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Last time we were talking about
the general interactions that

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are present in a chemical bond.
And we were,

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in particular,
looking at the energy of

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interaction, here,
as we brought two hydrogen

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atoms together.
We were looking at that energy

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00:00:40 --> 00:00:48
of interaction as a function of
the distance r between these two

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nuclei.
And we saw, of course,

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way out here,
that the energy of interaction

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00:00:56 --> 00:01:02
was minus 2,624 kilojoules per
mole.

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00:01:02 --> 00:01:06
As we brought the two hydrogen
atoms in closer together,

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that interaction energy went
down.

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It became a maximum negative
value at some r.

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00:01:12 --> 00:01:15
That r is the equilibrium bond
length.

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And then, as you try to push
the two nuclei closer together,

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the energy of interaction goes
up again, so far up that when

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you get them really close,
the energy of interaction is

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greater than that of the two
separated hydrogen atoms.

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And so, in this region,
the hydrogen atoms are no

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longer bound.
Wherever this energy is lower

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than that of the separated
hydrogen atom limit you have a

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00:01:45 --> 00:01:49
bound molecule.
This was the attractive part of

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the potential.
This was the well depth or the

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bond association energy,
measured from here to here.

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00:01:56 --> 00:02:01
That is how much energy you
would have to put in to pull the

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00:02:01 --> 00:02:08
two hydrogens apart.
This is the repulsive region of

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that interaction potential.
We were talking about how that

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curve, that energy,
was really the sum of three

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components.
That energy of interaction was

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the sum of the nuclear-nuclear
repulsion.

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That is, the repulsion between
the nucleus of this hydrogen and

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the nucleus of that hydrogen.
In addition to that

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nuclear-nuclear repulsion,
there is the electron-nuclear

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00:02:50 --> 00:02:53
attraction.
The electron-nuclear

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00:02:53 --> 00:02:59
attraction, between the electron
on the original nucleus and,

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00:02:59 --> 00:03:03
when the two hydrogens get
close enough,

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00:03:03 --> 00:03:10
the electron attraction between
the other nucleus.

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00:03:10 --> 00:03:14
And then, finally,
there is the electron-electron

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00:03:14 --> 00:03:17
repulsion.
When these two hydrogen atoms

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00:03:17 --> 00:03:21
come so close,
the electrons now are going to

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repel.
And so, this curve is actually

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the sum of those three
contributions.

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00:03:29 --> 00:03:34
And what we were trying to do
last time is to look at the

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dependence of these
interactions,

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individually,
on r.

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00:03:39 --> 00:03:45
And then we wanted to sum them
up to see why we actually have

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the shape of this interaction
potential that we do.

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We are trying to decompose
this.

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We are trying to understand
over what regions of r,

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which one of these interaction
energies is dominant.

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That is what we are doing.
And I think last time we

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started in the sense that we
recognized what the r dependence

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was for the nuclear-nuclear
repulsion.

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The nuclear-nuclear repulsion
is just the Coulomb interaction

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energy between two like positive
charges.

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That nuclear-nuclear repulsion
was e squared over 4 pi epsilon

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nought times r.

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And so that component I could
easily draw.

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And I did draw it last time,
I think.

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This is one over r
dependence.

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This is the e squared over 4 pi
epsilon nought r.

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That was one of them.
Now, next, these two terms are

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what I am going to call the
electron interactions because

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both of them involve the
electron.

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This one did not.
This was just the nucleus.

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It turns out that I don't have
a nice simple way to tell you

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what the r dependence between
the nuclei will be for the

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electron-nuclear attraction,
nor do I have a nice simple way

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to figure out what the r
dependence will be for the

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electron-electron repulsion.
I cannot do that without

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actually solving the Schrödinger
equation.

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I don't have a simple way to
break that down.

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However, what I can do is I can
estimate what the sum of these

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electron interactions are at two
extremes.

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00:06:14 --> 00:06:19
Is this noisy?
Can you hear me?

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I can see why it is noisy.

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I do know what it is at two
extremes.

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I know what those sums of those
interactions are for very large

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r, and I know what it is for r
equals 0.

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What I am going to do is
calculate it for r equals

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infinity and r equals 0.
And I am going to then put it

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on this plot.
And then to just estimate what

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the r dependence is,
I am going to draw a line from

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that point to that point.
That is the best I can do.

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Let's do that.

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00:07:20 --> 00:07:27


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00:07:27 --> 00:07:33
Let me start with this energy
of interaction at r equals

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infinity.
I want to evaluate what the

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repulsive interaction is between
the electrons at r equals

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infinity.
What is that interaction

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energy?
It is zero because the

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electrons are so far apart at r
equals infinity that there is no

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interaction energy.
It is the repulsive

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interaction.
It is this kind of interaction,

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r equals infinity.
That is going to be zero.

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00:08:05 --> 00:08:10
But now this term,
this electron-nuclear

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attraction.
When the two hydrogen atoms

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here are very far apart,
what is the energy of the

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00:08:20 --> 00:08:24
electron-nuclear attraction
there?

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I cannot hear you,
so I will tell you.

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00:08:30 --> 00:08:34
It is the binding energy of a
1s electron.

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00:08:34 --> 00:08:38
I mean that is the energy of
interaction.

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00:08:38 --> 00:08:42
When r is very large,
when r is infinity,

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00:08:42 --> 00:08:47
the energy of interaction is
just the 1s binding energy of

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00:08:47 --> 00:08:51
the electron to each of its
nuclei.

