Edited by DAN KALLUS Midland Senior High Schwl 906 W. Illinois Midland. TX 79705
chemical principle/ ted revi~i
RUSSELL D. LARSEN Texas Tech University Lubbock. TX 79409
The Chemical Bond Roger L. DeKock Calvin College, Grand Rapids, MI 49506 Toquote from an essay written by R. G. Parr ( l ) ,"Chemical bonds are the forces that hold iitnms together in molecules and solids." We should perhaps stop to reflect for a moment on the term molecule. Robert S. Mulliken, who received theNohel Prize in chcmistrv in 1966 for hisseminal work on the chemical bond states (27: A molecule may be thought of either as a structure built of atoms
bound together by chemical forces or as a structure in which two or more nuclei are maintained in some definite eeometrical eonfiguration by attractive forces from a surroundingswarm of electrons. We see that it is impossible to define the term molecule without mention of bonding and vice versa. Most definitions of the term molecule refer to atoms, but there is no agreement about what we mean by an atom in a molecule! The fundamental difficulty is that electrons are indistineuishable and therefore. once a molecule is formed. WP no longer know how to partition the space among the constituent "atoms". Althoueh elertrons are indistincuishable, they do follow certain r k e s of behavior. For example, the Pauli exclusion principle applies equally well for electrons in molecules as in atoms. Roughly stated,no more than twoelectrons may occupy a given orbital, whether that orbital be in an atom or in a molecule, and then only if the spins of the two electrons oppose each other. If we are a t all familiar with the discipline of chemistry we will agree with Kutzelnigg (3)that "The chemical bond is a highly complex phenomenon which eludes all attempts at simple description." Nevertheless, i t is my task t o attempt to provide some simple descriptions. In so doing we should never lose sight of the fact that we are dealing with simplified models of the chemical bond. Any article that purports to describe the chemical bond should list some of the adjectives that are applied to the noun bond. The following list is only partial: agostic, bent, polar, nonpolar, dative, bridged, bifurcated, delocalized, double, single, triple, electron-pair, one-electron, three-cen-
-
'
The symbol IQNa) refers to the ionization energy of the Na atom and EA(CI)refersto the electron affinity of the CI atom. We defineEA in the same sense as IE. so that the electron affinities of all neutral atoms are positive. Na(g) C1-k)
934
-
ter, two-center, localized, protonated, quadruple, sigma, pi, delta,phi, unusual, dangling, semipolar, weak, strong, covalent, Ionic, metallic, van der Waals, hydrogen, and coordinate covalent. We will divide our discussion into five parts, which will allow us to take up several of these types of bonds. The five parts are: ionic bonds, covalent bonds, hydrogen bonds, bonds in the solid state, and variation in bond strengths. lonlc Bonds (4) The simnlest bonds to describe are those that result from attractions between ions of opposite charge, as in most rrystalline solids. Unfortunatelv, even simple crvstalline solids have rather complicated connectivity patterns between atoms compared to simple molecules. For example, in a single crystal of ordinary table salt, each sodium atom is surrounded by six chlorine atoms and vice versa. Therefore, let us beein bv an examination of the bondine in gaseous diatomic N ~ I .his molecule exists in significant concentration only if the solid is heated in a vacuum to a t e m ~ e r a t u r of e several hundred degrees Celsius. We shall set o;t t o calculate the change in energy upon bond formation of the NaCKg) molecule. Nak) + CKg) NaCKg)
-
u
-
We should notice straight away that if we define the change in energy to be that of the products minus reactants, the resultant number will be negative. This results because the products are more stable than the reactants. Conversely, the bond dissociation enerw would he positive. (At this point it isasiumed that thestuhknt already~knowsaboutelec~mnegativitv trendsand theoctet ofelectronssothat the1.ewisdot structure for ionic NaCl(g) is given by [Na]' [:@:]We can use the following thermochemical cycle to calculate the change in energy upon bond formation if we assume that the oppositely charged ions can be treated as point charges and are attracted according to Coulomb's law of energy, e2/r,where e is the unit of electronic charge and r is the distance between the ions.'
