Chemistry
Deviation From Ideal Gas Law
Deviation from the ideal gas law refers to the differences observed between the behavior of real gases and the predictions made by the ideal gas law. These deviations occur at high pressures and low temperatures, where intermolecular forces become significant. Real gases deviate from ideal behavior due to their finite volume and the attractive forces between gas molecules.
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9 Key excerpts on "Deviation From Ideal Gas Law"
eBook - PDF- Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
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. 9.4 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). 9.5 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. The individual molecules of a gas exhibit a range of speeds, the distribution of these speeds being dependent on the temperature of the 9 • Summary 463 gas and the mass of its molecules. 9.6 Non-Ideal Gas Behavior Gas molecules possess a finite volume and experience forces of attraction for one another. Consequently, gas behavior is not necessarily described well by the ideal gas law. Under conditions of low pressure and high temperature, these factors are negligible, the ideal gas equation is an accurate description of gas behavior, and the gas is said to exhibit ideal behavior.
eBook - PDFChemistry
An Atoms First Approach
- Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste, , Steven Zumdahl, Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
Thus ideal gas behavior can best be thought of as the behavior approached by real gases under certain conditions. We have seen that a very simple model, the kinetic molecular theory, by making some rather drastic assumptions (no interparticle interactions and zero volume for the gas particles), successfully explains ideal behavior. However, it is important that we examine real gas behavior to see how it differs from that predicted by the ideal gas law and to determine what modifications are needed in the kinetic molecular theory to explain the observed behavior. Since a model is an approximation and will inevitably fail, we must be ready to learn from such failures. In fact, we often learn more about nature from the failures of our models than from their successes. 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 PVynRT depends on pressure. Plots of PVynRT versus P are shown for sev- eral gases in Fig. 8.25. For an ideal gas, PVynRT equals 1 under all conditions, but notice that for real gases, PVynRT approaches 1 only at very low pressures (typically below 1 atm). To illustrate the effect of temperature, PVynRT is plotted versus P for nitrogen gas at several temperatures in Fig. 8.26. Note that the behavior of the gas ap- pears to become more nearly ideal as the temperature is increased. The most important conclusion to be drawn from these figures is that a real gas typically exhibits behavior that is closest to ideal behavior at low pressures and high temperatures. One of the most important procedures in science is correcting our models as we col- lect more data. We will understand more clearly how gases actually behave if we can figure out how to correct the simple model that explains the ideal gas law so that the new model fits the behavior we actually observe for gases.
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- 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 - ePub- Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
- 2019(Publication Date)
- CRC Press(Publisher)
20 Working with Gas LawsI KINETIC THEORY OF GASES Phases of a compound or element (solid, liquid, gas) are determined by the balance between the strength of intermolecular forces and the average kinetic energy of the molecules. The gas phase is characterized by very weak attractive forces during which the average kinetic energy of motion dominates the physical properties of gases. For a restricted set of conditions, analysis of a gas is characterized by assuming that attractive forces between individual gas molecules are zero and that the volume occupied by the physical size of the molecules is essentially zero as compared to the volume of empty space between the molecules. Under these conditions, the gas, termed an ideal gas, is analyzed through the average statistical behavior of rapidly moving independent particles.Gases have very low density as there is a relatively large amount of empty space between individual molecules. Gases can have variable volumes; they can expand (molecules become farther apart) or be compressed (molecules are squeezed closer together). The pressure of a gas is produced by the kinetic energy of molecular collisions on the walls of the container. Gases can diffuse into each other; the rapidly moving molecules of two distinct gases can occupy the empty spaces between each other and form a gas solution (mixing at the molecular level).The kinetic energy of a gas molecule (or atom) in units of Joules is found from kE = ½ mv2 where m = the molecular (or atomic) mass in kilograms and v = velocity of the molecule in meters per second. The average kinetic energy of any sample of a specific molecular gas is determined by the molecular mass and the average or mean velocity: kE(average) = ½ m(v(average) )2 ; v(average) ≅ v(mean)
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.
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- Arther Adamson(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
Equation (1-35) is a statement of the Boltzmann 1-8 DEVIATIONS FROM IDEALITY-CRITICAL BEHAVIOR 13 principle and is of central importance in dealing with probability distributions, as in gas kinetic theory and in statistical thermodynamics. 1-8 Deviations from Ideality—Critical Behavior The equation of state of an actual gas is given in one form by Eq. (1-4), PV = A(T) + b(T)P + c(T)P 2 + ..., where b(T) ? c(T), and so on are not only functions of temperature, but also are characteristic of each particular gas.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
An alternative form of the ideal gas law is given by equation 14.2, where N is the number of particles and k = R N A is Boltzmann’s constant. A real gas behaves as an ideal gas when its density is low enough that its particles do not interact, except via elastic collisions. PV = nRT (14.1) PV = NkT (14.2) A form of the ideal gas law that applies when the number of moles and the temperature are constant is known as Boyle’s law. Using the subscripts ‘i’ and ‘f’ to denote, respectively, initial and final conditions, we can write Boyle’s law as in equation 14.3. A form of the ideal gas law that applies when the number of moles and the pressure are constant is called Charles’ law and is given by equation 14.4. P i V i = P f V f (14.3) V i T i = V f T f (14.4) 14.3 Apply the kinetic theory of gases to ideal gases. The distribution of particle speeds in an ideal gas at constant temper- ature is the Maxwell speed distribution (see figure 14.8). The kinetic theory of gases indicates that the Kelvin temperature T of an ideal gas is related to the average translational kinetic energy KE of a particle, according to equation 14.6, where v rms is the root‐mean‐square speed of the particles. KE = 1 2 mv 2 rms = 3 2 kT (14.6) The internal energy U of n moles of a monatomic ideal gas is given by equation 14.7. The internal energy of any type of ideal gas (e.g. monatomic, diatomic) is proportional to its Kelvin temperature. U = 3 2 nRT (14.7) 14.4 Solve diffusion problems. Diffusion is the process whereby solute molecules move through a solvent from a region of higher solute concentration to a region of lower solute concentration. Fick’s law of diffusion states that the mass m of solute that diffuses in a time t through the solvent in a channel of length L and cross‐sectional area A is given by equation 14.8, where ΔC is the solute concentration difference between the ends of the channel and D is the diffusion constant.
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