Nonideality thermodynamic

The increased density is caused by the clustering of the polar water molecules around the salt ions as illustrated in Figure 3.6. This process is called electrostriction. It is enhanced at lower temperatures, increasing the nonlinear behavior of density as a function of temperature and salinity as illustrated in Figure 3.4. As we will see in Chapter 6, this is one example of several nonideal thermodynamic behaviors that seawater exhibits as a consequence of its high concentration of dissolved salts. 

Experimental studies were carried out to derive correlations for mass transfer coefficients, reaction kinetics, liquid holdup, and pressure drop for the packing MULTIPAK (35). Suitable correlations for ROMBOPAK 6M are taken from Refs. 90 and 196. The nonideal thermodynamic behavior of the investigated multicomponent system was described by the NRTL model for activity coefficients concerning nonidealities caused by the dimerisation (see Ref. 72). 

Nonideal thermodynamic behavior has been observed with polymer solutions in which A Hm is practically zero. Such deviations must be due to the occurrence ofa nonideal entropy, and the first attempts to calculate the entropy change when a long chain molecule is mixed with small molecules were due to Flory [8] and Huggins [9]. Modifications and improvements have been made to the original theory, but none of these variations has made enough impact on practical problems of polymer compatibility to occupy us here. 

In the first step, the design alternatives are automatically generated using a superstructure. In the second step, the design alternatives are evaluated using the rectification body method (RBM) [5], a nonideal thermodynamic based shortcut method. Unlike simulation studies or MINLP optimization, shortcut methods allow fast evaluation of the single separation task without detailed specification of the distillation column. 

Although the procedure described above is effective for controlling for most reaction materials, there are some exceptions. First, water-soluble solvents and substrates, particularly saccharides and glycols, continuously adsorb water without reaching an equilibrium condition. ° ° In addition, salts may react with substrates. Furthermore, certain salts exhibit either nonideal thermodynamic behavior or too slow a rate of equilibration. ... 

Thermodynamic systems may be ideal or nonideal. An ideal thermodynamic system can be defined as a system in which molecule sizes can be considered to be negligible and in which interactions between molecules— repulsion or attraction—can be neglected. In a nonideal thermodynamic system such interactions have to be taken into account. 

In spite of their limitations, the Onsager-Fuoss theory appears to be useful to theo-retioally estimate the diffusion eoefificients, of these electrolytes in aqueous solutions and thus, to contribute to a better understanding of the stracture of those systems. Because slight variations in this a parameter have little effect on the final results of the ionic-size values used in Eqs. (1) to (4) were obtained as average ones from those in the literature and ours calculated from MM methods. In addition, for all systems, the variation in the diffusion coefficient, D, is mainly due to the variation of the ZCj. contribution (attributed to the nonideal thermodynamic behavior) and, to a lesser extent, to the electro phoretic effect in the mobility factor,... 

The method proposed in this monograph has a firm thermodynamic basis. For vapo/-liquid equilibria, the method may be used at low or moderate pressures commonly encountered in separation operations since vapor-phase nonidealities are taken into account. For liquid-liquid equilibria the effect of pressure is usually not important unless the pressure is very large or unless conditions are near the vapor-liquid critical region. 

Lee L L 1988 Molecular Thermodynamics of Nonideal Fluids (Boston ButtenA/orths)... 

Green, D. B. Rechtsteiner, G. Honodel, A. Determination of the Thermodynamic Solubility Product, Xsp, of Pbl2 Assuming Nonideal Behavior, /. Chem. Educ. 1996, 73, 789-792. 

In thermodynamics the formal way of dealing with nonideality is to introduce an activity coefficient 7 into the relationship between activity and mole fraction ... 

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... 

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. 

Since the infinite dilution values D°g and Dba. re generally unequal, even a thermodynamically ideal solution hke Ya = Ys = 1 will exhibit concentration dependence of the diffusivity. In addition, nonideal solutions require a thermodynamic correction factor to retain the true driving force for molecular diffusion, or the gradient of the chemical potential rather than the composition gradient. That correction factor is ... 

