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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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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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was minus 2,624 kilojoules per
mole.

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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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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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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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That is how much energy you
would have to put in to pull the

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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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attraction.
The electron-nuclear

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attraction, between the electron
on the original nucleus and,

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when the two hydrogens get
close enough,

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the electron attraction between
the other nucleus.

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And then, finally,
there is the electron-electron

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repulsion.
When these two hydrogen atoms

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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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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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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 Schrˆdinger
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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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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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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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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electron-nuclear attraction
there?

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I cannot hear you,
so I will tell you.

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It is the binding energy of a
1s electron.

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I mean that is the energy of
interaction.

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When r is very large,
when r is infinity,

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the energy of interaction is
just the 1s binding energy of

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the electron to each of its
nuclei.

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The energy of interaction,
the electron-nuclear attraction

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is just E sub 1s for
this one.

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And e sub 1s for that
one.

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In a hydrogen atom that is what
it is.

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It is the electron-nuclear
attraction.

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And so, right here,
this is equal to 2 times E sub

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1s.

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Now, you know that E sub 1s
is equal to minus

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2.18x10^-18 joules,
but in kilojoules per mole,

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that is equal to minus 1
kilojoules per mole.

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And, if we have two of them,
as we do, 2 times E sub 1s

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

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equal to 0.
When r is equal to 0,

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we have two hydrogen atoms
right on top of each other.

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00:10:55,000 --> 00:11:02,000
We have two hydrogen nuclei
right on top of each other.

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00:11:02,000 --> 00:11:06,000
That means, in our kind of
thought experiment here,

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that the charge on the nucleus
is Z equals 2.

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00:11:10,000 --> 00:11:15,000
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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nucleus.
And there is electron number

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one around it and electron
number two around it.

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00:11:26,000 --> 00:11:32,000
That looks like a helium atom.
What is the total electron

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interaction in the case of a
helium atom?

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00:11:36,000 --> 00:11:41,000
What is the total energy of
interaction there?

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00:11:41,000 --> 00:11:47,000
Well, the total energy of
interaction is going to be minus

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00:11:47,000 --> 00:11:53,000
the first ionization energy,
this is going to be the energy

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00:11:53,000 --> 00:12:00,000
of interaction of the helium,
for a helium atom.

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00:12:00,000 --> 00:12:05,000
Because minus the first
ionization energy of the helium

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atom is the binding energy of
the first electron to the helium

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plus minus the second ionization
energy of the helium atom.

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00:12:18,000 --> 00:12:22,000
In other words,
if I hid this one away,

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then the electron-nuclear
attraction between the helium

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nucleus in electron two is just
minus the second ionization

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energy of helium.
Does that make sense?

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You are too hot to think.
Okay.

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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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00:12:59,000 --> 00:13:01,000
mole.

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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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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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those nuclear-nuclear
repulsions.

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That is what determines the
bond length.

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That is fundamentally,
here, what determines the bond

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strength, the competition
between these overall attractive

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interactions due to the
electrons and the

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nuclear-nuclear repulsion.
That was the concept,

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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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You are going to see this curve
a lot.

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00:15:53,000 --> 00:15:58,000
All chemical bonds have this
kind of dependence on r,

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energy of interaction on r.
There is one other point I want

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to make.
That is that what we often and

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usually do is we reset our zero
of energy.

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Another words,
we are going to reset our zero

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00:16:19,000 --> 00:16:24,000
of energy, here,
so that the zero of energy

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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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00:16:41,000 --> 00:16:47,000
interaction between the electron
and its nucleus.

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00:16:47,000 --> 00:16:54,000
It did not have anything to do
with the attraction or repulsion

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00:16:54,000 --> 00:17:00,000
between the two atoms.
And so, when we want to talk

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00:17:00,000 --> 00:17:05,000
only about the chemical bond and
the energy changes when we make

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00:17:05,000 --> 00:17:09,000
a chemical bond,
it is often useful to shift our

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00:17:09,000 --> 00:17:13,000
zero of energy down,
so that the separated atom

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00:17:13,000 --> 00:17:18,000
limit is our zero of energy.
And now, everything that is

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negative relative to that is a
bound interaction.

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00:17:22,000 --> 00:17:26,000
When it gets too close,
it will be a positive

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00:17:26,000 --> 00:17:31,000
interaction and the atoms are no
longer bound.

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00:17:31,000 --> 00:17:36,000
I mean, we are not forgetting
about this energy here.

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00:17:36,000 --> 00:17:40,000
We know if you are calculating
the total energy,

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00:17:40,000 --> 00:17:45,000
it has to be there,
but oftentimes we just want to

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00:17:45,000 --> 00:17:51,000
talk about the relative changes
of the energy of interaction as

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00:17:51,000 --> 00:17:56,000
a function of r when we are
concerned only with forming a

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00:17:56,000 --> 00:17:58,000
bond.
Make sense?

