Sanderson indicated in his plot that the “secondary” linkages progressed from the 3rd Period to the 4th Period. Of particular note in the context of Chapter 9, he high-lighted in the article the closer resemblance in electronegativity (and electron configuration) of aluminum with the Group 3 elements, and of silicon with the Group 4 elements. The plot also showed the “saw-tooth” pattern in electronegativities that are observed when descending groups in the later main group elements.
Figure 2.1 Patterns in the Sanderson electronegativities of the elements (adapted from Ref. [15]).
The van Arkel–Ketelaar Bond Triangle
One of the many applications of the electronegativity concept is that of the bond triangle [16]. Devised by van Arkel, then improved upon by Ketelaar, the triangle categorizes elements, alloys, and compounds according to their degrees of ionic, covalent, and metallic character [17]. The triangle was originally more conceptual than detailed. However, using electronegativity values, Jensen semiquantified the diagram as shown in Figure 2.2 [18].
Sproul and his coresearchers have refined and updated the bond triangle, both from a practical and theoretical perspective [19]. The triangle has become popular as a means of assigning bonding in newly synthesized solid-state compounds, such as Y3AlC [20] and the AgXY2 family where X is a Group 13 element, and Y is a Group 16 element [21]. In addition, Sproul has attempted to revive the triangle in the context of teaching bond type at university level [22].
Figure 2.2 A semiquantitative bond triangle (adapted from Ref. [15]).
In Britain, an advanced high school qualification, called the Pre-U has been devised by the University of Cambridge International Examinations. A key part of the chemistry Pre-U is devoted to the van Arkel–Ketelaar Triangle as a basis for the bonding discussion [23].
Oxidation State
Another rather nebulous — but very useful — property is oxidation state [24]. To use the deductive approach as will be shown shortly, the value is determined upon the basis of comparative electronegativities.
According to Jensen, the first use of the term was by Talbot and Blanchard in 1907 [25]. Actually, there are two terms: “oxidation state” and “oxidation number.” In 1990, the International Union of Pure and Applied Chemistry (IUPAC) provided a set of recommended lengthy rules by which the “oxidation state” of any element could be calculated (given in Arabic numerals). IUPAC reserved the term “oxidation number” for the central atom in a coordination compound (given in Roman numerals) [26]. This latter usage corresponded to the use of Roman numerals in the Stock system of inorganic nomenclature.
The 1990 IUPAC definition of oxidation state was critiqued by Loock, who pointed out the significant shortcoming that the IUPAC method would only give an average oxidation state if there were two atoms in a compound in dissimilar environments. Instead, he proposed a succinct definition based on Pauling’s use of the term [27]:
The oxidation state of an atom in a compound is given by the hypothetical charge of the corresponding atom ion that is obtained by heterolytically cleaving its bonds such that the atom with the higher electronegativity in a bond is allocated all electrons in this bond. Bonds between like atoms (having the same formal charge) are cleaved homolytically.
Jensen strongly supported the Pauling/Loock definition, adding a summary of the difference in the approaches [28]:
…the memorized IUPAC rules …are ultimately traceable to an attempt to assign oxidation values based solely on the use of a species’ compositional formula, whereas the Pauling[/Loock] approach requires instead a knowledge of the species’ electronic bonding topology as represented by a Lewis diagram.
A variation of the Pauling/Loock approach — the “exploded structure method” — was devised by Kauffman [29], though its shortcomings were described by Woolf [30]. IUPAC subsequently reversed their view, changing from a mechanical rule-based approach (still widely used in textbooks) to the electronegativity–Lewis structure approach of Pauling/Loock. However, compared with Loock’s definition, the IUPAC definition seems technical and obtuse [31]:
The oxidation state of an atom is the change of this atom after ionic approximation of its heteronuclear bonds. Bonds between atoms of the same element are not replaced by ionic ones: they are always divided equally.
In many cases, both the algebraic and the electronegativity–Lewis structure approach give the same result. For example, in the sulfate ion, both methods assign an oxidation state of +6 for sulfur. However, very different results are obtained where there are two (or more) atoms of the same element in different environments.
An example is provided by the thiosulfate ion, S2O32−, with a peripheral and a central sulfur atom. When this ion decomposes in acid, the fates of the two sulfur atoms are quite different, indicating that they have come from very different environments and oxidation states in the thiosulfate ion itself. However, the algebraic calculation provides an average oxidation state of +2 for each sulfur atom. The Lewis structure of the ion (Figure 2.3) confirms the experimental finding of two very different electron environments for the sulfur atoms. Utilizing the Pauling/Loock electronegativity–Lewis structure approach, the central sulfur atom is assigned an oxidation state of +5 while the peripheral one has a resulting oxidation state of −1. These values make much more chemical sense.
Figure 2.3 Electron assignment for the thiosulfate ion to use for electronegativity determination by the Pauling/Loock deductive method.
Abegg’s Rule
The range of oxidation states for a specific element is sometimes alluded to in introductory chemistry. As examples, values for sulfur range from −2 to +6, while for chlorine the range is from −1 to +7. It was Abegg who, in 1904, noticed that the sum of the extreme oxidation states of an element often equaled eight. The popularization of this observation did not happen until 1916, in a long-overlooked contribution to chemical bonding by Lewis [32]. The rule can be states as