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The energy of interaction,
the electron-nuclear attraction

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00:08:56 --> 00:09:02
is just E sub 1s for
this one.

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00:09:02 --> 00:09:05
And e sub 1s for that
one.

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00:09:05 --> 00:09:09
In a hydrogen atom that is what
it is.

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00:09:09 --> 00:09:12
It is the electron-nuclear
attraction.

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00:09:12 --> 00:09:17
And so, right here,
this is equal to 2 times E sub

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00:09:17 --> 00:09:20
1s.

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00:09:20 --> 00:09:30


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00:09:30 --> 00:09:36
Now, you know that E sub 1s
is equal to minus

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00:09:36 --> 00:09:41
2.18x10^-18 joules,
but in kilojoules per mole,

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00:09:41 --> 00:09:47
that is equal to minus 1
kilojoules per mole.

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00:09:47 --> 00:09:54
And, if we have two of them,
as we do, 2 times E sub 1s

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00:09:54 --> 00:09:59
is minus 2
kilojoules per mole.

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I calculated what the electron

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interaction energy is at r is
equal to infinity.

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That is way out here.
This is hydrogen plus hydrogen.

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This is minus 2,624,
the same number I got over

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there.
Now, what we have to do --

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00:10:33 --> 00:10:42


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-- is calculate what that
energy of interaction is at r is

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00:10:47 --> 00:10:50
equal to 0.
When r is equal to 0,

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00:10:50 --> 00:10:55
we have two hydrogen atoms
right on top of each other.

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00:10:55 --> 00:11:02
We have two hydrogen nuclei
right on top of each other.

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00:11:02 --> 00:11:06
That means, in our kind of
thought experiment here,

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00:11:06 --> 00:11:10
that the charge on the nucleus
is Z equals 2.

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00:11:10 --> 00:11:15
That means when the two
hydrogen atoms are right on top

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of each other,
it looks like we have a helium

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00:11:18 --> 00:11:22
nucleus.
And there is electron number

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00:11:22 --> 00:11:26
one around it and electron
number two around it.

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00:11:26 --> 00:11:32
That looks like a helium atom.
What is the total electron

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00:11:32 --> 00:11:36
interaction in the case of a
helium atom?

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00:11:36 --> 00:11:41
What is the total energy of
interaction there?

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00:11:41 --> 00:11:47
Well, the total energy of
interaction is going to be minus

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00:11:47 --> 00:11:53
the first ionization energy,
this is going to be the energy

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00:11:53 --> 00:12:00
of interaction of the helium,
for a helium atom.

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00:12:00 --> 00:12:05
Because minus the first
ionization energy of the helium

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00:12:05 --> 00:12:12
atom is the binding energy of
the first electron to the helium

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00:12:12 --> 00:12:18
plus minus the second ionization
energy of the helium atom.

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00:12:18 --> 00:12:22
In other words,
if I hid this one away,

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00:12:22 --> 00:12:27
then the electron-nuclear
attraction between the helium

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00:12:27 --> 00:12:33
nucleus in electron two is just
minus the second ionization

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00:12:33 --> 00:12:39
energy of helium.
Does that make sense?

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00:12:39 --> 00:12:44


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You are too hot to think.
Okay.

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00:12:47 --> 00:12:52
That is what that is.
And if you look them up,

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the total energy of interaction
is minus 7,622 kilojoules per

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mole.

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00:13:01 --> 00:13:06


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I can plot that on this graph
at r equals 0.

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I have minus 7,622 kilojoules.
Now, I have two points.

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I have a point over here and a
point over there.

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I am going to draw a straight
line between the two.

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To get my total energy of
interaction, I am going to add

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this curve to that curve.
And when I do that,

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we are going to get something
that looks like that.

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The bottom line is that this
shape here is determined by the

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competition between the electron
interactions,

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which are always attractive.
They are always negative.

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00:14:05 --> 00:14:09
The electron interactions are
actually the sum of an

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attractive term and a repulsive
term, but the repulsive term is

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not so repulsive as to overcome
the attractive term.

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It is always negative.
Overall, the sum is still

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attractive.
The electron interactions are

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attractive.
This particular curve is the

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competition between the electron
interactions,

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those attractive interactions
and the nuclear interactions,

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which are repulsive.
In other words,

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you have to get the two
hydrogen atoms close enough in

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order for the attractive
interactions to take hold.

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But you cannot get them so
close because if you get them

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too close, the nuclear-nuclear
repulsions set in.

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Where your chemical bond length
is, is determined by that

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competition between the electron
attractive interactions and

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00:15:11 --> 00:15:14
those nuclear-nuclear
repulsions.

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00:15:14 --> 00:15:18
That is what determines the
bond length.

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00:15:18 --> 00:15:23
That is fundamentally,
here, what determines the bond

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strength, the competition
between these overall attractive

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00:15:29 --> 00:15:33
interactions due to the
electrons and the

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nuclear-nuclear repulsion.
That was the concept,

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00:15:39 --> 00:15:44
really, that I wanted to get
across here, those fundamental

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interactions that make up this
kind of curve.

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00:15:49 --> 00:15:53
You are going to see this curve
a lot.

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00:15:53 --> 00:15:58
All chemical bonds have this
kind of dependence on r,

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00:15:58 --> 00:16:05
energy of interaction on r.
There is one other point I want

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00:16:05 --> 00:16:09
to make.
That is that what we often and

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00:16:09 --> 00:16:14
usually do is we reset our zero
of energy.

