Phase behavior nonideal

Condensed phases of systems of category 1 may exhibit essentially ideal solution behavior, very nonideal behavior, or nearly complete immiscibility. An illustration of some of the complexities of behavior is given in Fig. IV-20, as described in the legend. 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

Eor nonideal vapor-phase behavior, the fugacity coefficient for component i in the mixture must be determined ... 

Perhaps the most significant of the partial molar properties, because of its appHcation to equiHbrium thermodynamics, is the chemical potential, ]1. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equihbrium problems. The natural logarithm of the Hquid-phase activity coefficient, Iny, is also defined as a partial molar quantity. For Hquid mixtures, the activity coefficient, y, describes nonideal Hquid-phase behavior. 

In systems that exhibit ideal liquid-phase behavior, the activity coefficients, Yi, are equal to unity and Eq. (13-124) simplifies to Raoult s law. For nonideal hquid-phase behavior, a system is said to show negative deviations from Raoult s law if Y < 1, and conversely, positive deviations from Raoult s law if Y > 1- In sufficiently nonide systems, the deviations may be so large the temperature-composition phase diagrams exhibit extrema, as own in each of the three parts of Fig. 13-57. At such maxima or minima, the equihbrium vapor and liqmd compositions are identical. Thus,... 

Since activity coefficients have a strong dependence on composition, the effect of the solvent on the activity coefficients is generally more pronounced. However, the magnitude and direc tion of change is highly dependent on the solvent concentration, as well as the liquid-phase interactions between the key components and the solvent. The solvent acts to lessen the nonideahties of the key component whose liquid-phase behavior is similar to the solvent, while enhancing the nonideal behavior of the dissimilar key. 

A common way of following the progress of a gas phase reaction with a change in the number of mols is to monitor the time variation of the total pressure, it. From this information and the stoichiometry, the partial pressures of the participants can be deduced, and a rate equation developed in those terms. Usually it is adequate to assume ideal gas behavior, but nonideal behavior can be taken into account with extra effort. Problem P3.03.06 is an example of nonideality. 

The furfural-cyclohexane phase diagram (Fig. 146) shows that you can have mixtures that exhibit nonideal behavior, without having to form an azeotrope. In sum, without the phase diagram in front of you, you shouldn t take the distillation behavior of any liquid mixture for granted. 

Due to the highly nonideal behavior of the hydrate phases, Equation 5.46 is not used to update the hydrate composition. However, the compositions of all nonhydrate phases are determined via Equation 5.46. All composition corrections of a given phase are scaled such that no composition in that phase is changed by more than 50% of its original value. The expression for the composition of species in the hydrate follows from a simple mass balance ... 

The low equilibrium constant and the strongly nonideal behavior that causes the forming of the binary azeotropes methyl acetate/methanol and methyl acetate/ water make this reaction system interesting as a possible RD application (33). Therefore, methyl acetate synthesis has been chosen as a test system and investigated in a semibatch RD column. Since the process is carried out under atmospheric pressure, no side reactions in the liquid phase occur (146). 

Henry s law in the form Pyf/kxf = 1 can be true only with the assumption that the gas phase behaves as an ideal gas or that the corrections for nonideal behavior are negligible. 

The compositions of the vapor and liquid phases in equilibrium for partially miscible systems are calculated in the same way as for miscible systems. In the regions where a single liquid is in equilibrium with its vapor, the general nature of Fig. 13.17 is not different in any essential way from that of Fig. I2.9< Since limited miscibility implies highly nonideal behavior, any general assumption of liquid-phase ideality is excluded. Even a combination of Henry s law, valid for a species at infinite dilution, and Raoult s law, valid for a species as it approaches purity, is not very useful, because each approximates real behavior only for a very small composition range. Thus GE is large, and its composition dependence is often not adequately represented by simple equations. However, the UNIFAC method (App. D) is suitable for estimation of activity coefficients. 

Debye-Hiickel theory — The interactions between the ions inside an electrolyte solution result in a nonideal behavior as described with the concepts of mixed-phase thermodynamics. Assuming only electrostatic (i.e., coulombic) interactions - Debye and - Hiickel suggested a model describing these interactions resulting in - activity coefficients y suitable for further thermodynamic considerations. Their model is based on several simplifications ... 

In this definition, the activity coefficient takes account of nonideal liquid-phase behavior for an ideal liquid solution, the coefficient for each species equals 1. Similarly, the fugacity coefficient represents deviation of the vapor phase from ideal gas behavior and is equal to 1 for each species when the gas obeys the ideal gas law. Finally, the fugacity takes the place of vapor pressure when the pure vapor fails to show ideal gas behavior, either because of high pressure or as a result of vapor-phase association or dissociation. Methods for calculating all three of these follow. 

Next, we specify the x, between 0 and 1, and estimate the total pressure P and yx from Eq. (1.193) to prepare the total pressure and equilibrium compositions shown in Table 1.10. In Figure 1.9, we can compare both the Tyx and Pyx diagrams obtained from Raoult s law and the NRTL model using the Aspen Plus simulator. As we see, ideal behavior does not represent the actual behavior of the acetone-water mixture, and hence we should take into account the nonideal behavior of the liquid phase by using an activity coefficient model. 

A modified Thiele-Geddes method, programmed for an IBM 370-155, was used to perform the calculations needed to size each required column. Experimental activity coefficient data were used to allow for nonideal liquid phase behavior while energy balances, using estimated enthalpy data, were used to correct for non-constant molal overflow. The Theta Method was used for convergence, and all plate efficiencies were assumed to be 100%. (See Reference 7 for additional calculational details and a program listing.)... 

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... 

In many cases, the use of ideal equivalent circuits is convenient but not always appropriate. Nonideal behavior might arise from interactions of species, resulting in frequency-dependent capacitances [C((D)]. Under these conditions, the physical process is more accurately described by a range of relaxation time constants instead of a unique value. Such distributed relaxation events are usually manifested as semicircles depressed below the real axis in the complex plane, and the angle of depression is related to the degree of nonideality. Various distribution functions and constant phase elements have been employed to describe such events. These nonidealities are especially evident in biological systems. 

Equation (1) is used to determine equilibrium between free products and dilute aqueous phases in terms of pure compound properties (solubility) adjusted for the composition of the product (mole fraction). The activity coefficient reflects the effect of phase composition on the equilibrium relation (nonideal behavior). If = 1, then Equation (1) reduces to Raoult s law, which states idealized... 

Nonideal Behavior. The discussion of phase behavior up to this point represents the ideal case. A number of factors cause deviation from ideality. The phases present may include liquid crystals, gels, or solid precipitates in addition to the oil, brine, and microemulsion phases (39, 40). The high viscosities of these phases are detrimental to oil recovery. To control the formation of these phases, the practice has been to add low-molecular-weight alcohols to the micellar solution these alcohols act as cosolvents or in some cases as cosurfactants. 

Equations of state (EOS) that are useful to predict the nonideal behavior of the vapor phase... 

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