Gases molecular motion

Molecular diffusion. The diffusion is molecular diffusion if the radius of pore in porous solids is larger than the mean free path of gas molecular motion, i.e., the probability of collision between molecules is larger than that between molecules and wall of pore. In this case, the resistance of transfer process mainly comes from the collision between molecules and is independent of the radius of pore. The main contribution is molecular diffusion for the systems with larger pore diameter (>10 cm, comparing with mean free path 10 cm at 101.3kPa) and with higher pressures. 

It is known from theory of ideal gas molecular motion ... 

Knudsen diffusion. If the radius of pore is smaller than the mean free path of gas molecular motion or gas molecules collide with the wall of pore rather than other molecules, the diffusion is called as Knudsen diffusion. The main contribution comes from Knudsen diffusion for the system with smaller radius of pore and with low gas pressures. 

Fig. 5.2-1. Molecular motion in a liquid. In contrast with a gas, molecular motion in a liquid takes place at high density (a). Diffusion is complex, involving many interactions and vacancies. The available kinetic theories are good, but complex. To avoid this, many use the simple model of a solute sphere in a solvent continuum (b).

As we have implied, diffusion is a rather complex process so far as molecular motion is concerned. Effusion, the flow of gas molecules at low pressures through tiny pores or pinholes, is easier to analyze using kinetic theory. 

This connection between the correlation time of perturbation and that of response is a very general result independent of a model of molecular motion. It is valid not only when a molecule is perturbed by a sequence of instantaneous collisions (as in a gas), but also when it is subjected to perturbations that are continuous in time (caused by the nearest... 

Perchard J. P., Murphy W. F., Bernstein H. J. Raman and Rayleigh spectroscopy and molecular motions. III. Self-broadening and broadening by inert gases of hydrogen halide gas spectra, Mol. Phys. 23, 535-45 (1972). 

We have shown that the contribution to the molar internal energy of a monatomic ideal gas (such as argon) that arises from molecular motion is jRT. We can conclude that if the gas is heated through AT, then the change in its molar internal energy, AUm, is Al/m = fTAT For instance, if the gas is heated from 20.°C to 1()0.°C (so AT = +80. K), then its molar internal energy increases by 1.0 kj-mol. ... 

This chapter discusses the apphcation of femtosecond lasers to the study of the dynamics of molecular motion, and attempts to portray how a synergic combination of theory and experiment enables the interaction of matter with extremely short bursts of light, and the ultrafast processes that subsequently occur, to be understood in terms of fundamental quantum theory. This is illustrated through consideration of a hierarchy of laser-induced events in molecules in the gas phase and in clusters. A speculative conclusion forecasts developments in new laser techniques, highlighting how the exploitation of ever shorter laser pulses would permit the study and possible manipulation of the nuclear and electronic dynamics in molecules. 

To determine molecular motions in real time necessitates the application of a time-ordered sequence of (at least) two ultrafast laser pulses to a molecular sample the first pulse provides the starting trigger to initiate a particular process, the break-up of a molecule, for example whilst the second pulse, time-delayed with respect to the first, probes the molecular evolution as a function of time. For isolated molecules in the gas phase, this approach was pioneered by the 1999 Nobel Laureate, A. H. Zewail of the California Institute of Technology. The nature of what is involved is most readily appreciated through an application, illustrated here for the photofragmentation of iodine bromide (IBr). 

The pressures exerted by gases demonstrate molecular motion. Gases are collections of molecules, so the pressure exerted by a gas must come from these molecules. Just as the basketball In Figure 2J exerts a force when it collides with a backboard, moving gas molecules exert forces when they collide with the walls of their container. The collective effect of many molecular collisions generates pressure. 

Rates of molecular motion are directly proportional to molecular speeds, so Equation predicts that for any gas, rates of effusion and diffusion increase with the square root of the temperature in kelvins. Also, at any particular temperature, effusion and diffusion are faster for molecules with small molar masses. 

Matter (anything that has mass and occupies space) can exist in one of three states solid, liquid, or gas. At the macroscopic level, a solid has both a definite shape and a definite volume. At the microscopic level, the particles that make up a solid are very close together and many times are restricted to a very regular framework called a crystal lattice. Molecular motion (vibrations) exists, but it is slight. 

The immediate impact of this research will be a clearer understanding of ligand motions during photoelimination reactions. In particular, comparative studies of molecular motions in the gas phase (using ultrafast electron diffraction) and in the liquid phase should become a source of very detailed understanding of the influence of solvation on chemical processes. Such combined studies in collaboration with Peter Weber, Dept, of Chemistry, Brown University are planned. 

Practically speaking, this concept explains the basis for the establishment of partial pressure equilibrium of anesthetic gas between the lung alveoli and the arterial blood. Gas molecules will move across the alveolar membrane until those in the blood, through random molecular motion, exert pressure equal to their counterparts in the lung. Similar gas tension equilibria also will be established between the blood and other tissues. For example, gas molecules in the blood will diffuse down a tension gradient into the brain until equal random molecular motion (equal pressure) occurs in both tissues. 

Due to the small dimensions of the channels in porous media, viscous forces usually suppress turbulence. Hence, diffusion through the pore space occurs by molecular motions. If the size of the pores is small, molecular motions are reduced. In gas-filled pores, this is the case if the pore size is similar to or smaller than the... 

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. 

One of the more important conclusions from kinetic-molecular theory comes from assumption 5—the relationship between temperature and EK, the kinetic energy of molecular motion. It can be shown that the total kinetic energy of a mole of gas particles equals 3RT/2 and that the average kinetic energy per particle is thus 3RT/2Na, where NA is Avogadro s number. Knowing this relationship makes it possible to calculate the average speed u of a gas particle. To take a helium atom at room temperature (298 K), for example, we can write... 

The constant motion and high velocities of gas particles lead to some important practical consequences. One such consequence is that gases mix rapidly when they come in contact. Take the stopper off a bottle of perfume, for instance, and the odor will spread rapidly through the room as perfume molecules mix with the molecules in the air. This mixing of different gases by random molecular motion with frequent collisions is called diffusion. A similar process in which gas molecules escape without collisions through a tiny hole into a vacuum is called effusion (Figure 9.13). 

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