Nat(g) + e-
IE(Na) = 118.5 kcdmol
From this cycle i t is clear that the calculated energy change is
CKg) + e-
EA(CI) = 83.2 kcdmol
IE(Na) - EA(C1) - e2r
Journal of Chemical Education
(1)
. - -.
ranges from 0% ionic (pure covalent) to 100% ionic (zero covalent). In a recent article in this Journal, Barbe (5) has shown that a useful formula to represent the fraction of ionic character h is
-- ..
character
withx,, > XH. where %nandxs referto theelectronegativities of atoms A and H, respectively. Notice that this formula exhihits the correct limits. For a hypothetical molecule with x~ = 0, weobtain 100woioniccharacter;if X A = X H weobtain a mulecule with OPo ionic character. For the NaCl molecule we can employ typical electronegativitie.s of 3.16 for C1 and 0.93 for Natoobtain a 70moionicbund (3O"ocovalent). The results obtained by Barbe for several molecules are shown in Figure 1.
Figure 1. A plot showing the perwm covaiem character as a hrnction of the electronegativityof the two atoms in a chemical born. The lines through the data poims indicate whetherthecompomdisa hydride, iodide, chloride,oxide. or fluoride (ref.5).
We represent NaCl(g) as Na* and C1- ions, separated by the exnerimental bond distance r = 2.36 h. From Coulomb's law, an energy of 332.1 kcal/mol is released when oppositely charged bodies (each with unit charge) are brought together to a distance of 1A.The calculated energy change for the process Naf C1NaCl(g) is -332.1/2.36 or -140.7 kcall m ~ l . ~ F r oeq m 1the energy change is 118.5 - 83.2 - 140.7 = -105.4 kcal/mol. The experimental value is -98 kcal/mol, so the ion-pair approximation allows us to calculate the DE within 7% of the experimental value.3 All that is needed to eo from this calculation on the diatomic molecule to the solid state is to take into account the longer hond distance in the solid and the geometric factor (Madelung term) of six for each ion surrounding the other. Such a calculation can be left for a later course. I t should be emphasized that the bond distance in solid NaCl is lon er than that in the diatomic molecule (2.814 A vs. 2.36 ), exactly as one might expect since each atom has multiple interactions instead of only one as in the diatomic.
+
-
Covalent Bonds We were able to discuss ionic bonding without any recourse to quantum mechanics, although a quantum mechanical calculation on NaCl(g)eprovides an essentially ionic picture of the bonding. For covalent bonding, we can again avoid any explicit use of quantum mechanics for afirst-level introduction. After all, Lewis proposed his electron pair idea and the octet of electrons in 1916, several years before the onset of modern quantum mechanics in 1925. Therefore we begin this discussion of the covalent bond with a thorough treatment of the Lewis electron-pair idea and proceed from there to a more formal understanding of the covalent bond. Lewis Electron Dot Structures (LEDSj of Simple Molecules In Figure 2 we present the usual LEDS for several simple molecules. These examples suffice to point out the concepts of (1) electron pairs, (2) octet of electrons, (3) lone pairs vs. hond pairs, and (4) single bonds vs. multiple bonds. LEDS are also foundational for (1) nredictine which molecular systems will be extremely reactive, (2) predicting molecular shape via the valence-ahell electron-pair repulsion method,
1
Degrees of lonicity in Polar Bonds In the above calculation. we assumed that the transfer of an electron was complete between the Na atom and the C1 atom. In fact, all chemical bonds have onlv a nartial transfer of electronic charge. Many methods have been proposed in order to illustrate that the variation in chemical bonds
-
&
The negative sign is simply reflecting the fact that energy is released in the process. That is, we are going down In energy to a more stable system. It is worthwhile to point out that the first two terms in eq 1, which describe the formation of the closed shell Ions Na+ and CI-, are net positive by 35.3 kcallmoi. That Is, the stability of NaCI(g) Is not due to the formation of the ions that have noble gas electronic configurations. Rather, the stability is due to the Coulomblc anractlon of the oppositely charged ions.