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00:16:14 --> 00:16:19
Another words,
we are going to reset our zero

199
00:16:19 --> 00:16:24
of energy, here,
so that the zero of energy

200
00:16:24 --> 00:16:30
corresponds to the separated
atom limit.

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Why do we do that?
Well, because this energy

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difference, the minus 2,624,
was really the attractive

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00:16:41 --> 00:16:47
interaction between the electron
and its nucleus.

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00:16:47 --> 00:16:54
It did not have anything to do
with the attraction or repulsion

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00:16:54 --> 00:17:00
between the two atoms.
And so, when we want to talk

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00:17:00 --> 00:17:05
only about the chemical bond and
the energy changes when we make

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00:17:05 --> 00:17:09
a chemical bond,
it is often useful to shift our

208
00:17:09 --> 00:17:13
zero of energy down,
so that the separated atom

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00:17:13 --> 00:17:18
limit is our zero of energy.
And now, everything that is

210
00:17:18 --> 00:17:22
negative relative to that is a
bound interaction.

211
00:17:22 --> 00:17:26
When it gets too close,
it will be a positive

212
00:17:26 --> 00:17:31
interaction and the atoms are no
longer bound.

213
00:17:31 --> 00:17:36
I mean, we are not forgetting
about this energy here.

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00:17:36 --> 00:17:40
We know if you are calculating
the total energy,

215
00:17:40 --> 00:17:45
it has to be there,
but oftentimes we just want to

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00:17:45 --> 00:17:51
talk about the relative changes
of the energy of interaction as

217
00:17:51 --> 00:17:56
a function of r when we are
concerned only with forming a

218
00:17:56 --> 00:17:58
bond.
Make sense?

219
00:17:58 --> 00:18:03
Okay.
That is the general phenomenon.

220
00:18:03 --> 00:18:22


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00:18:22 --> 00:18:31
Now, what I want to talk about
is one very simple model for an

222
00:18:31 --> 00:18:36
ionic bond.
This is a classical model.

223
00:18:36 --> 00:18:42
And the amazing thing about it
is that this simple classical

224
00:18:42 --> 00:18:50
model does give us insight into
the mechanism by which this bond

225
00:18:50 --> 00:18:54
is formed.
It is a mechanism that is only

226
00:18:54 --> 00:19:01
going to work when you form a
very ionic bond.

227
00:19:01 --> 00:19:05
This is particular for a very
ionic bond.

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00:19:05 --> 00:19:12
We want to take a look at this
mechanism because it is going to

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00:19:12 --> 00:19:19
give us some insight into how
the bond is actually formed.

230
00:19:19 --> 00:19:25
We are going to look at the
formation of sodium chloride,

231
00:19:25 --> 00:19:30
here.
We have a sodium atom and a

232
00:19:30 --> 00:19:35
chlorine atom,
and they are coming together,

233
00:19:35 --> 00:19:42
moving toward each other.
What happens is that at a

234
00:19:42 --> 00:19:47
certain distance from each
other, the sodium atom,

235
00:19:47 --> 00:19:51
believe it or not,
actually ejects an electron.

236
00:19:51 --> 00:19:55
And that electron hooks onto
the chlorine.

237
00:19:55 --> 00:20:00
When it does that,
of course the chlorine now

238
00:20:00 --> 00:20:05
becomes bigger than the sodium,
but now we have two charges

239
00:20:05 --> 00:20:10
separated.
A positive and a negative ion.

240
00:20:10 --> 00:20:17
And there is a large attractive
interaction between those two.

241
00:20:17 --> 00:20:23
What happens is these two ions
are attracted in to each other.

242
00:20:23 --> 00:20:28
They are just roped right in.
It is called the Harpoon

243
00:20:28 --> 00:20:32
Mechanism.
Why does the sodium and the

244
00:20:32 --> 00:20:36
chlorine just pull right into
each other?

245
00:20:36 --> 00:20:41
Well, because of that rope.
That rope is that Coulomb

246
00:20:41 --> 00:20:44
interaction.
This really happens.

247
00:20:44 --> 00:20:49
At some distance the sodium
atom ejects that electron,

248
00:20:49 --> 00:20:54
and then that sodium just pulls
that chlorine right into it

249
00:20:54 --> 00:20:59
until it gets close enough to
form a chemical bond,

250
00:20:59 --> 00:21:03
--
and you have sodium chloride.

251
00:21:03 --> 00:21:08
This is a reaction mechanism
that was elucidated many years

252
00:21:08 --> 00:21:11
ago, called the harpoon
mechanicism.

253
00:21:11 --> 00:21:15
It is a mechanics elucidated by
Dudley Herschbach,

254
00:21:15 --> 00:21:19
who is here at Harvard in the
Chemistry Department,

255
00:21:19 --> 00:21:22
who has since retired.
John Polanyi,

256
00:21:22 --> 00:21:25
who is at Toronto,
and Yuan Lee,

257
00:21:25 --> 00:21:30
who was at Berkeley,
for most of his career.

258
00:21:30 --> 00:21:34
They received the Nobel Prize
for this discovery of this

259
00:21:34 --> 00:21:40
mechanism, and many other kinds
of mechanism and dynamics of

260
00:21:40 --> 00:21:43
chemical reactions.
Yuan Lee right here,

261
00:21:43 --> 00:21:46
this gentleman was actually my
Ph.D.

