A Taxonomy of Relationships among the Elements Ronald L. Rich 112 S. Spring St., Bluffton,OH 45817-1 112 How do chemical properties depend on the fundamental characteristics of atoms? I n what ways can we compare elements with each other in order to discern the various patterns ofrelationships that exist among them? To answer such auestions we need to identifv the fundamental factors and then consider the possibilities of keeping some constant while varying others. A systematic analysis should help writers a s well a s teachers. We must emphasize, however, that this paper is presenting not another taxonomy of the elements themselues, i.e., another periodic table, but rather a more abstract taxonomy of relationships among the elements. At the most fundamental level, the chemical properties of charged or uncharged atoms depend almost entirely on (1)the number of protons and (2) the number and (3) the arrangement of electrons. In the ground states, the latter arrangements deoend onlv on the first two factors. Excitations can be complex, but it is often possible and convenient to consider the confieuration ofeledrons as a single varameter that is partly &dependent of their numbe; w e thus have essentially the three most fundamental factors just listed, or only two in the absence of excitation. To use the periodic table, however, we must handle the one-dimensional atomic number as a function of a period number, to be called P here, and a family or group number, here designatedF .We may choose to write F (Zn), e. g., a s d l 0 or 12, (or 11, IIA, IIB, M2, 12d, T12 ...), but without affecting the present analysis of types of comparisons, somewhat as radius ratios may be discussed without selecting the "meter" or "stadium", etc., a s the unit of radius. For ions and other species we also need the valence number or oxidation state, here called V. For comparisons of ground-state species we will then consider P, F: and V, oRen studyingseries in which two of these are constant. We wish to speak of isoperiodic series (labeled PI, isofamilial Where two parameters series (F), and isoualent series (V). are constant, we can use combined labels such a s FV. We need, moreover, to look a t series whose members have the same type of outer-electron structure, such a s (n l)d10ns2.Let us call these isotypical (TIand speak of a Partially presented at the 20th ACS Midwest Regional Meeting, Southern Illinois University, Carbondale, IL, 1985 Nov. 6-8.
828
Journal of Chemical Education
corresponding parameter, T, which depends mainly on F and V but also somewhat on P. (The number of outer electrons depends, of course, only on F and V. Neutral Cr and W atoms thus have six outer electrons each, but with a slightly different arrangement in the ground state. ) For the example given, we may say that T = (n - l)d10ns2. The term isostructural ( S ) could be used instead of isotypical but will refer here to a n identity of surrounding atomic, rather than outer electronic, configurations. (We should note that Ni(I1) and Cu(I1)species, for example, may be isostrudural, or nearly so, with some ligands but not others.) We see that isoelectronic series are already included, under the label PT (or TP);also the PF series could be called isoelemental, a t least with reference to the main element of interest, if we want to use that term incontrasting, say, Fez+and Fe304.Yet another property that could be kept constant is the overall ionic charge, 2, as with, say, Fe(CNIGs and Pod3- but this depends in turn on V and S (through the number and charge of the ligands) and is likewise not treated as independent in this paper. (Would isochargic, by the way, be a proper term for Z?) The radius is a n important parameter, however, that chemists customarily and usefully treat as fundamental even though it depends on the others (and partly because the dependence is not simple). Let us write R for isoradial series that are chosen for having similar (within perhaps 5 %), but presumably never strictly constant, R. Disagreements on reported radii will of course lead to some differences on which series are isoradial. Again, however, for the present analysis of the possible types of comparisons, no establishment of canonical sources is required or even desirable. Some other parameters, for example, ionization energy, may be better treated here as entirely dependent chemical properties even though they, in their turn, may be taken a s fundamental when dealing with, say, redox potentials. Ifwe hold constant only one of these six parameters, P, F: V, I: R, or S, we find unwieldy classes of atoms and monatomic ions, together with derived species in which these parameters are the focus of interest, but in which there is hardly enough chemical similarity to support a discussion.
FVTBS
Examples:
I
PVTS
1
P: PHs, ClW (isoperiodic); F: CORL, PbZ+(isofamilial): V: NO;, ThCI4(isovalent); T: Hg, Sb3+(isotypical); R: T-, Au+ (ismadial);and S: CCL, FeC14~(isostructural).
Even if we keep two variables constant, great hetemgeneity usually remains. Most often, therefore, useful chemical comparisons assume the constancy of a t least three parameters. We do have, however, a number of series, or a t least pairs, which show notable chemical similarities in spite of having constancy in only one or two variables. Two examples might , ~ Al(H20,$.; and 2 , VS: Cu'. and be: ( 1 , T: R e ~ H , O and Cd'+ risostructural only in some environments .The similarities of the first lund are normally ascribed to the cornoensatow effects of Vand N in a con~binrdfunction such a s ~"IR"; those of the second sort may arise from similar effects with T and R, for example. (Even if some describe the compensation as fortuitous, we may still want to look a t it.) To permit encompassing these interesting series resulting partly from the interplay of two (or more ) properties, none of which alone is (nearly ) constant, we shall simply refer here to isocharacteristic series having a constant characteristic C, under the catch-all label C. We could say isodiagonal (referring to the periodic table), but the isoradial series would also often be isodiagonal, and we wish to include pairs like Mg2' and MnZ+,where the diagonal would a t least be unconventional. Two further examples may establish the real need for this broad category. Ag+ and %Hg? are only isovalent, in the present approach, unless we recognize that their similar behavior toward halide and pseudohalide ions and other precipitants, as well a s toward reducants and other reaeents. points to a close relationship in some further und&lying but composite property This relationship, often closer than those with other neighbors in the periodic chart, appears to be derived from a certain compensation as we move simultaneously to a different column and a different row in that chart. We thus classify the two ions mentioned a s VC. Finally we just mention the polyborates and polysilicates, which would be only isotypical without acknowledgment that they share a n additional fundamental similarity related, as in the previous case, to their closeness on a diagonal in the periodic table. We label them TC We now have seven parameters: P, F, V, I: R,S, and C. Taking S and two others to be constant a t a time, we seem to have 15 useful combinations. Usually, however,
FVS = FTS = VTS = FVTS but the other 12 ternary combinations do define 12 different groups, which is one reason for eliminating neither F, Vnor T from consideration. Of these 13, the most important combinations appear to be eight, namely: FVTS, PFS, PVS, PTS, VRS, TRS, VCS, and TCS. Examples will be given of these, and of PRS, FRS, and a few non-S sets. Readers may wish to consider the remaining combinations with S: PCS, FCS, and RCS. If we look for more than three parameters to be constant a t one time, we do not findmany actual examples, although
............................ TBS PIIS P. PH#W PFa- (PNWr ..................... .... ............................ /:. En>+ .... V(CO).. V + VS+ V02+ vo,+ +&+ .... Sn4;..-. ............................ 'Lit --...Cd'+.'-. Fe(CN).'- R(CN).'.'+%+ --.p+".. is+ PV and PVS
.Nd
............................ SnF.
TsF,
..
XsF.
............................ C.+ ' ... v.+ ... PI'* ... Cu" ............................ UO,'*
NpO12t
PuOlZ4 AmOl'*
'.. SEl+
---p.p'+?-..
.....a*+'... nr.+ *..
.
..
=ha+
-..
VCS m-d VC ~ - --
..
-
....