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00:17:58,000 --> 00:18:03,000
Okay.
That is the general phenomenon.

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00:18:22,000 --> 00:18:31,000
Now, what I want to talk about
is one very simple model for an

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00:18:31,000 --> 00:18:36,000
ionic bond.
This is a classical model.

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00:18:36,000 --> 00:18:42,000
And the amazing thing about it
is that this simple classical

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00:18:42,000 --> 00:18:50,000
model does give us insight into
the mechanism by which this bond

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00:18:50,000 --> 00:18:54,000
is formed.
It is a mechanism that is only

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00:18:54,000 --> 00:19:01,000
going to work when you form a
very ionic bond.

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00:19:01,000 --> 00:19:05,000
This is particular for a very
ionic bond.

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00:19:05,000 --> 00:19:12,000
We want to take a look at this
mechanism because it is going to

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00:19:12,000 --> 00:19:19,000
give us some insight into how
the bond is actually formed.

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00:19:19,000 --> 00:19:25,000
We are going to look at the
formation of sodium chloride,

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00:19:25,000 --> 00:19:30,000
here.
We have a sodium atom and a

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00:19:30,000 --> 00:19:35,000
chlorine atom,
and they are coming together,

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00:19:35,000 --> 00:19:42,000
moving toward each other.
What happens is that at a

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00:19:42,000 --> 00:19:47,000
certain distance from each
other, the sodium atom,

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00:19:47,000 --> 00:19:51,000
believe it or not,
actually ejects an electron.

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00:19:51,000 --> 00:19:55,000
And that electron hooks onto
the chlorine.

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00:19:55,000 --> 00:20:00,000
When it does that,
of course the chlorine now

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00:20:00,000 --> 00:20:05,000
becomes bigger than the sodium,
but now we have two charges

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00:20:05,000 --> 00:20:10,000
separated.
A positive and a negative ion.

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00:20:10,000 --> 00:20:17,000
And there is a large attractive
interaction between those two.

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00:20:17,000 --> 00:20:23,000
What happens is these two ions
are attracted in to each other.

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00:20:23,000 --> 00:20:28,000
They are just roped right in.
It is called the Harpoon

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00:20:28,000 --> 00:20:32,000
Mechanism.
Why does the sodium and the

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00:20:32,000 --> 00:20:36,000
chlorine just pull right into
each other?

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00:20:36,000 --> 00:20:41,000
Well, because of that rope.
That rope is that Coulomb

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00:20:41,000 --> 00:20:44,000
interaction.
This really happens.

238
00:20:44,000 --> 00:20:49,000
At some distance the sodium
atom ejects that electron,

239
00:20:49,000 --> 00:20:54,000
and then that sodium just pulls
that chlorine right into it

240
00:20:54,000 --> 00:20:59,000
until it gets close enough to
form a chemical bond,

241
00:20:59,000 --> 00:21:03,000
--
and you have sodium chloride.

242
00:21:03,000 --> 00:21:08,000
This is a reaction mechanism
that was elucidated many years

243
00:21:08,000 --> 00:21:11,000
ago, called the harpoon
mechanicism.

244
00:21:11,000 --> 00:21:15,000
It is a mechanics elucidated by
Dudley Herschbach,

245
00:21:15,000 --> 00:21:19,000
who is here at Harvard in the
Chemistry Department,

246
00:21:19,000 --> 00:21:22,000
who has since retired.
John Polanyi,

247
00:21:22,000 --> 00:21:25,000
who is at Toronto,
and Yuan Lee,

248
00:21:25,000 --> 00:21:30,000
who was at Berkeley,
for most of his career.

249
00:21:30,000 --> 00:21:34,000
They received the Nobel Prize
for this discovery of this

250
00:21:34,000 --> 00:21:40,000
mechanism, and many other kinds
of mechanism and dynamics of

251
00:21:40,000 --> 00:21:43,000
chemical reactions.
Yuan Lee right here,

252
00:21:43,000 --> 00:21:46,000
this gentleman was actually my
Ph.D.

253
00:21:46,000 --> 00:21:50,000
thesis supervisor at Berkeley.

254
00:22:00,000 --> 00:22:04,000
This is a simple picture,
and this is exactly what is

255
00:22:04,000 --> 00:22:08,000
going on.
This seems a little strange to

256
00:22:08,000 --> 00:22:14,000
you, so let's try to understand
exactly how this is working.

257
00:22:14,000 --> 00:22:19,000
To understand this,
what we are going to have to do

258
00:22:19,000 --> 00:22:22,000
is look at the energetics of the
system.

259
00:22:22,000 --> 00:22:27,000
And now I am going to raise
this screen here,

260
00:22:27,000 --> 00:22:31,000
I think.
No, I don't want to.

261
00:22:31,000 --> 00:22:32,000
I am going to raise it a little
bit.

262
00:22:32,000 --> 00:22:33,000
How is that?