Figure 2. Lewis electron dot sbucturesfor sometypical chemical compounds. Volume 64 Number 11 November 1987
935
(3) introducing the concept of formal charge, (4) predicting molecular top&gy (connectivity), and (i) s t a t i ~ the ; ~ hyhridization of orbitals in the simplified valenre-bond theory. W r will make usr of these fiveaspertsshortly, and laterwe will point out some dittirulties associated with LEDS. First, we should review some rules for writine" I.l?DS. Numerous articles (6) have appeared in this Journal, each attempting to illustrate a new and better way t o teach LEDS. Some of these approaches are rather formal and include the introduction of aleebraic eauations that must be solved. Mv own a p p n ~ a r h(7) admits that a strict set of rules is probably not helpful or necessary although a set of guidelines is useful: 1. Determine the total number of valence electrons in the molecule or ion. 2. Write the atomic symbols in the proper order (connedivityl
topology)and first "satisfy" the external or terminal atoms. To satisfy these atoms means that the maximum numher of electrons surroundingany given terminal atom is two for hydrogen and helium and eight for all other atoms in the periodic table. At this point we must give the students the connectivity of the atoms, but later we will see how we canuse the LEDS to predict the most stable arrangement of atoms, at least in many simple inorganic systems. 3. If the central atom has not achieved an octet and if lone pairs (or nonbonded electrons) are available on the terminal atoms, allow these lone electrons to bond with the central atom by farming multiple bonds. 4. Among several LEDS, those with low formal charges (0,+1, -1) on each atom are preferred. This fourth guideline is the Pauling electroneutrality principle.
atom to the C1 atom, and we say that the oxidation state of Na is +1 and that of C1 is -1. In the formal-charge method electrons are not transferred in the countine Drocess. rather thev are counted as beine shared equally&en if the two atoms have different electroy negativities. Lone-pair electrons are counted completely for the atom on which they reside. In Figure 4 we present some examples. Notice that a formal charge should in no way be considered an actual charge, in the same way that oxidation numbers should not be thoueht of as actual charees. The sum of the formalcharges mus: add to the tatal charge on the molecule or ion. There are cases in which formal charge does prove useful, aside from its application in writing LEDS. In Figure 4 we see that the C atom in CO has a negative formal charge, whereas the 0 atom has a positive formal charge. This is contram to what one would ~ r e d i cbased t on simule electronegativity arguments. It is the triple hond in CO that causes this effect. Experimentally, the CO molecule has a very small dipole moment, with the negative end of the dipole on the carhcm atom. (The reader mav notice that all of the neutral molecules except CO listed in Figure 4 have zero formal charge on each atom.) Topology. Pauling (10) pointed out years ago that the
Applications of LEDS
Reactivity. The molecules presented in Figure 2 are all stable at room t e m ~ e r a t u r eand normal Dressure if laced in an inert container: All of these molecuies satisfy the octet rule. On the other hand.. eas e such as BHx, -~ h a s molecules CHs, CH2, and CH are extremely reactive; they have leis than the octet of electrons. The former substances can be ordered from numerous suppliers, whereas the latter are only available as transient molecules. This is not to say that the transient molecules are unimportant; especially the hydrocarhon free radicals mentioned above may be very important in flame rhrmistrv. We also do nor wish to e k e the impression that all stadle substances must satisfy &e octet rule. Such is certainlv not the case. For examule. . . there are numerous cage and cluster molecules for which the traditionaloctet rule is not satisfied. Yet for the tsvical molecules encountered in a high school chemistry course the octet rule remains eminently useful as a predictor of molecular reactivity. Valence-Shell E l e c t r o n - P a i r Repulsion M e t h o d (VSEPR). This method has received much attention in this Journal (8)as a simple approach to molecular shape. I t also has come under attack in the chemical community since i t did not seem to be firmly grounded in quantum mechanics. More recent work has shown that the method is in fact well grounded ( 9 ) for which we can breathe asigh of relief This is not to sav that there are no exceutions to the VSEPR method. ~ o w k v e r it , is an extremely useful introduction to the prrdiction of molecular geometry. The essence of the VSKI'R method is shown in Figure 3. Although hondanglev between 100" and 109°arequitecommon fo;moleculesin which the central atom is from the first row (C, N, 0 ) in the periodic table, angles close to 90° are much more common for the second and subsequent rows. Examples are given in Figure 3. Formal c h a r m This term s i m.~.l vrefers to a method of partitioning the electrons in a molecule. Consider again the gaseous NaCl molecule. In that case we formally thoueht of ;he bonding in terms of a transfer of an electronfrom the Na
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Journal of Chemical Education
-----I
tetrahedral
+--e
I
I'
uipnal pyramidal
Figure 3. Molecular shape asa function of me number of elechan pairs arwnd the central atom (VSEPR).
Geometric Structure and Hybridlratlon Number of Hybrid Orbitals
Type of Hybrid Orbitals
Rewlting Structure
two three four
SP sp2 sp3
linear trigonat pianav tetrahedrain
~entif one at me hybridorbitals is occupied by a lane pal.. 'Trisonal pyramidal if one of the hybrid owtab is ascupled by a ions pair and bent if two are so occupied.
