Gases behavior

Using the temperature dependence of 7 from Eq. III-l 1 with n - and the chemical potential difference Afi from Eq. K-2, sketch how you expect a curve like that in Fig. IX-1 to vary with temperature (assume ideal-gas behavior). 

Pressure-area isotherms for many polymer films lack the well-defined phase regions shown in Fig. IV-16 such films give the appearance of being rather amorphous and plastic in nature. At low pressures, non-ideal-gas behavior is approached as seen in Fig. XV-1 for polyfmethyl acrylate) (PMA). The limiting slope is given by a viiial equation... 

A monolayer of Streptavidin containing 1.75 mg of protein/m gives a film pressure of 0.070 erg/m at 15°C. Calculate the molecular weight of the protein, assuming ideal-gas behavior. 

The raie gas atoms reveal through their deviation from ideal gas behavior that electrostatics alone cannot account for all non-bonded interactions, because all multipole moments are zero. Therefore, no dipole-dipole or dipole-induced dipole interactions are possible. Van der Waals first described the forces that give rise to such deviations from the expected behavior. This type of interaction between two atoms can be formulated by a Lennaid-Jones [12-6] function Eq. (27)). 

Ideal Adsorbed Solution (IAS) Model For components i andassuming ideal gas behavior, this model (36) is... 

At room temperature and atmospheric pressure, 95% of the vapor consists of dimers (13). The properties of the vapor deviate considerably from ideal gas behavior because of the dimeri2ation. In the soHd state, formic acid forms infinite chains consisting of monomers linked by hydrogen bonds (14) ... 

Liquid solutions are often most easily dealt with through properties that measure their deviations, not from ideal gas behavior, but from ideal solution behavior. Thus the mathematical formaUsm of excess properties is analogous to that of the residual properties. 

Ideal Gas Behavior, In 1787 it was demonstrated that the volume of a gas varies directly with temperature if the pressure remains constant. Other investigations determined complementary correlating relations from which the perfect or ideal gas law was drawn (1 3). Expressed mathematically, the ideal gas law is... 

AH fluids, when compared at the same reduced temperature and reduced pressure have approximately the same compressibiHty factor and deviate from ideal gas behavior to the same extent, giving... 

The ideal gas is a useful model of the behavior of gases and serves as a standard to which real gas behavior can be compared. This is formalized by the introduction of residual properties. Another useful model is the ideal solution, which sei ves as a standard to which real solution behavior can be compared. This is formalized by introduction of excess propei ties. 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

Absolute humidity H equals the pounds of water vapor carried by 1 lb of diy air. If ideal-gas behavior is assumed, H = M p/[M P — p)], where M,, = molecular weight of water = molecular weight of air p = partial pressure of water vapor, atm and P = total pressure, atm. 

The specific volume of moist air in cubic feet per pound of dry air can be determined for other pressures, if ideal-gas behavior is assumed, by the following equation ... 

Compressibility of Natural Gas All gases deviate from the perfect gas law at some combinations of temperature and pressure, the extent depending on the gas. This behavior is described by a dimensionless compressibility factor Z that corrects the perfect gas law for real-gas behavior, FV = ZRT. Any consistent units may be used. Z is unity for an ideal gas, but for a real gas, Z has values ranging from less than 1 to greater than 1, depending on temperature and pressure. The compressibihty faclor is described further in Secs. 2 and 4 of this handbook. 

For a high-pressure non-ideal gas behavior, the term (TqTi/TtIo) is replaced by (ZqTqTi/ZTtIq), where Z is the compressiblity factor. To change to another key reactant B, then... 

Let Pg(atm) be the initial reactor pressure. Prove that ly2, the time required to achieve 50% conversion of A in the reactor, equals RT/kpg. Assume an ideal gas behavior. 

The volumetric flowrate depends on the temperature and changes as the temperature changes. Assuming a perfect gas behavior. 

The model contains a surface energy method for parameterizing winds and turbulence near the ground. Its chemical database library has physical properties (seven types, three temperature dependent) for 190 chemical compounds obtained from the DIPPR" database. Physical property data for any of the over 900 chemicals in DIPPR can be incorporated into the model, as needed. The model computes hazard zones and related health consequences. An option is provided to account for the accident frequency and chemical release probability from transportation of hazardous material containers. When coupled with preprocessed historical meteorology and population den.sitie.s, it provides quantitative risk estimates. The model is not capable of simulating dense-gas behavior. 

Whereas Fishbum was mainly interested in the detonative mode of explosion, Luckritz (1977) and Strehlow et al. (1979) focused on the simulation of generation and decay of blast from deflagrative gas explosions. For this purpose, they employed a similar code provided with a comparable heat-addition routine. Strehlow et al. (1979), however, realized that perfect-gas behavior, which is the basis in the numerical scheme for the solution of the gas-dynamic conservation equations, is an idealization which does not reflect realistic behavior in the large temperature range considered. 

