Hydration, ionic, entropy

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

Having obtained the individual value of the gram-ionic entropy of the hydrogen ion in solution, the individual entropy of hydration can be obtained by a straightforward calculation of the value of from statistical mechanical reasoning. 

To use this value of S to obtain the individual ionic entropies of other ions in solution, it is necessary to toow values for the entropy of hydration of a number of electrolytes containing H. Thereafter, the value of the entropy of the counterion can be obtained. It can then be used in conjunction with entropies of hydration of electrolytes containing the counterion to determine the absolute entropies of partner ions in the electrolyte containing the constant anion. Of course, in all cases, the value of the entropy of the ion in the gaseous state must be subtracted from that of the ion in solution to give the entropy ofhydration [i.e., = (S,)so, - (S,)g ]. 

Ionic entropy of hydration as AS =5 - Sj when Sf isthe gas-phase ionic entropy. 

The (idealized) radius of a polystyrene styrene sulfonate may be several hundred angstroms. Were you to measure the self-diffusion coefficient, what equation would you use to obtain a measure of the ion s size Explain the principles (showing appropriate equations) of obtaining an individual ionic entropy and an individual ionic entropy of hydration. 

Tables 9-11 list the predicted thermodynamic functions for the hydration of divalent, trivalent and tetravalent lanthanides as calculated by Bratsch and Lagowski (1985b). Values for yttrium hydration are also included when available. The formation values refer to the reaction Ln, Ln"a while the hydration values relate to the use of eqs. (28)-(30). The standard state ionic entropies given in table 10 are corrected for...

Heat of Solution Solution Cycles Heat of Hydration Ionic Solids in Water Solution Process and Entropy Change... 

Prediction of solubility for simple ionic compounds is difficult since we need to know not only values of hydration and lattice enthalpies but also entropy changes on solution before any informed prediction can be given. Even then kinetic factors must be considered. 

In cases where the solvation energies are large, as for example when ionic compounds dissolve in water, these hydrophobic effects, based on adverse changes in entropy, are swamped. Dissolving such compounds can be readily accomplished due to the very large energies released when the ions become hydrated. 

Water solubility of ionic substances is dependent on a fine balance between lattice energy, hydration energy and entropy of ions. The scheme shown hereunder as ... 

Table 1. Ionic Radii, hydration numbers, softness parameters a, surface charge densities, polarizabilities, free energies AG° enthalpies AH° and entropies A S° of hydration of metal cations from groups Za o,nd II ...

There are other close-range forces related to entropy changes, including various interactions between solution species and a solid surface, such as solvation (in water, hydration) forces. Hydration forces can occur when hydrated cations are adsorbed at interacting surfaces. As these surfaces approach each other closely, loss of water of hydration is necessary in order to allow closer approach. While these forces can be repulsive, attractive or oscillating, they are most likely to be repulsive under the conditions of CD. Such forces may be very important for CD, which is almost always carried out in the presence of a high ionic concentration. For example they could be a cause of poor adhesion of some CD films. Solvation forces are treated in detail in Israelachvili s book—see Further Reading at the end of this chapter, Forces subsection. 

Inspection of the values for the entropies of hydration of the Group 2 cations in Table 2.17 shows that, with the exception of that for Be2 +, the values become less negative as the ionic radius increases. This effect is similar to that observed for the Group 1 cations. The exception of Be2+ to the general trend is possibly because of its tendency to have a tetrahedral coordination that causes it to affect fewer molecules of water in the hydration process. 

A comparison of the entropies of hydration of Na +, Mg2+ and Al3+ shows that they become much more negative as the positive charge on the cation increases. The increasing charge would be expected to be more and more effective in restricting the movement of water molecules, and there would be more water molecules participating in the restricted volume of the hydration spheres of the ions. The decreasing ionic radius in the series amplifies the trend. 

The roles of hydration enthalpies and entropies in determining the solubilities of ionic compounds... 

This book offers no solutions to such severe problems. It consists of a review of the inorganic chemistry of the elements in all their oxidation states in an aqueous environment. Chapters 1 and 2 deal with the properties of liquid water and the hydration of ions. Acids and bases, hydrolysis and solubility are the main topics of Chapter 3. Chapters 4 and 5 deal with aspects of ionic form and stability in aqueous conditions. Chapters 6 (s- and p-block). 7 (d-block) and 8 (f-block) represent a survey of the aqueous chemistry of the elements of the Periodic Table. The chapters from 4 to 8 could form a separate course in the study of the periodicity of the chemistry of the elements in aqueous solution, chapters 4 and 5 giving the necessary thermodynamic background. A more extensive course, or possibly a second course, would include the very detailed treatment of enthalpies and entropies of hydration of ions, acids and bases, hydrolysis and solubility. 

Bonding Forces Between Dye and Fiber. Dye anions can participate in ionic interactions with fibers that possess cationic groups. However, the formation of ionic bonds is not sufficient to explain dye binding, because compounds that can dissociate are cleaved in the presence of water. Secondary bonds (dispersion, polar bonds, and hydrogen bonds) are additionally formed between dye and fiber [47], Close proximity between the two is a prerequisite for bond formation. However, this is counteracted by the hydration spheres of the dye and of wool keratin. On approach, these spheres are disturbed, especially at higher temperature, and common hydration spheres are formed. The entropy of the water molecules involved is increased in this process (hydrophobic bonding). In addition, coordinate and covalent bonds can be superimposed on secondary and ionic bonds. 

Table 18.1.3. Crystallographic ionic radii (pm) and hydration entropies (kJ mol 1) of the rare-earth elements in oxidation states +2, +3 and +4...

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