Aqueous solutions thermodynamic functions, molar

One of the main conceptual differences between the models discussed so far and aqueous solutions is that the units which are used to define thermodynamic functions are often different. This is because they apply to the properties which are actually measured for aqueous systems, and molarity (cj) and molality (m,) are far more common units than mole fraction. Molarity is defined as... 

Fig. 4 Molar fraction distribution as a function of pH, in aqueous solution at 25 °C, for the 4 -methoxyflavylium compound. Solid lines refer to the species obtained at the thermodynamic equilibrium. Dashed lines refer to species obtained by bringing...

The two primary reference works on inorganic thermochemistry in aqueous solution are the National Bureau of Standards tables (323) and Bard, Parsons, and Jordan s revision (30) (referred to herein as Standard Potentials) of Latimer s Oxidation Potentials (195). These two works have rather little to say about free radicals. Most inorganic free radicals are transient species in aqueous solution. Assignment of thermodynamic properties to these species requires, nevertheless, that they have sufficient lifetimes to be vibrationally at equilibrium with the solvent. Such equilibration occurs rapidly enough that, on the time scale at which these species are usually observed (nanoseconds to milliseconds), it is appropriate to discuss their thermodynamics. The field is still in its infancy of the various thermodynamic parameters, experiments have primarily yielded free energies and reduction potentials. Enthalpies, entropies, molar volumes, and their derivative functions are available if at all in only a very small subset. 

FIGURE 8.11 Behavior of A 2,ex(SR) and p" (Ci2 - C°j) for an infinitely dilute CsBr aqueous solution as a function of the solvent density along three supercritical isotherms in comparison with experimental data. (Data from J. Sedlbauer, E. M. Yezdimer, and R. H. Wood, 1998, Partial Molar Volumes at Infinite Dilution in Aqueous Solutions of NaCl, LiCl, NaBr, and CsBr at Temperatures from 550 K to 725 K, Journal of Chemical Thermodynamics, 30, 3.) Vertical arrow indicates the estimated critical density of the model solvent... 

FIGURE 9.7 Experimental (symbols) and fitted (lines) results for Henry s constants (H21) for Hydrogen sulfide (2) in water (1) from Equation 9.37 through Equation 9.41. (Reprinted with permission from A. Plyasunov, J. P. O Connell, R. H. Wood, and E. L. Shock, 2000, Infinite Dilution Partial Molar Properties of Aqueous Solutions of Nonelectrolytes. II. Equations for the Standard Thermodynamic Functions of Hydration of Volatile Nonelectrolytes over Wide Ranges of Conditions Including Subcritical Temperatures, Geochimica Et Cosmochimica Acta, 64, 2779, With permission from Elsevier.)... 

Plyasunov, A. V., J. P. O Connell, and R. H. Wood. 2000. Infinite dilution partial molar properties of aqueous solutions of nonelectrolytes. I. Equations for partial molar volumes at infinite dilution and standard thermodynamic functions of hydration of volatile nonelectrolytes over wide ranges of conditions. Geochimica et Cosmochimica Acta. 64,495. 

Table III The molar values of the thermodynamic functions of inclusion in aqueous solutions at 298.15 K...

In order to calculate the equOibrium composition of a system consisting of one or more phases in equilibrium with an aqueous solution of electrolytes, a review of the basic thermodynamic functions and the conditions of equilibrium is important, This is particularly true inasmuch as the study of aqueous solutions requires consideration of chemical and/or ionic reactions in the aqueous phase as well as a thermodynamic framework which is, for the most part, quite different from those definitions associated with nonelectrolytes. Therefore, in this section we will review the definition of the basic thermodynamic functions, the partial molar quantities, chemical potentials, conditions of equilibrium, activities, activity coefficients, standard states, and composition scales encountered in describing aqueous solutions. 

