Collision theory experimental rates compared

The reactions of the bare sodium ion with all neutrals were determined to proceed via a three-body association mechanism and the rate constants measured cover a large range from a slow association reaction with NH3 to a near-collision rate with CH3OC2H4OCH3 (DMOE). The lifetimes of the intermediate complexes obtained using parameterized trajectory results and the experimental rates compare fairly well with predictions based on RRKM theory. The calculations also accounted for the large isotope effect observed for the more rapid clustering of ND3 than NH3 to Na+. 

Consideration of a variety of other systems leads to the conclusion that very rarely does the collision theory predict rate( constants that will be comparable in magnitude to experimental values. Although it is not adequate for predictions of reaction rate constants, it nonetheless provides a convenient physical picture of the reaction act and a useful interpretation of the concept of activation energy. The major short-... 

The activation energy is defined by a=—7 dln/ (T)/d(l/T). Substituting the rate coefficient expression of equation (60), collision theory predicts that Fa — Vq+ /2RT, and in addition, from equation (58) it predicts that A — ( nksT/exp(l/2). Thus, the SCT model predicts that both the activation energy and the pre-exponential factor are temperature dependent quantities. To test collision theory, experimentally determined values of Fa and A can be compared with the above... 

In summary, polymeric flocculants generally increase peri-kinetic flocculation rates compared with perikinetic coagulation rates. This is not necessarily true for orthokinetic flocculation, and experimental results in the literature are seemingly in conflict. Collision rate theory predicts that the polymer adsorption step may become rate limiting in orthokinetic flocculation. The present study was designed to elucidate the relationship between polymer adsorption rates and particle flocculation rates under orthokinetic conditions. 

Simple collision theory assumes reaction occurs when molecules, with energy greater than a critical minimum, collide. Calculation of two quantities, the total rate of collision of reactant molecules and the fraction of molecules which have at least the critical energy, gives an equation to compare with the experimental Arrhenius... 

We can extend the collision theory to calculate the rate constant for bimolecular reactions of two species, A and B. Comparing observed and predicted rate constants gives the values of P shown in Table 18.1. As the colliding molecules become larger and more complex, P becomes smaller because a smaller fraction of collisions is effective in causing reaction. The steric factor is an empirical correction that has to be identified by comparing results of the simple theory with experimental data. It can be predicted in more advanced theories but only for especially simple reactions. 

The PSS method was also used for He (ls2s, 3S) + He (ls2s, 3S) -> He (Is2, 1S) + He+(ls) + e by von Roos (58). The cross section was estimated to be 10"2 sq. A. at 293°K. and is much smaller compared with experimental data (56). Besides the above, Ferguson (22) and Bates et al. (12) investigated similar process by simple collision theory. The processes include metastable excitation as well as the S-P case. Their procedures are similar. According to Bates et al., the rate coefficient for the ionization is expressed as... 

When reaction rates calculated using collision theory are compared to the experimental rates, the agreement is usually poor. In some cases, the agreement is within a factor of 2 or 3, but in other cases the calculated and experimental rates differ by 10 to 10. The discrepancy is usually explained in terms of the number of effective collisions, which is only a fraction of the total collisions owing to steric requirements. The idea here is that in order for molecules to react, (1) collision must occur, (2) the... 

This equation is called the Arrhenius expression and is the fundamental equation representing the temperature dependence of reaction rate constants. Comparing the Arrhenius expression Eq. (2.39), with rate constant Eq. (2.33) by the collision theory and (2.38) by the transition state theory, the temperature dependence of the exponential factor is exactly the same as derived by these theories, and Ea of the Arrhenius expression corresponds to the activation energy Ea of the transition state theory. A plot of the logarithm of a reaction rate constant, In k against MRT, is called an Arrhenius plot, and the experimental value of activation energy can be obtained from the slope of the Arrhenius plot. This linear relationship is known to hold experimentally for numerous reactions, and the activation energy for each reaction has been obtained. 

Meanwhile, the pre-exponential factor A in the Arrhenius Eq. (2.39) is the temperature independent factor related to reaction frequency. Comparing the Eq. (2.33) for the collision theory and Eq. (2.38) with the transition state theory, the pre-exponential factors in these theories contain temperature dependences of T and T respectively. Experimentally, for most of reactions for which the activation energy is not close to zero, the temperature dependence of the reaction rate constants are known to be determined almost solely by exponential factor, and the Arrhenius expression holds as a good approximation. Only for the reaction with near-zero activation energy, the temperature dependence of the pre-exponential factor appears explicitly, and the deviation from the Arrhenius expression can be validated. In this case, an approximated equation modifying the Arrhenius expression can be used. 

Collision rate constants for reactions resulting in N2H formation were predicted by classical theories such as the Langevin ion-induced dipole theory, the locked dipole theory, and the average dipole orientation theory. These rate constants, often compared with experimentally determined rate constants to estimate the reaction efficiency, are not treated in the following text. In case of N2 protonation, see for example [18 to 21], and In case of hydrogen atom abstraction by N2, see [18, 19, 22 to 26]. 

A further advance occurred when Chesnavich et al. (1980) applied variational transition state theory (Chesnavich and Bowers 1982 Garrett and Truhlar 1979a,b,c,d Horiuti 1938 Keck 1967 Wigner 1937) to calculate the thermal rate coefficient for capture in a noncentral field. Under the assumptions that a classical mechanical treatment is valid and that the reactants are in equilibrium, this treatment provides an upper bound to the true rate coefficient. The upper bound was then compared to calculations by the classical trajectory method (Bunker 1971 Porter and Raff 1976 Raff and Thompson 1985 Truhlar and Muckerman 1979) of the true thermal rate coefficient for capture on the ion-dipole potential energy surface and to experimental data (Bohme 1979) on thermal ion-polar molecule rate coefficients. The results showed that the variational bound, the trajectory results, and the experimental upper bound were all in excellent agreement. Some time later, Su and Chesnavich (Su 1985 Su and Chesnavich 1982) parameterized the collision rate coefficient by using trajectory calculations. 

Berend and Benson [49] have compared experimental rotational relaxation rates for / -H2-/ -H2, />-H2-He, and o-D2-He with their classical theory utilizing the two-dimensional model of Figure 3.5, with atom-centered Morse potentials. Their conclusion that H2-H2 collisions are more effective than are H2-He collisions differs from the predictions of Roberts and is not confirmed experimentally however, there is fair agreement with regards to both magnitude and temperature dependence, particularly for the H2-H2 case. 

The results presented by KPS were mostly in the form of integral cross sections as a function of collision velocity and thermal rate constants as a function of temperature. There were no experimental cross sections to compare with back then, so most of the analysis was concerned with the comparison of thermal rate constants with either experiment, or with other theories such as transition-state theory. The comparisons with experiment were actually quite good, but KPS included many cautions towards the end of their paper to note the many uncertainties associated with these comparisons. These uncertainties include errors in the potential surface used, uncertainties in the experimental results, and errors due to the use of classical mechanics. They conclude by saying that no unequivocal answer [could] be given concerning. .. the direct applicability of the present study to specific chemical reactions. The authors were, in retrospect, far too pessimistic about the accuracy and usefulness of their results, as I now discuss. 

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