Chemistry
Real Gas
A real gas is a gas that does not behave exactly according to the ideal gas law at all conditions, particularly at high pressures and low temperatures. Unlike ideal gases, real gases have volume and experience intermolecular forces. These deviations from ideal behavior are accounted for using the van der Waals equation or other more complex equations of state.
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10 Key excerpts on "Real Gas"
eBook - PDF- R. Prasad(Author)
- 2016(Publication Date)
- Cambridge University Press(Publisher)
Ideal to a Real Gas, Viscosity, Conductivity and Diffusion 2.0 The Ideal Gas In the earlier chapter properties of an ideal gas were discussed. It was also mentioned that any gas at very low pressure when its density is very small, may be treated as an ideal gas. It essentially means that the laws of ideal gas may be applied to any gas when much larger volume of space is available to each gas molecule in comparison to its size. It is, however, evident that an ideal gas is only a conceptual gas that does not exist in real terms. 2.1 Difference between an Ideal Gas and The Real Gas Finite molecular size and attraction between molecules A Real Gas differs from an ideal gas in two respects: first, the molecules of a Real Gas are not point particles but have a finite size. This means that the actual volume available to the gas molecules for their motion is restricted by the amount of the volume occupied by the molecules themselves. Secondly, in the case of a Real Gas the gas molecules attract each other. The force of molecular attraction, called the Van der Waals force, originates from the net electrostatic force of attraction between the electron cloud of one constituent atom and the nucleus of the other atom of the molecule minus the force of repulsion between the nuclei and the electron clouds of the atoms in the molecule. Since electrostatic forces have infinite range, the net electrostatic force of attraction exceeds beyond the molecular dimensions. The Van der Waals force may also be looked as the net resultant of the forces of attraction between the electron cloud of one molecule and the nuclei of the other molecule and the forces of repulsion between the electron clouds and nuclei of the two molecules as shown in Fig. 2.1. This leaked or residual force of attraction (Van der Waals force) is responsible for the molecular attraction in Real Gases.
eBook - PDF- George C. King(Author)
- 2023(Publication Date)
- Wiley(Publisher)
5 Real Gases So far, we have discussed ideal gases and described them in terms of kinetic theory. The main assumptions we made were that molecules have a negligible size and that there are no forces of attraction or repulsion operating between them. The molecules thus move independently of each other. Using kinetic theory, we derived the equation of state for an ideal gas; the equation that expresses the relation between the three state variables, pressure P, volume V, and absolute temperature T: PV = RT, for one mole of gas. We made the point that most gases, like helium and argon, obey this ideal gas law under ordinary conditions of pres- sure and temperature. However, they do deviate from the ideal gas law at high pressures and low tempera- tures. Perhaps the simplest way to see the breakdown of the ideal gas law for a Real Gas is to make a plot of PV/RT against increasing pressure P. Since the ideal gas law says that PV/RT is constant, a plot of PV/RT against P should give a straight horizontal line, as shown by the dashed line in Figure 5.1. However, for a Real Gas, the plot deviates from a straight line, as shown by the solid curves. At high pressure, the ideal gas law breaks down essentially because the average distance between the molecules becomes small, and so the finite size of the molecules and the intermolecular forces are no longer negligible. Further evidence that the ideal gas law breaks down under certain conditions is that gases can be liquefied and even solidified. It is the interactions between molecules that make matter condense into liquid and solid forms. In this chapter, we discuss how the behaviour of Real Gases with respect to pressure, volume, and tem- perature can be described. The way this is done is to modify the ideal gas law PV = RT in such a way that it can also deal with conditions where the finite size of the molecules and their mutual interactions cannot be neglected.
