Prof: Okay,
let's start up.
So last time we got to the
point of asking the question,
are there atoms and molecules
-- and well,
I anticipate that the answer is
yes --
and what force holds the atoms
together?
Because if we really understand
the force that holds them,
we've got chemistry all solved.
 
So when you come to the idea of
forces, in the first place,
one goes back to Newton and
Principia Mathematica.
And he had the idea,
or developed the idea,
the mathematics of gravity.
 
And the interesting thing about
it was there was no mechanism
for it.
 
There were no springs or
strings that connected the
things.
 
It was action at a distance.
 
So there were other ideas.
 
Like, Descartes had the idea
that gravity resulted from
blocked repulsion,
that the universe was full of
particles zipping around and
bombarding things.
So like the moon would be
bombarded by particles from all
directions, but there'd be no
net force on it because they'd
all balance out.
 
However, if you put the earth
in the way, there'd be a shadow,
and now you'd have more things
hitting the moon from the right
than from the left.
 
So it would seem to be
attracted to the earth.
So that's a great mechanism.
 
Now, it was important for
Newton that the force be
proportional to r^2,
to inverse r^2,1/r^2.
Does this work for that?
 
If you pulled the earth back,
how would you change things?
What do you say?
 
Student:  I don't know.
 
It doesn't work for this.
 
Prof: It doesn't work?
 
Would it block more or fewer
things if you pulled it back?
Students:  Fewer.
 
Prof: How many fewer?
 
Suppose you made it twice as
far back, how many fewer would
be blocked from hitting the
moon?
Student:  Wouldn't it be
r^2?
Prof: It would be 1/r^2.
 
You can think about that.
 
So that aspect of it would work.
 
How about -- you know gravity
is proportional to the mass of
the things.
 
How does that figure?
 
You can think about that
yourselves, okay?
But anyhow, there were other
ideas.
But Newton didn't think about
the mechanism,
he thought about the law,
that it was 1/r^2 and
proportional to the masses.
 
Now in 1717,
he published the Second Edition
of Opticks.
 
He published the First Edition
in 1704, and the reason he
published it in 1704 was that
Robert Hooke died in 1703.
He'd actually -- Newton had
done this work in the 1660s and
'70s,
but he didn't publish it until
Hooke died because he didn't
want Hooke to get on his case,
criticizing it.
 
But in the Second Edition,
in 1717, he put some additional
material;
you see, "with Additions.
" And the additional
material, even though the book
is about optics,
the additional material is
about chemistry.
 
And it's at the end,
and posed not as hypotheses but
as questions,
because Baconian people,
following Francis Bacon,
weren't supposed to make
hypotheses,
but they could ask questions.
So here are some of the
questions.
Question thirty-one,
the one that has most to do
with chemistry:
"Have not the small
Particles of Bodies certain
Powers,
Virtues, or Forces by which
they act at a distance,
not only on the Rays of Light
to reflect,
refract and inflect them,
but also upon one another for
producing a great part of the
Phaenomena of Nature?"
(And this attraction between
the particles or repulsion)
"For it's well known that
Bodies act upon one another by
the Attractions of Gravity,
Magnetism and Electricity;
and these Instances shew the
Tenor and Course of Nature,
and make it not improbable but
that there may be more
attractive Powers than these.
 
For Nature is very consonant
and conformable to her self.
How these Attractions may be
perform'd, I do not here
consider.
 
What I call Attraction may be
perform'd by
impulse…"
Where did he get that idea?
Where did he get the idea that
there are impulses that can
cause attraction?
 
Student:
>
Prof: That was
Descartes' idea,
that we just explained.
 
"…or by some other
means unknown to me.
I use that Word here to signify
only in general any Force by
which Bodies tend toward one
another, whatsoever be the
Cause.
 
For we must learn from the
Phaenomena of Nature what Bodies
attract one another,
and what are the Laws and
Properties of attraction,
before we enquire the Cause by
which the Attraction is
perform'd."
(So get the law first so you
can do mathematics on it,
and then worry about how it
works.)
"The Attractions of
Gravity, Magnetism and
Electricity, react to very
sensible distances…"
(He doesn't mean reasonable,
he means ones that you can
sense.)
 
"…and so have been
observed by vulgar Eyes."
(You can see the distances over
which electrostatic attraction
works, obviously gravity,
magnetism.)
"And there may be others
which reach to so small
distances as hitherto to escape
observation;
and perhaps electrical
Attraction may reach to such
small distances,
even without being excited by
Friction."
 
