Absolute ionic entropies

Born Treatment. Several attempts have been made to evaluate absolute ionic entropies by means of the Born equation (eqn. 2.11.18) or the modified Born equation. The method consists mainly of employing the temperature coefficient of the ionic free energies of solvation as discussed in sect. 2.11.2 to obtain the entropy of solvation. The entropy of the individual gaseous ions can be calculated by the methods also discussed in sect. 2.11.2 and consequently ionic entropies evaluated. 

Standard Absolute Ionic Entropies (cal mol" K ) at 25 C (Hypothetical 1 Molal Standard State) ... 

Standard Absolute Ionic Entropies at 25" C (Mol Fraction and Ideal Gas Standard State)" ... 

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. 

Absolute Standard Partial Gram-Ionic Entropies of H and Cf lons ... 

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 ]. 

Spectroscopic methods, molten salts, 702 Spectroscopy detection of stmctnral nnits in liquid silicates, 747 and structure near an ion, 72 Standard partial gram ionic entropies, absolute, II Thermodynamics, applied to heats of solvation, 51 of ions in solution, 55 Time average positions of water near ions. 163 Tools, for investigating solvation, 50 Transformation, chemical, involving electrons, 8 Transition metals... 

For a given solvent, one should be able, with reasonable confidence, to estimate the entropy of simple univalent ions by eqn. 2.11.36, if the constants a and b for that solvent are known. In this respect the equation is useful for filling in the few holes which exist in the data listed in Table 2.11.14. It would be interesting to know whether eqn. 2.11.36 is also useful for making estimations of ionic entropies of complex and polyvalent ions. Fortunately, a few experimental entropies are available for 2 1 electrolytes for comparison. If eqn. 2.11.36 is modified to include the absolute ionic charge, z, it will account for divalent ions. With the charge included, eqn. 2.11.36 becomes... 

This identity was used in [265] to determine the absolute value of ionic entropy. The analysis shows that for such a calculation we must know the ratio of the ideal preexponential factors (the ratio K d/K d actually assumed in [265] to be equal to unity). An attempt to express this ratio in terms of the ratio of experimentally measurable quantities leads to an equation which does not contain the entropies of individual ions. 

The higher ion charges in MgO (2+ and 2-) as compared to the ion charges in NaF (1+ and 1-) hold the MgO ionic solid together more tightly so the ions vibrate less, leading to lower absolute entropy. 

The second indicator of kosmotropicity is the standard molar entropy of hydration. For all ions it is highly negative the higher its absolute value, the more water is ordered upon ionic hydration, and the higher the electrolyte kosmotropicity [2,21]. 

Because of this, the number and types of defects, which can appear in the solid, are limited. This restricts the number of defect types we need to consider, in both elemental (all the same kind of atom) and ionic lattices (having both cations and anions present). We have shown that by stacking atoms or propagation units together, a solid with specific symmetry results. If we have done this properly, a perfect solid should result with no holes or defects in it. Yet, the 2nd law of thermodynamics demands that a certain number of point defects (vacancies) appear in the lattice. It is impossible to obtain a solid without some sort of defects. A perfect solid would violate this law. The 2nd law states that zero entropy is only possible at absolute zero temperature. Since most solids exist at temperatures far from absolute zero, those that we encounter are defect-solids. It is natural to ask what the nature of these defects might be, particularly when we add a foreign cation (activator) to a solid to form a phosphor. 

In these equations, the referenee states of H tq) are, by convention, equal to zero as are the functions AHf e[g ) and AG ( ( ,). The absolute entropies for the gaseous ions are calculated from statistical mechanics (Bratsch and Lagowski 1985a) and agree fairly well with the experimental values reported by Bertha and Choppin (1969), who interpreted the S-shaped dependence of standard state entropies on ionic radius in terms of a change in the overall hydration of the cation across the lanthanide series. Hinchey and Cobble (1970) proposed that this S-shaped relationship was an artifact of the method of data treatment and calculated a set of entropies from lanthanide... 

Nearly all current attempts to divide partial molal entropies of electrolytes in organic solvents into their ionic components have required a knowledge of the absolute entropy of the corresponding ions in water. Consequently, it appears worthwhile to examine some of the methods which have been used to evaluate absolute values in this solvent. 

Millcro has also used the correspondence principle method to evaluate ionic volumes in NMP as well as in methanol. Similar to the case for entropies, ionic volumes in the non-aqueous system are plotted against the absolute 5n(aq) values, and the Vi (X) for the non-aqueous system assigned so that values for both cations and anions fall on the same line. The volumes can be expressed, similar to eqn. 2.11.36, as... 

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