Regular enthalpy

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

All the elements have stable electronic configurations (Is or ns np ) and, under normal circumstances are colourless, odourless and tasteless monatomic gases. The non-polar, spherical nature of the atoms which this implies, leads to physical properties which vary regularly with atomic number. The only interatomic interactions are weak van der Waals forces. These increase in magnitude as the polarizabilities of the atoms increase and the ionization energies decrease, the effect of both factors therefore being to increase the interactions as the sizes of the atoms increase. This is shown most directly by the enthalpy of vaporization, which is a measure of the energy required to overcome the... 

A particular type of nonideal solution is the regular solution which is characterized by a nonzero enthalpy of mixing but an ideal entropy of mixing. Thus, for a regular solution,... 

Thus the integral molar excess free energy of mixing as well as the enthalpy of mixing are independent of temperature for a regular solution. 

However at elevated temperatures (T2 > Tj, Figure 9) the increased entropy (TAS) associated with an open shell structure overcomes the ti —ti enthalpy of dimerisation associated with these distorted Ti-stacked structures and they undergo a solid-solid phase transition (Figure 9) The high temperature phase is typically associated with a Ti-stack of regularly spaced radicals which exhibit longer inter-radical S- S contacts (ca. 3.7 A). This process was first observed by Oakley60 in the DTA radical thiadiazolopyrazine-l,3,2-dithiazolyl 26, and a number of other derivatives have subsequently been identified which exhibit similar behaviour. These are compiled in Table 1. 

A classic method14 for examining the thermochemical regularity of an organic homologous series is plotting the standard molar enthalpies of formation versus the number of carbon atoms in the compounds. The linear relationship may be expressed as equation 1 where all the enthalpies of formation are in either the gaseous or a condensed phase, a is the slope, ft is the y-intercept and nc is the number of carbon atoms in the compound. 

The enthalpies of formation of selected perovskite-type oxides are given as a function of the tolerance factor in Figure 7.17. Perovskites where the A atom is a Group 2 element and B is a d or / element that readily takes a tetravalent state [19, 20] show a regular variation with the tolerance factor. Empirically, it is suggested that the cations that give t close to 1 have the most exothermic enthalpies of formation. When t is reduced, the crystal structure becomes distorted from cubic symmetry and this also appears to reduce the thermodynamic stability of the... 

Still, the strain enthalpy is of particular importance. An elastic continuum model for this size mismatch enthalpy shows that, within the limitations of the model, this enthalpy contribution correlates with the square of the volume difference [41,42], The model furthermore predicts what is often observed experimentally for a given size difference it is easier to put a smaller atom in a larger host than vice versa. Both the excess enthalpy of mixing and the solubility limits are often asymmetric with regard to composition. This elastic contribution to the enthalpy of mixing scales with the two-parameter sub-regular solution model described in Chapter 3 (see eq. 3.74) ... 

The first term is the ideal entropy of mixing while the second term is the enthalpy of mixing in the regular solution approximation ... 

Entropies can be calculated or estimated, and hence enthalpies can be derived from equilibrium measurements. Gaseous entropies are calculated by statistical mechanics using experimental or estimated molecular dimensions and fundamental frequencies (93). For solids, numerous methods based on additivity rules, or regularities in series of compounds, are available. Khriplovich and Paukov (140), for example, list 20 such relationships and were able to estimate entropies to about 1%. Empirical equations are also available for ion entropies (59). 

A general survey has been given by Long (158), who points out that enthalpy regularities would only be expected over restricted areas of the periodic table. Discontinuities would be expected where an increase in coordination number occurred between Periods 4 and 5, or where the relative stability of valence states changed, or where ion configurations were stabilized. Examples of trends in mean bond energies are presented in Section V,C. 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

Distribution Laws And Regular Solid Solutions. For so-called regular solid solutions (15), Equation (9) still holds but by definition the expression for their enthalpy of mixing is ... 

Figure 8. Free enthalpy of mixing G of binary solid solutions (regular) Ca,. (PO ) OH F as a function of x at W/2.303 RT = 1.4.

Freund and Knobel (62) have found that in addition to F-OH-F complexes, F-OH pair interactions are important. Therefore, a mixed type regular and subregular model of the solid solutions should be more appropriate. To a first approximation, the enthalpy of mixing should then have the form ... 

When can a set of data be regarded as a database Guidelines such as the number of records or the publication medium may not be useful. CODATA values, for example, which are the recommended starting point for any database (or any thermochemical calculation, for that matter), involve only about 150 species. Also, the CODATA reports have been printed in regular scientific journals before the final set was released as a book and later posted on the Internet. Second, we could have distinguished between databases and data compilations. The former involve recalculation of quantities such as standard enthalpies of formation to ensure a consistent set of values (see section 2.5). Databases may also include data assessment, leading to recommended values. Data compilations, on the other hand, are just collections of literature values. Although this distinction is important (see table Bl), a data compilation can be rather useful for the expert user and save many hours of literature search. 

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