Entropy aqueous ions

Returning now to silver chloride, let us apply these ideas to its saturated aqueous solution at 25°. From the value given in Table 42, we see that in solid AgCl the entropy per ion pair is almost exactly 1 milli-electron-volt per degree, which is equivalent to 23.0 cal/deg/mole. It makes no difference whether we express the entropies per ion pair in electron-volts per degree or in the equivalent calories per degree per mole. In the electrochemical literature the calorie per degree per mole is used and is called one entropy unit. (This is abbreviated e.u.) ... 

Table 25. Conventional Paivtial Molal Entropies of Ions in Aqueous Solution...

Standard molar entropies of elements, compounds, and aqueous ions are listed in Table 17.1 (p. 456). Notice that—... 

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

By procedures analogous to those described in the preceding two examples, we can obtain entropies for many aqueous ions. A list of such values is assembled in Table 20.1. 

Standard Molar Entropies,. V, for Some Aqueous Ions... 

Table 2.15 Absolute standard molar entropies for some aqueous ions (in J K" mol - )...

AS0 is the change in entropy (entropy of products minus entropy of reactants) when all species are in their standard states. The positive value of AS° indicates that a mole of K +(aq) plus a mole of Cl (aq) is more disordered than a mole of KCI(.v). For Reaction 6-3, AS° = —130.4 J/(K-mol) at 25°C. The aqueous ions are less disordered than gaseous HC1. 

The entries all correspond to aqueous ions. Because ions cannot actually be separated and measured independently, a reference point that defines Sm°(H+, aq) = 0 has been established. This definition is then used to calculate the standard entropies for the other ions. The fact that their values are negative arises in part because the solvated ion M(H20)xM+ is more ordered than the isolated ion and solvent molecules (MK+ + x HzO). 

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

Standard molar entropies S° are tabulated for a number of elements and compounds in Appendix D. If Cp is measured in J moP, then the entropy S° will have the same units. For dissolved ions, the arbitrary convention S° H (aq)) = 0 is applied (just as for the standard enthalpy of formation of discussed in Section 12.3). For this reason, some S° values are negative for aqueous ions—an impossibility for substances. 

But take care these will also be dependent on the convention used in the determination of the individual partial molar entropies of ions in aqueous solution. 

For the hydration processes M (g) — M (aq) and X (g) — X (aq), the entropy changes depend upon the values of the entropies of the gaseous ions as well as the absolute entropies of the aqueous ions ... 

Franks and Reid, using data from the literature, have evaluated partial molal entropies of ions in aqueous methanol and dioxan. The data are listed in Appendix 2.4.42. In their division they made the assumption that -----for each solvent system, which appears reason-... 

If you scan the values for 5° in Appendix E, you will see that several aqueous ions have values that are less than zero. The third law of thermodynamics states that for a pure substance the entropy goes to zero only at 0 K. Use your understanding of the solvation of ions in water to explain how a negative value of S° can arise for aqueous species. 

During the last feiv years, CRISS and COBBLE (1) have developed a principle of entropy correspondence for aqueous ions which predicts ionic heat capacities over wide ranges of temperature (0 - 300°). The entropy relations can be summarized as ... 

This reference book contains a compilation of thermodynamic data for about 2000 chemical compounds and aqueous ions (mostly inorganic). The thermodynamic properties tabulated are A-G , A,H , S , and C at 298.15 K, electrode potentials, enthalpies and entropies for phase transitions, A,G of inorganic aqueous ions from 25 to 350 C, partial molar heat capacities from 10 to 130 C, and the partial molar volumes of aqueous electrolytes at high temperatures and pressures. There are 1550 references given to the primary literature and to the literature evaluations of others. 

Aqueous ions heat capacity, osmotic coefficient, entropy 256... 

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). 

Aqueous ions heat capacity, osmotic coefficient, entropy The heat capacities and osmotic coefficients of aqueous solutions of some salts of most of the ions have been determined by Spedding and others (Rard 1985,1987). 

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)...

You will find that tables, including Appendix 2, contain negative absolute entropies for some aqueous ions, although the explanation for this is beyond the scope of this book. 

Another, quite empirical, method assumes that Aj5 (I , W- S) = fl(5) -i- (5)5°° (I, W), that is, a linear function of the standard molar entropy of the aqueous ion with different coefficients a and b for each solvent, proposed by Criss et al. [44]. This requires estimates ofAt5"(I, W->S) from other sources to establish a and b for a given solvent and may be used, for this solvent, for ions for which only 5 (I, W), but not the entropy of transfer, is known. There being no theoretical basis for the linear relationship, this linearity has to be reestablished for each new solvent. 

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... 

Thermodynamic properties of ions in nonaqueous solvents are described in terms of the transfer from water as the source solvent to nonaqueous solvents as the targets of this transfer. These properties include the standard molar Gibbs energies of transfer (Table 4.2), enthalpies of transfer (Table 4.3), entropies of transfer (Table 4.4) and heat capacities of transfer (Table 4.5) as well as the standard partial molar volumes (Table 4.6) and the solvation numbers of the ions in non-aqueous solvents (Table 4.10). The transfer properties together with the properties of the aqueous ions yield the corresponding properties of ions in the nonaqueous solvents. 

A correlation function P(M) that connects the trivalent gaseous lanthanide atoms with their aqueous ions changes systematically as a function of atomic number [322]. The same property is moderately well-behaved for trivalent actinides [322-324, or 368]. Each experimental datum needed to calculate P(Am) is well-established but P(Am) is about 20 kJ greater than expected from neighboring actinides (see 17.5.2 and Fig. 17.6). This anomaly has been attributed to the large positive change in entropy of vaporization of Am [325]. 

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