Thermodynamic parameters from osmotic data

CR2 Cramond, D.N. and Urwin, J.R., Solution properties of block copolymers of poly(isoprene-styrene) 11. Thermodynamic parameters from osmotic data, Eur. Polym. J., 5, 45, 1969. 

Whereas the positive enthalpies of association expected from observed heats of dilution data are qualitatively consistent with the hydrophobic interaction mechanism other thermodynamic parameters such as positive entropy and a negative heat capacity are more reliable characteristics. Furthermore, little is known of associations constants of amides, lactams and ureas in aqueous solution but they are thought to be small. For N-methyl acetamide the association constant is - 0.006 m" [17, 18] (calorimetric and spectroscopic) and for urea the association constant is 0.041 m as measured by heat of dilution data [16, 19], combination of heat of dilution and osmotic coefficient data [20] and temperature dependence of the non ideality of urea... 

Using the model parameters of Table II the calculated osmotic coefficient is within 0.15% or better for all solutions investigated. Agreement with the experimental results (17) is within 0.02% or better if ( ci.Br.K = 0.0003 (Table III) instead of zero (Table II). We may conclude from this comparison that the thermodynamic model of Pitzer (Table II) is very realistic. An uncertainty of 0.0003 in i(ic Br K leads to uncertainties of less than 0.4% in log K(x). The largest uncertainty in equilibrium constants may thus be attributed to the original analytical data (j3). 

The derivative equations for osmotic and activity coefficients, which are presented below, were applied to the experimental data for wide variety of pure aqueous electrolytes at 25°C by Pitzer and Mayorga (23) and to mixtures by Pitzer and Kim (11). Later work (24-28) considered special groups of solutes and cases where an association equilibrium was present (H PO and SO ). While there was no attempt in these papers to include all solutes for which experimental data exist, nearly 300 pure electrolytes and 70 mixed systems were considered and the resulting parameters reported. This represents the most extensive survey of aqueous electrolyte thermodynamics, although it was not as thorough in some respects as the earlier evaluation of Robinson and Stokes (3). In some cases where data from several sources are of comparable accuracy, a new critical evaluation was made, but in other cases the tables of Robinson and Stokes were accepted. 

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. 

Calculations of departures from ideality in ionic solutions using the MSA have been published in the past by a number of authors. Effective ionic radii have been determined for the calculation of osmotic coefficients for concentrated salts [13], in solutions up to 1 mol/L [14] and for the computation of activity coefficients in ionic mixtures [15]. In these studies, for a given salt, a unique hard sphere diameter was determined for the whole concentration range. Also, thermodynamic data were fitted with the use of one linearly density-dependent parameter (a hard core size o C)., or dielectric parameter e C)), up to 2 mol/L, by least-squares refinement [16]-[18], or quite recently with a non-linearly varying cation size [19] in very concentrated electrolytes. 

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