263
00:23:00,000 --> 00:23:04,000
All right.
What we are seeing is this gas

264
00:23:04,000 --> 00:23:10,000
phase sodium atom ejecting an
electron to form this gas phase

265
00:23:10,000 --> 00:23:15,000
sodium ion, plus this electron.
And of course,

266
00:23:15,000 --> 00:23:21,000
that is going to cost energy.
The energy change is the

267
00:23:21,000 --> 00:23:25,000
ionization energy,
which for sodium is

268
00:23:25,000 --> 00:23:31,000
kilojoules per mole.
But, at the same time,

269
00:23:31,000 --> 00:23:35,000
that electron is being caught
by the chlorine.

270
00:23:35,000 --> 00:23:40,000
And when a chlorine and an
electron recombine to form the

271
00:23:40,000 --> 00:23:45,000
Cl minus gas phase,
there is an energy

272
00:23:45,000 --> 00:23:49,000
release, as we saw.
That energy release is minus

273
00:23:49,000 --> 00:23:52,000
the electron affinity of
chlorine.

274
00:23:52,000 --> 00:23:56,000
That is equal to minus
kilojoules per mole.

275
00:23:56,000 --> 00:24:02,000
Overall, going from a gas phase

276
00:24:02,000 --> 00:24:08,000
sodium atom plus a
gas phase chlorine atom

277
00:24:08,000 --> 00:24:13,000
to a gas phase sodium ion
and a gas phase

278
00:24:13,000 --> 00:24:19,000
chlorine ion,
the overall energy change here,

279
00:24:19,000 --> 00:24:24,000
which is now the ionization
energy minus the electron

280
00:24:24,000 --> 00:24:29,000
affinity, that overal energy
change is 147 kilojoules per

281
00:24:29,000 --> 00:24:33,000
mole.
Although we get some energy

282
00:24:33,000 --> 00:24:38,000
back when that electron attaches
to the chlorine,

283
00:24:38,000 --> 00:24:44,000
we don't get enough energy back
to compensate for having to pull

284
00:24:44,000 --> 00:24:49,000
the electron off of the sodium.
Right now, this still looks

285
00:24:49,000 --> 00:24:53,000
like an overall endothermic
reaction.

286
00:24:53,000 --> 00:25:00,000
We have to put 147 kilojoules
into the system to make it go.

287
00:25:00,000 --> 00:25:05,000
It is beginning to seem a
little peculiar.

288
00:25:05,000 --> 00:25:11,000
How does this work?
Well, we have to remember that

289
00:25:11,000 --> 00:25:17,000
once we make that sodium plus
and the chlorine minus,

290
00:25:17,000 --> 00:25:23,000
that there is that Coulomb
interaction.

291
00:25:23,000 --> 00:25:28,000
The Coulomb interaction,
bringing the sodium ion plus

292
00:25:28,000 --> 00:25:33,000
the chlorine ion together to
make the sodium chloride,

293
00:25:33,000 --> 00:25:37,000
that delta E,

294
00:25:37,000 --> 00:25:41,000
if I take two ions,
sodium and chlorine,

295
00:25:41,000 --> 00:25:46,000
in from infinity and bring them
together at the bond length,

296
00:25:46,000 --> 00:25:51,000
that energy change is minus
kilojoules per mole.

297
00:25:51,000 --> 00:25:57,000
If I add up all three reactions
to get sodium gas plus chlorine

298
00:25:57,000 --> 00:26:03,000
gas to make sodium chloride in
the gas phase,

299
00:26:03,000 --> 00:26:08,000
the overall energy change there

300
00:26:08,000 --> 00:26:13,000
is minus 445 kilojoules per
mole.

301
00:26:13,000 --> 00:26:17,000
And, of course,
the reaction is downhill.

302
00:26:17,000 --> 00:26:23,000
But that still doesn't give you
a really good feeling for what

303
00:26:23,000 --> 00:26:28,000
is really going on here.
To do that, let's look at an

304
00:26:28,000 --> 00:26:33,000
energy level diagram.
You want to kill the front

305
00:26:33,000 --> 00:26:36,000
lights.
This is going to be back and

306
00:26:36,000 --> 00:26:38,000
forth here.
All right.

307
00:26:38,000 --> 00:26:42,000
What have I draw here?
I have drawn the energy of

308
00:26:42,000 --> 00:26:47,000
interaction between a sodium
atom and a chlorine atom,

309
00:26:47,000 --> 00:26:53,000
just like I did for hydrogen.
I said all chemical bonds have

310
00:26:53,000 --> 00:26:56,000
this same shape of energy of
interaction.

311
00:26:56,000 --> 00:27:01,000
Here is the bond length.
2.36 angstroms.

312
00:27:01,000 --> 00:27:06,000
Here is the well depth or the
dissociation energy.

