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PROFESSOR: OK, I want to take
10 more seconds now the

00:00:23.990 --> 00:00:27.670
clicker slide.

00:00:27.670 --> 00:00:31.680
This is giving us one more try
on the vsper geometries,

00:00:31.680 --> 00:00:37.100
because it didn't go so
well on Wednesday.

00:00:37.100 --> 00:00:38.150
All right, excellent.

00:00:38.150 --> 00:00:40.320
So that is a very good job.

00:00:40.320 --> 00:00:43.880
Let's quickly go over why.

00:00:43.880 --> 00:00:45.620
We have p h 3.

00:00:45.620 --> 00:00:50.040
We told you that phosphorous has
5 valence electrons plus 3

00:00:50.040 --> 00:00:52.390
from each of the hydrogens,
so we have a total

00:00:52.390 --> 00:00:54.860
of 8 valence electrons.

00:00:54.860 --> 00:00:57.300
How many do we need to get
full valence shells

00:00:57.300 --> 00:00:58.100
everywhere?

00:00:58.100 --> 00:01:00.340
STUDENT: [INAUDIBLE]

00:01:00.340 --> 00:01:00.620
PROFESSOR: 14.

00:01:00.620 --> 00:01:03.330
So, we need 14 minus 8.

00:01:03.330 --> 00:01:09.380
That leaves us with 6
bonding electrons.

00:01:09.380 --> 00:01:15.330
And if we put that in our bond
here, we have 1, 2, 3 bonds,

00:01:15.330 --> 00:01:18.630
plus we have one lone
pair left over.

00:01:18.630 --> 00:01:21.000
So this is our Lewis
structure here.

00:01:21.000 --> 00:01:24.940
If these bonds were all
completely of equal distance

00:01:24.940 --> 00:01:28.300
apart, whether is was a lone
pair or bonding electrons, the

00:01:28.300 --> 00:01:29.990
angles would be 109 .

00:01:29.990 --> 00:01:31.130
5 degrees.

00:01:31.130 --> 00:01:34.640
But because there's this lone
pair here, it's pushing down

00:01:34.640 --> 00:01:38.270
on the other bonds, so we
end up with an angle of

00:01:38.270 --> 00:01:40.080
less than 109 .

00:01:40.080 --> 00:01:40.970
5 degrees.

00:01:40.970 --> 00:01:44.630
All right, so let's switch
over to notes for today.

00:01:44.630 --> 00:01:46.710
So we're going to finish
talking about molecular

00:01:46.710 --> 00:01:50.410
orbital theory, and then we'll
switch over to discussing

00:01:50.410 --> 00:01:54.180
bonding in larger molecules,
even larger than diatomic, so

00:01:54.180 --> 00:01:59.690
we'll move on to talking about
valence bond theory and

00:01:59.690 --> 00:02:00.010
hybridization.

00:02:00.010 --> 00:02:01.510
So, clearly you don't have your
notes in front of you

00:02:01.510 --> 00:02:04.230
yet, so you can just listen,
take it all in.

00:02:04.230 --> 00:02:07.650
What I'll do is I'll post the
notes filled in to the point

00:02:07.650 --> 00:02:10.420
where you actually get your
class notes today.

00:02:10.420 --> 00:02:13.930
So, this will be a little bit
more like a seminar to start

00:02:13.930 --> 00:02:17.460
with, and a little bit less
like a lecture in class.

00:02:17.460 --> 00:02:20.550
But let's go ahead and start
our discussion in terms of

00:02:20.550 --> 00:02:23.910
molecular orbital theory.

00:02:23.910 --> 00:02:27.650
So where we had left off with
was we'd fully discussed up to

00:02:27.650 --> 00:02:31.000
the point of considering
homonuclear diatomic

00:02:31.000 --> 00:02:34.370
molecules, so molecules that
both have the same nucleus.

00:02:34.370 --> 00:02:37.990
And where we had left off was
we were going to start one

00:02:37.990 --> 00:02:41.400
example of thinking about now
where we have a heteronuclear

00:02:41.400 --> 00:02:47.080
diatomic molecules, so two
different atoms in terms of

00:02:47.080 --> 00:02:48.590
forming the molecule.

