Ideal and nonideal gases

Equation (2.1) can be derived from the kinetic theory of gases assuming the gas molecules to behave as perfectly elastic spheres having negligible volume with no intermol-ecular attraction or repulsion. 

In some types of aerosol (compressed gas aerosols) an inert gas under pressure is used to 

Where it is clear that equation (2.1) is inadequate in describing the behaviour of a particular gaseous system, however, a better approximation to real behaviour may be achieved using the van der Waals equation  

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AH partial pressures in a given mixture add to the total pressure. This applies to mixtures of both ideal and nonideal gases. 

The concept of free energy is useful in defining the possibility of a reaction and in determining its limiting or equilibrium conversion. The formal definition of the equilibrium state of a chemical reaction is the state for which the total free energy is a minimum. Thus the well-known rule reaction can occur if AG is negative it cannot occur if AG is positive. Now we shall present the main features of the equilibrium state for ideal and nonideal gases. 

The fourth property lies in the contrasts between ideal and nonideal gases. The former demonstrate several properties beginning with the ideal gas law. An ideal gas further expresses Cy and independently of temperamre. For an ideal gas, the dependence of U and H is only on n and T and not at aU on F For an ideal gas, the response functions have elementary forms = T and Pj. = /r. A nonideal gas... 

This fourth property accordingly marks the differences between ideal and nonideal gases along information lines. An ideal gas offers zero and over all pathways, as long as n is constant And for a gas to be ideal, zero Ix u x h 4 Ix a Ditist apply to all isotherms. An ideal gas likewise expresses zero for isobars. Nonideal gases lack these characteristics, and their pathway information is case specific as a result. Figure 4.10 presented isotherms for 1.00 mole each of... 

Figure 12-15 Comparison of ideal and nonideal behavior of gases. For a gas that behaves ideally,...

EOS is normally either the Soave-Redlich-Kwong (SRK) or the Peng-Robinson (PR). Both are cubic EOSs and hence derivations of the van der Waals EOS, and like most equations of state, they use three pure component parameters per substance and one BIP per binary pair. There are other more complex EOSs (see Table 8.4). EOS models are appropriate for modeling ideal and real gases (even in the supercritical region), hydrocarbon mixtures, and light-gas mixtures. However, they are less reliable when the sizes of the mixture components are significantly different or when the mixture comprises nonideal liquids, especially polar mixtures. 

Treat the solubility of gases in liquids using Henry s law for both ideal and nonideal behavior. Correct reported Henry s law coefficients for pressure or temperature. Perform LLE, VLLE, SLE, and SSE phase equilibria calculations. Determine whether a liquid mixture is inherently instable and will split into two liquid phases. 

Equations 1 and 5 apply only to ideal gases. For nonideal gases one writes43... 

We will see that the relationships that are derived for mixtures of ideal gases will form convenient bases for the treatment of nonideal gases and solutions. 

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. 

EXAMPLE 10.2 The Dispersion Force and Nonideality of Gases. The nonideality of gases arises from the repulsive and attractive forces between atoms. As a consequence, the deviation of the properties of a gas from ideal gas behavior can be traced to the interatomic or intermolec-ular forces. Assume that methane follows the van der Waals equation of state at sufficiently low densities. It is known from experiments that (see Israelachvili 1991)... 

Example 4.1 illustrates this kind of calculation and compares the result with that obtained by taking the steam to behave as an ideal gas. For nonideal gases with known PVT equations of state and low pressure heat capacities, the method of calculation is the same as for compressors which is described in that section of the book. 

The final temperature is read off directly from a thermodynamic diagram when that method is used for the compression calculation, as in Example 7.7. A temperature calculation is made in Example 7.10. Such determinations also are made by the general method for nonideal gases and mixtures as in Example 7.8 and for ideal gases in Example 7.4. 

It should be noted that gases do deviate from ideality, and there are equations that can adjust calculations to compensate for nonideal situations. These equations, however, are complex and are beyond the focus of this review. 

For the equilibrium properties of an ideal gas it is thus the distribution function of the velocities which is required. For nonideal gases or liquids, a position-distribution function is needed for a system not at Equilibrium but changing in time, distribution functions of velocity and position which were the proper functions of time would similarly serve to establish the properties of the system. 

The differential energy balances of Eqs. (6.10) and (6.15) with the friction term of Eq. (6.18) can be integrated for compressible fluid flow under certain restrictions. Three cases of particular importance are of isentropic or isothermal or adiabatic flows. Equations will be developed for them for ideal gases, and the procedure for nonideal gases also will be indicated. 

Density is a frequently needed physical property of a process fluid. For example, engineers often know volumetric flow rates (F) of process streams from flowmeter readings but need to know mass flow rates m) or molar flow rates (h) for material balance calculations. The factor needed to calculate m or h from V is the density of the stream. This chapter illustrates the uses of both tabulated data and estimation formulas for calculating densities. Section 5.1 concerns solids and liquids Section 5.2 covers ideal gases, gases for which the ideal gas equation of state (PV - nRT) is a good approximation and Section 5.3 extends the discussion to nonideal gases. 

In this section we discuss the ideal gas equation of state and show how it is applied to systems containing single gaseous substances and mixtures of gases. Section 5,3 outlines methods used for a single nonideal gas (by definition, a gas for which the ideal gas equation of state does not work well) and for mixtures of nonideal gases. 

Table B.2 lists coefficients of polynomial expressions for Cp(7)[kJ/(mol- C)] at P = 1 atm. The expressions should be accurate for solids, liquids, and ideal gases at any pressure and for nonideal gases only at 1 atm.

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