Entropies of Aqueous Ions

Therefore, a consistent convention would set the standard entropy of aqueous ion... 

An empirical relationship has been proposed by Powell and Latimer US) for the partial molal entropies, of aqueous ions ... 

The hydration entropy for the ion A y8S°(M" ) represents the standard entropy change (usually at 298K) for the process M" (g)-> M" (aq). This property should reflect lanthanide-actinide differences because the final state represents the ion with all the water molecules in the primary and outer hydration spheres. Bratsch and Lagowski (1985b, table I) proposed a set of hydration parameters Ay and by which hydration entropies could be calculated for the lanthanides. Rizkalla and Choppin (1991, table 11) used these parameters to tabulate entropies of hydration for the lanthanides. However, it is not reasonable to extend these entropies for a lanthanide-actinide comparison because there are no experimental data from which independent actinide hydration entropy parameters Ay and can be calculated (see section 2.2.2 for experimental entropies of aqueous ions). 

Entropies of aqueous ions can be determined directly by measuring the enthalpy of solution of the metal to form the aquo ion and the free energy of solution of a salt of the ion. Upon correction to standard state, these data yield standard enthalpy and free energy of formation of the ion, from which its standard entropy... 

Standard-state entropies of aqueous ions are by convention referenced to S°(H (aq)) = 0. Alternatively, the temperature coefficient of the electromotive force of an equilibrium reaction involving the ion can be used to calculate the entropy of the reaction, and from the reaction entropy as well as necessary auxiliary data the entropy of formation of the ion can be calculated. Four actinide aquo-ion entropies (Th , Pu, UOj, and NpO ) have been determined by the former method. The other aquo-ion entropies of uranium, neptunium, and plutonium have been connected by the latter method. 

Heat capacities, as well as entropies, of aqueous ions are the fundamental thermodynamic properties that reflect their structure and hydration. Heat capacities are also necessary for calculation of other thermodynamic properties at... 

Criss, C.M. Cobble, J.W., "Thermodynamic Properties of High Temperature Aqueous Systems. IV Entropies of the Ions up to 200°C and the Correspondence Principles", JACS, 1964, 86,... 

J. W. Cobble, High-temperature aqueous solutions. Science, 152, 1479-1485 (1966) C. M. Criss and J. W. Cobble, The thermodynamic properties of high temperature aqueous solutions. IV. Entropies of the ions up to 200 °C and the correspondence principle. V. The calculation... 

Since the transition-state model for solution reactions is an equilibrium model, the true testing ground for solution theories will be not kinetic data but rather thermodynamic data. From this point of view, the continuum model of the solvent has had only fair success— for example, in correlating thermodynamic data for ions. Laidler has recently shown that the entropies of aqueous monatomic ions of molecular weight M with reference to = —5.5 e.u. may be repre.sented by the empirical... 

For estimation of thermodynamic properties of dissolved species, one can use the Entropy Correspondence Principle ( ), where the entropy of an ion at a given temperature is regarded as a function of the charge, the dielectric constant, mass, radius, and other variables. The function depends mainly upon the choice of the standard state, solvent, and temperature. The temperature dependency of entropy was derived based on the above principles and experimental data. By conducting the a square regression on Criss-Cobble s data ( ), we obtained the following eqtiation for calculating the entropies of species in aqueous solution. 

These relate to the process of transferring the ion from the gas phase to the aqueous phase. They can be calculated from the tabular data of partial molar entropies of the ion in solution and statistical mechanical calculations on the ion in the gas phase. 

Ionic entropies in all the non-aqueous solvents examined up to the present time can be expressed as a linear function of the entropies of the ions in water as ... 

