Chemical Education Today
Letters The Role of Triads Since 2004, Eric Scerri has championed at least three different arrangements for the periodic table (1–3). Now in a recent article (4), he presents his new proposed arrangement of the periodic table as his Figure 3 (reproduced as Figure 1, below). This is a left-step-Janet table with H and He moved from above Li and Be to above F and Ne. Scerri is quite clear about his criterion for pursuing this arrangement: it gives a “completely new perfect triad (H, F, Cl)” (4, p 588). He applies the term “perfect” to triads in which the atomic number of the middle element is exactly one half of the sum of the atomic numbers of the first and third elements. An example of a perfect triad is the classic case of Cl, Br, I. But surely this triad (H, F, Cl) is not “new”; there have been many periodic tables over the years with H above F and Cl, as well as He above Ne. What is important is the number of “perfect” triads that are within the table. It is immediately obvious in Figure 1 that with the lanthanoids jutting out to the left, no triads are possible for elements La to Yb. One can try Sc (21), Y (39), Lu (71). It fails. One can try Sc (21), Y (39), La (57). This is a “perfect” triad. Does this perhaps suggest a table with a different arrangement of the elements? One can try the halogens: F (9), Cl (17), Br (35). This fails. Is there a different third element El (Z)? Try F (9), Cl (17), El (Z). Z is (2 × 17) − 9 = 25. The element is manganese: a metal! Is this crazy? Not at all. Mn(VII) is tetrahedral permanganate, isostructural with perchlorate, both being oxidizing agents. This triad places Mn directly below Cl, which also calls for a table with a different arrangement. In fact this is the arrangement of elements in the 1871 periodic table of Dmitri Mendeleev, and it
is seen again in his table of 1905 and in the 1934 Periodic Table Monument in St. Petersburg (see ref 5 for an image of this and brief discussion). Of course, this set of three elements does not satisfy the spirit of Johann Wolfgang Döbereiner’s triads that the elements should show a smooth gradation in physical and chemical properties. (But is that true of H, F, Cl?) Recently Sami Ibrahim (6) has shown nicely how to estimate atomic weights of the trans-lawrencium elements starting with Y, Lu, and Lr, and ending at Z = 118. Here the triad concept is stepping out of the confines of the periodic table as it is currently arranged. Mendeleev also used a horizontal triad to give him information when he set out to predict the properties of the (as yet) undiscovered elements: Eka-B, Eka-Al, Eka-Si. He in fact discussed his technique using the horizontal triad As, Se, Br as an example to estimate the atomic weight of selenium (4). He also grouped the metals Fe, Co, Ni and their congeners in threes as “transition” elements in group VIII, and these metals are specifically labeled “TRIADS” (“ТРИАДЫ”) in Figure 6 of ref 5. One can try a horizontal triad among the lanthanoid metals: La (57), Gd (64), Lu (71). This is a “perfect” triad, and it reflects the physical properties of these metals. As a final example, consider Mn (25), Tc (43), El (Z). Z is (2 × 43) − 25 = 61 This element is Pm, which—like Tc—is radioactive, and does not exist in nature, and falls directly below Tc. This triad predicted something quite unexpected. None of the triads that are described above exist in the “new proposed periodic table” (see Figure 1). Worse still, the left-step-Janet layout has chemically similar elements widely separated. Consider Mg and Zn, Al and Sc, and of course Be, Al, Ti (7).
H He Li Be 1,2 B C N O F Ne Na Mg
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Al Si P S Cl Ar K Ca
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Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr
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Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba
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La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra
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Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr Rf Db Sg Bh Hs Mt Ds Rg
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Figure 1. The modified left-step-Janet table, which is Figure 3 in reference 4. The rightmost numbers are values of n + ℓ for each period (not principal quantum numbers).
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Chemical Education Today
Letters H
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Ne Na Mg Al Si P S Cl
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Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
Xe Cs Ba La Ce Pr Nd Pm Sm 54 55 56 57 58 59 60 61 62
Figure 2. A periodic table with the lanthanoids repositioned and incorporated into the body of the table. The series Li to F and Na to Cl and the inert gases are duplicated, thus increasing the number of patterns linking the chemical properties of the elements.
Eu Gd Tb Dy Ho Er Tm 63 64 65 66 67 68 69
Yb Lu Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86
Rn Fr Ra Ac Th Pa U Np Pu 86 87 88 89 90 91 92 93 94
Am Cm Bk Cf Es Fm Md 95 96 97 98 99 100 101
No Lr Rf Db Sg Bh Hs Mt 102 103 104 105 106 107 108 109
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There is a periodic table in the literature (8) that does have in it all of the above triads (as well as the classical diagonal relationship, which is entirely missing from the left-step-Janet arrangement). This periodic table is shown here as Figure 2. The triads F, Cl, Mn; Sc, Y, La; and Mn, Tc, Pm are there, as are H, F, Cl; He, Ne, Ar; P, As, Sb; N, P, V; Be, Mg, Ca; Mg, Zn, Cd; Ca, Sr, Ba; and Sn, Pb, 114. There are more triads, regular and irregular, even Y, Lu, Lr. Also well positioned are the elements La, Gd, Lu, as a “perfect” vertical triad, with the melting point and density of gadolinium falling nicely intermediate between those of lanthanum and lutetium. I conclude that there is no perfect ideal periodic table; you choose the periodic table that shows the most patterns and relationships and is most useful for your purposes; you get back from your periodic table what you put into it (9). I am pleased that Eric Scerri has reminded us of the significance of the concept of triads, and of their important role in the development of the periodic table, and of the power of triads to predict chemical properties of elements. Literature Cited 1. Scerri, E. R. The Best Representation for the Periodic System: The Role of the n + ℓ Rule and of the Concept of an Element as a Basic Substance. In The Periodic Table: Into the 21st Century; Rouvray, D. H., King, R. B., Eds.; Research Studies Press: Baldock, England, 2004; pp 148–152.
