Polarization of a gas

Schematic representation of the frequency dependence of the molar polarization of a gas of permanent dipoles. Dashed lines indicate ranges of complex behavior.

Let us now consider whether neglecting the atomic polarization P is justified. A simple classical treatment of atomic polarization of a gas molecule has been given by Van Vleck, Coop and Sutton, and Smyth. It is based on the approximation that the vibrations of the molecule are harmonic. Van Vleck argues that the result of this classical treatment is (to the same level of approximation) valid also under quantum mechanics. 

Clausius-Mosotti equation (for polarization of a gas) (1.4.4.10) clay minerals (general) 1.5.99... 

The Clausius-Mossotti function or total polarization, of a gas can be expanded in inverse powers of the molar volume, V ... 

By insertine the mean dipole moment (2S2a) into the polarization fonnula (2S1) and using the definitions (246) and (2S0), one obtains the change in molar polarization of a gas due to the square of the electric field strength ... 

Only a minority of distortion polarizations are available from experiment, a fairly extensive study of the dependence of the total dielectric polarization of a gas upon absolute temperature being required to provide a confident value for DP via the Debye equation... 

The total polarization of a gas may be due to polarization of the electrons in the gas molecules (for fixed nuclear positions), polarization of the nuclei (with change in the relative positions of the nuclei in the molecules), and orientation of molecules with permanent electric dipole moments. We are here discussing only the first of these mechanisms the second is usually unimportant, and the third is treated briefly in Section 49/. 

The free energy of activation at the QCISD(T)/6-31 H-- -G(d,p) level amounts to 21.1 kcal/mol. According to the authors, the large electron density redistribution arising upon cyclization makes it necessary to use extended basis sets and high-order electron correlation methods to describe the gas-phase thermodynamics, which indicates clearly the gas-phase preference of the azido species. However, the equilibrium is shifted toward the tetrazole as the polarity of a solvent is increased. For instance, SCRF calculations (e = 78.4) yield a relative free energy of solvation with respect to the cw-azido isomer of —2.4 kcal/mol for the tmns-zziAo compound and of —6.8 kcal/mol for the tetrazole isomer. At a much lower level, the... 

Here e is the dielectric constant of the gas, F the strength of the applied field, N the number of molecules in unit volumes, n the permanent electric moment of a molecule, and a the coefficient of induced polarization of a molecule cos 9 is the average value of cos 9 for all molecules in the gas, and cos 9 is the time-average of cos 9 for one molecule in a given state of motion, 6 being the angle between the dipole axis and the lines of force of the applied field. 

Fig. 30. Cathodic polarization of a nickel gas-diffusion electrode before and after sulfidation with H2S.

Interpreting Data Were your data consistent with the ideal gas law Evaluate the pressure and temperature at which your experiment was done, and the polarity of the gas. Would you expect the gas in your experiment to behave as an ideal gas or a real gas ... 

As the temperature of a gas system is lowered, the speed of the molecules decreases. When these lower-speed molecules collide with one another, attractive forces between the molecules become more significant, and a temperature will be reached where condensation occurs - the vapor state converts to liquid. Di-pole-dipole attractive forces are most important in causing condensation, and molecules with substantial partial charges, resulting from polar covalent bonds, t3q3ically have high condensation temperatures. (Condensation temperature will be the same as the boiling point of a liquid, approached from the opposite direction. )... 

The method has been applied, for example, in electrochemical investigations (110) and also for surface catalytic reactions in the presence of a gas phase 111). When PM-IRRAS is used with a thin-layer cell, as depicted in Fig. 37, the contribution from dissolved molecules in the liquid phase can be minimized. Still, the layer thickness has to be small to prevent complete absorption of the IR radiation by the solvent. The combination of polarization modulation and ATR for metal films was demonstrated recently and applied in an investigation of self-assembled octadecylmercaptan monolayers on thin gold films 112). This combination could emerge as a valuable technique for the investigation of model catalysts. 

Let us first consider the dielectric constant of a gas. We assume that the molecules are far enough apart for them to contribute independently to the polarization and that the electric field E induces an electric dipole moment aE in each molecule. The quantity a is called the electric polarizability of the molecule. The number of moles per unit volume of gas is the density p divided by the tnolecular weight M, and the number of molecules in unit volume is this ratio multiplied by Avogadro s number A. Hence the polarization of the gas (the induced dipole moment per unit volume) is given by the following equation ... 

In the forming of these polar bonds, electrons of the metals are withdrawn from the metal. The binding of electrons can be shown by the increase of the secondary electron emission (86,87), and conductivity measurements (88,89) and measurements of contact resistances (90,91) show that conduction electrons have been occupied by these bonds. The physical adsorption of a gas on a metallic surface, on the other hand, causes a slight increase of the conductivity of the metal (92,93). 

The solubility selectivity of a membrane for a specific gas pair could be increased (in principle) by inducing specific interactions between the polymer and the more soluble component of the gas pair. For example, the substitution of certain polar groups in some rubbery polymers has been found to increase their solubility selectivity for CO2 relative to CH4 (Story and Koros, 1991 Koros, 1985). Unfortunately, the increase in the polarity of a polymer also tends to increase its chain packing density, and as a result, decreases the gas diffusivity in membranes made from that polymer. 

The authors of [297] have presented the most consistent classical approach for the description of the polarization of a molecular gas by a strong light wave. The basic and principal difference between the methods of polarization spectroscopy and laser probing of dichroism consists of the fact that polarization spectroscopy demands the application of monochromatic single-frequency radiation, whilst probing of dichroism is based on the employment of a broad spectral irradiation. 

The first chemical clue relating the structure of anesthetics to their potency was discovered in 1899 by a pharmacologist, Hans Horst Meyer, and an anesthetist, Charles Ernst Overton. Working independently, Meyer and Overton noted a strong correlation between the polarity of a compound and its potency as an anesthetic. They expressed polarity as the oil/gas partition coefficient, while anesthetic potency was expressed as the partial pressure in atmospheres. Figure 11.10 is a Meyer-Overton correlation for 18 anesthetics used on mice. Note that olive oil is used, and it has become the most commonly used reference solvent. 

The polarization density of a gas of permanent dipoles of number density N in a constant electric field of magnitude E is then... 

Gas Chromatography. The basic components of a gas chromatograph are a carrier gas system, a column, a column oven, a sample injector, and a detector. Very pure helium is the near-universal carrier gas for environmental and many other analyses. Open tubular GC columns are constructed of fused silica with low-bleed stationary phases of varying polarity chemically bonded to the silica surface. Columns are typically 30-75 m in length and have inside diameters (ID) in the range of about 0.25-0.75 mm. The column oven is capable of precise temperature control and temperature programming at variable rates for variable times. 

Gases for use in experiments may be collected in a variety of ways. Two things that should be kept in mind when collecting a gas are the density and the polarity of the gas. For example, you would not collect a polar gas (such as ammonia) in water because water and ammonia have like polarities that allow the two substances to mix. 

Measurement of dipole moments. When a solution of polar molecules is placed between two oppositely-charged plates, they will tend to align themselves along the direction of the field. This process consumes energy which is returned to the electrical circuit when the field is switched off, an effect known as electrical capacitance. Measurement of the capacitance of a gas or solution is easy to carry out and serves as a means of determining the magnitude of the dipole moment of a substance. 

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