Kinetic model of gas

Sirovich, L. 1962 Kinetic modeling of gas mixtures. Physics of Fluids 5, 908-918. 

Kinetics models of gas-solid non-catalytic reaction include uniform conversion model (UCN), multiple fine particle model (GPM), crack core model (CCM), phase-change model (PCM), change void model (CVM), thermal decomposition model (TDM), shrinking core model with multi-step reactions, and multi-step reaction model of formation porous structure in reaction etc. Among these models, the shrinking core model (SCM) is the most important and most widely used. For conversion of solid it is also the most simple and practical model. Commonly it is suitable for experimental data. However, it can only be used in some reactions of many solid reactions. A more complex model must be used in other cases. 

Chemistry of Superheavy Elements ). The application of Monte-Carlo simulation methods in gas-phase adsorption chromatography is based on ideas given in [17]. All models use a microscopic description of the chromatographic adsorption-desorption process on the atomic scale. Hence, they are kinetic models of gas-adsorption chromatography. They can be applied to thermochromatography as well as to chromatography in the isothermal regime. To determine of the... 

The BET treatment is based on a kinetic model of the adsorption process put forward more than sixty years ago by Langmuir, in which the surface of the solid was regarded as an array of adsorption sites. A state of dynamic equilibrium was postulated in which the rate at which molecules arriving from the gas phrase and condensing on to bare sites is equal to the rate at which molecules evaporate from occupied sites. 

The purpose of this section is to present a general theoretical model of gas-liquid-particle operations, with a number of simplifying assumptions that make possible, at least in principle, the calculation of the conversion and yield from a specified amount of information regarding transport phenomena and reaction kinetics. 

In Section 4.4, we used a molecular model of a gas to explain qualitatively why the pressure of a gas rises as the temperature is increased as a gas is heated, its molecules move faster and strike the walls of their container more often. The kinetic model of a gas allows us to derive the quantitative relation between pressure and the speeds of the molecules. 

The kinetic model of gases is consistent with the ideal gas law and provides an expression for the root mean square speed of the molecules vnns = (3RT/M)l/2. The molar kinetic energy of a gas is proportional to the temperature. 

Do all the molecules of a gas strike the walls of their container with the same force Justify your answer on the basis of the kinetic model of gases. 

To set up a quantitative theory based on this qualitative picture, we need to know the rate at which molecules collide and the fraction of those collisions that have at least the energy Emin required for reaction to occur. The collision frequency (the number of collisions per second) between A and B molecules in a gas at a temperature T can be calculated from the kinetic model of a gas (Section... 

Semibatch reactors are often used to mn highly exothermic reactions isothermally, to run gas-liquid(-solid) processes isobarically, and to prevent dangerous accumulation of some reactants in the reaction mixture. Contrary to batch of)eration, temperature and pressure in semibatch reactors can be varied independently. The liquid reaction mixture can be considered as ideally mixed, while it is assumed that the introduced gas flows up like a piston (certainly this is not entirely true). Kinetic modelling of semibatch experiments is as difficult as that of batch, non-isotherma experiments. 

Kinetic Molecular Theory model that defines an ideal gas and assumes the average kinetic energy of gas molecules is directly proportional to the absolute temperature... 

Figure 7. The first known attempt to envision gas pressure in terms of a kinetic model of atoms and molecules. (From D. Bernoulli, Hydrodynamica, 1738). 

FIGURE 4.24 In the kinetic model of an ideal gas, the pressure arises from the force exerted on the walls of the container when the impacting molecules are deflected in a different direction. We need to know the force of each impact and the number of impacts in a given interval. 

There are also two factors that have already been noted in the numerical analysis of the kinetic model of CO oxidation (1) fluctuations in the surface composition of the gas phase and temperature can lead to the fact that the "actual multiplicity of steady states will degenerate into an unique steady state with high parametric sensitivity [170] and (2) due to the limitations on the observation time (which in real experiments always exists) we can observe a "false hysteresis in the case when the steady state is unique. Apparently, "false hysteresis will take place in the region in which the relaxation processes are slow. 

We wish to thank John Plane, Kim Holmen, Dennis Savoie, and Rana Fine for helpful discussions on the subject of kinetic modelling and gas exchange. This work was supported by grant ATM 87-09802 from the National Science Foundation. 

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. 

Figure 3.5 Reaction scheme of the gas phase phenol acylation with acetic acid (AcOH) over HMFI at 553 K. Reprinted with permission from Industrial Engineering Chemistry Research, Vol. 34, Guisnet et al., Kinetic modelling of phenol acylation with acetic acid on HZSM5, pp. 1624-1629, Copyright (1995), American Chemical Society...

A traditional kinetic model of steady-state catalytic reaction assumes quasi-steady-state concentrations of intermediate species on the catalyst surface. This assumption is often invalid for unsteady-state conditions characterized by continuous changes in a fluid phase composition and temperature above the catalyst surface. Additionally, the catalyst itself can interact with the reaction mixture and can undergo significant changes, influenced by changing conditions in the gas phase. Such a modification of the catalyst can be con-... 

A number of research groups have used SIFT instruments for measurements directed toward IS chemistry. The Birmingham group of Adams and Smith, the inventors of the SIFT technique [16], was particularly active in this regard and a major focus of their SIFT measurements was the systematic study of reactions of hydrogenated ions, e.g. CH,, CjH,, NH , HnS+, HnCO+ etc., with numerous molecular species [18]. Further contributions by this group include detailed studies of isotope exchange in ion-neutral reactions, studies for which the SIFT is eminently suited, since the ion source gas and the reactant gas are not mixed. From these studies and detailed kinetic models of interstellar ionic reactions, it is now understood that the observed enhancement of the rare isotopes (e.g. D, 13C) in some IS molecules is due to the process of isotope fractionation in ion-neutral reactions [19]. 

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