R. T. SANDERSON State University of Iowa, Iowa City
THIS paper describes a new chart representing the valence structure of atoms. By studying this chart, with the help of a few simple rules, students of elementary chemistry can acquire a useful understanding of chemical comhination. The fundamentals of the scheme are indicated in Figure 1. Each covalent bond formed by an atom requires both an unpaired electron and a low energy vacancy capable of accommodating an electron of another atom. To the trained chemist, it may seem redundant to specify both the unpaired electron and the vacancy, because as he knows, the word "unpaired" automatically implies the existence of the vacancy. The beginning student, however, needs t o have the requirements fully specified. This comhination of requirements for covalence is represented in Figure 1 by a black bar for the electron, with a har-shaped vacancy beside it. The depth t o which the bar, and the vacancy, are imbedded in the atom, represented as a shaded circle, shows the relative attraction of the atom for electrons. This attraction is known as the relative electronegativity, and varies from a minimum in the alkali metals t o a maximum in oxygen and fluorine. Thus, in Figure 1, an atom of low electronegativity (Na) is represented as having an outer electron only slightly imbedded, to show that this electron can he lost relatively easily, and having very shallow vacancies, indicating a corresponding lack of attraction for outside electrons. Conversely, an atom of high electronegativity ( F in Figure 1) is represented by deep penetration of its own electrons, showing them t o be tightly held, and deep vacancies, corresponding to strong attraction for outside electrons. Beginning with Period 3, although most commonly the elements utilize only the s and/or p orbitals of the outermost shell, the possibility of expanding the "valence octet" by promoting electrons to the outer d orbitals exists. Where this possibility can make an especially contribution t o the valence of an - important . element, the outer d levels are indicated schematically as an outer broken circle with five pairs of vacancies. In Figure 1, this is illustrated by phosphorus, wherein it is indicated that this element, with a "normal" valence of 3, can acquire the requisites for forming two more covalent bonds if one of the pair of electrons is promoted to the higher energy level. The nvailability of underlying d orbitals and electrons, which characterizes the transition elements, is represented as shown in Figure 1 for trivalent iron, by an inner solid circle indicating the appropriate number of electrons plus vacancies equal to ten. It is of course impossible t o depict three dimensions by such representations, but possible t o draw the atoms to scale. The diagrams in Figure 2 represent correct VOLUME 35, NO. 10, NOVEMBER, 1958
relative covalent radii, and the valence structure, of the atoms of 72 elements, together with the principal electronic configurations. Only the outer shell and the underlying (d) shell (when available) are shown in detail, and with maximum multiplicity (minimum electron pairing) as exists when the atoms are ready for chemical comhination. It is desirable that a beginning student learn something of s, p, d, and f electrons and orbitals, but not absolutely essential here. If he understands t,hegeneral significance of Figure 2, he can acquire much information from it, provided he keeps in mind the following rules.
SOME RULES OF VALENCE (1) An atom can form as many, but only &S many covalent bonds as it has combinations of unpaired outer electron and outer vaertncy. I n the transition elements, "outer" includes comhinations directly underlying the outermost.
(a) An atom tends to form the maximum number of covalent bonds of which its outor shell is capable, and normally no eombinatian of electron and vaoancy in this shell will remain unutilized when the atom unites chemically. I n the transition element,^, the mazrimnm number of covalent bonds includes those made possible through use of the underlying (dj electrons and vacanci~s,as shown in Figure 2. (3) An outer un~haredpair of electrons ran be used in the formation of two covalent bonds only if another pair of vacancies (orbital) in avnilahl,hle, to which one of the paired electrons can be shifted. Availability of such vacancies beyond the outer octet is shown in th? diagrams by broken lines. (4) An outer nnshared pair of electrons can be used in the formation of a single covalent bond if the other atom has a pair of stable vacancies (empty orhitd) available. Here both electrons are supplied by one atom, both vacancies by the other, and the electrons are attracted t o both nuclei. Such a bond is called R "coordinate covalent" or "donor-acceptor" band.
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(5) If the honded atoms were initially unlike in electroneeativitv. the elertrons formine the honds are imevenlv shared. crystals, and bond polarity in geueral exerts a very significant in-
about the n&bs as far apart as possible. This results in covslent bonds bcing directional, and the most common directional eharacterifities can be predicted simply and logically from this mle. Thus, when the outer shell electrons plus vacancies are 2-6, two covalent bonds can be farmed. The f a r t h e ~apart t two electron pairs can possibly get is on directly opposite rides of the nucleus. The experimentally determined fact is that such bonds are linear as predi~ted( s p hybrids, 180°). S i m i l d y , the farthest apart three elertron pairs (formed when the electronvacancies is 3-5) can bp is rtt the corners of an equilateral tri-
VALENCE STRUCTURE :
ELEMENTS
K E Y t Black b a r = electr-on,
protrusion = availability z.White well =vacancy f o r electron, depth = electrone~ativitc~. 3.Covalent radius shown by outer solid circle. 4. Inner solid circle = inner d level. s.Outer broken circle = o u t e r d level.
