Ionic
Bonds |
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.
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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.
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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?
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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.
+-+-+-+-+-+-+-+-+-+-+-+-
-+-+-+-+-+-+-+-+-+-+-+-+
+-+-+-+-+-+-+-+-+-+-+-+-
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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!
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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!
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Lattice
Energy
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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.)
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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) _____
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| - 349 kJ |
| + 418 kJ |
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| ___K+(g) + Cl-(g)__|
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_|__K(g) + Cl(g)__ |
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| + 122 kJ |
_|__K(g) + ½Cl2(g)__ |
| + 89 kJ | Lattice
Start_|__K(s) + ½Cl2(g)__0 kJ | Enthalpy
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| - 437 kJ |
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_V__________KCl(s)___________V__Finish
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But is ionic the only column in the Roman Empire? No.
So why should it be the only bonding in Chemistry, eh?
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Covalent
Bonding |
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.
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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!
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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.)
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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.)
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Lewis
Symbols
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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.
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. . . . . . ..
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.)
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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!
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Electron
Promotion
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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.
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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.
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Lewis
Structures |
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:
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H
| .. ..
H-P-H :Cl-Cl:
¨ ¨ ¨
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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.
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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).
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Rules |
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).
- 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 Structure...as described below.
- 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!
- 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.
- 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.
- 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 shared...it 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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