In an extension of these ideas, Franks and Reid have examined the ionic entropies in mixed water-methanol solutions (see Appendix 2.4.42) and in 20 % aqueous dioxan, and have observed that the entropies of the ions for each of these systems can be expressed by an equation having the same form as eqn. 2.11.36. Similar to the pure solvent systems, the entropy of a given ion has no correlation with the solvent dielectric constant, nor is there a linear correlation of the entropy with solvent composition. Instead, the entropies reach a maximum in the vicinity of 40 mol per cent methanol. The authors explain this in terms of the solvent having the highest degree of structure near this composition. As in the pure non-aqueous solvents, the relative magnitude of the effect of ions on the solvent structure is the same for all ions, both negative and positive. This observation led the authors to conclude that there is no evidence for preferential solvation in these mixed solvent systems. 

Frank and Robinson (1940) suggested that the partial molar entropy of the water in aqueous electrolyte solutions is affected by the structure-making or -breaking properties of their ions. Frank and Evans (1945) suggested that rather the entropies of hydration of the ions shed light on these properties. Gurney (1953) showed that a linear relationship exists between the partial molar entropy of monatomic ions, and their viscosity coefficients (see Sect. 3.1.1). Nightingale (1959) reverted to the Frank and Evans emphasize of partial molar entropies of hydration of the... 

H2. Gardner, W.L. R.E. Mitchell, J.W. Cobble, "The thermodynamic properties of high-temperature aqueous solutions. X. The electrode potentials of sulfate ion electrodes from 0-100°. Activity coefficients and the entropy of aqueous sulfuric acid", J. Phys. Chem., v73, 6, pp2021-2024 (1969)... 

Cobble, J.W., "Empirical Considerations of Entropy III. A Structural Approach to the Entropies of Aqueous Organic Solutes and Complex Ions", J. Chem. Phys., v21, 9, ppl451-1456 (1953)... 

The standard molar entropies of aqueous electrolytes, 2°°, are preferably obtained from the temperature coefficients of the electromotive forces of galvanic cells. The absolute values for individual ions are based on 5°°(H", aq) = —22.2 1.4 J K moP at 298.15 K, from data for thermocells [1]. The S °° values increase with the masses of the ions but are small or negative for multi-charged ions. 

Table 2.1 Revised HKF parameters, entropy and effective radii of aqueous ions (Reproduced from Geochimica et Cosmochimica Acta, Calculation of the thermodynamic and transport properties of aqueous species at high pressures and temperatures with permission from Elsevier)...

Criss, C. M Cobble, J. W. (1964), The Thermod5mamic Properties of High Temperature Aqueous Solutions. IV. Entropies of the Ions up to 200° and the Correspondence Principle, Journal of die American Chemical Society, V0I.86, pp.5385-5393, ISSN 0002-7863... 

The properties of ions in solution depend, of course, on the solvent in which they are dissolved. Many properties of ions in water are described in Chapters 2 and 4, including thermodynamic, transport, and some other properties. The thermodynamic properties are mainly for 25°C and include the standard partial molar heat capacities and entropies (Table 2.8) and standard molar volumes, electrostriction volumes, expansibilities, and compressibilities (Table 2.9), the standard molar enthalpies and Gibbs energies of formation (Table 2.8) and of hydration (Table 4.1), the standard molar entropies of hydration (Table 4.1), and the molar surface tension inaements (Table 2.11). The transport properties of aqueous ions include the limiting molar conductivities and diffusion coefficients (Table 2.10) as well as the B-coefficients obtained from viscosities and NMR data (Table 2.10). Some other properties of... 

In Chapter 14 (Solutions and Their Physical Properties), we have added a section to describe the standard thermodynamic properties of aqueous ions. We use the concepts of entropy and chemical potential in Chapter 13 to explain vapor pressure lowering and why gasoline and water don t mix. 

Sodium Chlorite. The standard enthalpy, Gibbs free energy of formation, and standard entropy for aqueous chlorite ions ate AH° = —66.5 kJ/mol ( — 15.9 kcal/mol), AG = 17.2 kJ/mol (4.1 kcal/mol), and S° = 0.1883 kJ/(molK) (0.045 kcal/(molK)), respectively (107). The thermal decomposition products of NaClO, in the 175—200°C temperature range ate sodium chlorate and sodium chloride (102,109) ... 

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