Gases kinetic-molecular description

This equation was derived independently by James C. Maxwell, a Scottish physicist, and Ludwig E. Boltzmann, an Austrian physicist who did much of the fundamental theoretical work on the kinetic molecular description of an ideal gas. The product of f(u)du represents the fraction of gas molecules with velocities between u and u + du, where du represents an infinitesimal velocity increment. This function is the one plotted in Figs. 5.15 and 5.16. 

The kinetic molecular theory (KMT see Sidebar 2.7) of Bernoulli, Maxwell, and others provides deep insight into the molecular origin of thermodynamic gas properties. From the KMT viewpoint, pressure P arises merely from the innumerable molecular collisions with the walls of a container, whereas temperature T is proportional to the average kinetic energy of random molecular motions in the container of volume V. KMT starts from an ultrasimplified picture of each molecule as a mathematical point particle (i.e., with no volume ) with mass m and average velocity v, but no potential energy of interaction with other particles. From this purely kinetic picture of chaotic molecular motions and wall collisions, one deduces that the PVT relationships must be those of an ideal gas, (2.2). Hence, the inaccuracies of the ideal gas approximation can be attributed to the unrealistically oversimplified noninteracting point mass picture of molecules that underlies the KMT description. 

When Bernie Shizgal arrived at UBC in 1970, his research interests were in applications of kinetic theory to nonequilibrium effects in reactive systems. He subsequently applied kinetic theory methods to the study of electron relaxation in atomic and molecular moderators,46 hot atom chemistry, nucleation,47 rarefied gas dynamics,48 gaseous electronics, and other physical systems. An important area of research has been the kinetic theory description of the high altitude portion of planetary atmospheres, and the escape of atmospheric species.49 An outgrowth of these kinetic theory applications was the development of a spectral method for the solution of differential and integral equations referred to as the quadrature discretization method (QDM), which has been used with considerable success in statistical, quantum, and fluid dynamics.50... 

The extended liquid-solid BET isotherm describes well the adsorption behavior corresponding to types II or III isotherms of the van der Waals classification of isotherms (see Figure 3.1). Its expression parallels that of the BET isotherm model which is often applied in gas-solid equiUbtia [3]. It assiunes the same molecular description the solute molecules can adsorb from the solution onto either the bare surface of the adsorbent or a layer of solute already adsorbed. The equation of the model is derived from kinetic adsorption-desorption relationships, assuming first order kinetics [10,85]. The expression obtained after a rather lengthy derivation is... 

I Pitault, D Nevicato, M Forissier, J R Bernard. Kinetic model based on a molecular description for catalytic cracking of vacuum gas oil. Chemical Engineering, 49 (1994) 24A, pp. 4249-4262... 

In the kinetic modelling of catalytic reactions, one typically takes into account the presence of many different surface species and many reaction steps. Their relative importance will depend on reaction conditions (conversion, temperature, pressure, etc.) and as a result, it is generally desirable to introduce complete kinetic fundamental descriptions using, for example, the microkinetic treatment [1]. In many cases, such models can be based on detailed molecular information about the elementary steps obtained from, for example, surface science or in situ studies. Such kinetic models may be used as an important tool in catalyst and process development. In recent years, this field has attracted much attention and, for example, we have in our laboratories found the microkinetic treatment very useful for modelling such reactions as ammonia synthesis [2-4], water gas shift and methanol synthesis [5,6,7,8], methane decomposition [9], CO methanation [10,11], and SCR deNO [12,13]. 

In many cases, there must be energy transfer between the reacting molecules. For reactions that take place in the gas phase, molecular collisions constitute the vehicle for energy transfer, and our description of gas phase reactions begins with a kinetic theory approach to collisions of gaseous molecules. In simplest terms, the two requirements that must be met for a reaction to occur are (1) a collision must occur and (2) the molecules must possess sufficient energy to cause a reaction to occur. It will be shown that this treatment is not sufficient to explain reactions in the gas phase, but it is the starting point for the theory. 

