The role of electrons in interatomic relations

Similarly, I think you will agree that the effect of the work of diplomats cannot be reliably predicted while ... istry, it seems best to confine my c...
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THE ROLE OF ELECTRONS I N INTERATOMIC RELATIONS' WILLIAM F. EHRET New York University, New York

IP THE t i t l e of this talk had been "The Role of Diplomats in International Relations" we all mould know what to expect. We have long been familiar with the duties of these agents, how they act as gobetweens and are instrumental in cementing such ties as may exist between nations. My topic today, "The 'Role of Electrons in Interatomic Relations" bears more than a rhetorical resemblance to the one I have just mentioned. Electrons are also the gobetweens, one might say the "diplomats," in the ties that are formed between atoms in the various types of compounds we recognize today. If one pursues this analogy further, however, one soon comes upon a number of differences. For instance, diplomats are very real and tangible, whereas individual electrons are still considerably beyond human perception. Similarly, I think you will agree that the effect of the work of diplomats cannot be reliably predicted while that of electrons may be foreshadowed with a high order of accuracy. Furthermore, diplomats enjoy the privilege of roving about without restriction; a n electron could do this only if it were in a perfect vacuum and at infinite distance from other charges. The subject to vhich I have addressed myself is as broad as chemistry itself, for all chemical reactions involve electrons. Therefore, it becomes necessary to limit the discussion to that part of chemistry which is appropriate to the occasion, and which can be dealt nith in our limited period of time. Since most of us are concerned with the teaching of elementary chemistry, it seems best to confine my comments largely to the part played by electrons in the formation of simple compounds by combination of the elements. This necessarily shelves a number of important types of reactions such as the acid-base and complicated changes involving oxidation and reduction. I n making my choice of materials I have tried to bear in mind a comment I overheard last winter a t a chemistry teachers ' Presented before the Ninth Summer Conference of the N.E.A.C.T. at Wellesley College, August 20, 1947.

meeting. The speaker's topic was "The Atom and Its Electrons" and he proceeded to introduce various ideas from wave mechanics and data obtained from spectroscopic observations. Before long a high-school teacher whispered to his neighbor facetiously, "I'm going to tell this to my kids first thing in the morning." It is not my intention, however, to provide you with a lesson plan that is watered down to the twelfth year level, for such a scheme, like all lesson plans, would be useful only to the person who drew it up. I n teaching this subject we must, each one of us, work according to a plan that is bLed upon our own knowledge and is patterned accordmg to the previous training of ourstudents. As we survey the field of simple combination reactions between atoms, we notice immediately that two kinds are possible: between like atoms and between unlike. This distinction is, however, not significant since similar mechanisms are encountered in either type of combination. We may, therefore, proceed directly t o examine the three major ways by vhich atoms with their complements of electrons may come together and stay united. In each case we shall find that the outermost or valence electrons, those in the outermost s, p, d, and, more seldom, the f sublevels, play a significant role in establishing the bond between atoms. We shall also find that while three modes of combination &re generally recognized, namely, ionic valence, covalence, and metallic valence, most known compounds do not represent ideal examples of any one of these modes. Thus, some ionic valence compounds have considerable covalence character and many covalence compounds have some ionic character. Nevertheless, for purposes of classification and discussion, it is convenient to use the three terms and to assign each compound to the particular category in which it fits best. Into our first division then fall the ionic valence compounds: sodium chloride, calcium oxide, barium fluoride, and many other salts and oxides. A large number of physical criteria indicate that these substances contain ions; for instance, as solids they have a

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definite though very slight electrical conductivity, when melted the conductance becomes quite good; they have high melting and boiling points, an indication that there are strong forces holding the primary particles together, thus ruling out molecules; their refractive indices can be shown to be the result of two independent, known effects, the refractivity of the positive ion and that of the negative; and their X-ray diffraction patterns show that ions rather than molecules are acting as diffraction centers. The part that the valence electrons play in the formation of ions seems straightforward enough. Electrons are transferred from atoms of one sort to those of another, usually upon direct contact, as shown by the following steps: X

+ te-

,

-

X-

A

.

