Property of ideal-gas mixture

A substance is in the ideal gas state when the volume of its molecules is a zero fraction of the total volume taken up by the substance and when the individual molecules are far enough apart from each other so that there is no interaction between them. Although this only occurs at infinite volume and zero pressure, in practice, ideal gas properties can be used for gases up to a pressure of two atmospheres with little loss of accuracy. Thermal properties of ideal gas mixtures may be obtained by mole-fraction averaging the pure component values. 

From (4.1.15) we can derive expressions for all properties of ideal-gas mixtures for example, we can immediately determine the pressure. To do so, we use the fundamental equation (3.2.12) to write any mixture or pure-component pressure as... 

To obtain the partial molar properties of ideal-gas mixtures we apply the partial molar derivative (3.4.5) either to the ideal-gas law, to obtain the partial molar volume, or to the general expression (4.1.15), to obtain other properties. The generic expression (4.1.15) yields... 

To obtain the properties of ideal-gas mixtures we simply accumulate the partial molar properties according to (3.4.4), all at the same T and P,... 

Further, the difference between the heat capacities for ideal-gas mixtures is the same as for pure ideal gases (4.1.4). In summary, all first-law properties of ideal-gas mixtures are rigorously obtained by mole-fraction averaging pure ideal-gas properties. For second-law properties, we substitute (4.1.35)-(4.1.37) into (3.4.4) to find... 

In 4.1.4 we found that to compute the thermodynamic properties of ideal-gas mixtures, we need only the mixture composition plus the pure ideal-gas properties at the same state condition as the mixture. In other words, tire properties of ideal-gas mixtures are easy to compute. We would like to take advantage of this, even for substances that are not ideal gases. To do so we introduce, for a generic property F, a residual property P, which serves as a difference measure for how our substance deviates from ideal-gas behavior. 

Property of ideal-gas mixture Property of mixing Partial molar... 

The fugacity coefficient is a function of pressure, temperature, and gas composition. It has the useful property that for a mixture of ideal gases (Pi = 1 for all i. The fugacity coefficient is related to the volumetric properties of the gas mixture by either of the exact relations (B3, P5, R6) ... 

The defining characteristic of ideal gas mixtures is the absence of any interactions. Thus, all thermodynamic properties separate into their partial contributions for example,... 

These two equations are applicable to mixtures of ideal gases as well as to pure gases, provided n is taken to be the total number of moles of gas. However, we must consider how the properties of the gas mixture depend upon the composition of the gas mixture and upon the properties of the pure gases. In particular, we must define the Dalton s pressures, the partial pressures, and the Amagat volumes. Dalton s law states that each individual gas in a mixture of ideal gases at a given temperature and volume acts as if it were alone in the same volume and at the same temperature. Thus, from Equation (7.1) we have... 

For chemical reactions in ideal gases, it is possible to express the equilibrium condition in more convenient forms by relating pi to other properties of the gas mixture. Substituting equation (15) into equation (21) yields... 

Properties The diffusion coeflicient of helium in air (or air in helium) at normal atmospheric conditions is Dgg = 7.2 x 10 m% (Table 14-2). The molar masses of air and helium are 29 and 4 kg/kmol, respectively (Table A-1). Analysis This is a typical equimolar counterdiffusion process since the problem involves two large reservoirs of ideal gas mixtures connected to each other by a channel, and the concentrations of species in each reservoir (the pipeline and the atmosphere) remain constant. 

In the previous section, we have derived the equations for the thermodynamic quantities of ideal-gas mixtures. We could also compute all of these quantities from the knowledge of the molecular properties of the single molecules. Once we get into the realm of liquid densities, we cannot expect to obtain that amount of detailed information on the thermodynamics of the system. 

By using the ideal gas law, we can determine many properties of an individual gas. In many instances, however, we encounter interesting situations with more than one gas present. Our consideration of the levels of pollutants in air is an obvious example. Even if we ignore any pollutants present, clean air is already a mixture of gases. Aside fi-om the possibility of chemical reactions, how do the observed properties of a gas mixture differ from those of pure gases ... 

An ideal gas is a model gas comprised of imaginary molecules of zero volume that do not interact. Each chemical species in an ideal gas mixture therefore has its own private properties, uninfluenced by the presence of other species. The partial pressure of species i (i = 1,2,... , N) in an ideal gas mixture is defined by equation 142 ... 

For the Gibbs energy of an ideal gas mixture, — T the parallel relation for partial properties is equation 149 ... 

If the hquid phase is an ideal solution, the vapor phase an ideal gas mixture, and the hquid-phase properties independent of pressure, then 7, = 1,... 

The partial molar property, other than the volume, of a constituent species in an ideal gas mixture is equal to the corresponding molar property of the species as a pure ideal gas at the mixture temperature hut at a pressure equal to its partial pressure in the mixture. 

Partial molar availability, 24 692 Partial molar entropy, of an ideal gas mixture, 24 673—674 Partial molar Gibbs energy, 24 672, 678 Partial molar properties, of mixtures, 24 667-668... 

The physics of the problem under study is assumed to be governed by the compressible form of the Favre-filtered Navier-Stokes energy and species equations for an ideal gas mixture with constant specific heats, temperature-dependent transport properties, and equal diffusion coefficients. The molecular Schmidt, Prandtl, and Lewis numbers are set equal to 1.0, 0.7, and 1.43, respectively [17]. 

It is often possible to predict with accuracy many properties of ideal solutions, such as dilute gas mixtures, as well as liquid mixtures of closely related substances such as pentane and hexane. On the other hand, liquid mixtures of substances with different... 

However, two types of systems are sufficienfry important that we can use them almost exclusively (1) liquid aqueous solutions and (2) ideal gas mixtures at atmospheric pressure, hr aqueous solutions we assume that the density is 1 gtcvc , the specific heat is 1 cal/g K, and at any solute concentration, pressure, or temperature there are -55 moles/hter of water, hr gases at one atmosphere and near room temperature we assume that the heat capacity per mole is R, the density is 1/22.4 moles/hter, and aU components obey the ideal gas equation of state. Organic hquid solutions have constant properties within 20%, and nonideal gas solutions seldom have deviations larger than these. 

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