Uniqueness principle

Therefore, the body will consist of two spherical layers the inner layer (ball) with a negative density, and the outer layer with a positive density. Thus we come to an idea of the existence of a density distribution that generates a zero external gravity field. This idea is the centerpiece of the non-uniqueness principle for gravity field inverse problems. One can add this kind of density distribution to any given density model and obtain another model generating the same gravity field. 

In many ways, the anomalies mentioned earlier for the second series elements, such as their smaller-than-expected electron affinities and bond dissociation enthalpies, are more of the rule than the exception. In general, the physical properties of the second series elements are not always representative of their groups, a characteristic that is often referred to as the uniqueness principle. Consider, for example, the melting points of the chlorides shown in Table 5.9. The melting points of the second series compounds are very different from the remainder of the group. 

TABLE 5.9 Melting points of selected chlorides, illustrating the second series anomaly known as the uniqueness principle. 

TABLE 5.10 Boiling points of the nonmetal hydrides, illustrating the uniqueness principle for the second series elements. 

A third characteristic of the uniqueness principle is the lack of availability of low-lying d orbitals for participation in bonding. Hence, the second series elements cannot violate the octet rule in the formation of compounds. Consider, for example, the mixed halogens with fluorine as the central atom Fj and CIF, and BrF compared with those of chlorine, bromine, or iodine, which take higher coordination numbers CIF3, CIF5, BrF3, BrFj, IF3, IF5, and IF7. Similarly, the carbon atom in CF4 is sp hybridized, while the Si atom in SiF is d sp hybridized. The extent to which the... 

The three reasons for the uniqueness of the first element in each group are summarized in Figure 9.14, which highlights each groups top element. A color version of Figure 9.14 is shown inside the front cover of the book. In our future discussions, the uniqueness principle wiU be represented by the icon shown at left. It symbolically reminds us that the representative elements at the top of the periodic table are special. 

A summary of three reasons for the uniqueness principle, which states that the chemistry of the second-period elements (Li, Be, B, C, N, 0, F, and Ne) is significantly different from that of their congeners. 

To make sense out of the descriptive chemistry of the representative elements, we have defined and discussed the basis of the first five components of a network of interconnected ideas for understanding the periodic table. These organizing principles are (1) the periodic law, (2) the uniqueness principle, (3) the diagonal effect, (4) the inert-pair effect, and (5) the metal-nonmetal line. The definitions of these components are summarized in Table 9.5. The five components are also summarized in Figure 9.20. A color version of this figure is shown on the inside front cover of the text. 

Mastering the descriptive chemistry of the main-group or representative elements of the periodic table is a formidable task. In order to bring some order to our study of this topic, we have started to construct a network of interconnected ideas. Five components have been described in this chapter. Three additional components will be defined and described in the next few chapters. The first five components are the periodic law, the uniqueness principle, the diagonal effect, the inert-pair effect, and the metal-nonmetal line. 

Sketch the icon that represents the uniqueness principle. Briefly explain how the icon symbolically represents the second component of the interconnected network of ideas for understanding the periodic table. 

The concept of charge density was developed in connection with the introduction of the uniqueness principle in Chapter 9. In a short, well-written paragraph, explain how charge density is used to explain why nonmetal hydrides are always covalent. 

Our network of interconnected ideas helps us to account for many expected properties of the alkali metals. The hydrides, oxides, hydroxides, and halides of these elements are ionic. The oxides and hydroxides are basic in character. Lithium, although stiU an alkali metal with much in common with its congeners, is certainly a good example of the uniqueness principle. It has much in common with magnesium, as forecast by the diagonal effect. 

Relate the hindered rotation found in hydrogen peroxide to the uniqueness principle. 

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