Interactions between gas particles

The a term reflects the strength of the interaction between gas particles, and the b term reflects the particle s size. 

The van derWaals Constanta represents the pressure correction and is related to the magnitude of the interactions between gas particles.The van derWaals constant b is the volume correction and is related to the size of the gas particles. 

Forces between the particles in a real gas or liquid affect the virial, and thence the pressure. The total virial for a real system equals the sum of an ideal gas part (—3P V) and a contribution due to interactions between the particles. The result obtained is ... 

In an ideal gas there are no interactions between the particles and so the potential ener function, 1 ), equals zero. exp(- f (r )/fcBT) is therefore equal to 1 for every gas partic in the system. The integral of 1 over the coordinates of each atom is equal to the volume, ai so for N ideal gas particles the configurational integral is given by (V = volume). T1 leads to the following result for the canonical partition function of an ideal gas ... 

By combining Equations (8.4) and (8.6) we can see that the partition function for a re system has a contribution due to ideal gas behaviour (the momenta) and a contributii due to the interactions between the particles. Any deviations from ideal gas behaviour a due to interactions within the system as a consequence of these interactions. This enabl us to write the partition function as ... 

This result makes it clear that particle stress is strongly dependent on the interaction between the particles and the interface, so that electrostatic and also hydrophobic and hydrophilic interactions with the phase boundary are particularly important. This means that the stress caused by gas sparging and also by boundary-layer flows, as opposed to reactors with free turbulent flow (reactors with impellers and baffles), may depend on the particle system and therefore applicability to other material systems is limited. 

It follows from these eqnations that in dilute ideal solutions, said effects depend only on the concentration, not on the nature of the solute. These relations hold highly accnrately in dilnte solntions of nonelectrolytes (up to about lO M). It is remarkable that Eq. (7.1) coincides, in both its form and the numerical value of constant R, with the eqnation of state for an ideal gas. It was because of this coincidence that the concept of ideality of a system was transferred from gases to solntions. As in an ideal gas, there are no chemical and other interactions between solnte particles in an ideal solution. 

In reality, the adsorption of gas particles on a real surface can be simultaneously influenced by inhomogeneity of the surface and interaction between absorbed particles. Presumably, it is the nature of a specific absorbate-adsorbent pair that controls the major mechanism in each case. 

The effects of temperature and pressure on fluidized-bed systems cannot be considered independently of particle size. Whether temperature and pressure have an effect (and indeed, even the direction of that effect) on a system, depends strongly on particle size. In addition, the type of interaction between gas and solids, i.e., whether the interaction is due to momentum or drag, determines if gas viscosity has an effect upon the system. As will be shown, gas viscosity is not important in systems in which momentum is important, but is important in systems dominated by drag. 

Sander, R. Modeling atmospheric chemistry Interactions between gas-phase species and liquid cloud/aerosol particles, Surv. Geophys., 20, 1-31, 1999. 

As a direct consequence of the large intermolecular separations, we can safely say no interactions form between the molecules in ammonia gas. The molecules are simply too far apart. We saw in the previous chapter how the property known as pressure is a macroscopic manifestation of the microscopic collisions occurring between gas particles and, say, a solid object such as a container s walls. But the gas particles can also strike each other on the same microscopic scale we say the resultant interactions between molecules are intermolecular. 

The working of a chemical sensor is based on the interaction between free particles (e g. gas molecules) and the surface of a solid. This interaction might be a physical absorption and in that case the sensor can be used at low temperatures because the absorption forces will not be great. However, the absorption might also be chemical and then there is question of a strong chemical bond to the surface of the sensor. This can lead to very specific changes in the electrical sensor properties. 

In case of an ideal gas, the interaction between the elementary particles, that is, the atoms or molecules, can be neglected. Forthis purpose, the distance between the individual atoms ormolecules needs to be large. Thus, tbfrepresents the volume of the individual atom, molecule felntlhe Avogadro numbehlA, that is, the number of molecules per mole, no interaction between the particles can be expected for... 

The interaction between adsorbed particles was also taken into account in terms of some models of induced inhomogeneity (see the above representation), e.g. in de Boer s dipole-dipole interaction model [64], but compared with the lattice gas model, they must be treated as semi-empirical. A semi-empirical model for the collective interaction of adsorbed particles with catalyst surface was also suggested by Snagovskii and Ostrovskii [37]. 

The physical condition of the kinetic theory of gases can be described by elastic collisions of monodispersed spheres with the Maxwellian velocity distribution in an infinite vacuum space. Therefore, for an analogy between particle-particle interactions and molecular interactions to be directly applicable, the following phenomena in gas-solid flows should not be regarded as significant in comparison to particle-particle interactions the gas-particle... 