eBook - PDF- David Ball(Author)
- 2014(Publication Date)
- Cengage Learning EMEA(Publisher)
One model of ideal gases is that (a) they are composed of particles so tiny compared to the volume of the gas that they can be considered zero-volume points in space, and (b) there are no interactions, attractive or repulsive, between the individual gas par-ticles. However, Real Gases ultimately have behaviors due to the facts that (a) gas atoms and molecules do have a size, and (b) there is some interaction between the gas par-ticles, which can range from minimal to very large. In considering the state variables of a gas, the volume of the gas particles should have an effect on the volume V of the gas. The interactions between gas particles would have an effect on the pressure p of the gas. Perhaps a better equation of state for a gas should take these effects into account. In 1873, the Dutch physicist Johannes van der Waals (Figure 1.9) suggested a corrected version of the ideal gas law. It is one of the simpler equations of state for Real Gases, and is referred to as the van der Waals equation: a p 1 an 2 V 2 b ( V 2 nb ) 5 nRT (1.20) where n is the number of moles of gas, and a and b are the van der Waals con-stants for a particular gas. The van der Waals constant a represents the pressure correction and is related to the magnitude of the interactions between gas parti-cles. The van der Waals constant b is the volume correction and is related to the size of the gas particles. Table 1.6 lists van der Waals constants for various gases, which can be determined experimentally. Unlike a virial equation, which fits be-havior of Real Gases to a mathematical equation, the van der Waals equation is a mathematical model that attempts to predict behavior of a gas in terms of real physical phenomena (that is, interaction between gas molecules and the physical sizes of atoms).
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
A Real Gas, like oxygen, deviates from ideal behavior for two important reasons. First, in an ideal gas there would be no attractions between molecules, but in a Real Gas molecules do experience weak attractions toward each other. Second, the model of an ideal gas assumes that gas molecules are infinitesimally small, in other words we are assuming that the individual molecules have no volume. But real molecules do take up some space. (If all of the kinetic motions of the gas molecules ceased and the molecules settled, you could imagine the net space that the molecules would occupy in and of themselves.) At room temperature and atmospheric pressure, most gases behave nearly like an ideal gas, also for two reasons. First, the molecules are moving so rapidly and are so far apart that the attractions between them are hardly felt. As a result, the gas behaves almost as though there are no attractions. Second, the space between the molecules is so large that the volume occupied by the molecules themselves is insignificant. By doubling the pressure, we are able to squeeze the gas into very nearly half the volume. Let’s examine Figure 10.15 more closely. Starting at low pressures, close to P = 1, gases often behave as ideal gases. As the pressure is increased along the x-axis, the gas particles must be closer together. The first effect noticed as gas particles get closer is attractive forces. These forces between molecules reveal themselves by causing the pressure of a Real Gas to be slightly lower than that expected for an ideal gas. The attractions cause the paths of the molecules to bend whenever they pass near each other (Figure 10.16). Because the molecules are not traveling in straight lines, as they would in an ideal gas, they have to travel farther between collisions with the walls.
eBook - PDFPhysical Chemistry
A Modern Introduction, Second Edition
- William M. Davis(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
23 2 Ideal and Real Gases Examinationofthegaseousstateofmatteroffersanexcellentmeansforunderstanding certainbasicsofthermodynamicsandforseeingconnectionswithatomicandmolecu-larlevelbehavior�Thischapterisconcernedwithexplainingthedifferencesbetweenthe behaviorofrealgasesandthebehaviorofahypotheticalgascalledanidealgasbecause ofitsparticularlysimplebehavior�Theidealgasisamodelthatundercertainconditions canserveasagoodapproximationofrealgasbehavior,andwebeginbyconsideringthe relationshipoftemperaturetootherpropertiesofanidealgas� 2.1 The Ideal Gas Laws Experimentsthatarenowcenturiesoldhaverevealedrelationshipsamongthreeproper-tiesofgases,thevolume, V ,thepressure, P ,andthetemperature, T �Volumeissimplythe three-dimensionalspaceoccupiedbythegassample�Itisfixedbythegeometryofthecon-tainerholdingthegas�Pressureisaforceperunitarea,anditcanbemeasuredbybalancing againstanexternalforceofknownsize�AsshowninFigure2�1,apistonassemblyprovides