the crystal lattice, e is the charge on the electron, N is the Avogadro number, r is the distance between centers of positive and negative ions in the lattice, and the numerical value of n depends upon the total number of electrons in the ions producing the solid. This equation enables us to test our theory of the constitution of ionic valence compounds, for if the theory is correct then the value of U(theor.)calculated should agree with the lattice energy obtained from experimental values. The latter may be called Ua,,) and can be found by the following scheme:

energy

Tables of ionization potentials will show that, in general, it takes less energy to remove electrons from atoms of the metals than the nonmetals: the former. therefore. more readily become the donors of electrons and form positive ions. Again, tables of electron affiities show that the atoms of some nonmetals (F, C1, Br, I) accept electrons spontaneously; to make the atoms of other S, Se) accept electrons only small ennonmetals (0, ergies need be expended, hence the atoms of the nonmetallic elements become the electron acceptors and form the negative ions. The formation of positive and negative ions is, of course, only the beginning of the process which results in an ionic valence compound. The rest is almost too readily accepted by most everyone, probably because we learned while quite young that positive attracts negative. As we grew older we learned to express the same idea more elegantly as Coulomb's law of force. That the operation of this law is a very important factor in the formation of an ionic valence compound is immediately conceded when it is discovered that the energy balance in the aforementioned steps always turns out negative, which means that a positive factor must come in somewhere to swing the balance in the opposite sense else no combination will occur. The positive factor is the energy that is set free when the positive and negative ions are brought to within very short distances of one another, it is called the lattice energy U. If we imagine that the charges which result from the gain or loss of electrons by the atoms are concentrated at the centers of the ions, it is possible from purely electrostatic considerations to set up an equation which permits the calculation of the lattice energy for ions of particular size, charge, and arrangement :

wherein U is the energy, in kilocalories, theoretically set free per mole, A is a factor that depends upon the valences of the ions involved and upon the geometry of

There are two ways of preparing solid M+X-; method (2) goes through several steps whereas method (3) is direct, but whatever the route the same energy H should be involved in passing from the solid metal (M(,)) and solid nonmetal (X(%))to the end product. Consequently the sum of the energy steps in (2) should equal the energy in (3), or H = St

+ I + Sz + F + Ucex..)

The values of all the factors in dhis equation are known from experiment, except U(.,,). This is then found algebraically and, in Table 1, the values for some typical compounds are compared with those obtained from the theoretical equation (1). TABLE 1 Lattice Energies of Ionic Valence Compounds Urtheor.l ealeulaled in Uc.,.) found in accordance with schemes accordance wilh Compound

equation ( 1 )

The concordance of the values in the two columns leads us to believe that our conception of the role played by electiks in the formation of ionic valence compounds is essentially correct. Having thus developed some degree of confidence in our theoretical equation for calculating the lattice energies concerned in the formation of ionic valence compounds we may, by an indirect method, test it still further. We may use it to calculate the energy of formation of CaCl(,), CaCl,(,), and CaCL(,). The values in Table 2, obtained according to a scheme

