The Energies of Solution Formation

Dissolving solutes in liquids is very common. We dissolve salt in the water used to cook vegetables, sugar in iced tea, stains in cleaning fluid, gaseous carbon dioxide in water to make soda water, ethanol in gasoline to make gasohol, and so on. 

Solubility is important in other ways. For example, because the pesticide DDT is fat-soluble, it is retained and concentrated in animal tissues, where it causes detrimental effects. This is why DDT, even though it is effective for killing mosquitos, has been banned in the United States. Also, the solubility of various vitamins is important in determining correct dosages. The insolubility of barium sulfate means it can be used safely to improve X rays of the gastrointestinal tract, even though Ba ions are quite toxic. 

What factors affect solubility The cardinal rule of solubility is like dissolves like. We find that we must use a polar solvent to dissolve a polar or ionic solute and a nonpolar 

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The formation of a liquid solution can be divided into three steps (1) expanding the solute, (2) expanding the solvent, and (3) combining the expanded solute and solvent to form the solution. 

What factors affect solubihty The cardinal rule of solubiUty is like dissolves like. We find that we must use a polar solvent to dissolve a polar or ionic solute and a nonpolar solvent to dissolve a nonpolar solute. Now we will tty to understand why this behavior occurs. To simpUly the discussion, we will assume that the formation of a Uquid solution takes place in three distinct steps  

Separating the solute into its individual components (expanding the solute) 

Overcoming intermolecular forces in the solvent to make room for the solute (expanding the solvent) 

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Free energy of solution formation, consisting of the same amount of solvent and degradated molecules, is presented as follows ... 

A quite reliable estimate of the solvent effect results from theories that combine micro- and macro-scopic parameters of solute and solvent. For example, in the solvophobic theory, the energy of a solute molecule in solvent, Ejoin, is given as the sum of isolated molecule energy, Ej, and the solvation term, Ejo,v. The latter term encompasses the energy of cavity formation in the solvent to accommodate the solute, E, v, and the energy of subsequent solvent-solute interactions, Ej ,. The interaction part is composed of the energy of dispersion, Edi.p> and electrostatic, interactions. The final expression for E i can be written as... 

In its substance it shows how much energy of the component i under the solution conditions differs from the energy of its formation imder standard conditions. The concept of thermodynamic concentration was introduced by Gilbert Newton Lewis (1875-1946) in 1907 for diluted gas solutions and later expanded for other solutions. In this connection, determination of the activity values depends on the nature and state of the component. In this respect gas, non-polar hydrophobic and polar hydrophilic components should be distinguished. 

E(A ]B) is the energy of solution of a metallic atom A in a matrix B, A+1 is the (Z+1) element relative to A. Fig,6 shows the result of a study of some forty dilute alloys AB where the concentration of the dilute component A is 10% or less. The experimental shifts are analysed in terms of alloy heat of formation data according to a semi-empirical scheme due to Miedena. Again, the agreement with the above formula is good. For details, see ref. 8. 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

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 ... 

J mol ). This is additional evidence in favor of rate limitation by inner diffusion. However, the same reaction in the presence of Dowex-50, which has a more open three-dimensional network, gave an activation energy of 44800 J mol , and closely similar values were obtained for the hydrolysis of ethyl acetate [29] and dimethyl seb-acate [30]. The activation energy for the hydrolysis of ethyl acetate on a macroreticular sulphonated cationic exchanger [93] is 3566 J mol . For the hydrolysis of ethyl formate in a binary system, the isocomposition activation energy (Ec) [28,92] tends to decrease as the solvent content increases, while for solutions of the same dielectric constant, the iso-dielectric activation energy (Ed) increases as the dielectric constant of the solvent increases (Table 6). 

The first term inside the brackets evidently is the energy of a solute molecule J in the perfect gas (cf. Eq. 10) hence we have for the energy of formation of the clathrate from and the gaseous solute at constant volume per molecule of Q... 

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