Figure 4. Formal charges for a few atoms in compounds
far a pocket computer to tell what you are supposed to say when seeing a given chromophore. most stahle connectivities of the atoms in a molecule can he deduced by a simple nuclear repulsion theory. We here employ LEDS to accomplish a similar goal. Suppose we are asked to nredict the molecular structure for the molecule HC'OF, which has I 8 valence electrons. Will this molecule be linear HCOF. HOCF. HFCO. HFOC. HOFC, or HCFO'! Or will i t be nonlinear, and if so,'will i t be plana;? We have developed a set of emdrical "rules" that seem to he valid for the irediction of tl;e most stahle topology of many molecules (11). These rules are not foolproof, hut they do p&ide reasonahk guidelines for deducing stahle topoloriesof molecules. The priority oftherulesshuuld be taken in the order listed 1. Hydrogen atoms are terminal. Example: HCN not CHN. 2. For two elements from the same row in the neriodic chart. the rlemrnt fanhrr to thr right will be terminal. Example: HCN. The H N C isomer is lefisscablr. ~
~~~
We present in the table the sort of "electronic parrot" that Jorgensen refers to. The concept of hybridization is mostlv employed in organic chemistry, and even there i t is not df much use except for the carbon atom. Recently, it has been shown that the ratio of s t o p character should not he taken too literally (14). Pauling continues to find refreshing ways in which to apply the concepts of hybrid orbitals (15). Difficult Areas for LEDS Resonance. We are so familiar with this nrohlem that we may not even think of it a s a problem! Yet. whether in SO,or in t~enzencwe need to use more than one LEDS to descrihc the full symmetry of the molecule. Delocalization introduces a problem for what is essentiallv a localized theorv of the e ~ & r o n - ~ a ihond. r
~
3. Structures with three-membered rings generally do not form the most stable isomer for a given compound. Example: isoeyanic acid has the molecular topology HNCO and does not form a three-membered ring between the N, C, and 0 atoms. (Notice how rules 1 and 2 are also obeyed for HNCO.) Threemembered rings are very common in molecules that do not obey the traditional octet rule, for example, the boranes. 4. Structures in which terminal atoms have an octet are preferred. (Of course,for H this is the duet!) Example: H-CsN:, not H-C=N:. 5. Structures that obtain low formal charges on the atoms are preferred. (This rule generally follows automatically after applying rules 1-4.)Example:
The first structure is the proper one for the most stahle isomer of HCN. Applying these rules t o the molecule HCOF, we can write three isomers, each involving a different topology:
The first structure best obeys rules 2 and 5, and this structure corresponds t o the most stable isomer of HCOF. Hybridization. The concept of hybridization of orbitals was first introduced by Pauling (12). The author agrees with Jorgensen (13): The hybridization model was a refreshinginnovation,when it was introduced by Pauling in 1931, hut the commentators in texthooks have gone very far along a sterile scholastic desert trail. The main field of use today is describing hond angles, but the conclusions are a posteriori. It would he easy to construct a programme
../s,..
0
-, . 0;
0:
s\..
0
Electron-deficient compounds. Actually this term applies to two t w e s of molecules: those that are trulv electron deficient andthose that are only said to be deficient in the lore of chemistry. Among the former we could include the BH3 molecule and its isoelectronic counterpart, the methyl cation CH;. Such species have available only six electrons and hence they are very electrophilic. In the second category we have simple molecules such as H: and B2He which lack fewer electrons than two for each of the "sticks" in the topological structure. Three resonance structures are reouired to denict the hondine in H?. and 20 are required for B ~ (16). H ~k e t each of these rnoi&ules is readily handled if we allow for the possibility of three-center two-electron chemical bonds. Such bonds are depicted helow with the use of acircle in the case of H t and acumed line in the case of B2Hs. Electron deficienciis not something unique to boron chemistry. Many solid-state structures couid he considered t o hc elbrtrvn deficient, as well as many carbocations in the field of organic rhemi.itry.
