Several Real Gases

We can understand gas behavior more completely if we examine the characteristics of several common gases. Note from Fig. 5.25 that the gases FI2, N2, CFI4, and CO2 show dif- 

A low value for a reflects weak intermolecular forces among the gas molecules. 

Also notice that although the compressibility for N2 dips below 1.0, it does not show as much deviation as that for CFI4, which in turn does not show as much deviation as the compressibility for CO2. Based on this behavior we can surmise that the importance of intermolecular interactions increases in this order  

This order is reflected by the relative a values for these gases in Table 5.3. In Section 10.1, we will see how these variations in intermolecular interactions can be explained. The main point to be made here is that real gas behavior can tell us about the relative importance 

The chemistry occurring in the troposphere, the layer of atmosphere closest to the earth s surface, is strongly influenced by human activities. Millions of tons of gases and particulates are released into the troposphere by our highly industrial civilization. 

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Table 12.1 Molar Volume of Several Real Gases at STP 8. A certain set of conditions allows 4.0 mol of gas to be held in a 70 L container. What volume do 6.0 mol of gas need under the same conditions of temperature and pressure 9. At STP, a container holds 14.01 g of nitrogen gas, 16.00 g of oxygen...

You know that ideal gases have a volume of 22.4 L at STP. Do real gases have the same volume The volumes of several real gases at STP are given in Table 12.1. All the volumes are very close to 22.4 L/mol, the molar volume of an ideal gas. Scientists have decided that 22.4 L/mol is an acceptable approximation for any gas at STP when using gas laws. Although the volumes are the same, one mole of a gas will have a different mass and density than one mole of another gas. (See Figure 12.7.)... 

FIGURE 9.17 A plot of z = PV/nRT against pressure shows deviations from the ideal gas law quite clearly, for an ideal gas, z is represented by the straight horizontal line, (a) Deviation of several real gases at 25°C. (b) Deviation of nitrogen at several temperatures. 

Figure 5.19 The behavior of several real gases with increasing external pressure. The horizontal line shows the behavior of 1 mol of ideal gas PV/RT = 1 at all Pext- At very high pressures, all real gases deviate significantly from such ideal behavior. Even at ordinary pressures, these deviations begin to appear (expanded portion).

Two new sections have been added. Section 5.11, Characteristics of Real Gases, emphasizes the properties of several real gases. Section 16.12, Nanotechnology, provides an introduction to a very important new area of chemistry and technology. 

A Figure 10.19 The effect of pressure on the behavior of several real gases. Data for 1 mol of... 

The phenomena that cause slight deviations under standard conditions exert more influence as the temperature deaeases and pressure increases. Figure 5.21 shows a plot of PV/RT versus external pressure (P xt) for 1 iriol of several real gases and an ideal gas. The values on the horizontal axis are the external pressures at which the PV/RT ratios were calculated. The PV/RT values range from normal (at P xt = 1 atm, PV/RT = 1) to very high (at P xt 10(X) atm, PV/RT == 1.6 to 2.3). For the ideal gas, PV/RT is 1 at any P xf... 

CHEMKIN REAL-GAS A Fortran Package for Analysis of Thermodynamic Properties and Chemical Kinetics in Nonideal Systems, Schmitt, R. G., Butler, P. B. and French, N. B. The University of Iowa, Iowa City, IA. Report UIME PBB 93-006,1993. A Fortran program (rglib.f and rgin-terp.f) used in connection with CHEMKIN-II that incorporates several real-gas equations of state into kinetic and thermodynamic calculations. The real-gas equations of state provided include the van der Waals, Redlich-Kwong, Soave, Peng-Robinson, Becker-Kistiakowsky-Wilson, and Nobel-Abel. 

To start, convert the flow to values estimated to be the compressor inlet conditions. Initially, the polytropic head equation (Equation 2.73) will be used with n as the polytropic compression exponent. If prior knowledge of the gas indicates a substantial nonlinear tendency, the real gas compression exponent (Equation 2.76) should be substituted. As discussed m Chapter 2, an approximation may be made by using the linear average ut the inlet and outlet k values as the exponent or for the determination of the polytropic exponent. If only the inlet value of k is known, don t be too concerned. The calculations will be repeated several times as knowledge of the process for the compression cycle is developed. After selecting the k value, u,se Equation 2.71 and an estimated stage efficiency of 15 / to de clop the polytropic compression exponent n. 

A set of calculations using real gas tables illustrates the performance of the several types of gas turbine plants discussed previously, the [CBT]ig, [CBTX]ig, [CBTBTX]ig, [CICBTXIig and [CICBTBTX]ig plants. Fig. 3.15 shows the overall efficiency of the five plants, plotted against the overall pressure ratio (r) for = 1200°C. These calculations have been made with assumptions similar to those made for Figs. 3.13 and 3.14. In addition (where applicable), equal pressure ratios are assumed in the LP and HP turbomachinery, reheating is set to the maximum temperature and the heat exchanger effectiveness is 0.75. 

There are several papers in the literature which give details of cycle calculations, and include details of how the cooling flow quantity may be estimated and used. Here we describe one such approach used by the author and his colleagues. Initially, we summarise how i/rcan be obtained (fuller details are given in Appendix A). We then illustrate how this information is used in calculations, once again using a computer code in which real gas effects are included. 

Fig. 3.16 showed carpet plots of efficiency and specific work for several dry cycles, including the recuperative [CBTX] cycle, the intercooled [CICBTX] cycle, the reheated [CBTBTX] cycle and the intercooled reheated [CICBTBTX] cycle. These are replotted in Fig. 6.17. The ratio of maximum to minimum temperature is 5 1 (i.e. T nx 1500 K) the polytropic efficiencies are 0.90 (compressor), 0.88 (turbine) the recuperator effectiveness is 0.75. The fuel assumed was methane and real gas effects were included, but no allowance was made for turbine cooling.

