Chemistry
Ideal and Real Gases
Ideal gases are hypothetical gases that perfectly follow the gas laws under all conditions. They have no volume and do not interact with each other. Real gases, on the other hand, deviate from ideal behavior at high pressures and low temperatures due to intermolecular forces and the finite volume of gas particles.
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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- 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 - PDFThermodynamics
From Concepts to Applications, Second Edition
- Arthur Shavit, Chaim Gutfinger(Authors)
- 2008(Publication Date)
- CRC Press(Publisher)
83 5 Ideal Gas In this chapter we introduce the idea of an ideal gas, which is defined by a simple equa-tion of state. Such a definition has the advantage that all the properties may be calculated mathematically in a closed form without the need to resort to tables. Moreover, quasistatic processes may also be evaluated in a closed form. Although the concept of the ideal gas is just a mathematical idea, which does not neces-sarily have to describe real gas behavior, still for many situations the ideal gas assumption renders reasonable approximations. The concept of the ideal gas is combined with the first law of thermodynamics to solve problems. 5.1 Definition of an Ideal Gas It is an experimental fact that for simple substances the property pv / T approaches a fixed limit lim lim 0 → → pv T pv T R v (5.1) where R is a constant characteristic of the substance, independent of temperature. Equation 5.1 is rewritten in terms of molar specific volume v – as lim v pv T R →∞ (5.2) where R – is the universal gas constant, which is independent of the substance. R 8.31434 8.31434 J/mol K or kJ/kmol K (5.3) As v = v – / M it follows that R R M (5.4) An ideal gas is defined as one for which the following equation of state holds pv RT (5.5) It follows from Equation 5.1 that all substances approach ideal gas behavior at low densi-ties. Equation 5.5 may be rewritten in several alternative useful forms. pv RT (5.6) 84 Thermodynamics: From Concepts to Applications pV mRT (5.7) pV nRT (5.8) where n = m / M is the number of moles of the substance. There is no real substance that satisfies the ideal gas definition for the entire range of states. Therefore, the ideal gas is a concept rather than a reality.
eBook - PDF- Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
Under the same conditions of temperature and pressure, equal volumes of all gases contain the same number of molecules (Avogadro’s law). The equations describing these laws are special cases of the ideal gas law, PV = nRT, where P is the pressure of the gas, V is its volume, n is the number of moles of the gas, T is its kelvin temperature, and R is the ideal (universal) gas constant. 8.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions The ideal gas law can be used to derive a number of convenient equations relating directly measured quantities to properties of interest for gaseous substances and mixtures. Appropriate rearrangement of the ideal gas equation may be made to permit the calculation of gas densities and molar masses. Dalton’s law of partial pressures may be used to relate measured gas pressures for gaseous mixtures to their compositions. Avogadro’s law may be used in stoichiometric computations for chemical reactions involving gaseous reactants or products. 8.4 Effusion and Diffusion of Gases Gaseous atoms and molecules move freely and randomly through space. Diffusion is the process whereby gaseous atoms and molecules are transferred from regions of relatively high concentration to regions of relatively low concentration. Effusion is a similar process in which gaseous species pass from a container to a vacuum through very small orifices. The rates of effusion of gases are inversely proportional to the square roots of their densities or to the square roots of their atoms/molecules’ masses (Graham’s law). 8.5 The Kinetic-Molecular Theory The kinetic molecular theory is a simple but very effective model that effectively explains ideal gas behavior. The theory assumes that gases consist of widely separated molecules of negligible volume that are in constant motion, colliding elastically with one another and the walls of their container with average speeds determined by their absolute temperatures.
eBook - ePubPhysical Chemistry
How Chemistry Works
- Kurt W. Kolasinski(Author)
- 2016(Publication Date)
- Wiley(Publisher)
CHAPTER 3 Non-ideal gases and intermolecular interactionsPREVIEW OF IMPORTANT CONCEPTS
- The cause of non-ideal behavior is intermolecular interactions.
- There are a number of interactions that change the energy of molecules and ensembles of molecules. Many are electrostatic in nature and therefore depend on the distance between particles.
- Anything that takes a molecule away from the condition ‘neutral with a spherical charge distribution’ will lead to increased intermolecular interactions.
- A multipole expansion can be used to approximate the charge distribution and interaction energies between molecules as long as their orbitals are not overlapping.
- Some examples of long-range interactions include charge–charge, charge–dipole, charge-induced dipole, dipole-induced dipole, and higher multipole interactions.
- Short-range interactions include chemical bonding, hydrogen bonding and Pauli repulsion.
- A virial expansion represents an approach to represent the equation of state of a real gas.
- Another approximation to the equation of state of a real gas is the van der Waals equation.
- Consequences of non-ideal behavior include not only a change in the equation of state but also that gases can condense into condensed phases with finite volumes.
- A supercritical fluid exists above the critical temperature Tc and cannot be condensed merely by compression at or above Tc .
