Osmotic coefficient evaluation

Park has also obtained osmotic coefficient data for the aqueous solutions of NaOH-NaCl- NaAl(OH)4 at 25°C employing the isopiestic method (Park and Englezos, 1999 Park, 1999). The solutions were prepared by dissolving AlCl r6H20 in aqueous NaOH solutions. The osmotic coefficient data were then used to evaluate the unknown Pitzer s binary and mixing parameters for the NaOH-NaCI-NaAl(OH)4-H20 system. The binary Pitzer s parameters, [3(0), P0). and C9, for NaAI(OH)4 were found to be -0.0083, 0.0710, and 0.00184 respectively. These binary parameters were obtained from the data on the ternary system because it was not possible to prepare a single (NaAl(OH)4) solution. 

Rard (1992) reported the results of isopiestic vapor-pressure measurements for the aqueous solution of high-purity NiCl2 solution form 1.4382 to 5.7199 mol/kg at 298.1510.005 K. Based on these measurements he calculated the osmotic coefficient of aqueous NiCb solutions. He also evaluated other data from the literature and finally presented a set of smoothed osmotic coefficient and activity of water data (see Table IV in original reference). 

Goldberg, R. N. Nuttall, R. L. "Evaluated Activity and Osmotic Coefficients for Aqueous Solutions The Alkaline Earth Metal Halides" J. Phys. Chem. Ref. Data, 1978, 7,... 

Staples, B. R. Nuttall, R. L. "Computer Programs for the Evaluation of Activity and Osmotic Coefficients" Nat. 

Critical evaluations of activity and osmotic coefficient data were undertaken early in the 1930-1940 period by Harned and Owen (1958) and by Robinson and Stokes, (1965). Wu and Hamer (1968) evaluated activity and osmotic coefficient data for a series of electrolytes but their work on polyvalent electrolytes was not completed. Their work on the 1 1 electrolytes was published in 1972. The evaluation of polyvalent electrolyte data has been continuing in the Electrolyte Data Center at the National Bureau of Standards, and this paper will summarize the methods used in evaluating data for over 100 aqueous polyvalent electrolytes. 

Activity and osmotic coefficient data derived from ten experimental methods have been critically evaluated and correlating equations have been formulated for more than 100 aqueous polyvalent electrolyte systems at 298 K. Evaluations for the major reference solutions KC1 and NaCl (Hamer and Wu, 1972), and CaCl (Staples and Nuttall, 1977) have been published that for (Staples,... 

Generally, agreement has been found between our correlations and those of Pitzer, and others (1972, 1973, 1974, 1975, 1976) and Rard, and others (1976, 1977). Many of our correlations agree fairly well with Robinson and Stokes, (1965) and Harned and Owen, (1958) but in most cases a much larger data base and more recent measurements have been incorporated into the evaluations. It has been observed that agreement with Pitzer s equations is found below moderate concentrations (several molal), but often deviate at higher concentrations where the Pitzer equations do not contain enough parameters to account for the behavior of the activity (or osmotic) coefficient. 

In addition, the critical evaluation of enthalpies of dilution and solution, as well as evaluations of heat capacities have been initiated. These evaluations will allow calculations and correlations of activity and osmotic coefficients as a function of temperature and composition. 

Figure 1. Osmotic coefficient of aqueous sulfuric acid (up to 2m) at 298 K as a function of the square-root of molality ((Q) Pitzer evaluation ( -) experimental...

The techniques used in the critical evaluation and correlation of thermodynamic properties of aqueous polyvalent electrolytes are described. The Electrolyte Data Center is engaged in the correlation of activity and osmotic coefficients, enthalpies of dilution and solution, heat capacities, and ionic equilibrium constants for aqueous salt solutions. 

Formalism According to Pitzer. The most common method for the evaluation of the activity and osmotic coefficients of an electrolyte in a binary mixture of strong electrolytes with a common ion is by Scatchard s Equations (23), the McKay-Perring treatment (24), Mayers Equations... 

In order to evaluate (j), the total excess free energy expression given in equation 17 will be differentiated with respect to the solvent concentration. This involves no changes in the concentration ratios of any ionic specie m to the total concentration of all ionic species m. Differentiation of equation 17 with respect to m results in the working equation for the osmotic coefficient of a mixed electrolyte solution. Details of the differentiation are given elsewhere (15,16). 

The Activity Coefficient of Any Component Salt in the Aqueous Electrolyte Mixture. Analogous to the derivation of the osmotic coefficient expression, equation 17 was differentiated with respect to m to give a relationship between and the activity coefficient, and then that relationship was evaluated by substituting in the value of obtained by differentiation of G from equation 14 with respect to m, where m is now the result of a change in m, m, added to the initial m, m as caused by a... 

