Frequency, of collisions

The frequency of collisions and consequent deviations from an initial ion trajectory... 

The experimental data in Table l-II show that decreasing the volume by one-half doubles the pressure (within the uncertainty of the measurements). How does the particle model correlate with this observation We picture particles of oxygen bounding back and forth between the walls of the container. The pressure is determined by the push each collision gives to the wall and by the frequency of collisions. If the volume is halved without changing the number of particles, then there must be twice as many particles per liter. With twice as many particles per liter, the frequency of wall collisions will be doubled. Doubling the wall collisions will double the pressure. Hence, our model is consistent with observation Halving the volume doubles the pressure. 

Relations (2.46) and (2.47) are equivalent formulations of the fact that, in a dense medium, increase in frequency of collisions retards molecular reorientation. As this fact was established by Hubbard within Langevin phenomenology [30] it is compatible with any sort of molecule-neighbourhood interaction (binary or collective) that results in diffusion of angular momentum. In the gas phase it is related to weak collisions only. On the other hand, the perturbation theory derivation of the Hubbard relation shows that it is valid for dense media but only for collisions of arbitrary strength. Hence the Hubbard relation has a more general and universal character than that originally accredited to it. 

How does the frequency of collisions of the molecules of a gas with the walls of the container change as the volume of the gas is decreased at constant temperature Justify your answer on the basis of the kinetic model of gases. 

The following factors affect net diffusion of a substance (1) Its concentration gradient across the membrane. Solutes move from high to low concentration. (2) The electrical potential across the membrane. Solutes move toward the solution that has the opposite charge. The inside of the cell usually has a negative charge. (3) The permeability coefficient of the substance for the membrane. (4) The hydrostatic pressure gradient across the membrane. Increased pressure will increase the rate and force of the collision between the molecules and the membrane. (5) Temperature. Increased temperature will increase particle motion and thus increase the frequency of collisions between external particles and the membrane. In addition, a multitude of channels exist in membranes that route the entry of ions into cells. 

Gas density has a significant effect on the interactions among molecules of a gas. As molecules move about, they collide regularly with one another and with the walls of their container. Figure 5-13 shows that the frequency of collisions depends on the density of the gas. At low density, a molecule may move all the way across a container before it encounters another molecule. At high density, a molecule travels only a short distance before it collides with another molecule. As our Tools for Discovery Box describes, many scientific experiments require gas densities low enough to provide collision-free environments. 

The rate of particle agglomeration depends on the frequency of collisions and on the efficiency of particle contacts (as measured experimentally, for example, by the fraction of collisions leading to permanent agglomeration). We address ourselves first to a discussion of the frequency of particle collision. 

Frequency of Collisions between Particles. Particles in suspension collide with each other as a consequence of at least three mechanisms of particle transport ... 

The rate of coagulation of particles in a liquid depends on the frequency of collisions between particles due to their relative motion. When this motion is due to Brownian movement coagulation is termed perikinetic when the relative motion is caused by velocity gradients coagulation is termed orthokinetic. 

The frequency of binary encounters during perikinesis is determined by considering the process as that of diffusion of spheres (radius a2 and number concentration n2) towards a central reference sphere of radius a, whence the frequency of collision I is given by 27 ... 

Assuming an attractive potential only, given by equation 5.26, Smoluchowski showed that the frequency of collisions per unit volume between particles of radii ax and a2 in the presence of a laminar shear gradient y is given by ... 

An interesting question is why reactions without activation barriers actually occur with different rates. The reason has to do with the preexponential term (or A factor ) in the rate expression, which depends both on the frequency of collisions and their overall effectiveness. These factors depend on molecular geometry and accessibility of reagents. Discussion has already been provided in Chapter 1. 

An understanding of reaction rates can be explained by adopting a collision model for chemical reactions. The collision theory assumes chemical reactions are a result of molecules colliding, and the rate of the reaction is dictated by several characteristics of these collisions. An important factor that affects the reaction rate is the frequency of collisions. The reaction rate is directly dependent on the number of collisions that take place, but several other important factors also dictate the speed of a chemical reaction. 

Feed material in ball mills is nsnally smaller than about 50 p.m, and the solids contents of slurries range from 30% to 70%. The size of the spherical grinding media is in the range of 0.5-5 mm. Very rapid attrition is produced in ball mills by the intense combination of compression and shearing forces and the frequency of collisions, which is very high. 

Given the same concentration of CH and Cl- or Br-, the frequency of collisions should be the same. Because of the similarity of the two reactions, A5 for each is about the same. The difference must be due to the AH, which is less (17kJ/mol) for Cl- than for Br- (75kJ/mol). 

The frequency of collisions is also expected to be greater in a polydisperse system than in a monodisperse system by the same logic as presented in item 1. 

The primary condition for a bimolecular reaction is the close approach of iwo interacting partners. In ground state, the molecules can approach as close as their van der Waals radii and they are said to be in collision. The frequencies of collisions between unlike molecules and like molecules are given by kinetic theory of gases. 

Frequency of collisions. The mean frequency of collisions is similarly expressed in the hard spheres approximation as... 

The Boltzmann distribution of the populations of a collection of molecules at some temperature T was discussed in Section 8.3.2. This distribution, given by Eq. 8.46 or 8.88, was expressed in terms of the quantum mechanical energy levels and the partition function for a particular type of motion, for instance, translational, vibrational, or rotational motion. It is useful to express such population distributions in other forms, particularly to obtain an expression for the distribution of velocities. The velocity distribution function basically determines the (translational) energy available for overcoming a reaction barrier. It also determines the frequency of collisions, which directly contributes to the rate constant k. 

The one-dimensional velocity distribution function will be used in Section 10.1.2 to calculate the frequency of collisions between gas molecules and a container wall. This collision frequency is important, for example, in determining heterogeneous reaction rates, discussed in Chapter 11. It is derived via a change of variables, as above. Equating the translational energy expression 8.9 with the kinetic energy, we have... 

Collisions between Identical Molecules The frequency of collision between a molecule and others of the same chemical species (i.e., 1-1 or 2-2 collisions) is very similar to Eq. 10.49, with a few correction terms. Beginning with Eq. 10.49, write... 

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