Nonideal mixture

Mixture phase equilibrium calculations, types of, 24 680-681 Mixture-process design type, 8 399 commercial experimental design software compared, 8 398t Mixtures. See also Multicomponent mixtures Nonideal liquid mixtures acetylene containing, 2 186 adsorption, 2 593-594 adsorption isotherm models,... 

Determination of T y. In the formulation of the phase equilibrium problem presented earlier, component chemical potentials were separated into three terms (1) 0, which expresses the primary temperature dependence, (2) solution mole fractions, which represent the primary composition dependence (ideal entropic contribution), and (3) 1, which accounts for relative mixture nonidealities. Because little data about the experimental properties of solutions exist, Tg is usually evaluated by imposing a model to describe the behavior of the liquid and solid mixtures and estimating model parameters by semiempirical methods or fitting limited segments of the phase diagram. Various solution models used to describe the liquid and solid mixtures are discussed in the following sections, and the behavior of T % is presented. 

In low- to moderate-density vapors, mixture nonidealities are not very large, and therefore equations of state of the type discussed in this text can generally be used for the prediction of vapor-phase fugacities of all species. [However, mixtures containing species that associate (i.e., form dimers, trimers, etc.) in the vapor phase, such as acetic acid, are generally described using the virial equation of state with experimentally determined virial coefficients.] The Lewis-Randall rule should be used only for approximate calculations it is best to use an equation of state to calculate the vapor-phase fugacity of vapor mixtures. 

There are important differences between the true equilibrium constant Ka and the equilibrium ratios defined here. First, Ka depends only on temperature and the standard states of the reactants and products the equilibrium ratios, such as Kc, Kx, and Ky. however, depend on mixture nonidealities (through and Ky) and on the total pressure or the total molar concentration. Consequently, while the thermodynamic equilibrium constant Ka can be used to study the same reaction with different diluents or solvents, the ratios K, Kx, and Ky have meaning only in the situation in which they were obtained. Finally, Ku is nondimensional, whereas Kp has units of (pressure) ii i and Kx has units of (concentration)2 i. 

The most important characteristic that differentiates these heterogeneous reactions from the homogeneous reactions considered in the previous section is that in the calculation of the equilibrium state for heterogeneous reactions, the activity of each species is affected by either dilution or mixture nonideality only by other components that appear in the same phase. Thus, to analyze the production of hydrogen fluoride gas by the reaction of Eq. 13.2-1, we have... 

Kim, S.B., G.J. Ruiz, and A.A. Linninger, Rigorous separation design. 1. Multicomponent mixtures, nonideal mixtures, and prefractionating column networks. Industrial and Engineering Chemistry Research, 2010, 49(14) 6499 6513. 

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i ... 

This chapter presents a general method for estimating nonidealities in a vapor mixture containing any number of components this method is based on the virial equation of state for ordinary substances and on the chemical theory for strongly associating species such as carboxylic acids. The method is limited to moderate pressures, as commonly encountered in typical chemical engineering equipment, and should only be used for conditions remote from the critical of the mixture. 

Chemical" Theory of Vapor Nonideality for Strongly Interacting Substances (Mixtures Containing Carboxylic Acids)... 

A component in a vapor mixture exhibits nonideal behavior as a result of molecular interactions only when these interactions are very wea)c or very infrequent is ideal behavior approached. The fugacity coefficient (fi is a measure of nonideality and a departure of < ) from unity is a measure of the extent to which a molecule i interacts with its neighbors. The fugacity coefficient depends on pressure, temperature, and vapor composition this dependence, in the moderate pressure region covered by the truncated virial equation, is usually as follows ... 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

The convergence rate depends somewhat on the problem and on the initial estimates used. For mixtures that are not extremely wide-boiling, convergence is usually accomplished in three or four iterations,t even in the presence of relatively strong liquid-phase nonidealities. For example, cases 1 through 4 in Table 1 are typical of relatively close-boiling mixtures the latter three exhibit significant liquid-phase nonidealities. 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

In principle, extractive distillation is more useful than azeotropic distillation because the process does not depend on the accident of azeotrope formation, and thus a greater choice of mass-separating agent is, in principle, possible. In general, the solvent should have a chemical structure similar to that of the less volatile of the two components. It will then tend to form a near-ideal mixture with the less volatile component and a nonideal mixture with the more volatile component. This has the effect of increasing the volatility of the more volatile component. 

Because of this parallel with liquid-vapor equilibrium, copolymers for which ri = l/r2 are said to be ideal. For those nonideal cases in which the copolymer and feedstock happen to have the same composition, the reaction is called an azeotropic polymerization. Just as in the case of azeotropic distillation, the composition of the reaction mixture does not change as copolymer is formed if the composition corresponds to the azeotrope. The proportion of the two monomers at this point is given by Eq. (7.19). 

Those involving solution nonideality. This is the most serious approximation in polymer applications. As we have already seen, the large differences in molecular volume between polymeric solutes and low molecular weight solvents is a source of nonideality even for athermal mixtures. 

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... 

Early in the synthesis of separation schemes for nonideal Hquid mixtures, it may not be known exactly where in the flow sheet a strategic separation is going to be, only that it is required some place in some form in order to overcome or exploit a particular critical feature. Thus, strategic separations often... 

The computer effort required for convergence depends on the number and complexity of the recycles ia the dowsheet, the nonlinearities ia the physical properties, and the nonlinearities ia the calculation of phase or chemical equiHbria. In sequential-modular simulators these calculations are converged one at a time, sequentially, and ia a nested manner. In equation-oriented simulators they are converged as a group and, ia the case of complex dow sheets involving nonideal mixtures, there could be significant reduction ia computer effort. 

Salting-out crystalli tion operates through the addition of a nonsolvent to the magma ia a crystallizer. The selection of the nonsolvent is based on the effect of the solvent on solubiHty, cost, properties that affect handling, iateraction with product requirements, and ease of recovery. The effect of a dding a nonsolvent can be quite complex as it iacreases the volume required for a given residence time and may produce a highly nonideal mixture of solvent, nonsolvent, and solute from which the solvent is difficult to separate. 

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. 

Vigne.s empirically correlated mixture diffusivity data for 12 binary mixtures. Later Ertl et al. evaluated 122 binary systems, which showed an average absolute deviation of only 7 percent. None of the latter systems, however, was veiy nonideal. 

Density and Specific Gravity For binary or pseudobinary mixtures of hquids or gases or a solution of a solid or gas in a solvent, the density is a funcrion of the composition at a given temperature and pressure. Specific gravity is the ratio of the density of a noncompress-ible substance to the density of water at the same physical conditions. For nonideal solutions, empirical calibration will give the relationship between density and composition. Several types of measuring devices are described below. 

The SB method is not presented here, but is presented in detail in the sixth edition of Peny s Chemical Engineers Handbook. Extensions of the SB method to nonideal mixtures and complex configurations are developed by Eckert and Hlavacek [Chem. Eng. ScL, 33, 77 (1978)] and Eckert [Chem. Eng. Sci., 37, 425 (1982)] respectively but are not discussed here. However, the approximate and very useful method of Kremser [Nat. Pet. News, 22(21), 43 (May 21, 1930)] for application to absorbers and strippers is discussed at the end of this subsec tion. 

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