Thermodynamic Properties of the Mixtures

1 Thermodynamic Properties of the Mixtures In those cases where F represents a molar thermodynamic property of the binary mixture of water and the cosolvent, the partial molar quantities of the components are of interest. Differentiation of Equation 3.43 with respect to the mole fractions yield the partial molar excess values. The excess partial molar value for water is  

Note that in there are no constant and first-order terms in x. The coefficients y are related to the coefficients y of Equation 3.43 as follows (if toe latter are limited 

Similarly, toe excess partial molar value for toe cosolvent starts with toe second- 

The coefficients y. of the Redlich-Kister expression (3.43) for the molar excess Gibbs energies and enthalpies of the miscible aqueous cosolvents on the list are shown in Table 3.13 adapted from [56]. It should be noted that whereas the G (Xj.) curves for many aqueous cosolvent systems are fairly symmetrical, the curves for some systems are quite skew, even changing sign from negative at water-rich compositions to positive beyond a certain 

The excess molar entropies of mixing water with cosolvents are obtained from the corresponding enthalpies and Gibbs energies, (x) = [// (Xs)-G (jCs)]/r, from the data in Table 3.13 (provided the same temperature is employed for both enthalpies and Gibbs energies). 

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The thermodynamic properties of the mixture that appear in the energy equation are given as mass-weighted averages of the individual species properties. Specifically of interest here is the enthalpy... 

The heteromolecular production of particles in a vapor mixture is estimated from a model similar to the homogeneous case above. However, the production rate depends on the energy of formation of mixed embryos, the composition of which depends on the thermodynamic properties of the mixture. 

The structure of separations is determined by the composition and the thermodynamic properties of the mixture leaving the reactor. The first separation step is... 

The values in Tables 2-23 to 2-26 were generated from the NIST REFPROP software (Lemmon, E. W, McLinden, M. O., and Huber, M. L., NIST Standard Reference Database 23 Reference Fluid Thermodynamic and Transport Properties—REFPROP, Version 7.0, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, Md., 2002). The primary source for the properties of aqueous ammonia mixtures is R. Tillner-Roth and D. G. Friend, A Helmholtz Free Energy Formulation of the Thermodynamic Properties of the Mixture Water + Ammonia, /, Phys. Chem. Ref. Data 27 63-96(1998). 

Our main interest here will be in determining how the thermodynamic properties of the mixture depend on species concentrations. That is, we would like to know the concentration dependence of the mixture equations of state. 

We refer to a mixture for which Equation 58 or 59 is satisfied as an ideal mixture. Clearly this concept of an ideal mixture is an idealization that is not realized in practice. Real mixtures will show deviations from the ideal results. However, the properties of an ideal mixture are convenient reference states for thermodynamic properties. For example, it is conventional to use excess thermodynamic properties of mixing that are defined as the difference between the thermodynamic property of the mixture and those of an ideal mixture of the components at the same temperature and pressure. 

The structure of the separations is determined by the composition and the thermodynamic properties of the mixture leaving the reactor. The first phase-split is essential, because it enables the decomposition of the separation problem in subproblems or subsystems, where specific systematic procedures can be applied. Therefore, we will start the flowsheet development by examining this key topic. 

We now deduce basic thermodynamic properties of the mixture of fluids with linear transport properties discussed in Sect. 4.5. Among others, we show that Gibbs equations and (equilibrium) thermodynamic relationships in such mixtures are valid also in any non-equilibrium process including chemical reactions (i.e. local equilibrium is proved in this model) [56, 59, 64, 65, 79, 138]. 

Although the lattice model of the liquid state, upon which equations (26) and (27) are based, is open to criticism the treatment does describe a well-defined procedure for dividing a molecule into segments, counting the segment interactions of various kinds, and relating these to the thermodynamic properties of the mixture. The lattice model has frequently been applied at any one of three... 

Industrial separation processes typically consist of various distillative and alternative separation steps that are coupled by material and eneigy streams. Such processes often have very complex stractures caused by the properties of the systems at hand and by the constraints set by cost and energy savings. In most cases, a rather empirical approach is used for process design. Novel developments concern a conceptual process design (e.g., Douglas 1988 Smith 1995 Blass 1997 Stichl-mair and Fair 1998 Seider et al. 1999 Doherty and Malone 2001 Mersmaim et al. 2005), which is based on the thermodynamic properties of the mixture at hand. 

We have seen that systems of hard rods form SI solutions. Therefore, all the excess thermodynamic quantities are zero. We have already examined the dependence of the local properties on the ratio of diameters in Section 2.6. Therefore, in this section, we choose equal diameters for the particles = Ogg = 1, and explore the dependence of the thermodynamic properties of the mixture on the ratio of the energy parameter e. In the succeeding calculation, we choose dimensionless parameters. 

Partial molar quantities n. The partial molar quantity of the substance A in a mixture of n components is the change in a thermodynamic property of such mixture per mole of component A. The partial molar quantities show the contribution of component A to the total thermodynamic properties of the mixture. 

The Flory — Huggins theory considers that the two components, i.e. solute and solvent, have identical local structures thus it does not take account of the influence of structural characteristics of components on the thermodynamic properties of the mixture. Therefore (a) the volume change at mixing, is zero and (b) the enthalpy of mixing may be assigned only to the differences in contact energies. 

Mansoori GA, Carnahan NF, Starling KE, Leland TW Equihbrium thermodynamic properties of the mixture of hard spheres, J Chem Phys 54(4) 1523—1525, 1971. 

From (4.3.10) we may deduce all thermodynamic properties of the mixture. Let us notice that F (F, T) is the free energy of the perfect solution for which fn = 1. This indudes the corresponding... 

In such cases the mixing process can no longer be described by a simple change in the reduced variables but the thermodynamic properties of the mixtures depend in general on some supplementary variables. Therefore we can no longer express the excess functions in terms of the properties of pure liquids and intermolecular forces alone but we have to use some specific statistical model (for example the cell model). 

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