Solid-state chemistry. This area of chemistry has not been well served by LEDS. Even metallic sodium, where each sodium atom is surrounded by 12 nearest neighbors, could he considered to be electron deficient. We can use LEDS to discuss a few solid-state structures. For exam~le. the two allotropes of carhon are well handled by LEDS. 'bhe bond angles - are tetrahedral in diamond and trieonal in graphite. Transition metal chemistry. After repeatedly emphasizing to our students that they should keep track of the electron count when doing LEDS, we proceed to ignore the count Volume 64
Number 11
November 1987
937
for something as simple as octahedral Cr(CO)61 Why do we depict only the 12 electrons between the Cr atom and the six CO ligands?
where the 1s and 2s electrons are not explicitly shown and the 2p orhitals are drawn in their usual two-lobed fashion if in the plane and as a circle if perpendicular to the plane. The Is1 configuration of H is given simply as
Then in order to depict the bonding between the H and F atoms to form HF, one can use the following diagram The answer t o this question is that LEDS does not in general provide useful results in transition-metal chemistry for the prediction of molecular shape via the VSEPR approach. Therefore we choose to imore the "nonbondine" dtype electrons on the metal center, although nonbondgg sand . p-type .. electrons are very important in -predictions of molecular shape for main-group eiements. T o he fair, we do employ the electron count for many organometallic compounds where i t is expected that for a stable molecule to exist we should achieve an 18 electron count. In this case we count the six "nonbonding" electrons on the Cr atom. This rule is not obeyed as often as the eightelectron rule. Com~lexessuch as Cr(HIO)? are stable in aqueous solution aihough they do not aihilve the requisite 18 electrons. (It is relativelv easv t o understand whv we have rules of 2, 8, and 18 e~ectrbnsfor different e l e m e k in the periodic table. I t simply depends on how many valence orhitals are available. Hydrogen and helium have only s orhitals; the rest of the main group elements have s and p orbitals, whereas the transition elements have s, p, and d orhitals (\ 1- .7I1. ,1
Hyperualent compounds. The term hypemalent refers to main group compounds that have electron counts around the central atom that exceed eight. Hence, this includes compounds such as PF5, SFs, and CLF6, which have 10,12, and 12 electrons surrounding the central atom, resoectivelv. Even SO2 could be written with adouhle bond betu;een the^ atom and each 0 atom, resulting in 10 electrons surrounding the central atom (18). This is not a problem for the electronpair theory itself, hut rather for the octet aspect of it. We summarize this discussion of LEDS by pointing out that it has been and continues to be a very useful starting point for chemists t o consider the electronic structure and bonding of many molecules, particularly in the realm of o r ~ a n i cchemistrv. However. students should never be taight to consideithe octetruie as something that all chemical com~oundsmust obey. I have perhaps emphasized the limitations, but this has been done simply to be sure that we are all aware of the pitfalls of the simple LEDS model.
"Aobnced" LEOS
We have touted the advantages and disadvantages of simple LEDS. The Generalized Valence-Bond (GVB) method (19)represents one way in which LEDS can be enhanced in order to overcome some of its deficiencies. In the GVB method one keeps track of the type of atomic orhitals that are used t o form chemical bonds. For example, the usual electronic configuration of the fluorine atom is presented as 1s2 2s2 zP: 2p$ ZP& In the GVB method this is depicted as 938
Journal of Chemical Education
I t might be argued that such a diagram has no advantages over the normal LEDS and in this case that essentially would he true. There is aslight advantage in that this picture shows the bond is formed from a 2p orbital on F and a 1s orbital on H, hut this advantage is offset hy the fact that the 2s valence electrons of F are not represented a t all. The real advantage of GVB can be illustrated by considering the oxvaen molecule (19). This molecule is difficult for I.~I)S heckse it does not hint at the fact that rhere are two unpaired electrons, alrhvuah this is readily handled in the GVB method. The oxygenatom has one less electron than the fluorine atom. Coupling two of these atoms together results in two GVB configurations labelled A and B.
