Kinetic theory of molecules

When applying the results of the kinetic theory of polyatomic gases, one has to take into account the influence of vibrational and sometimes hindered rotational modes on the transport properties. The kinetic theory of molecules possessing vibrational modes of motion is still in its formative stages and is nowhere near as well-developed as that of rigid rotor molecules (see Section 14.2). Thus, the type of analysis that has been carried out for nitrogen is not possible in its entirety for polyatomic fluids. Nevertheless, a modified analysis, based on an empirical extension of the kinetic theory of diatomic gases, turned out to be possible (Hendl et al. 1991,1994 Vesovic et al. 1994). 

If the fraction of sites occupied is 0, and the fraction of bare sites is 0q (so that 00 + 1 = 0 then the rate of condensation on unit area of surface is OikOo where p is the pressure and k is a constant given by the kinetic theory of gases (k = jL/(MRT) ) a, is the condensation coefficient, i.e. the fraction of incident molecules which actually condense on a surface. The evaporation of an adsorbed molecule from the surface is essentially an activated process in which the energy of activation may be equated to the isosteric heat of adsorption 4,. The rate of evaporation from unit area of surface is therefore equal to... 

Translational energy, which may be directly calculated from the classical kinetic theory of gases since the spacings of these quantized energy levels are so small as to be negligible. The Maxwell-Boltzmann disuibution for die kinetic energies of molecules in a gas, which is based on die assumption diat die velocity specuum is continuous is, in differential form. 

The kinetic theory of gases has been used so far, the assumption being that gas molecules are non-interacting particles in a state of random motion. This... 

It is one of the wonders of the history of physics that a rigorous theory of the behaviour of a chaotic assembly of molecules - a gas - preceded by several decades the experimental uncovering of the structure of regular, crystalline solids. Attempts to create a kinetic theory of gases go all the way back to the Swiss mathematician, Daniel Bernouilli, in 1738, followed by John Herapath in 1820 and John James Waterston in 1845. But it fell to the great James Clerk Maxwell in the 1860s to take... 

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. 

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. 

This is called Avogadro s theorem (1811) it appears here simply as a definition of molecular weighty and this is really the manner in which the relation is applied in chemistry. The kinetic theory of gases gives a new, and much deeper, significance to the statement by introducing the conception of the molecule this, however, does not concern us in thermodynamics, and since the molecular weights are purely relative numbers, the deductions made in this hook are equally strict whichever standpoint is adopted. 

An explanation of potential energy involves an explanation of force both terms are simply another way of saying that we know nothing about the thing to be explained. A distinct advance is made when a force can be explained in terms of the kinetic energy of a system in motion, an illustration of which is afforded by the kinetic theory of gases, which replaced the supposed forces of repulsion between the molecules of gases (the existence of which is disproved by Joule s experiment, 73) by molecular impacts. 

Wherever heat is involved temperature also fulfils an important role firstly because the heat content of a body is a function of its temperature and, secondly, because temperature difference or temperature gradient determines the rate at which heat is transferred. Temperature has the dimension 9 which is independent of M,L and T, provided that no resort is made to the kinetic theory of gases in which temperature is shown to be directly proportional to the square of the velocity of the molecules. 

The molecular diffusivity D may be expressed in terms of the molecular velocity um and the mean free path of the molecules Xrn. In Chapter 12 it is shown that for conditions where the kinetic theory of gases is applicable, the molecular diffusivity is proportional to the product umXm. Thus, the higher the velocity of the molecules, the greater is the distance they travel before colliding with other molecules, and the higher is the diffusivity D. 

In the previous section, the molecular basis for the processes of momentum transfer, heat transfer and mass transfer has been discussed. It has been shown that, in a fluid in which there is a momentum gradient, a temperature gradient or a concentration gradient, the consequential momentum, heat and mass transfer processes arise as a result of the random motion of the molecules. For an ideal gas, the kinetic theory of gases is applicable and the physical properties p,/p, k/Cpp and D, which determine the transfer rates, are all seen to be proportional to the product of a molecular velocity and the mean free path of the molecules. 

In bulk diffusion, the predominant interaction of molecules is with other molecules in the fluid phase. This is the ordinary kind of diffusion, and the corresponding diffusivity is denoted as a- At low gas densities in small-diameter pores, the mean free path of molecules may become comparable to the pore diameter. Then, the predominant interaction is with the walls of the pore, and diffusion within a pore is governed by the Knudsen diffusivity, K-This diffusivity is predicted by the kinetic theory of gases to be... 

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) ... 

Some opportunities of such approximations are well illustrated by considering two characteristic examples. The first example will be a dusty-gas model, where porous media is considered as one of components of a gas mix of huge molecules (or particles of a dust), mobile or rigidly fixed in space [249,252,253], Such a model allows a direct application of methods and results of kinetic theory of gases and is effectively applied to the description of mass transfer processes in PS. The history of such an approach, the origins of which can be found in the works by Thomas Graham (1830 to 1840) is considered in Ref. [249], Actually, the model was first proposed by James Maxwell (1860), further it was independently reported by Deryagin and Bakanov (1957), and then also independently reported by Evans, Watson, and Mason (1961 see Refs. [249,252]). 

The answer, Meyer thought, lies in the kinetic theory of heat and matter. This physical theory had been given explicit chemical meaning by Williamson s inference from studies of the synthesis of diethyl ether that atoms in chemical compounds must be continually changing places.56 Molecules are not empty boxes in translation or rotation but little Pandora-like boxes filled with active entities. The goal of chemistry must be the understanding of chemical phenomena using theories of motion, not just theories of species or types. 

---