Elementary kinetic theory

The properties of temperature, pressure, and composition which have been used in Chapter 1 to define rate laws refer to the averages of these quantities for the system 

The exchange of kinetic energy, and thus velocity, as illustrated will ensure the existence of a distribution of velocities energy is conserved in collisions where velocity is not conserved. 

For our purposes it is most convenient to work with the velocity distribution without regard to individual component directions, since the medium is isotropic. This is expressed in terms of the speed, c 

This equation will be of use later in coimection with the analysis of energy requirements for chemical reactions [ ... only a small percentage will profit by your most zealous energy. —George Gissing], 

With the distribution laws established, we can now attack the problem that is central to a collision theory of reaction the number of collisions experienced per molecule per second in the Maxwellian gas. Clearly the magnitude of this collision number is a function of temperature (through the constant a), and if we define a total collision number, collisions of all molecules per second per volume, it will also depend on molecular density (i.e., concentration). Thus, the two independent variables of concentration and temperature used in power-law rate equations will appear in the total collision number. 

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This result is identical to that obtained in elementary kinetic theory. There is, in effect a contribution of RT to the energy per mole for each of the three directions in space. Furthermore, this result allows the identification /J = 1 fkTy as suggested earlier. 

If not available experimentally, the binary diffusion coefficient, Ay, may also be calculated using elementary kinetic theory (Chapman-Enskog equation proposed by Cussler [61]). A first order approximation for DtJ is given by Yakabe et al., as follows [57] ... 

In order to predict the value of the frequency factor, one may assume that all collisions between reactant molecules with sufficient activation energy result in the instantaneous formation of the reaction products. With this simple hypothesis (collision theory), if the activation energy is known, then the problem of computing the reaction rate reduces to the problem of computing the rate of collision between the appropriate reactant molecules in the ideal gas mixture. This last problem is easily solved by the elementary kinetic theory of gases. 

An expression for v 2 is derived from elementary kinetic theory in Section E.2.3. By using this result in equation (61), we find that... 

An alternative approach is to calculate the constant p from elementary kinetic theory, identifying the intensity at zero height in the flame... 

Unlike the elementary kinetic theory, the three collision integrals ( 2D AB, Qu and T2a) are introduced in the Chapman-Enskog theory. Moreover, the collision diameter (er ) is used instead of the molecular diameter (d ). 

Within the control volume the molecules of species 1 may lose (or gain) momentum each time they collide with the atoms or molecules of the other species. Accounting for the momentum exchange on collision is one part of the elementary kinetic theory of diffusion that follows. 

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