Gases ideal behavior

Until now our discussions have dealt with ideal behavior of gases. By this we mean that the identity of a gas does not affect how it behaves, and the same equations should work equally well for all gases. Under ordinary conditions most gases do behave ideally their P and Vare well described by the ideal gas laws, so they do obey the postulates of the kinetic-molecular theory. According to the kinetic-molecular model, (1) all but a neghgible volume of a gas sample is empty space, and (2) the molecules of ideal gases do not attract one another because they are so far apart and are considered point masses without any volume. 

Nonideal gas behavior (deviation from the predictions of the ideal gas laws) is most significant at high pressures and/or Icrw temperatures, that is, near the conditions under which the gas liquefies. 

Johannes van derWaals (1837-1923) studied deviations of gases from ideal behavior. In 1867, he empirically adjusted the ideal gas equation 

PV = nRT at all pressures, so PV/nRT = 1 at all pressures horizontal line). We can test a gas for ideal behavior by measuring P, V, n, and Tfor a sample of the gas at various pressures and then calculating PV/nRT. At pressures up to a few atmospheres, all of these plots show PV/nRT near 1, or nearly ideal behavior. Different gases deviate differently from ideal behavior, and these deviations from ideality become more pronounced at higher pressures. 

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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 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 ... 

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 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. 

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... 

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. 

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. 

Moreover, since the mean free path is of the order of 100 times the molecular diameter, i.e., the range of force for a collision, collisions involving three or more particles are sufficiently rare to be neglected. This binary collision assumption (as well as the molecular chaos assumption) becomes better as the number density of the gas is decreased. Since these assumptions are increasingly valid as the particles spend a larger percentage of time out of the influence of another particle, one may expect that ideal gas behavior may be closely related to the consequences of the Boltzmann equation. This will be seen to be correct in the results of the approximation schemes used to solve the equation. 

For nearly oxygen-balanced expls equilibrium (1) will dominate and control the compn of the detonation products. As already stated this equilibrium is expected to be independent of pressure if the gases behave ideally. But even for ideal gas behavior and an oxygen-balanced expl, no direct comparison can be made between theoretical detonation product calcns and observed products. This is so because measurements are made at temps much lower than detonation temps, and the products reequilibrate as the temp drops. Further complications arise because the reequilibration freezes at some rather high temp. This is a consequence of re-, action rates. At temps below some frozen equb... 

E2.12 Calculate ASmiX for the mixing of 0.25 moles of D2 (deuterium gas) with 0.75 moles of H2 at a total constant pressure of 100 kPa. Assume ideal gas behavior. 

E3.8 A sample of Ne gas contains 90 mole% 20Ne and 10 mole% 22Ne. Calculate AGm and A5m at 300 K. for the separation of one mole of this gas into two isotopically pure fractions, one containing only 20Ne and the other 22Ne. Assume ideal gas behavior so that the isotopes behave independently in the separation, and that the pressure is 0.10 MPa. 

We used the system (.vic-Q,H 1CH3 +. vic-CeH ) as an example of a system that closely approximates ideal behavior. Figure 6.5 showed the linear relationship between vapor pressure and mole fraction for this system. In this Figure, vapor pressure could be substituted for vapor fugacity, since at the low pressure involved, the approximation of ideal gas behavior is a good one, and... 

Suppose a homogeneous, gas-phase reaction occurs in a constant-volume batch reactor. Assume ideal gas behavior and suppose pure A is charged to the reactor. 

Example 3.4 Find the mean residence time in an isothermal, gas-phase tubular reactor. Assume that the reactor has a circular cross section of constant radius. Assume ideal gas behavior and ignore any change in the number of moles upon reaction. 

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