(So you know that friction can
generate static electricity
that'll make things attract,
but maybe even without friction
you can get things that'll
attract a very short distance by
electricity.)
 
"The Parts of all
homogeneal hard Bodies which
fully touch one another,
stick together very
strongly."
 
Did you ever have that
experience of having two really
flat things, put them together
and they're very hard to get
apart;
what?
Student: Slides.
 
Student:  Small things.
 
Prof: Microscope slides.
 
Ever take out new microscope
slides?
They can be very hard to get
apart.
"And for explaining how
this may be, some have invented
hooked Atoms,
which is begging the Question;
and others tell us that Bodies
are glued together by rest,
that is, by an occult Quality,
or rather by nothing,
and others that they stick
together by conspiring motions,
that is by relative rest among
themselves."
(These are other theories that
are sort of complicated;
we don't need to go into it.)
 
"I had rather infer from
their Cohesion,
that their Particles attract
one another by some Force,
which in immediate Contact is
exceeding strong,
at small distances performs the
chymical Operations above
mention'd,
and reaches not far from the
Particles with any sensible
Effect."
(So a very short-range,
a very strong attraction.)
"…reaches not far
from the Particles with any
sensible Effect."
 
So maybe it's even more
dramatic than 1/r^2.^( )1/r^2
changes very rapidly when r gets
very small,
but maybe it's even a law
that's more distance dependant
than that,
but only works at really,
really small distances.
 
"The Attraction"
(and he's talking about between
glass plates separated by a thin
film of the Oil of Oranges;
so you know,
microscope slides,
they put a little drop of
something and stick them
together and they're really hard
to get apart) "may be
proportionally greater"
(the attraction) "and
continue to increase until the
thickness do not exceed that of
a single Particle of Oil."
 
(Imagine Newton,
350 years ago or 300 years ago
here, thinking about a single
particle of oil.
Could he possibly measure that?
 
We'll think about that later.
 
Okay.)
 
"There are therefore
Agents in Nature able to make
the Particles of Bodies stick
together by very strong
Attractions.
 
And it is the business of
experimental Philosophy to find
them out."
 
That's what we need to
find, what is it that holds
these particles together?
 
"Experimental
philosophy"
means science.
 
And we're going to engage in
this business,
and it'll take us about five
weeks to figure out what it is
that holds these things
together.
Now, let's just look,
from physics,
at the amount of binding energy
you get from different kinds of
laws.
 
First there's Coulomb's law;
so it charges over the
distance.
 
I think you all know that one.
 
Then there's magnetic
interaction, two magnetic
dipoles, and the energy is
1/r^3, falls off very rapidly.
Then there's the
"strong"
binding that holds particles
together in the nuclei of atoms.
And gravitation, of course.
 
And the chemical bond.
 
So here's a scale of energies,
and we use, in this course,
the old fashioned
kilocalories/mol,
which American organic chemists
like to use.
Some day it'll change to
kilojoules/mol,
but for me it's still
kilocalories/mol.
Okay, this is a logarithmic
scale, so it covers a very wide
range.
 
Now Coulomb,
if you have a proton and an
electron,
as far apart as the distance of
the carbon-carbon bond,
that's 216 kilocalories/mol,
right in the middle of this,
or near the middle.
Magnetic interaction is much
weaker.
If you have two electron spins,
at the same distance from one
another, their energy is what?
 
One, two, three,
four, five orders of magnitude
smaller, 10^5th smaller.
 
The "strong"
binding that holds a proton and
a neutron together is in the
deuterium nucleus,
that is within the nucleus,
not at 1.54 Ångstroms,
is 10^5th stronger than
Coulombic interaction.
And gravity is ever so much
weaker.
If you had two carbon atoms,
that were at that distance,
the energy would be 10^-32
kilocalories/mol.
So forget gravity as a way of
holding things together.
But then we have Coulombic up
or down by 5 orders of
magnitude.
 
Now what is a chemical bond;
how strong is it?
A chemical bond is about -- the
carbon-carbon bond is about 90
kilocalories/mol.
 
So not so far from the Coulomb
energy, from electrostatic
attraction.
 
So maybe this hints that
electrostatic attraction has
something to do with it.
 
But maybe not,
maybe it's something entirely
new.
 