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like (21, show clearly that, whereas the formation of and results in the filling up of the electronic orbitals CaCL(,) is attended by the release of much energy, with pairs of electrons. Sometimes it is just a pair of, and should therefore be a spontaneous process, the electrons that is shared, as in HC1, but any number up formation of CaClb) and CaCla(,) requires the intro- to eight-pairs, as in OsF* may be involved. LuderJ duction of energy. The latter compounds should not has recently. given an excellent report on the details form unless this energy is aviailable from the sur- of this process. The telltale of covalence is the absence roundmgs. Further, if we succeed in making them, of charged atoms or groups of atoms. Consequently, the compounds, being endothermal, would, a t ordinary those physical properties t,hat were earlier mentioned temberature, tend to decompose into stabler products as characteristic of ionic valence compounds will not by processes which liberate energy, e. g., he in evidence for the covalence compounds. The sharing of electrons between atoms brings about associ2CaCI CaCL + Ca + energy ations which we call molecules and these have their Now in all of our experience no one has found any 0 x 3 unique properties. For instance, they generally evidence of CaCI3 which the calculation shows should are only weakly attracted to neighboring molecules, be an exce~dinglyunstable substance. On the other with the consequence that only low levels of thermal hand, there have been reports of the preparation of agitation (i. e., temperature) are needed to melt the CaCl by indirect methods and in impure form.2 This, solid or boil the liquid. Further the molecules often too, is consistent with the value for its heat of formation contain an asymmetric dist.ribution of charge which as calculated. We would predict that there was a manifests itself in the form of a measurable dipole possibility of preparing it at elevated temperature and moment. Then also the molecules are not rigid, their then, upon cooling rapidly to room temperature, it atoms vibrate with respect to one another, and the might persist because of a very slow rate of decomposi- aggregate may rotate. These motions are associat,ed tion. with characteristic amounts of enerw -" which are absorbed when infra red radiation plays upon the molecules. By their absorption spectra, then, we can detect TABLE 2 molecules, i. e., covalence compounds. Of course, Calculated Energies of Formation of Some Chlorides of and electron diffraction studies, give inCalcium (in Kilocalories per Mole) formation about lattice and molecular structures. are CECIW -2 (approx.) additional aids in distinguishing the covalent from CtaCl.e, +I70 CaCbc., -339 (approx.) the ionic valence compounds. Unfortunately, the almost intuitive approach which the student has toward ionic valence -iompounds is The foregoing appears to be our answer to the lacking for the case of covalence. I t is difficult for him questions, "Why is the calcium atom divalent? Why to see why the sharing of outer electrons should result does it not lose just one or perhaps three electrons when in a force which holds atoms together. Nor do we .it enters into combinations?" Similar calculations have any simple set of rules or reasons which we could may he made for the other elements that form ionic use to justify the existence of the force. I t is h e that valence compounds and also for those, like the inert wave mechanics has supplied a complete and satisfying gases, which do not enter into this type of combination. theory of the electron-pair bond and has provided For the latter elements the energy of formation as equations which permit the calculation of the force calculated for possible compounds comes out highly and energy of the bond, but these are so deeply rooted negative. When all the calculated values are com- in higher mathematics that they are mere abstract pared with laboratory experience, and the degree of symbols to the average college student. Furthermore, accord noted, we come to the conclusion that our whole this theory, because of its very complexity, has thus conception of the way electrons enter into the fonnation far been successiully applied to only a few covalence of ionic valence compounds must be on the right track. bonds existing between the simplest of atoms. What These calculations show clearly that the ionic valence then shall we offer as an explanation for the attractive or valences which an element exhibits depend upon the force due t'o valence electrons shared between atoms? electronic structure of its atoms and more particularly My only suggestion is to fall back upon some feeble upon the amount of energy involved in the loss or gain qualitative reasoning based, again, upon electrostatics. of certain electrons in the outermost energy levels and If we assume two neighboring atoms, MI and M2, and upon the energy set free when its ions combine with divest each of an electron, e, and e2,then the remaining others. The number of electrons actually transferred effective charge upon each atom, centered a t the determines, of course, the valence number assigned to nucleus, will be one unit, positive. If the electrons the element. remain in the proximity of these positive charges, the Our next large class of compounds results from the crudest sort of picture then calls for four forces of operation of what is called covalence. In brief, this attraction as against two of repulsion, as shown by means the sharing of valence electrons between atoms arrows in the following sketch:

-

WOHLERAND RODEWALD, Z. a w g . Chem., 61, 54 (1909); A., GUNTZ, AND F. BENOIT, Bull. Soc. Chim.,35,709 (1924).

8 1 , u ~W. ~~ F.,, J. CHEM.EDUC.,22,221 (1945).

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value for the heat of formation of hydrogen peroxide is 33.59 kil.-cal./mole. As another illustration of the power of the method we may try to use bond energies to calculate the heat of formation of propane from graphite and hydrogen.

