Periodic Table, The: Past, Present, And Future
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24.Y. T. Oganessian and K. P. Rykaczewski, “A Beachhead on the Island of Stability,” Phys. Today 68, 32 (01 August 2015).
25.P. J. Karol, “The Mendeleev-Seaborg Periodic Table: Through Z = 1138 and Beyond,” J. Chem. Educ. 79, 60–63 (2002).
Chapter 2
Selected Trends in Atomic Properties
This book cannot be a comprehensive compilation of all the periodic properties. And it is certainly not intended to be a turgid, endless, boring, collection of tabulated data and graphical plots. In this chapter, there will be a focus just upon four major parameters: electronegativity, ionization energy, electron affinity, and relativistic factors. But first …
What is a chemical element? This question may seem self-evident, but it is not. In Chapter 1, a chemical element was defined, by inference, as an atom with a specific number of protons. Now, entering the world of chemistry, things become murkier. Many electrons have been put to work to produce erudite articles on the subject [1–3].
An atom clearly is a chemical element. It is a minuscule fragment of matter with no color, and no sense of whether it is supposed to be a metal or nonmetal; or have any other bulk properties. It does have an electron configuration, an ionization energy, and an electron affinity. However, to define its electronegativity (discussed in the next section), comparison must be undertaken using a pair of dissimilar atoms.
But most chemists deal with real, visible materials, that is, “elements and compounds,” rather than “atoms and molecules.” Thus, the question arises, if the word “element” is used to describe the identity of an atom, can it also be used to do double duty for a bulk collection of atoms [4]? And, indeed, at what size does a cluster of atoms begin to exhibit bulk properties [5]?
The proposal has been made to use the term “elementary substance” for a bulk substance that does not undergo chemical decomposition into other substances [6]. There are two challenges with adoption of this new terminology: first, the cumbersomeness of a two-word term; and second, the acceptance among, not just chemists, but also the wider community at large. As much as this author, in general, espouses precise and correct terminology wherever feasible, here, the word “element” will continue to do “double duty.”
Electronegativity
It may seem odd that the first parameter in this chapter is not a simple measurable property of an atom. However, the concept of electronegativity underlies much of our interpretation of chemical properties and behavior. Jensen has traced the origins of the electronegativity concept back to the early 1800s, with Berzelius naming the concept “electronegativity” in 1811 [7]. In fact, it was in the late 19th and first half of the 20th centuries when the concept became refined into its modern form [8].
Electronegativity as a Fundamental Property
Leach has produced a comprehensive study of the various parameters that have been used to obtain numerical values for electronegativity. He argued that even though electronegativity is not a single parameter of an atom’s properties, it is a fundamental property itself. Among his conclusions were the following (edited) statements [9]:
•Electronegativity is an extremely successful but ill-defined heuristic concept for the description of central properties of entities in the dappled chemical world.
•Electronegativity is a theoretical construction than a natural property. That is, it is cannot be measured directly.
•Electronegativity’s main applications (descriptions of polarities and bonding modes in substances, depiction of oxidation numbers, explanation of reaction mechanisms and acidity, etc.) are qualitative. In Leach’s view, the mathematization of electronegativity is excessive and tends to lead to apparent scientificity.
•Electronegativity is a dimensionless number that — like other measures in the applied sciences — has a complex referential background. It is conceptually rooted in the realm of chemical reactivity on the one hand, but it is supplied by the physics of isolated particles on the other.
Electronegativity Scales
Though electronegativity is commonly associated with Pauling and his scale [10], there are many other scales, including the widely used Allred–Rochow [11]. All numerical ranges share a common definition:
Electronegativity is a chemical property that describes the tendency of an atom to attract a shared pair of electrons (or electron density) toward itself.
If electronegativity is such a vague concept with disparate definitions, why is it so important, and why has it not been replaced by a clearly quantifiable atomic parameter? It was Rodebush in 1924 who provided an elegant answer [12]:
I had hoped that we might be able to substitute electron affinity or ionizing potential for the wretched term electronegativity, but these quantities are measured for the gaseous state and our ordinary chemical properties are concerned with the condensed phases.
Even in the 21st century, the nature of electronegativity is a continuing topic of discourse and debate [13, 14].
The Sanderson Electronegativity Scale
In addition to the well-known scales, in an oft-overlooked series of articles, Sanderson developed and applied his own electronegativity scale [15]. Though his value system did not gain acceptance, the plot that he generated provided a useful qualitative overview of comparative electronegativities (Figure 2.1).
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 s
ignificant 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 follows:
Abegg’s Law states that, for a main group element, the total difference between the maximum negative and positive oxidation states of an element is frequently eight and is in no case more than eight.
As an example, sulfur has the oxidation state limits of −2 and +6. Thus, applying Abegg’s law: [{+6} − {−2}] = +8.
Electron Gain and Loss
Having devoted the first part of this chapter to the variously defined concept of electronegativity, the second part will be on the very specifically defined topics of ionization energy and electron affinity. Values of which are mostly known to considerable precision.
