Laws of perfect gases

Deviations from the simple laws. The exact proportionality between the osmotic pressure and the concentration can only hold in dilute solutions. No matter how we account for the osmotic pressure laws, whether by an attraction between the solvent and the solute, or by the impacts of the dissolved molecules, or whether we deduce them from the lowering of the vapour pressure of the solution, we are always forced to restrict the applicability of the simple laws of van t Holf to the region of very dilute solutions. Similarly, the laws of perfect gases can only be regarded as valid in the limiting case of very great... 

If we extend the line of reasoning followed by these authors to account for the deviations from the laws of perfect gases, we should be led to conclude that these are also exclusively due to associations or dissociations. 

Mendeleev s early scientific work involved a detailed examination of the chemical properties as well as the specific volumes of many substances. Between 1859-61 he spent some time working at Robert Bunsen s laboratory in Heidelberg, where he studied the behavior of gases and their deviations from the laws of perfect gases. By 1860, he had become sufficiently prominent a chemist to be... 

The use of a gas mixture presents a two-part problem. If the state of the mixture is such that it may be considered a mixture of perfect gases, classical thermodynamic methods can be applied to determine the state of each gas constituent. If, however, the state of the mixture is such that the mixture and constituents deviate from the perfect gas laws, other methods must be used that recognize this deviation. In any case, it is important that accurate thermodynamic data for the gases are used. 

The conditions that apply for the saturated liquid-vapor states can be illustrated with a typical p-v, or (1 /p), diagram for the liquid-vapor phase of a pure substance, as shown in Figure 6.5. The saturated liquid states and vapor states are given by the locus of the f and g curves respectively, with the critical point at the peak. A line of constant temperature T is sketched, and shows that the saturation temperature is a function of pressure only, Tsm (p) or psat(T). In the vapor regime, at near normal atmospheric pressures the perfect gas laws can be used as an acceptable approximation, pv = (R/M)T, where R/M is the specific gas constant for the gas of molecular weight M. Furthermore, for a mixture of perfect gases in equilibrium with the liquid fuel, the following holds for the partial pressure of the fuel vapor in the mixture ... 

In other words, one mole of NG produces 7.25 molar volumes of gas (since a molar volume is the volume of one mole of gas). These molar volumes at 0°C and latm form an actual volume of 7.25 x 22.4 = 162.4 liters of gas (provided the products H20 and C02 are in gaseous form). Thus, volume of the products of explosion can be predicted for any quantity of explosive. Further, by employing Charles Law for perfect gases, the volume of the products of explosion may be calculated for any given temperature. Therefore,... 

Systems lor which /t, has this form possess remarkably simple properties. Moreover, mixtures of perfect gases (i.e., gases under cundilions which can be approximated with sufficient accuracy by the ideal gas law) and very dilute solutions have these properties. 

In most physical applications of statistical mechanics, we deal with a system composed of a great number of identical atoms or molecules, and are interested in the distribution of energy between these molecules. The simplest case, which we shall take up in this chapter, is that of the perfect gas, in which the molecules exert no forces on each other. We shall be led to the Maxwell-Boltzmann distribution law, and later to the two forms of quantum statistics of perfect gases, the Fermi-Dirac and Einstein-Bose statistics. 

This expression is known as the general gas law and describes the behavior of a perfect gas. No gas is perfeot, and all actual gases deviate more or less from this simple law. However, the behavior of perfect gases will be discussed more fully before considering any deviations that may occur. 

The second is the one discovered by Berthollet and which is known under the name of law of the mixture of gases To keep in equilibrium at a given volume and pressure a mixture of perfect gases, it is necessary to submit it to a pressure equal to the sum of the pres-sures which would he maintained separately, at the same volume and temperature, by each of the mixed gases. 

These several laws completely characterize, from the thermodynamic point of view, the properties of a mixture of perfect gases they lead in fact to the following proposition, which allows calculating all these properties when those of mixed gases are known ... 

Law of equilibrium for the 83rstems studied.—Suppose the S3rstem in equilibrium at the absolute temperature T in a vessel where it is either alone or in the presence of perfect gases which do not take part in the reaction let Pi, ft,.. . p/,, ... 

The quantity of heat set free by a system which undergoes a transformation does not depend solely upon the initial and final states, page 86.-32. Example from the study of perfect gases, 37.—33. Case in which the quantity of heat set free by a system depends solely upon the initial and final states, 88.—34. Utility, in chemical calorimetry, of the preceding law, 89.-35. Exothermic and endothermic reactions, 41.—36. Heats of formation under constant pressure and at constant volume, 44.—37. Case in which the two heats of formation are equal to each other, 45.— 38. General relation between the two heats of formation, 45.—39. Case in which the compound is a perfect gas, 46.—40. The distinction between the two heats of formation has small importance in practice, 46.—41. Infiuence of temperature on the heats of formation, 47.-42. Heat of formation referred to a temperature at which the reaction considered is impossible, 48.—... 