And we haven't talked about
kinetic energy.
Does that have anything to do
with the strength of the bond?
So we'll get back to that later
on.
Okay, so is there a chemical
force law, the thing that Newton
was looking for?
 
Now here's an interesting way
to phrase that.
Suppose you had a chain of
atoms, a thread that was single
atoms bonded to one another,
and you started stretching it.
It would stretch,
and at some point it would pop.
Now let's just take three of
the atoms and we'll put stiff
rods on the outer ones and we'll
start stretching it.
So it'll stretch,
stretch, stretch,
stretch, pop.
 
Now the question is how far do
you stretch it before it pops?
What determines how far you
stretch it before it pops?
Okay, this must have to do with
the force law between atoms,
which then will have to do with
molecular structure.
So it could be like springs,
Hooke's law,
Ut tensio,
sic vis.
Okay, so the force is
proportional to the
displacement,
and the energy to the square of
the displacement and the energy
then,
the potential energy,
is a parabola.
We define zero when they're at
the standard,
unstretched distance,
and then you stretch it or
compress it and the energy goes
up, like a parabola.
Now the slope of that parabola
tells you what?
Student:  The force.
 
Prof: The force.
 
That's what's linear.
 
As we stretch it further and
further, the slope gets bigger.
The force is proportional to
the displacement.
Okay, now there could be other
kinds of force laws,
like electrical charges,
Coulomb, or gravity.
So that's a different force
law, inverse square force law,
and the energy then is
proportional to the
displacement,
in this way.
So very different.
 
Notice the zero of this one's
at the top when -- zero defined
when they're very far apart.
 
Here it's zero when they're at
the standard distance.
And so as you bring oppositely
charged particles together,
the energy goes down
infinitely, as they get really
close.
 
Okay, and now if we look at the
force here, as we go out the
force gets smaller,
the slope gets smaller.
Now suppose you had a particle
that was connected to a spring
on each side,
as in this chain that we're
stretching.
 
And just to be general I made
the second string -- oh I say
stronger, it's in fact weaker;
it doesn't go up as rapidly --
I'll have to change that.
 
Okay now, but at some point the
slopes of the red and the blue,
at some distance,
some position,
will be equal and opposite.
 
There.
 
Okay, what's the force on the
central particle at that point?
Students:  Zero.
 
Prof: Zero.
 
They balance.
 
So if we added those two
energies together to get the sum
of the two, on this central
particle, it looks like that.
So there's a balanced minimum.
 
There's a well defined position
where the particle in the center
of this chain will just sit
there and it'll be hard to
displace.
 
So it can vibrate.
 
Okay?
 
Now how about in the other case?
 
How about if it were electrical
charges or gravity or something
like that, an inverse square law
that's holding things together?
Then the second one is going to
look like that,
and that one is indeed
stronger.
So they're two flanking bodies
and we're interested in the
position of the one in the
middle.
And again, there'll be some
point where they balance,
right there,
where they're equal and
opposite slopes.
 
How will this differ from the
first case?
Can you see what's going to
happen when we add these two
together?
 
Is it going to look more or
less like the one on the left?
Student: 
>
Prof: It's going to look
like that.
And now there is no balanced
minimum in the middle.
There's not a position where
the thing will just sit there,
because it's always more
strongly affected,
and attracted,
by the one it's closer to.
There's some place where
there's zero force but it's not
a stable position.
 
Because if it displaces ever so
slightly, it'll keep on going.
So that one is a -- for the two
of them -- is a single minimum,
and this one is a double
minimum.
And for the people who came
early, there was a contest that
if you won it,
you could get an A in the
course, and the contest is this.
 
Here's a magnet, hanging here.
 
And I'll stop it.
 
Okay, and here are two magnets,
the ones that will flank that
one.
 
And if I get it just right,
it'll just sit there,
the attraction to the two will
balance it.
So I'll put it on here,
and try to get my A.
So I'll get the string where it
would balance right there.
Ah.
 
Okay?
 
There is no stable position.
 
Nobody got their A that way.
 
Right?
 
Because it's an inverse law,
so it's always more strongly
attracted to the closer thing.
 
So you can't win with that,
you can't get a balanced
position.
 
Now I'm going to get these off
here.
And back to the show.
 
So with springs you might be
able to make a stable polyatomic
molecule from point atoms --
we saw a spring model before in
the last lecture --
but you can't do it with ions
and you can't do it with
magnets.
However, Hooke's law can't do
it -- it can't be springs,
because Hooke's law never
breaks.
So we need a different kind of
force law.
Does anybody know a force law
-- what it looks like -- the
form of the force between atoms
or the energy for stretching a
bond?
 