00:02:48.590 --> 00:02:50.760
But first, I just want to remind
you when we're talking

00:02:50.760 --> 00:02:53.440
about molecular orbital theory,
this is treating

00:02:53.440 --> 00:02:56.350
electrons as waves, so what
we're actually able to do is

00:02:56.350 --> 00:03:00.370
either constructively or
destructively combine atomic

00:03:00.370 --> 00:03:01.970
orbitals to form molecular
orbitals.

00:03:01.970 --> 00:03:06.080
So you should remember that
any time we combine 2 s

00:03:06.080 --> 00:03:09.290
orbitals, what we're going to
find is if we constructively

00:03:09.290 --> 00:03:11.420
interfere those two orbitals,
we're going to

00:03:11.420 --> 00:03:13.220
form a bonding orbital.

00:03:13.220 --> 00:03:16.250
And that's going to be lower
in energy than the two

00:03:16.250 --> 00:03:18.350
individual atomic orbitals.

00:03:18.350 --> 00:03:21.850
And we call that, for this case,
our sigma 2 s orbital.

00:03:21.850 --> 00:03:26.740
In contrast, if we have
destructive interference, what

00:03:26.740 --> 00:03:30.300
we're going to form is a sigma
2 s star, and what does the

00:03:30.300 --> 00:03:31.630
star designate?

00:03:31.630 --> 00:03:32.830
STUDENT: [INAUDIBLE]

00:03:32.830 --> 00:03:33.630
PROFESSOR: Anti-bonding, yup.

00:03:33.630 --> 00:03:35.440
So it's an Anti-bonding
orbital.

00:03:35.440 --> 00:03:38.320
It's going to be higher in
energy than the individual

00:03:38.320 --> 00:03:38.950
atomic orbitals.

00:03:38.950 --> 00:03:41.300
All right, great.

00:03:41.300 --> 00:03:43.860
So, I think we have these
molecular orbital energies

00:03:43.860 --> 00:03:46.140
down, so let's move on
to talking about

00:03:46.140 --> 00:03:48.390
more complex molecules.

00:03:48.390 --> 00:03:51.520
And to do this we're going to
introduce valence bond theory,

00:03:51.520 --> 00:03:56.270
and the idea of hybridization
of orbitals.

00:03:56.270 --> 00:03:59.420
So the idea behind valence bond
theory is very easy to

00:03:59.420 --> 00:04:00.090
understand.

00:04:00.090 --> 00:04:03.330
Essentially what you have is
bonds resulting from the

00:04:03.330 --> 00:04:05.880
pairing of unpaired electrons.

00:04:05.880 --> 00:04:09.910
So the simplest case we can
think of is with h 2 where we

00:04:09.910 --> 00:04:14.550
have two unpaired electrons,
each in a 1 s orbital of a

00:04:14.550 --> 00:04:16.570
separate h atom.

00:04:16.570 --> 00:04:20.120
And if we picture those two
coming together, we form the h

00:04:20.120 --> 00:04:21.620
2 molecule.

00:04:21.620 --> 00:04:25.110
And again, we have the pairing
of the unpaired electrons, and

00:04:25.110 --> 00:04:28.170
we have two orbitals
coming together.

00:04:28.170 --> 00:04:31.350
So in molecular orbital theory,
what we did was we

00:04:31.350 --> 00:04:33.920
named orbitals based
on their symmetry.

00:04:33.920 --> 00:04:37.310
In valence bond theory, the
focus is on discussing the

00:04:37.310 --> 00:04:40.210
bonds, but it should look very
familiar to you, because

00:04:40.210 --> 00:04:43.040
there's two types of bonds that
we want to discuss here.

00:04:43.040 --> 00:04:46.570
We want to discuss sigma
bonds and pi bonds.

00:04:46.570 --> 00:04:49.340
So this is very similar to what
we saw in terms of sigma

00:04:49.340 --> 00:04:51.160
orbitals and pi orbitals.

00:04:51.160 --> 00:04:53.470
So in this first case
here, what we're

00:04:53.470 --> 00:04:55.770
seeing is a sigma bond.

00:04:55.770 --> 00:04:59.010
And a sigma bond forms any time
you have two orbitals

00:04:59.010 --> 00:05:02.250
coming together and interacting
on that

00:05:02.250 --> 00:05:05.150
internuclear axis.

