Nonideal Real Gases

The data in Table 6.2 provide us with clear evidence that real gases are not ideal. We should comment briefly on the conditions imder which a real gas is ideal or nearly so and what to do when the conditions lead to nonideal behavior. A useful measure of how much a gas deviates from ideal gas behavior is found in its compressibility factor. The compressibility factor of a gas is the ratio PV/nRT. From the ideal gas equation we see that for an ideal gas, PV/nRT = 1. For a real gas, the compressibility factor can have values that are significantly different 

A number of equations can be used for real gases, equations that apply over a wider range of temperatures and pressures than the ideal gas equation. Such equations are not as general as the ideal gas equation. They contain terms that have specific, but different, values for different gases. Such equations must correct for the volume associated with the molecules themselves and for intermolecular forces of attraction. Of all the equations that chemists use for modeling the behavior of real gases, the van der Waals equation, equation (6.26), is the simplest to use and interpret. 

In (a), a significant fraction of the container is empty space and the gas can still be compressed to a smaller volume. In (b), the molecules occupy most of the available space. The volume of the system is only slightly greater than the total volume of the molecules. 

A FIGURE 6-21 The behavior of real gases—compressibiliW factor as a function of pressure at 0 °C Values of the compressibility factor less than one signify that intermolecular forces of attraction are largely responsible for deviations from ideal gas behavior. Values greater than one are found when the volume of the gas molecules themselves is a significant fraction of the total gas volume. 

Attractive forces of the red molecules for the green molecule cause the green molecule to exert less force when it collides with the wall than if these attractions did not exist. 

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The methods shown in this section will apply equally well to nonideal (real) gases, with van der Waals equation used in place of the ideal gas equation. However, real gases require the use of van der Waals constants from appropriate tables. 

For nonideal (real) gases, H and depend on pressure, as well as temperature, as shown in Eq. B-4. Numerical values of H and C/int can be obtained from tables of thermodynamic data or relations. 

Applications of the Ideal Gas Equation 6-9 Nonideal (Real) Gases... 

Nonideal (Real) Gases—Because of finite molecular size and intermolecular forces of attraction (Figs. 6-22 and 6-23), real gases generally behave ideally only at high temperatures and low pressures. Other equations of state, such as the van dcr Waals equation (equation 6.26), take into account the factors causing nonideal behavior and often work when the ideal gas equation fails. 

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. 

What factors in a real gas cause the gas to behave in a nonideal manner How are these factors taken into account in the van der Waals equation ... 

The van der Waals equation is a modification of the ideal gas equation that takes into account the nonideal behavior of real gases. It corrects for the fact that real gas molecules do exert forces on each other and that they do have volume. The van der Waals constants are determined experimentally for each gas. 

C02 is considered to be a nonideal gas. That is, it obeys the real gas law, PV = znRT. Using a mass balance, the mass remains constant both at... 

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... 

In order to correct for the nonideal behavior of the real gas the pressure is replaced by the fiigadty/. The Gibbs energy of a real gas is... 

SECTION 10.9 Departures from ideal behavior increase in magnitude as pressure increases and as temperature decreases. The extent of nonideality of a real gas can be seen by examining the quantity PV = RT for one mole of the gas as a function of pressure for an ideal gas, this quantity is exactly 1 at all pressures. Real gases depart from ideal behavior because the molecules possess finite volume and because the molecules experience attractive forces for one another. The van der Waais equation is an equation of state for gases that modifies the ideal-gas equation to account for intrinsic molecular volume and intermolecular forces. 

When the postulates of the kinetic theory are not valid, the observed gas will not obey the ideal gas equation. In many cases, including a variety of important engineering applications, gases need to be treated as nonideal, and empirical mathematical descriptions must be devised. There are many equations that may be used to describe the behavior of a real gas the most commonly used is probably the... 

