Equation Setschenow

It is interesting to note that the molecule-ion interaction contribution in equation (5) is consistent with the well-known Setschenow equation. The Setschenow equation is used to represent the salting-out effect of salts on molecular nonelectrolyte solutes, when the solubilities of the latter are small (Gordon, (15)). The Setschenow equation is... 

To test the validity of the extended Pitzer equation, correlations of vapor-liquid equilibrium data were carried out for three systems. Since the extended Pitzer equation reduces to the Pitzer equation for aqueous strong electrolyte systems, and is consistent with the Setschenow equation for molecular non-electrolytes in aqueous electrolyte systems, the main interest here is aqueous systems with weak electrolytes or partially dissociated electrolytes. The three systems considered are the hydrochloric acid aqueous solution at 298.15°K and concentrations up to 18 molal the NH3-CO2 aqueous solution at 293.15°K and the K2CO3-CO2 aqueous solution of the Hot Carbonate Process. In each case, the chemical equilibrium between all species has been taken into account directly as liquid phase constraints. Significant parameters in the model for each system were identified by a preliminary order of magnitude analysis and adjusted in the vapor-liquid equilibrium data correlation. Detailed discusions and values of physical constants, such as Henry s constants and chemical equilibrium constants, are given in Chen et al. (11). 

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)). 

For non-electrolytes in solutions of electrolytes the prediction of activity coefficients for these species is not nearly as advanced. Most predictions are variations of the well-known Setschenow equation. 

From these equations we obtain the empirical Setschenow equation... 

Salt effects of lithium chloride and calcium chloride on the solubility of carbon dioxide in a mixture of methanol and water were observed at 25°C and 1 atm. Experimental results can be correlated by the Setschenow equation for a fixed solvent composition of salt-free basis. The salting-out parameter is not linear with solvent composition, which is opposite to the results obtained when a mixed salt is used. 

The salt effect of single or mixed electrolytes on the solubility of a gas in water is of considerable industrial and theoretical interest. Methods to predict or correlate these effects have been presented by various workers and have been reviewed briefly (I). With the exception of a study by Clever and Reddy (2), previous investigations found no salt effect data on gas solubility in non-aqueous or mixed solvents. Clever and Reddy (2) observed the solubilities of helium and argon in methanol solutions of sodium iodide at 30° C and showed that the following Setschenow equation is not always applicable to such a system. 

Building Quantitative Models for the Hofmeister Series and Cohn-Edsall and Setschenow Equations... 

While the Hofmeister series and the Cohn-Edsall and Setschenow equations are useful tools for the estimation of protein stability and precipitation behavior, their usefulness is limited because of the lack of a quantitative relationship to molecular or solution properties. The goal of past and current efforts is to quantify the Hofmeister series and to predict the constants Ks and /3 (or Ks and log [E]0) in the Cohn-Edsall or Setschenow equations, respectively. Some of the most relevant efforts focus on ... 

Finally, this section has focused primarily on ions in aqueous solution but it should be remembered that aqueous solutions also contain important dissolved neutral species, e.g. O2, CO2, H2CO3, Si(OH)4. For non-ideal solutions, the Setschenow Equation (1899) has traditionally been used to describe the ionic strength dependence of the activity coefficients for dissolved neutral species and can be written as... 

The solubilities of carbon dioxide in aqueous solutions of mixed salts chosen from eight electrolytes (NaCl, KCl, Na2SO>, NH Cl, AfgSOj, (HHh)2SOh, CaCl2, KNOs) were measured at 25° C and 1 atm by the saturation method. Experimental results for the mixed-salt system were not described easily by the modified Setschenow Equation. However, they were correlated very well by an empirical two-parameter equation. The parameters in the equation for the binary and ternary salt solutions could be estimated easily from these equations for the components of the mixed salts. 

The data have, however, been obtained for only a few systems by Onda et al. (J), Joosten and Danckwerts (2), and Hikita et al. (3). These authors also proposed methods for estimating the solubility of gases in aqueous mixed-salt solutions from the corresponding data for each salt in the systems. These studies are extensions of the empirical method proposed by van Krevelen and Hoftijzer (4) on the basis of the following modified Setschenow Equation. 

The range of applicability of the Setschenow Equation on the salt concentration in aqueous single-salt solutions varies with the system (gas plus an electrolyte) and is never confirmed clearly. Van Krevelen and Hoftijzer (4) showed the range to be up to 2 mol/L of ionic strength in all the systems, while Onda et al. (5) showed that the equation could be applied to the more concentrated solutions for some systems, such as up to 15 mol/L of ionic strength for carbon dioxide systems at the maximum. 

However, from the measurements of solubilities of oxygen (6,7) and carbon dioxide (8) in aqueous single-salt solutions over a wide range of salt concentration, it was found that data for many systems could not be correlated by the empirical Setschenow Equation. Therefore, the modified Setschenow Equation can not always be used to estimate satisfactorily the gas solubility data over a wide range of salt concentrations. 

Figure 3 shows the plot for potassium chloride-calcium chloride binary salt system. Figure 4 shows the plot for sodium chloride-sodium sulfate-ammonium chloride ternary salt system. As shown in these figures, the plots of log(L0/L) vs. salt concentration all curve upward convexly, and the effects of these mixed salts on the solubility of carbon dioxide in the aqueous solutions do not show a direct correlation by the Setschenow Equation. These features are the same in all the mixed-salt systems considered here. 

Other than specific effects that result from conventional chemical interactions (such as acid-base or complex formation), the main factors to be considered are hydration of ions, electrostatic effects, and change in dielectric constant of the solvent. For example, hydration of ions of added salt effectively removes some of the free solvent, so that less is available for solution of the nonelectrolyte. The Setschenow equation probably best represents the activity coefficient of dilute solutions (less than 0.1 M) of nonelectrolytes in aqueous solutions of salts up to relatively high concentrations (about 5 M) ... 

The effect of a solute additive on the solubility of another solute may be quantified by the Setschenow equation ... 

Additives might increase or decrease the solubility of a solute in a given solvent. In the case of salt, those that increase the solubility are said to "salt in" the solute, and those that decrease the solubility "salt out" the solute. The effect of the additive depends very much on the influence it has on the structure of the water or its ability to compete with solvent water molecules. Both effects are described by the empirically derived Setschenow equation ... 

This equation describes the relationship between the aqueous solubility of sparingly soluble salts (So) and the empirical Setschenow salting-out constant k = 0.217/Sq. This relationship and the Setschenow equation are valid only at low concentrations of added salt. As the concentration of added salt increases, the apparent k value is not constant, but is dependent on the solubility and the rate of change of solubility with added salt concentration. It was concluded that the Setschenow treatment is generally inappropriate for description and analysis of common ion equilibria. 

Henry s law (Eqn. 2) can be rearranged to consider the mole fraction solubility of i in pure water, where Yi 1, and the mole fraction solubility of i in a saline solution at the same partial pressure, respectively, enabling the Setschenow equation to be rearranged with respect to the mole fraction solubilities... 

Theoretical relationships for activity coefficients. The Setschenow equation is used to calculate the activity coefficients of aqueous molecular species in salt solutions. The Pitzer based methods may be used for binary or multicomponent solution activity coefflcient calculations for all species in the solution. 

The Setschenow equation for the activity coefficient of the gas was then expressed ... 

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