Thermodynamic properties osmotic coefficient

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

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. 

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. 

Solutions are usually classified as nonelectrolyte or electrolyte depending upon whether one or more of the components dissociates in the mixture. The two types of solutions are often treated differently. In electrolyte solutions properties like the activity coefficients and the osmotic coefficients are emphasized, with the dilute solution standard state chosen for the solute.c With nonelectrolyte solutions we often choose a Raoult s law standard state for both components, and we are more interested in the changes in the thermodynamic properties with mixing, AmjxZ. In this chapter, we will restrict our discussion to nonelectrolyte mixtures and use the change AmjxZ to help us understand the nature of the interactions that are occurring in the mixture. In the next chapter, we will describe the properties of electrolyte solutions. 

In order to discuss thermodynamic properties in dilute aqueous solutions at temperatures other than 298.15 K, it is necessary to have the standard enthalpies of the species involved. Over narrow ranges of temperature, calculations can be based on the assumption that Af// values are independent of temperature, but more accurate calculations can be made when Cpm(i) values are known. It is also necessary to take into account the temperature dependencies of the numerical coefficients in equations 3.6-4 to 3.6-6. Clarke and Glew (1980) calculated the Debye-Hiickel slopes for water between 0 and 150°C. They were primarily concerned with electrostatic deviations from ideality of the solvent osmotic... 

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water—protein—cosolvent mixtures is developed. The Kirkwood—Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water—protein—cosolvent mixtures. These properties can be divided into two groups (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water—cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions (1) one due to the protein—solvent interactions which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B p ), and (3) a third one representing an ideal mixture contribution The cosolvent composition dependencies of these three contributions... 

Rard, J. A., and Archer, D. G., 1995, Isopiestic investigation of the osmotic and activity coefficients of aqueous NaBr and the solubility ofNaBr.2H20(cr) at 298.15 K. Thermodynamic properties of the NaBr+H20 system over wide ranges of temperature and pressure Journal of Chemical and Engineering Data, v. 40, p. 170-185. 

In this chapter some aspects of the present state of the concept of ion association in the theory of electrolyte solutions will be reviewed. For simplification our consideration will be restricted to a symmetrical electrolyte. It will be demonstrated that the concept of ion association is useful not only to describe such properties as osmotic and activity coefficients, electroconductivity and dielectric constant of nonaqueous electrolyte solutions, which traditionally are explained using the ion association ideas, but also for the treatment of electrolyte contributions to the intramolecular electron transfer in weakly polar solvents [21, 22] and for the interpretation of specific anomalous properties of electrical double layer in low temperature region [23, 24], The majority of these properties can be described within the McMillan-Mayer or ion approach when the solvent is considered as a dielectric continuum and only ions are treated explicitly. However, the description of dielectric properties also requires the solvent molecules being explicitly taken into account which can be done at the Born-Oppenheimer or ion-molecular approach. This approach also leads to the correct description of different solvation effects. We should also note that effects of ion association require a different treatment of the thermodynamic and electrical properties. For the thermodynamic properties such as the osmotic and activity coefficients or the adsorption coefficient of electrical double layer, the ion pairs give a direct contribution and these properties are described correctly in the framework of AMSA theory. Since the ion pairs have no free electric charges, they give polarization effects only for such electrical properties as electroconductivity, dielectric constant or capacitance of electrical double layer. Hence, to describe the electrical properties, it is more convenient to modify MSA-MAL approach by including the ion pairs as new polar entities. 

In the AMSA the thermodynamic properties contain three different contributions the hard-sphere (HS) contribution, the contribution from the mass action law (MAL) and the contribution from electrostatic ion-ion interaction (EL) [6,13,14], For example, the osmotic coefficient, = p/(pikT), can be represented in the form,... 

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. 

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. 

On the basis of the above result, it is suggested that the osmotic pressure approach may be as useful for the estimate of thermodynamic properties of simple electrolyte mixtures in mixed solvents as in aqueous media. Additional research with alkali chlorides in alcohol-water mixtures is in progress to substantiate this conclusion. The mean molal coefficient data that are published for the alkali chlorides (12) are expected to facilitate a meaningful prognosis of the osmotic pressure model. 

As pointed out earlier, the contributions of the hard cores to the thermodynamic properties of the solution at high concentrations are not negligible. Using the CS equation of state, the osmotic coefficient of an uncharged hard sphere solute (in a continuum solvent) is given by... 

The thermodynamic properties calculated by different routes are different, since the MS solution is an approximation. The osmotic coefficient from the virial pressure, compressibility and energy equations are not the same. Of these, the energy equation is the most accurate by comparison with computer simulations of Card and Valleau [ ]. The osmotic coefficients from the virial and compressibility equations are... 

Friedman s model fits the thermodynamic excess functions (osmotic coefficient, excess volume, and excess energy) of aqueous solutions of alkali and earth alkaline halides up to l-M ionic strength and of tetraalkylammo-nium halides up to 0.4 M. The variation of the A/y parameters with the ionic parameters is chemically meaningful and permits the estimation of thermodynamic properties of unknown systems by the combination of the parameters known from appropriate other systems. 

Electrostatic interactions give a large deviation from ideality in equilibrium properties of solutions containing low molecular weight electrolytes. This deviation was most successfully disposed of by the Debye-Huckel theory [2]. According to this theory, the ionic species are not distributed in solution in a random manner, but form an ionic atmosphere structure, and the thermodynamic properties such as the activity coefficient of solvent (or the osmotic coefficient), the mean activity coefficient of solute, and the heat of dilution, decrease linearly with the square root of the concentration, in conformity with experimental observations. 

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... 

This 268 page article is concerned with the prediction of the thermodynamic properties of aqueous electrolyte solutions at high temperatures and pressures. There is an extensive discussion of the fundamental thermodynamics of. solutions and a discussion of theoretical concepts and models which have been used to describe electrolyte solutions. There is a very extensive bibliography ( 600 citations) which contains valuable references to specific systems of interest. Some specific tables of interest to this bibliography contain Debye-Hiickel parameters at 25 C, standard state partial molar entropies and heat capacities at 25 °C, and parameters for calculating activity coefficients, osmotic coefficients, relative apparent and partial molar enthalpies, heat capacities, and volumes at 25 °C. 

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