313
00:27:06,000 --> 00:27:11,000
In this case,
I show it measured from here to

314
00:27:11,000 --> 00:27:14,000
there.
It is minus delta E sub d,

315
00:27:14,000 --> 00:27:16,000
minus 445.

316
00:27:16,000 --> 00:27:22,000
Here I set the zero of energy
at the separated atom limit,

317
00:27:22,000 --> 00:27:28,000
sodium plus chlorine.
When sodium and chlorine are

318
00:27:28,000 --> 00:27:31,000
way out here,
when r is really large,

319
00:27:31,000 --> 00:27:37,000
we saw that it is going to take
147 kilojoules to make a sodium

320
00:27:37,000 --> 00:27:41,000
ion from sodium and a chlorine
ion from chlorine.

321
00:27:41,000 --> 00:27:45,000
That is what I calculated,
right here.

322
00:27:45,000 --> 00:27:50,000
If the two are far apart,
if you pull an electron off a

323
00:27:50,000 --> 00:27:55,000
sodium and put it onto chlorine,
it is still going to require

324
00:27:55,000 --> 00:28:03,000
energy, 147 kilojoules per mole.
However, I also said that when

325
00:28:03,000 --> 00:28:08,000
the sodium and the chlorine come
close enough,

326
00:28:08,000 --> 00:28:15,000
the ions are pulled in close
enough such that they can form a

327
00:28:15,000 --> 00:28:20,000
chemical bond,
the energy you get back is

328
00:28:20,000 --> 00:28:24,000
kilojoules per mole.
On this diagram,

329
00:28:24,000 --> 00:28:30,000
where is that?
Well, that is this energy.

330
00:28:30,000 --> 00:28:36,000
From up here to down there is
592 kilojoules per mole.

331
00:28:36,000 --> 00:28:42,000
Where did I get that number,
592 kilojoules per mole?

332
00:28:42,000 --> 00:28:50,000
Well, I calculated it using the
Coulomb potential energy of

333
00:28:50,000 --> 00:28:57,000
interaction, which I am calling,
here, U of r sub E

334
00:28:57,000 --> 00:29:03,000
at this value of r.
The Coulomb potential energy of

335
00:29:03,000 --> 00:29:07,000
interaction is right here for a
point charge.

336
00:29:07,000 --> 00:29:12,000
If you treat the sodium as a
plus one charge and you treat

337
00:29:12,000 --> 00:29:15,000
the chlorine as a minus one
charge.

338
00:29:15,000 --> 00:29:19,000
All of a sudden,
we are forgetting everything

339
00:29:19,000 --> 00:29:24,000
about the other electrons.
We are just treating sodium ion

340
00:29:24,000 --> 00:29:29,000
and chlorine ion as two point
charges.

341
00:29:29,000 --> 00:29:34,000
If you forget completely about
the other electrons and just

342
00:29:34,000 --> 00:29:40,000
treat them as point charges,
that is the interaction energy

343
00:29:40,000 --> 00:29:44,000
right here.
That 592 comes from taking that

344
00:29:44,000 --> 00:29:48,000
expression and plugging in 2.36
angstroms.

345
00:29:48,000 --> 00:29:51,000
That is how much energy you get
back.

346
00:29:51,000 --> 00:29:55,000
Now we understand the energies
a little bit,

347
00:29:55,000 --> 00:30:01,000
but we still don't understand
exactly how this electron jump

348
00:30:01,000 --> 00:30:07,000
process is happening.
Because the way I have it

349
00:30:07,000 --> 00:30:13,000
drawn, here, it still looks like
we have an electron jumping from

350
00:30:13,000 --> 00:30:19,000
sodium to chlorine way out here.
And we have to put in

351
00:30:19,000 --> 00:30:23,000
kilojoules before we get any
energy back.

352
00:30:23,000 --> 00:30:28,000
Well, that is not the case.
And that is not the case

353
00:30:28,000 --> 00:30:32,000
because of this.
This blue curve,

354
00:30:32,000 --> 00:30:36,000
here, is just the Coulomb
energy of interaction.

355
00:30:36,000 --> 00:30:40,000
We evaluated that point,
that number,

356
00:30:40,000 --> 00:30:43,000
from here to here using this
expression.

357
00:30:43,000 --> 00:30:48,000
But you know that this is a
minus one over r

358
00:30:48,000 --> 00:30:52,000
dependence.
If you are way up here and you

359
00:30:52,000 --> 00:30:57,000
treat this as a zero of energy
for a plus charge and a minus

360
00:30:57,000 --> 00:31:03,000
charge, one over r kind of looks
like this.

361
00:31:03,000 --> 00:31:09,000
That is the blue curve.
But you also notice that right

362
00:31:09,000 --> 00:31:17,000
here, you see that that Coulomb
interaction is intersecting with

363
00:31:17,000 --> 00:31:24,000
this interaction potential
between a neutral sodium atom

364
00:31:24,000 --> 00:31:31,000
and a neutral chlorine atom,
right in there.