In A the overlapping p, and py orbitals each have three electrons. Because of the Pauli exclusion principle, the third electron must reside in an orbital that is orthogonal to the first two electrons. (The effect of the three electrons in thep, orhitals is to produce a net of one bonding electron, likewise for the three electrons in the py orbitals. Consequently, the GVB configuration A does predict a double bond for 02.1 In any case we are left with one unpaired electron in eachof the p, and p, type of orhitals, and hence we have successfully explained the paramagnetism of the 0 2 molecule without resorting to a very complicated theory. The GVB configuration B results in a diamagnetic molecule, but we predict this state to lie higher in energy than A because of the bad pairpair repulsions in the py orhitals. In fact the Oz molecule does have a state B which is higher in energy than A by about 38 kcallmol. The Nature of the Covalent Chemical Bond
I t is worthwhile to investigate the nature of the chemical bond in a simple molecule such as Hz. The LEDS is merely a
Kutzelnigg's comment (3), "The chemical bond is a highly complex phenomenon which eludes all attempts a t simple description.'' Polar Molecules and Hydrogen Bonds (21) Polar molecules in general can attain a lower energy in the $gas, liquid, or solid state by the attractive interaction of oppositely charged ends of the molecules. A particularly important kind of polar interaction is the hydrogen bond. This is a relatively weak bond-about 5 kcallmol-between a positively charged H atom and a small, electronegative atom, usually N, 0,or F. (Recall that a typical covalent or ionic bond is about 100 kcalJmol.) Let us examine the structures of the gas phase dimers of H F and Hz0 in order to illustrate some of the pertinent features of hydrogen-bonded systems. Figure 5. The total energy measured in unitsof the H2bond energy, plotled as a function of internuclear distance, measured in units of theequilibrium HSbond length.
Distance
I
In particular, for the former we can make the following observations: The rnulrculnr unit3 retnin their identity. The Ha-F, and HbFh Irmd lengths are0.!12 A, identical uithin rxperimental rrror to that frntnd fur tnonc,merir HC'. 2. The Fa- - -Hb-Fb bond is linear. 3. The hydrogen atom that is bonded between the two F atoms is asymmetrically positioned. Only in very strong hydrogen honds, such as FHF-, is the H atom in a symmetrical position. 4. The angle 0 is usually between 100° and 120°. For (HF)z, the H s F . - - -Hb angle is found to be 115" 5". 1.
Figure 6. The total energy W, the average eiectmn kinetic energy T. and the average diatomic potential energy V of HZ. ploned as a function of the internuclear distance. The units are the same as in Figure 5. This figure has been taken from Winn. J. S. J. Chem. Phys. 1981. 74,608.
bookkeeping device. What really is i t that brings ahout the stability of the Hz molecule? H,
-
H
+H
dissociation energy = 103 kcaL'mol
Let us consider the four-particle system with the nuclei fixed a t a distance R from each other. The total energy will he determined by the total potential energy and the total kinetic energy. Since we take the nuclei t o he fixed, the kinetic energy is due solely t o the electrons. The total energy varies as a function of distance and is usuallv exhibited in what is mistakenly called a potential energy curve (Fig. 5). We are interested in how this total enerev is com~osedof kinetic energy and potential energy. The results arepresented in Figure 6 and show that the shape of the total energy curve is a subtle interplay between the kinetic energy and potential energy. We will not attempt to discuss these curves here, since entire chapters of books have been devoted to this topic, and a recent article in this Journal (20) has also discussed these matters. Suffice it to say that i t is not entirely correct to say that the electrons are simply the "glue" that bind nuclei together; such a statement implies that binding is due solely to potential energy. In the early part of the curve (large R ) it is the change in kinetic energy that is bringing the nuclei together, then just as the kinetic energy begins to increase the change in potential energy swoops in to save the day. Perhaps this is a fitting place to repeat
Hydrogen bonding has important consequences for the solid-state structures adopted by H F and H20,Figure 7. The structure of H F is found to exhihit a zigzag chain of H F molecules, linked together by hydrogen honds. The structure of ice shows that each oxygen atom of a polar H20 molecule is tetrahedrallv coordinated to four other oxveen atoms in a structure that somewhat resembles that o i k a mond. Each oxveen atom is hound to its four neiehbor oxvgen atoms by hidrogen bonds. In two of t h e ~ ~ h y d r o g e n honds the central Hz0 molecule s u ~ p l i e sthe hvdroeen atoms; in the other two honds the H &oms come fromvneighboring water molecules. Although the hydrogen honds are relatively weak compared to typical covalent bbnds, they are nonetheless important because there are so many of them in the solid and liquid phases. This explains the high boiling point, for example, of H 2 0 (100 OC) compared to H2S (-61 "C). Since hydrogen bonding causes an open network in ice (Fig. I ) ,ice is less dense than water a t the melting temperature. Upon melting, part of the open-cage structure collapses, so that the liquid is more compact than the solid. The measured heat of fusion of ice is only 1.4 kcallmol, whereas the enerw of its hvdroeen honds is about 5 kcallmol. This contrast jndicates that only about one-third of the hydrogen Volume 64 Number 11 November 1987
