Single salt solutions

Equilibrium constants calculated from the composition of saturated solutions are dependent on the accuracy of the thermodynamic model for the aqueous solution. The thermodynamics of single salt solutions of KC1 or KBr are very well known and have been modeled using the virial approach of Pitzer (13-15). The thermodynamics of aqueous mixtures of KC1 and KBr have also been well studied (16-17) and may be reliably modeled using the Pitzer equations. The Pitzer equations used here to calculate the solid phase equilibrium constants from the compositions of saturated aqueous solutions are given elsewhere (13-15, 18, 19). The Pitzer model parameters applicable to KCl-KBr-l O solutions are summarized in Table II. 

In the equations developed by Reilly and Wood (15) from the cluster Integral model (1 6), y+ is calculated in complex solutions from excess properties of single salt solutions. Note that the cluster Integral approach 1s based upon terms which represent the contributions of pair-wise ion interactions 1n various types of clusters to the potential interaction energy. Then, the partition function and the excess properties of the solution can be evaluated. The procedure is akin to the vlrial expansion 1n terms of clusters. 

Horita J, Wesolowski DJ, Cole DR (1993a) The activity-composition relationship of oxygen and hydrogen isotopes in aqueous salt solution 1. Vapor-liquid water equilibration of single salt solutions for 50 to 100°C. Geochim Cosmochim Acta 57 2797-2817... 

A second example is provided by a semiempirical correlation for multi-component activity coefficients in aqueous electrolyte solutions shown in Fig. 2. This correlation, developed by Fritz Meissner at MIT [3], presents a method for scale-up activity-coefficient data for single-salt solutions, which are plentiful, are used to predict activity coefficients for multisalt solutions for which experimental data are rare. The scale-up is guided by an extended Debye-Hilckel theory, but essentially it is based on enlightened empiricism. Meissner s method provides useful estimates of thermodynamic properties needed for process design of multieffect evaporators to produce salts from multicomponent brines. It will be many years before sophisticated statistical mechanical techniques can perform a similar scale-up calculation. Until then, correlations such as Meissner s will be required in a conventional industry that produces vast amounts of inexpensive commodity chemicals. 

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. 

The complexation constants of the individual major seawater ions with otFeOOH determined in single salt solutions can be used to predict the titratable charge and surface species distribution of goethite in seawater. This prediction can then be compared with the experimentally determined charge of goethite in a mixed seawater type electrolyte. 

It has been shown elsewhere (10) that the data for the single salt solutions are more important than the binary common ion solution data in calculations involving equations 18 and 19. 

Osmotic and Activity Coefficient Interpolation From Published Tables. Glueckauf (17) has developed equations for the osmotic and activity coefficients of single salt solutions which, when "tuned to measured data, will accurately interpolate between measured values and predict values to ionic strengths well above those usually encountered in natural brines. For brines of ionic strengths above 2 molal, the following equations for the osmotic and activity coefficients were developed (17)i... 

Only single ion molarities are given as input data, therefore, published (18) single salt solution data relating solute concentrations to solvent concentrations were necessary in the computing of the ratio for each major component salt, dom... 

The Carbonate System. Since no osmotic or activity coefficient data are available for single salt solutions of carbonate and bicarbonate salts, estimates had to be made of the activities of these ligands in solution, as well as for the activities of carbonate and bicarbonate salt cations. 

Ba (Dove and Nix, 1997). Rate enhancements in single salt solutions can be predicted by equations that follow the form of Langmuir-type isotherms, whereas in mixed salt solutions, behavior follows a competitive cation-surface interaction model (Dove, 1999). Dove and co-workers argue that the alkali and alkaline earth cations enhance dissolution by modifying characteristics of the solvent at the mineral-solution interface. 

Table A6.2 includes historical information on the comparison of ion activity coefficients at the effective ionic strength of seawater. Activity coefficients measured in single salt solutions are compared with those measured in seawater and those calculated from an association model. We have to distinguish between total activity coefficients (cf. equations 3 and 4)...

Figure 1. Relation between temperature and composition of a single salt solution. Tjg is eutectic temperature...

The individual-ion activity coefficients for the free ions were based on the Macinnis (18) convention, which defines the activity of Cl to be equal to the mean activity coefficient of KCl in a KCl solution of equivalent ionic strength. From this starting point, individual-ion activity coefficients for the free ions of other elements were derived from single-salt solutions. The method of Millero and Schreiber (14) was used to calculate the individual-ion, activity-coefficient parameters (Equation 5) from the parameters given by Pitzer (19). However, several different sets of salts could be used to derive the individual-ion activity coefficient for a free ion. For example, the individual-ion activity coefficient for OH could be calculated using mean activity-coefficient data for KOH and KCl, or from CsOH, CsCl, and KCl, and so forth. 

Ernst, M., Bismarck, A., Springer, J. and Jekel, M. 2000. Zeta-potential and rejection rates of a polyethersulfone nanofiltration membrane in single salt solutions. 1 5 ... 

These Fj terms may also be expressed as functions of the activity coefHcients of single salt solutions ... 

The solvent-salt parameters may be obtained from single salt solution parameters. The salt-salt parameters must be obtained from data regression of ternary solution data. 

Water containing only a single salt solution, such as NaCl or KCl. This is most commonly the choice for laboratory-scale experiments in the literature. 

When real water is chosen (option 1), one must decide on what pretreatment to use to remove particulate matter, biological species, and organic pollutants. Because ionic mixtures are used in options 1 and 2, the effluent freshwater produced must be analyzed using offline individual ion detection, such as inductively coupled plasma in combination with optical emission spectroscopy or mass spectroscopy. However, in option 3, when using only single salt solutions, the measurement of conductivity is sufficient. In single salt solutions, we have to consider that the diffusion coefficients of the anion and cation may be (almost) equal (KCl) or are different (NaCl). 

---