Microscopic Properties of Gas Molecules

How is the phenomenon of temperature explained on the basis of the kinetic molecular theory What microscopic property of gas molecules is reflected in the temperature measured ... 

On the continuum level of gas flow, the Navier-Stokes equation forms the basic mathematical model, in which dependent variables are macroscopic properties such as the velocity, density, pressure, and temperature in spatial and time spaces instead of nf in the multi-dimensional phase space formed by the combination of physical space and velocity space in the microscopic model. As long as there are a sufficient number of gas molecules within the smallest significant volume of a flow, the macroscopic properties are equivalent to the average values of the appropriate molecular quantities at any location in a flow, and the Navier-Stokes equation is valid. However, when gradients of the macroscopic properties become so steep that their scale length is of the same order as the mean free path of gas molecules,, the Navier-Stokes model fails because conservation equations do not form a closed set in such situations. 

The calculation of the electric properties of individual molecules as found in an infinitely dilute gas has for long been of great interest to quantum chemists. This curiosity has been spurred in recent decades by the increasing importance of the communications industry in the world and the parallel need for materials having specific properties for electronic, optical, and other devices. In particular, the nonlinear-optical quantities, defined at the microscopic level as hyperpolarizabilities and at the macroscopic level as nonlinear susceptibilities, have played a... 

The oriented gas model was first employed by Chemla et al. [4] to extract molecular second-order nonlinear optical (NLO) properties from crystal data and was based on earlier work by Bloembergen [5]. In this model, molecular hyperpolarizabilities are assumed to be additive and the macroscopic crystal susceptibilities are obtained by performing a tensor sum of the microscopic hyperpolarizabilities of the molecules that constitute the unit cell. The effects of the surroundings are approximated by using simple local field factors. The second-order nonlinear response, for example, is given by... 

Our discussion has so far been concerned with the microscopic response of a molecule to an external electric field, and thus with an expansion of the molecular energy in orders of the response with respect to the external field, giving rise to the molecular (hyper)polarizabilities. Although experimental data for nonlinear optical properties of molecules in the gas phase do exist [55], the majority of experimental measurements are done in the liquid or solid states, as these states also are the ones that are of greatest interest with respect to developing materials with specifically tailored (non)linear optical properties. 

Statistical mechanics describe how reversible microscopic equations of motion can lead to irreversible macroscopic behavior. Statistical thermodynamics predicts the macroscopic properties of a system using information about the microscopic nature of the system, since the large number of molecules in any system allows the use of statistics. For example, the result of longtime average over many molecular collisions of gas molecules with the container walls is a finite force or measured pressure. Similarly, other macroscopic... 

The kinetic theory of gases attempts to explain the macroscopic nonequilibrium properties of gases in terms of the microscopic properties of the individual gas molecules and the forces between them. A central aim of this theory is to provide a microscopic explanation for the fact that a wide variety of gas flows can be described by the Navier-Stokes hydrodynamic equations and to provide expressions for the transport coefficients appearing in these equations, such as the coefficients of shear viscosity and thermal conductivity, in terms of the microscopic prop>erties of the molecules. We devote most of our attention in this article to this problem. 

The principal advantage of the time correlation function method is that it provides a new set of microscopic functions for a fluid, the time correlation functions, which can be studied directly by experimental observations of the fluidt or by computer-simulated molecular dynamics. The time correlation functions depend even more sensitively on the microscopic properties of the fluid molecules than the transport coefficients, which are expressed as time integrals of the correlation functions. Thus, a further test of kinetic theory has been found it must not only lead to expressions for the transport coefficients for dilute and dense gases that are in agreement with experiment, but also describe the dependence of the time correlation functions on both time and the density of the gas. One of the principal successes of kinetic theory is that it provides a quantitatively correct description of the short- and long-time... 

In summary, IGC is a simple, relatively inexpensive approach using standard GC instrumentation to obtain the surface thermodynamic properties of solids. The theoretical interpretation of the experimental resnlts is now well established, and the deduction of acid-base properties of materials can now be regarded as being routine. IGC provides a complementary method to the nse of wetting Uqnids, insomuch as it probes the microscopic properties of the solid surface, (as the probe molecules are invariably small and in the gaseous phase, and are at infinite dilntion, i.e. there is no interaction between adjacent probe molecules on the solid snrface or in the gas phase), while the use of liquids in techniques such as dynamic contact angle analysis probes the macroscopic properties. 

