Interaction activity coefficients

Standard free energies, enthalpies and entropies are important because they relate only to solvent-solute interactions. Activity coefficients are of interest since they relate to the departure of the system from ideal conditions. 

The situation for electrolyte solutions is more complex theory confimis the limiting expressions (originally from Debye-Htickel theory), but, because of the long-range interactions, the resulting equations are non-analytic rather than simple power series.) It is evident that electrolyte solutions are ideally dilute only at extremely low concentrations. Further details about these activity coefficients will be found in other articles. 

The binary interaction parameters are evaluated from liqiiid-phase correlations for binaiy systems. The most satisfactoiy procedure is to apply at infinite dilution the relation between a liquid-phase activity coefficient and its underlying fugacity coefficients, Rearrangement of the logarithmic form yields... 

Since activity coefficients have a strong dependence on composition, the effect of the solvent on the activity coefficients is generally more pronounced. However, the magnitude and direc tion of change is highly dependent on the solvent concentration, as well as the liquid-phase interactions between the key components and the solvent. The solvent acts to lessen the nonideahties of the key component whose liquid-phase behavior is similar to the solvent, while enhancing the nonideal behavior of the dissimilar key. 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

In an attempt to explain the nature of polar interactions, Martire et al. [15] developed a theory assuming that such interactions could be explained by the formation of a complex between the solute and the stationary phase with its own equilibrium constant. Martire and Riedl adopted a procedure used by Danger et al. [16], and divided the solute activity coefficient into two components. 

This relationship depends on the assumption that two similar stationary phases, irrespective of their polarity, can be considered to differ by measuring the ratio of the activity coefficients of two noncomplexing solutes (this basically implies the solute is nonpolar and will only interact with the stationary phase by dispersion forces). If this were true then. 

Another method to determine infinite dilution activity coefficients (or the equivalent FFenry s law coefficients) is gas chromatography [FF, F2]. In this method, the chromatographic column is coated with the liquid solvent (e.g., the IL). The solute (the gas) is introduced with a carrier gas and the retention time of the solute is a measure of the strength of interaction (i.e., the infinite dilution activity coefficient, y7) of the solute in the liquid. For the steady-state method, given by [FF, F2] ... 

For those dilute mixtures where the solute and the solvent are chemically very different, the activity coefficient of the solute soon becomes a function of solute mole fraction even when that mole fraction is small. That is, if solute and solvent are strongly dissimilar, the relations valid for an infinitely dilute solution rapidly become poor approximations as the concentration of solute rises. In such cases, it is necessary to relax the assumption (made by Krichevsky and Kasarnovsky) that at constant temperature the activity coefficient of the solute is a function of pressure but not of solute mole fraction. For those moderately dilute mixtures where the solute-solute interactions are very much different from the solute-solvent interactions, we can write the constant-pressure activity coefficients as Margules expansions in the mole fractions for the solvent (component 1), we write at constant temperature and at reference pressure Pr ... 

The Debye-Hiickel formula for the activity coefficient of an ion was developed by a consideration of ion atmosphere effects.10 It starts with an electrostatic expression for the free energy of interaction for one ion with one mole of others ... 

As it happens, the product Ba is near unity. In particular, it is about one in water if a (the interaction distance) is 3 X 10 10 m. This is not an unreasonable distance. Even if a is somewhat different, the simplification that Ba is nearly unity is a fair approximation, and one that is often made. This is allowed because Ba occurs as a multiplier of fju in the denominator of Eq. (9-39), where this product is invariably less than the unity to which it is added. And the equations for the activity coefficients are in any event reliable only at low ionic strength. For these reasons, and because of the resulting simplification, we shall approximate the expression for the activity coefficient as... 

With different pectins, one found that the activity coefficient of calcium has a value half that of magnesium this is interpreted as the basis of a dimer formation in presence of calcium. The specific interaction of calcium was described as the egg-box model first proposed for polyguluronate in which oxygen atoms coordinated to calcium [46]. Recently, the comparative behaviour of Mg and Ca with homogalacturonan was reexamined [47]. 

Therefore, the activity coefficients in solutions are determined primarily by the energy of electrostatic interaction w j between the ions. It is only in concentrated solutions when solvation conditions may change, that changes in (but not the existence of) solvation energy must be included, and that nonelectrostatic interactions between ions must be accounted for. 

All deviations from ideal behavior, which are directly (electrostatically) or indirectly (through the solvent) caused by ion-ion interactions are usually treated by scaling the concentration with a so-called activity coefficient fj, which leads to the activity =fiCi [Atkins, 1990]. Inserting the activity into (5.2) gives... 

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