365
00:31:31,000 --> 00:31:37,000
Right at this value of r,
which we are going to call r

366
00:31:37,000 --> 00:31:44,000
star, the potential energy of
interaction from here to here is

367
00:31:44,000 --> 00:31:50,000
equal to the sum of this
ionization energy minus the

368
00:31:50,000 --> 00:31:55,000
electron affinity.
Right here, the electron can

369
00:31:55,000 --> 00:32:03,000
jump without having to put any
energy into the system.

370
00:32:03,000 --> 00:32:09,000
You are close enough for the
electron to jump because that

371
00:32:09,000 --> 00:32:15,000
Coulomb interaction has gotten
lower, and it is right at that

372
00:32:15,000 --> 00:32:21,000
point when you can have that
electron transfer and not have

373
00:32:21,000 --> 00:32:26,000
to put any energy into the
system to get it to go.

374
00:32:26,000 --> 00:32:31,000
In other words,
right here, the energy from

375
00:32:31,000 --> 00:32:37,000
right there to this point is
minus e squared 4 pi epsilon

376
00:32:37,000 --> 00:32:44,000
nought r star.

377
00:32:44,000 --> 00:32:49,000
That energy right at that point
is equal to, if I am measuring

378
00:32:49,000 --> 00:32:53,000
here from the top minus the
quantity ionization energy of

379
00:32:53,000 --> 00:32:58,000
sodium minus the electron
affinity of chlorine.

380
00:32:58,000 --> 00:33:02,000
In order to solve for this

381
00:33:02,000 --> 00:33:07,000
distance r at which the electron
jumps, for which that electron

382
00:33:07,000 --> 00:33:13,000
jump is energetically allowed,
I am going to set this equal to

383
00:33:13,000 --> 00:33:16,000
this.
I know what the ionization

384
00:33:16,000 --> 00:33:21,000
energy and the electron affinity
of sodium and chlorine are.

385
00:33:21,000 --> 00:33:27,000
I know everything except r star,
so I am going to solve

386
00:33:27,000 --> 00:33:30,000
for r star.
Let's do that.

387
00:33:30,000 --> 00:33:33,000
I am going to need the lights,
here.

388
00:33:40,000 --> 00:33:45,000
If I rearrange that equation,
r star is equal to e squared

389
00:33:45,000 --> 00:33:50,000
over 4 pi epsilon nought times
the ionization energy of sodium

390
00:33:50,000 --> 00:33:53,000
minus the electron affinity of
chlorine.

391
00:33:53,000 --> 00:33:58,000
I know

392
00:33:58,000 --> 00:34:04,000
what e star is.
It is 1.602x10^-19 Coulomb's

393
00:34:04,000 --> 00:34:08,000
squared.
I have a 4 pi epsilon nought.

394
00:34:08,000 --> 00:34:14,000
I know what epsilon nought is.
And then, the difference

395
00:34:14,000 --> 00:34:21,000
between the ionization energy
and the electron affinity I

396
00:34:21,000 --> 00:34:27,000
calculated over there.
That is 147 kilojoules per mole

397
00:34:27,000 --> 00:34:35,000
or 1.47x10^5 joules per mole.
But now, and this is what

398
00:34:35,000 --> 00:34:42,000
everybody forgets on an exam,
I have to calculate r star per

399
00:34:42,000 --> 00:34:49,000
molecule, not per mole because
per mole does not make sense.

400
00:34:49,000 --> 00:34:54,000
And I have this energy written
here per mole,

401
00:34:54,000 --> 00:35:03,000
so I need an Avogadro's number
up here, 6.022x10^23 per mole.

402
00:35:03,000 --> 00:35:11,000
Don't forget Avogadro's number
when you calculate r.

403
00:35:11,000 --> 00:35:18,000
What is r star?
Well, it comes out to be

404
00:35:18,000 --> 00:35:26,000
9.45x10^-10 meters.
Let's get a perspective on

405
00:35:26,000 --> 00:35:34,000
these distances.
The sodium atom diameter is 3.8

406
00:35:34,000 --> 00:35:39,000
angstroms.
Chlorine atom diameter,

407
00:35:39,000 --> 00:35:45,000
2 angstroms.
What I am saying is that this

408
00:35:45,000 --> 00:35:51,000
electron can jump,
or does jump from sodium to

409
00:35:51,000 --> 00:35:59,000
chlorine at this distance r
star, which is equal to 9.45

410
00:35:59,000 --> 00:36:04,000
angstroms.
So, the sodium and the chlorine

411
00:36:04,000 --> 00:36:09,000
really are a considerable
distance apart when that

412
00:36:09,000 --> 00:36:12,000
electron jumps.
But that electron can jump

413
00:36:12,000 --> 00:36:18,000
because it is at that point that
the Coulomb interaction is large

414
00:36:18,000 --> 00:36:24,000
enough here to compensate for
the difference in the ionization

415
00:36:24,000 --> 00:36:27,000
energy and the electron
affinity.