You ever seen a picture of such
a thing?
Student: 
>
Prof: It's called the
Morse potential,
or one form of it at least is
called the Morse potential.
And it's not something
fundamental, it's not a law of
nature.
 
It was thought up by a
physicist at Princeton in 1929,
because it's mathematically
convenient;
so you could solve quantum
mechanical problems if you used
Morse potentials.
 
And the idea is this.
 
You have two neighbors and you
look at the position of the one
on the right and it could be
there and the energy would be
minimum;
that's the bond distance, right?
And if you move it further to
the right, the energy goes up;
move it to the left,
the energy goes up.
Okay, that's the Morse
potential, and we're just
holding the neighbor on the left
fixed.
Now we could put another
neighbor on the other side and
have another curve of the same
sort;
stretching the second bond.
 
Or we could have it be a chain
and have both neighbors there,
and the sum of those two now
has a minimum in the middle.
It's a single minimum,
like we got with Hooke's law.
So that means that atom in the
middle would just stay there.
And now we're going to grab
those sticks on either side and
pull the neighbors apart.
 
So if we pull them apart,
it's still a single minimum.
And if we pull them apart
further, it's still a single
minimum, although it's very
flat.
And if we pull it further,
it pops and it becomes a double
minimum.
 
And if we keep going the double
minimum gets more pronounced.
Now here's an interesting
question.
At what point -- how far do you
have to stretch it before it
pops?
 
That's the question we were
asking, right?
How can you look at those
curves and tell how far apart
you have to stretch it before
the chain pops?
Shai?
 
Student:  The bottom is
flat.
So when the curve and the plot
was flat, then that's as far as
it could go because --
Prof: What do you mean
flat?
 
There's a name for a thing like
that in graphs.
Student:  Inflection.
 
Prof: It's the
inflection point.
It's when the curvature changes
from being this way,
like Hooke's law,
to being this way,
right?
 
So when the inflection points
cross, then the chain pops.
Okay, so force laws are going
to make a lot of difference in
how atoms behave,
and if really knew the force
law we'd be in a great position
for understanding chemistry.
It snaps at the inflection
point where it changes from a
direct to an inverse dependence
on distance for force.
Okay, but what
are bonds?
Newton said,
"We'll look for the
law."
 
And it's sort of,
the law is sort of like Morse,
but we don't know where it came
from,
because we don't know how it
works,
we don't know what it really is.
 
So can we find out what it
really is?
Well in the nineteenth century
they discovered bonds.
And this is a picture from
1861, we'll talk about this
later.
 
It's one of the first
depictions that's recognizable
by people today of bonds between
atoms.
So there are different numbers
of these lines,
valences, for different atoms.
 
Hydrogen has one;
carbon has four;
oxygen two; nitrogen three.
 
Why do the elements differ?
 
Why don't they all have the
same valence?
And even more complicated,
sometimes nitrogen is three and
sometimes it's five.
 
For example,
you have NH_3_ but
you also have NH_4Cl,
where there are five things
associated with the nitrogen.
 
So how do you understand the
valence?
That was the challenge for
people.
They had figured out that there
was valence, but why?
How could you predict the
valence of a new element?
Well Gertrude and Robert
Robinson published a paper in
1917 which showed this picture
of ammonia, NH_3.
What's the loop?
 
Pardon me?
 
>
Prof: Someone said --
hold your hand up so that people
can hear you.
 
Okay yes.
 
Student:  A lone pair on
nitrogen.
Prof: A lone pair on
nitrogen -- wrong.
It looks like the lone pair on
nitrogen but the lone pair
didn't come along that soon.
 
What the loop means,
if you look at it in the
context, is what makes NH_3_
reactive?
In this term,
this is what they wrote:
"It may reasonably be
assumed that the partial
dissociation is a stage in the
complete process."
So the bonds begin to break.
 
This loop begins to break to
become a weaker loop and two
other partial valences,
in this theory.
And those valences begin to
associate with partial valences
from HCl.
 
Right?
 
The loop is a
"latent"
valence.
 
You know what 'latent' means?
 
Latent is the opposite of
patent.
Latent means hidden;
patent is revealed.
When you get a patent on
something it means that you tell
everybody how to do it but the
government protects your right
to do it for a certain period of
time.
Latent means it's hidden.
 