The experimental approach discussed in this article is, in contrast, particularly amenable to investigating solvent contributions to the interfacial properties 131. Species, which electrolyte solutions are composed of, are dosed in controlled amounts from the gas phase, in ultrahigh vacuum, onto clean metal substrates. Sticking is ensured, where necessary, by cooling the sample to sufficiently low temperature. Again surface-sensitive techniques can be used, to characterize microscopically the interaction of solvent molecules and ionic species with the solid surface. Even without further consideration such information is certainly most valuable. The ultimate goal in these studies, however, is to actually mimic structural elements of the interfacial region and to be able to assess the extent to which this may be achieved. 

The ultimate aim of scientists has always been to be able to see molecules while active. In order to achieve this goal, the microscope should be able to operate under ambient conditions. Further, all kinds of molecular interactions between a solid and its environment (gas or liquid or solid), initially, can take place only via the surface molecules of the interface. It is obvious that, when a solid or liquid interacts with another phase, knowledge of the molecular structures at these interfaces is of interest. The term surface is generally used in the context of gas-liquid or gas-solid phase boundaries, while the term interface is used for liquid-liquid or liquid-solid phases. Furthermore, many fundamental properties of surfaces are characterized by morphology scales of the order of 1 to 20 nm (1 nm = 10-9 m = 10 A (Angstrom = 10-8 cm). 

Molecular properties can be classified according to their end-poinl observables, such as chemical I reactivity. solubility, acid-basel. physical (a function of physical state gas. liquid, solid thermodynamic), or biological (ligand or enzyme agonist or antagonist). These properties reflect macroscopic, or bulk, properties, which exist only for the bulk material, e.g.. heat of crystallization, ur microscopic properties, which exist for an ensemble of the molecule. As use of CAMM methods... 

When other kinds of work are involved, it is necessary to specify more variables, but the point is that when a small number of properties are specified, all the other properties of the system are fixed. This is in contrast with the very large number of properties that have to be specified to describe the microscopic state of a macroscopic system. In classical physics the complete description of a mole of an ideal gas would require the specification of 3NA components in the three directions of spatial coordinates and 3NA components of velocities of molecules, where NA is the Avogadro constant. 

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. 

Let us ask what the randomness that we associated with entropy in Chap. I means in terms of the assembly. A random system, or one of large entropy, is one in which the microscopic properties may be arranged in a great many different ways, all consistent with the same large-scale behavior. Many different assignments of velocity to individual molecules, for instance, can be consistent with the picture of a gas at high temperatures, while in contrast the assignment of velocity to molecules at the absolute zero is definitely fixed all the molecules are at rest. Then... 

Therefore, the effect of the monolayer is brought down to additional resistance of the equivalent by thickness aqueous layer h. It was shown that the permeability of the adsorption layer depends on surface tension (packing density) and size of the diffusing gas molecules [482], For many surfactants h is within the range of 7 to 12 nm. This means that the permeability of thick films is determined by the rate of molecular diffusion, while for black films (h 10 nm) Eq. (3.147) is valid and their permeability is determined by the properties of the surfactant monolayers. Electrolytes do not affect significantly the permeability of monolayers. It was considered that gas diffusion through the monolayer occurred as a result of creation of microscopic vacancies between the surfactant molecules. This model was called model of energy barrier. However, later this model proved unsatisfactory. [483]... 

In order to understand the nature of radiocolloids, knowledge of the general properties of colloids is needed. Colloids are finely dispersed particles in a liquid phase, a gas phase or a solid. The size of colloidal particles is in the range between that of molecules or ions and that of particles visible by means of a light microscope, i.e. between about 1 nm and about 0.45 pm. The upper value corresponds to the mean wavelength of visible light. Large molecules, in particular polymers and biomolecules, approach or exceed the upper value and may also form colloids. 

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