Periodic Table, The: Past, Present, And Future
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Laing identified the sets of elements having atomic numbers: 29 to 31, 47 to 51, and 79 to 84, as marking the boundaries of the knight’s move (see Figure 10.1). The three pairs upon which Laing focused were: zinc and tin; silver and thallium; and mercury. In addition, using the knight’s move, he made predictions about chemistry of element 114 (flerovium).
Figure 10.1 The elements with potential to form knight’s move relationship pairs (plus flerovium, element 114) according to Laing (from Ref. [1]).
Figure 10.2 The White Knight in Alice Through the Looking Glass (from Ref. [4]).
The choice of the chess analogy was particularly interesting in that there was already a link between chess and chemistry. The link involved Oxford University chemist Augustus Vernon Harcourt [2]. Vernon Harcourt, a very affable, gentle, and forgetful chemist, is widely believed to have been the model or part of, for the White Knight in the story of Alice Through the Looking-Glass [3] (Figure 10.2).
Laing’s Knight’s Move (K-M) Claims
To support his claim of the existence of the knight’s move (K-M) relationship, Laing provided evidence from widely different aspects of element chemistry. For example, he noted that for the zinc–tin K-M pair, their respective compounds are nonpoisonous, while for the cadmium–lead K-M pair, their respective compounds are extremely poisonous.
Knight’s Move Links among the Elements
For the zinc–tin K-M pair, Laing noted that both these elements plated steel. Also, zinc and tin formed alloys with copper: brass (zinc and copper) and bronze (tin and copper). There is even a ternary alloy of 96% copper, 2% zinc, and 2% tin. Then for the tin–polonium K-M pair, Laing pointed out that the elements themselves had very similar melting points: tin at 232°C, and polonium at 254°C.
Knight’s Move Links among Compound Melting Points
Laing compared melting and boiling points among pairs of K-M related compounds. A melting point pair from each K-M set that he quoted is given in Table 10.1.
Table 10.1 Comparisons of melting points for some K-M pairs (from Ref. [1])
Knight’s Move Chemical Relationships
In chemical similarities, Laing pointed out that silver chloride and thallium(I) chloride are both water-insoluble compounds. However, they differ in that silver chloride reacts with ammonia to give the soluble linear [Ag(NH3)2]+ ion while thallium chloride does not react with ammonia. Also, Laing noted that the crystal structures of zinc oxide and tin(II) oxide are similar.
Knight’s Move Prediction of Properties for Element 114
Laing used the K-M concept to predict some properties of the then-undiscovered element 114 (now called flerovium). He made his predictions of flerovium chemistry by comparison with mercury, the K-M match. Laing predicted flerovium would be a metal with very low melting point and a density of about 16 g·cm−3. By comparison with mercury, he stated that flerovium should form a chloride, FlCl2, and an oxide, FlO (which would be thermally unstable).
Some chemistry of flerovium has since been reported. Eichler et al. state that [5]:
Identification of three atoms of element 114 in thermochromatography experiments . . . indicates that this element is at least as volatile as simultaneously investigated elements Hg, At, and element 112. This behaviour is rather unexpected for a typical metal of group 14.
Laing’s prediction of a similarity to mercury seems to have been confirmed.
Laing’s Knight’s Move Legacy
Laing’s many contributions to the discussions on the Periodic Table are sprinkled throughout this book. On the basis of that one article, the knight’s move has become accepted as a genuine periodic relationship, having been included in such resources as: a conference proceedings on the Periodic Table [6]; and a definitive work on the history and structure of the Periodic Table [7]. And now, in this work, a whole K-M chapter. It will be through the K-M that Laing’s name will live on [8].
Reevaluation of the Knight’s Move Relationship
An overriding and oft-forgotten point about the chemical elements is that each element is unique. It is this individuality that makes inorganic chemistry such an interesting but, at the same time, gargantuan field of study. Thus, in looking for relationships, one should not expect total congruence among the elemental behaviors; on the other hand, one should be hoping to find consistent patterns that are more than simple probability. For this reason, the knight’s move concept needs to be tested by looking systematically and comprehensively at one or more pairs of elements.
