Kinetic theory of collisions

According to Trautz and Lewis, who gave the first treatment of reaction rates in terms of the kinetic theory of collisions in 1916-1918, the rate of collisions (not yet reaction) between the spheres A and B is jtd u... 

Oxidative chain reactions of organic compounds are current targets of theoretical and experimental study. The kinetic theory of collisions has influenced research on liquid-phase oxidation. This has led to determining rate constants for chain initiation, branching, extension, and rupture and to establishing the influence of solvent, vessel wall, and other factors in the mechanism of individual reactions. Research on liquid-phase oxidation has led to studies on free radical mechanisms and the role of peroxides in their formation. 

The kinetic theory of collisions, which has been so effective in developing the kinetics of vapor-phase reactions, has substantially influenced research on the processes of liquid-phase oxidation and in describing these processes. It has been thought that the lack of laws on which to base liquid-state theory (in contrast to the well-developed kinetic theory of gases) would in principle severely limit the development of a quantitative theory of liquid-phase reactions. At present the characteristics of the liquid state are carefully considered in discussing the mechanism of intermolecular reactions, influence of the medium on reactivity of compounds, etc. 

This shows that bubbles are driven very strongly by the liquid. The relative acceleration can be as much as twice the vector difference of gravity and liquid acceleration. Since the bubbles are essentially mass-less, the analogy to the kinetic theory of collisions is not appropriate. Bubbles do not collide they only come into contact while moving generally in the same direction. 

Consider a reaction between molecules A and B. The rate expression for molecules that are essentially billiard balls, or hard spheres, will be discussed first. Later studied will be features due to the presence of internal degrees of freedom, which are absent in hard spheres. The description of reaction rates in terms of the kinetic theory of collisions was given by Max Trautz in 1916 and William Lewis in 1918. The rate for collisions between hard spheres is... 

Here, a molecule of C is formed only when a collision between molecules of A and B occurs. The rate of reaction r. (that is, rate of appearance of species C) depends on this collision frequency. Using the kinetic theory of gases, the reaction rate is proportional to the product of the concentration of the reactants and to the square root of the absolute temperature ... 

There is a restriction on this simple model for the C0-N02 reaction. According to the kinetic theory of gases, for a reaction mixture at 700 K and concentrations of 0.10 M, every CO molecule should collide with about 109 N02 molecules in one second. If every collision were effective, the reaction should be over in a fraction of a second. In reality, this does not happen under these conditions, the half-life is about 10 s. This implies that not every CO-N02 collision leads to reaction. 

Z, the collision frequency, which gives the number of molecular collisions occurring in unit time at unit concentrations of reactants. This quantity can be calculated quite accurately from the kinetic theory of gases, but we will not describe that calculation. 

The pressure behavior shown in Figure 4-3 is readily explained in terms of the kinetic theory of gases. There is so much space between the molecules that each behaves independently, contributing its share to the total pressure through its occasional collisions with the container walls. The water molecules in the third bulb are seldom close to each other or to molecules provided by the air. Consequently, they contribute to the pressure exactly the same amount they do in the second bulb—the pressure they would exert if the air were not present. The 0.0011 mole of water vapor contributes 20 mm of pressure whether the air is there or not. The 0.0050 mole of air contributes 93 mm of pressure whether the water vapor is there or not. Together, the two partial pressures, 20 mm and 93 mm, determine the measured total pressure. 

The kinetic theory of radon progeny attachment to aerosol particles assumes that unattached atoms and aerosol particles undergo random collisions with the gas molecules and with each other. The attachment coefficient, 3(d), is proportional to the mean relative velocities between progeny atoms and particles and to the collision cross section (Raabe, 1968a) ... 

The BET surface area equation is based on Langmuir s kinetic theory of monolayer gas adsorption on surfaces [6], Langmuir theorized that the collision... 

The species diffusivity, varies in different subregions of a PEFC depending on the specific physical phase of component k. In flow channels and porous electrodes, species k exists in the gaseous phase and thus the diffusion coefficient corresponds with that in gas, whereas species k is dissolved in the membrane phase within the catalyst layers and the membrane and thus assumes the value corresponding to dissolved species, usually a few orders of magnitude lower than that in gas. The diffusive transport in gas can be described by molecular diffusion and Knudsen diffusion. The latter mechanism occurs when the pore size becomes comparable to the mean free path of gas, so that molecule-to-wall collision takes place instead of molecule-to-molecule collision in ordinary diffusion. The Knudsen diffusion coefficient can be computed according to the kinetic theory of gases as follows... 

Arrhenius recognized that for molecules to react they must attain a certain critical energy, E. On the basis of collision theory, the rate of reaction is equal to the number of collisions per unit time (the frequency factor) multiplied by the fraction of collisions that results in a reaction. This relationship was first developed from the kinetic theory of gases . For a bimolecular reaction, the bimolecular rate constant, k, can be expressed as... 

The concept that a gas comprises a large number of distinct particles between which - aside from the collisions - there are no effective forces, has led to a number of theoretical considerations which we summarize today under the designation kinetic theory of gases". 

The gas molecules fly about and among each other, at every possible velocity, and bombard both the vessel walls and collide (elastically) with each other. This motion of the gas molecules is described numerically with the assistance of the kinetic theory of gases. A molecule s average number of collisions over a given period of time, the so-called collision index z, and the mean path distance which each gas molecuie covers between two collisions with other molecules, the so-called mean free path length X, are described as shown below as a function of the mean molecule velocity c the molecule diameter 2r and the particle number density molecules n - as a very good approximation ... 

The collision frequency /xb can be calculated from the kinetic theory of gases. The result is (cf., Atkins, 1982, p. 872)... 

The bi are derived from the collision radii of the molecular species at high temperature and, as in the kinetic theory of gases at moderate pressure, are equal to four times the molecular volume multiplied by Avogadro s number. Despite the use of diminished covolumes in the equation and despite the apparent theoretical basis of the model, the equation is oversimplified and the results of detonation calculations quite clearly show it to be inaccurate. 

Kinetic Theory of Gases Velocity Distribution Speed Distribution Collision Frequency Meen Free Path Determine average and RMS speeds from data Plot radial distribution functions... 

From kinetic theory of gases (see Atkins 1994), the number of collisions per unit area per unit time Z between gas molecules and a wall equals... 

---