The polyion domain volume can be computed by use of the acid-dissociation equilibria of weak-acid polyelectrolyte and the multivalent metal ion binding equilibria of strong-acid polyelectrolyte, both in the presence of an excess of Na salt. The volume computed is primarily related to the solvent uptake of tighdy cross-linked polyion gel. In contrast to the polyion gel systems, the boundary between the polyion domain and bulk solution is not directly accessible in the case of water-soluble linear polyelectrolyte systems. Electroneutrality is not achieved in the linear polyion systems. A fraction of the counterions trapped by the electrostatic potential formed in the vicinity of the polymer skeleton escapes at the interface due to thermal motion. The fraction of the counterion release to the bulk solution is equatable to the practical osmotic coefficient, and has been used to account for such loss in the evaluation of the Donnan phase volume in the case of linear polyion systems. 

This last equation enables the activity coefficient of the solute to be evaluated if the osmotic coefficient of the solvent is known for all solutions more dilute than the solution under consideration. 

To evaluate from freezing point measurements it is thus necessary to have a knowledge of e. If this is not known then we can do no more than calculate an apparent osmotic coefficient (j>a, which is calculated as though the substance 2 were not dissociated (e = 0) or a coefficient cf)a by assuming complete dissociation (e = 1). These are related by the equations... 

Goldberg. R. N. 1979. Evaluated activity and osmotic coefficients for aqueous solutions Bi-univalent compounds of lead, copper, manganese and uranium. J. Phys. Chem. Ref Data ft(4) i005-50. 

G The ion interaction coefficient s(An, CP) for An = Am and Cm is assumed to equal to s(Nd , CP) which is calculated from trace activity coefficients of Nd ion in 0 to 4 m NaCl. These trace activity coefficients are based on the ion interaction Pitzer parameters evaluated in [97KON/FAN] from osmotic coefficients in aqueous NdCP-NaCl and NdCfr-CaCfr. 

Much deeper insights into the water sorption properties of polyelectrolytes can be provided by evaluating the (nNa)p term directly. By the use of the activity coefficient of Na+ ions in the PA A polyelectrolyte phase, (yNa)p, (aNa)p can be expressed as (aNa)p = (yNa)P [Na]p. Two concentration terms, i.e., (1) Na+ ions present in the polyelectrolyte phase to neutralize free car-boxylate groups and (2) Na+ ions imbibed in the polyelectrolyte phase in the form of NaCl, contribute the [Na]p term. Escape of Na+ ions from the polyelectrolyte phase due to their thermal motion, which produces a site vacancy of the polyion, should also be taken into consideration. The fraction of site vacancy of polyelectrolytes is available as a practical osmotic coefficient, c/>p-Na, which can simply be related to the linear charge separation of the PAA polyion. It has been revealed that PiNa is not affected by the change in the polyion concentration nor Cs, which is known as an additivity rule [16,17]. Thus the (aNa)p term can finally be expressed as... 

Several sources exist [72-74] containing evaluated data for the activity and/or osmotic coefficients of single electrolytes in water at 25°C. Data at other temperatures, or for mixed salts, are more scarce, but some compilations and databases exist [13, 74-76]. 

The properties selected for evaluation include most of the thermodynamic properties which we normally evaluate in the course of our work in the data centers. They include enthalpies of formation, solution, and dilution Gibbs energies of formation and solution entropies of formation and solution heat capacities and equilibrium constants (solubility, ionization, etc) as well as activity and osmotic coefficients, relative apparent molal enthalpies and apparent molal heat capacities. 

For the uni-univalent compounds, and the unsymmetrical charge types, uni-bi and bi-univalent compounds the activity and osmotic coefficients have been calculated from the Hamer-Wu, Lietzke-Stoughton equations used in previous evaluations (8,9). 

The principal interests in this study are osmotic and activity coefficients of NaCl(ac ) and KCl(aq) solutions at temperatures to 350°C and up to saturation concentration. In the range 25-300 C and at 1 bar or saturation pressure, NaCl(aq) osmotic coefficients up to 4 m were taken from a comprehensive thermodynamic treatment of Pitzer et al. (9). Above 4 m, the values were taken from Liu and Lindsay (39). At temperatures above 300°C, osmotic coefficients were calculated from vapor pressure data of Wood et al. (4. Additional vapor pressure data are given in Refs. 41-47, but a critical evaluation of these data indicated that these are less precise measurements and were therefore given smaller weights in the regression. For KCl(aq), osmotic coefficients to 6 m at temperatures from 25-325 C at 1 bar or saturation pressure were taken from the ion interaction model of Pabalan and Pitzer (9). Additional values up to 350 C and saturation concentration were derived from Refs. 40,41, and 48. 

The parameters for NaCl(acO and KCl(aq) evaluated from the osmotic coefficients are given in Table III. These parameters, together with those of Table II, permit the calculation of osmotic and activity coefficients of NaCl and KCl solutions to saturation concentration at pressures to 1 kb from 25-300 C, and at pressures to 200 bars above 300 C. 

Table III. Parameters for Equation 20 for Wj and Uj for NaCl and KCl Solutions Evaluated from Osmotic Coefficients up to 350 C at a Reference Pressure of 200 Bars...

Several approaches exist for evaluating activity coefficients. For non-aqueous systems the most common method has been from electrochemical cells, (sects. 2.5-2.7). Of the remaining approaches available, the freezing point technique is most commonly employed and is considered in sects. 2.8-2.10. This gives osmotic coefficients and activity... 

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