onemeansofmeasuringpressure�Thegaspressureisexertedagainstthepiston,andthe piston is loaded until its position is unchanging, that is, until it reaches the point of bal-ance�Theforceexertedbythepistonisthegravitationalforceofthemass( m )loadedonit, andthatforceisthegravitationalconstant g times m �Asdiscussedinthepreviouschapter, onefundamentaldefinitionoftemperatureisrelatedtodistributionsamongtheavailable energystates�Inpractice,certainmechanicalchangeshavebeenshowntovarylinearlywith temperature,atleastovercertainranges�Thevolumeofmercuryoverafairlywiderange aroundroomtemperatureisoneofthese�Hence,measuringthevolumeofmercuryinatube (athermometer)servestomeasurethetemperature� Asthetemperatureofasampleoffixedvolumeincreases,thepressureincreases� If the external pressure acting on a gas sample contained in a piston assembly is increased,thevolumewilldiminish�Thesearestatementsofobservedphenomena,
eBook - PDF- A. Roth(Author)
- 2012(Publication Date)
- North Holland(Publisher)
CHAPTER 2 Rarefied gas theory for vacuum technology 2.1. Physical states of matter A collection of molecules can occur either in the solid, liquid or gaseous state depending on the strength of the intermolecular forces, and the average kinetic energy per molecule (temperature). The state in which molecules are most independent of each other is called an ideal or perfect gas. This is a theoretical concept which corresponds to the assump-tions that : (a) the molecules are minute spheres; (b) their volume is very small compared with that actually occupied by the gas; (c) the molecules do not exert forces upon each other; (d) they travel along rectilinear paths in a perfectly ran-dom fashion; (e) the molecules make perfectly elastic collisions. Some Real Gases, such as hydrogen, nitrogen, oxygen, argon, helium, krypton, neon, xenon, approximate closely at atmospheric pressures the behavior assumed for ideal gases. At lower pressures (vacuum) many more gases approach the ideal gases. Real Gases, unlike ideal ones, have intermolecular forces. At pressures and temperatures where the molecules of the gas are brought close to each other they will begin to form new structures, which will have properties very different from those of the gas. When these new structures begin to form, the gas is said to be liquefying. Figure 2.1 shows a plot of pressure versus volume for different temperatures of a Real Gas (e.g. carbon dioxide). Curves A and B, for which the tempera-tures are high, are hyperbolas conforming to Boyle's law, describing a behavior assumed for ideal gases. At temperature T 3 , curve C is no longer completely hyperbolic. A small bump has formed at point P. At still lower temperatures, curves D and Ε show complete departure from the hyperbola of ideal gases; a flat plateau appears. When the system has the pressure and volume associated with points 17 18 RAREFIED GAS THEORY FOR VACUUM TECHNOLOGY (CH. 2) Fig.
eBook - PDF- Joseph Kestin(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
PART 2 Applications This page intentionally left blank .ϋ*Ην*!Ϊ# ;:''°.t ' ' -. ' - ' ' Λ < ' ν Λ ' -'-.'> CHAPTER 7 m-m m m m m m m K ?m PROPERTIES OF Real GasES 7.1. Introductory Remarks In the preceding chapter we have been concerned with systems consisting of statistically independent elements; the exact quantum-mechanical energy levels were known, and we were able to compute the thermodynamic proper-ties to any desired degree of approximation. As a rule, however, real systems are not adequately described by such simple mechanical models, and we must now study systems whose elements interact with one another. In a Real Gas which consists of nonpolar molecules, the interaction can be described by one of the simple intermolecular force potentials discussed in Section 2.3.2; the interaction is more complex if the molecules are polar. In this chapter we propose to calculate the thermodynamic properties of nonpolar monatomic gases thus neglecting possible contributions from internal motions. Even this goal cannot be carried out completely, and we shall be forced to rely on heuristic approximations. This will lead to a theory whose validity is restricted to gases of moderate density, that is, to densities which are fractions of that at the critical point. The scheme of approximation which we shall introduce presently will allow us to expand the thermodynamic properties of gases in powers of w 0 3 , that is, in powers of the ratio of the volume of a molecule (~ r 0 3 ) to that available per molecule in the space occupied by the gas, v ~ l/n. Finally, we shall discuss the van der Waals equation of state which provides a qualitative description of the properties of gases near liquefaction and up to the critical 297 298 7. PROPERTIES OF Real GasES point, devoting additional space to a discussion of the mathematical nature of the critical point itself.