Kinetic-molecular theory (5.6) Description of a gas as a collection of a very large number of atoms or molecules in constant, random motion. The ideal gas law can be derived from the postulates of the kinetic theory. 

Draw a particulate illustration of five particles in the gas phase in a box. Show the particles at a lower temperature, in the liquid phase, in a new box. Now show the particles at an even lower temperature, in the solid phase, in a new box. Write a description of your illustrations in terms of the kinetic molecular theory. 

The book is divided into four parts. The first part focuses on the macroscopic properties of physical systems. It begins with the descriptive study of gases and liquids, and proceeds to the study of thermodynamics, which is a comprehensive macroscopic theory of the behavior of material systems. The second part focuses on dynamics, including gas kinetic theory, transport processes, and chemical reaction kinetics. The third part presents quantum mechanics and spectroscopy. The fourth part presents the relationship between molecular and macroscopic properties of systems through the study of statistical mechanics. This theory is applied to the structure of condensed phases. The book is designed so that the first three parts can be studied in any order, while the fourth part is designed to be a capstone in which the other parts are integrated into a cohesive whole. 

For a quantitative description of the behavior of gases, we will employ some simple gas laws and a more general expression called the ideal gas equation. These laws will be explained by the kinetic-molecular theory of gases. The topics covered in this chapter extend the discussion of reaction stoichiometry from the previous two chapters and lay some groundwork for use in the following chapter on thermochemistry. The relationships between gases and the other states of matter— liquids and solids—are discussed in Chapter 12. 

In kinetic theory, the macroscopic quantities are found as averages over the motion of many molecules each molecular event is assumed to take place over a microscopic time interval, so that a measurement that is made over a macroscopic time interval involves many molecules. The kinetic-description is, therefore, a probabilistic one in that assumptions are made about the motion of one molecule and the results of this motion are averaged over all of the molecules of the gas, giving proper weight to the probability that the various molecules of the gas can have the assumed motion. 

A correlation between surface and volume processes is described in Section 5. The atomic-molecular kinetic theory of surface processes is discussed, including processes that change the solid states at the expense of reactions with atoms and molecules of a gas or liquid phase. The approach reflects the multistage character of the surface and volume processes, each stage of which is described using the theory of chemical kinetics of non-ideal reactive systems. The constructed equations are also described on the atomic level description of diffusion of gases through polymers and topochemical processes. 

Even with an adequate description of molecular velocities near the particle surface, it is not possible to completely establish all variables influencing thermal force. This is because there also exists a so-called thermal slip flow or creep flow at the particle surface. Reynolds (see Niven, 1965) and others have pointed out that as a consequence of kinetic theory, a gas must slide along the surface of a solid from the colder to the hotter portions. However, if there is a flow of gas at the surface of the particle up the temperature gradient, then the force causing this flow must be countered by an opposite force acting on the particle, so that the particle itself moves in an opposite direction down the temperature gradient. This is indeed the case, known as thermal creep. Since the velocity appears to go from zero to some finite value right at the particle surface, this phenomenon is often described as a velocity jump. A temperature jump also exists at the particle surface. 

On the basis of a molecular model for sorption kinetics Jdntti introduced a method to calculate equilibria shortly after a change of the pressure of the sorptive gas. In the present paper we apply that method for the description of multilayer adsorption. 

Adsorption (desorption) energies or enthalpies of molecules and atoms on various surfaces are of primary and major interest in the experimental gas-phase radiochemical studies of the heaviest elements. In practice, pertinent data can be obtained almost exclusively in the experiments based on chromatographic principles. In the pioneering works [1-3] the required values were derived using the simplest description of the processes in columns in terms of molecular kinetics (see Sect. 4.2). Later [4] the task of finding the adsorption enthalpies was examined using a thermodynamic approach. It revealed that the molecular-kinetic treatment... 

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