So there's a hidden valence,
these loops,
but they can become available,
right?
It must be assumed in some
cases, as for example the
combination of ammonia with
hydrochloric acid.
Now, so you can get a reaction
and get the product,
which has all five valences of
nitrogen now.
But how do you know there's not
another loop on nitrogen,
that you could break open and
make it seven valent,
or nine, or eleven?
 
Or maybe you could break a loop
into three.
So might latent valence loop
explain the trivalence and
pentavalence of nitrogen,
or the amine-HCl reactivity?
The trouble is it's too
slippery a concept.
It explains everything.
 
You could explain anything you
wanted to.
You could explain eighty-four
valence of nitrogen or
something.
 
Anything that comes along,
you'd say, "Ah ha,
there are that many latent
valences."
But how do you know there are
not more?
Why do you have latent valences?
 
When do you have them?
 
When and why do you have
partial dissociation?
This thing didn't explain
anything, or explained
everything.
 
Now, at this point I want you
to smile so I can learn who you
are.
 
<<Professor McBride takes
pictures of the class
members>>
 
Prof: So the electron
was discovered in 1897.
So maybe that has something to
do with it.
And the guy who had associated
electrons with valence was
G.N. Lewis.
 
And this is a picture of him as
a Harvard undergraduate in 1894.
And this is eight years later,
when he was an instructor at
Harvard,
and he then went to establish
the Chemistry Department at the
University of California at
Berkley.
 
Student:  Yay!
 
>
 
Prof: But when he was at
Harvard in 1902 he used these
lecture notes,
and what he was trying to
explain was the periodic table,
why you go across in eight and
then another eight and another
eight,
and so on, and why you have
electron transfers from some
atoms to other atoms.
 
And he said if the electrons in
an atom are arranged at the
corners of a cube,
then you -- eight is this very
special number,
because that occupies all the
corners of the cube.
 
So if there's a desire,
for some reason,
to complete octets,
then you can explain
periodicity and see why some
atoms give up an electron to
lose the outer shell and others
gain one to complete the outer
shell.
 
Okay, so but it also could
explain how you get bonding,
if you like to have octets;
not just electron transfer but
the formation of covalent bonds.
 
So, for example,
here's two chlorines.
Each has only seven;
the octet isn't complete.
But if you bring them together
and they share an edge,
then both octets are complete.
 
He doesn't say
why octets should
be so great, but if they're
octets then you could explain
bonds.
 
How about double bonds?
 
Suppose you had two oxygen
atoms.
What do you do now?
 
Anybody see?
 
What?
 
Student:  Put the faces
together.
Prof: Put faces
together, share two edges,
and then both have an octet.
 
Now, suppose you want to put
nitrogens together and form a
triple bond.
 
Now how do you do it?
 
Student:  Squish it.
 
Prof: Push it hard,
force it like a picture puzzle?
Student:  Yes.
 
Prof: Put it in there.
 
Student: You need to
push it.
Student:  You did it.
 
Prof: It won't do it.
 
But about ten years later he
figured out how to do it.
What you do is take the
electrons -- nitrogen has 5 --
but instead of using an octet,
you contract it along opposing
edges this way.
 
So what was an octet,
what was a cube,
becomes what?
 
Student:  A tetrahedron.
 
Prof: A tetrahedron.
 
And now if you take two
tetrahedra, you can put a face
together and complete both
octets.
But this wasn't such a great
development.
He did this,
published this,
in 1916.
 
But the tetrahedral
distribution of the bonds in
carbon had been known by organic
chemists for 40 years by that
time,
that the tetrahedron was a very
important structure.
 
So a good theory should be
realistic and it should be
simple.
 
But there's a tension between
these things.
It should at least be as simple
as possible, but that may not be
very simple;
that's why it takes us five
weeks.
 
In regard to the facts it
should allow a number of
properties.
 
It should allow prediction.
 
You should be able to say how
will these atoms react;
how will this molecule react;
what valence should nitrogen
have;
how can it be both pentavalent
and trivalent?
 
A little below this on the
scale of desirability is
suggestion.
 
A theory may -- even if it
doesn't give you the proper
thing, may at least suggest some
experiment that would be really
good to do.
 
Below that is explanation --
according to my theory all these
known facts fit together,
but who knows about any new
thing.
 
