Real solutions, thermodynamic properties

When the ideal solution is used as the reference for real solutions, thermodynamic properties are designated by (RL) for Raoulfs law reference. This reference is often used in solutions in which all solutes are liquids at the temperature of interest, especially when the compositions of components are varied over a considerable range. In this case, for every component, we write Eq. (3) as... 

The thermodynamic properties of real electrolyte solutions can be described by various parameters the solvent s activity Oq, the solute s activity the mean ion activities a+, as well as the corresponding activity coefficients. Two approaches exist for determining the activity of an electrolyte in solution (1) by measuring the solvent s activity and subsequently converting it to electrolyte activity via the thermodynamic Gibbs-Duhem equation, which for binary solutions can be written as... 

The analytic solutions and the numerical simulations look very nice, but are they correct, that means do they agree with real measurements To test that we have to make measurements on real models or heat stores and compare them with calculations based on the thermodynamic properties of the PCM used. The determination of these properties is discussed later. 

We can summarize our conclusions about the thermodynamic properties of the solute in the hypothetical 1-molal standard state as follows. Such a solute is characterized by values of the thermodynamic functions that are represented by p2. 77m2. and 5m2- Frequently a real solution at some molality m2(j) also exists (Fig. 16.4) for which p.2 = that is, for which the activity has a value of 1. The real solution for which // i2 is equal to H 2 is the one at infinite dilution. Furthermore, 5 n,2 has a value equal to 5 2 for some real solution only at a molahty m2(k) that is neither zero nor m2( j). Thus, three different real concentrations of the solute exist for which the thermodynamic qualities p,2, //mi. and S a respectively, have the same values as in the hypothetical standard state. 

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. 

We have seen that the properties of non-ideal or real solutions differ from those of ideal solutions. In order to consider the deviation from ideality, we may divide thermodynamic mixing properties into two parts ... 

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,... 

Activities of Electrolytes.—When the solute is an electrolyte, the standard states for the ions are chosen, in the manner previously indicated, as a hypothetical ideal solution of unit activity in this solution the thermodynamic properties of the solute, e.g., the partial molal heat content, heat capacity, volume, etc., will be those of a real solution at infinite dilution, i.e., when it behaves ideally. With this definition of the standard state the activity of an ion becomes equal to its concentration at infinite dilution. 

Since the surface tension is a thermodynamic property, one of the main problems is to define the surface tension of the ideal solution. The first attempt to define the behavior of the ideal solution was made by introducing the simple additivity law based on the molar fraction scale. However, such a behavior was never observed in real systems and several sophisticated attempts were therefore made to describe the composition dependence of surface tension in binary systems with sufficient accuracy taking into account the properties of both the components. Most approaches are based on the substitution of molar fractions by the volume fractions. Such an approach seems not to be quite reliable because of the energetics and not because of the volume character of this quantity. 

Several formalisms have been developed leading to what may be called practical thermodynamics. These treatments include the analog of solution thermodynamics, where the adsorbent and the adsorbate are considered as components in a two-phase equilibrium [6]. Another way to study the system is to use the surface excess approach, whereby the properties of the adsorbed phase are determined in terms of the properties of the real two-phase multicomponent... 

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... 

Compatibility signifies the ability of two or more substances to mix intimately to form a homogeneous composition with useful plastic properties. The anomalies of why one solvent will dissolve a given resin, another will only swell it, and a third will leave the resin unaffected have promoted a considerable amount of empirical work and extensive theoretical explanation. Applying thermodynamic theory to real solutions led to several the Hildebrand solubility parameter 6 based on cohesive energy (12). the Flory-Huggins parameter, X (13). and several newer parameters with sharper precision but which are more difficult to apply. 

In the following sections we will quantify some of the thermodynamic properties of mechanical mixtures and ideal and non-ideal solutions. As we detail the properties of ideal solutions, it will become clear that they are strictly hypothetical another thermodynamic concept, like true equilibrium , which is a limiting state for real systems. Ideal solutions, in other words, are another part of the thermodynamic model, not of reality. It is a useful concept, because real solutions can be compared to the hypothetical ideal solution and any differences described by using correction factors (activity coefficients) in the equations describing ideal behavior. These correction factors can either be estimated theoretically or determined by actually measuring the difference between the predicted (ideal) and actual behavior of real solutions. 

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 ... 

The Margules equations such as those in Table 15.1 can be fitted by standard least-squares regression analysis to data for real solutions. For example, if data for the total free energy of a binary asymmetric solution is available over a range of compositions at different T and P, you could fit equation (15.41) for Greai (or the equation for in Table 15.1) and obtain Wq, and ITcj as regression parameters. The same could be done with the equations for excess enthalpy, entropy, and so on. This permits construction of phase diagrams and determination of thermodynamic properties based... 

In this chapter, we apply some of the general principles developed heretofore to a study of the bulk thermodynamic properties of nonelectrolyte solutions. In Sec. 11-1 we discuss conventions for the description of chemical potentials in nonelectrolyte solutions and introduce the concept of an ideal component. In Sec. 11-2, we demonstrate how the concept of solution molecular weight can be introduced into thermodynamics in a natural fashion. Section 11-3 is devoted to a study of the properties of ideal solutions. In Sec. 11-4, we discuss the properties of solutions that can be considered to be ideal when they are dilute but are not necessarily ideal when they are more concentrated. In Sec. 11-5, regular solutions are defined and some of their properties are derived. Section 11-6 is devoted to a study of some of the approximations that prove useful in the derivation of the properties of real solutions. Finally, in Sec. 11-7, some of the experimental techniques utilized for the measurement of chemical potentials and activity coefficients of components in solution are described. 

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