The attenuation of the reflected shock wave over 12 cycles of reflection within cylindrical and spherical vessels has been examined. Computations without added dissipation simulate the qualitative features of the measured pressure histories, but the shock amplitudes and decay rates are incorrect. Computations using turbulent channel flow dissipation models have been compared with measurements in a cylindrical vessel. These comparisons indicate that the nonideal aspects of the experiments result in a much more rapid decay of the shock wave than predicted by the simple channel flow model. Dissipation mechanisms not directly accounted for in the present model include multidimensional flow associated with transverse shock waves (originating in detonation or shock instability) separated flow due to shock wave-boundary layer interactions the influence of flow in the initiator tube arrangement and real gas (dissociation and ionization) effects and fluid dynamic instabilities near the shock focus in cylindrical and spherical geometries. 

Equation (2.4.15) relates the chemical potential of an ideal gas to / Tln P,- in accordance with (i), this suggests that for a real gas should be specified by an analogous expression, namely RT In i, where f is termed the fugacity of the ith constituent of the gas. To satisfy (ii), this quantity must converge on the pressure P, at ideality. Since /x,- is specified only to within an arbitrary constant, only the difference in chemical potential of the nonideal gas in two states, 1 and 2, may be uniquely specified as... 

If the gas were ideal, all X, values would be zero, and so X represents the nonideality of the real gas. We can regard each X, as the value of some function X P,V,T) at the point (Pi, Vi, T, and then the objective in fitting is to find that function. There is a mathematical basis for claiming that this function in general can be written as an infinite power series of the three variables, though there may be simpler expressions that are more suitable. 

For nonideal gases and real vents Equation 9-8 is modified by (1) including the compressibility factor z to represent a nonideal gas and (2) including a backpressure correction Kb. The result is... 

All known gases, called real gases, are nonideal, which means that they do not obey the fundamental gas laws and the equation pv =RT [See under "Detonation (and Explosion), Equations of State , in this Volume]. Specific heats of "real gases vary with temperature and the product composition depends upon both temperature and pressure. 

Since both the osmotic pressure of a solution and the pressure-volume-temperature behavior of a gas are described by the same formal relationship of Equation (25), it seems plausible to approach nonideal solutions along the same lines that are used in dealing with nonideal gases. The behavior of real gases may be written as a power series in one of the following forms for n moles of gas ... 

Therefore, the K-factor for a component of a real solution depends not only on pressure and temperature but also on the types and quantities of other substances present. This means that any correlation of K-factors must be based on at least three quantities pressure, temperature, and a third property which describes nonideal solution behavior. This property must represent both the types of molecules present and their quantities in the gas and liquid. 

The mathematical relationship between pressure, volume, temperature, and number of moles of a gas at equilibrium is given by its equation of state. The most well-known equation of state is the ideal gas law, PV=RT, where P = the pressure of the gas, V = its molar volume (V/n), n = the number of moles of gas, R = the ideal gas constant, and T = the temperature of the gas. Many modifications of the ideal gas equation of state have been proposed so that the equation can fit P-V-T data of real gases. One of these equations is called the virial equation of state which accounts for nonideality by utilizing a power series in p, the density. 

The mass balances [Eqs. (Al) and (A2)] assume plug-flow behavior for both the gas/vapor and liquid phases. However, real flow behavior is much more complex and constitutes a fundamental issue in multiphase reactor design. It has a strong influence on the reactor performance, for example, due to back-mixing of both phases, which is responsible for significant effects on the reaction rates and product selectivity. Possible development of stagnant zones results in secondary undesired reactions. To ensure an optimum model development for CD processes, experimental studies on the nonideal flow behavior in the catalytic packing MULTIPAK are performed (168). 

There are many equations that correct for the nonideal behavior of real gases. The Van der Waals equation is one that is most easily understood in the way that it corrects for intermolecular attractions between gaseous molecules and for the finite volume of the gas molecules. The Van der Waals equation is based on the ideal gas law. 

D is correct. An ideal gas has a PV/RT equal to one. Real volume is greater than predicted by the ideal gas law, and real pressure is less than predicted by the ideal gas law. Volume deviations are due to the volume of the molecules, and pressure deviations are due to the intermolecular forces. Thus, a negative deviation in this ratio would indicate that the intermolecular forces are having a greater affect on the nonideal behavior than the volume of the molecules, (see the graph on page 27)... 

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