And lowest is classification
and remembering;
like Roy G. Biv allows you to
remember the colors of the
spectrum, but there's nothing
fundamental about that.
So even if you have a crummy
thing it might allow you to at
least remember some facts and
organize them maybe.
Okay, but those last two are
not prediction,
they're post-diction;
you only use it to explain
things that are already known as
a way of remembering them.
So from the number of valence
electrons we'd like to predict
how many atoms of different
types come together to form
molecules.
 
That's constitution -- the
nature and the sequence of bonds
-- and the valence.
 
We'd like to know the structure
of molecules,
the distance between atoms,
angles.
We'd like to know how charge is
distributed within molecules.
Are some regions positive and
others negative?
We'd like to know what the
energy of the molecule is.
Is this arrangement of the
atoms better or worse than an
alternative arrangement?
 
And we'd like to know about
reactivity.
So Lewis explains constitution,
the nature and the sequence of
bonds.
 
"Nature"
means like single,
double, triple,
and "sequence"
means which atoms are connected
to which.
So he has electrons,
valence, and also he added
unshared pairs.
 
So you count up how many,
from the atomic weight or the
atomic number or the position in
the periodic table.
You get how many valence
electrons, how many of these
outer octets are there.
 
And then you can figure that
the valence of hydrogen should
be one, boron three,
carbon four,
but then down again,
three, two, one.
So here's ammonia, NH_3.
 
It works fine and it has an
unshared pair.
But why do you have octets?
 
Why not sextets?
 
And why do you have a pair for
hydrogen?
Why not an octet for hydrogen
also?
Okay, so let's just apply it to
HCN.
So if carbon has four,
that makes possible a single
bond to hydrogen,
a triple bond to carbon.
Everybody has their octet
except hydrogen that only wants
two.
 
So everybody's happy.
 
And we can abbreviate it this
way, and leave the dot.
Lewis actually thought of
drawing a colon,
a pair of dots,
to denote an unshared pair.
So that's his notation.
 
So NH_3.
 
Bingo!
 
How about BH_3?
 
Just fine.
 
But here's something new.
 
The organic chemists would
already have known this,
they knew the valence numbers.
 
The electrons just added
something to it but didn't say
anything really new.
 
But here's something new,
that BH_3_ reacts
with NH_3, to give a new bond.
 
Now here's a puzzle.
 
It's also true that BH_3 reacts
with BH_3_.
That doesn't look like
Lewis.
And the bond is reasonably
strong, it's half as strong as a
carbon-carbon bond.
 
So what's the glue that holds
B_2H_6 together?
And we'll come back to that
fourteen lectures from now.
But there's another thing.
 
There's bookkeeping that you do
with Lewis structures to assign
what's called formal charges;
not real charges,
just what charges you write in
the formula, and you hope they
mean something.
 
And the bookkeeping scheme you
use is that each atom is
assigned half interest in the
bonding pair.
So if there's a bonding pair,
for bookkeeping purposes you
assign one electron to each.
 
It may be they aren't evenly
shared, but the bookkeepers
don't care.
 
Incidentally,
speaking of bookkeepers not
caring,
there's -- people have had a
lot of nonsense trying to get
signed up for lab,
because the people who run the
system don't allow teachers to
have access to the thing to see
the problems you face.
So I have no way of telling --
I can't get on to your system.
Has everybody figured out how
to sign up for lab by now?
Student:  Yes.
 
Prof: If anybody still
has problems,
after class Dr. DiMeglio can
take you to the computer center
here and help you.
 
So next year presumably it'll
be easier.
This is a new system this year.
 
But anyhow, back to the
bookkeepers here.
So these formal charges are not
necessarily real charges,
they're just what you write
when you draw the formulas.
Okay, so we split the BN
electrons between the B and the
N, and we split the hydrogen
bonds as well.
So nitrogen now has those four
electrons, where it brought five
to the table originally.
 
So it has a positive charge.
 
Tetravalent nitrogen is
positive in the Lewis structure.
Why?
 
Because in forming a fourth
bond, it gave up half-interest
in one of its electron ,
the ones in the unshared pair.
So it lost a charge,
a negative charge,
and becomes positive.
 
By the same token,
what else can you write in this
structure?
 
>
Student:  It's negative.
 
Prof: A negative charge
on boron, because it got
half-interest in a pair.
 
But that's just bookkeeping.
 
So when you write a Lewis
structure you'd write plus on
nitrogen and minus on boron.
 
Now is it real?
 
Is there a positive charge on
nitrogen and negative charge on
boron?
 