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2. Scerri, E. R. The Periodic Table: Its Story and Its Significance; Oxford University Press: New York, 2007; pp 283–284. 3. Scerri, E. R. American Scientist 2008, 96, 52–58. 4. Scerri, E. R, J. Chem. Educ. 2008, 85, 585–589. 5. Laing, M. J. Chem. Educ. 2008, 85, 63–67. 6. Ibrahim, S. A. J. Chem. Educ. 2005, 82, 1658–1659. 7. Bent, H. A.; Weinhold, F. J. Chem. Educ. 2007, 84, 1145– 1146. 8. Laing, M. Found. Chem. 2005, 7, 203–233. 9. (a) Laing, M. J. Chem. Educ. 1989, 66, 746. (b) Laing, M. J. Chem. Educ. 2001, 78, 877. (c) Laing, M. Patterns in the Periodic Table—Old and New. In The Periodic Table: Into the 21st Century; Rouvray, D. H., King, R. B., Eds.; Research Studies Press: Baldock, England, 2004; pp 123–141.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2009/Oct/abs1183.html Abstract and keywords Full text (PDF) Links to cited JCE articles Michael Laing 61 Baines Road Durban 4001, South Africa Professor Emeritus, University of KwaZulu-Natal
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Chemical Education Today
Letters Response to The Role of Triads: I am pleased to see how closely Michael Laing has been following my writings on the periodic table. He begins by suggesting that I have “championed at least three arrangements for the periodic table”. In fact I supported one arrangement, the left-step table, in my book (1), but have now changed my allegiance in favor of a new arrangement of the periodic table, which I proposed in this Journal (2). As I have stressed repeatedly, my concern is with alternative placements of troublesome elements such as hydrogen and helium and not with mere changes in shape of the periodic table. Of course I am not the first to move hydrogen to the halogen group as I acknowledged in my article (2). Let me turn to triads. Since the discovery of the periodic system, which was first hinted at by the discovery of triads of elements, many chemists have fallen prey to numerological pitfalls. One example, discussed in my book, was Ernst Lennsen who believed he had discovered up to 20 triads and even triads of triads. Most of these claims turned out to be spurious. The latest victim of this pitfall may be Laing. In criticizing my proposal of a perfect atomic number triad involving H, F, Cl, Laing suggests what he regards as many other viable triads, most of which I regret to say are not even contenders. But first let me explain what I take to be a valid atomic number triad such as Cl, Br, I. The existence of such triads is in no way mysterious and follows immediately from the fact that period lengths occur in pairs, with the exception of the first very short period (at least in the conventional periodic table). Valid triads are those that involve three elements, the second and third of which occur in periods of equal length on a left-step table. Thus Cl, Br, I form a perfect triad because the “distance” between chlorine and bromine is 18 elements, as is the distance between bromine and iodine. It is no surprise therefore that bromine falls precisely between the atomic numbers of the first and third member of the triad. So the fact that Sc (21), Y (39), Lu (71) fail to form a triad, as Laing points out, is not so startling because Y and Lu occur in periods of unequal lengths. Alternatively, Y (39), Lu (71), Lr (103) do form a triad and this is significant because the second and third members belong to periods with 32 elements.1 Moreover, Ibrahim’s triads are consistent even if they involve “stepping out of the confines of the table as it is currently represented” (4). But it is precisely the representation of the elements that I am questioning in my article. Moreover,
this is surely an inconsistent criticism because Laing goes on to propose a periodic table that is rather far from what is currently presented. Laing also proposes some horizontal triads such as La (57), Gd (64), Lu (71), which he claims to be physically significant. But such horizontal triads are also nonstarters because this and similar examples amount to claiming that [Z + (Z + 14)] ∙ 2 = Z + 7. Even more trivial would be the suggestion of a horizontal triad involving C (6), N (7), O (8) because this would be a case of [Z + (Z + 2)] ∙ 2 = Z + 1. The periodic table that Laing proposes may well incorporate these triads, which are spurious in my view, but it does so at a rather high cost given that as many as 21 elements are permitted to occur in more than one place. Contrary to Laing’s conclusion I do believe that it is worth seeking a perfect and ideal periodic table of elements because I take it that chemical periodicity reflects independently existing trends in nature rather than merely being an artificial classification designed for our convenience and as an aid to teaching chemistry. Note 1. This triad also lends support to Jensen’s proposal that group 3 should consist of Sc, Y, Lu, Lr, and not Sc, Y, La, Ac (3).
Literature Cited 1. Scerri, E. R. The Periodic Table: Its Story and Its Significance; Oxford University Press: New York, 2007. 2. Scerri, E. R. J. Chem. Educ. 2008, 85, 585–589. 3. Jensen, W. B. J. Chem. Educ. 1982, 59, 634–639. 4. Ibrahim, S. A. J. Chem. Educ. 2005, 82, 1658–1659.
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2009/Oct/abs1185.html Abstract and keywords Full text (PDF) Links to cited JCE articles Eric Scerri Department of Chemistry and Biochemistry University of California, Los Angeles Los Angeles, CA 90095
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