262
00:21:46 --> 00:21:50
thesis supervisor at Berkeley.

263
00:21:50 --> 00:22:00


264
00:22:00 --> 00:22:04
This is a simple picture,
and this is exactly what is

265
00:22:04 --> 00:22:08
going on.
This seems a little strange to

266
00:22:08 --> 00:22:14
you, so let's try to understand
exactly how this is working.

267
00:22:14 --> 00:22:19
To understand this,
what we are going to have to do

268
00:22:19 --> 00:22:22
is look at the energetics of the
system.

269
00:22:22 --> 00:22:27
And now I am going to raise
this screen here,

270
00:22:27 --> 00:22:31
I think.
No, I don't want to.

271
00:22:31 --> 00:22:32
I am going to raise it a little
bit.

272
00:22:32 --> 00:22:33
How is that?

273
00:22:33 --> 00:23:00


274
00:23:00 --> 00:23:04
All right.
What we are seeing is this gas

275
00:23:04 --> 00:23:10
phase sodium atom ejecting an
electron to form this gas phase

276
00:23:10 --> 00:23:15
sodium ion, plus this electron.
And of course,

277
00:23:15 --> 00:23:21
that is going to cost energy.
The energy change is the

278
00:23:21 --> 00:23:25
ionization energy,
which for sodium is

279
00:23:25 --> 00:23:31
kilojoules per mole.
But, at the same time,

280
00:23:31 --> 00:23:35
that electron is being caught
by the chlorine.

281
00:23:35 --> 00:23:40
And when a chlorine and an
electron recombine to form the

282
00:23:40 --> 00:23:45
Cl minus gas phase,
there is an energy

283
00:23:45 --> 00:23:49
release, as we saw.
That energy release is minus

284
00:23:49 --> 00:23:52
the electron affinity of
chlorine.

285
00:23:52 --> 00:23:56
That is equal to minus
kilojoules per mole.

286
00:23:56 --> 00:24:02
Overall, going from a gas phase

287
00:24:02 --> 00:24:08
sodium atom plus a
gas phase chlorine atom

288
00:24:08 --> 00:24:13
to a gas phase sodium ion
and a gas phase

289
00:24:13 --> 00:24:19
chlorine ion,
the overall energy change here,

290
00:24:19 --> 00:24:24
which is now the ionization
energy minus the electron

291
00:24:24 --> 00:24:29
affinity, that overal energy
change is 147 kilojoules per

292
00:24:29 --> 00:24:33
mole.
Although we get some energy

293
00:24:33 --> 00:24:38
back when that electron attaches
to the chlorine,

294
00:24:38 --> 00:24:44
we don't get enough energy back
to compensate for having to pull

295
00:24:44 --> 00:24:49
the electron off of the sodium.
Right now, this still looks

296
00:24:49 --> 00:24:53
like an overall endothermic
reaction.

297
00:24:53 --> 00:25:00
We have to put 147 kilojoules
into the system to make it go.

298
00:25:00 --> 00:25:05
It is beginning to seem a
little peculiar.

299
00:25:05 --> 00:25:11
How does this work?
Well, we have to remember that

300
00:25:11 --> 00:25:17
once we make that sodium plus
and the chlorine minus,

301
00:25:17 --> 00:25:23
that there is that Coulomb
interaction.

302
00:25:23 --> 00:25:28
The Coulomb interaction,
bringing the sodium ion plus

303
00:25:28 --> 00:25:33
the chlorine ion together to
make the sodium chloride,

304
00:25:33 --> 00:25:37
that delta E,

305
00:25:37 --> 00:25:41
if I take two ions,
sodium and chlorine,

306
00:25:41 --> 00:25:46
in from infinity and bring them
together at the bond length,

307
00:25:46 --> 00:25:51
that energy change is minus
kilojoules per mole.

308
00:25:51 --> 00:25:57
If I add up all three reactions
to get sodium gas plus chlorine

309
00:25:57 --> 00:26:03
gas to make sodium chloride in
the gas phase,

310
00:26:03 --> 00:26:08
the overall energy change there

311
00:26:08 --> 00:26:13
is minus 445 kilojoules per
mole.

312
00:26:13 --> 00:26:17
And, of course,
the reaction is downhill.

313
00:26:17 --> 00:26:23
But that still doesn't give you
a really good feeling for what

314
00:26:23 --> 00:26:28
is really going on here.
To do that, let's look at an

315
00:26:28 --> 00:26:33
energy level diagram.
You want to kill the front

316
00:26:33 --> 00:26:36
lights.
This is going to be back and

317
00:26:36 --> 00:26:38
forth here.
All right.

318
00:26:38 --> 00:26:42
What have I draw here?
I have drawn the energy of

319
00:26:42 --> 00:26:47
interaction between a sodium
atom and a chlorine atom,

320
00:26:47 --> 00:26:53
just like I did for hydrogen.
I said all chemical bonds have

321
00:26:53 --> 00:26:56
this same shape of energy of
interaction.

322
00:26:56 --> 00:27:01
Here is the bond length.
2.36 angstroms.

323
00:27:01 --> 00:27:06
Here is the well depth or the
dissociation energy.

324
00:27:06 --> 00:27:11
In this case,
I show it measured from here to

325
00:27:11 --> 00:27:14
there.
It is minus delta E sub d,

326
00:27:14 --> 00:27:16
minus 445.

