Nonideal gases

Because of the relatively strong adsorption bond supposed to be present in chemisorption, the fundamental adsorption model has been that of Langmuir (as opposed to that of a two-dimensional nonideal gas). The Langmuir model is therefore basic to the present discussion, but for economy in presentation, the reader is referred to Section XVII-3 as prerequisite material. However, the Langmuir equation (Eq. XVlI-5) as such,... 

The matter of surface mobility has come up at several points in the preceding material. The subject has been a source of confusion—see Ref. 112. Actually, two kinds of concepts seem to have been invoked. The first is that invoked in the discussion of physical adsorption, which has to do with whether the adsorbate can move on the surface so freely that its state is essentially that of a two-dimensional nonideal gas. For an adsorbate to be mobile in this sense, surface barriers must be small compared to kT. This type of mobile adsorbed layer seems unlikely to be involved in chemisorption. 

With flashes carried out along the appropriate thermodynamic paths, the formalism of Eqs. (6-139) through (6-143) applies to all homogeneous equihbrium compressible flows, including, for example, flashing flow, ideal gas flow, and nonideal gas flow. Equation (6-118), for example, is a special case of Eq. (6-141) where the quahty x = and the vapor phase is a perfect gas. 

Since non-ideal gases do not obey the ideal gas law (i.e., PV = nRT), corrections for nonideality must be made using an equation of state such as the Van der Waals or Redlich-Kwong equations. This process involves complex analytical expressions. Another method for a nonideal gas situation is the use of the compressibility factor Z, where Z equals PV/nRT. Of the analytical methods available for calculation of Z, the most compact one is obtained from the Redlich-Kwong equation of state. The working equations are listed below ... 

The application of information in Figure 6.19 requires some explanation. The decision as to which calculation method to choose should be based upon the phase of the vessel s contents, its boiling point at ambient pressure T its critical temperature Tf, and its actual temperature T. For the purpose of selecting a calculation method, three different phases can be distinguished liquid, vapor or nonideal gas, and ideal gas. Should more than be performed separately for each phase, and the... 

Method for Explosively Flashing Liquids and Pressure Vessel Bursts with Vapor or Nonideal Gas... 

Rgure 6.29. Calculation of energy of flashing liquids and pressure vessel bursts filled with vapor or nonideal gas. 

Very little has been published covering such nonideal, but very realistic, situations. Two publications by Wiederman (1986a,b) treat nonideal gases. He uses a co-volume parameter, which is apparent in the Nobel-Abel equation of state of a nonideal gas, in order to quantify the influence on flragment velocity. The co-volume parameter is deflned as the difference between a gas s initial-stage speciflc volume and its associated perfect gas value. 

For gas-phase reactions, the molar density is more useful than the mass density. Determining the equation of state for a nonideal gas mixture can be a difficult problem in thermod5mamics. For illustrative purposes and for a great many industrial problems, the ideal gas law is sufficient. Here it is given in a form suitable for flow reactors ... 

For nonideal gases and real vents Equation 9-8 is modified by (1) including the compressibility factor z to represent a nonideal gas and (2) including a backpressure correction Kb. The result is... 

Such equations are used in the analysis of experimental data in Section P3.3. An example with a nonideal gas is in problem P3.03.06... 

For high-pressure nonideal gas behavior replace j, where z is... 

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. 

For a perfect gas, differentiating the equation of state shows that fl = /T. For a liquid, or nonideal gas, the value of /S must be measured. In general, it depends on pressure and temperature, often in complicated ways. 

Chapter 12 gives the equations for nonideal gas-liquid equilibria calculations. The quantities of gas and liquid leaving the separator on a basis of lb moles per lb mole of separator feed will be designated as ngl and nu. See Figure 13-2. 

A gas may also be cooled hv making it do work in the course of an expansion. When an ideal gas is expanded Ihruugh an aperture into a constant volume, no work is done, since there are no interactions between the molecules anil the molecules themselves occupy no volume. When a nonideal gas is so expanded, however, an amount of internal work. (W =... 

Note that the denominator of Equation 5.21 contains the internal portion of the particle partition function and the ideal gas contribution, so that the division indicated accounts for the nonideal gas effect. When Equation 5.21 is put into Equation 5.17, Qjj, the fractional filling of cavity i by a type J molecule, is obtained ... 

Equation 5.21 shows that the Langmuir constant is a direct function of the particle partition function within the cavity qj/, in particular Cjj contains the nonideal gas translation term. When the fluid in equilibrium with the hydrate is a nonideal gas, the pressure of component J in Equation 5.22a is replaced with its fugacity,//. 

Corrections to the ideal gas law can be introduced in many different ways. One well-known form is the van der Waals equation for a nonideal gas ... 

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