Well we'll get later on to know
about what a surface potential
is.
 
Surface potential is the energy
a proton would have if it was on
different points on the
molecular surface.
For this purpose you have to
define what the surface is of
BNH_6.
 
There's a way of doing that;
we won't talk about it now,
that's jumping the gun.
 
But that's the surface,
and it's color coded to show
the energy a proton would have
if it were on the surface at
that point.
 
So what you see is that the
energy of the proton would be
high, if it's here,
where it's very blue.
The energy of the proton would
be low if it's in this region
here.
 
Is that consistent with what we
were talking about?
Student:  Yes.
 
Prof: Where would a
proton be low in energy?
Where there's negative charge,
and it would be high in energy
when there is positive charge.
 
So this molecule,
according to quantum mechanics,
is positive on the left and
negative on the right.
And that's exactly what we
have, it's consistent with what
we have.
 
And now Lewis also explains
where pentavalent nitrogen comes
from, because there's an ionic
bond there too.
Tetravalent nitrogen is plus.
 
So there's just a Coulombic
attraction between ammonium and
chloride.
 
So that's a great contribution.
 
Now there are other things you
can understand in terms of Lewis
structures.
 
Like you have an amine and it
can react with an oxygen to give
an amine oxide,
which is positive on nitrogen,
negative on oxygen.
 
Or you can have a sulfide,
which can react with an oxygen,
to give a sulfoxide.
 
Or what else can happen,
with a sulfur,
what additionally can happen?
 
Student:  Another oxygen.
 
Prof: It could do
another oxygen,
and give a sulfone,
as it's called.
So Lewis explains this.
 
So there are problems to drill
on Lewis structures.
They're on the Web,
go look at them.
One of them is draw Lewis dot
structures for HNC,
in that order,
H then N -- we did HCN;
but do HNC.
 
And then try HCNO with CNO in
all six linear orders;
that is, nitrogen in the
middle, carbon in the middle,
oxygen in the middle,
and then hydrogen on either
end.
 
And it's also possible to make
a ring of CNO and put the
hydrogen on any of the
positions.
So just practice drawing Lewis
structures of those.
And start memorizing functional
groups.
We do precious little
memorizing in this course,
compared to most organic
chemistry courses.
We try to figure out how things
work so that you can predict
without memorizing it.
 
But there are some things you
have to know,
like the names of groups.
 
Otherwise it takes forever to
talk about them.
So here are the ones you have
to learn,
and on the fist exam,
coming up in three weeks or
whatever,
I'll give you a question where
you have to draw one of these
structures from the name,
or give the name for a
structure.
These are all on the webpage;
you don't have to copy them
down.
 
But those are simple functional
groups.
>
 
And here are -- whoops,
oh there you go,
sorry.
 
>
 
There.
 
They're also conjugated
functional groups.
So you could run it yourself.
 
Okay, now the final question
here, for today,
is a thing that comes up when
you talk about Lewis structures,
or structures in general,
Lewis structures in particular,
is equilibrium and resonance.
 
How many people know what
resonance is?
What is it?
 
Student:  Like the same
molecule but different
structure.
 
Prof: Speak up a little
bit.
Student:  It's the same
molecule but a different
structure.
 
Prof: The same molecule
but a different structure.
But isn't structure a molecule?
 
Student: But with that I
guess --
Prof: You know like,
let me just interject a minute
here.
 
Like, one of the problems is
HCNO in any order.
So there would be different
molecules with C in the middle,
N in the middle,
O in the middle.
Is that what you mean?
 
Student:  No.
 
I mean like it's -- if you have
a double or a triple bond,
it's in a different location,
it's around the central atom.
Prof: Ah,
now let's -- actually resonance
is one of those things where
people try to hide ignorance
from ignominy.
 
And let me show you what I mean
by that.
So here's the structure for
HCNO.
And here it has all octets.
 
If you go through you'll figure
that out.
It has charge separation though.
 
You don't like to have that in
your structures.
You like not to have charges if
you can avoid it.
Obviously in BNH_6 you can't
avoid it.
Okay, now but you can get rid
of the charge separation by
shifting that electron pair
that's on oxygen to be shared
between oxygen and nitrogen;
then you don't have the charge
on oxygen anymore.
 
Everybody see that?
 
Student:  Yeah sure.
 
Prof: What's the problem
when you do that?
Nitrogen now has too many
electrons.
So you could shift a pair from
-- that's in the CN bond,
onto the carbon,
in your drawing you make.
Okay, so you get this structure
shown below which has all
octets.
 