The existence of a solid itself, the solid surfaces, the phenomena of adsorption and absorption of gases are due to the interactions between different components of a system. The nature of the interaction between the particles of a gas-solid system is quite diverse. It depends on the nature of the solid s atoms and the gas-phase molecules. The theory of particle interactions is studied by quantum chemistry [4,5]. To date, one can consider that the prospective trends in the development of this theory for metals and semiconductors [6,7] and alloys [8] have been formulated. They enable one to describe the thermodynamic characteristics of solids, particularly of phase equilibria, the conditions of stability of systems, and the nature of phase transitions [9,10]. Lately, methods of calculating the interactions of adsorbed particles with a surface and between adsorbed particles have been developing intensively [11-13]. But the practical use of quantum-chemical methods for describing physico-chemical processes is hampered by mathematical difficulties. This makes one employ rougher models of particle interaction - model or empirical potentials. Their choice depends on the problems being considered. 

The present state of the theories of atomic and molecular processes in condensed phases is characterized by great non-uniformity of its development. Matters are much problematic in the theory of the kinetics of processes at a molecular level. The kinetics of surface processes mainly employs models taking no account of the interaction of the adsorbed particles (the law of masses or surface action) [14-16]. This does not reflect the real properties of a gas solid interface. There is also a diversity of models when considering the interaction of the particles because various approximations are used (equilibrium is described with a view to the correlation effects, while kinetics ignores them). The problem of approximations is of a fundamental significance in the theory of condensed systems. Interaction between the particles causes all the particles to be bound to... 

Thermodynamics deals with relations among bulk (macroscopic) properties of matter. Bulk matter, however, is comprised of atoms and molecules and, therefore, its properties must result from the nature and behavior of these microscopic particles. An explanation of a bulk property based on molecular behavior is a theory for the behavior. Today, we know that the behavior of atoms and molecules is described by quantum mechanics. However, theories for gas properties predate the development of quantum mechanics. An early model of gases found to be very successftd in explaining their equation of state at low pressures was the kinetic model of noninteracting particles, attributed to Bernoulli. In this model, the pressure exerted by n moles of gas confined to a container of volume V at temperature T is explained as due to the incessant collisions of the gas molecules with the walls of the container. Only the translational motion of gas particles contributes to the pressure, and for translational motion Newtonian mechanics is an excellent approximation to quantum mechanics. We will see that ideal gas behavior results when interactions between gas molecules are completely neglected. 

The aim of this Chapter is the development of an uniform model for predicting diffusion coefficients in gases and condensed phases, including plastic materials. The starting point is a macroscopic system of identical particles (molecules or atoms) in the critical state. At and above the critical temperature, Tc, the system has a single phase which is, by definition, a gas or supercritical fluid. The critical temperature is a measure of the intensity of interactions between the particles of the system and consequently is a function of the mass and structure of a particle. The derivation of equations for self-diffusion coefficients begins with the gaseous state at pressures p below the critical pressure pc. A reference state of a hypothetical gas will be defined, for which the unit value D = 1 m2/s is obtained at p = 1 Pa and a reference temperature, Tr. Only two specific parameters, Tc, and the critical molar volume, VL, of the mono-... 

The first term wt = (l+2rc)1/2 of the power series w defined in Eq. (6-10) plays a special role within the interaction model in that it represents a perfect gas phase. If Vo, pc, Tc and R represent the molar volume of a compound, the critical pressure and critical temperature of the system and the gas constant, then the product pcV0 is reduced to llw of the product RTC due to the interaction between the particles in the system. Taking into account an empty (free) volume fraction in the critical state, the critical molar volume is written as Vc = V(). Consequently, a dimensionless critical... 

The term chemisorption was coined in order to classify the interaction between a particle in the gas phase and a solid surface, i.e. the result of the adsorption process [1]. If the interaction leads to the formation of a chemical bond the adsorbate formed is called a chem-isorbate. Where chemical bond formation is not important the process is classified as physisorption. There are several conceptual problems with such a differentiation which we briefly address in the following, and which indicate that a more detailed look at the entire process of adsorbate formation is needed before a reliable classification may be carried out. In fact, as it turns out, for a conclusive classification one would need the full theoretical and experimental understanding of the system under investigation. Such an approach must include the static aspects, i.e. the energies involved, as well as the dynamic aspects, i.e. the processes involved in the formation of the adsorptive interactions. 

Presently, we will review microscopic models that provide molecular insight to the interactions between gas molecules and aerosol particles. 

The quantum mechanical/molecular mechanical aerosol model was developed to describe the interaction between gas phase molecules and atmospheric particles. This method has been utilized for the calculation of interaction energies and... 

The solids movement in a spouted bed is initiated by the interaction between the particles and the high-velocity gas jet, so that particle flow in the spout region shapes the entire solids-flow pattern. While a mutual dependence between the solids flow in the spout and in the annulus is inherent to a spouted bed, it is nevertheless convenient to discuss the flow in the spout and in the annulus separately. 

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