Ideal solution formation

Chemical reaction - formation of intermetollic compounds Diffusion in solid solutions (dilute ideal solutions between solute 300 to 5 X 1 O ... 

Thus the formation of an ideal solution from its components is always a spontaneous process. Real solutions are described in terms of the difference in the molar Gibbs free energy of their formation and that of the corresponding ideal solution, thus ... 

A very simple treatment can be carried out by assuming that the liquid phase is a series of ideal solutions of lead and thallium, and that in the solid phase isomorphous replacement of thallium atoms in the PbTl3 structure by lead atoms occurs in the way corresponding to the formation of an ideal solution. For the liquid phase the free energy would then be represented by the expression... 

The entropy of formation of an ideal solution at a given temperature can be obtained from the following equation... 

The variation of the entropy of formation of an ideal solution with composition is shown inFigure3.10. It is again a characteristic ofan ideal solution that the partial (ASA,ld, A. Sg1, ld) and the integral molar (ASM,ld) entropies of its formation are independent of temperature. 

By using a thermodynamic model based on the formation of self-associates, as proposed by Singh and Sommer (1992), Akinlade and Awe (2006) studied the composition dependence of the bulk and surface properties of some liquid alloys (Tl-Ga at 700°C, Cd-Zn at 627°C). Positive deviations of the mixing properties from ideal solution behaviour were explained and the degree of phase separation was computed both for bulk alloys and for the surface. 

This evaluation assumes an ideal solution and the formation of a 1 1 complex. 

In a recent publication, Schafer and coworkers point out the utility of the electrode as a reagent which is effective in promoting bond formation between functional groups of the same reactivity or polarity [1]. They accurately note that reduction at a cathode, or oxidation at an anode, renders electron-poor sites rich, and electron-rich sites poor. For example, reduction of an a, -un-saturated ketone leads to a radical anion where the )g-carbon possesses nucleophilic rather than electrophilic character. Similarly, oxidation of an enol ether affords a radical cation wherein the jS-carbon displays electrophilic, rather than its usual nucleophilic behavior [2]. This reactivity-profile reversal clearly provides many opportunities for the formation of new bonds between sites formally possessing the same polarity, provided only one of the two groups is reduced or oxidized. Electrochemistry provides an ideal solution to the issue of selectivity, given that a controlled potential reduction or oxidation is readily achieved using an inexpensive potentiostat. 

If Equation (14.2), Equation (14.6), or Equation (14.7) is used to define an ideal solution of two components, values for the changes in thermodynamic properties resulting from the formation of such a solution follow directly. 

In a similar way we can consider an integral mixing process for the formation of an ideal solution from the components, as illustrated in Eigure 14.2. The mixing process can be represented by the equation... 

Figure 14.2. Thermodynamics of formation of ideal solution from pure components.

One of the approaches to calculating the solubility of compounds was developed by Hildebrand. In his approach, a regular solution involves no entropy change when a small amount of one of its components is transferred to it from an ideal solution of the same composition when the total volume remains the same. In other words, a regular solution can have a non-ideal enthalpy of formation but must have an ideal entropy of formation. In this theory, a quantity called the Hildebrand parameter is defined as ... 

For a binary system of surfactants A and B, the mixed micelle formation can be modeled by assuming that the thermodynamics of mixing in the micelle obeys ideal solution theory. When monomer and micelles are in equilibrium in the system, this results in ... 

Non-ideal solution theory is used to calculate the value of a parameter, S, that measures the interaction between two surfactants in mixed monolayer or mixed micelle formation. The value of this parameter, together with the values of relevant properties of the individual, pure surfactants, determines whether synergism will exist in a mixture of two surfactants in aqueous solution. 

The nature of surface adsorption and micelle formation of various mixed FC- and HC-surfactants systems can be conveniently and well investigated by the non-ideal solution theory semi-emplrlcally applied in the surface layer and micelles. The weak "mutual phobic" interaction between FC- and HC-chains has been clearly revealed in the anionic-anionic and nonlonic-nonionic systems as Indicated by the positive values. value cannot be obtained... 

The thermodynamics of mixing upon formation of the bilayered surface aggregates (admicelles) was studied as well as that associated with mixed micelle formation for the system. Ideal solution theory was obeyed upon formation of mixed micelles, but positive deviation from ideal solution theory was found at all mixture... 

Scamehorn et. al. (20) also presented a simple, semi—empirical method based on ideal solution theory and the concept of reduced adsorption isotherms to predict the mixed adsorption isotherm and admicellar composition from the pure component isotherms. In this work, we present a more general theory, based only on ideal solution theory, and present detailed mixed system data for a binary mixed surfactant system (two members of a homologous series) and use it to test this model. The thermodynamics of admicelle formation is also compared to that of micelle formation for this same system. 

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