Collisions frequency

To calculate the number of collisions per unit volume and per unit time in air at 1 atm and 25 C (a) between Ng and Og molecules, (b) between pairs of Ng molecules. 

We denote the number of molecules of two kinds per unit volume by Cj, Cg respectively. We denote their masses by respectively 

For the sake of simplicity we shall take the composition of air as 4 parts Ng to 1 part Og. We shall assume collision diameters as follows (Chapman and Cowling, The mathematical theory of non-uniform gases , Cambridge University Press, 1939, p. 229) 

We rewrite formula (1) in terms of the number of moles per unit volume Cl, Cg and the molar masses ( molecular weights ) Afi, Afg. 

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The final equation obtained by Becker and Doting may be written down immediately by means of the following qualitative argument. Since the flux I is taken to be the same for any size nucleus, it follows that it is related to the rate of formation of a cluster of two molecules, that is, to Z, the gas kinetic collision frequency (collisions per cubic centimeter-second). 

The rate of physical adsorption may be determined by the gas kinetic surface collision frequency as modified by the variation of sticking probability with surface coverage—as in the kinetic derivation of the Langmuir equation (Section XVII-3A)—and should then be very large unless the gas pressure is small. Alternatively, the rate may be governed by boundary layer diffusion, a slower process in general. Such aspects are mentioned in Ref. 146. 

Our first result is now the average collision frequency obtained from the expression, (A3.1.10). by dividing it by the average number of particles per unit volume. Here it is convenient to consider the equilibrium case, and to use (A3.1.2) for f. Then we find that the average collision frequency, v, for the particles is... 

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

We start from a model in which collision cross sections or rate constants for energy transfer are compared with a reference quantity such as average Leimard-Jones collision cross sections or the usually cited Leimard-Jones collision frequencies [54]... 

With this convention, we can now classify energy transfer processes either as resonant, if IA defined in equation (A3.13.81 is small, or non-resonant, if it is large. Quite generally the rate of resonant processes can approach or even exceed the Leimard-Jones collision frequency (the latter is possible if other long-range potentials are actually applicable, such as by pennanent dipole-dipole interaction). 

Resonant rotational to rotational (R-R) energy transfer may have rates exceeding the Leimard-Jones collision frequency because of long-range dipole-dipole interactions in some cases. Quasiresonant vibration to rotation transfer (V-R) has recently been discussed in the framework of a simple model [57]. 

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

CFIDF end group, no selective reaction would occur on time scales above 10 s. Figure B2.5.18. In contrast to IVR processes, which can be very fast, the miennolecular energy transfer processes, which may reduce intennolecular selectivity, are generally much slower, since they proceed via bimolecular energy exchange, which is limited by the collision frequency (see chapter A3.13). 

Microwave discharges at pressures below 1 Pa witli low collision frequencies can be generated in tlie presence of a magnetic field B where tlie electrons rotate witli tlie electron cyclotron frequency. In a magnetic field of 875 G tlie rotational motion of tlie electrons is in resonance witli tlie microwaves of 2.45 GHz. In such low-pressure electron cyclotron resonance plasma sources collisions between tlie atoms, molecules and ions are reduced and the fonnation of unwanted particles in tlie plasma volume ( dusty plasma ) is largely avoided. 

A number of simulation methods based on Equation (7.115) have been described. Thess differ in the assumptions that are made about the nature of frictional and random forces A common simplifying assumption is that the collision frequency 7 is independent o time and position. The random force R(f) is often assumed to be uncorrelated with th particle velocities, positions and the forces acting on them, and to obey a Gaussiar distribution with zero mean. The force F, is assumed to be constant over the time step o the integration. 

All of these time correlation functions contain time dependences that arise from rotational motion of a dipole-related vector (i.e., the vibrationally averaged dipole P-avejv (t), the vibrational transition dipole itrans (t) or the electronic transition dipole ii f(Re,t)) and the latter two also contain oscillatory time dependences (i.e., exp(icofv,ivt) or exp(icOfvjvt + iAEi ft/h)) that arise from vibrational or electronic-vibrational energy level differences. In the treatments of the following sections, consideration is given to the rotational contributions under circumstances that characterize, for example, dilute gaseous samples where the collision frequency is low and liquid-phase samples where rotational motion is better described in terms of diffusional motion. 

Electrons from a spark are accelerated backward and forward rapidly in the oscillating electromagnetic field and collide with neutral atoms. At atmospheric pressure, the high collision frequency of electrons with atoms induces chaotic electron motion. The electrons gain rapidly in kinetic energy until they have sufficient energy to cause ionization of some gas atoms. 

Decrease contact displacement to reduce wear Decrease contacting hy lowering mixing and collision frequency (e.g., mixer impeller speed, fluid-hed excess gas velocity, drum rotation speed). 

The ohmic case is the most complex. A particular result is that the system is localised in one of the wells at T = 0, for sufficiently strong friction, viz. rj > nhjlQo. At higher temperatures there is an exponential relaxation with the rate Ink oc (4riQllnh — l)ln T. Of special interest is the special case t] = nhl4Ql. It turns out that the system exhibits exponential decay with a rate constant which does not depend at all on temperature, and equals k = nAl/2co. Comparing this with (2.37), one sees that the collision frequency turns out to be precisely equal to the cutoff vibration frequency Vo = cojln. 

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 ... 

In chemiluminescence, some of the chemical reaction products developed remain in an excited state and radiate light when the excitation is discharged. This is particularly so at low pressures, when the collision frequency is low the excitation is discharged as light radiation. The extra energy bound to the excited molecule can discharge through impact or molecular dissociation. 

The product of the collision energy E(L) and collision frequency f L) is integrated over all crystals in the distribution to obtain the total rate of energy transfer. Different approaches have been used to estimate E(L) and f L), both for particle impacts and turbulent fluid induced attrition. 

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. 

For collision frequencies large compared with the frequency of the electric field, the current remains in phase with the electric field in the reverse case, the current is 90° out of phase. The in-phase component of the current gives rise to an energy loss from the field (Joule heating loss) microscopically, this is seen to be due to the energy transferred from the electrons to the atoms upon collision. 

The quantity / is just a further combination of constants already in Eq. (10-70). The value of Z is taken to be the collision frequency between reaction partners and is often set at the gas-phase collision frequency, 1011 L mol-1 s-1. This choice is not particularly critical, however, since / is nearly unity unless is very large. Other authors29-30 give expressions for Z in terms of the nuclear tunneling factors and the molecular dimensions. 

The change of average z projection of the angular momentum per unit time is its change for a single collision A/ = (D — l)Jo(t) multiplied by the collision frequency Tq 1 ... 

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