eBook - PDF- Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
As mentioned in the previous modules of this chapter, however, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws. In this section, the reasons for these deviations from ideal gas behavior are considered. One way in which the accuracy of PV = nRT can be judged is by comparing the actual volume of 1 mole of gas (its molar volume, V m ) to the molar volume of an ideal gas at the same temperature and pressure. This ratio is called the compressibility factor (Z) with: Ideal gas behavior is therefore indicated when this ratio is equal to 1, and any deviation from 1 is an indication of non-ideal behavior. Figure 9.35 shows plots of Z over a large pressure range for several common gases. FIGURE 9.35 A graph of the compressibility factor (Z) vs. pressure shows that gases can exhibit significant deviations from the behavior predicted by the ideal gas law. As is apparent from Figure 9.35, the ideal gas law does not describe gas behavior well at relatively high pressures. To determine why this is, consider the differences between Real Gas properties and what is expected of a hypothetical ideal gas. Particles of a hypothetical ideal gas have no significant volume and do not attract or repel each other. In general, Real Gases approximate this behavior at relatively low pressures and high temperatures. However, at high pressures, the molecules of a gas are crowded closer together, and the amount of empty space between the molecules is reduced. At these higher pressures, the volume of the gas molecules themselves becomes appreciable relative to the total volume occupied by the gas. The gas therefore becomes less compressible at these high pressures, and although its volume continues to decrease with increasing pressure, this decrease is not proportional as predicted by Boyle’s law.
eBook - PDF- Don Shillady(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
For that reason, this author favors the simple formula in terms of percent uncertainties, which can be (subjectively) estimated numerically. NONIDEAL GAS BEHAVIOR While the ideal gas law works well for pressures up to about 10 atm and higher temperatures above 25 8 C, many common processes (air conditioning, refrigeration) involve higher pressures and lower temperatures. If the ideal gas law is truly universal we could de fi ne the ‘‘ compressibility factor ’’ as Z ¼ PV nRT ¼ 1 and expect that if we plot Z against the pressure we should get a fl at line (Figure 1.6). When such graphs are plotted for real data, there are large deviations, particularly at low temperatures and = or high pressures. There are other ways to plot these data to exaggerate the deviations from Z ¼ 1, but on the other hand we can see that over a fairly large range of temperatures and pressures the ideal gas law is approximately correct. What are the reasons for the deviations from the ideal? Let us try to patch the ideal gas law for a more detailed treatment. We start by setting up the basic PV behavior and allow for corrections. ( P þ ? 1 )( V þ ? 2 ) ¼ nRT Consider a correction to the pressure, P . If indeed the pressure we measure is due to molecular impacts with a surface in a manometer or a diaphragm in a pressure gauge, is that the actual pressure within the gas? We are creeping up on a new concept that models a gas as a collection of small Ideal and Real Gas Behavior 13 molecules fl ying around with a lot of space between them (recall Dalton ’ s law). That idea should include collisions of molecules within the volume. Consider a collision of an auto with a fi xed wall compared to a head-on collision with another similar auto.
eBook - PDF- L. D. Landau, E. M. Lifshitz(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
C H A P T E R V I I NON-IDEAL GASES § 74. Deviations of gases from the ideal state T H E equation of state of an ideal gas can often be applied to actual gases with sufficient accuracy. This approximation may, however, be inadequate, and it is then necessary to take account of the deviations of an actual gas from the ideal state which result from the interaction between its component mole-cules. Here we shall do this on the assumption that the gas is still so rarefied that triple, quadruple, etc., collisions between molecules may be neglected, and their interaction may be assumed to occur only through binary collisions. To simplify the formulae, let us first consider a monatomic actual gas. The motion of its particles may be treated classically, so that its energy has the form E(p,q)= Σ^+^' (74.1) where the first term is the kinetic energy of the Ν atoms of the gas, and U is the energy of their mutual interaction. In a monatomic gas, U is a function only of the distances between the atoms. The partition function j e~ E(p * q)IT άΓ becomes the product of the integral over the momenta of the atoms and the integral over their coordinates. The latter integral is J . . . $e-u * T dVi...dV N9 where the integration over each dV a = dx a dy a dz a is taken over the whole volume V occupied by the gas. For an ideal gas, U = 0, and this integral would be simply V N . It is therefore clear that, on calculating the free energy from the general formula (31.5), we obtain F = F i d -r i o g J L J . . . J V ^ d K i . . . dV N9 (74.2) where F id is the free energy of an ideal gas. 225 226 Non-ideal Gases Adding and subtracting unity in the integrand, we can rewrite formula (74.2) as For the subsequent calculations we make use of the following formal device. Let us suppose that the gas is not only sufficiently rarefied but also so small in quantity that not more than one pair of atoms may be assumed to be colliding in the gas at any one time.
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