It shows experimental values of the molar conductance of NaCl in aqueous solutions at the supercritical temperatures of 400 and 500 C as a function of the mole fraction of the salt (22). Measurements could not be made beyond x = 0.1. The molar conductance of the fused salt has been determined, however. It is not very temperature dependent, so that an extrapolation of the conductance to an assumed supercooled liquid at 400 C or 500 C seems to be possible. These values are shown in Fig. 15. It is clear that solutions with salt mole fractions of x = 0.2 and higher have properties closer to the pure fused salt than to the dilute solutions as far as the conductance is concerned. A large fraction of the ions is already in some way associated which must influence the thermodynamic functions accordingly. 

In this review isentropic compressibility data have been compiled for aqueous solutions of the amino acids, including all those found in proteins, of various peptides of low molar mass, and of many proteins. For both the small molecule and protein systems, it is clear that this thermodynamic property is a particularly sensitive measure of hydration effects in aqueous solution. For the small solutes attempts have been made to rationalize the compressibility data in terms of the interactions that occur between the various functional groups and solvent water. For proteins it has been shown that the compressibilities are not correlated with any one structural characteristic. Various characteristics such as amino acid composition, hydrophobicity and the degree of secondary structure all influence, to some degree, the compressibility of a protein. Compressibility measurements on protein solutions also provide an important means to determine the volume fluctuation of a protein. We believe that compressibility measurements on aqueous solutions of these biologically important molecules provide a very powerful means of probing and characterizing solute -water interactions in these systems. 

Another method suggested by the authors for predicting the solubility of gases and large molecules such as the proteins, drugs and other biomolecules in a mixed solvent is based on the Kirkwood-Buff theory of solutions [18]. This theory connects the macroscopic properties of solutions, such as the isothermal compressibility, the derivatives of the chemical potentials with respect to the concentration and the partial molar volumes to their microscopic characteristics in the form of spatial integrals involving the radial distribution function. This theory allowed one to extract some microscopic characteristics of mixtures from measurable thermodynamic quantities. The present authors employed the Kirkwood-Buff theory of solution to obtain expressions for the derivatives of the activity coefficients in ternary [19] and multicomponent [20] mixtures with respect to the mole fractions. These expressions for the derivatives of the activity coefficients were used to predict the solubilities of various solutes in aqueous mixed solvents, namely ... 

The approach to the thermodynamics of solubilization in micellar solutions is based on the determination of a given partial molar property of the solute (volume, enthalpy, heat capacity, compressibility) as a function of the surfactant content. The simplest approach is to use the pseudophase model. The partial molar quantity, L will thus be an average value of Y in the micellar and aqueous phases, as described by... 

A striking feature of the partial molar volumes and heat capacities of aqueous electrolytes is their inverted-U shape as a function of temperature. Experimental data that cover a sufficiently large range of temperature invariably exhibit a maximum, generally somewhere between 50 and 100 °C. This was illustrated in Figures 10.6 and 10.12, which show data for the partial molar volume and heat capacity of NaCl. The existence of singular temperatures for water at -45 "C (228 K, Angell, 1982, 1983) and 374 °C (the critical temperature) makes it seem entirely reasonable that thermodynamic parameters of solutes in water should approach oo at these limits, and therefore reasonable that they should exhibit extrema (or inflection points) between these temperatures. ... 

The tables in this chapter include Debye-HUckel parameters for the osmotic coefficient, enthalpy, and heat capacity as a function of temperature parameters for the activity and osmotic coefficients of approximately 270 aqueous strong electrolytes at 25 C parameters for the relative apparent molar and excess enthalpy of %90 strong electrolytes at 25 C a table of parameters for the activity and osmotic coefficients ofss75 binary mixtures with and without common ions and with up to three solutes present and parameters for the thermodynamic properties of aqueous NaCI and H2SO4 as a function of temperature. The author has included references to his earlier papers ivhich also contain valuable data on electrolyte solutions (also see item [121]). 

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