Properties of Ideal Gases

A substance is in the ideal gas state when the volume of its molecules is a zero fraction of the total volume taken up by the substance and when the individual molecules are far enough apart from each other so that there is no interaction between them. Although this only occurs at infinite volume and zero pressure, in practice, ideal gas properties can be used for gases up to a pressure of two atmospheres with little loss of accuracy. Thermal properties of ideal gas mixtures may be obtained by mole-fraction averaging the pure component values. 

Burcat Thermodynamic Properties of Ideal Gas Nitro and Nitrate Compounds [43]... 

From (4.1.15) we can derive expressions for all properties of ideal-gas mixtures for example, we can immediately determine the pressure. To do so, we use the fundamental equation (3.2.12) to write any mixture or pure-component pressure as... 

To obtain the partial molar properties of ideal-gas mixtures we apply the partial molar derivative (3.4.5) either to the ideal-gas law, to obtain the partial molar volume, or to the general expression (4.1.15), to obtain other properties. The generic expression (4.1.15) yields... 

To obtain the properties of ideal-gas mixtures we simply accumulate the partial molar properties according to (3.4.4), all at the same T and P,... 

Further, the difference between the heat capacities for ideal-gas mixtures is the same as for pure ideal gases (4.1.4). In summary, all first-law properties of ideal-gas mixtures are rigorously obtained by mole-fraction averaging pure ideal-gas properties. For second-law properties, we substitute (4.1.35)-(4.1.37) into (3.4.4) to find... 

In 4.1.4 we found that to compute the thermodynamic properties of ideal-gas mixtures, we need only the mixture composition plus the pure ideal-gas properties at the same state condition as the mixture. In other words, tire properties of ideal-gas mixtures are easy to compute. We would like to take advantage of this, even for substances that are not ideal gases. To do so we introduce, for a generic property F, a residual property P, which serves as a difference measure for how our substance deviates from ideal-gas behavior. 

Property of ideal-gas mixture Property of mixing Partial molar... 

The actual compression diagram naturally deviates from the ideal the extent varying with the physical characteristics of the cylinder and the properties of the gas, Figures 12-12, 12-12A, and 12-12B. 

The fugacity coefficient is a function of pressure, temperature, and gas composition. It has the useful property that for a mixture of ideal gases (Pi = 1 for all i. The fugacity coefficient is related to the volumetric properties of the gas mixture by either of the exact relations (B3, P5, R6) ... 

If the gas deviates appreciably from the ideal gas laws over the range of conditions considered, the work of compression is most conveniently calculated from the change in the thermodynamic properties of the gas. 

The ideal gas equation relates the number of moles of gas to the physical properties of that gas. When a chemical reaction involves a gas, the ideal gas equation provides the link between P-V-T data and molar amounts. 

Statistical mechanics enables one to express the chemical potential i, for an ideal gas phase system in terms of the spectroscopic properties of individual gas phase molecules. The reader is referred to standard statistical mechanics texts (e.g. D. A. McQuarrie Statistical Mechanics , reading list) for the development of the relationship between the system Helmholtz free energy, A , and the corresponding canonical partition function Qi... 

Steele, W.V., Chirico, R.D., Cowell, A.B., Knipmeyer, S.E., and Nguyen, A. Thermodynamic properties and ideal-gas enthalpies of formation for 2-aminoisobutyric acid (2-methylalanine), acetic acid, ( -5-ethylidene-2-norbornene, mesityl oxide (4-methyl-3-penten-2-one), 4-methylpent-l-ene, 2,2 -bis(phenylthio)propane, and glycidyl phenyl ether (1,2-epoxy-3-phenox3q>ropane), / Chem. Eng. Data, 42(6) 1053-1066, 1997. 

Fugacity is a thermodynamic property related to the deviation of the p—V—T properties of the gas from those of an ideal gas. At very low pressures, the fugacity of a real gas tends to its partial pressure... 

It is often possible to predict with accuracy many properties of ideal solutions, such as dilute gas mixtures, as well as liquid mixtures of closely related substances such as pentane and hexane. On the other hand, liquid mixtures of substances with different... 