416
00:36:27,000 --> 00:36:31,000
And this actual number,
here, was verified in these

417
00:36:31,000 --> 00:36:36,000
experiments by Herschbach and
Lee.

418
00:36:36,000 --> 00:36:41,000
It actually does happen.
And this very simple classical

419
00:36:41,000 --> 00:36:46,000
model, where we are actually
treating the sodium and the

420
00:36:46,000 --> 00:36:51,000
chlorine as point charges,
we have forgotten everything

421
00:36:51,000 --> 00:36:55,000
else about the electrons,
that works remarkably well.

422
00:36:55,000 --> 00:37:01,000
Now, what this model does not
give you very well is the bond

423
00:37:01,000 --> 00:37:06,000
energy.
Because, if you look at this

424
00:37:06,000 --> 00:37:12,000
diagram again right in here,
let me go back on here,

425
00:37:12,000 --> 00:37:17,000
this 147 kilojoules here,
that I can look up.

426
00:37:17,000 --> 00:37:22,000
This 592 kilojoules,
that is just the Coulomb

427
00:37:22,000 --> 00:37:29,000
interaction between a positive
and a negative charge at 2.36

428
00:37:29,000 --> 00:37:32,000
eV.
That is all that is.

429
00:37:32,000 --> 00:37:36,000
You can calculate that.
And so, therefore,

430
00:37:36,000 --> 00:37:41,000
if I want to calculate the bond
energy of sodium chloride,

431
00:37:41,000 --> 00:37:46,000
the bond energy is just the
difference between this energy

432
00:37:46,000 --> 00:37:50,000
and that energy,
and that is 435 kilojoules per

433
00:37:50,000 --> 00:37:53,000
mole.
Well, that does not come out so

434
00:37:53,000 --> 00:37:57,000
well in terms of the actual bond
energy.

435
00:37:57,000 --> 00:38:03,000
The actual bond energy is
kilojoules per mole.

436
00:38:03,000 --> 00:38:07,000
And we know why that did not
come out too well.

437
00:38:07,000 --> 00:38:14,000
That is because this depends on
all of the interactions that are

438
00:38:14,000 --> 00:38:20,000
much closer into the nucleus.
By the time you get down here,

439
00:38:20,000 --> 00:38:24,000
the repulsive interactions are
present.

440
00:38:24,000 --> 00:38:30,000
The nuclear-nuclear repulsions
are present.

441
00:38:30,000 --> 00:38:34,000
And, in our simple model,
we did not take that into

442
00:38:34,000 --> 00:38:37,000
account, the nuclear-nuclear
repulsions.

443
00:38:37,000 --> 00:38:42,000
This simple model worked to get
r star because r star is further

444
00:38:42,000 --> 00:38:45,000
out.
The nuclear-nuclear repulsions

445
00:38:45,000 --> 00:38:49,000
have not really set in yet.
Therefore, the simple model

446
00:38:49,000 --> 00:38:54,000
works when you are at a far
distance, when r is large.

447
00:38:54,000 --> 00:39:00,000
But to get the bond strength,
here, you are much closer in.

448
00:39:00,000 --> 00:39:04,000
You are at 2.36 angstroms.
That is the difference in

449
00:39:04,000 --> 00:39:08,000
energy from here to there.
We forgot about the repulsive

450
00:39:08,000 --> 00:39:13,000
interactions between the two
nuclei, so the model is not

451
00:39:13,000 --> 00:39:18,000
going to work so close to the
nucleus, but it does a really

452
00:39:18,000 --> 00:39:22,000
good job of getting r star far
away from the nucleus.

453
00:39:22,000 --> 00:39:27,000
Again, this simple model only
works for very ionic compounds,

454
00:39:27,000 --> 00:39:32,000
very ionic bonds like sodium
chloride.

455
00:39:32,000 --> 00:39:39,000
It won't work very well for
hydrogen chloride,

456
00:39:39,000 --> 00:39:43,000
for example.
Questions on that?

457
00:39:43,000 --> 00:39:45,000
Yes?

458
00:39:55,000 --> 00:39:59,000
We are going to deal with
entropy and Gibbs free energy

459
00:39:59,000 --> 00:40:03,000
changes in a week or two.
Right now, what I am writing

460
00:40:03,000 --> 00:40:07,000
here are energy changes.
I am actually dealing with

461
00:40:07,000 --> 00:40:10,000
single molecules.
I might have,

462
00:40:10,000 --> 00:40:13,000
in my mind, here,
energies per mole.

463
00:40:13,000 --> 00:40:18,000
But what I am thinking about is
not an ensemble of molecules.

464
00:40:18,000 --> 00:40:23,000
I am actually thinking about
what is happening in each

465
00:40:23,000 --> 00:40:28,000
individual single molecule
interaction.

