Molal osmotic coefficient, calculation

Helgeson, H. C., D. H. Kirkham and G. C. Flowers, 1981, Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high temperatures and pressures, IV. Calculation of activity coefficients, osmotic coefficients, and apparent molal and standard and relative partial molal properties to 600 °C and 5 kB. American Journal of Science 281, 1249-1516. 

Osmolality is calculated as molality (2.0molkg ) multiplied by the number of solute particles (n), in this case 2 (one from Na and one from Cl), multiplied by the osmotic coefficient (0 0.983), which equals 3.932 osmolkg . ... 

The Osmotic Coefficient.—Instead of calculating activity coefficients from freezing-point and other so-called osmotic measurements, the data may be used directly to test the validity of the Debye-Hiickel treatment. If 6 is the depression of the freezing point of a solution of molality m of an electrolyte which dissociates into v ions, and X is the molal freezing-point depression, viz., 1.858° for water, a quantity , called the osmotic coefficient, may be defined by the expression... 

As the osmotic coefficient < r for the reference substance at the molality mn is known, the value of at the isopiestic molality m of the experimental electrolyte can be determined by means of equation (39.55). If the results are obtained for a series of concentrations of the latter, the activity coefficient at any molality can then be calculated from equation (39.54), as described above. ... 

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]. 

Search the DDE (free Explorer Version) for osmotic coefficients for the system water-sodium chloride. From the data at 333 K, calculate the activity coefficient of the solvent water as function of the molality of the salt. 

Using their experimentally determined isopiestic molalities, Mesmer et al. calculated the osmotic coefficients. with the following relation ... 

Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures IV. Calculation of Activity Coefficients, Osmotic Coefficients, and Apparent Molal and Standard Relative Partial Molal Properties to 600 °C and 5 kb... 

Rard and Miller used published measurements of the freezing points of dilute aqueous solutions of Na2S04 to calculate the osmotic coefficients of these solutions at 298.15 K. Use their values listed in Table 10.2 to evaluate the mean ionic activity coefficient of Na2S04 at 298.15 K and a molality of wb = 0.15molkg For the parameter a in the Debye-Hiickel equation (Eq. 10.4.7), use the value a = 3.0 x 10 ° m. 

Figure 5.1 LR experimental and calculated osmotic coefficients for LiCl (0)> LiBr (+), and LiNOj ( ), as a function of the salt molality.

In principle the activity coefficients yb of solute substances B in a solution can be directly determined from the results of measurements at ven temperature of the pressure and the compositions of the liquid (or solid) solution and of the coexisting gas phase. In practice, this method fails unless the solutes have volatilities comparable with that of the solvent. The method therefore usually fails for electrolyte solutions, for which measurements of ye in practice, much more important than for nonelectrolyte solutions. Three practical methods are available. If the osmotic coefficient of the solvent has been measured over a sufficient range of molalities, the activity coefficients /b can be calculated the method is outlined below under the sub-heading Solvent. The ratio yj/ys of the activity coefficients of a solute B in two solutions, each saturated with respect to solid B in the same solvent but with different molalities of other solutes, is equal to the ratio m lm of the molalities (solubilities expressed as molalities) of B in the saturated solutions. If a justifiable extrapolation to Ssms 0 can be made, then the separate ys s can be found. The method is especially useful when B is a sparingly soluble salt and the solubility is measured in the presence of varying molalities of other more soluble salts. Finally, the activity coefficient of an electrolyte can sometimes be obtained from e.m.f. measurements on galvanic cells. The measurement of activity coefficients and analysis of the results both for solutions of a single electrolyte and for solutions of two or more electrolytes will be dealt with in a subsequent volume. Unfortunately, few activity coefficients have been measured in the usually multi-solute solutions relevant to chemical reactions in solution. 

Predictions from the model for the osmotic coefficient can be made when the binary parameter between nmidissociated repeating units and the counterion of the low molecular weight salt, as well as the influence of that salt on the configurational parameter b are neglected. Figure 16 shows comparisons between experimental data and calculation results for the osmotic coefficient for aqueous solutions of a sodium poly(acrylate) (NaPA 15) and NaCl. The osmotic coefficient (on molality scale) is plotted versus the overall solute molality m, that is defined as ... 

The Margules expansion model has been tested on some ionic systems over very wide ranges of composition, but over limited ranges of temperature and pressure (33,34). In this study, the model is applied over a wider range of temperature and pressure, from 25-350 C and from 1 bar or saturation pressure to 1 kb. NaCl and KCl are major solute components in natural fluids and there are abundant experimental data from which their fit parameters can be evaluated. Models based on the ion-interaction ajiproach are available for NaCl(aq) and KCl(aq) (8,9), but these are accurate only to about 6 molal. Solubilities of NaCl and KCl in water, however, reach 12 and 20 m, respectively, at 350 C, and ionic strengths of NaCl-KCl-H20 solutions reach more than 30 m at this temperature (35). The objective of this study is to describe the thermodynamic properties, particularly the osmotic and activity coefficients, of NaCl(aq) and KCl(aq) to their respective saturation concentrations in binary salt-H20 mixtures and in ternary NaCl-KCl-H20 systems, and to apply the Margules expansion model to solubility calculations to 350 C. 

The exact calculation equations are given in [25], where it has also been proved that the Gibbs-Duhem equation is fulfilled. As well, NRTL parameters have been fitted up to molalities of 30mol/kg for a number of systems. Together with the ionic diameters, they are listed in [25]. Osmotic and mean ionic activity coefficients could be reproduced in an excellent way for a number of systems. Furthermore, the parameters fitted to binary systems have been successfully applied to ternary systems, that is, one salt in a binary solvent mixture, which always causes problems with the Electrolyte NRTL model [25]. 

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