Although at the present time there is no indication of the existence of a compound with a real Ga-Ga double bond, a discussion regarding the Ga-Ga triple bond has raged for several years. This was initiated by a remarkable experimental result in which a compound with an anionic Ga2R2 unit 3 and bridging Na+ cations was structurally elucidated (Figure 2.3-2) [19] and interpreted on the basis of quantum chemical calculations [20],... 

If equilibrium has not been reached between a mixture of components, the condition is referred to as partial saturation. At partial saturation the gas mixture obeys real gas laws. There are several ways to express the concentration of a vapor in a mixture of gases. Most often, weight or mole fraction is used. Other definitions are relative saturation (relative humidity), molal saturation (molal humidity) and absolute saturation (absolute humidity). 

No actual gas follows the ideal gas equation exactly. Only at low pressures are the differences between the properties of a real gas and those of an ideal gas sufficiently small that they can be neglected. For precision work the differences should never be neglected. Even at pressures near 1 bar these differences may amount to several percent. Probably the best way to illustrate the deviations of real gases from the ideal gas law is to consider how the quantity PV/RT, called the compressibility factor, Z, for 1 mole of gas depends upon the pressure at various temperatures. This is shown in Figure 7.1, where the abscissa is actually the reduced pressure and the curves are for various reduced temperatures [9]. The behavior of the ideal gas is represented by the line where PV/RT = 1. For real gases at sufficiently low temperatures, the PV product is less than ideal at low pressures and, as the pressure increases, passes through a minimum, and finally becomes greater than ideal. At one temperature, called the Boyle temperature, this minimum... 

To help quantify the deviation of a real gas from ideality, a compression factor Z has been defined by Z = PV/nRT. Figure 1 shows how the compression factor for ammonia depends on pressure at several different temperatures. 

Equations of state for fluids are considered in detail in Chapter 6. To illustrate the use of the mass and energy balance equations in a simple form, we briefly consider here the equation of state for the ideal gas and the graphical and tabular display of the thermodynamic properties of several real fluids. 

Air as a Real Gas in Chemical Equilibrium. At reentry speeds, the high enthalpies introduce Prandtl number variations and the nonideal effects of dissociation and ionization in the behavior of equilibrium air. Several studies [12-17] have determined the effects of these property variations on the behavior of the laminar boundary layer for successively increasing speeds. A characteristic common to these theories because of the complexity of the behavior of air at elevated enthalpies is the reliance on completely numerical computation of a relatively limited number of examples. The results, however, are not markedly different from the... 

The fact that the behavior of a real gas approaches that of the ideal gas as the pressure is lowered is used as a basis for the precise determination of the molar masses of gases. According to Eq. (2.20), the ratio of density to pressure should be independent of pressure p/p = M/RT. This is correct for an ideal gas, but if the density of a real gas is measured at one temperature and at several different pressures, the ratio of density to pressure is found to depend slightly on the pressure. At sufficiently low pressures, p/p is a linear function of... 

At the Boyle temperature the Z versus p curve is tangent to the curve for the ideal gas at p = 0 and rises above the ideal gas curve only very slowly. In Eq. (3.8) the second term drops out at 7, and the remaining terms are small until the pressure becomes very high. Thus at the Boyle temperature the real gas behaves ideally over a wide range of pressures, because the effects of size and of intermolecular forces roughly compensate. This is also shown in Fig. 3.4. The Boyle temperatures for several different gases are given in Table 3.2. 

Several authors have described their experience in resolving S5mtheti-cally overlapping and real gas chromatographic peaks by the curve-fitting procedure. 

We will examine the experimentally observed behavior of real gases by measuring the pressure, volume, temperature, and number of moles for a gas and noting how the quantity PV/nRT depends on pressure. Plots of PV/nRT versus P are shown for several gases in Fig. 5.22. For an ideal gas PV/nRT equals 1 under all conditions, but notice that for real gases PV/nRT approaches 1 only at low pressures (typically 1 atm). To illustrate the effect of temperature, we have plotted PV/nRT versus P for nitrogen gas at several temperatures in Fig. 5.23. Notice that the behavior of the gas appears to become more nearly ideal as the temperature is increased. The most important conclusion to be drawn from these plots is that a real gas typically exhibits behavior that is closest to ideal behavior at low pressures and high temperatures. 

The application was supported by DSS (Lopes et al, 2009) designed for risk analysis using multi criteria decision analysis to consider three relevant risk dimensions in a real gas pipeline system. The DSS allows the decision makers to analyze the gas pipeline system considering several relevant variables and also to make a sensitivity analysis of the main parameters in order to verify the robustness of the analysis. 

The real gas stream has several input variables that change simultaneously in a complicated way, which will lead to numerical problems. Thus, the presented simplified alternatives are attractive in the preliminary rating of catalytic converters. In the studied converters a good prediction of warm-up has been obtained even if the concentration variations at the converter inlet have been ignored. 

The Ideal Gas Law Volume and Number of Moles 5.9 Characteristics of Several Real... 

The measurement of wj in Eq. (51) is usually made by thermoanemometer. As the length of the wire of this device is only several times smaller than the channel dimension in the packing in horizontal direction, the measurement of the real gas velocity in this case is not exact, i.e. the value of A is not ract either. The di d ssperimental error does not influence the value of the penetration depth. 

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