Properties, partial molal

Shock EL, Sassani DC, Betz H (1997) Uranium in geologic fluids estimates of standard partial molal properties, oxidation potentials and hydrolysis constants at high temperatures and pressures. Geochim Cosmochim Acta 61 4245-4266... 

Calcium-sodium-chloride-type brines (which typically occur in deep-well-injection zones) require sophisticated electrolyte models to calculate their thermodynamic properties. Many parameters for characterizing the partial molal properties of the dissolved constituents in such brines have not been determined. (Molality is a measure of the relative number of solute and solvent particles in a solution and is expressed as the number of gram-molecular weights of solute in 1000 g of solvent.) Precise modeling is limited to relatively low salinities (where many parameters are unnecessary) or to chemically simple systems operating near 25°C. 

Helgeson, H. C. and D. H. Kirkham, 1974, Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures, II. Debye-Hiickel parameters for activity coefficients and relative partial molal properties. American Journal of Science 274, 1199-1261. 

The pressure-volume-temperature (PVT) properties of aqueous electrolyte and mixed electrolyte solutions are frequently needed to make practical engineering calculations. For example precise PVT properties of natural waters like seawater are required to determine the vertical stability, the circulation, and the mixing of waters in the oceans. Besides the practical interest, the PVT properties of aqueous electrolyte solutions can also yield information on the structure of solutions and the ionic interactions that occur in solution. The derived partial molal volumes of electrolytes yield information on ion-water and ion-ion interactions (1,2 ). The effect of pressure on chemical equilibria can also be derived from partial molal volume data (3). 

Absolute properties are distinguished from conventional properties i.e., a generic standard partial molal property of an aqueous ion j (H°) is related to the absolute property by... 

Because the conventional standard partial molal properties of a hydrogen ion is zero, it follows that the conventional standard partial molal properties of a generic anion A are identical to the experimental values of the corresponding acid electrolyte. Moreover, based on equation 8.104, the standard partial molal properties of a generic cation C can be calculated, once the experimental values for aqueous electrolytes H +A and are... 

Each partial molal property of a yth aqueous ion in solution is considered to be composed of two terms the intrinsic property of the solute (3 j) and an electroconstriction contribution (AH° f) ... 

The partial molal property of the solute is thus composed of one ) plus one solvation ) term i.e., for a generic ion j, nonsolvation term... 

The standard partial molal properties of neutral organic aqueous molecules behave similarly to their inorganic counterparts (i.e., at pressures corresponding to liquid-vapor equilibrium, with increasing T they reach a minimum at intermediate T values and then approach +00 as P approaches the critical point of H2O see figure 8.27B). 

Figure 8.28 Correlation of standard partial molal properties of aqueous -polymers with the number of moles of carbon atoms in the alkyl chain. Reprinted from E. L. Shock and H. C. Helgeson, Geochimica et Cosmochimica Acta, 54, 915-946, copyright 1990, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

The linearity in the standard partial molal properties of the aqueous polymers as a function of the length of the chain (in terms of C atoms) observed by Shock and Helgeson (1990) is the result of the principle of equal reactivity of cocondensing functional groups (which, as we have already seen in section 6.1.2, also holds for silica polymers). This principle is, however, strictly valid only when the length of the chain is sufficiently elevated and small departures are observed for chains with one or two carbon atoms (cf figure 8.28). 

Table 8.21 Correlation parameters between the standard partial molal properties of aqueous -polymers and nnmber of moles of carbon in the alkyl chain (T = 25 °C, P = I bar Shock and Helgeson, 1990). See section 8.11 and tables 8.11, 8.12, and 8.13 for identihcation of symbols and nnits.

Table 8.22 Partial molal thermodynamic properties of organic aqueous species at 25 HKF model, after Shock and Helgeson (1990). 

Discrete values of the HKF model parameters for various organic aqueous species are listed in table 8.22. Table 8.23 lists standard partial molal thermodynamic properties and HKF model parameters for aqueous metal complexes of monovalent organic acid ligands, after Shock and Koretsky (1995). 

Table 9.14 Standard partial molal properties and coefficients of HKF model for neutral molecules in aqueous solution. and in cal/mole Sp p in cal/(mole X K)) Vp p in cm /mole... 

In table 9.14, for the sake of completion, we list the thermodynamic parameters of the HKF model concerning neutral molecules in solution (Shock et al., 1989). Calculation of partial molal properties of solutes (see section 8.11), combined with calculation of thermodynamic properties in gaseous phases (Table 9.5), allows rigorous estimates of the various equilibrium constants at all P and T of interest. 

Shock E. L. and Helgeson H. C. (1990). Calculations of the thermodynamic and transport properties of aqueous species at high pressures and temperatures Standard partial molal properties of organic species. Geochim. Cosmochim. Acta, 54 915-946. 

Shock E. L. and Koretsky C. M. (1995). Metal-organic complexes in geochemical processes Estimation of standard partial molal thermodynamic properties of aqueous complexes between metal cations and monovalent organic acid ligands at high pressures and temperatures. Geochim. Cosmochim. Acta, 59 1497-1532. 

In 1954, Mullins, in a modification to the Overton hypothesis, proposed that besides the membrane concentration of the anesthetic, its volume, expressed as its volume fraction (mole fraction X partial molal volume), is important. This reasoning implied that the anesthetic, due to its solubility properties, expands the cell membrane, and that anesthesia occurs when a critical expansion value is reached, at about 0.3-0.5% of the original volume. 

Strictly speaking, eqn (1.12) is correct at constant temperature and pressure. Because the partial molal volume is defined as having an additive property. 

Equation (1.16) is one example of the Gibbs-Duhem equation, which is one of the most useful formulae in thermodynamics. Thus, the partial molal quantity defined as the quantity satisfying the additive property is easily understandable. 

In several previous papers, the possible existence of thermal anomalies was suggested on the basis of such properties as the density of water, specific heat, viscosity, dielectric constant, transverse proton spin relaxation time, index of refraction, infrared absorption, and others. Furthermore, based on other published data, we have suggested the existence of kinks in the properties of many aqueous solutions of both electrolytes and nonelectrolytes. Thus, solubility anomalies have been demonstrated repeatedly as have anomalies in such diverse properties as partial molal volumes of the alkali halides, in specific optical rotation for a number of reducing sugars, and in some kinetic data. Anomalies have also been demonstrated in a surface and interfacial properties of aqueous systems ranging from the surface tension of pure water to interfacial tensions (such as between n-hexane or n-decane and water) and in the surface tension and surface potentials of aqueous solutions. Further, anomalies have been observed in solid-water interface properties, such as the zeta potential and other interfacial parameters. 

Monnin C (1989) An ion interaction model for the volumetric properties of natural waters density of the solution and partial molal volumes of electrolytes to high concentrations at 25 °C. Geochim Cosmochim Acta 53 1177-1188... 

Probably the most significant comparisons which can be made are of values of properties determined from calorimetric measurements with values calculated from adsorption isotherms. Two general methods are available for the comparison of values of enthalpies determined from experiments of the two types. One involves two differentiations The change in the partial molal enthalpy, AH2, of X2, for Process 4, is determined from the differentiation with respect to n2/n1 of the integral heat of adsorption measured in a series of calorimetric experiments of the type represented by Equation 1. The values of the differential heats of adsorption (heats corresponding to the differential Process 4) are compared with values determined from the temperature variation of AG2/T for a series of values of n2/n in Process 4. This type of comparison has been made successfully by several groups of authors (3, 5, 10). 

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