Entropy values ideal mixture

For an ideal mixture, the enthalpy of mixing is zero and so a measured molar enthalpy of mixing is the excess value, HE. The literature concerning HE -values is more extensive than for GE-values because calorimetric measurements are more readily made. The dependence of HE on temperature yields the excess molar heat capacity, while combination of HE and GE values yields SE, the molar excess entropy of mixing. The dependences of GE, HE and T- SE on composition are conveniently summarized in the same diagram. The definition of an ideal mixture also requires that the molar volume is given by the sum, Xj V + x2 V2, so that the molar volume of a real mixture can be expressed in terms of an excess molar volume VE (Battino, 1971). 

With these values we calculate the ideal-gas entropy of the mixture ... 

Here we have a heat of mixing differing from zero, while the entropy of mixing retains as before the ideal value. Such mixtures which are realizable in great number in the domain of low molecular weight substances, Hildebrand has termed regular solutions. 

For a so-called ideal mixture, = 0. The entropy of mixing at T = 0 K is also zero. Hence at that very low temperature, ideal mixtures have a straight Gp (x) line between the G-values of the components P x = 1) and Q x = 0). Now, if T > 0, the second term b (which is less than 0) starts to contribute and the Gpg(x) curve, even of an ideal mixture, is no longer linear and touches the vertical axes at x = 0 and X = 1. In a nonideal mixture at OK, 0 and the first term a is no longer linear but parabolic in x. The value of can be positive or negative, depending... 

Although the molar entropy of mixing to form an ideal mixture is positive, this is not true for some nonideal mixtures. McGlashan cites the negative value A5m(mix) = —8.8 J mol for an equimolar mixture of diethylamine and water at 322 K. 

Because of insufficient information concerning the properties of mixtures, calculations of H and S for the present purpose were made assuming ideal mixing. Values of enthalpy and entropy for the pure components were taken from diagrams prepared at Leiden. From the latter, values for mixtures were obtained through the relations... 

Since the 0 s are fractions, the logarithms in Eq. (8.38) are less than unity and AGj is negative for all concentrations. In the case of athermal mixtures entropy considerations alone are sufficient to account for polymer-solvent miscibility at all concentrations. Exactly the same is true for ideal solutions. As a matter of fact, it is possible to regard the expressions for AS and AGj for ideal solutions as special cases of Eqs. (8.37) and (8.38) for the situation where n happens to equal unity. The following example compares values for ASj for ideal and Flory-Huggins solutions to examine quantitatively the effect of variations in n on the entropy of mixing. 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

So far, we have seen that deviation from ideal behavior may affect one or more thermodynamic magnitudes (e.g., enthalpy, entropy, volume). In some cases, we are able to associate macroscopic interactions with real (microscopic) interactions of the various ions in the mixture (for instance, coulombic and repulsive interactions in the quasi-chemical approximation). In practice, it may happen that none of the models discussed above is able to explain, with reasonable approximation, the macroscopic behavior of mixtures, as experimentally observed. In such cases (or whenever the numeric value of the energy term for a given substance is more important than actual comprehension of the mixing process), we adopt general (and more flexible) equations for the excess functions. 

In these equations V, l/i, C, Cf, and S S are ideal gas state values—the values that a PVT system would have were the ideal gas equation the true equation of state. They apply equally to pure species and to constant-composition mixtures, and they show that Ifi, C, PPi, and Cf, are functions of temperature only, independent of P and V. The entropy, however, is a function of both T and P or of both T and V. Regardless of composition, the ideal gas volume is given by V = KT/P, and it provides the basis for comparison with true molar volumes through the compressibility factor Z. By definition. 

Binary mixtures of non-aromatic fluorocarbons with hydrocarbons are characterized by large positive values of the major thermodynamic excess functions G , the excess Gibbs function, JT , the excess enthalpy, 5 , the excess entropy, and F , the excess volume. In many cases these large positive deviations from ideality result in the mixture forming two liquid phases at temperatures below rSpper. an upper critical solution temperature. Experimental values of the excess functions and of Tapper for a representative sample of such binary mixtures are given in Table 1. 

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