Molal properties

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. 

Helgeson, H. C. Kirkham D. H. and Flowers, G. C. Theoretical prediction of the thermod5mamic behavior of aqueous electrolytes at high pressure and temperatures IV. Calculation of activity coefficients, osmotic coefficients and apparent molal properties to 600°C and 5 kb, Am. J. Sci., 1981, 281, 1249-1516. 

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 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. 

If the quantity of adsorbent should be increased by the addition of more material in the same state of subdivision, we could measure changes in volume, in heat capacity, and in certain other extensive properties which can be directly observed. We could differentiate any one of these properties with respect to the number of moles of adsorbent (whether the system contains one, two, or more components) to obtain a partial molal property. The partial molal property so obtained would be the weighted average for interior and exterior adsorbent and is in harmony with Equations 9 and 11. 

Shock, E. L., Oelkers, E. H., Johnson, J. W., Sveijensky, D. A. Helgeson, H.C. (1992). Calculation of the thermodynamic behavior of aqueous species at high pressures and temperatures effective electrostatic radii, dissociation constants, and standard partial molal properties to 1000 °C and 5 kb. Journal of the Chemical Society (London) Faraday Transactions, 88, 803—26. 

Notice that partial molal properties of B are properly specified only when the partial derivatives are taken while holding only the intensive variables fixed thus one should note the difference between (1.25.10a) and (1.25.10b) with regard to the quantity labeled as B. 

The physical-chemical properties of natural waters are determined from the apparent molal properties () of the components of the mixture. The apparent molal property is related to the change that occurs when a salt is added to water. The apparent molal property is defined by... 

Tanger, j. C., IV, and H. C. Helgeson. 1988. Calculation of the thermodynamic and transpon properties of aqueous. species at high pressures and temperatures Revised equations of state for the standard partial molal properties of ions and electrolytes. Am. J. Set. 288 19-98. 

Since GE is a thermodynamic property which is additive with respect to RT In Yh it follows that RT In Yt may be considered as a partial molal property. 

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