Nonfatal Attractions

Chm 1311 Lecture for 20 June 2000

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Opposite charges attract. (Like charges repel.) And although the negative electrons in an atom can lower their potential energy indefinitely by snuggling ever closer to protons in the nucleus, they don't just disappear into the nucleus because they must obey their matter waves which only fit into the nuclear attraction potential at unique energies, viz., the quantum states of the atom. So those electron-proton attractions aren't fatal.
Chemistry would be lots easier if chemical bonding occurred in this mindlessly simple way, the attraction of opposite charges, and for quite a few molecules, that's exactly what happens! That is, metallic atoms with low ionization potentials can be persuaded by some voracious non-metallic atoms to give up j valence electrons to become cations (M j+ ). Of course, charge (like mass and energy) is conserved; so the stolen electrons become excess negative charge on the now anionic non-metal (A j- ). And the two oppositely charged ions should bond, attracted by their opposite charges but buffered apart by their uninvolved core electrons.
But as we peruse the tables of ionization potentials and electron affinities, we find that the former (IPs), even for alkali metals, are lots larger than the latter (EA), even for halogens! For example, it takes ~500 kJ/mol to rip the valence electron off Na but you only get back ~350 kJ/mol by putting it on Cl. Does this mean that NaCl can't form as [Na + ][Cl - ]? Not at all. Not only does it form, but it forms vigorously! Where's the missing 150 kJ/mol?
True, we've not figured into the calculation the attractive potential of the cation for the anion, but there's something more fundamental: it's not just the one cation and anion pair. To make NaCl(s), you condense some NAv Na + and Cl - pairs together into a simple crystal lattice...indeed, the simplest:

-+-+-+-+-+-+-+-+-+-+-+-+  etc.

where any particular + cation is bonded ionically to six neighboring anions. ("I see only 4! Where are the two I can't see?," you ask (provocatively); they lie one each in the planes above and below the one shown here. That's lots better than a single cation-anion attraction!
But we're being too generous! Look again at some (interior) + cation in that crystal structure. Diagonal to it are 8 other + cations (4 you see and two more both above and below) which repel our victim cation! Now it sounds like we're losing ground! 6 attractions and 8 repulsions?!? Not to worry! Notice how the repulsions are on diagonals, and thus further away hence weaker!
In fact, this being just geometry, we can keep up looking at still weaker attactions and repulsions even further from our victim, but they'll inevitably add up to a sizeable attraction (lowering of potential energy) for having been in the crystal over having only a single anion mate. And this overall attraction is denoted Lattice Energy, always exothermic! We get it from the imaginary process of imploding the crystal from a gas of its ions. (Imagine each charge above staying in an orderly array but getting uniformly further from its neighbors until it can no longer feel them; that's the reverse of implosion which releases Lattice Energy.)
The text speaks of a Hess's Law cycle whose final step is the formation of the crystal lattice via that implosion and how that saves the bacon of ionic bonding, providing the exothermic punch to make it work. However, the energy stages diagrammed in the text aren't proper, and a better diagram of the process of creating an ionic salt crystal from its elements would be:
     _____K+(g) + e-(g) + Cl(g) _____
      |                           |
      |                           |
      |                 - 349 kJ  |
      |  + 418 kJ                 |
      |                           |
      |         ___K+(g) + Cl-(g)__|
      |                           |
     _|__K(g) + Cl(g)__           |
      |                           |
      | + 122 kJ                  |
     _|__K(g) + ½Cl2(g)__         |
      | + 89 kJ                   | Lattice
Start_|__K(s) + ½Cl2(g)__0 kJ     | Enthalpy
      |                           |
      |                           |
      |                           |
      | - 437 kJ                  |
      |                           |
      |                           |
But is ionic the only column in the Roman Empire? No. So why should it be the only bonding in Chemistry, eh?