- If the pressure, temperature and volume are expressed as reduced properties, then the equation of state is the same for all gases. The reduced properties are obtained by dividing the property by its critical value. This is known as the law of corresponding states.
3.1 Non-ideal behavior
Whereas all gases act ideally at low pressure where they are on average far from each other, all gases act non-ideally as they approach conditions that promote condensation. At low enough T and high enough p, real gases should condense into a liquid. Indeed, at 1 atm and low enough T every element except He condenses into a liquid. He condenses into a solid at 1 atm and requires p
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 - ePubEngineering Thermodynamics
Fundamental and Advanced Topics
- Kavati Venkateswarlu(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
In reality, there seems to be no gas that behaves like an ideal gas or a perfect gas. The real gases such as oxygen, hydrogen, nitrogen, and air are assumed to behave like a perfect gas at very low pressures or very high temperatures.8.2 Other Equations of State
Van der Waals Equation of State
The kinetic theory of gases, proposed by Clerk Maxwell, forms the basis for establishing the ideal gas equation of state. The ideal gas equation is developed based on certain assumptions as given below:- The molecules of a gas are spaced apart that there is little or no attraction between them.
- The volume occupied by the molecules themselves is quite low compared to the volume of gas.
- Molecules are in random motion, which follows Newton’s law of motion.
- The kinetic energy of the molecules and their momentum are conserved as molecules and walls of the container are perfectly elastic.
The real gases do not obey the assumptions made in the kinetic theory of gases. At very low pressures or very high temperatures, real gas obeys the ideal gas equation as intermolecular attraction and volume occupied by molecules compared to the total volume are not considered at this state. When the pressure increases, intermolecular forces increase and the volume of molecules becomes considerable when compared to that of gas. Thus real gases deviate from the ideal gas equation of state appreciably with an increase in pressure. Van der Waals introduced two correction factors ‘a’ and ‘b’ in the ideal gas equation, first one to account for intermolecular attraction and the second one to account for volume of molecules. The Van der Waals equation is(8.5)(p +)aν 2(= R Tν − b)the termais called the force of cohesion and b the co-volume. At high pressures, all real gases obey the Van der Waals equation of state; however, it is not true at all ranges of pressures and temperatures. Table 8.1ν 2
- Armand Berman(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
1 Ideal Gases 1.1 The Ideal Gas Law If an ideal gas, specified by the quantities p { (pressure) and V! (volume) at temperature 7, changes its state to another set of quantities p 2 > ^2 a t ^ 2 » t n e n , ,/ , =p 2 V 2 /T 2 (1.1) where T is the thermodynamic temperature measured in degrees Kelvin (see Appendix, Table A.20). 1.2 Boyle's Law For a given mass of gas, held at T = const. p x V x = p 2 V 2 = const. (1.2) 13 Charles's Law For a given mass of gas, held at p = const. Vi/ T i = V 2 /T 2 = const. (1.3) IA Gay-Lussac'sLaw For a given mass of gas, held at V = const. f>i/ T i = Pi/^i = const. (1.4) 1 2 1 Ideal Gases 1.5 Mole Amount The amount of moles n M in a given mass W t of substance having a molar mass M is n M = W t /M [mol (moles)] (1.5) The molar mass M of a substance (also known as moiar weight) is the mass divided by the amount of substance. The SI base unit is kg mol -1 , and the practical unit is g mol -1 (Compendium of Chemical Technology, 1987, p. 260). 1.6 Dalton's Law In a mixture of gases, each component exerts the pressure that it would exert if it were present alone at the same temperature in the volume occupied by the gas mixture. The total pressure p of a gas mixture is the sum of partial pressures Pv Pv - -· » Pi °f t n e individual components. P = Px + Pi + *·· +ft = ÎPi (1.6) The partial pressure of each component is equal to the total pressure multiplied by its mole fraction c, in the mixture (for c,·, see Eq. 1.7c). Dalton's law holds true for ideal gases. At pressures below atmosphere, gas mixtures can be regarded as ideal gases.