The Significance of Oxidation Number
In the opinion of this Author, it is the compounds of the same oxidation states that provide the knight’s move with its main validity. In fact, this matching of oxidation states — generally the lower one — seems to be the key feature of the linkages (Figure 10.3).
The K-M Silver(I) — Thallium(I) Similarities
The most intriguing example of the K-M relationship is that of silver(I) and thallium(I). Some of the similarities are as follows:
Figure 10.3 The common oxidation states of the “Knight’s Move” elements with the less common oxidation state indicated in parentheses.
•For silver and thallium, unique in their respective Groups, the +1 state is stable and preferred in aqueous solution.
•Silver(I) and thallium(I) halides are whitish except for the iodides that are yellow.
•Silver(I) fluoride and thallium(I) fluoride are water soluble and all other silver and thallium(I) halides are insoluble.
•Unique among chromates, insoluble silver(I) chromate, Ag2CrO4, and thallium(I) chromate, Tl2CrO4 are both brick red in color.
•In the mineral, crookesite, Cu7(Ag,Tl)Se4, silver(I) and thallium(I) occupy the same lattice sites.
•Thallium(I) tetrafluoroborate, TlBF4, has been proposed as a substitute reagent for silver(I) perchlorate, AgClO4 [9].
A Thallium Detour
Earlier, the knight’s move linkage of thallium(I) with silver(I) was explored. In Chapter 9, the limited (n) and (n + 10) relationship of silver with the alkali metals was briefly mentioned. Combining these two links, a most curious connection is that of thallium(I) with the heavier alkali metals. For example, thallium, like potassium, forms a hydroxide, TlOH, which is very water soluble to produce a very basic solution. Thallium(I) is also one of the cations that fits the large monopositive ion site in an alum as a substitute for an alkali metal ion [10].
Thallium(I) ion is highly poisonous. It enters the body through the potassium ion uptake pathways. Once absorbed, it is the attraction to sulfur ligands that provide thallium(I) with its toxicity (and difference from the alkali metal ions). In this way, the thallium(I) ion disrupts many cellular processes by interfering with the function of proteins that incorporate the sulfur-containing amino acid, cysteine [11].
Knight’s Move Relationships among “Double Pairs”
In addition to simple pairs, there are also “double pairs” of K-M related elements. These are copper–indium/indium–bismuth and zinc–tin/tin–polonium, in which each central element has two other elements linked by potential Knight’s Move relationships (Figure 10.4).
To summarize Laing’s claims, he proposed that the following specific features indicate the existence of a knight’s move pattern:
•Similarities of metal melting points.
•Patterns in compound formulas and structures.
•Parallels in melting and boiling points of compounds of the same formulation.
Figure 10.4 The two sets of “double pair” K-M related elements, one double pair is in italic.
Here the three aspects will be examined in the context of the two “double pairs.”
Are Metal Melting Points Irrelevant to K-M?
Laing noted in his paper [1] the similarity in melting points between tin (232°C) and polonium (254°C). Looking at the melting and boiling points of the first double pair of zinc–tin–polonium (see Table 10.2), there does seem to be a similarity of melting points (tin–polonium) and boiling points (zinc–polonium), tho
ugh there is no systematic pattern involving all three metals.
The matching table for the copper–indium–bismuth double pair indicates that low melting points are characteristic of all the lower p-block metallic elements (see Table 10.3). In fact, the closest match in melting and boiling points does not come from knight’s move pairs. Instead, by comparing Tables 10.2 and 10.3, the major similarity for the main group elements is controlled by Period. Thus, tin and indium have similar melting and boiling points; as do bismuth and polonium. Therefore, similarities in metal melting points and boiling points do not seem to be a defining K-M feature [12].