00:05:05.150 --> 00:05:08.830
So we talk about a sigma bond
as being cylindrically

00:05:08.830 --> 00:05:11.980
symmetric about the bond axis,
and it's important to point

00:05:11.980 --> 00:05:15.950
out that it has no nodal plane
across this bond axis.

00:05:15.950 --> 00:05:17.840
This is in direct contrast
to when we're

00:05:17.840 --> 00:05:20.000
thinking about pi bonds.

00:05:20.000 --> 00:05:25.520
So pi bonds have electron
density both above and below

00:05:25.520 --> 00:05:29.560
the bond axis, but they actually
have a nodal plane at

00:05:29.560 --> 00:05:31.940
this z, this bond axis here.

00:05:31.940 --> 00:05:34.990
And remember for this class,
we always define z as the

00:05:34.990 --> 00:05:37.570
internuclear or the bond axis.

00:05:37.570 --> 00:05:40.700
So it might look like here, if
you don't understand about p

00:05:40.700 --> 00:05:42.950
orbitals, which I know all you
do, but if someone else was

00:05:42.950 --> 00:05:45.100
just looking and seeing, it kind
of looks like there's two

00:05:45.100 --> 00:05:46.090
bonds here.

00:05:46.090 --> 00:05:49.320
There's not two bonds, that's
one pi bond, and the reason is

00:05:49.320 --> 00:05:52.440
because it's 2 p orbitals coming
together, and remember

00:05:52.440 --> 00:05:55.805
p orbitals have electron density
above and below the

00:05:55.805 --> 00:05:58.290
axis, so when they come
together, it kind of looks

00:05:58.290 --> 00:06:00.670
like one bonds, but essentially
what we have here

00:06:00.670 --> 00:06:03.270
is one pi bond.

00:06:03.270 --> 00:06:07.330
So let's think about how we can
classify single and double

00:06:07.330 --> 00:06:09.360
and triple bonds, which is
what we're really used to

00:06:09.360 --> 00:06:11.920
dealing with in terms
of these sigma bonds

00:06:11.920 --> 00:06:13.750
and these pi bonds.

00:06:13.750 --> 00:06:16.340
So, if we take a look at what
a single bond is, and let me

00:06:16.340 --> 00:06:19.720
grab some molecules here.

00:06:19.720 --> 00:06:22.570
If we're talking about a single
bond, we're talking

00:06:22.570 --> 00:06:27.070
about 2 orbitals overlapping
in the internuclear axis.

00:06:27.070 --> 00:06:29.860
So if we have a single bond
here, would you consider that

00:06:29.860 --> 00:06:33.300
a sigma bond or a pi bond?

00:06:33.300 --> 00:06:33.830
STUDENT: [INAUDIBLE]

00:06:33.830 --> 00:06:35.510
PROFESSOR: Right, it's
a sigma bond.

00:06:35.510 --> 00:06:38.020
Essentially what we're
seeing is overlapping

00:06:38.020 --> 00:06:40.450
in this z axis here.

00:06:40.450 --> 00:06:44.130
In contrast, if we talk about a
double bond, what we're now

00:06:44.130 --> 00:06:47.450
talking about is having
both a sigma bond

00:06:47.450 --> 00:06:49.750
and also one pi bond.

00:06:49.750 --> 00:06:53.210
And I apologize, I intended to
set this up right before

00:06:53.210 --> 00:06:55.840
class, but that didn't
happen today.

00:06:55.840 --> 00:06:59.760
All right, so what we see here
is we have our sigma bond

00:06:59.760 --> 00:07:03.470
that's along the internuclear
axis here, but we also have a

00:07:03.470 --> 00:07:07.210
pi bond, because each of these
atoms now has electrons in

00:07:07.210 --> 00:07:09.510
it's in a p orbital, so we're
going to overlap of electron

00:07:09.510 --> 00:07:13.540
density above and
below the bond.

00:07:13.540 --> 00:07:16.900
So that's exactly what our
definition of a pi bond is, so

00:07:16.900 --> 00:07:20.160
we have one sigma bond,
and one pi bond.

00:07:20.160 --> 00:07:22.310
So now let's think about
a triple bond.