Importance of the variations that changes of temperature cause in the heats of formation, 49.—44. Case of perfect gases which combine without condensation. Delaroche and B rard s law. The heats of formation are independent of the temperature, 49. 

In very dilute solutions the heat of dilution is found by experiment to be very small, and may be neglected in practice (just as the dilution of perfect gases involves no change in their energy). For such a solution the relative lowering of the vapour pressure is the same at all temperatures. This law has been confirmed by V. Babo in a large number of cases. 

This is the extension to real gases of the Guldberg and Waage law of mass action. By introducing fugacities we have been able to preserve, for all real gases, the same form for the equations for the affinity and the law of mass action as in the case of perfect gases. 

The partial pressure of a gas in a mixture of gases is the pressure the gas would exert if it occupied alone the same container as the mixture at the same temperature, It is a limiting law because it holds exactly only under conditions where the gases have no effect upon each other. This can only be true in the limit of zero pressure where the molecules of the gas are very far apart, Hence, Dalton s law holds exactly only for a mixture of perfect gases for real gases, the law is only an approximation. 

Partington, A Short History of Chemistry, 3rd ed., p. 169, Dover Publications, New York (1989). In a lecture at the Royal Institution in 1810, Dalton attributed the origin of this atomic theory to attempts to explain his law of partial pressures (1801 1802), which states that the pressure exerted by a mixture of perfect gases is the sum of the pressures exerted by the individual gasses occup3fing the same volume. The partial pressure of a gas is the pressure a gas would exert if it occu pied the container alone and if it behaved perfectly. Dalton s law of partial pressure is a more general form of Henry s law, which states that the amount of gas absorbed by a liquid is proportional to the pressure. 

Much of the preliminary discussion above has been lacking in precision. However, aU that we require for a systematic treatment of the second law is the fact, which is securely based on experience, that it is impossible to carry out Joule s experiment in reverse (Statement A below). As a postulate, to be justified later, we shall also assume the existence of reversible paths. On this basis the development of the second law may be carried out in several different ways. In the following we shall describe the traditional method, as used by dausiuef and Poincar, which depends on the use of heat engines. The main alternatives are the methods of Planck, which depends on the existence of perfect gases, and of Bom and Carathto-dory, II which is based on the properties of Pfaffian differential expressions. 

In the ideal case of perfect solutions of perfect gases, the fugacity coefficient for each of the gases is equal to 1, and the fugacity is identical to the partial pressure. The law of mass action then becomes ... 

Benoit Paul Emile Clapeyron (1799-1864) A French engineer and physicist and one of the founders of thermodynamics. In 1843, Clapeyron further developed the idea of a reversible process, already suggested by Carnot, and made a definitive statement of Carnot s principle, which is now known as the second law of thermodynamics. Clapeyron also worked on the characterization of perfect gases, the calculation of the statics of continuous beams, and on phase transitions, Eq. (3.1.45). 

A mixture of perfect gases, such as to a good approximation the atmosphere, behaves like a single perfect gas. According to Dalton s law, the total pressure of such a mixture is the sum of the partial pressures of the constituents, the pressure to which each gas would give rise if it occupied the container alone ... 

Specific Volume. The volume occupied by 1 lb of vapor is called the specific volume. According to the laws governing the behavior of perfect gases, the volume varies inversely as the pressure (Boyle s law) and directly as the absolute temperature (Gay-Lussac s or Charles law) or... 

The law of Dalton is a limiting law which is never followed perfectly strictly, although the deviations with the permanent gases under moderate pressures are very small. Andrews (1876) found that there was an expansion when strongly compressed nitrogen and carbon dioxide were mixed. Braun (1888) observed... 

Purely phenomenological as well as physically based equations of state are used to represent real gases. The deviation from perfect gas behaviour is often small, and the perfect gas law is a natural choice for the first term in a serial expression of the properties of real gases. The most common representation is the virial equation of state ... 

That the attribution, by the alchemists, of moral virtues and vices to natural things was in keeping with some deep-seated tendency of human nature, is shown by the persistence of some of their methods of stating the properties of substances we still speak of "perfect and imperfect gases," "noble and base metals," "good and bad conductors of electricity," and "laws governing natural phenomena."... 

All gas particles have some volume. All gas particles have some degree of interparticle attraction or repulsion. No collision of gas particles is perfectly elastic. But imperfection is no reason to remain unemployed or lonely. Neither is it a reason to abandon the kinetic molecular theory of ideal gases. In this chapter, you re introduced to a wide variety of applications of kinetic theory, which come in the form of the so-called gas laws. ... 

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