Nonideal Solution Behavior

Therefore, the K-factor for a component of a real solution depends not only on pressure and temperature but also on the types and quantities of other substances present. This means that any correlation of K-factors must be based on at least three quantities pressure, temperature, and a third property which describes nonideal solution behavior. This property must represent both the types of molecules present and their quantities in the gas and liquid. 

Compute the Gfj parameters for the Wilson equation. General engineering practice is to establish liquid-phase nonideality through experimental measurement of vapor-liquid equilibrium. Models with adjustable parameters exist for adequately representing most nonideal-solution behavior. Because of these models, the amount of experimental information needed is not excessive (see Example 3.9, which shows procedures for calculating such parameters from experimental data). 

If any of the identified rates cannot be reasonably fitted with a power function of the corresponding concentrations, or if the powers are incompatible with Eq. (2.5-56), then the assumptions of the analysis should be reviewed. Such behavior might arise from one or more neglected chemical steps, or from nonideal solution behavior. 

The limiting Henry constant can be predicted from nonideal solution behavior through the relation... 

Mixtures exhibiting nonideal solution behavior present both challenges and opportunities in connection with separation processes. Azeotropes cannot be separated by ordinary distillation, yet the formation of azeotropes itself may be used as a means for carrying out certain separations. The formation of two liquid phases in a column may complicate the separation process however, the coexistence of liquid phases with distinct compositions provides one more separation tool. Chemical reactions concurrent with distillation may be used either to enhance the separation or to perform both the reaction and the separation in one process. 

The activity coefficient expresses the nonideal-solution behavior of fugacity. The formal development of models for the activity coefficient in solution thermodynamics follows. 

The Newton-Raphson method is formulated first for an absorber in which one chemical reaction occurs per plate. Then, the method is modified as required to describe distillation columns in which chemical reactions occur. Although the resulting algorithm is readily applied to systems which are characterized by nonideal solution behavior, it is an exact application of the Newton-Raphson method for those systems in which ideal or near ideal solution behavior exists throughout the column. The algorithm presented is recommended for absorption-type columns which exhibit ideal or near ideal solution behavior. 

T Tc for each species however, (<5 — 82) is often nearly temperature independent, at least over limited temperature ranges. Therefore, the solubility parameters listed in Table 9.6-1 may be used at temperatures other than the one at which they were obtained (see Eq. 9.3-22, however). Also, referring to Eq. 9.6-10, it is evident that liquids with very different solubility parameters, such as neopentane and carbon disulfide, can be expected to exhibit highly nonideal solution behavior (i.e., y > 1), whereas adjacent liquids in Table 9.6-1 will-form nearly ideal solutions. This is useful information. 

For the more nonvolatile species of mixtures, dependency of K-values on composition is due primarily to nonideal solution behavior in the liquid phase. Prausnitz, Edmister, and Chao showed that the relatively simple regular solu-... 

Equation 11.3 assumes that the solution is sufficiently dilute that it can be considaed to be ideal. For more concentrated solutions (> 0.05 M for singly charged species), ion-pair formation and other types of intermolecular interactions can lead to nonideal solution behavior, and the ion activities ( effective concentrations ) that go into Equation 11.2 will differ somewhat from the molarities. In that case, concentrations calculated from Equation 11.3 will deviate from the actual concentrations in the solution. 

Often semiempirical models for determination of the activity coefficients that account for nonideal solution behavior are used. An application-oriented introduction is given in Ref [12]. Here, several easy-to-use approximate calculations for solubility estimation are discussed. In principle, such methods are recommended to be applied as complementary tools to experimental solubility determination that can help to reduce the experimental efforts required. 

The preceding survey suggests that the binary mixture of GB fluid has not been studied so far by simulation or numerical methods although, as already mentioned, this is important because real systems are more likely to possess either size, shape, or interaction asymmetry, or any combination of them. The veriflcation of hydrodynamic relations is important for uncovering the nature of solute-solvent interactions in these more complex but model systems. This will certainly help to understand the composition dependence of the binary mixture of GB fluids. One expects in these studies a high degree of nonlinearity in composition dependence because asymmetric interaction-induced nonideal solution behavior has been observed for LJ mixtures of size-symmetric particles [22,23]. 

Example 8.3 How much difference does nonideal solution behavior make in the acetone-water VLE To answer this, compute the boiling temperature and vapor composition that would correspond to a liquid with Xacetone = 0.05, if this were an ideal solution (7, = 1.00),—Raoult s law—and compare them to the experimental values. 

Combined solution-diffusion film theory models have been presented already in several publications on aqueous systems however, either 100% rejection of the solute is assumed or detailed experimental flux and rejection results are required in order to find parameters by nonlinear parameter estimation (Murthy and Gupta, 1997). Consequently, it is difficult to apply these models for predictive purposes. Peeva et al. (2004) presented the first consideration of concentration polarization in OSN. They coupled the solution-diffusion membrane transport model, Eq. (16.4), with film theory to describe flux and rejection of toluene/ docosane and tolune/TOABr binary mixtures. This approach was able to integrate concentration polarization and nonideal solution behavior into OSN design models and predict fluxes over a wide range of solvent mixtures from a limited data set of the pure solvent fluxes. The only parameters to be estimated, other than physical properties, are the mass transfer coefficients, which may be measured, and the permeabUilies, which may... 

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