M,

3Cmspbw

+ 4H*w

+

CJb

The bonds involved and the number of times they must be taken are:

The inaccuracies of this static picture are patent, but it may serve a useful purpose as a stopgap. Although it seems unlikely that we shall be able to impart to the beginning student anything more than a nebulous notion of the nature of the covalent bond, it may be well to remind oureelves that a great wealth of empirical data concerning this type of bond between all sorts of atoms has accumulated. We have tables of bond energies (the work necessary to rupture the electron-pair bond between particular atoms), bond distances, and bond moments (dipole moments). With them it is possible to interpret successfully an amazing amount of chemical information. The covalent bond energies are approximately additive, so that it becomes possible to calculate in advance with moderate accuracy the amount of energy that will be set free (or absorbed) when the electron-pair bonds are ruptured in the reactants and reconstituted in the products. In fact this additivity of bond energies is often used as a criterion of the presence of covalence bonds. As a hypothetical illustration we may think of the formation of the molecule AzBzfrom molecules Apand Bt:

Each line joining A to B represents an electron pair or covalence bond. Here it is clear that energy must be supplied to rupture the bonds between the A atoms in A2 and the B atoms in BI, also that energy is recovered when the four A-B bonds are formed. Assuming that tables of bond energies are a t hand, our energy balance (the heat of reaction) is found as the snm of -EA-A -EB-B ~EA-B. 4 few actual cases may now be in order. When hydrogen peroxide is formed from hydrogen and oxygen:

+

one H-H and one 0=0 bond (a double bond) must be broken, whereas one 0-0 and two 0-H bonds are formed. The energies necessary for rupture are: H-H, 103 kg.-cal./mole; and 0=0, 118. But the energy of formation of an 0-0 bond is 35, and twice the energy for an 0-H bond is 220. The sum of energy absorbed a d released is thus: -103-118 35 220 = 34 kg.-cal./mole. The experimental

+ +

The summation of these hypothetical steps leads to 22 kil.-cal./mole whereas the experimental heat of formation of propane is 24.75. Many similar calculations have been made in attempts to discover the heats of formation of compounds still unknown and to find better ways of making those that are known. In general, these have met with enough success to warrant our continued use of the principle of additivity of covalence bond energies. Before leaving the subject of convalence it may be worth while to digress from the main theme slightly and discuss briefly bow the valence number of an element entering into a covalence compound is determined. Ideally we should count the number of pairs of electrons shared by an atom of the element with atoms of other elements in the molecule they form. (When atoms share electrons with like atoms, as in C1: CI, the valence number is considered zero.) This assumes, of course, that much is known concerning the structure of the molecule. When we are on less secure ground, or are dealing with complex compounds, we generally fall back- upon the rule of identical total valence which assumes as a basis that hydrogen and oxygen have. valences of 1+ and 2-, respectively, and that the valences of other elements in molecules containing them can be obtained by simple algebra. Occasionally the valence can be obtained unequivocally by carrying out a cell reaction and noting the number of Faradays required to convert one gram at,om of the element in question to the compound form. We turn now to the last of the important types of bonds or attractive forces created between atoms by valence electrons. It is the metallic bond. I t . is evident that in a metal, say copper or iron, the atoms cannot be joined by ionic valence forces, for t,bis type of valence presupposes the presence of atoms of two sorts, electron donors and the receivers; nor can the atoms in a metal be held to their large number of neighbors (usually 8 or 12) through sharing of valence electrons with them. There just are not enough electrons to go around. What then has the mind of the physical chemist conjured up to explain the strong forces existing betveen the atoms of a metal? Some fifty years ago the "electron gas" theory mas postulated by Drude, according to which the atoms in metals lost t,heir valence electrons and these formed an electron gas which drifted through the interstices between