Table 10.2 The phase change temperatures for the Zn–Sn–Po double pair
Table 10.3 The phase change temperatures for the Cu–In–Bi double pair
Copper(I)–Indium(I) and Indium(III)–Bismuth(III) Double T-M Links
It is always the lower oxidation state of the 5th Period element that matches an oxidation state of the 4th Period element. Then it is the higher oxidation state of the 5th Period element that matches the lower oxidation state of the 6th Period element. For the double T-M links here, the pairs are compounds of copper(I) and indium(I); and then corresponding compounds of indium(III) and bismuth(III). Four main sources of information have been used [13–16].
The usual aqueous oxidation state for copper is +2 while that for indium is +3. For both copper and indium, the +1 oxidation state is a comparative rarity. It is found mostly in insoluble solid-state species, though in itself, the existence of this matching oxidation state is notable in the context of the knight’s move. Table 10.4 shows some of the simple copper(I) and corresponding indium(I) compounds known. Also of note, fluorides are unknown for both copper(I) and indium(I).
The comparative chemistry of indium(III) and bismuth(III) is more extensive. The parallels between indium(III) and bismuth(III) are particularly strong as +3 is the more common oxidation state for both elements. Bismuth exemplifies the phenomenon that the elements of the later 6th Period tend to favor the lower oxidation states over the highest. Some of the similarities are as follows:
Table 10.4 Some corresponding copper(I) and indium(I) compounds
•All tripositive halides and chalcogenides are known for both elements.
•Indium(III) and bismuth(III) form corresponding tetra-and hexa-coordinate halo-complex ions: and
•Indium(III) and bismuth(III) form isostructural alums: MIMIII(SO4)2.12H2O, where MI is a large monopositive ion and MIII is indium(III) or bismuth(III).
•Indium(III) and bismuth(III) form stable oxo-halides of matching formula, such as InOCl and BiOCl.
Zinc–Tin(II) and Tin(IV)–Polonium(IV) Double T-M Links
Though here we focus on knight’s move resemblances, it is important to note that an element in this region can also possess similarities to elements elsewhere in the Periodic Table. Zinc may hold the record in this context. In Chapter 9, the similarity of zinc (Group 12) to magnesium (Group 2) by the (n) and (n + 10) relationship is discussed, a linkage also reported by Laing [17]; while Massey has pointed out similarities of zinc with beryllium (Group 2) in compound formulas [18]. Massey also found similarities of zinc with gallium in chemical behavior (though not formula) [19].
The comparative chemistry of the zinc–tin(II) certainly provides several similarities.
•Zinc and tin(II) exhibit amphoteric behavior, their hydroxides dissolving in excess hydroxide ion to form zincates and stannates, respectively.
•Aqueous solutions of their divalent chlorides hydrolyze to give insoluble Zn(OH)Cl and Sn(OH)Cl.
•In the presence of high chloride ion concentrations, the chlorides give parallel chloro-complex ions: and and and
•Zinc and tin(II) form dialkyls of the form R2Zn and R2Sn (though the zinc series tend to be monomeric while the tin(II) compounds are polymeric).
Though some compounds of polonium(VI) are known, polonium, like bismuth, prefers lower oxidation states. There are a wide range of compounds of polonium(IV) together with some compounds of polonium(II). It was noted by Brasted over 45 years ago [20] that polonium bore little resemblance in its chemistry to tellurium and instead that polonium(II) behaved more like lead(II) of Group 14. Curiously, in one respect, polonium(II) has a resemblance to zinc(II): that is, polonium forms volatile dimethylpolonium(II), (CH3)2Po [21] analogous to (CH3)2Zn.
Despite Brasted’s claim of a link between polonium(II) and lead(II), there seem to be more similarities between polonium(IV) and tin(IV), than polonium(IV) and lead(IV). Following are examples of some matching formulas.
•There are matching chlorides and hexachloro-ions, SnCl4 and PoCl4, and [SnCl6]2− and [PoCl6]2−.
•The only solid stable nitrates of both metals correspond: Sn(NO3)4 and Po(NO3)4.
•There are matching oxides in the +4 oxidation state: SnO2 and PoO2.