But there's still charge
separation, and in fact it's
worse because the negative
charge, instead of being on
oxygen, is now on carbon.
 
So there are these two
different Lewis structures you
can draw and each has its own
properties, or good things and
bad things.
 
Now what are the geometric
implications of there being two
structures?
 
It could mean that in the
middle one, in the lower one,
nitrogen is exactly halfway
between carbon and oxygen,
because they are both double
bonds.
But in the top one,
nitrogen is much closer to
carbon than to oxygen.
 
That could be the meaning of
this.
So that if you draw a picture
of the energy,
as a function of the position
of the nitrogen,
you could get two different
structures,
one where it's further to the
left,
where the nitrogen is further
to the left you have this
structure,
and when the nitrogen's in the
middle you have that structure.
 
And you have to go up hill in
energy, it'll click;
as you start pushing the
nitrogen it starts,
it'll click,
and it's the other one.
Okay?
 
That could be the way the atoms
really behave.
That's called a double minimum;
we already saw a double minimum
today.
 
But maybe in truth it's not
this way.
Maybe it's a single minimum.
 
Maybe the best position for the
nitrogen is neither to the left
nor in the middle,
but in between;
maybe that's the lowest energy.
 
And that is what resonance is.
 
Resonance is when you -- the
true structure is in between the
structures you draw.
 
So really what it is,
is a failure of the notation.
Does everybody see how that's
so?
It's that the notation you use
doesn't show the right
structure, and when that happens
there's said to be
"resonance";
although actually all it is is
that the true structure is a
single minimum,
not the double minimum you'd
expect from your drawing.
It's a failure of the way you
draw.
And notice that for resonance
you use a double headed arrow
whereas if I back up a second
here --
equilibrium,
when you have a double minimum,
there are two arrows,
two different structures.
So the question is which is it?
 
Is the real molecule a double
minimum;
or the real molecules a double
minimum, are there two
structures?
 
Or is there in truth only one
structure?
So you need to choose.
 
The choice between whether
there's resonance or equilibrium
must be based on experimental
facts or on a theory that's
better than Lewis's theory,
to be able to know which is
true;
something that can distinguish
between a single and a double
minimum.
So equilibrium is two arrows,
and there are two structures
that go back and forth,
and resonance is a single
structure,
that our notation isn't very
good at drawing.
 
So two real species,
or one real species but two
reasonable formulas we could
draw for it, or that Lewis would
draw for it.
 
So really what it is,
resonance is a failure of
simplistic notation,
and it's associated with
unusual stability.
 
Now when I say 'unusual,' that
implies that you know what usual
stability is.
 
So compared to what is it
unusual?
And we'll address that question
later on.
So let me just give you finally
an example of equilibrium versus
resonance.
 
So this, as you'll learn when
you learn functional groups,
is a carboxylic acid,
and you could have the hydrogen
attached to this oxygen or it
could be attached to the other
oxygen.
 
So these are not just the same
thing upside down.
It's the hydrogen being
attached to one or being
attached to the other of the two
oxygens.
And, in fact, it is that way.
 
There are two structures and
you go back and forth between
them;
two species.
But how about if you take the
hydrogen atom away and have this
thing that's called a free
radical,
where you don't have a complete
octet on this oxygen?
There are only two,
four, six, seven electrons
there.
 
It has the ability to form
another bond by sharing an
electron.
 
Is that two different species?
 
Or is it one species -- watch
-- with an intermediate geometry
where you don't really have
double and single bonds but
something in between?
 
And how do you know which it is?
 
The only way is to do some
experiment that tells you.
And there is an experiment that
tells you it's only one nuclear
geometry.
 
And we don't have time in the
last thirty seconds to tell you
how that proof works,
but I'll tell you that the
technique is electron
paramagnetic resonance
spectroscopy
>
, shows that in truth,
although this is two species,
this is one species.
 
So there's equilibrium at the
top and resonance at the bottom.
And if you add an extra
electron to make a carboxylate
anion, infrared spectroscopy
tells you that it's symmetrical
too.
 
There's resonance in this case.
 
It's an intermediate structure.
 
But that is "lore."
 
You didn't predict that from
Lewis structure ahead of time.
It could've been either way,
and in fact there were many
people who thought it was one
way or the other.
It's only experiment that does
it.
So, next time we'll talk more
about lore.