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the positive ions just as gas TABLE 3 molecules would diffuse Chart of Phases in the Coppar-Zinc System of Alloys (Brasses) through a pile of marbles. The importance of this R a t i o of electron gas from our point valence Bleetrws of view is that it is supposed to *toms to act as a cementing matrix between the positive ions of ~ o m u l s sSameArbitrarily the metal. Thus a metal is 'tineslisrimed constructed in some respect? like an ionic valence comcrystal *trvet"rs pound, it is built up of ions; but it also resembles the covalence compounds in that Phases a t Room the bonding electrons are TemperafYPB shared. The physical characteristics of atoms bound in this way are, however, so different from those ioiued bv . " ionic or covalence that one need only mention some of them by namet,husatfording an approach to the continuum of energies excellent electrical and heat conductance, strong re- postulated under the Drude theory. flection of light, and plastic deformation-to suggest As was the case with ionic and covalellce bonds we that the valence electrons in metals must act in quite ft are interested in the role played by the valence electrons different way from those in the ionic or covalence com- hen atoms of different metals are brought together pounds. i. e., when alloys are formed as by fusion and subsequent, The electron gas theory is simple, and it explained cooling. The major requirement is for the atoms to many of the properties of metals, at least qualitatively. release one or more electrons to the common swarm The need for .modifying it arose when it was realized while the positive ions find lattice sites. If the sizes of that if metals were so constituted they should have the atoms of the metals are closely alike, we find that abnormally large specific heats due to the presence of the ions of the one can substitute for those of the other two independent sets of particles, the positive ions and indiscriminately throughout its lattice. Splid soluthe electron gas. But metals do not have specific tions rather than compounds of fixed stoichiometric heats that are abnormal to this extent. A modification proportions are thus formed. When the atomic radii of the theory, intended to take care of the defect just differ by more than 15 per cent the tendency to form mentioned, established the "free" electrons on a fied solid solutions falls off rather sharply. In this case, lattice which interpenetrated that of the positive ions. and particularly if the metals differ appreciably in Like its predecessor, this theory accounted fairly well electronegativity, what might be called "intermetallic for most of the properties of metals but was not con- compounds" appear in the mixture. Their composition sistent with their extraordinary electrical conductance. is also generally variable; in other wvords, they too are Even the feeblest potential difference starts electrons solid solutions of limited range. A better name for moving in a metal; this would not be expected of them would be phases, such as body-centered cubic electrons in a fixed lattice. phase, close-packed hexagonal phase, etc. The system The present theory is the result of the application of of alloys known as brasses, formed between copper and the Fermi-Dirac statistics t o . the so-called "free" zinc, illustrates the aforementioned tendency to form electrons within the metal. In essence it is the same as solid solution phases (Table 3). None of these iuterthe older electron gas theory; both postulate that the metallic phases has constant composition. Even zinc positive ions in the metal are held in place in the dissolves a small amount of copper, forming the ?I-phase. lattice by the electrostatic attraction of the surrounding The ar, 0, y, and r phases are extensive solid solutions. electrons. Simultaneously, of course, the electrons are This characteristic of uniting to form distinct crystalline kept from escaping from the metal by the presence of phases of variable composition is the point of strongest the positive ions. In the newer theory the electrons difference between intermetallic combinations and are not quite as free as in the electron gas of Drude. those resulting from ionic or covalence. That the They are no longer unqualifiedly detached from their number of valence electrons available is apparently respective atoms. Under the new theory energy values quite significant in determining the structure of interascribed to the valence electrons are no longer con- n~etallicphases has been found by observation of many tinuous as in the free gas theory, but are restricted to alloy systems. The p, y, and e phases frequently values within particular bands or zones, hence this is appear when trhe ratio of valence electrons to atoms often called the zone theory of metals. These allowed is the same as that shown for these phases in the zones of electron energies may overlap to some extent, (Continued on page 300)

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THE ROLE OF ELECTRONS IN INTERATOMIC RELATIONS (Continuedfrom page 896)

copper-zinc system. Here copwr is assigned a valence of 1 and zinc 2, consistent pith their places in the Periodic Table. These odd valence electron-atom ratios have recently been accounted for by the zone theory of metals,&referred to previously. The question is sometimes asked, "How does one assign valence numbers to the elements in intermetallic combinations, i. e., alloys?" An examination of some approximate formulas, such %s the ones just given, CusZm, CnZn3, will serve to show that no valence numbers can be here conceived which mould be a t all consistent with the numbers assigned to the same elements in ionic or covalence compounds. This is not surprising, for few actual compounds exist in alloy 4 Mom, N. F.,AND H. JONES, "Theory of the Properties of Metals and Alloys," Oxford University Press, 1936, Chapter V.

systems, solid solutions being the rule, and thus the term valence, in the sense in which we usually use it, is not applicable. In concluding these remarks on the role of electrons in interatomic relations, I believe that not all of what has been said should be told "to our kids first thing in the morning" but I think most of it should be in our minds when we do present the subjects of atomic and molecular structure to our students on whatever level that may be. By keeping a reserve store of information we fortify our own thinking, bolster our own convictions, and are ready to cope with such questions as are asked by our more intelligent students. True this requires constant attention to the literature, a constant "keeping on your toes," but I believe the good teachers of chemistry are just the ones who find that easy to do.