Molecular kinetics collision diameter

Using gas kinetic molecular theory, show that under typical atmospheric conditions of pressure and temperature corresponding to an altitude of 5 km (see Appendix V) collisional deactivation of a C02 molecule will be much faster than reemission of the absorbed radiation. Take the collision diameter to be 0.456 nm and the radiative lifetime of the 15-/rm band of C02 to be 0.74 s (Goody and Yung, 1989). 

These measurements have been carried out in collaboration with de Maeyek[4]). The rate constant was found to be (1 3 0-2)-10n litres/ mol-sec thus the neutralization reaction is the fastest known bi-molecular reaction in aqueous solution. Molecular-kinetic considerations show that the velocity of recombination is solely determined by the collision frequency of the ions. Furthermore, the effective cross section of the proton is so large that the reaction already proceeds spontaneously when ions approach each other within a distance of two to three H-bonds. This means that the motion of the proton within the hydration complex (the diameter of which corresponds to about two to three H-bonds) proceeds rapidly compared to the actual movement of the ions towards each other. 

Based on kinetic-theory principles and the Eucken correction, develop a general expression for the thermal conductivity of diatomic gases. Collect and combine all the constants, such that the expression depends on the molecular weight (g/mol), temperature (K), collision diameter (A), and reduced temperature T (nondimensional). 

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 ). 

Kinetic theory predicts the self-diffusion coefficient, tbei is, the diffusion coefficient for a gas mixture in which all molecules have identical molecular weights and collision diameters, to be12... 

According to the kinetic theory of gases, the mean free path in a gas with a molecular collision diameter ri at an absolute temperature T and pressure P is... 

The identification of v can be carried out readily for a hypothetical reaction consisting of the collision between two hard spheres A and B. Indeed the rate of collision between two such molecular species of diameters a a and [Pg.42]

The chance of a collision will obviously depend upon the number of gas molecules per unit volume or, alternatively, upon the pressure. The chance of a collision will also depend upon the size of the gas molecules. For example, the chance of two basketballs thrown toward one another undergoing a collision is much greater than the chance of having a similar collision between two golf balls. An expression for the mean free path in terms of pressure and molecular diameter may be derived from kinetic theory. We give only the result, which may be expressed as... 

It has also been suggested that the molecular diameter of nitrogen pentoxide is effectively much greater for activating collisions, as well as for deactivating collisions, than that calculated in the ordinary way from the kinetic theory. The difficulty about this suggestion is that the... 

Thus the only way to make a complex is to transfer some of the internal energy to another system. In practice, this means three or more molecules have to all be close enough to interact at the same time. The mean distance between molecules is approximately (V/N)1 /3 (the quantity V/N is the amount of space available for each molecule, and the cube root gives us an average dimension of this space). At STP 6.02 x 1023 gas molecules occupy 22.4 L (.0224 m3) so (V/N)1/3 is 3.7 nm—on the order of 10 molecular diameters. This is expected because the density of a gas at STP is typically a factor of 103 less than the density of a liquid or solid. So three-body collisions are rare. In addition, if the well depth V (rmin) is not much greater than the average kinetic en-... 

The kinetic theory of dilute gases accounts for collisions between spherical molecules in the presence of an intermolecular potential. Ordinary molecular diffusion coefficients depend linearly on the average kinetic speed of the molecules and the mean free path of the gas. The mean free path is a measure of the average distance traveled by gas molecules between collisions. When the pore diameter is much larger than the mean free path, collisions with other gas molecules are most probable and ordinary molecular diffusion provides the dominant resistance to mass transfer. Within this context, ordinary molecular diffusion coefficients for binary gas mixtures are predicted, with units of cm /s, via the Chapman-Enskog equation (see Bird et al., 2002, p. 526) ... 

From the kinetic theory of gases, it is possible to calculate the frequency that molecules collide as a function of velocity, which depends on molecular weight and temperature, and molecular diameter. If every collision at 25°C resulted in a reaction, a rate constant of the order of 3-5 x 10 ° cm molecule s ... 

Except for the fact that in the case of a porous medium the probability of reaction per collision is raised to the one-half power, these two conditions may be considered as identical The characteristic size L of the homogeneous reactor where the chain reaction proceeds is replaced by the characteristic thickness L of the porous layer where the catalytic reaction proceeds. The characteristic length for molecular motion in the gas phase, namely the mean free path X, is replaced by the characteristic length for molecular motion in the porous medium, the average diameter of the pores 8. Thus kinetic phenomena that seem at 6rst glance to be very different, are actually governed by very similar laws. 

Bulk diffusion or free molecular diffusion. This diffusion phenomena is driven by kinetic energy of the gas molecules and is hmited by the intermolecular collisions. Therefore, bulk diffusion is dominant in pores having large diameters in which collision with the wall do not play a significant role, i.e. the pore diameter significantly exceeds the mean free path. 

For gas-solid systems with a low gas density in which gas molecules diffuse through long narrow pores, the mean free path of the molecules is much larger than the pore diameter. In this type of diffusion, so-called Knudsen diffusion, the transport properties are essentially determined by eollisions of the gas moleeules with the pore walls rather than by collisions with other gas molecules. Based on the kinetic theory of gases, in the Knudsen approach all rebounds are assumed to be governed by the cosine law of reflection. In a straight cylindrical pore of diameter d ore, the Knudsen diffusion coefficient Dk,i for component i with molecular mass Mi is given by... 

The collision theory gives the fundamental perspective of how the colliding molecules give rise to the chemical conversion. The kinetic theory of gases gives us an estimate on the collision frequency or collision number as a function of mean molecular diameter, the temperature, and the reduced mass of the colliding particles as... 

It must be noted, however, that the question of which temperature dependence for the molecular diameter one should employ in these computations is not yet settled. Only for hard spheres is the diameter of the particles a well-defined quantity and temperature independent. For simple fluids, say argon, methane, etc., one may reasonably argue that the effective hard-core diameter should be a decreasing function of the temperature. The physical idea is that as one increases the temperature, the kinetic energy of the particles increases. Hence, on the average, interparticle collisions would lead to more extensive penetration into the repulsive region of the pair potential for the two particles. Indeed, it has been demonstrated that if such a negative temperature dependence of is adopted,... 

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