327
00:27:16 --> 00:27:22
Here I set the zero of energy
at the separated atom limit,

328
00:27:22 --> 00:27:28
sodium plus chlorine.
When sodium and chlorine are

329
00:27:28 --> 00:27:31
way out here,
when r is really large,

330
00:27:31 --> 00:27:37
we saw that it is going to take
147 kilojoules to make a sodium

331
00:27:37 --> 00:27:41
ion from sodium and a chlorine
ion from chlorine.

332
00:27:41 --> 00:27:45
That is what I calculated,
right here.

333
00:27:45 --> 00:27:50
If the two are far apart,
if you pull an electron off a

334
00:27:50 --> 00:27:55
sodium and put it onto chlorine,
it is still going to require

335
00:27:55 --> 00:28:03
energy, 147 kilojoules per mole.
However, I also said that when

336
00:28:03 --> 00:28:08
the sodium and the chlorine come
close enough,

337
00:28:08 --> 00:28:15
the ions are pulled in close
enough such that they can form a

338
00:28:15 --> 00:28:20
chemical bond,
the energy you get back is

339
00:28:20 --> 00:28:24
kilojoules per mole.
On this diagram,

340
00:28:24 --> 00:28:30
where is that?
Well, that is this energy.

341
00:28:30 --> 00:28:36
From up here to down there is
592 kilojoules per mole.

342
00:28:36 --> 00:28:42
Where did I get that number,
592 kilojoules per mole?

343
00:28:42 --> 00:28:50
Well, I calculated it using the
Coulomb potential energy of

344
00:28:50 --> 00:28:57
interaction, which I am calling,
here, U of r sub E

345
00:28:57 --> 00:29:03
at this value of r.
The Coulomb potential energy of

346
00:29:03 --> 00:29:07
interaction is right here for a
point charge.

347
00:29:07 --> 00:29:12
If you treat the sodium as a
plus one charge and you treat

348
00:29:12 --> 00:29:15
the chlorine as a minus one
charge.

349
00:29:15 --> 00:29:19
All of a sudden,
we are forgetting everything

350
00:29:19 --> 00:29:24
about the other electrons.
We are just treating sodium ion

351
00:29:24 --> 00:29:29
and chlorine ion as two point
charges.

352
00:29:29 --> 00:29:34
If you forget completely about
the other electrons and just

353
00:29:34 --> 00:29:40
treat them as point charges,
that is the interaction energy

354
00:29:40 --> 00:29:44
right here.
That 592 comes from taking that

355
00:29:44 --> 00:29:48
expression and plugging in 2.36
angstroms.

356
00:29:48 --> 00:29:51
That is how much energy you get
back.

357
00:29:51 --> 00:29:55
Now we understand the energies
a little bit,

358
00:29:55 --> 00:30:01
but we still don't understand
exactly how this electron jump

359
00:30:01 --> 00:30:07
process is happening.
Because the way I have it

360
00:30:07 --> 00:30:13
drawn, here, it still looks like
we have an electron jumping from

361
00:30:13 --> 00:30:19
sodium to chlorine way out here.
And we have to put in

362
00:30:19 --> 00:30:23
kilojoules before we get any
energy back.

363
00:30:23 --> 00:30:28
Well, that is not the case.
And that is not the case

364
00:30:28 --> 00:30:32
because of this.
This blue curve,

365
00:30:32 --> 00:30:36
here, is just the Coulomb
energy of interaction.

366
00:30:36 --> 00:30:40
We evaluated that point,
that number,

367
00:30:40 --> 00:30:43
from here to here using this
expression.

368
00:30:43 --> 00:30:48
But you know that this is a
minus one over r

369
00:30:48 --> 00:30:52
dependence.
If you are way up here and you

370
00:30:52 --> 00:30:57
treat this as a zero of energy
for a plus charge and a minus

371
00:30:57 --> 00:31:03
charge, one over r kind of looks
like this.

372
00:31:03 --> 00:31:09
That is the blue curve.
But you also notice that right

373
00:31:09 --> 00:31:17
here, you see that that Coulomb
interaction is intersecting with

374
00:31:17 --> 00:31:24
this interaction potential
between a neutral sodium atom

375
00:31:24 --> 00:31:31
and a neutral chlorine atom,
right in there.

376
00:31:31 --> 00:31:37
Right at this value of r,
which we are going to call r

377
00:31:37 --> 00:31:44
star, the potential energy of
interaction from here to here is

378
00:31:44 --> 00:31:50
equal to the sum of this
ionization energy minus the

379
00:31:50 --> 00:31:55
electron affinity.
Right here, the electron can

380
00:31:55 --> 00:32:03
jump without having to put any
energy into the system.

381
00:32:03 --> 00:32:09
You are close enough for the
electron to jump because that

382
00:32:09 --> 00:32:15
Coulomb interaction has gotten
lower, and it is right at that

383
00:32:15 --> 00:32:21
point when you can have that
electron transfer and not have

384
00:32:21 --> 00:32:26
to put any energy into the
system to get it to go.

385
00:32:26 --> 00:32:31
In other words,
right here, the energy from

386
00:32:31 --> 00:32:37
right there to this point is
minus e squared 4 pi epsilon

387
00:32:37 --> 00:32:44
nought r star.

388
00:32:44 --> 00:32:49
That energy right at that point
is equal to, if I am measuring

389
00:32:49 --> 00:32:53
here from the top minus the
quantity ionization energy of

390
00:32:53 --> 00:32:58
sodium minus the electron
affinity of chlorine.

