Mixture excess properties

Homogeneous mixtures, excess properties, VLB, SLE, LLE in non-electrolyte systems, activity coefficient models. 

This definition is analogous to the definition of a residual property as given by Eq. (4-67). However, excess properties have no meaning for pure species, whereas residual properties exist for pure species as well as for mixtures. In addition, analogous to Eq. (4-99) is the partial-property relation,... 

Property changes of mixing and excess properties find greatest application in the description of hqnid mixtures at low reduced tempera-... 

Evolved gas analysis (ega), 14 234 Ewens-Bassett numbers, 17 391, 392 Examiners citations, 18 237, 238 Exanta, 4 100t, 102 Excess properties, ideal mixture and,... 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

In order to calculate explicitly the excess properties of a mixture A + B from the formulas of Section II, we need the values of the six quantities ... 

It has been stressed in Section I that it is essentially these four parameters d, p, 0, and a which determine the values of the excess properties of the mixture A + B should all these parameters be equal to zero then all excess functions vanish. 

In the following sections we shall discuss some of the excess properties of the following mixtures ... 

The situation is quite different for the excess properties of one particular mixture A + B, where it is now — ( bb/ aa) 1 and p = (r B/r A) — 1 which are required (and not simply bb/ aa and Tbb/ aa) it is essential here to get values which are as accurate as possible for these quantities. We shall therefore deduce 8 and p (or alternatively bb/ aa and bbAaa) from different source data, see how far these values agree with each other, and finally select from them an average value. The following experimental data were used ... 

We now extend the discussion of excess properties to examples that help us to better understand the nature of interactions in a variety of nonelectrolyte mixtures. We will give examples showing temperature and pressure effects, including an example of solutions near the critical locus of the mixture and into the supercritical fluid region. 

Fig. 6.14 shows the same excess mixture properties and logarithmic activity coefficients for a mixture of acetone and dimethyl ether. Since this mixture behaves ideally (see discussion in section 6.3) the excess properties and logarithms of activity coefficients are very close to zero (note the scale of the axes) in this case. 

An important excess property is the excess Gibbs energy GE. Many models have been developed to describe and predict GE from the properties of the molecules in the mixture and their mutual interactions. GE models often refer to the condensed state, the solid and liquid phases. In case significant changes in the volume take place upon mixing, or separation, the Helmholtz energy A, defined as... 

An excess property is the difference between the actual property value of a solution and the ideal solution value at the same composition, temperature, and pressure. Therefore, excess properties represent the nonideal behavior of liquid mixtures. The major thermodynamic properties for ideal mixtures are... 

Example 1.14 Estimation of partial excess properties The heat of mixing (excess enthalpy) for a binary mixture is... 

Peculiarities of liquid-mixture behavior are dramatically revealed in the excess properties. Those of primary interest are G , H, and. The excess Gibbs energy comes from experiment tluough reduction of vaporAiquid equilibrium data, and is detenuinedby mixing experiments (Chap. 12). The excess entropy is not measured directly, but is found from... 

Excess properties for liquid mixtures depend primarily on temperature and composition therefore comparison of data for different mixtures is best done at fixed T and x. Since many data are available at near-ambient temperatures, T is chosen as 298.15 K (25°C). Because extreme values for often occur near equimolar composition we fix a i = X2 = 0.5. 

Figure 16.5 Equimolar excess properties for 135 binary mixtures at 298.15 K (25°C)...

Before 2001, only a few pure component properties (densities, viscosities, etc.) and mixture properties (phase equilibrium behavior, excess properties) involving ionic liquids were available. For a better understanding of their behavior and for the... 

For the industrial application of ionic liquids, as selective solvents for separation processes or other applications, a reliable knowledge of the pure component properties and mixture data (phase equilibria, excess properties) is required. Although... 

Behavior of Binary Liquid Solutions Property changes of mixing and excess properties find greatest application in the description of liquid mixtures at low reduced temperatures, i.e., at temperatures well below the critical temperature of each constituent species. The properties of interest to the chemical engineer are V (= AV), (= AH), S, AS, G, and AC. The activity coefficient is also of special importance because of its application in phase equilibrium calculations. 

Gmehling, J. Potential of group contribution methods for the prediction of phase equilibria and excess properties of complex mixtures. Pure Appl. Chem. 2003, 75, 875-888. 

The limiting activity coefficient is also of great theoretical interest At infinite dilution each solute molecule is surrounded by only solvent mol ules, and the most nonideal conditions are represented, yi is in fact an excess property, so like-pair interactions are normalized out. Since only unlike-pair interactions are involved, any composition dependence of the solute on the properties of the mixture are removed. 

For low pressures (a few atmospheres and lower) we can apply the ideal gas model for gases and ideal mixture models for liquids. This formulation is very common in reactor technology. In some cases at higher pressures, the pressure effect on the gas phase is important. A suitable model for these systems is to use an EOS for the gas phase, and an ideal mixture model for liquids. However, in most situations at low pressures the liquid phase is more non-ideal than the gas phases. Then we will rather apply the ideal gas law for the gas phase, and excess properties for liquid mixtures. For polar mixtures at low to moderate pressures we may apply a suitable EOS for gas phases, and excess properties for liquid mixtures. All common models for excess properties are independent of pressure, and cannot be used at higher pressures. The pressure effect on the ideal (model part of the) mixture can be taken into account by the well known Poynting factor. At very high pressures we may apply proper EOS formulations for both gas and liquid mixtures, as the EOS formulations in principle are valid for all pressures. For non-volatile electrol3d es, we have to apply a suitable EOS for gas phases and excess properties for liquid mixtures. For such liquid systems a separate term is often added in the basic model to account for the effects of ions. For very dilute solutions the Debye-Htickel law may hold. For many electrolyte systems we can apply the ideal gas law for the gas phase, as the accuracy reflected by the liquid phase models is low. 

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