Thermodynamic excess properties

In Section 11.5a of Chapter 11, we indicated that for the mixing process, represented by 

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Denotes excess thermodynamic property Denotes value for an ideal solution Denotes value for an ideal gas Denotes liquid phase... 

Wisniak, J. Tamir, A. "Mixing and Excess Thermodynamic Properties. A Literature Source Books" Elsevier Scientific Publishing Co., New York, 1978. 

This should certainly be a good approximation as the isotopomers are quite similar, one to the other. Even so we will improve on it later when we consider (the quite small) nonideality of isotopomer solutions and their excess thermodynamic properties. For Raoult s law solutions... 

As with other excess thermodynamic properties (Section 16.7), the excess volume is defined as... 

The excess thermodynamic properties correlated with phase transitions are conveniently described in terms of a macroscopic order parameter Q. Formal relations between Q and the excess thermodynamic properties associated with a transition are conveniently derived by expanding the Gibbs free energy of transition in terms of a Landau potential ... 

Petrie, S. E. B. The effect of excess thermodynamic properties versus structure formation on the physical properties of glassy polymers. J. Macromol. Sci., Phys. 12, 225 (1976)... 

In real solutions, we describe the excess thermodynamic property Z. It is the excess in Z over that for the ideal solution. That is,... 

Nonpolar + Nonpolar mixtures Figure 17.3 summarizes the excess thermodynamic properties for (cyclohexane + hexane) mixtures.J 4 We have chosen this... 

Alkanes that we will use as examples in this section may have a small dipole moment. We may instead have appropriately titled this section as Almost (Nonpolar + Nonpolar) Mixtures . The mixtures we describe first are at ambient pressure p ss 0.1 MPa). Later we will describe the effect of pressure on the excess thermodynamic properties. 

The Excess Thermodynamic Properties and (Liquid + Liquid) Phase Equilibrium... 

The excess thermodynamic properties for (cyclohexane + hexane) were obtained from the following sources Excess enthalpies come from K. N. Marsh and R. H. Stokes, Enthalpies of Mixing of n-Hexane + Cyclohexane at 25 °C , J. Chem. Thermodyn., 1, 223-225 (1969) and M. B. Ewing and K. N. Marsh, The Enthalpy of Mixing of n-Hexane + Cyclohexane at... 

Chapters 17 and 18 use thermodynamics to describe solutions, with nonelectrolyte solutions described in Chapter 17 and electrolyte solutions described in Chapter 18. Chapter 17 focuses on the excess thermodynamic properties, with the properties of the ideal and regular solution compared with the real solution. Deviations from ideal solution behavior are correlated with the type of interactions in the liquid mixture, and extensions are made to systems with (liquid + liquid) phase equilibrium, and (fluid -I- fluid) phase equilibrium when the mixture involves supercritical fluids. 

Wisniak, J., and Tamir, A. (1982, 1986). Mixing and Excess Thermodynamic Properties A Literature Source Book. Amsterdam Elsevier. 

Thus, an excess thermodynamic property is also the difference between the thermodynamic property for mixing the real and ideal solutions. For the Gibbs free energy, this becomes, using Eq. (3) and Eq. (35) of Chapter 8,... 

FIGURE 7-7 Schematic diagram of excess thermodynamic properties as a function of solution composition (various properties can be negative, depending on the system). 

Brace AD, Cowley RA (1980). Stractnral Phase Transitions. Taylor Francis, London Cai Y, Thorpe MF (1989) Floppy modes in network glasses. Phys Rev B 40 10535-10542 Carpenter MA, Salje EKH, Graeme-Batber A, Wrack B, Dove MT, Knight KS (1998) Cahbration of excess thermodynamic properties and elastic corrstant variatiorts dne to the a-p phase transition in quartz. Am Mineral 83 2-22... 

If the excess thermodynamic properties of the three binary subsystems of the A-B-C ternary system are similar to each other, the ternary system is symmetric. If the deviation of the binary system A-B and A-C from the ideal behavior are similar, but differ markedly from that of the binary system B-C, then the A-B-C ternary system is asymmetric. In the asymmetric system the component A in two binary subsystems with thermodynamic similarity should be chosen as the thermodynamic asymmetric component. ... 

After a systematic comparison of the calculated and measured results of excess thermodynamic properties and phase diagrams, it can be concluded that the key point in the choice of the suitable geometric model to predict ternary thermodynamic properties from the binary ones is to choose reasonably between the symmetric or asymmetric models. In most cases, the main source of error in the calculation arises from the incorrect choice of the asymmetric component in the asymmetric model. 

An excess thermodynamic property ME is equal to the difference between the actual property M and the property for an ideal solution at the same T, P and x. Here M represents extensive properties V, U, H, Cp,... 

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