Properties changes on mixing

To characterize this change, the property change on mixing AT"" is defined as the difference between the property of the mixture and the properties of the pure components ... 

Other thermodynamic property changes on mixing can be defined similarly. 

General equation relating the partial molar property to the pure component property and the property change on mixing... 

Any property change on mixing AmjxP of a real mixture can be written in terms of the analogous property of an ideal mixture plus an additional term as follows ... 

The Equation-of-state terms as calculated by Flory and co-workers , which take account of volume changes on mixing become more unfavourable at higher temperatures. The effect of the polymer properties and the resultant phase diagrams using this theory have been explored by McMaster... 

The first two tenns on the right side of each equation express a difference liaving the form, M — These quantities are property changes of mixing, symbol AM. By definition. 

The relations between excess properties and property changes of mixing (Sec. 12.3) facilitate discnssionof the molecular phenomena which give rise to observed excess-property behavior. An essential coimectionis provided by Eq. (12.33), which asserts the identity of and AH. Tims we focus on the mixing process (and hence on for explainingthe behavior of. ... 

It is convenient to study the intensive property, which is the energy change on mixing per site ... 

In Chapter 4, we examined the properties of ideal solutions. Many properties of an ideal solution do not change on mixing. For example, the volume of a mixture is equal to the sum of the volume of the original unmixed solutions. In this situation, it is straightforward to assign how much volume is occupied by each component in the system — it is simply the volume occupied by components in their unmixed state. 

For more accurate calculations of the partial molar volume (or any other partial molar property), an analytical, rather than graphical, procedure is used. First, one fits the volume change on mixing, AmixY. with a polynomial in mole fraction, and then the necessary derivative is found analytically. Since AmixY must equal zero at X = 0 and xi = 1 (,X2 = 0), it is usually fit with a polynomial of the Redlich-Kister form ... 

One can also show that if is any molar property of the mixture (not the change on mixing, which is An,i.x0), we have... 

Using the energy, volume, and entropy changes on mixing given here, one can easily compute the other thermodynamic properties of an ideal gas mixture (Problem 9.1). The results are given in Table 9.1-1. Of particular interest are the expressions for... 

That is, the excess properties are the differences between the real and ideal-solution changes of properties on mixing. The result (5.2.2) can be used for any ideal solution defined relative to any standard state for example, when excess properties are relative to the Lewis-Randall ideal solution, we substitute the ideal-solution expressions (5.1.22)-(5.1.27) into (5.2.2) to obtain the following relations between/ and/ . First-law excess properties are identical to the changes on mixing. 

The Flory-Huggins theory does not permit volume change on mixing, and it ignores the equation of state properties of the pure components. It also does not properly consider the enormous size differences between polymer and solvent. 

For a pure substance, any partial molar property is the same as the molar property for example, the pure species partial molar volume is the same as the pure species molar volume. If we add one mol of pure water to a large number mols of pure water, the volume of the original sample of water will increase by the exact amount of the volume of the water added, because there is no volume change on mixing pure anything with itself. However, in mixtures of more than one species, the two are generally not the same, as shown by Examples 6.1, 6.2, and 6.3. 

The other thermodynamic properties follow in standard fashion from the partition function. In particular, unlike the original lattice treatment, the theory accommodates a nonvanishing excess volume the volume change on mixing... 

The results of the above mentioned study on mixed oxides prepared by thermal decomposition [84] are not in contradiction to the results obtained on reactively sputtered electrodes. A premise for common d-band formation is the formation of a solid solution with homogeneous properties which is probably not obtained during thermal decomposition. Indeed the authors find a trend towards the behaviour of the sputtered electrodes when homogeneity is improved by changing the solvent for the starting compounds. 

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