Collision rates

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... 

Several processes are unique to ions. A common reaction type in which no chemical rearrangement occurs but rather an electron is transferred to a positive ion or from a negative ion is tenued charge transfer or electron transfer. Proton transfer is also conunon in both positive and negative ion reactions. Many proton- and electron-transfer reactions occur at or near the collision rate [72]. A reaction pertaining only to negative ions is associative detaclunent [73, 74],... 

Several instniments have been developed for measuring kinetics at temperatures below that of liquid nitrogen [81]. Liquid helium cooled drift tubes and ion traps have been employed, but this apparatus is of limited use since most gases freeze at temperatures below about 80 K. Molecules can be maintained in the gas phase at low temperatures in a free jet expansion. The CRESU apparatus (acronym for the French translation of reaction kinetics at supersonic conditions) uses a Laval nozzle expansion to obtain temperatures of 8-160 K. The merged ion beam and molecular beam apparatus are described above. These teclmiques have provided important infonnation on reactions pertinent to interstellar-cloud chemistry as well as the temperature dependence of reactions in a regime not otherwise accessible. In particular, infonnation on ion-molecule collision rates as a ftmction of temperature has proven valuable m refining theoretical calculations. 

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... 

This chapter deals with qnantal and semiclassical theory of heavy-particle and electron-atom collisions. Basic and nsefnl fonnnlae for cross sections, rates and associated quantities are presented. A consistent description of the mathematics and vocabnlary of scattering is provided. Topics covered inclnde collisions, rate coefficients, qnantal transition rates and cross sections. Bom cross sections, qnantal potential scattering, collisions between identical particles, qnantal inelastic heavy-particle collisions, electron-atom inelastic collisions, semiclassical inelastic scattering and long-range interactions. 

B2.2.2.2 COLLISION RATES, COLLISION FREQUENCY AND PATH LENGTH... 

Micellization is a second-order or continuous type phase transition. Therefore, one observes continuous changes over the course of micelle fonnation. Many experimental teclmiques are particularly well suited for examining properties of micelles and micellar solutions. Important micellar properties include micelle size and aggregation number, self-diffusion coefficient, molecular packing of surfactant in the micelle, extent of surfactant ionization and counterion binding affinity, micelle collision rates, and many others. 

Above 600 K, this reaction takes place as a direct result of collisions between CO and N02 molecules. When the concentration of CO doubles (Figure 11.6), the number of these collisions in a given time increases by a factor of 2 doubling the concentration of N02 has the same effect. Assuming that reaction rate is directly proportional to the collision rate, the following relation should hold ... 

S.K. Sinha W.D. Patwardhan, Explosiv-stoffe 16 (10), 223-25 (1968) CA 70,49144 (1969) The mechanism causing the plateau effect in the combustion of proplnts with ad-mixt of Pb compds (ie, the independence of pressure of the combustion rate in a certain range) is discussed. This effect is caused by the transport of free Pb alkyl radicals from the foam zone to the fizz zone, which decomn there, causing a more efficient combustion, and increase the temp of this zone by reaction1 with NO. An increase of pressure is assumed to displace the free radicals from this zone because of the increase of the collision rate . this leads... 

When mass transfer rates are very high, limitations may be placed on the rate at which a component may be transferred, by virtue of the limited frequency with which the molecules collide with the surface. For a gas, the collision rate can be calculated from the kinetic theory and allowance must then be made for the fact that only a fraction of these molecules may be absorbed, with the rest being reflected. Thus, when even a pure gas is brought suddenly into contact with a fresh solvent, the initial mass transfer rate may be controlled by the rate at which gas molecules can reach the surface, although the resistance to transfer rapidly builds up in the liquid phase to a level where this effect can be neglected. The point is well illustrated in Example 10.4. 

However, for the La example, where T = 2p, the minimum is not pronounced. In fact for F/p > 2 the minimum is not obvious and the spectrum of such doublets looks like it is continuously broadened with increase of the collision rate proportional to n. In contrast, for 1 < F/p < 2 the minimum is much deeper. In the extreme case... 

Einwohner T., Alder B. J. Molecular dynamics. VI. Free-path distributions and collision rates for hard-sphere and square-well molecules, J. Chem. Phys. 49, 1458-73 (1968). 

Collision theory is mute about the value of fji. Typically,1, so that the number of molecules colliding is much greater than the number reacting. See Problem 1.2. Not all collisions have enough energy to produce a reaction. Steric effects may also be important. As will be discussed in Chapter 5, fji is strongly dependent on temperature. This dependence usually overwhelms the dependence predicted for the collision rate. 

Considering the fact that the particle-wall collision rate... 

The temperature for conversion between the vapor and a condensed phase depends strongly on pressure. Qualitatively, this is because compressing a gas increases the collision rate and makes condensation more favorable. We describe the quantitative details of this variation in Section 14.5. 

When a reaction proceeds in a single elementary step, its rate law will mirror its stoichiometry. An example is the rate law for O3 reacting with NO. Experiments show that this reaction is first order in each of the starting materials and second order overall NO + 03- NO2 + O2 Experimental rate = i [N0][03 J This rate law is fully consistent with the molecular view of the mechanism shown in Figure 15-7. If the concentration of either O3 or NO is doubled, the number of collisions between starting material molecules doubles too, and so does the rate of reaction. If the concentrations of both starting materials are doubled, the collision rate and the reaction rate increase by a factor of four. 

In 1990, Schroder and Schwarz reported that gas-phase FeO" " directly converts methane to methanol under thermal conditions [21]. The reaction is efficient, occuring at 20% of the collision rate, and is quite selective, producing methanol 40% of the time (FeOH+ + CH3 is the other major product). More recent experiments have shown that NiO and PtO also convert methane to methanol with good efficiency and selectivity [134]. Reactions of gas-phase transition metal oxides with methane thus provide a simple model system for the direct conversion of methane to methanol. These systems capture the essential chemistry, but do not have complicating contributions from solvent molecules, ligands, or multiple metal sites that are present in condensed-phase systems. 

---