Activity Coefficients of Molecular Solutes

A second type of ternary electrolyte systems is solvent -supercritical molecular solute - salt systems. The concentration of supercritical molecular solutes in these systems is generally very low. Therefore, the salting out effects are essentially effects of the presence of salts on the unsymmetric activity coefficient of molecular solutes at infinite dilution. The interaction parameters for NaCl-C02 binary pair and KCI-CO2 binary pair are shown in Table 8. Water-electrolyte binary parameters were obtained from Table 1. Water-carbon dioxide binary parameters were correlated assuming dissociation of carbon dioxide in water is negligible. It is interesting to note that the Setschenow equation fits only approximately these two systems (Yasunishi and Yoshida, (24)). 

From a practical viewpoint we may conclude that molecular solutes have activity coefScients near unity up to an ionic strength of 0.1 and that deviations are moderate even at ionic strengths of the order of unity. In contrast to those of ionic solutes, activity coefficients of molecular solutes usually are slightly greater than unity. 

Since values of k vary for the most part between 0.01 and 0.10, activity coefficients of molecular solutes can be considered to be effectively unity in solutions whose ionic strengths are <0.2, i.e., log y < 0.02. 

Coct and Cair are the moles of compound per m3 of octanol and air, poct and Moct are the density (820 kg/m3 at 20°) and molecular weight (130 g/ mol) of octanol, and yoct is the activity coefficient of the solute in octanol. Eliminating P,s from equations (17) and (21) gives... 

This is the activity coefficient of the solute in the stationary phase (y ). The value of y is determined by molecular interactions between the solute and the stationary phase. Therefore, (chemically) different stationary phases will lead to different values for y. This explains the availability of many different stationary phases for GC, many of which show different selectivity (see section 2.3.2). 

Recently Purnell and collaborators (80) re-examined most of the results published on complexing studies of miscible low molecular weight substances. It was found that the activity coefficient of the solute in the mixed stationary phase could be described by the following relation ... 

When it is necessary to estimate activity coefficients where no data or very limited data are available, estimates may be made by using a group contribution method. In this case, a molecule is divided into fimctional groups, or subgroups of the molecule. These subgroups are assumed to act independently of the molecule in which they appear. Molecular interactions are accounted for by properly weighted sums of group interactions. Fredenslund, Jones, and Prausnitz developed the method for UNIQUAC and named it as universal functional activity coefficient (UNIFAC). Smith, van Ness, and Abbott report the equations for the activity coefficients of multicomponent solutions and their parameters. These equations are very... 

In a similar fashion, solubility measurements (of a gas in a liquid, a liquid in a liquid, or a solid in a liquid) can be used to determine the activity coefficient of a solute in a solvent at saturation. Also, measurements of the solubility of a solid solute in two liquid phases can be used to relate the activity coefficient of the solute in one liquid to a known activity coefficient in another liquid, and freezing-point depression or boiling-point elevation measurements are frequently used to determine the activity of the solvent in a solute-solvent mixture. We have also showed that osmotic-pressure measurements can be used to determine solvent activity coefficients, or to determine the molecular weight of a large polymer or protein. 

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. 

If the molecular species of the solute present in solution is the same as those present in the crystals (as would be the case for nonelectrolytes), then to a first approximation, the solubility of each enantiomer in a conglomerate is unaffected by the presence of the other enantiomer. If the solutions are not dilute, however, the presence of one enantiomer will influence the activity coefficient of the other and thereby affect its solubility to some extent. Thus, the solubility of a racemic conglomerate is equal to twice that of the individual enantiomer. This relation is known as Meyerhoffer s double solubility rule [147]. If the solubilities are expressed as mole fractions, then the solubility curves are straight lines, parallel to sides SD and SL of the triangle in Fig. 24. 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

In applying this equation to multi-solute systems, the ionic concentrations are of sufficient magnitude that molecule-ion and ion-ion interactions must be considered. Edwards et al. (6) used a method proposed by Bromley (J7) for the estimation of the B parameters. The model was found to be useful for the calculation of multi-solute equilibria in the NH3+H5S+H2O and NH3+CO2+H2O systems. However, because of the assumptions regarding the activity of the water and the use of only two-body interaction parameters, the model is suitable only up to molecular concentrations of about 2 molal. As well the temperature was restricted to the range 0° to 100 oc because of the equations used for the Henry1s constants and the dissociation constants. In a later study, Edwards et al. (8) extended the correlation to higher concentrations (up to 10 - 20 molal) and higher temperatures (0° to 170 °C). In this work the activity coefficients of the electrolytes were calculated from an expression due to Pitzer (9) ... 

By extending regular solution theory for binary mixtures of AEg in aqueous solution to the adsorption of mixture components on the surface (3,4), it is possible to calculate the mole fraction of AEg, Xg, on the mixed surface layer at tt=20, the molecular interaction parameter, 6, the activity coefficients of AEg on the mixed surface layer, fqg and f2s and mole concentration of surfactant solution, CTf=20 3t surface pressure tt=20 mn-m l (254p.l°C). The results from the following equations are shown in Table I and Table II. 

So far, we have focused on how differences in molecular structure affect the solubilities and activity coefficients of organic compounds in pure water at 25°C. The next step is to evaluate the influence of some important environmental factors on these properties. In the following we consider three such factors temperature, ionic strength (i.e., dissolved salts), and organic cosolutes. The influence of pH of the aqueous solution, which is most important for acids and bases, will be discussed in Chapter 8. 

Mitchell, B. E., and P. C. Jurs, Prediction of infinite dilution activity coefficients of organic compounds in aqueous solution from molecular structure , J. Chem. Inf. Comput. Sci., 38, 200-209 (1998). 

Munz, C. H., and P. V. Roberts, The effects of solute concentration and cosolvents on the aqueous activity coefficients of low molecular weight halogenated hydrocarbons , Environ. Sci. Technol., 20, 830-836 (1986). 

The influence of molar mass, charge density as well as chain branching was also determined in the presence of low molecular mass salt. As seen in Fig. 16, the differences between theory and experiment are more important to low molar masses. In Fig. 16 the concentration dependence of the activity of the low molecular salt has been taken into account when calculating fac=fexp/fo [H4, 126], where fac and fexp are calculated and experimentally determined counterion activity coefficients, respectively f0 is the activity coefficient of the added low molecular salt in aqueous solution without polyelectrolyte. 

ACAL - a FORTRAN subroutine which has all the function equations to calculate the activity coefficients of all the ionic and molecular species in the aqueous solution as well as the activity of water. 

Debye-Hiickel developed a theory for the activity coefficients of an ionic solution at a molecular level. A selected ion in the ideally diluted solution is statistically well distributed and there are no interactions between ions present in the solution. In contrast, the ion in the concentrated solution is surrounded by the excess of counter ions in the vicinity of the ion, as the counter ions are attracted by Coulombic forces, while ions of the same charge are repelled. Thus, ion atmosphere is created. As a result, there is a difference in reversible work between the concentrated wrev and dilute solutions wrev ideal ... 

This method is to be used to predict the activity coefficient of a low molecular weight solvent in a solution with a polymer. This procedure requires the structure of all components in the mixture, group reference volumes for all groups in the solution as well as the group interaction parameters for all groups. Use of the number average molecular weight of the polymer is recommended. 

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