Reexamining the Diagonal Relatinnshin~ Timothy P. Hanusa Vanderbilt University, Nashville, TN 37235
Chemical similarities between the first-row elements and those diagonally to their lower right (e.g., Li-Mg, Be-A1, BSi) have been recognized since a t least the 1860's (I). As an illustration of the anomalous chemical behavior of the firstrow elements relative to their heavier congeners, the "diagonal rule" is still included in the descriptive chemistry sections of many general and inorganic chemistry textbooks (2), and practical uses of the concept have been recentlv described (3). A widely used interpretation of the diagonal phenomena was proposed by Cartledge (4), who suggested that the relationships stem from agreement in ionic potentials ($), 6 = Zlr
where Z i s the charge on the ion and r is the ionic radius. The actual numerical agreement between the potentials for the traditionally paired elements, however, is poor. With Pauling radii, for example, the ratios $(Li+)/$(Mg2+), $(Be2+)/ $(AIH), and $(B3+)/$(Si4+) (all ideally 1.0) are 0.54,1.1, and 1.5, respectively (5). Using Shannon effective ionic radii optimized for CN = 4, the three ratios are 0.48,0.96, and 1.8, respectively (6). Certainly a major reason for such discrepancies lies in the absence of any ability by an ionic model to account for covalent character in the compounds, a shortcoming that is especially serious for species with high formal charges (e.g., "B3+","Si4+"). Neglect of covalency might not he as serious with the Be2+/A13+group (or rather, the polarizing ability of each cation might be more nearly equal), and its ionic potential ratio is in fact closer to unity. However, since many of the common compounds of lithium and magnesium are "classically ionic", failure to account for covalency cannot be used to rationalize tbe large @(Li+)/ $(Mg2+) error. In this case the source of the inaccuracy would seem to lie more with the pairing of Li with Mg than with the ionic potential analysis itself. An examination of a table of ionic potentials (Table 1) indicates that Li+ and Mg2+ could each be matched with several other ions more like themselves in potential. If one of the larger alkaline earth metal cations were coupled with Li+, for example, the agreement in potentials would then range from 0.85 (@(Lif)/ $(Ca2+)) to 1.1 ($(Li+)/$(Ba2+)).The Mg2+ ion, in turn,
might be paired with a number of other species, including Y3+,most of the trivalent lanthanides, and Zn2+.Additional "nonconventional" combinations also suggest themselves: the potentials of Sc3+ and Th4+, for instance, are nearly equal: $(Sc3+)/$(Th4+) = 0.95. That all such alternate groupings are not simply arbitrary fixes for an inadequate theory is indicated by the fact that many facets of the chemistry of Li+ can be correlated just as readily with those of Ca2+,Sr2+,and Ba2+as with those of Mg2+; the same is true of the alternate weirs for Me2+.The most extensive illustrations of this cor;rlntion are"a\.ailable for the Li- Cadspair. but reasonahle amuunts of data for the Me2'A"' and Sc,-/ " Th4+grollps can also he gathered.' Table 2 lists a number of comparative benchmarks between the chemistry of Li, Ca, Mg, Y, Sr, and Th. I t should be apparent that many of the chemical properties that could be cited as illustrations of a diagonal relationship between Lif and Mg2+,for example, apply with equal, if not greater, force to Li+ and CaZf. Electronegativities, reduction potentials, and especiallv the thermodvnamic stabilities of manv compounds bf the new pairs are generally more nearly equal than with the traditional groups. In some cases, the differences can be dramatic: with ;he metal hydrides MH,, fop instance, the dissociation pressure of Hp above LiH, MgH2, and CaH2 reaches 10 mm a t 550 "C, 85 OC, and 885 "C, respectively (14). Better correlation of all properties is not uniformly found, but the general trends seem to be clear.2
'The poor agreement between the Li+lMg2+potentials and the improvement offered by a Lif/Ca2+match has been noted before (see ref Za, p 130, footnote 2); the consequences of this were not pursued, however, since the blame for the anomaly was laid on deficienciesof the ionic potential approach rather than on the association of Li+ with Mg2+. The relative insolubilities of the phosphates, fluorides, and carbonates of lithium and magnesium are oiten mentioned as evidence of the diagonal relationship between them. This is somewhat misleading, since these salts are "insoluble" for all the metals Mg-Ba. In addition, the solubility of a compound depends upon a complex set of thermodynamic terms, none af which are simply related to the ionic potential. For further discussion of this point, see ref 15.
Table 1. lonlc Potentials 01 Common Cationsa Ion Z/r
Ian Z/r
17 (4) 10 (4) 7.3 (4) Fib+ 6 6 (6) Cs+ 6 0 (6) NH,' 7 33 pH,+ 6.4b Me4Nt 5.0"
Be2+ 74 (4) Mg2+ 35 (4) Ca2+ 20 (6) Sr2+ 17 (6) Ba2+ 15 (6)
Lit Nat Kt
Ion Z/r
sc3+40 (6) Y3+ 33 (6) La3+ 29 (6)
Ion Z/r
Ion Z/r
Ion Z/r
Zn2+ 33 (4) Cd2+ 21 (4) Hg2+ 21 (4)
B3+ 273 (4) AI3+ 77 (4) Ga4+ 64 (4) In" 44 (4) TIs+ 40 (4)
C4+ 267 (4) Si4+ 154 (4) Ge4+ 55 (6) Sn4+ 58 (6) Pb4+ 34 (6)
Lanthanides: (Ln3+. CN = 6): 30(Ce3+)-35(Lu3+) Actinides: (An4+, CN = 6): 43(Th4+); 45(U4+)
'Except where indicated. Shaman effective atomic radii are used (61: me cowdination number of the ion is in parenthere. following the patentiai. bThermochemical radii (7).