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angle planar with the nucleus. The actual bonds are indeed so directed (sp* hybrids, 120'). Four electron pairs (resulting from G4 electrons-vacancies) are farthest apart when they are at the corners of a regular tetrahedron, and this is the orientation of such bonds ( s p a hybrids, 109'28'). When the electronsvacancies are 5-3, or 6-2, the covalent bonds formable are only 3 or 2, but there are also unshared electron pairs, making in effect a t o t d of four electron pair8 which also tend to be tetr~hedrd. Although small deviations are observed, the angle between any
two such bonds is almost never less than 90".
USE OF THE CHART
With the help of these rules, a student cannot only predict, but also begin to understand, the valence of the elements as it results from the structures indicated in Figure 2. Thus he can see that an atom of hydrogen can only form one covalent bond and then its maximum capacity is used. He can understand why hydrogen atoms combine into HZ molecules, and why they cannot join to other atoms until the bond in Hz is broken. He can also observe that hydrogen is intermediate in electronegativity and therefore can be expected to become partially negative in combination with elements of lower electronegativity-mostly metalsand partially positive in combination with elements of higher electronegativity. He can see that helium atoms not only have no unpaired electrons and no vacancies in the outer shell, but also hold their electron pair so tightly that it is unavailable for coordinate bond formation. Hence helium is chemically inert. Lithium as depicted in Figure 2 can form a single covalent bond but its vacancies are not very stable and its electron can relatively easily be removed. In combination with almost any other element, the lithium will therefore become positive, and ionic when the other element is strongly electronegative, as, for example, fluorine. Beryllium is shown to be able to form just two covalent honds, but might begin to use its vacancy pairs as electron acceptors in coordinate covalence. The two covalent bonds are of course linear, hut if four electron pairs surround the beryllium, as in its coordination complexes, the structure must normally he tetrahedral. Boron, as depicted in Figure 2, has the capacity to form three, planar covalent honds, and furthermore has an outer pair of vacancies (orbital) able to accept an electron pair from some other atom. Of course, if it does so accept, this fourth electron pair forces the other three out of their positions in the same plane with the boron nucleus, and the structure becomes tetrahedral. The characteristic tetracovalence of carhon is readily understood from the diagram, and the characteristic structure from rule 6. The absence of both unshared electron pairs and vacancies, when the carhon has formed four bonds, shows that tetracovalent carbon can have no coordinate covalence. The electronegativity, somewhat above the median, shows that carbon, in combination with metals, can hecome negative, but in combination with hydrogen it is only very slightly negative and with more electronegative nonmetals it is positive. It is clear from the diagram of nitrogen in Figure 2 that although each atom has five outer electrons, VOLUME 35, NO. 10, NOVEMBER, 1958
only three can become involved in ordinary covalent bonds because only three vacancies are available. When nitrogen has formed three covalent bonds, however, there is still a fourth electron pair, unshared. The three bonds are therefore not planar but a t nearly tetrahedral angles, the extra pair occupying the fourth space. This extra pair allows the nitrogen to serve as electron donor in forming a coordinate covalent. bond. As shown by the oxygen diagram, an oxygen atom can only form two covalent bonds, but it has two electron pairs that allow combined oxygen to serve as electron donor. Normally only one pair so functions a t one time. It can be seen that here is a highly electronegative atom that becomes negative in practically all its compounds. Fluorine has only the ability to form one bond, and the three unshared electron pairs are so tightly held as to be unavailable for coordinate covalence (except when made more available through acquisition of high negative charge by the fluorine). As shown by the high electronegativity, fluorine is negative in all its compounds, without exception. Neon, like helium, is shown to hold its electrons too tightly for sharing, and there are neither single electrons nor vacancies permitting ordinary covalence. From here on, the trend through calcium follows the preceding one, except that electronegativities are lower in this third period, and also that with the increasing nuclear charge, the possibility of utilizing electron vacancies beyond the shell of eight increases. Thus even aluminum and silicon may coordinate more than four other atoms, and in phosphorus, the "unshared pair" can split, forming two more covalent honds and bringing the number of shared electron pairs to five. In sulfur, both the unshared pairs can likewise split to give hexavalent sulfur. No chlorine atom forms seven single covalent bonds, but a t least one of the unshared pairs can split to form two more single honds for a total of three, and in all these elements including chlorine, vacancies beyond the outer eight can be used in multiple bonding (where more than two electrons are used per bond). Therefore the extra vacancies possible are indicated in the dotted outer circles in Figure 2. Students should bear in mind that the availability of these extra vacancies for stable bonds increases with increasing withdrawal of electrons from the atom, which means that the higher valences tend to be shown when the element is combined with the more electronegative elements. Skipping, for the present, the transition and copper and zinc groups, students can see that beyond major Groups I and 11, there is a notable change in the electronic configurations from period 3 to period 4. This is a change from an inert element structure to a shell of 18 electrons, immediately underlying the valence shell. Although the valence shells are sufficiently similar to justify inclusion of these elements as "major group" elements where it is convenient to do so (from Group I11 on), the underlying difference produces an increase in electronegativity, as shown in Figure 2, that prevents these 18-shell elements from continuing all the chemical trends begun from period 2 to period 3. In these elements again exists the possibility of using vacancies beyond the outer octet,
