Nonideal gases description

For strongly associated fluids, the virial equation is not useful for the description of nonideal-gas behavior. The theory of association is a more suitable approach see Equation (4.214). 

If (10.2.16) is not met, one has to include non-ideal effects in the two-dimensional phase description. It is worth pointing that in the model of ideal two-dimensional gas the lower point of phases co-existence for the phases 1 and 2 ( 2c) is not defined at all, while the upper one ( j ) is introduced only formally. In the models of nonideal gas these points can be determined from the coverage versus the chemical potenticJ curve. 

As its name implies, a tower reactor typically has a height-to-diameter (h/D) ratio considerably greater than 1. Types of tower or column reactors (the words tower and column may be used interchangeably) go by descriptive names, each of which indicates a particular feature, such as the means of creating gas-liquid contact or the way in which one phase is introduced or distributed. The flow pattern for one phase or for both phases may be close to ideal (PF or BMF), or may be highly nonideal. 

The law of mass action is widely applicable. It correctly describes the equilibrium behavior of all chemical reaction systems whether they occur in solution or in the gas phase. Although, as we will see later, corrections for nonideal behavior must be applied in certain cases, such as for concentrated aqueous solutions and for gases at high pressures, the law of mass action provides a remarkably accurate description of all types of chemical equilibria. For example, consider again the ammonia synthesis reaction. At 500°C the value of K for this reaction is 6.0 X 10 2 F2/mol2. Whenever N2, H2, and NH3 are mixed together at this temperature, the system will always come to an equilibrium position such that... 

We next consider the dissolution of a mixture of gases in a liquid. We separate this situation into two different cases. First, if the concentrations of the dissolved gases in the liquid are relatively low, so that there are no nonideality departures from Henry s law, it is reasonable to assume that the solubility of each gas would be the same as if it were the only gas present at its gas-phase partial pressure. However, if the concentrations of the gases in the liquid are high enough that there are departures from the Henry s law limit, so that the activity coefficients yT need be included in the description, then the solubility of each species is affected by the presence of others through the values of the activity coefficients. 

The simplest type of phase behavior to understand is the solubility of a solid solute, such as naphthalene, in a supercritical fluid. When the solute is a crystalline solid, the solid phase may be assumed to be pure and only the supercritical phase is a mixture. Imagine solid naphthalene in a closed vessel under one atmosphere of carbon dioxide at 40°C. The reduced temperature and reduced density of CO2 are 1.03 and 3.7x10 respectively. At this pressure, the gas phase is ideal and the naphthalene solubility is determined by its vapor pressure. As the container volume is decreased isothermally, the solubility initially decreases when the gas phase is still nearly ideal. As the pressure is increased further, however, the gas phase density becomes increasingly nonideal and approaches the mixture critical density (near the critical density of CO2 because the gas phase is still mostly CO2). The reduced density of CO2 increases rapidly near the critical region as shown in Figure 2. The solvent power of CO2 is related to the density which leads to a rapid solubility increase. A brief description of intermolecular interactions is helpful in understanding this behavior. 

When the postulates of the kinetic theory are not valid, the observed gas will not obey the ideal gas equation. In many cases, including a variety of important engineering applications, gases need to be treated as nonideal, and empirical mathematical descriptions must be devised. There are many equations that may be used to describe the behavior of a real gas the most commonly used is probably the... 

The gas-phase mixture is considered an ideal gas, and in this case Dalton s law states that concentrations are equal to partial pressures divided by the overall pressure p (N m" ). According to HEA, these partial pressures are equal to the saturation pressures of the liquid aerosols. The appropriate description of such saturation pressures depends on the circumstances (see Table 18.2). A hydrocarbon gas does not readily dissolve in water, and therefore two sets of immiscible aerosols will exist in independent equilibrium with the gas phase. Raoult s law describes equilibrium over dilute mixtures, whereas equilibrium over nonideal binary solution requires contaminant-specific empirical models. An example of the latter is Wheatley s model, which states that ... 

A main advantage of the virial equation, as compared to the other EoS, is that there is an exact relationship between B mixture) and the B values of the mixture components and their pairs, as we will see in Chapter 11. It finds, thus, extensive application in the description of the vapor phase nonideality in distillation or gas absorption design up to moderate pressures. 

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