For one thing, many ionization potentials are far, far in excess of electron affinities; too much to be compensated for by lattice energy. In those cases, the electrons will refuse to cross over. But they're still interested. Why? Bonding with another atom allows the valence electrons of both to taste the attraction of not one but two positive nuclei. The question is whether the taste is sufficiently enticing to overcome The Problem? The Problem is, that those nuclei can feel one another's influence as well. Fortunately, if the atom's can't merge, nucleus A will be further from B than B's own valence electrons, and vice versa. So B's electron's screen B from A and vice versa...the old "effective charge" argument. So the repulsion of the A and B nuclei is likely to be overcome by their attraction to one another's electron.
Indeed, the long-range forces between all atoms and molecules is attractive. (A good thing too or we'd not be able to solidify anything.) But as the nuclei of two or more atoms approach one another, one of two things might happen. Worst case? The electrons might begin to avoid the space between the nuclei; an example would be if the two electrons were the same spin. Pauli's Prohibition would be responsible for such avoidance. If that were the case, the positive nuclei would no longer be well shielded along their line-of-sight, and their repulsions would dominate. Such atoms would avoid bonding!
Covalent Binding Curve Best case? The approaching electrons were of opposite spin, Pauli is foiled "Curses, foiled again!" permitting electron density to accumulate more richly between the nuclei. That shields the nuclear repulsions and lowers the electronic potentials because they're attracted by two positive charge centers! Now it's not all peaches and cream; biased build up of electrons between the nuclei means that electronic repulsions must rise. So the nuclei can't get indefinitely close. But there's some happy medium where repulsions and attractions are balanced at an overall reduction in potential below that of the separated atoms. That potential difference is the Bond Dissociation Energy, De, and the internuclear distance at which this balance is struck, is the Equilibrium Bond Distance, Re. And the curvature in the potential as it pulls up from its minimum is the force constant of the Daltonian spring that is the bond; its oscillation frequency is related to (the square root of) that force constant. (We'll need to know that in a couple of semesters when we want to find the identical frequency of light which makes molecules vibrate; that's a powerful identification tool.)
G.N. Lewis (UC Berkeley!, 1912-46) is responsible for identifying (non-ionic) shared electron bonds, called Covalent Bonds. We chemists still use his notation for shorthand electronic configuration of both atoms (Lewis Symbols) and molecules (Lewis Structures). (He also generalized the notion of acids and bases, and the theory of valences as a consequence of atomic structure is the Langmuir-Lewis theory.)
Lewis Symbols are more than just a count of the valence electrons (those in the outermost shell). They also anticipate valence (bonding capacity) in their positioning. And they anticipate bonding incapacity of pairs of electrons called lone pairs as distinct from those bonding pairs engaged in the formation of covalent bonds.

            .    .  .   .    .    .     ..
Na.  .Mg.  .Al.  .Si.  .P.  .S:  :Cl:  :Ar:
                        ¨   ¨    ¨     ¨

(I need to apologize for the crude Lewis Symbols, HTML is a little impoverished in its typography.)
Each dot ( . ) is a valence electron. Paired dots ( : or .. ) are spin-paired electrons. Unpaired electrons are available for sharing in covalent bonds, so says Lewis. But wait, isn't Mg [Ne] 3s²? Those are paired! Why don't they show up as :Mg? The semi-facetious answer is that by unpaired those electrons, they can steal two bonds instead of none, lowering their potential energy. But to unpair the 3s², we must take at least one of them out of the 3s, and the obvious target is a 3p at higher energy!
This promotion of the electron to an excited state, Mg* [Ne] 3s 3p, requires less energy than is returned by the formation of two bonds, as in MgCl2. The same thing happens in Al; 3s² 3p becomes 3s 3p² to yield 3 unpaired electrons (remember the subshell boxes for each ml prefer lone electrons) for AlCl3. And Si can move to 4 bonds, SiCl4, by half-filling all its p orbitals at the expense of one formerly paired electron in s.
Of course, the rest of that row hasn't that same advantage. For example, P is 3s2 3p3, so all three (of the 3p) electrons are unpaired, and there's nowhere to put the (paired) 3s electron...or is there? The Lewis Symbols show only up to complete octets, but we know that P has some empty 3d orbitals (at still higher energy) which could serve as a home for that surplus s electron. In that case, P could bond five ways! Of course, the energy deficit is greater for promotion to d orbitals, so the gain would have to compensate. This would only work with really voracious bonding partners like, oh, say, oxygen; hence P4O10, phosphoric acid's anhydride! Since oxygen makes two bonds, 10 oxygens are worth 20 bonds divided by 4 phosphoruses are 5 bonds each! Viola. Promotion from s to d looks promising.


