Activity coefficient in aqueous salt

WOLERY JACKSON Activity Coefficients in Aqueous Salt Solutions... 

Wolery, T. J. and Jackson, K. J., 1990, Activity coefficients in aqueous salt solutions. Hydration theory equations, in (eds., D. C. Melchior and R. L. Bassett). Chemical Modeling of Aqueous Systems II. ACS Symposium Series 416. Washington, DC American Chemical Society, pp. 16-29. 

Above an ionic strength of approximately 1 M. activity coefficients of most ions increase, as shown for ff + in NaCI04 solutions in Figure 8-5. We should not be too surprised that activity coefficients in concentrated salt solutions are not the same as those in dilute aqueous solution. The solvent is no longer ff20 but. rather, a mixture of H20 and NaC104. ffeieafter, we limit our attention to dilute aqueous solutions. 

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. 

Examples of Values of L and AF°. As a first example we may evaluate both L and AF° for a moderately soluble salt in aqueous solution. At 25° a saturated solution of potassium perchlorate has a concentration of 0.148 mole of KCIO4 in a 1000 grams of water that is to say, y+ = y = 0.148/55.5. The activity coefficient in the saturated solution has been taken1 to be 0.70 + 0.05. Using this value, we can estimate the work required to take a pair of ions from the crystal surface to mutually distant points, when the crystal is in contact with pure solvent at 25°C ... 

The Change of Solubility with Temperature. The solubilities of various salts have been measured in aqueous solution at various temperatures. But from these measurements we cannot derive values of L as a function of temperature, until the activity coefficients in the various saturated solutions have been accurately measured. In dilute solutions... 

Long, F.A. McDevit, W.F. "Activity Coefficients of Nonelectrolyte Solutes in Aqueous Salt Solutions," Chem. Rev.,... 

Bretti. C.. Crea. F.. Foti. C.. and Sammartano. S. Solnbility and acivity coefficients of acidic and basic nonelectrolytes in aqueous salt solutions. 1. Solnbility and activity coefficients o-phthalic and L-cystine in NaCl(aq). (CHsl NCUaq). and (C2Hs) NI(aq) at different ionic strengths and at t= 25 °C. Ind. Eng. Chem., 50(5) 1761-1767. 2005. 

Gordon, J. E., and R. L. Thorne, Salt effects on non-electrolyte activity coefficients in mixed aqueous electrolyte solutions. II. Artificial and natural sea waters , Geochim. Cosmochim. Acta, 31, 2433-2443 (1967b). 

F.A. Long and W.F. McDevit, Activity coefficients of nonelectrolyte solutes in aqueous salt solutions, Chem. Rev. 51... 

Osol, A., Kilpatrick, M. (1933) The salting-out and salting-in of weak acids. I. The activity coefficients of the molecules of ortho, meta, and para chlorobenzoic acids in aqueous salt solutions. J. Am. Chem. Soc. 55, 4430-4440. 

Figure 2. The Henry constant of oxygen in aqueous solutions of sodium sulfate at 25 °C (O) experimental data (a) the Henry constant calculated with eq 24 using for the mean activity coefficient of dissolved salt the Debye-Hiickel equation (b) the Henry constant calculated with eq 24 using for the mean activity coefficient of dissolved salt the extended Debye-Hiickel equation (c) the Henry constant calculated with eq 24 using for the mean activity coefficient of dissolved salt the Bromley equation (d) the Henry constant calculated with eq 15.

For NaCl, the results are not too accurate at high molalities. However, it is well-known that most models fail to represent accurately the mean activity coefficient for the NaCl + H2O mixtures at high molalities. One can, therefore, conclude that the gas solubility in aqueous salt solutions can be well described by eq 24 when accurate expressions for the mean activity coefficient of the salt in the binary water + salt mixtures are used. 

Parkhurst, D. L. 1990. Ion-association models and mean activity coefficients of various salts. In Chemical modeling of aqueous systems fl, ed D. C. Melchior and R. L. Bassett, Am. Chem. Soc. Symp. Ser. 416, pp. 30-43. Washington DC Am. Chem. Soc. 

Values of electrolyte activities, as measured by osmotic pressures, freezing point depression, and other experimental methods are in the literature (References 5 and 6, for example) or one can calculate activity coefficients based on models of molecular-level interactions between ions in electrolyte solutions. For illustrative purposes, mean molal activity coefficients for various salts at different aqueous molal (mj concentrations at 25°C are listed in Table 26.3 [7]. 

Calculations using the aqueous model from WATEQ and an aqueous model modified from WATEQ were compared to experimental mean activity coefficients for various salts to determine the range of applicability and the sources of errors in the models. An ion-association aqueous model was derived by least-squares fitting of ion-association stability constants and individual-ion, activity-coefficient parameters to experimental mean activity coefficients for various salts at 25°C. 

In this report, calculations made using ion-association aqueous models were compared to experimental mean activity coefficients for various salts to determine the range of applicability and the sources of errors in the models. An ion-association aqueous model must reproduce the mean activity coefficients for various salts accurately or it does not describe the thermodynamics of aqueous solutions correctly. Calculations were made using three aqueous models (1) The aqueous model obtained from WATEQ (3), WATEQF (4), and WATEQ2 (6), referred to as the WATEQ model (2) the WATEQ model with modifications to the individual-ion, activity-coefficient equations for the free ions, referred to as the amended WATEQ model and (3) an aqueous model derived from least-squares fitting of mean activity-coefficient data, referred to as the fit model. 

The mean activity coefficient for a salt can be calculated from experimental data, but the individual-ion activity coefficients used in ion-association aqueous models cannot be determined experimentally. Several formulas were used for individual-ion activity coefficients in the calculations presented in this report. Three formulas were used in the WATEQ model the extended Debye-Huckel formula including an ion-size parameter, a[ (Equation 2) modified extended Debye-Huckel formula with two fitted parameters, a[ and 6i (Equation 3) and the Davies equation (Equation 4). 

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