391
00:32:58 --> 00:33:02
In order to solve for this

392
00:33:02 --> 00:33:07
distance r at which the electron
jumps, for which that electron

393
00:33:07 --> 00:33:13
jump is energetically allowed,
I am going to set this equal to

394
00:33:13 --> 00:33:16
this.
I know what the ionization

395
00:33:16 --> 00:33:21
energy and the electron affinity
of sodium and chlorine are.

396
00:33:21 --> 00:33:27
I know everything except r star,
so I am going to solve

397
00:33:27 --> 00:33:30
for r star.
Let's do that.

398
00:33:30 --> 00:33:33
I am going to need the lights,
here.

399
00:33:33 --> 00:33:40


400
00:33:40 --> 00:33:45
If I rearrange that equation,
r star is equal to e squared

401
00:33:45 --> 00:33:50
over 4 pi epsilon nought times
the ionization energy of sodium

402
00:33:50 --> 00:33:53
minus the electron affinity of
chlorine.

403
00:33:53 --> 00:33:58
I know

404
00:33:58 --> 00:34:04
what e star is.
It is 1.602x10^-19 Coulomb's

405
00:34:04 --> 00:34:08
squared.
I have a 4 pi epsilon nought.

406
00:34:08 --> 00:34:14
I know what epsilon nought is.
And then, the difference

407
00:34:14 --> 00:34:21
between the ionization energy
and the electron affinity I

408
00:34:21 --> 00:34:27
calculated over there.
That is 147 kilojoules per mole

409
00:34:27 --> 00:34:35
or 1.47x10^5 joules per mole.
But now, and this is what

410
00:34:35 --> 00:34:42
everybody forgets on an exam,
I have to calculate r star per

411
00:34:42 --> 00:34:49
molecule, not per mole because
per mole does not make sense.

412
00:34:49 --> 00:34:54
And I have this energy written
here per mole,

413
00:34:54 --> 00:35:03
so I need an Avogadro's number
up here, 6.022x10^23 per mole.

414
00:35:03 --> 00:35:11
Don't forget Avogadro's number
when you calculate r.

415
00:35:11 --> 00:35:18
What is r star?
Well, it comes out to be

416
00:35:18 --> 00:35:26
9.45x10^-10 meters.
Let's get a perspective on

417
00:35:26 --> 00:35:34
these distances.
The sodium atom diameter is 3.8

418
00:35:34 --> 00:35:39
angstroms.
Chlorine atom diameter,

419
00:35:39 --> 00:35:45
2 angstroms.
What I am saying is that this

420
00:35:45 --> 00:35:51
electron can jump,
or does jump from sodium to

421
00:35:51 --> 00:35:59
chlorine at this distance r
star, which is equal to 9.45

422
00:35:59 --> 00:36:04
angstroms.
So, the sodium and the chlorine

423
00:36:04 --> 00:36:09
really are a considerable
distance apart when that

424
00:36:09 --> 00:36:12
electron jumps.
But that electron can jump

425
00:36:12 --> 00:36:18
because it is at that point that
the Coulomb interaction is large

426
00:36:18 --> 00:36:24
enough here to compensate for
the difference in the ionization

427
00:36:24 --> 00:36:27
energy and the electron
affinity.

428
00:36:27 --> 00:36:31
And this actual number,
here, was verified in these

429
00:36:31 --> 00:36:36
experiments by Herschbach and
Lee.

430
00:36:36 --> 00:36:41
It actually does happen.
And this very simple classical

431
00:36:41 --> 00:36:46
model, where we are actually
treating the sodium and the

432
00:36:46 --> 00:36:51
chlorine as point charges,
we have forgotten everything

433
00:36:51 --> 00:36:55
else about the electrons,
that works remarkably well.

434
00:36:55 --> 00:37:01
Now, what this model does not
give you very well is the bond

435
00:37:01 --> 00:37:06
energy.
Because, if you look at this

436
00:37:06 --> 00:37:12
diagram again right in here,
let me go back on here,

437
00:37:12 --> 00:37:17
this 147 kilojoules here,
that I can look up.

438
00:37:17 --> 00:37:22
This 592 kilojoules,
that is just the Coulomb

439
00:37:22 --> 00:37:29
interaction between a positive
and a negative charge at 2.36

440
00:37:29 --> 00:37:32
eV.
That is all that is.

441
00:37:32 --> 00:37:36
You can calculate that.
And so, therefore,

442
00:37:36 --> 00:37:41
if I want to calculate the bond
energy of sodium chloride,

443
00:37:41 --> 00:37:46
the bond energy is just the
difference between this energy

444
00:37:46 --> 00:37:50
and that energy,
and that is 435 kilojoules per

445
00:37:50 --> 00:37:53
mole.
Well, that does not come out so

446
00:37:53 --> 00:37:57
well in terms of the actual bond
energy.

447
00:37:57 --> 00:38:03
The actual bond energy is
kilojoules per mole.

448
00:38:03 --> 00:38:07
And we know why that did not
come out too well.

449
00:38:07 --> 00:38:14
That is because this depends on
all of the interactions that are

450
00:38:14 --> 00:38:20
much closer into the nucleus.
By the time you get down here,

451
00:38:20 --> 00:38:24
the repulsive interactions are
present.

452
00:38:24 --> 00:38:30
The nuclear-nuclear repulsions
are present.