00:07:22.310 --> 00:07:26.400
A triple bond, again is going to
have one sigma bond on the

00:07:26.400 --> 00:07:28.130
internuclear axis.

00:07:28.130 --> 00:07:29.930
How many pi bonds would
you expect?

00:07:29.930 --> 00:07:31.410
STUDENT: [INAUDIBLE]

00:07:31.410 --> 00:07:32.670
PROFESSOR: Two, great.

00:07:32.670 --> 00:07:34.460
So, we're going to
see two pi bonds.

00:07:34.460 --> 00:07:38.120
The first one will be above
and below the bond axis is

00:07:38.120 --> 00:07:40.650
where we'll see the electron
density, and the second will

00:07:40.650 --> 00:07:44.050
be perpendicular to that, so it
will be a density in front

00:07:44.050 --> 00:07:45.860
of and behind the bond axis.

00:07:45.860 --> 00:07:48.680
So we can kind of flip it this
way -- this will be one pi

00:07:48.680 --> 00:07:50.690
bond, this will be another
interacting

00:07:50.690 --> 00:07:51.740
between these p orbitals.

00:07:51.740 --> 00:07:56.040
All right, so that's really all
there is to thinking about

00:07:56.040 --> 00:07:58.400
valence bond theory in
terms of the most

00:07:58.400 --> 00:08:00.160
simple explanation here.

00:08:00.160 --> 00:08:02.500
But what we're going is we're
going to start trying to apply

00:08:02.500 --> 00:08:05.200
it to a molecule, and I actually
picked a molecule

00:08:05.200 --> 00:08:07.630
that it's not going to work for,
even though it would work

00:08:07.630 --> 00:08:10.410
even just at this level for
many, many molecules.

00:08:10.410 --> 00:08:13.510
And I picked looking at methane
so we could see if

00:08:13.510 --> 00:08:16.470
there are other factors that
we're not considering, that we

00:08:16.470 --> 00:08:19.920
need to maybe tweak our model
a little bit, and I think

00:08:19.920 --> 00:08:24.150
we'll find that we do if we take
a look at a polyatomic

00:08:24.150 --> 00:08:27.660
molecule, methane, so c h 4.

00:08:27.660 --> 00:08:32.560
So let's think about methane
using valence bond theory.

00:08:32.560 --> 00:08:36.010
So, using our simple valence
bond theory, what we would

00:08:36.010 --> 00:08:40.790
expect is that we want to pair
up any unpaired electrons in

00:08:40.790 --> 00:08:44.580
methane with unpaired electrons
from hydrogen and

00:08:44.580 --> 00:08:46.280
form bonds.

00:08:46.280 --> 00:08:49.410
But what we see we have is that
we only have two unpaired

00:08:49.410 --> 00:08:51.000
electrons here.

00:08:51.000 --> 00:08:55.180
Because we have paired set in
a 2 s orbital, so all we're

00:08:55.180 --> 00:08:58.360
left essentially is two
electrons that are available

00:08:58.360 --> 00:08:59.200
for bonding.

00:08:59.200 --> 00:09:01.780
So this should immediately look
like a problem because we

00:09:01.780 --> 00:09:04.850
know, in fact, that methane is
tetravalent, and this is

00:09:04.850 --> 00:09:07.130
telling us it's only divalent.

00:09:07.130 --> 00:09:10.380
Essentially it would only allow
for us to bond to two

00:09:10.380 --> 00:09:14.650
hydrogen atoms. So if it did
this, it now looks like, from

00:09:14.650 --> 00:09:17.610
looking at the paired electrons
that we have a

00:09:17.610 --> 00:09:21.930
stable structure here, and our
structure is not c h 4, it's a

00:09:21.930 --> 00:09:25.740
stable structure of c h 2, and
it will actually predict,

00:09:25.740 --> 00:09:29.740
also, what this h c h
bond angle it is.

00:09:29.740 --> 00:09:32.510
So according to this model
what is that bond angle?

00:09:32.510 --> 00:09:35.660
STUDENT: [INAUDIBLE]

00:09:35.660 --> 00:09:37.760
PROFESSOR: One more time.

00:09:37.760 --> 00:09:39.250
OK, I hear a mix.

00:09:39.250 --> 00:09:42.630
So, according to this model,
what we're seeing is a bond

00:09:42.630 --> 00:09:44.150
angle of 90 degrees.