466
00:40:28,000 --> 00:40:33,000
That is why I have not talked
about delta G here at all.

467
00:40:33,000 --> 00:40:38,000
And, in the field of chemical
dynamics, that is where we want

468
00:40:38,000 --> 00:40:44,000
to look at individual events as
opposed to a Boltzmann average

469
00:40:44,000 --> 00:40:48,000
of events.
That is what I am talking about

470
00:40:48,000 --> 00:40:53,000
right here, but we are going to
talk about collections of

471
00:40:53,000 --> 00:40:58,000
molecules and the energy
changes.

472
00:40:58,000 --> 00:41:05,000
I am going to change my
definition from delta E to delta

473
00:41:05,000 --> 00:41:11,000
H, the bond enthalpy,
in a couple of days or so.

474
00:41:11,000 --> 00:41:14,000
Other questions?
Okay.

475
00:41:14,000 --> 00:41:22,000
Well, there is one other just
rather brief topic that I wanted

476
00:41:22,000 --> 00:41:27,000
to talk about.
That is, measuring dipole

477
00:41:27,000 --> 00:41:32,000
moments.
And then, from the dipole

478
00:41:32,000 --> 00:41:37,000
moments, getting out some ionic
character to a chemical bond.

479
00:41:37,000 --> 00:41:41,000
Your book actually calls ionic
bonds polar covalent bonds.

480
00:41:41,000 --> 00:41:46,000
And that is fine because even a
very ionic bond like sodium

481
00:41:46,000 --> 00:41:51,000
chloride is not completely
ionic, in the sense that when it

482
00:41:51,000 --> 00:41:56,000
is the molecule you know that it
is not a point charge on sodium

483
00:41:56,000 --> 00:42:02,000
and a point charge on chlorine.
You have an electron

484
00:42:02,000 --> 00:42:06,000
distribution when you are that
close.

485
00:42:06,000 --> 00:42:13,000
And so, what you have in an
ionic bond or a polar covalent

486
00:42:13,000 --> 00:42:18,000
bond, here, is an asymmetric
charge distribution.

487
00:42:18,000 --> 00:42:23,000
In HCl, here,
you have both electrons,

488
00:42:23,000 --> 00:42:28,000
on the average,
being closer to the chlorine

489
00:42:28,000 --> 00:42:34,000
nucleus than to the hydrogen
nucleus.

490
00:42:34,000 --> 00:42:39,000
And you have that because you
have a bond between atoms with

491
00:42:39,000 --> 00:42:42,000
two very different
electronegativities.

492
00:42:42,000 --> 00:42:45,000
So, that is a polar covalent
bond.

493
00:42:45,000 --> 00:42:51,000
Now, what we are going to do is
we are going to use this symbol

494
00:42:51,000 --> 00:42:56,000
delta here as a measure of the
amount of electron transfer.

495
00:42:56,000 --> 00:43:01,000
Delta is the fraction of a full
charge that is asymmetrically

496
00:43:01,000 --> 00:43:05,000
distributed.
This plus delta,

497
00:43:05,000 --> 00:43:09,000
this delta that was on the
hydrogen, is now on the

498
00:43:09,000 --> 00:43:12,000
chlorine.
That is the interpretation of

499
00:43:12,000 --> 00:43:15,000
that symbol.
That asymmetric charge

500
00:43:15,000 --> 00:43:20,000
distribution leads to a dipole
moment, which is defined as q,

501
00:43:20,000 --> 00:43:25,000
where q is the magnitude of the
charge separation,

502
00:43:25,000 --> 00:43:28,000
times r, where r is that charge
separation.

503
00:43:28,000 --> 00:43:34,000
It is, strictly speaking,

504
00:43:34,000 --> 00:43:39,000
a vector.
Q times R is what we define as

505
00:43:39,000 --> 00:43:44,000
a dipole moment.
The units of dipole moment is

506
00:43:44,000 --> 00:43:49,000
Coulombs times meters.
You can see that from Q times

507
00:43:49,000 --> 00:43:52,000
R.
A dipole moment is also a

508
00:43:52,000 --> 00:43:57,000
vector.
I have the vector on this slide

509
00:43:57,000 --> 00:44:03,000
going from the positively
charged end to the negatively

510
00:44:03,000 --> 00:44:07,000
charged end.
That is the way your present

511
00:44:07,000 --> 00:44:09,000
book does it.
In your notes,

512
00:44:09,000 --> 00:44:12,000
I have it reversed.
I have it reversed because the

513
00:44:12,000 --> 00:44:16,000
last time I taught this,
I was using a book that used a

514
00:44:16,000 --> 00:44:20,000
different notation and I sent it
out for Xeroxing before I

515
00:44:20,000 --> 00:44:23,000
noticed it was different.
So, change it around.