453
00:38:30 --> 00:38:34
And, in our simple model,
we did not take that into

454
00:38:34 --> 00:38:37
account, the nuclear-nuclear
repulsions.

455
00:38:37 --> 00:38:42
This simple model worked to get
r star because r star is further

456
00:38:42 --> 00:38:45
out.
The nuclear-nuclear repulsions

457
00:38:45 --> 00:38:49
have not really set in yet.
Therefore, the simple model

458
00:38:49 --> 00:38:54
works when you are at a far
distance, when r is large.

459
00:38:54 --> 00:39:00
But to get the bond strength,
here, you are much closer in.

460
00:39:00 --> 00:39:04
You are at 2.36 angstroms.
That is the difference in

461
00:39:04 --> 00:39:08
energy from here to there.
We forgot about the repulsive

462
00:39:08 --> 00:39:13
interactions between the two
nuclei, so the model is not

463
00:39:13 --> 00:39:18
going to work so close to the
nucleus, but it does a really

464
00:39:18 --> 00:39:22
good job of getting r star far
away from the nucleus.

465
00:39:22 --> 00:39:27
Again, this simple model only
works for very ionic compounds,

466
00:39:27 --> 00:39:32
very ionic bonds like sodium
chloride.

467
00:39:32 --> 00:39:39
It won't work very well for
hydrogen chloride,

468
00:39:39 --> 00:39:43
for example.
Questions on that?

469
00:39:43 --> 00:39:45
Yes?

470
00:39:45 --> 00:39:55


471
00:39:55 --> 00:39:59
We are going to deal with
entropy and Gibbs free energy

472
00:39:59 --> 00:40:03
changes in a week or two.
Right now, what I am writing

473
00:40:03 --> 00:40:07
here are energy changes.
I am actually dealing with

474
00:40:07 --> 00:40:10
single molecules.
I might have,

475
00:40:10 --> 00:40:13
in my mind, here,
energies per mole.

476
00:40:13 --> 00:40:18
But what I am thinking about is
not an ensemble of molecules.

477
00:40:18 --> 00:40:23
I am actually thinking about
what is happening in each

478
00:40:23 --> 00:40:28
individual single molecule
interaction.

479
00:40:28 --> 00:40:33
That is why I have not talked
about delta G here at all.

480
00:40:33 --> 00:40:38
And, in the field of chemical
dynamics, that is where we want

481
00:40:38 --> 00:40:44
to look at individual events as
opposed to a Boltzmann average

482
00:40:44 --> 00:40:48
of events.
That is what I am talking about

483
00:40:48 --> 00:40:53
right here, but we are going to
talk about collections of

484
00:40:53 --> 00:40:58
molecules and the energy
changes.

485
00:40:58 --> 00:41:05
I am going to change my
definition from delta E to delta

486
00:41:05 --> 00:41:11
H, the bond enthalpy,
in a couple of days or so.

487
00:41:11 --> 00:41:14
Other questions?
Okay.

488
00:41:14 --> 00:41:22
Well, there is one other just
rather brief topic that I wanted

489
00:41:22 --> 00:41:27
to talk about.
That is, measuring dipole

490
00:41:27 --> 00:41:32
moments.
And then, from the dipole

491
00:41:32 --> 00:41:37
moments, getting out some ionic
character to a chemical bond.

492
00:41:37 --> 00:41:41
Your book actually calls ionic
bonds polar covalent bonds.

493
00:41:41 --> 00:41:46
And that is fine because even a
very ionic bond like sodium

494
00:41:46 --> 00:41:51
chloride is not completely
ionic, in the sense that when it

495
00:41:51 --> 00:41:56
is the molecule you know that it
is not a point charge on sodium

496
00:41:56 --> 00:42:02
and a point charge on chlorine.
You have an electron

497
00:42:02 --> 00:42:06
distribution when you are that
close.

498
00:42:06 --> 00:42:13
And so, what you have in an
ionic bond or a polar covalent

499
00:42:13 --> 00:42:18
bond, here, is an asymmetric
charge distribution.

500
00:42:18 --> 00:42:23
In HCl, here,
you have both electrons,

501
00:42:23 --> 00:42:28
on the average,
being closer to the chlorine

502
00:42:28 --> 00:42:34
nucleus than to the hydrogen
nucleus.

503
00:42:34 --> 00:42:39
And you have that because you
have a bond between atoms with

504
00:42:39 --> 00:42:42
two very different
electronegativities.

505
00:42:42 --> 00:42:45
So, that is a polar covalent
bond.

506
00:42:45 --> 00:42:51
Now, what we are going to do is
we are going to use this symbol

507
00:42:51 --> 00:42:56
delta here as a measure of the
amount of electron transfer.

508
00:42:56 --> 00:43:01
Delta is the fraction of a full
charge that is asymmetrically

509
00:43:01 --> 00:43:05
distributed.
This plus delta,

510
00:43:05 --> 00:43:09
this delta that was on the
hydrogen, is now on the

511
00:43:09 --> 00:43:12
chlorine.
That is the interpretation of

512
00:43:12 --> 00:43:15
that symbol.
That asymmetric charge

513
00:43:15 --> 00:43:20
distribution leads to a dipole
moment, which is defined as q,

514
00:43:20 --> 00:43:25
where q is the magnitude of the
charge separation,

515
00:43:25 --> 00:43:28
times r, where r is that charge
separation.