00:09:44.150 --> 00:09:48.060
What do you know the bond
angle should be?

00:09:48.060 --> 00:09:49.270
It's 109 .

00:09:49.270 --> 00:09:51.370
5 is what we would expect
for methane because it's

00:09:51.370 --> 00:09:54.370
tetravalent, but here we're just
seeing something that's

00:09:54.370 --> 00:09:56.740
divalent, and they're both
in p orbitals that are

00:09:56.740 --> 00:09:58.290
perpendicular to each other.

00:09:58.290 --> 00:10:01.620
So what we're predicting is a
bond angle of 90 degrees.

00:10:01.620 --> 00:10:05.790
This is totally wrong, this is
the wrong picture altogether.

00:10:05.790 --> 00:10:07.950
If you had your notes, you could
do some fun scribbling

00:10:07.950 --> 00:10:10.110
right now, so you can
do that at home.

00:10:10.110 --> 00:10:14.320
We're going to need to tweak our
explanation here, and take

00:10:14.320 --> 00:10:17.970
into account another factor,
and that factor is the fact

00:10:17.970 --> 00:10:21.460
that we know that we must have
four unpaired electrons in

00:10:21.460 --> 00:10:24.400
carbon if we're going
to form four bonds.

00:10:24.400 --> 00:10:26.580
So the way that we can explain
this is through something

00:10:26.580 --> 00:10:28.580
called electron promotion and

00:10:28.580 --> 00:10:30.460
hybridization of atomic orbitals.

00:10:30.460 --> 00:10:34.440
So let's take a look at
what we mean by this.

00:10:34.440 --> 00:10:39.160
So if we take our carbon atom
here, which has two electrons

00:10:39.160 --> 00:10:44.130
in the 2 s orbital, and we
promote one of these electrons

00:10:44.130 --> 00:10:49.090
into a 2 p orbital, what we see
now is that yes, we do, we

00:10:49.090 --> 00:10:50.460
have four unpaired electrons.

00:10:50.460 --> 00:10:53.450
So, looking at this,
this might not

00:10:53.450 --> 00:10:54.440
look so good for you.

00:10:54.440 --> 00:10:58.610
What we're proposing here is
that you take a nice low

00:10:58.610 --> 00:11:01.090
energy s electron and
move it into a

00:11:01.090 --> 00:11:02.790
higher energy p orbital.

00:11:02.790 --> 00:11:05.750
And the truth is that yes, this
costs energy, we're going

00:11:05.750 --> 00:11:07.740
up to a higher energy state.

00:11:07.740 --> 00:11:10.300
But it doesn't actually cost
as much energy as you might

00:11:10.300 --> 00:11:13.350
think, because in this s orbital
here we have a paired

00:11:13.350 --> 00:11:16.530
electron situation where we're
moving up to a p orbital where

00:11:16.530 --> 00:11:19.040
the electron is no longer
paired, so it won't feel quite

00:11:19.040 --> 00:11:22.050
as much electron repulsion, but
nonetheless, this is going

00:11:22.050 --> 00:11:23.140
to cost us energy.

00:11:23.140 --> 00:11:25.210
So we'll have to think about
where that energy is going to

00:11:25.210 --> 00:11:27.530
come from and we'll see
that in just a minute.

00:11:27.530 --> 00:11:30.440
But let's assume that this is,
in fact, going to happen.

00:11:30.440 --> 00:11:33.760
So now what we have is four
unpaired electrons.

00:11:33.760 --> 00:11:36.510
That's great, but it's still not
quite the picture we need,

00:11:36.510 --> 00:11:39.430
because actually, all the
electrons are not in equal

00:11:39.430 --> 00:11:43.040
orbitals -- one's in an s
orbital, and 3 are in p.

00:11:43.040 --> 00:11:46.270
But what we need to remember is
the fact that we're talking

00:11:46.270 --> 00:11:47.990
about electrons which
are waves.

00:11:47.990 --> 00:11:50.490
When we're talking about
orbitals, we're talking about

00:11:50.490 --> 00:11:51.350
wave functions.

00:11:51.350 --> 00:11:53.750
So we can actually
constructively and

00:11:53.750 --> 00:11:57.320
destructively combine these
waves, these atomic orbitals

00:11:57.320 --> 00:11:59.620
to make a hybrid.

