PARTIAL AND APPARENT MOLAR PROPERTIES

Figure 6.1 illustrates the concept of the apparent molar volume. AB is the portion of the total volume AC for n2 moles of solute that is attributed to the pure solvent. Then, the volume BC is apparently due to the solute. The slope of the line passing through point C and V is the apparent molar volume. The slope of the curve of the total volume at point C is the partial molar volume of component 2. Indeed, the slope of the total volume curve at any point is the partial molar volume of component 2 at that concentration. It is obvious that partial molar properties and apparent molar properties are both functions of concentration. 

In order to indicate the fact that the value of G as given by equation (42.1) applies to the constituent 2, i.e., the solute, a subscript 2 is sometimes included. However, this is usually omitted, for in the great majority of cases it is understood that the apparent molar property refers to the solute. It i.s seen from equation (42.1) that o is the apparent contribution of 1 mole of the component 2 to the property G of the mixture. If the particular property were strictly additive for the two components, e.g., volume and heat content for ideal gas and liquid solutions, the value of 4>q would be equal to the actual molar contribution, and hence also to the partial molar value. For nonideal systems, however, the quantities are all different. 

Relative Partial Molar and Apparent Relative Partial Molar Thermal Properties... 

The apparent partial molar quantities are often used in electrolyte solutions, and, in fact, are usually preferred over the partial molar properties by thermodynamicists who specialize in the treatment of electrolyte solutions. 

Because in the west of China some salt lake brines contain abundant boron and lithium, in which solute-solvent and solute-solute interactions are complex, studies on the ihermochemical properties for the systems related with the brines are essential to understand the effects of temperature on excess free energies and solubility, and to build a thermodynamic model that can be applied for prediction of the properties. Yin et al. [43] measured the enthalpies of dilution for aqueous Li2B407 solutions from 0.0212 to 2.1530 mol/kg at 298.15 K. The relative apparent molar enthalpies and relative partial molar enthalpies of the solvent and solute were also calculated, and the thermodynamic properties of the complex aqueous solutions were represented by a modified Pitzer ion-interaction model. 

The properties of a dissolved substance are described in terms of partial, apparent, and excess total or molar properties, so we begin by discussing these terms, using volume as an example. 

And, as with the other partial molar properties (except fi), it is convenient to use apparent properties, so from Equation (10.9),... 

ELDAR contains data for more than 2000 electrolytes in more than 750 different solvents with a total of 56,000 chemical systems, 15,000 hterature references, 45,730 data tables, and 595,000 data points. ELDAR contains data on physical properties such as densities, dielectric coefficients, thermal expansion, compressibihty, p-V-T data, state diagrams and critical data. The thermodynamic properties include solvation and dilution heats, phase transition values (enthalpies, entropies and Gibbs free energies), phase equilibrium data, solubilities, vapor pressures, solvation data, standard and reference values, activities and activity coefficients, excess values, osmotic coefficients, specific heats, partial molar values and apparent partial molar values. Transport properties such as electrical conductivities, transference numbers, single ion conductivities, viscosities, thermal conductivities, and diffusion coefficients are also included. 

Gibbs functions for a real salt solution and the corresponding ideal salt solution containing m2 moles of salt in a kilogram of solvent. GE can be calculated for many aqueous salt solutions from published values of 0 and y . In the same way, the corresponding excess enthalpy HE can be defined and this equals the apparent partial molar enthalpy. Thus the properties of salt solutions can be examined in plots of GE, HE, and T SE against m2, where SE is the... 

Quite striking extrema are observed in the dependence of apparent partial molar heat capacities on salt concentration for alkylammonium salts and related compounds, e.g. Bu4N+ octanoate, and these can be understood in terms of long-range hydrophobic interactions (Leduc and Desnoyers, 1973). However, the properties of n-alkylamine hydrobromides have indicated that there are still... 

The composition dependence of the total volume of a solution at constant temperature and pressure is expressed in terms of the partial molar volumes of the solute and the solvent. Since we are concerned with solvation properties, the quantities which we need to discuss are the partial molar volumes in infinite dilution of the solute so that solute-solute interactions make no contribution. In practice, partial molar volumes are obtained indirectly from precise density measurements. The partial molar volumes at infinite dilution of the amino acids are compiled in Table 2 [7]. It is apparent from these data that an approximately linear correlation exists between the partial molar volume and the number of carbon atoms in the backbone. The data indicate volume contributions from the polar head group (NH, COj) and from the CH2 group and to be about... 

The drawbacks of a simplified relative fo approach become apparent in the case of the relative volumetric properties of EeO and Ec203 in sihcate melts even at relatively low pressures (Kress and Carmichael, 1991). There are two problems first, the pressure dependence of EeO-Ec203 equilibria is different from the pressure dependence of the nickel-nickel oxide (NNO) buffer such that use of NNO as a normalization for relative/oj can be misleading. The volume change of the FMQ buffer (0.17 log/o units per GPa) is much closer to the redox state of a silicate melt than is that of the NNO buffer (0.51 log/o units per GPa). Second, the compressibilities of FeO and Fe203 are much different, so that even pressures of 1-2 GPa will have a large effect on their partial molar volumes. Any calculation of relative /o should include an assessment of the volumetric properties of both the buffer phases, and the phases involved in the redox reaction. 

A single homogeneous phase such as an aqueous salt (say NaCl) solution has a large number of properties, such as temperature, density, NaCl molality, refractive index, heat capacity, absorption spectra, vapor pressure, conductivity, partial molar entropy of water, partial molar enthalpy of NaCl, ionization constant, osmotic coefficient, ionic strength, and so on. We know however that these properties are not all independent of one another. Most chemists know instinctively that a solution of NaCl in water will have all its properties fixed if temperature, pressure, and salt concentration are fixed. In other words, there are apparently three independent variables for this two-component system, or three variables which must be fixed before all variables are fixed. Furthermore, there seems to be no fundamental reason for singling out temperature, pressure, and salt concentration from the dozens of properties available, it s just more convenient any three would do. In saying this we have made the usual assumption that properties means intensive variables, or that the size of the system is irrelevant. If extensive variables are included, one extra variable is needed to fix all variables. This could be the system volume, or any other extensive parameter. 

The ratio of properties in Equation 9.24 is called the Krichevskii function, and identified at the solvent critical point as the Krichevskii parameter (Levelt Sengers 1991). The first EST correlation for partial molar volumes of gases in liquids was done by Brelvi (Brelvi and O Connell 1975c), using characteristic properties for his correlation of the reduced bulk modulus (Brelvi and O Connell 1972). Recent work (Ellegaard, Abildskov, and O Connell 2011) has used the form of Equation 9.4 for partial molar volumes of gases in ILs. The comparisons with data for these systems seem not to be as successful as for their compressibilities and phase equilibria, for reasons that are not apparent. 

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. 

Fig. 5a - c. Molecular properties of bovine serum albumin as a function of the molar concentration, C3, of the denaturant guanidinium chloride (from [83D1]). a apparent isopotential specific volume (in cm g ) b extinction coefficient c intrinsic viscosity (in cm g ). For experimental details see the original reference. Reprinted from International Journal of Biological Macromolecules, Vol. 5, H. Durchschlag and R. Jaenicke, Partial specific volume changes of proteins ultracentrifugal and viscometric studies, pp. 143-148, 1983, with permission from Elsevier Science. 

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