Assumption ideal gas

We begin by assuming that our ensemble is an ideal gas. The first consequence of this assumption, since ideal gas molecules do not interact with one another, is that we may rewrite the partition function as 

A second consequence of the ideal gas assumption is that PV in Eq. (10.4) may be replaced by Nk T. In the special case where we are working with one mole of molecules, in which case N = (Avogadro s number), we may replace PV with RT, where R is tlie universal gas constant (8.3145 J moV K ). 

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Unfortunately, the ideal-gas assumption can sometimes lead to serious error. While errors in the Lewis rule are often less, that rule has inherent in it the problem of evaluating the fugacity of a fictitious substance since at least one of the condensable components cannot, in general, exist as pure vapor at the temperature and pressure of the mixture. 

Molecular enthalpies and entropies can be broken down into the contributions from translational, vibrational, and rotational motions as well as the electronic energies. These values are often printed out along with the results of vibrational frequency calculations. Once the vibrational frequencies are known, a relatively trivial amount of computer time is needed to compute these. The values that are printed out are usually based on ideal gas assumptions. 

One of the hsted assumptions for Ottengraf s kinetic model was that no gas-phase interactions occur between different chemical species (the ideal-gas assumption). Under ac tual operating conditions, gas-phase interactions can either have a negative or positive impact on biofilter operation. These interactions include ... 

An application of Eq. (19) is shown in Fig. 4, which gives the solubility of solid naphthalene in compressed ethylene at three temperatures slightly above the critical temperature of ethylene. The curves were calculated from the equilibrium relation given in Eq. (12). Also shown are the experimental solubility data of Diepen and Scheffer (D4, D5) and calculated results based on the ideal-gas assumption (ordinate scale is logarithmic and it is evident that very large errors are incurred when corrections for gas-phase nonideality are neglected. 

Setting T = 973 K gives AHp = 117,440 + 11,090 =128,530 J. The temperature is high and the pressure is low relative to critical conditions for all three components. Thus, an ideal gas assumption is reasonable, and the pressure change from 1 bar to 0.5 atm does not affect the heat of reaction. 

Solution Example 7.10 found AG/ = 83,010 J. Equation (7.29) gives Kthermo = 2 xl0 SO that equilibrium at 298.15 K overwhelmingly favors ethylbenzene. Suppose the ideal gas assumption is not too bad, even at this low temperature (7 (, = 617K for ethylbenzene). The pressure is 0.5066 bar and p = 1. The reaction has the form A —> B + C so the reaction coordinate formulation is similar to that in Example 7.13. When the feed is pure ethylbenzene, Equation (7.31) becomes... 

The use of Equations 12-6 or 12-7 to predict gas-liquid equilibria is restricted severely for several reasons. First, Dalton s equation is based on the assumption that the gas behaves as an ideal solution of ideal gases. For practical purposes the ideal-gas assumption limits the equations to pressures below about 100 psia and moderate temperatures. 

Because P is low, we have assumed ideal gases, and for small xe let ye y P. For volume fraction in the vapor, the ideal-gas assumption provides ye, and for the liquid phase, with xe small... 

The second consequence of the ideal gas assumption is that enthalpies are only a function of the temperature. Thus the enthalpy change for an ideal gas can be readily calculated from ... 

Though the ideal gas assumption would cause some error in predicting result, the reasonableness of the above suggested models can be explained by HIO (Higashi, Ito, Oishi) model (Higashi et al., 1963) which is based on the random walk of molecules. The HIO model was same with the model 4 in this paper when the single layer adsorption was assumed. 

Well-mixed conditions at both sides. Constant effective diffusivities within the membrane. Ideal gas assumption. No pressure difference across the membrane. 

Values of parameters for the Margules, van Laar, Wilson, NRTL, and UNIQUAC equations are given for many binary pairs by Gmehling et ai in a summary collection of the world s published VLB data for low to moderate pressures. These values are based on reduction of experimental data through application of modified Raoult s law,Eq. (10.5). On the other hand, data reduction for determination of parameters in the UMFAC method (App. H) does not include tlie ideal-gas assumption, and is carried out with Eq. (14.1). 

Suitable computational models for each of the layers discussed above were developed on the basis of available information and a time scale analysis of flow in OXY reactors (see Ranade, 1999b for more details). Because of the magnitude of pressure drop across the grid, it was found necessary to employ compressible flow equations. An ideal gas assumption was used to calculate the density of gas at any point (as a... 

This result is hardly different from that based on the ideal gas assumption. The fugacity coefficients in the equilibrium equation clearly cancel one another. This is not uncommon in reaction equilibrium calculations, as there are always products and reactions, making the ideal gas assumption far more useful than might be expected. 

Carrero-Mantilla and Llano-Restrep present results for a wide range of conditions, both for the ideal gas assumption and for calculations wherein Pi values are determined from the Soave-Redlich-Kwong equation of state. In no case are these calculated conversions significantly divergent. 

Raoult s law assumes that the liquid phase is an ideal solution and the vapor phase is an ideal gas. With an equation of state, such as the van der Waals equation of state, the vapor phase can now described more realistically, and we do not need to make the ideal gas assumption. In this situation, the chemical potential of the vapor phase... 

When we add these assumptions to our model for gases, we call it the ideal gas model. As the name implies, the ideal gas model describes an ideal of gas behavior that is only approximated by reality. Nevertheless, the model succeeds in explaining and predicting the behavior of typical gases under typical conditions. In fact, some actual gases do behave very much in accordance with the model, and scientists may call them ideal gases. The ideal gas assumptions make it easier for chemists to describe the relationships between the properties of gases and allow us to calculate values for these properties. 

Equation 4.74 is used with the mole balance, Equation 4.72, to solve gas-phase PFR problems under the ideal-gas assumption. To evaluate the concentrations for use with the reaction rate expressions, one then... 

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