molecules in the gas phase are governed by physical (ion-dipole, ion-induced dipole) rather than chemical forces, it is possible to calculate rather accurately the collision rate constant (6, 7). We then express the efficiency of the reaction as the fraction of collisions which lead to products. 

This question was addressed by use of classical trajectory techniques with an ion-quadrupole plus anisotropic polarizability potential to determine the collision rate constant (k ). Over one million trajectories with initial conditions covering a range of translational temperature, neutral rotor state, and isotopic composition were calculated. The results for the thermally average 300 K values for are listed in the last column of Table 3 and indicate that reaction (11) for H2/H2, D2/D2, and HD /HD proceeds at essentially the classical collision rate, whereas the reported experimental rates for H2/D2 and D2/H2 reactions seem to be in error as they are significantly larger than k. This conclusion raises two questions (1) If the symmetry restrictions outlined in Table 2 apply, how are they essentially completely overcome at 300 K (2) Do conditions exist where the restriction would give rise to observable kinetic effects ... 

In Table 1 (pp. 251-254), IM rate constants for reaction systems that have been measured at both atmospheric pressure and in the HP or LP range are listed. Also provided are the expected IM collision rate constants calculated from either Langevin or ADO theory. (Note that the rate constants of several IM reactions that have been studied at atmospheric pressure" are not included in Table I because these systems have not been studied in the LP or HP ranges.) In general, it is noted that pressure-related differences in these data sets are not usually large. Where significant differences are noted, the suspected causes have been previously discussed in Section IIB. These include the reactions of Hcj and Ne with NO , for which pressure-enhanced reaction rates have been attributed to the onset of a termolecular collision mechanism at atmospheric pressure and the reactions of Atj with NO and Cl with CHjBr , for which pressure-enhanced rate constants have been attributed to the approach of the high-pressure limit of kinetic behavior for these reaction systems. 

This gives a collision rate constant for a second-order reaction as... 

Troe, J., Theory of Thermal Unimolecular Reactions in the Fall-Off Range. Strong Collision Rate Constants, Her. Bunsenges. Phys. Chem., 87, 161-169 (1983). 

In the scheme of Fig. 3, the rate constant k2 is identified with the collision rate constant, kADO, lc 1 = k3 and k2 = 2. Thus the experimental rate constant is given by (35). For exothermic reactions, it is reasonable to assume that k 2 k3, and the observed rate constant will take the form of (36). 

An alternative to the hard-sphere collision rate constant in Eq. 10.155 is used for the case of a Lennard-Jones interaction potential between the excited molecule (1) and the collision partner (2) characterized by a cross section a 2 and well depth en... 

J. Troe. Theory of Thermal Unimolecular Reactions at Low Pressures. II. Strong Collision Rate Constants. Applications. J. Chem. Phys., 66(11) 4758—4775,1977. 

Studies of proton transfers involving small ions with localized charge have shown that these reactions may proceed indeed with rate constants close to or even slightly larger than the collision rate constants predicted by the ADO theory (Mackay et al., 1976). However, rate-constant measurements of proton-transfer reactions between delocalized anions (Farneth and Brau-man, 1976) and sterically hindered pyridine bases (Jasinski and Brauman, 1980) and of SN2 displacement reactions (Olmstead and Brauman, 1977 Pellerite and Brauman, 1980 Pellerite and Brauman, 1983 Caldwell et al., 1984 for a review see Riveros et al., 1985) have shown that the rate constants can span the range from almost collision controlled values down to ones too slow to be observed. For these reactions the wide variation in rate constants has been explained on the basis of a double potential-well model which for a hypothetical SN2 substitution is schematically shown in Fig. 4. 

Here k2 is the collision rate constant which for cases involving polar molecules can be estimated quite well by use of (6). The ratio between kobs and k3 is termed the reaction efficiency, which gives an estimate of the number of collisions resulting in product formation. For an exothermic reaction it can be assumed that 2 4 k3, kobs will then be given by (9), which leads to eqn (10) for the reaction efficiency. The efficiency of the... 

Transfer of energy to another molecule at distance (rate constant k[) or by collision (rate constant k q) (Figure 7.1). 

Lindemann assumed that every collision of an energized A molecule would be deactivating, so that the rate coefficient k- may be identified with the second-order collision rate constant Zam- The rate constant for the reaction step ki was to be determined from experimental results. 

Radiationless transitions occur in complexes formed with a rate constant ki, which equals the collision rate constant, 10 M s for intermolecular processes or the rotational frequency, 10 s" , for intramolecular processes. Assuming the complex dissociates with a rate constant fc-j s v k , the TET rate constant is given by... 

Let us again examine the reaction of A and B. Clearly the reaction cannot occur more rapidly than the rate at which A and B collide. If we assume that the particles behave as hard spheres, then the collision rate constant between these two particles is defined by... 

Rates. Rate data for reaction 4 are shown in Figure 6. What is plotted is not a rate constant for the reaction but a reaction efficiency per collision. Analysis shows that the rate constant for an ion and a polar molecule simply to collide is itself temperature-dependent (28). What is of chemical interest is the property plotted—the fraction of the collisions that actually result in reaction. This reaction efficiency per collision is the ratio of the experimental rate constant to the calculated collision rate constant (29). 

Figure 6. Temperature dependence of the reaction efficiency per collision for the reactions of OD + CH3Cl (open circles), 0D D20 + CH3Cl (filled circles and 0D (D20)2 + CH3Cl (half-filled circles). The reaction efficiency per collision is the experimental rate constant divided by the calculated collision rate constant, calculated by Clary using the adiabatic capture centrifugal sudden approximation (ACCSA) (28). For experimental reasons (29), the measurements were made with completely deuterated...

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