Chapter 10 sets down the basic assumptions of the kinetic molecular theory of gases, a set of ideas that explains gas properties in terms of the motions of gas particles. In summary, kinetic molecular theory describes the properties of ideal gases, ones that conform to the following criteria ... 

Gas properties are functions of temperature, pressure, and total moles as dictated by the ideal gas law. The assumption of ideal gas behavior will be accurate as long as the operating temperatures of the reactor are much higher than the critical temperatures of the component species and the pressures are relatively low and is in general valid for most gaseous reaction systems. 

For all calculations, we need the characteristic properties of the gas phase. Since the gas phase consists of 90% oxygen, we can assume that the gas properties can be represented by the properties of the oxygen alone. The gas density can be evaluated using the ideal gas law... 

EXAMPLE 10.2 The Dispersion Force and Nonideality of Gases. The nonideality of gases arises from the repulsive and attractive forces between atoms. As a consequence, the deviation of the properties of a gas from ideal gas behavior can be traced to the interatomic or intermolec-ular forces. Assume that methane follows the van der Waals equation of state at sufficiently low densities. It is known from experiments that (see Israelachvili 1991)... 

So far, in this discussion we have considered mechanical properties of the gas (in the sense of classical mechanics) that involve m and v. Nonmechanical properties are quantities like the temperature and thermodynamic functions. We can begin to make a connection between the two by comparing Eq. 8.6 with the ideal gas law pV = nRT. Equating the two, we obtain the kinetic theory result... 

The defining characteristic of ideal gas mixtures is the absence of any interactions. Thus, all thermodynamic properties separate into their partial contributions for example,... 

The properties of a gas can be described by four interrelated quantities pressure, volume, temperature, and number of particles. Boyles, Charles s, and Avo-gadro s gas laws each describe how one quantity varies relative to another so long as the remaining two are held constant. We can combine these three laws into a single law, called the ideal gas law, which shows the relationship of all these quantities in a single equation ... 

The ideal gas equation is the outcome of a model devised for understanding the properties of a gas, in which there is no interaction between the atoms or molecules occupying the volume, V. In mathematical terms, however, this ideal gas equation remains a formula until we know how to use it as a function, a key aspect of which is developed next. 

Unlike solids and liquids, different gases show remarkably similar physical behavior regardless of their chemical makeup. Helium and fluorine, for example, are vastly different in their chemical properties yet are almost identical in much of their physical behavior. Numerous observations made in the late 1600s showed that the physical properties of any gas can be defined by four variables pressure (P), temperature (T), volume (V), and amount, or number of moles in). The specific relationships among these four variables are called the gas laws, and a gas whose behavior follows the laws exactly is called an ideal gas. 

The thermodynamic properties of a substance in the state of ideal gas are calculated as the sums of contributions from translation and rotation of a molecule as a whole, vibrations and internal rotation in the molecule, and electronic excitation. For example, for entropy and heat capacity the following equations hold ... 

These two equations are applicable to mixtures of ideal gases as well as to pure gases, provided n is taken to be the total number of moles of gas. However, we must consider how the properties of the gas mixture depend upon the composition of the gas mixture and upon the properties of the pure gases. In particular, we must define the Dalton s pressures, the partial pressures, and the Amagat volumes. Dalton s law states that each individual gas in a mixture of ideal gases at a given temperature and volume acts as if it were alone in the same volume and at the same temperature. Thus, from Equation (7.1) we have... 

PROPERTIES OF IDEAL GASES 7.2.1 Assumptions Behind the Ideal Gas Law... 

The equation for V gives the ideal-gas value. The equations for H and U show these properties to be functions of T only, which conforms to ideal-gas behavior. The equation for S shows its relation to P to be that of an ideal gas. The equations for CP and Cv show these properties to be functions of T only, which conforms to ideal-gas behavior, as does the result, Cp = Cv + R- We conclude that the given equation of state is consistent with the model of ideal-gas behavior. 

In this frame we bring together the properties of ideal gases (See Sections 4.1 and 4.2 Frame 4) and the specific calculation of work done when a gas is expanded (Frame 7). 

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