The pressure vessel under consideration in this subsection is spherical and is located far from surfaces that might reflect the shock wave. Furthermore, it is assumed that the vessel will fracture into many massless fragments, that the energy required to mpture the vessel is negligible, and that the gas inside the vessel behaves as an ideal gas. The first consequence of these assumptions is that the blast wave is perfectly spherical, thus permitting the use of one-dimensional calculations. Second, all energy stored in the compressed gas is available to drive the blast wave. Certain equations can then be derived in combination with the assumption of ideal gas behavior. 

In many cases, pressurized gases in vessels do not behave as ideal gases. At very high pressures, van der Waals forces become important, that is, intermolecular forces and finite molecule size influence the gas behavior. Another nonideal situation is that in which, following the rupture of a vessel containing both gas and liquid, the liquid flashes. 

We must start with fluid behavior to understand the basic concepts of unified chromatography. We must forget most of what we know from common experience about liquid and gas behavior since this experience is tied with ambient conditions. Instead, we must embrace the new possibilities afforded by temperatures and pressures that are different from ambient. This new view requires phase diagrams (17, 18). 

If the gas behavior deviates markedly from ideal, the real gas law can be w ritten as Ps... 

The material in this section is divided into three parts. The first subsection deals with the general characteristics of chemical substances. The second subsection is concerned with the chemistry of petroleum it contains a brief review of the nature, composition, and chemical constituents of crude oil and natural gases. The final subsection touches upon selected topics in physical chemistry, including ideal gas behavior, the phase rule and its applications, physical properties of pure substances, ideal solution behavior in binary and multicomponent systems, standard heats of reaction, and combustion of fuels. Examples are provided to illustrate fundamental ideas and principles. Nevertheless, the reader is urged to refer to the recommended bibliography [47-52] or other standard textbooks to obtain a clearer understanding of the subject material. Topics not covered here owing to limitations of space may be readily found in appropriate technical literature. 

The above method is commonly used for gases and infrequently for liquid mixtures. At atmospheric conditions when ideal gas behavior is realized, the total volume of the mixture equals the sum of the pure-component volumes ( V ). That is, V = V and... 

Ideal (or perfect) gas behavior is approached by most vapors and gases in the limit of low pressures and elevated temperatures. Two special forms of restricted utility known as the Boyle s law and the Charles law preceded the development of the perfect gas law. 

Although real gases deviate from ideal gas behavior and therefore require different equations of state, the deviations are relatively small under certain conditions. An error of 1% or less should result if the ideal gas law were used for diatomic gases whenV> 5 f/ gm-mole (80 ftyib-mole) and for other gases and light hydrocarbon vapors when V > 20 f/gm-mole (320 ftyib-mole) [61, p. 67]. 

A volatile compound of chlorine has been analyzed to contain 61.23% of oxygen (Op and 38.77% of chlorine (Cl ) by weight. At 1 atm and 27°C, 1000 cm of its vapor weighs 7.44 g. Assuming ideal gas behavior for the vapor, estimate its molecular weight and deduce its molecular formula. 

Although GA are undeniably powerful computational tools and have been successfully applied to an impressive variety of problems (see below), they certainly do not represent a cure-all solution to all types of problems. One finds that, in practice, certain problems arc more amenable to this kind of solution scheme than others, and that it is not always obvious why that is so. Much foundational work still remains to be done in developing a complete theory of GA behaviors and capabilities. Figure 11.10 illustrates the basic steps involved in applying a GA. 

Deviation of methane gas from ideal gas behavior. Below about 350 atm, attractive forces between methane (CH4) molecules cause the observed molar volume at 25°C to be less than that calculated from the ideal gas law. At 350 atm, the effect of the attractive forces is just balanced by that of the finite volume of CH4 molecules, and the gas appears to behave ideally. Above 350 atm, the effect of finite molecular volume predominates and V, > 1C... 

We should point out that the calculations involved in Example 12.6 assume ideal gas behavior. At the conditions specified (1 atm, relatively high temperatures), this assumption is a good one. However, many industrial gas-phase reactions are carried out at very high pressures. In that case, intermolecular forces become important, and calculated yields based on ideal gas behavior may be seriously in error. 

Pressure is an important quantity in a discussion of gas behavior. The applicability of the kinetic theory to an understanding of gas pressure is, then, an important success (see Section 2-1.1). We shall investigate this success in more detail, but first we should investigate how pressure is measured. 

Our knowledge of gas behavior helps us interpret the evaporation of liquids. We have considered, thus far, vaporization of a liquid at its usual... 

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