516
00:44:23,000 --> 00:44:26,000
Not that it is every going to
make any difference,

517
00:44:26,000 --> 00:44:29,000
but your book has this
convention from positive to

518
00:44:29,000 --> 00:44:31,000
negative.

519
00:44:37,000 --> 00:44:40,000
This unit, though,
of a Coulomb meter,

520
00:44:40,000 --> 00:44:44,000
is a very large unit,
an inconvenient unit,

521
00:44:44,000 --> 00:44:48,000
so we have another unit.
It is called the Debye,

522
00:44:48,000 --> 00:44:53,000
named after Peter Debye who
first studied these polar

523
00:44:53,000 --> 00:44:56,000
covalent molecules.
And a Debye,

524
00:44:56,000 --> 00:45:00,000
here, is defined as the
following.

525
00:45:00,000 --> 00:45:05,000
It is defined as if you have a
full unit charge,

526
00:45:05,000 --> 00:45:09,000
not a delta,
moved from here to here,

527
00:45:09,000 --> 00:45:15,000
and the charge is separated by
0.208 angstroms,

528
00:45:15,000 --> 00:45:20,000
that defines this unit called
the Debye.

529
00:45:20,000 --> 00:45:26,000
So, there are 0.208 angstroms
per Debye.

530
00:45:31,000 --> 00:45:36,000
If you knew the fraction of
charge that is separated and you

531
00:45:36,000 --> 00:45:41,000
knew the bond length in
angstroms, and then you have our

532
00:45:41,000 --> 00:45:46,000
definition for a Debye,
which is 0.208 angstroms per

533
00:45:46,000 --> 00:45:51,000
Debye, you could calculate the
dipole moment in Debye.

534
00:45:51,000 --> 00:45:57,000
Usually what we do is not to
calculate the dipole moment.

535
00:45:57,000 --> 00:46:02,000
We usually measure the dipole
moment and calculate the partial

536
00:46:02,000 --> 00:46:08,000
charge distribution.
Because we usually don't know

537
00:46:08,000 --> 00:46:10,000
this.
We can measure that.

538
00:46:10,000 --> 00:46:14,000
We can measure the dipole
moments in kind of a capacitor

539
00:46:14,000 --> 00:46:18,000
arrangement, where we have some
molecules that have a dipole

540
00:46:18,000 --> 00:46:23,000
moment, a positive charge on one
plate, a negative charge on the

541
00:46:23,000 --> 00:46:25,000
other.
And, when you do that,

542
00:46:25,000 --> 00:46:30,000
of course, these electric
dipoles are going to align.

543
00:46:30,000 --> 00:46:32,000
That is going to change the
capacitance.

544
00:46:32,000 --> 00:46:36,000
If this capacitor is part of a
resonant circuit,

545
00:46:36,000 --> 00:46:39,000
it is going to change the
resonant frequent.

546
00:46:39,000 --> 00:46:43,000
The resonant frequency is
related to the dipole moment.

547
00:46:43,000 --> 00:46:46,000
And, in that way,
you calculate or measure the

548
00:46:46,000 --> 00:46:49,000
dipole moment.
That is how it was originally

549
00:46:49,000 --> 00:46:52,000
done.
However, you can now measure

550
00:46:52,000 --> 00:46:56,000
dipole moments very accurately
by rotational spectroscopy.

551
00:46:56,000 --> 00:47:02,000
And we are going to look at
that in a few lectures or so.

552
00:47:02,000 --> 00:47:05,000
But take HCl right here.
Here is HCl.

553
00:47:05,000 --> 00:47:10,000
Here is the measured dipole
moment, and here is the bond

554
00:47:10,000 --> 00:47:13,000
length.
We can use these two pieces of

555
00:47:13,000 --> 00:47:19,000
information to calculate the
fraction of charge distributed.

556
00:47:19,000 --> 00:47:23,000
And, in the case of HCl,
that is about 0.18.

557
00:47:23,000 --> 00:47:28,000
Sometimes, we refer to this in
a percentage.

558
00:47:28,000 --> 00:47:32,000
So, this would be 18% of a
charge separation.

559
00:47:32,000 --> 00:47:36,000
Sometimes we say 18% ionic
character in HCl.

560
00:47:36,000 --> 00:47:43,000
That compares to something like
70% or 80% in sodium chloride or

561
00:47:43,000 --> 00:47:48,000
lithium chloride.
So, HCl is not anywhere near as

562
00:47:48,000 --> 00:47:51,000
ionic.
The charge distribution is not

563
00:47:51,000 --> 00:47:59,000
as asymmetric as it is in sodium
chloride or lithium chloride.

564
00:47:59,000 --> 00:48:03,000
Thank you very much for hanging
in here today.

565
00:48:03,000 --> 00:48:07,000
It has been hot.
Have a nice cool weekend.

566
00:48:07,875 --> 00:48:10,000
See you next Wednesday.