Standard free energy of solution

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

Heat of Precipitation. Entropy of Solution and Partial Molal Entropy. The Unitary Part of the Entropy. Equilibrium in Proton Transfers. Equilibrium in Any Process. The Unitary Part of a Free Energy Change. The Conventional Standard Free Energy Change. Proton Transfers Involving a Solvent Molecule. The Conventional Standard Free Energy of Solution. The Disparity of a Solution. The E.M.F. of Galvanic Cells. 

The Conventional Standard Free Energy of Solution. Returning now to the solution of a crystalline solid, let us consider the free energy of solution. Taking a uni-univalent substance let AF denote the change in free energy per mole when additional ions are added to a solution at temperature T where the solute has the mole fraction x and let us fix attention on the quantity... 

The left-hand side of (97) is just the usual standard free energy of solution AF°. We see that... 

In agreement with (98), the left-hand side is just the standard free energy of solution AF°. Here y, as defined by (106), is the usual activity coefficient on the molality scale. In particular, when the solid is in contact with its saturated solution, there is no change in the free energy when additional ions are taken into solution. In this case, if in (108) we write m, t and y,at, the values of m and y in the saturated solution, we may set AF equal to zero. This will be discussed in Sec. 100. 

From the values given in the table the equilibrium constants of the hydrogen halogenides can be calculated by use of the equation AF° = —RTlnK. The calculated values are somewhat uncertain because of uncertainty in the estimate of the standard free energy of solution of the dissociated molecules. The values obtained in this way are 2 X 10 for HC1, 5 X 10s for HBr, and 2 X 109 for HI. These acids are accordingly very strong acids. 

Fig. 12.45. The standard free energy of adsorption of families of organics as a function of the standard free energy of solution. Note the difference in sign. Adsorption occurs more readily as the tendency to dissolve declines. (Reprinted with permission from E. Blomgren, J. O M Bockris, and K. Jesch, J. Phys. Chem. 65 2006, copyright 1961 American Chemical Society.)...

This reaction, which is the displacement of hydrogen ions from the solution and their liberation as hydrogen gas, is virtually that occurring when a metal dissolves in a dilute acid solution, provided there are no accompanying complications, e.g., formation of complex ions. It follows, therefore, that — zFE may be regarded as the standard free energy of solution of the metal. 

Thus, the crystallization of cristobalite and quartz directly from natural waters seems unlikely. However, the partial precipitation of silica in amorphous form is possible in areas where fluvial and marine waters mix. Precipitation of silica as gels followed by the formation of opal-like silica is possible in practice only in areas of intensive volcanic activity.The heat and standard free energy of solution were calculated from the solubility of quartz in water found analytically to be within the temperature range 25-473 °C (Van Tier et al. i960). Analogous calculations were made for cristobalite and other silica forms (Fournier and Rowe 1962 Table 3.5). 

When the solute is in equilibrium with its ions, AG = 0 and one obtains the standard free energy of solution... 

Here AG°(w) and AG°(5 ) may be either the standard free energies of solution (AGJoin) or solvation (AGJoiv) corresponding to the processes... 

A change of a factor of 10 in the solubility product corresponds to a change of only 5.7 kJ/mole in the free energy of solution, so that the energetic difference between soluble and insoluble salts is a very small one. For example, the standard free energy of solution of potassium nitrate is less than 12 kJ/mole more negative than that of potassium perchlorate, yet the first is classified as soluble and the second as insoluble. 

Conventionally the standard free energy of solution is given by eq. [5.5.2],... 

Table 13.1.1. Standard free energies of solution of sodium chloride in various solvents at 25°C. Data of AG° are from reference 19...

Fig. 7.4. Standard free energy of solution A/jls (in cal/mole) of methane as a function of mole fraction of ethanol at three temperatures.

We now consider a specific example of real solutes. Consider two methane molecules. The standard free energy of solution of methane, is well known in water and in nonaqueous solvents (Chapter 7). Suppose that we start with two methane molecules at infinite separation and replace them by the corresponding field of force. Next, we move the centers of the field of force from infinity to the final distance / = (Tj = 1.533 A, (Tj being the carbon-carbon distance in the ethane molecule. 

Once we have made the replacement of the two sources of the field of force by a single molecule, we identify the average quantity on the rhs of (8.54) as the standard free energy of solution of the ethane molecule. 

The second case includes molecules that possess internal rotations, in which case (8.73) should be understood as an average over all the conformations of the molecule. It is convenient, in this case, to introduce an auxiliary quantity, the standard free energy of solution of the molecule in a specific configuration Y,... 

We conclude this section by pointing out that quite a variety of information on HI can be obtained by processing the same experimental data in various ways. For example, having the standard free energies of solution of methane, ethane, and butane, we can obtain the HI for three different reactions, which we write schematically as... 

Second, relation (8.83) shows that the HI at zero separation for hard spheres and the corresponding standard free energy of solution provide the same information on the properties of the solvent. This finding brings us back to Kauzmann s idea that may serve as a measure of the... 

In the first form on the rhs, we recognize the first term as the standard free energy of solution of a hypothetical solute, the field of force of which is twice the field of force of a single solute S. By twice we mean the following The field of force Z7(X /Ri,R2) given in (8.82) has the form... 

That is, the HI at zero separation between two solutes a and b, with b much smaller than a, is determined by the standard free energy of solution of the solute b. 

Let us return to relation (8.90) for two solutes S which are to be replaced by a single solute S with a field of force approximately twice as strong as that of S. It is claimed that if we find a solute S having the same diameter as S, we already have a reasonable approximation for (8.90). The reason is based on the splitting of the standard free energy of solution into two contributions (see Section 7.3)... 

The solution of gases in rubbers occurs exothermally even in constant volume systems (33,6O), with the possible exceptions of helium and hydrogen. This must be contrasted with the endothermic heats of solution of many gases in organic liquids (61). The solubility constant k for a perfect gas is related to the standard free energy of solution,... 

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