The ideal gas mixture

As discussed in Sec. 3.5.1, an ideal gas (whether pure or a mixture) is a gas with negligible intermolecular interactions. It obeys the ideal gas equation p = nRT/V (where n in a mixture is the sum ,) and its internal energy in a closed system is a function only of temperature. The partial pressure of substance i in an ideal gas mixture is pi = ytp = yinRT/V but equals n, giving 

Equation 9.3.3 is the ideal gas equation with the partial pressure of a constituent substance replacing the total pressure, and the amount of the substance replacing the total amount. The equation shows that the partial pressure of a substance in an ideal gas mixture is the pressure the substance by itself, with all others removed from the system, would have at the same T and V as the mixture. Note that this statement is only true for an ideal gas mixture. The partial pressure of a substance in a real gas mixture is in general different from the pressure of the pure substance at the same T and V, because the intermolecular interactions are different. 

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Note that this has resulted in the separation of pressure and composition contributions to chemical potentials in the ideal-gas mixture. Moreover, the themiodynamic fiinctions for ideal-gas mixing at constant pressure can now be obtained ... 

For the third factor, the analogy is an ideal gas mixture of N molecules of type 1 and N2 molecules of type 2, so that the canonical partition function for the ideal gas mixture is... 

With an ideal gas mixture we also have the same equation as Eq. 7.5 for the chemical potential T,p) of one of the constituent substances, i, in the ideal gas mixture at the total pressure p and at temperature Tas shown in Eq. 7.6 ... 

In order to predict the value of the frequency factor, one may assume that all collisions between reactant molecules with sufficient activation energy result in the instantaneous formation of the reaction products. With this simple hypothesis (collision theory), if the activation energy is known, then the problem of computing the reaction rate reduces to the problem of computing the rate of collision between the appropriate reactant molecules in the ideal gas mixture. This last problem is easily solved by the elementary kinetic theory of gases. 

By convention we select for pP the standard value of 1 bar, then 1) = [x9 T) is the standard chemical potential for component i of the ideal gas mixture. Thus, we obtain the final formulation. 

The application of Eq. (11.6) in later chapters to specific phase-equilibrium problems requiresuse of models of solutionbeliavior, wliichprovideexpressionsfor G and (ii as functions of temperature, pressure, and composition. The simplest of these, the ideal-gas mixture and tire ideal solution, are treated in Secs. 11.4 and 11.8. 

Ideal Gas Mixture Model The ideal gas mixture model is useful because it is molecularly based, is analytically simple, is realistic in the... 

The integration of the species transport equations was followed by a density update due to the change in the ideal gas mixture composition ... 

There exist several reference states of solutions referred to as ideal state, for which we can say something on the behavior of the thermodynamic functions of the system. The most important ideal states are the ideal-gas mixtures, the symmetric ideal solutions and the dilute ideal solution. The first arises from either the total lack of interactions between the particles (the theoretical ideal gas), or because of a very low total number density (the practical ideal gas). The second arises when the two (or more) components are similar. We shall discuss various degrees of similarities in sections 5.2. The last arises when one component is very dilute in the system (the system can consist of one or more components). Clearly, these are quite different ideal states and caution must be exercised both in the usage of notation and in the interpretations of the various thermodynamic quantities. Failure to exercise caution is a major reason for confusion, something which has plagued the field of solution chemistry. 

As we mentioned in Section II.C, one of the most important requirements, which is applicable to the overall structure of reaction schemes, is its thermodynamic consistency. In other words, the scheme, as written, must allow the process to proceed asymptotically to its equilibrium state at infinite time. This can be reached only if any elementary step is included into the overall scheme together with its reverse reaction. Let us consider the consequences for the description of the process kinetics. For the sake of simplicity, we assume that the reaction proceeds in the ideal gas mixture. The value of rate constants k( for forward and k( ) for reverse reactions must satisfy the connecting equation... 

Since the exiting stream is at chemical equilibrium, we are able to use the equilibrium relations discussed in Section 4.5.2. With the exiting temperature equal to T the equilibrium constant for the ideal-gas mixture at the outlet is equal to... 

Here we have used the superscripts IG and IGM to indicate properties of the ideal gas and the ideal gas mixture, respectively, and taken pressure and temperature to be the independent variables. From Eq. 8.1-12 it then follows that for the ideal gas mixture... 

Thus, for the ideal gas mixture, the partial pressure of species i is equal to the pressure that would be exerted if the same number of moles of that species. N alone were contained in the same volume V and maintained at the same temperature T as the... 

In analogy with Eq. 7.4-6, the fugacity of species i in a mixture, denoted by f is defined with reference to the ideal gas mixture as follows ... 

Equations 9.3-3 to 9.3-5 resemble those obtained in Sec. 9.1 for the ideal gas mixture. There is an important difference, however. In the present case we are considering an ideal mixture of fluids that are not ideal gases, so each of the pure-component properties here will not be an ideal gas property, but rather a real fluid property that must either be measured or computed using the techniques described in Chapter 6. Thus, the molar volume Vj is not equal to RT/P, and the fugacity of each species is not equal to the pressure. 

The Ideal-Gas Mixture A gaseous mixture is defined as ideal if the chemical potential of its ith component satisfies... 

The vapor compositions now are computed from the phase equilibrium conditions. The fugacities of all components in the ideal-gas mixture are equal to their partial pressures. Therefore, equating these... 

From (4.423) (cf. (4.213)) we can also see that the partial specific volumes are independent of temperature in the ideal gas mixture... 

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