Melting Points of Some Copper(I)–Indium(I) and Indium(III)–Bismuth(III) Halides
Laing [1] noted close-matching melting points among the following halide pairs: AgCl/TiCl; AgBr/TlBr; CdI2/PbI2; ZnCl2/SnCl2; and GaCl3/SbCl3. The question arises whether such patterns are pervasive, or just found for a few selected cases. Here, as an example, the melting point series are provided for the halides of two double pairs, copper(I)–indium(I) (Table 10.5) and indium(III)–bismuth(III) (Table 10.6).
Table 10.5 Melting points of corresponding copper(I) and indium(I) halides
Table 10.6 Melting points of corresponding indium(III) and bismuth(III) halides
As can be seen from the data earlier, there are no clear patterns among these K-M pairs. Nor could any consistent pattern be found for any other K-M pairs.
The Knight’s Move Relationship and the “Inert Pair” Effect
Having established that there is indeed a K-M relationship, the question needs to be asked as to the reason for it. Laing attempted to answer the question [1]:
Is the “knight’s move” merely a special case of the “inert pair effect” applied to metals with a d10 electron configuration?
The Inert Pair Effect
First, a digression onto the definition of the “inert pair” effect. This phenomenon was first described by Sidgwick in 1927 [22]. The observation was concisely explained by Orgel [23]:
Many B subgroup [main-group] metals exhibit a stable valency two smaller than the group valency. This tendency is most pronounced for thallium, lead, and bismuth and is also important for many lighter elements such as tin and antimony.
The contention then, is that, in the cases of ionic bonding, the ns2 electrons are significantly more tightly bound than the npx electrons. Or to reverse the statement, the npx electrons are more easily removed. For example, the noble gas core electron configuration of tin is: [Kr]5s24d105p2; the configuration of the more common ion, Sn2+, would be [Kr]5s24d10; and that of the less common ion, Sn4+, would be [Kr]4d10. The prevalence of the tin(II) ion would therefore be attributable to the inert pair effect.
However, with many of these compounds, the bonding is believed to be more covalent than ionic. Drago developed an explanation of the inert pair effect in terms of the low bond enthalpies of the heavy p-block metals [24]. Laing, himself, recognized this problem [1]:
There is more behind the knight’s move than meets the eye. We are dealing here with an extremely complex phenomenon, not easy to explain. … Nevertheless, application of the idea of the knight’s move among metals with d10 configurations on the bottom right hand side of the Periodic Table leads to many correct predictions that would not be made by applying the usually accepted trends in the Periodic Table.
“Inert Pair” as a Relativistic Effect
It is relativistic effects, first mentioned in Chapter 2, that provide the most logical explanations for most of the inert pair phenomenon [25–27]. When electron relativistic effects are considered, the energy of the electrons in the s-orbital drops significantly, that is, the electrons are more tightly bound to the nucleus. This pattern is shown in Figure 10.5 for tin and lead.
As can be seen, there is a small (yet significant) decrease in the energy of the 5s orbital for tin while there is a dramatic decrease in the energy of the 6s orbital for lead, that is, the 6s2 electron pair is exceptionally strongly bound to the nucleus. Thus, it would seem that there is indeed a satisfactory explanation for most aspects of the knight’s move relationship.
Commentary
The indication of a periodic pattern is the consistent applicability of a phenomenon to a subset of the Periodic Table of Elements. On this basis, the justification of the knight’s move relationship should be made primarily on the basis of similarities in formulas and chemistry of compounds of knight’s move pairs of elements in the lower right quadrant of the Periodic Table.
Though there are a few specific resemblances in melting and boiling points among pairs of “Knight’s Move” compounds, they are not widespread and consistent enough to be regarded as evidence of a systematic pattern. Thus, it is the chemical, rather than the physical, properties that should be emphasized as evidence for this relationship.
References
1.M. Laing, “The Knight’s Move in the Periodic Table,” Educ. Chem. 36, 160–161 (1999).
2.J. Shorter, “Vernon Harcourt: A Founder of Chemical Kinetics and a Friend of ‘Lewis Carroll’,” J. Chem. Educ. 57, 411–416 (1980).