00:11:59.620 --> 00:12:02.410
So if we go ahead and hybridize
our p orbitals and

00:12:02.410 --> 00:12:06.130
our s orbitals, we'll switch
from having these original

00:12:06.130 --> 00:12:10.170
orbitals to having something
called hybrid orbitals.

00:12:10.170 --> 00:12:13.810
And hybrid orbitals are all
going to be completely equal,

00:12:13.810 --> 00:12:16.690
and you'll notice that they're
higher in energy than the s

00:12:16.690 --> 00:12:20.400
orbital, and lower in energy
than the p orbital.

00:12:20.400 --> 00:12:23.540
That should make sense because
they come from combining s

00:12:23.540 --> 00:12:25.360
orbitals and p orbitals.

00:12:25.360 --> 00:12:28.080
And specifically, when we give
them a name it's very clear

00:12:28.080 --> 00:12:30.690
exactly which orbitals they
come from combining, we're

00:12:30.690 --> 00:12:34.540
calling these s p 3 orbitals
-- that's because they come

00:12:34.540 --> 00:12:38.230
from combining 1 s orbital
and 3 p orbitals.

00:12:38.230 --> 00:12:41.070
You should never get the names
of hybrid orbitals wrong

00:12:41.070 --> 00:12:42.720
because it's very
straightforward.

00:12:42.720 --> 00:12:46.770
If it has 1 s and 3 p's,
we call it s p 3.

00:12:46.770 --> 00:12:49.200
Naming doesn't always make sense
in chemistry, so I like

00:12:49.200 --> 00:12:51.320
to point out this is a place
where naming does

00:12:51.320 --> 00:12:52.490
make a lot of sense.

00:12:52.490 --> 00:12:56.200
All right, so let's consider our
methane situation now that

00:12:56.200 --> 00:12:58.850
we have our hybrid orbitals.

00:12:58.850 --> 00:13:01.650
So I want to mention also, these
are exactly equivalent,

00:13:01.650 --> 00:13:04.540
they're equivalent in energy,
they're equivalent in shape.

00:13:04.540 --> 00:13:06.420
The only thing that is different
about these orbitals

00:13:06.420 --> 00:13:08.540
is their orientation in space.

00:13:08.540 --> 00:13:10.500
So actually, first let's
take a look at how

00:13:10.500 --> 00:13:11.890
we got these orbitals.

00:13:11.890 --> 00:13:14.710
We got them from combining
again, 1 s

00:13:14.710 --> 00:13:17.310
orbital and the 3 p orbitals.

00:13:17.310 --> 00:13:21.040
If we hybridize these, what we
end up seeing are these four

00:13:21.040 --> 00:13:22.080
hybrid orbitals.

00:13:22.080 --> 00:13:24.780
You'll notice the shape is the
same, all that's different is

00:13:24.780 --> 00:13:26.360
their orientation.

00:13:26.360 --> 00:13:29.510
So essentially, each of these
orbitals come from linear

00:13:29.510 --> 00:13:33.330
combinations of all of the
original orbitals, and it's

00:13:33.330 --> 00:13:36.260
hard to picture exactly how that
happens, but one that you

00:13:36.260 --> 00:13:38.350
can at least start to get an
idea is if you think about

00:13:38.350 --> 00:13:42.000
combining the 2 s and the 2 p
z here, which is not quite

00:13:42.000 --> 00:13:44.290
accurate because of course,
we're combining all of them.

00:13:44.290 --> 00:13:45.530
But it would just give
you a little bit

00:13:45.530 --> 00:13:46.580
of an idea of shape.

00:13:46.580 --> 00:13:50.050
You can see if we combine the s
with the top lobe of the p,

00:13:50.050 --> 00:13:51.810
they're going to constructively
interfere

00:13:51.810 --> 00:13:53.720
because they have
the same sign.

00:13:53.720 --> 00:13:57.090
So you see in the hybrid orbital
we actually have a

00:13:57.090 --> 00:14:01.340
larger lobe on top where they
constructively interfered.

00:14:01.340 --> 00:14:04.250
If you compare the s orbital
with the bottom lobe, these

00:14:04.250 --> 00:14:05.830
have a different sign
so they're going to

00:14:05.830 --> 00:14:07.580
destructively interfere.