With flashes carried out along the appropriate thermodynamic paths, the formalism of Eqs. (6-139) through (6-143) applies to all homogeneous equihbrium compressible flows, including, for example, flashing flow, ideal gas flow, and nonideal gas flow. Equation (6-118), for example, is a special case of Eq. (6-141) where the quahty x = and the vapor phase is a perfect gas. 

Another implementation of homotopy-continuation methods is the use of problem-dependent homotopies that exploit some physical aspect of the problem. Vickeiy and Taylor [AIChE J., 32, 547 (1986)] utilized thermodynamic homotopies for K values and enthalpies to gradually move these properties from ideal to ac tual values so as to solve the MESH equations when veiy nonideal hquid solutions were involved. Taylor, Wayburn, and Vickeiy [I. Chem. E. Symp. Sen No. 104, B305 (1987)] used a pseudo-Murphree efficiency homotopy to move the solution of the MESH equations from a low efficiency, where httle separation occurs, to a higher and more reasonable efficiency. 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

The reactant mixture may be so nonideal that Equation (7.28) is inadequate. The rigorous thermodynamic approach is to replace the concentrations in Equation (7.28) with chemical activities. This leads to the thermodynamic equilibrium constant. 

For nonideal solutions, the thermodynamic equilibrium constant, as given by Equation (7.29), is fundamental and Ei mettc should be reconciled to it even though the exponents in Equation (7.28) may be different than the stoichiometric coefficients. As a practical matter, the equilibrium composition of nonideal solutions is usually found by running reactions to completion rather than by thermodynamic calculations, but they can also be predicted using generalized correlations. 

Equation (7.28) may not provide a good fit for the equilibrium data if the equilibrium mixture is nonideal. Suppose that the proper form for Kkmetic is determined through extensive experimentation or by using thermodynamic correlations. It could be a version of Equation (7.28) with exponents different from the stoichiometric coefficients, or it may be a different functional form. Whatever the form, it is possible to force the reverse rate to be consistent with the equilibrium constant, and this is recommended whenever the reaction shows appreciable reversibility. 

By virtue of the function (3.6), concentrations, which are readify determined parameters, can be used instead of chemical potentials in the thermodynamic equations for ideal systems. The simple connection between the concentrations and chemical potentials is lost in real systems. To facilitate the changeover from ideal to nonideal systems and to avoid the use of two different sets of equations in chemical thermodynamics,... 

In electrolyte solutions, nonideality of the system is much more pronounced than in solutions with uncharged species. This can be seen in particular from the fact that electrolyte solutions start to depart from an ideal state at lower concentrations. Hence, activities are always used in the thermodynamic equations for these solutions. It is in isolated instances only, when these equations are combined with other equations involving the number of ions per unit volume (e.g., equations for the balance of charges), that concentrations must be used and some error thus is introduced. 

Of great importance for the development of solution theory was the work of Gilbert N. Lewis, who introduced the concept of activity in thermodynamics (1907) and in this way greatly eased the analysis of phenomena in nonideal solutions. Substantial information on solution structure was also gathered when the conductivity and activity coefficients (Section 7.3) were analyzed as functions of solution concentration. 

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

Linear momentum (L) operator, time reversal symmetry and, 243-244 Linear scaling, multiparticle collision dynamics, nonideal fluids, 137 Linear thermodynamics entropy production, 20-23 formalities, 8-11... 

Critical currents, 23 821-823 in superconducting, 23 819-825 Critical event (CE), 15 462 Critical failure, 26 982 Critical features, in separating nonideal liquid mixtures, 22 307 Critical fields, thermodynamic, 23 809-811 Critical flocculation concentration, 11 631 Critical item evaluation, for reliability, 26 991... 

Cruz, Jose-Luis and H. Renon, "A New Thermodynamic Representation of Binary Electrolyte Solutions Nonideality in the Whole Range of Concentrations," AIChE J., 1978, 24, 817. 

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