First a comment upon a statement that appears in many introductory chemistry texts: “Ionic compounds form because metals want to give up valence electrons and non-metals want to gain valence electrons.” The statement is a convenient fiction for students starting out in chemistry, but nothing could be farther from the truth! This false explanation can be demolished by simply considering the ionization energy (IE1) and electron affinity (EA1) of the sodium atom:
As can be seen from the values, sodium actually “wants” to gain an electron not lose one! It is only the fact that the nonmetal counter-atom has a higher electron affinity that “forces” sodium to lose its valence electron. That is, ionic bonding is not benign, but atomic “nature red in tooth and claw,” in other words, a competition for the valence electrons [33]. The two related phenomena are discussed in the following.
Ionization Energy
One pattern explicable in terms of electron configuration is that of ionization energy. Usually we are interested in the 1st ionization energy. As the orbital occupancy may change between the neutral atom and the ionized ion, a correct definition is as follows [34]:
The experimental 1st ionization energy is equal to the difference between the total electronic energy of the atom X and the total electronic energy of the ion X+, both in their ground states. That is, X(g) → X+(g) + e−
Periodic Trends in Ionization Energy
Unlike the molecule-dependent values of covalent radii, ionization energies can be measured with great precision. Figure 2.4 shows the IE1 for the 1st, 2nd, and 3rd Period elements. As can be seen, the pattern is repetitious, the Group 1 elements at the low point and the Group 18 elements at the peaks. Most of the variations can be explained in terms of screening/shielding from the nucleus of the outermost electron by the inner electrons [35].
Figure 2.4 1st ionization energy for the first 19 elements (adapted from Ref. [35]).
Instead of discussing IE1 of each element shown, one cycle will be chosen for examination: that of the 2nd Period elements. The patterns can be explained as follows:
•Lithium has a small IE1 as the 2s electron is largely shielded from the nuclear attraction by the 1s2:
[He]2s1 → [He]
•Beryllium has a larger IE1 primarily as a result of the greater effective nuclear charge:
[He]2s2 → [He]2s1
•Boron has a lower IE1 as, even though there is an increase in nuclear charge, the 2p electron is partially shielded by the 2s2 electrons:
[He]2s22p1 → [He]2s2
•Carbon has a higher IE1 primarily as a result of the greater effective nuclear charge:
[He]2s22p2 → [He]2s22p1
•Nitrogen has a higher IE1 primarily as a result of the greater effective nuclear charge:
[He]2s22p3 → [He]2s22p2
•Oxygen has a lower IE1 which will be discussed separately in the following:
[He]2s22p4 → [He]2s22p3
•Fluorine has a higher IE1 primarily as a result of the greater effective nuclear charge:
[He]2s22p5 → [He]2s22p4
•Neon has a much higher IE1 primarily as a result of the greater effective nuclear charge:
[He]2s22p6 → [He]2s22p5
The Half-Filled Shell Myth
Ingrained in the vocabulary of chemistry is the term “the stability of the half-filled shell.” However, it is not the “stability” of the p3 configuration, but the reduced “stability” of the subsequent electrons, which accounts for the break in near-linearity of the plot. Cann has compared some of the explanations for the discontinuity and concluded the following one to be the best [35]:
Because of the Pauli Exclusion Principle, electrons with parallel (unpaired) spins tend to avoid each other, thus decreasing the electrostatic repulsion between them. This will be the situation when filling the first half of the shell. When electrons are forced to doubly occupy orbitals in the second half, their spins are constrained to be paired (antiparallel). Because they are no longer obliged to avoid each other, the [inter-electron] electrostatic repulsion increases.
In Figure 2.5, the IE1 are shown for the 2p and 3p block elements. Continuin
g the line of the p1 to p3 configurations, a line parallel to the actual p4 to p6 values is obtained. The difference between the two represents the coulombic repulsion between pairs of electrons within the same orbital. For the 2p series, this amounts to about 430 kJ⋅mol−1, while for the 3p series it is 250 kJ⋅mol−1. Cann attributed the difference between the two series to the more diffuse 3p orbitals compared with the 2p orbitals. Thus, any paired 3p electrons are sharing a larger volume of space and therefore have less mutual repulsive forces.
Figure 2.5 First ionization energy for the p-block elements of the 2nd and 3rd Periods (adapted from Ref. [35]).
To review, there is nothing exceptional about the “half-filled shell.” It is instead the interelectron repulsive forces between the electron pairs beyond the p3 configuration, which result in a lower ionization energy. To reinforce the point, as Rich and Suter added [36]:
Likewise, when one compares the energy to remove an electron from the half-filled p subshell with that needed for a p2 structure, nothing special is found.
Rich and Suter then referred to the claimed stability of the “filled shell.” They continued [36]:
Similarly, the large energy difference between electrons in 3s1 and 2p6 configurations is readily explained by the difference in principal quantum number; this again indicates no more “extra” stability of a filled p shell than it does for a p5 or any other structure in which the electron being removed is at the lower principal number.
3d-Series Metal Ionization Energies
The 1st and 2nd ionization energies of the 3d-series metals, corresponding to the removal of each of the 3s2 electrons, show a steady increase without any major deviations [37]. More interesting are the 3rd ionization energies, IE3, of the 3d-series metals. With these subsequent ionization energies, it is the d electrons that are being “plucked off” one by one. As can be seen from Figure 2.6, it is an almost identically shaped plot to that for the 2p and 3p electrons in Figure 2.5, except that the greater coulombic repulsion between any electron pairs commences with the d6 configuration (instead of p4), as expected.