939
Valence Electrons per Atom Figure 8. Plot ol the bond energies (expressed as 1/ZA2- A) ol gaseous homonuclear diatomic molecules and the corresponding atomization energies of solid State substance3 as a function of the number of valence electrons. Figure 7. The solid state structures of HF and H20. structures that show double, triple, and quadruple bonds, respectively, for these diatomics. After all, why not maximize the use of these electrons for chemical h ~ n d i n g ? ~ ) honds are broken when ice melts. Some of the hydrogen honds in liquid water are thought to be bifurcated (22). We can explain that gas phase Ben has a hond order of zero, whereaithe solid material has anatomization energy of 76 kcallmol, by noting the relative energies of the excited sp confimration comnared to the s2confieuration. As the atoms " come closer together in forming the solid, the energy of the total system is lower with the sp configuration than with the s2 configuration. Two electrons are bonding in the former configuration, whereas in the latter the electron pairs on each atom repel each other. This concept is shown in Figure 9. In fact, for a tiny microcrystal of Mg (isovalent withBe) to form, there must he a nucleation site. Experiments show that Mg gas in a container coated with an alkali halide, so as to avoid nucleation sites, will remain as a semipermanent gas at 10V torr a t room temperature and not condense to the solid state (24). This occurs in spite of the fact that the equilibrium vapor pressure a t this temperature is about torr! For the solid elements, the atomization energy per valence electron is nearly constant (kcallmol):
-
Bondlng In Solld-Slate Elements (23)
In Figure 8, we compare the bond energies of gaseous homonuclear diatomic molecules and the corresponding enthalpies of atomization of the solid state substances as a function of the group number in the periodic table (i.e., the number of valence electrons). For the gaseous diatomics, the fact that there is a peak a t N2 is well understood from LEDS, since we achieve a maximum triple hond a t that point. The reason why Be2 has a bond order of zero, B2 a bond order of one, and C2 a hond order of two is not so easily understood with LEDS. (We might well imagine the student exhibiting 940
Journal of Chemical Education
This indicates that all of the valence electrons are involved in the bonding in the solid state. By contrast, the results shown in Figure 9 indicate that the 2s electrons must not he too involved for the diatomic molecules. "Of course, the answer lies in the fact that the 2s and 2p orbitals are not energetically identical, and hence each atom retains a lone pair of electrons (2sZ)even in the diatomic molecule.
BOND STRENGTH (kcal l m o l )
GAS
METAL
Figure 10. A histogram of the bond energiesof 131 diatomic maleculesfound i n three tables i n ref. 4 (see ref. 25) Category A contains van der W a d s and hydrogen bonds (0.1-10 kcallmol). None of thesetypes of molecular interactions are shown. Category B contains weak chemical bonds (10-50 kcallmol), category C contains typical chemical bonds (50-170 kcallmol), and category
Figure 9. Schematic plot of lhe total energy of a collection of Be atoms for the s2 and sp electron configurations as a function of internuelear distance.
-
a.
Variation In Slrenaths of Chemlcal Bonds
I t is worthwhile to obtain an overview of chemical bond strengths. This can best be accomplished by a histogram plot for a set of molecules (251,Figure 10. Notice that the weakest bonds consist of van der Waals bonds and hydrogen bonds, neither of which are depicted in the histogram. Roughly, they have bond strengths between 0.1 and 10 kcallmol. Then we have weak bonds in the range 10-50 kcallmol. Typical chemical bonds range from about 50-170 kcallmol. Molecules with such bond strengths could he covalent, polarcovalent, or ionic; if covalent, they could he single, double, or trinle bonds. Bevond 170 kcal/mol we encounter the verv strong chemical bonds. The iitrungest chemirnl ixmd depicted is that of C O and the second srronpcsr is K?. ~
Acknowledgment is made t o the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. ~~
~
1. P s ~ rR. , G.McCrolu HilIEneyrlopedioof Chemisfry,Parker,S. P.,Ed.: McCraw-Hill:
New York. 1983: p 134. 2. Mul1iken.R.S. In ret 1.~628.
0 contains the strong bonds. The points labelled E and F refer to N2 and CO. respectively.
Kutzelnigg, W. Angew. Chrm. Inl. Ed.Engl. 1984.28.272.
4. Muchofthe material in this soction istskon from DeKoek,R. L.;Gw, H. B. Chamieol
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..".,
19Ld f-. ir , l l d
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