666
Journal of Chemical Education
Table 2.
Comparative Physical and Chemlcal Propertles 01 LI-Ca, Mg-Y, Sc-m, and Thelr Compounds
Ca
Li
Mg
T h e i m p r o v e d fit hetween the chemistry of the inorganic compounds of Li and Ca extends tosome of their organumetallic as well (16. ds ~ - ~ comnlexes - - ~ . . c ~ ~ m m ) u n of , . 17). . The RMtX) all three metals can function as alkylating agents, hut many alkvl lithium and alkvl calcium halide com~lexesare unstab1e"in ethereal solvents (diethyl ether, T*) (la),whereas diethvl ether is a standard medium for the ~ r e ~ a r a t i oand n storage of Grignard reagents. carbonation-of rign nard reagents to produce carboxylic acids is a straightforward and high-yield procedure, hut the reaction of C O 2 with hoth Li and Ca complexes is more complex, and ketones and various alcohols can be found upon workup The parallels extend to more exotic examples as well: hoth phenyl lithium and phenyl calcium iodide, for instance, react with nitrous oxide to form the diazotates Ph-N=N-OLi (19) and Ph-N=N-OCal (20), respectively; Grignard reagents do not react with the gas (19). ~
~
~
.~ ~
~
Y
m
SC
Ref
equal potentials should he considered when attempting to correlate their physical and chemical properties.
~
(In.
Organometallic parallels between magnesium-yttrium and scandium-thorium systems are not as readily found, primarily because the chemistry of the latter three elements is not as extensively developed as that for magnesium. T h e compounds [ ( C 5 H 5 ) M g H ( T H F ) ] 2 (21) a n d [ ( C 5 H 5 ) 2 Y H ( T H F ) ] 2 (22), however, are hoth strongly hydridic, and (C5Me5)~ScH(THF) (23) and [ ( C 5 M e 5 ) 2 T h H 2 ] 2 (24) react readily with alkenes to yield alkyl complexes. From all of the above. it should he a.~.~ a r ethat n t -moper matching of ions is critically important to the evaluation of the validitv of an ionic ~otentialanalvsis of their chemistry. Only those sets of ionsihich in fact possess approximately
1. Ihde, A. J. The Development ofModorn Charnirery;Douer: New York, 1984; p 247. 2. See, for exempl.: (a) Huheey,J. E. Inorganic Chemistry, Principles of Structure and ReorfiuiQ, 3rd ed.: Herper and Row: New York, 1983;pp 129 fC lbl Petrucei, R. H. Genarol Chamisfrv. Princidm and Modern A~irlicalions. 4th ed.: MacMillan: New .. York, 19% p373: 3. Feinsfein, H. I. J. Cham. Edue. 1984.61.128. 4. Cartledge, G. H. J.Am Chem.Sor. 1928.50.2855.2863; 1930.52.3076. 5. Psu1ing.L. TheNolun ofthe Chrmirol Bond, 3rd ed.; CorneilUniverslty: Ithsca.NY, 1960, p 514. 1976,A32,751. 6. Shannon. R. D. Aero Cryalollo~~. 7. Jenkin8.H. 0. B.;Thakur,K.P. J. Chem.Edue. l979,56,576. 8. Calculated vaing Peuling's procedure; see: Allred, J. L. J . Inorg. Nucl. Chem. 1961.17, 215. 9. Al1red.J. L.: Rochow, E. G. J. lnorg. Nucl. Cham. 1958.5.264. 10. Weast. R. C., Ed. Handbook 01 Chemiatry nnd Physics, 67th ed.; Chemical Rubber Comoanv: Cleveland.. OH. 1986: o 0.158. 11. Ref 1 0 , b pE-76, E-77. 12. Ref 10. pp 0-57-0-92. 13. Sanderson, R. T. Inorganic Chem'xtry: Van Nastrsnd Reinhold: New York, 1967: PB 16&356. Oxford, 19W 14. Greenwood,N. N.;Esrnshaw.A. Chemhfryo/theEI~menfs;Psrgamon: p 72. Ch~rnistw. 15. Johnson. D. A. S o n Thermodvnomic Aaoaeta of Inolponic .. 2nd ed.: camh;idge Uniuemity: Cambr;dge, 1982; chapter 5. 16. For a review olorganoalkalinc earth chemistry, see Lindsell, W.E. In Comprehensive Organomefcdlic Chemistry; Wilkinson, G.: Stone, F. G.A.;Abel, E., Eds.;Pergamon: Oxford, 1982; Vol. I. Chapters 3.4. 17. Bryce-Smith, D.;Skinner, A.C. J . Chem.Sor. 1963.577. 18. Gilman, H.:Schwebke, G. L. J. Orgonomat. Chrm. 1985.4.483. 19. Berineer.F.M.:Fsrr. J.A.:Sands. S. J . Am. Chom.Soc. 1953.75.3984.
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..
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23. Thompon. M. E.; Berunu. J. E. Pure Appl. Chem. 1984,56(11, 1. 24. Fagan,P.J.;Manriquez, J.M.:Mastta,E.A.;Seyam,A.M.;Msrks.T.J. J.Arn. Chem. Soc. 1981,103,6650.
Volume 64
Number 8
August 1967
887