00:14:07.580 --> 00:14:10.900
So what you see is actually a
diminished lobe on the back

00:14:10.900 --> 00:14:12.960
part of this s p 3 orbital.

00:14:12.960 --> 00:14:16.580
So s p 3 orbitals always have
one huge lobe and one really

00:14:16.580 --> 00:14:17.410
little lobe.

00:14:17.410 --> 00:14:20.140
A lot of times when people draw
them, they even only draw

00:14:20.140 --> 00:14:22.710
the big lobe just to keep their
paper looking nicer, but

00:14:22.710 --> 00:14:27.290
there is that little tiny
lobe on the other side.

00:14:27.290 --> 00:14:30.470
All right, so in terms of s
p 3 hybrid orbitals, let's

00:14:30.470 --> 00:14:34.690
combine all four together on
one axis, because this is

00:14:34.690 --> 00:14:37.680
what's going to happen in
an s p 3 carbon atom.

00:14:37.680 --> 00:14:39.480
So in this case, what
would you say that

00:14:39.480 --> 00:14:40.650
the angle is here?

00:14:40.650 --> 00:14:43.320
STUDENT: [INAUDIBLE]

00:14:43.320 --> 00:14:43.770
PROFESSOR: Right, great.

00:14:43.770 --> 00:14:45.750
So, we've achieved the angle
that we observed, which is

00:14:45.750 --> 00:14:47.260
good, which is a 109 .

00:14:47.260 --> 00:14:48.600
5.

00:14:48.600 --> 00:14:52.170
So we can think about now doing
bonding, and now we have

00:14:52.170 --> 00:14:56.130
four equal orbitals with
one electronic each.

00:14:56.130 --> 00:14:58.940
So we can bring in four hydrogen
atoms, which will

00:14:58.940 --> 00:15:01.500
each contribute another
unpaired electron.

00:15:01.500 --> 00:15:05.360
So now what we have
is four bonds.

00:15:05.360 --> 00:15:08.000
And we can think about where
we did get that energy for

00:15:08.000 --> 00:15:10.370
electron promotion that I
mentioned before where we

00:15:10.370 --> 00:15:13.460
moved the electron from
the 2 s to the 2 p.

00:15:13.460 --> 00:15:14.490
We get that from bonding.

00:15:14.490 --> 00:15:16.510
We're going to release a lot
of energy for bonding, it's

00:15:16.510 --> 00:15:18.760
going to more than make up for
the fact that we actually had

00:15:18.760 --> 00:15:22.540
to spend some energy to
promote that electron.

00:15:22.540 --> 00:15:26.400
So, we can think about now how
do we describe this bond in

00:15:26.400 --> 00:15:28.050
valence bond theory.

00:15:28.050 --> 00:15:30.890
So the way that you describe
a bond is you describe the

00:15:30.890 --> 00:15:33.350
orbitals that the bond comes
from, and also the

00:15:33.350 --> 00:15:34.740
symmetry of the bond.

00:15:34.740 --> 00:15:37.080
So would you expect this
to be a pi bond or

00:15:37.080 --> 00:15:38.340
a sigma bond here?

00:15:38.340 --> 00:15:41.210
STUDENT: [INAUDIBLE]

00:15:41.210 --> 00:15:43.630
PROFESSOR: OK, so I'm hearing
some mixed answers.

00:15:43.630 --> 00:15:45.820
It turns out that it's
a sigma bond.

00:15:45.820 --> 00:15:49.350
The reason that it's a sigma
bond is because the s p 3

00:15:49.350 --> 00:15:52.090
hybrid orbital is directly
interacting with the 1 s

00:15:52.090 --> 00:15:55.810
orbital of the hydrogen atom,
and that's going to happen on

00:15:55.810 --> 00:15:58.070
the internuclear axis, they're
just coming together.

00:15:58.070 --> 00:16:01.550
Any time two orbitals come
straight on together in that

00:16:01.550 --> 00:16:05.690
internuclear axis, you're going
to have a sigma bond.