516
00:43:28 --> 00:43:34
It is, strictly speaking,

517
00:43:34 --> 00:43:39
a vector.
Q times R is what we define as

518
00:43:39 --> 00:43:44
a dipole moment.
The units of dipole moment is

519
00:43:44 --> 00:43:49
Coulombs times meters.
You can see that from Q times

520
00:43:49 --> 00:43:52
R.
A dipole moment is also a

521
00:43:52 --> 00:43:57
vector.
I have the vector on this slide

522
00:43:57 --> 00:44:03
going from the positively
charged end to the negatively

523
00:44:03 --> 00:44:07
charged end.
That is the way your present

524
00:44:07 --> 00:44:09
book does it.
In your notes,

525
00:44:09 --> 00:44:12
I have it reversed.
I have it reversed because the

526
00:44:12 --> 00:44:16
last time I taught this,
I was using a book that used a

527
00:44:16 --> 00:44:20
different notation and I sent it
out for Xeroxing before I

528
00:44:20 --> 00:44:23
noticed it was different.
So, change it around.

529
00:44:23 --> 00:44:26
Not that it is every going to
make any difference,

530
00:44:26 --> 00:44:29
but your book has this
convention from positive to

531
00:44:29 --> 00:44:31
negative.

532
00:44:31 --> 00:44:37


533
00:44:37 --> 00:44:40
This unit, though,
of a Coulomb meter,

534
00:44:40 --> 00:44:44
is a very large unit,
an inconvenient unit,

535
00:44:44 --> 00:44:48
so we have another unit.
It is called the Debye,

536
00:44:48 --> 00:44:53
named after Peter Debye who
first studied these polar

537
00:44:53 --> 00:44:56
covalent molecules.
And a Debye,

538
00:44:56 --> 00:45:00
here, is defined as the
following.

539
00:45:00 --> 00:45:05
It is defined as if you have a
full unit charge,

540
00:45:05 --> 00:45:09
not a delta,
moved from here to here,

541
00:45:09 --> 00:45:15
and the charge is separated by
0.208 angstroms,

542
00:45:15 --> 00:45:20
that defines this unit called
the Debye.

543
00:45:20 --> 00:45:26
So, there are 0.208 angstroms
per Debye.

544
00:45:26 --> 00:45:31


545
00:45:31 --> 00:45:36
If you knew the fraction of
charge that is separated and you

546
00:45:36 --> 00:45:41
knew the bond length in
angstroms, and then you have our

547
00:45:41 --> 00:45:46
definition for a Debye,
which is 0.208 angstroms per

548
00:45:46 --> 00:45:51
Debye, you could calculate the
dipole moment in Debye.

549
00:45:51 --> 00:45:57
Usually what we do is not to
calculate the dipole moment.

550
00:45:57 --> 00:46:02
We usually measure the dipole
moment and calculate the partial

551
00:46:02 --> 00:46:08
charge distribution.
Because we usually don't know

552
00:46:08 --> 00:46:10
this.
We can measure that.

553
00:46:10 --> 00:46:14
We can measure the dipole
moments in kind of a capacitor

554
00:46:14 --> 00:46:18
arrangement, where we have some
molecules that have a dipole

555
00:46:18 --> 00:46:23
moment, a positive charge on one
plate, a negative charge on the

556
00:46:23 --> 00:46:25
other.
And, when you do that,

557
00:46:25 --> 00:46:30
of course, these electric
dipoles are going to align.

558
00:46:30 --> 00:46:32
That is going to change the
capacitance.

559
00:46:32 --> 00:46:36
If this capacitor is part of a
resonant circuit,

560
00:46:36 --> 00:46:39
it is going to change the
resonant frequent.

561
00:46:39 --> 00:46:43
The resonant frequency is
related to the dipole moment.

562
00:46:43 --> 00:46:46
And, in that way,
you calculate or measure the

563
00:46:46 --> 00:46:49
dipole moment.
That is how it was originally

564
00:46:49 --> 00:46:52
done.
However, you can now measure

565
00:46:52 --> 00:46:56
dipole moments very accurately
by rotational spectroscopy.

566
00:46:56 --> 00:47:02
And we are going to look at
that in a few lectures or so.

567
00:47:02 --> 00:47:05
But take HCl right here.
Here is HCl.

568
00:47:05 --> 00:47:10
Here is the measured dipole
moment, and here is the bond

569
00:47:10 --> 00:47:13
length.
We can use these two pieces of

570
00:47:13 --> 00:47:19
information to calculate the
fraction of charge distributed.

571
00:47:19 --> 00:47:23
And, in the case of HCl,
that is about 0.18.

572
00:47:23 --> 00:47:28
Sometimes, we refer to this in
a percentage.

573
00:47:28 --> 00:47:32
So, this would be 18% of a
charge separation.

574
00:47:32 --> 00:47:36
Sometimes we say 18% ionic
character in HCl.

575
00:47:36 --> 00:47:43
That compares to something like
70% or 80% in sodium chloride or

576
00:47:43 --> 00:47:48
lithium chloride.
So, HCl is not anywhere near as

577
00:47:48 --> 00:47:51
ionic.
The charge distribution is not

578
00:47:51 --> 00:47:59
as asymmetric as it is in sodium
chloride or lithium chloride.

579
00:47:59 --> 00:48:03
Thank you very much for hanging
in here today.

580
00:48:03 --> 00:48:07
It has been hot.
Have a nice cool weekend.

581
00:48:07.875 --> 48:10
See you next Wednesday.