and in Figure 2 this possibility is represented by the dotted circles. Studying Figure 2 as a unit, a student can begin to acquire a real understanding of chemical periodicity from the viewpoint of both periodic trends and major group similarities and variations. One irnportant lesson to be learned from this figure is that the tendency of active elements to become, through chemical combination, like the inert elements in electronic configuration is more a convenient coincidence than a fundamental incentive to reaction. Many elementary chemistry books overwork this convenience, implying that active metals actually seek t o lose electrons, and active nonmetals to gain them, for lo! by so doing they "become like the inert elements." In fact, of course, no element comes close to complete inertness through achieving, actually or "in effect," the electronic number of an inert element. Furthermore, it requires about 90 kilocalories per mole to remove the loosest electron of any atom, that of cesium, despite the fact that the cesium ion is isoelectronic with xenon. Moreover, energy must he expended to persuade an oxygen atom to become an oxide ion, even though this ion is isoelectronic with neon. This does not mean that the "inert gas number" concept is not useful, hut only that its real significance ought not to be misunderstood. A fluorine atom, with its great initial attraction for an electron, stops when it has acquired one, for two reasons. F i s t , by acquisition of an extra electron, its attraction for electrons has been greatly reduced. Second, there just is not any other vacancy that could accommodate a second electron. The latter fact is of course related to the stability of a shell of eight but not specifically to the resemblance to neon, which actually is not very close because of the difference in nuclear charge. Similarly, as can be seen from Figure 2, the alkali metals, which lose electrons most easily, lose only one electron because all the others are held too tightly, in a more stable energy level, and are held even more tightly when the one is lost. Quite unlike the isoelectronic neon, sodium ion can attract and hold electrons. Also, consider a carbon atom attached to four other atoms of equal electronegativity by covalent bonds which therefore must be nonpolar. Even if the valence electrons are evenly shared, there can hardly he a close similarity of carbon to neon which has the same numher of electrons all to itself. Carbon does not unite to "become like neon"; it forms four and only four bonds because it possesses the requisites to form four and lacks the requisites for forming more than four. Indeed, if sharing were a satisfactory substitute for acquiring, t,he diatomic molecules of the halogens would be inert.
TRANSITION ELEMENTS
It is more difficult to represent the valence structures of the transition elements in an adequately meaningful way, because of the idiosyncracies of these elements both as a class and individually. An attempt is made, however, in Figure 2. Here electronegativities are only approximated because although the values are believed to be of similar magnitudes, most are not accurately known. The maximum valences are equal to the total number of electron-vacancy combinations in each diagram. There seems as yet to be no simple or consistent rule for predicting when or whether a lower oxidation state will result or under what conditions. Indeed, the most stable oxidation states in binary compounds of the transition metals with oxygen are not always the same as those with fluorine, and there are other differences among the different halides. Furthermore, the oxidation state does not necessarily tell the number of bonds; e.g., chromium(I1) chloride is Cr2C1, in the vapor even a t 1500". One can only make the general observation that the first member of a transition group is more stable in lower oxidation states, and less stable in the maximum oxidation states, than the next two members, especially the third. It may also he observed that the tendency toward maximum valence in preference to lower valence is greatest in the scandium group, which never exhibits lower than plus three states in its compounds, and diminishes across the periodic table, iron, cobalt, and nickel never forming the theoretical maxima of covalent bonds. The copper group elements are diagramed as transition elements despite the usual assignment of 18 electrons in the next-to-outermost shell. This is because these elements clearly exhibit transitional properties, with oxidation states greater than plus one, in addition to having some rather unique properties of their own. But other than convenience, there is no justification whatever for the common classification of the zinc group as transitional. These elements are clearly 18-shell elements, using only the outermost principal energy level for valence, and zinc, for example, bears exactly the same kind of relationship to magnesium as gallium to aluminum and germanium to silicon. The valence structure of ions has not been included in Figure 2 as such, but in most cases it can easily he inferred from the structure of the corresponding atom. An instructor can easily prepare an extensive list of questions about valence and the prediction of both formulas and properties of compounds. Practice in answering these with the help of this new chart should be extremely instructive and useful to students learning chemistry.
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