Lewis Symbols are atoms and their (octet) valence atoms. Lewis Structures are the molecules which can be made from the Symbols by electron sharing. But while Li:H (a legitimate molecule, by the way), does aptly connote the electrons spending more of their time between the nuclei than before to constitute the bond, the structure is more often displayed as Li-H. That dash will mean bonding pair, and is always read as two electrons. The reason for this is to distinguish bonding electrons from non-bonding, "lone pair", electrons as in phosphine or chlorine, for example:
  |      .. ..
H-P-H   :Cl-Cl:
  ¨      ¨ ¨
The rationale for Lewis Structures is not that they evolve from any heavy-duty theory but rather that they, like the VSEPR diagrams that we'll investigate shortly, correlate a lot of useful bonding lore. To see that unambiguously, we need to add multiple bonds and expansion of the octet to our toolkit.
Indeed, that expansion we hinted at already in the possibility of phosphorus using its 3d orbitals to promote electrons. With 5 bonding pairs around P in P4O10, we've gone the octet two better! And the value of double bonds is apparent in this molecule if you follow this link and remember to return here with your Back button. If you followed that page to its end, you have a notion of how to create a Lewis Structure of a non-octet and multiply-bonded molecule, viz., chloric acid (HClO3).


Just remember the rules and you can not only knock out the details of electrons bonding in really neat, weird molecules, but you can even make quite intelligent guesses as to how they're wired (i.e., what the skeletal bonding structure really is).
  1. Construct the single bond skeleton of the molecule.
    • That's often called the s skeleton for reasons that will become apparent later.
    • In Freshman Chemistry, we'll give you that skeleton, but we probably don't have to. If you have a triatomic molecule to try to "build," you can only do it 4 ways: A-B-C, A-C-B, B-A-C, and as a triangle which has each atom bonded to both others. Only one of those is likely to give a reasonable Lewis described below.

  2. Subtract the bonding electron pairs from the sum of all the valence electrons of all the atoms in the molecule and any ionic charge too!

  3. Distribute those as yet unused electrons to make octets as non-bonding electron pairs.
    • If you have to shortchange anyone, let it be the central atom 'cause we can fix that below.

  4. If any octets are incomplete (and don't try to make one around hydrogen, please!), convert a lone pair to a multiple bond to up the ante around the deficient atom without changing the octet about the donor!
    • That's the beauty of octets counting all shared electrons as if they belonged to both partners. If an atom sacrifices a lone pair to make a double bond from a single one, it still gets to count both electrons as part of its octet! The only known case of having your cake and eating it too.

  5. Minimize formal charges with more such conversions.
    • But don't lower the formal charges if the only way to do it is to undo somebody's octet unless the atom is from row 3 or beyond and thus has 3d orbitals to exceed an octet!
    • Right. You haven't been introduced to formal charges yet...even though that link up there used them! OK...preview from next lecture: Just as there are valence electrons, there are an equal number of protons to keep them happy. If in counting the electrons surrounding an atom in the Lewis Structure, you find a couple more than the neutral atom would've had, that atom has a formal charge of - 2. If there were three fewer than there should've been, that's a + 3 formal charge. But here you can't have your cake and eat it too! A formal charge on an atom can't count BOTH electrons of a covalent bond to that atom; those electrons are can count only half the electrons in its bonds!
    • If an atom must inherit a formal charge, it should at least be consistent with its electronegativity. The more electronegative element in a bond ought to bear the more negative formal charge, but zero would still be preferred. (Sometimes violating even this common sense rule seems inevitable. For example, carbon monoxide is :C:::O: with all electrons shown explicitly. The formal charge for oxygen is "expecting 6 but seeing only 5...Heavens! I'm + 1!" But oxygen is considerably more electronegative than carbon. Tough. Oh...for completeness, we should do the carbon too, but since formal charges add up to the molecule's charge, the carbon will have to be - 1 here.)

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Last modified 19 June 2000. Chris Parr