Atomicity, of a gas

We see that, as L (the length of the box) or m (the mass of the particle) increases, the separation between neighboring energy levels decreases (Fig. 1.26). That is why no one noticed that energy is quantized until they investigated very small systems such as an electron in a hydrogen atom the separation between levels is so small for ordinary particles in ordinary-sized vessels that it is completely undetectable. We can, in fact, ignore the quantization of the motion of the atoms of a gas in a typical flask. 

Four types of counters are currently in use proportional, Geiger, scintillation, and semiconductor. All depend on the power of x-rays to ionize atoms, whether they are atoms of a gas (proportional and Geiger counters) or atoms of a solid (scintillation and semiconductor counters). A general treatment of the first three types has been given by Parrish [7.8]. 

Consider any piece of matter.. . . Contemplate any solid object a vase, it may be, or a jewel, or a statue what is it that holds the atoms together in that particular shape If the atoms were not connected they would be moving about at random, like the atoms of a gas but they are connected, crystallized as it were, together by the forces of cohesion. Even in a liquid they are held together into a body of definite size, though not a definite shape a liquid has size... 

When the dimension is smaller than the order of 1 nm, the rules of quantum mechanics prevail. The concept of a single, well-defined particle must be abandoned we know neither the exact dimension nor position nor velocity of each particle. Our picture of a single electron is more like an electron gas or cloud, with a certain probability of finding it at a certain position. So it is also for the atoms of a gas. However, atoms in a solid evidently have more well-defined positions (e.g., in a crystal). But because of thermal vibrations, it is even here a question of a most probable position. Thermal (Brownian) movements are proportional to thermal energy and the Boltzmann factor kT, indicating an increasing uncertainty with temperature. 

The individual molecules or atoms of a gas each have a negligible volume compared to the container. 

The mean kinetic energy of the molecules or atoms of a gas is directly proportional to its absolute temperature on the thermodynamic scale. The kinetic energy of a gaseous molecule or atom is given by the expression jurw, where m represents the mass of the particle and v represents its speed. 

Vapor pressure is the pressure exerted by the molecules or atoms of a gas in equilibrium with its liquid state in the same sealed container. 

According to gas kinetic theory, the average translational energy of the atoms of a gas is equal to... 

If the diffusion flux does not change with time, a steady-state condition exists. One common example is the diffusion of atoms of a gas through a vessel or tube for which the concentrations (or pressures) of diffusing species on both surfeices (external and internal) are held constant. This is represented in Figure M.5. Then... 

As indicated in the previous section, the adsorption of a gas by a solid is the outcome of the forces of attraction between the individual molecules of the gas and the atoms or ions composing the solid. These forces have been studied theoretically over a number of decades, and though impressive advances have been made in recent years these remain more in the nature of refinements than of fundamental changes in the ideas themselves. And since. 

To apply these various equations to the adsorption of a gas on a solid, it is necessary to consider the interaction of the surface layers of a solid composed of atoms (or ions) of a substance Y, say, with isolated molecules of gas X. The individual interactions of each atom in gas molecule X with each atom of the solid Y have to be added up to obtain the potential 0(z) of a single molecule of the gas with reference to the solid ... 

An approximate equilibrium is set up in the plasma, with the electrons, ions, and atoms having velocity distributions similar to those of a gas that has been heated to temperatures of 7,000 to 10,000°C. Since the plasma is ignited toward the end of the concentric tubes from which argon gas is issuing, the plasma appears as a pale-blue-to-lilac flame coming out of the end of the tube, which is why the system is referred to as a torch, as in a welding torch. 

Infrared spectroscopy has broad appHcations for sensitive molecular speciation. Infrared frequencies depend on the masses of the atoms iavolved ia the various vibrational motions, and on the force constants and geometry of the bonds connecting them band shapes are determined by the rotational stmcture and hence by the molecular symmetry and moments of iaertia. The rovibrational spectmm of a gas thus provides direct molecular stmctural information, resulting ia very high specificity. The vibrational spectmm of any molecule is unique, except for those of optical isomers. Every molecule, except homonuclear diatomics such as O2, N2, and the halogens, has at least one vibrational absorption ia the iafrared. Several texts treat iafrared iastmmentation and techniques (22,36—38) and thek appHcations (39—42). 

An ingenious method to avoid or reduce segregation of alloying elements involves preparing small spheres of material by the atomization of a Hquid stream through a nozzle to produce a powder. This powder can be compacted, often hot and triaxially by gas pressure, to form a material where, on further heating, the residual pores close by diffusion to approach 100% density. 

Electron spectroscopic techniques require vacuums of the order of 10 Pa for their operation. This requirement arises from the extreme surface-specificity of these techniques, mentioned above. With sampling depths of only a few atomic layers, and elemental sensitivities down to 10 atom layers (i. e., one atom of a particular element in 10 other atoms in an atomic layer), the techniques are clearly very sensitive to surface contamination, most of which comes from the residual gases in the vacuum system. According to gas kinetic theory, to have enough time to make a surface-analytical measurement on a surface that has just been prepared or exposed, before contamination from the gas phase interferes, the base pressure should be 10 Pa or lower, that is, in the region of ultrahigh vacuum (UHV). 

Besides these parameters, the properties of a gas ion are sometimes characterized with mean free path A,, which illustrates the mean distance between successive impacts with gas atoms or molecules. The mean free path of ions in air is in the range of 10 to 2 10" m. ... 

Space-Filling Models. For most of this century, chemists have tried to answer the size question by using a special set of molecular models known as space-filling or CPK models. The space-filling model of an atom is simply a sphere of fixed radius. A different radius is used for each element, and the radii are chosen to reproduce certain experimental observations, such as the compressibility of a gas, or the spacing between atoms in a crystal. 

Langmuir (1916), whp put forward the fir quantitative theory of the adsorption of a gaS, assumed that a gas molecule condensing from the gas phase-would adhere to the surface fora short time before evaporating and that the condensed layer was only one atom or molecule thick. If 0 is the fraction of the surface area covered by adsorbed molecules at any time, the rate of desorption is proportional to 0 and equal to k 0 where is a constant at constant temperature. Similarly the rate of adsorption will be proportional to the area of bare surface and to the rate at which the molecules strike the surface (proportional to the gas pressurep). At equilibrium the rate of desorption equals the rate of adsorption... 

Charles s and Gay-Lussac s law Relation stating that at constant P and n, the volume of a gas is directly proportional to its absolute temperature, 106-107, 111 Chelating agent Complexing ligand that forms more than one bond with a central metal atom the complex formed is called a chelate, 411-412 natural, 424-425 synthetic, 424-425 Chemical equation Expression that describes the nature and relative amounts of reactants and products in a reaction, 60-61. See also Equation, net ionic. 

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