eBook - PDF- Arthur Adamson(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
14 CHAPTER 1: IDEAL AND NONIDEAL GASES particular temperature, the plot of Ζ versus Ρ approaches the Ζ == 1 line asymptotically as Ρ approaches zero. This is known as the Boyle temperature. The analytical condition is The partial differential sign, d, and the subscript, T, mean that the derivative of Ζ is taken with respect to Ρ with the temperature kept constant. A gas at its Boyle temperature behaves ideally over an exceptionally large range of pressure essentially because of a compensation of intermolecular forces of attraction and repulsion. The gas of a substance which can exist in both the gas and liquid states at a given temperature is often distinguished from gases generally by being called a vapor. Clearly, as a vapor is compressed at constant temperature, condensation will begin to occur when the pressure of the vapor has reached the vapor pressure of the liquid. The experiment might be visualized as involving a piston and cylinder immersed in a thermostat bath; the enclosed space contains a certain amount of the substance, initially as vapor, and the piston is steadily pushed into the cylinder. The arrangement is illustrated in Fig. 1-7. At the point of condensation, reduction in volume ceases to be accompanied by a rise in pressure; more and more vapor simply condenses to liquid at constant pressure P°. Eventually all the vapor is condensed, and the piston now rests against liquid phase; liquids are generally not very compressible, and now great pressure is needed to reduce the volume further. The plot of Ρ versus F corresponding to this experiment is shown in Fig. 1-8, where P° denotes the vapor pressure of the liquid and V its molar volume. The plots FIG. 1-7. 1-8 DEVIATIONS FROM IDEALITY-CRITICAL BEHAVIOR 15 o v i v; ν FIG. 1-8. P-Visotherms for a real vapor. are for constant temperature, or isothermal, processes and are therefore called isotherms.
eBook - PDF- Arther Adamson(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
14 CHAPTER 1: IDEAL AND NONIDEAL GASES particular temperature, the plot of Ζ versus Ρ approaches the Ζ = 1 line asymptotically as Ρ approaches zero. This is known as the Boyle temperature. The analytical condition is The partial differential sign, d 9 and the subscript, T, mean that the derivative of Ζ is taken with respect to Ρ with the temperature kept constant. A gas at its Boyle temperature behaves ideally over an exceptionally large range of pressure essentially because of a compensation of intermolecular forces of attraction and repulsion. The gas of a substance which can exist in both the gas and liquid states at a given temperature is often distinguished from £ases generally by being called a vapor. Clearly, as a vapor is compressed at constant temperature, condensation will begin to occur when the pressure of the vapor has reached the vapor pressure of the liquid. The experiment might be visualized as involving a piston and cylinder immersed in a thermostat bath; the enclosed space contains a certain amount of the substance, initially as vapor, and the piston is steadily pushed into the cylinder. The arrangement is illustrated in Fig. 1-7. At the point of condensation, reduction in volume ceases to be accompanied by a rise in pressure; more and more vapor simply condenses to liquid at constant pressure P°. Eventually all the vapor is condensed, and the piston now rests against liquid phase; liquids are generally not very compressible, and now great pressure is needed to reduce the volume further. The plot of Ρ versus V corresponding to this experiment is shown in Fig. 1-8, where P° denotes the vapor pressure of the liquid and V x its molar volume. The plots as (1-38) FIG. 1-7. 1-8 DEVIATIONS FROM IDEALITY-CRITICAL BEHAVIOR 15 FIG. 1-8. P-V isotherms for a real vapor. are for constant temperature, or isothermal, processes and are therefore called isotherms.
eBook - ePub- Irving Granet, Jorge Alvarado, Maurice Bluestein(Authors)
- 2020(Publication Date)
- CRC Press(Publisher)
7 Mixtures of Ideal GasesLearning Goals
After reading and studying the material in this chapter, you should be able to- 1. Apply the ideal gas relation to a gas mixture.
- 2. Understand and use the term partial pressure .
- 3. Apply Dalton’s law to a gas mixture.
- 4. Define the mole fraction of a gas.
- 5. Arrive at the simple conclusion that the total number of moles of gas in a mixture is the sum of the moles of each of its constituents.
- 6. Use the fact that the mole fraction of a component of a gas mixture equals the partial pressure of that component.
- 7. Apply the ideal gas equation to both the components and the entire mixture.
- 8. Utilize the conclusion that the mole fraction is also equal to the volume fraction of a component of the mixture.
- 9. Convert from volume fraction to weight fraction and from weight fraction to volume fraction.
- 10. Recall that the thermodynamic properties of a mixture are each equal to the sum of the mass average of the individual properties of the components of the mixture.
- 11. Understand and use the terms that are used in conjunction with air–water vapor mixtures.
- 12. Determine the properties of air–water vapor mixtures.
- 13. Understand and use the psychrometric chart.
7.1 Introduction
Many mixtures of gases are of thermodynamic importance. For example, atmospheric air is principally a mixture of oxygen and nitrogen with some water vapor and other gases in minute quantities. The products of combustion from power plants and internal combustion engines are also mixtures of gases that are of interest. From the simple kinetic considerations of Chapter 1 , it was possible to deduce an equation of state to relate the pressure, temperature, and volume of a gas. This particular equation, pv = RT , formed the basis of most of the work in Chapter 6 . As we have remarked several times, it is surprising that so simple an equation can represent real gases with any degree of accuracy. The success of this equation for a single gas leads us to hope that mixtures of gases can be represented equally well by an equally simple equation of state. To some extent, this hope is realized for some real gaseous mixtures, but for others, it has not been possible to write a simple p , v , T relation in terms of the properties of the individual components of the mixture. With the use of semiempirical methods, it has been found possible to correlate experimental p , v , T
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