Excess thermodynamic properties ideal solutions

The difference between the thermodynamic properties of solution, based on K, and the analogous properties of concentration from the 101-325 kPa ideal gas state may be evaluated directly from the solute activity coefficient and can be identified with the excess thermodynamic properties of solution ... 

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

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

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. 

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,... 

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,... 

Nonideal solution. In the understanding of a nonideal solution, excess functions are often defined. Excess functions are thermodynamic properties of solutions that are in excess of those of an ideal solution at the same pressure, temperature, and composition. For an ideal solution, therefore, all excess functions are zero. Let us show all thermodynamic properties by E and all excess functions by E then... 

In the last decades the progress of statistical mechanics has opened the possibility of treating quantitatively the effect of ionic interactions at the Mc-Millan Mayer level for clusters [8] [9] [10]. It is possible to include the non ideal contribution in the statistical formulation of the thermodynamic properties of ionic solutions [11] [12] [13]. This can be done combining the concept of ionic association to the evaluation of excess thermodynamic properties. 

If M represents the molar value of any extensive thermodynamic property, an excess property is defined as the difference between the actual property value of a solution and the value it would have as an ideal solution at the same temperature, pressure, and composition. Thus,... 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

As in the nonelectrolyte case, the problem of representing the thermodynamic properties of electrolyte solutions is best regarded as that of finding a suitable expression for the non-ideal part of the chemical potential, or the excess Gibbs energy, as a function of composition, temperature, dielectric constant and any other relevant variables. 

An alternative way of expressing the deviation from ideal solution behavior is by means of excess thermodynamic functions. These are defined as the difference between a thermodynamic property of a solution and the thermodynamic property it would have if it were an ideal solution ... 

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... 

The difference between the thermodynamic function of mixing (denoted by superscript M) for an actual system, and the value corresponding to an ideal solution at the same T and jp, is called the thermodynamic excess function (denoted by superscript E). This quantity represents the excess (positive or negative) of a given thermodynamic property of the solution, over that in the ideal reference solution. nnhn< ... 

Most real solutions are neither ideal nor regular. As a result a realistic description of their thermodynamic properties must consider the fact that both the excess enthalpy of mixing, and excess entropy, are non- zero. Wilson... 

When analyzing thermodynamic properties of polymer solutions it is sufficient to consider only one of the components, which for reasons of simplicity normally is the solvent. It is convenient to separate Eq. (3.88) for solvent (i = 1) into ideal and nonideal (or excess) contributions by defining... 

We have now seen that for real non-ideal solutions all the thermodynamic properties such as G, S, H, V and the internal energy U can differ significantly from the ideal values. This deviation from ideality can be conveniently expressed as a difference from the ideal quantities. The differences are called excess thermodynamic functions ... 

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