00:16:05.690 --> 00:16:09.120
So if we go ahead and name this
bond, what we're going to

00:16:09.120 --> 00:16:15.750
name it is sigma, because that's
the -- basically the

00:16:15.750 --> 00:16:17.620
shape of the bond or
that's how our

00:16:17.620 --> 00:16:19.100
bond is coming together.

00:16:19.100 --> 00:16:21.330
And then we're going to name the
atomic orbitals that make

00:16:21.330 --> 00:16:26.050
it up, and it's being made up
of a carbon 2 s p 3 orbital,

00:16:26.050 --> 00:16:30.090
and a hydrogen 1 s orbital.

00:16:30.090 --> 00:16:32.570
All right, so let's think of
a case now that's getting a

00:16:32.570 --> 00:16:33.720
little bit more complicated.

00:16:33.720 --> 00:16:36.090
We were talking about
methane, which has

00:16:36.090 --> 00:16:37.780
only one central atom.

00:16:37.780 --> 00:16:40.750
We can also talk about atoms
that have two or more central

00:16:40.750 --> 00:16:44.540
atoms. So let's talk about
ethane now, which is c h 2.

00:16:44.540 --> 00:16:48.580
So let's take our carbon s p 3
hybridized carbon and just

00:16:48.580 --> 00:16:53.490
move it around here so we can
make the z inter- bonding axis

00:16:53.490 --> 00:16:56.080
between the two carbons
right here.

00:16:56.080 --> 00:16:58.840
So if we still have an
angle of a 109 .

00:16:58.840 --> 00:17:03.200
5 degrees, and again, we still
have four unpaired electrons

00:17:03.200 --> 00:17:06.850
available for bonding, we can
make one of those bonds with

00:17:06.850 --> 00:17:10.550
another s p 3 hybridized carbon,
so we're going to make

00:17:10.550 --> 00:17:13.830
up one pair here.

00:17:13.830 --> 00:17:16.320
If we think about that, that's
a sigma bond, right, they're

00:17:16.320 --> 00:17:22.730
coming together along
the nuclear axis.

00:17:22.730 --> 00:17:25.810
We also have six spots available
to form hydrogen

00:17:25.810 --> 00:17:28.260
bonds, so we can go ahead
and fill in those

00:17:28.260 --> 00:17:30.750
electrons as well.

00:17:30.750 --> 00:17:33.950
So in terms of thinking about
ethane, we actually have two

00:17:33.950 --> 00:17:38.680
bond types that we're going to
be describing just in terms of

00:17:38.680 --> 00:17:42.730
the carbon-carbon bond and
then the carbon h bonds.

00:17:42.730 --> 00:17:45.660
So let's talk about ethane and
how we would actually write

00:17:45.660 --> 00:17:47.180
these bonds.

00:17:47.180 --> 00:17:52.250
If we have the molecule ethane,
then what we're going

00:17:52.250 --> 00:17:55.810
to have first is our sigma bond
that we described between

00:17:55.810 --> 00:17:57.670
the two carbons.

00:17:57.670 --> 00:18:00.000
So it's going to be carbon,
and then what's the

00:18:00.000 --> 00:18:01.160
hybridization here?

00:18:01.160 --> 00:18:05.500
STUDENT: [INAUDIBLE]

00:18:05.500 --> 00:18:06.410
PROFESSOR: All right, start
again, what's the

00:18:06.410 --> 00:18:07.530
hybridization of the
carbon atom?

00:18:07.530 --> 00:18:10.190
STUDENT: [INAUDIBLE]

00:18:10.190 --> 00:18:14.820
PROFESSOR: OK, so it's 2 s p
3, and our second carbon is

00:18:14.820 --> 00:18:17.250
also 2 s p 3.

00:18:17.250 --> 00:18:21.560
All right, so this is our
first type of bond here.

00:18:21.560 --> 00:18:24.420
Our second bond is going to be
between the carbon and the

00:18:24.420 --> 00:18:28.380
hydrogen atoms. Is that
a sigma or a pi bond?

00:18:28.380 --> 00:18:28.830
STUDENT: [INAUDIBLE]

00:18:28.830 --> 00:18:30.050
PROFESSOR: Sigma, good.

00:18:30.050 --> 00:18:35.000
So again, our carbon is
going to be 2 s p 3.

00:18:35.000 --> 00:18:37.300
And what will our hydrogen be?

00:18:37.300 --> 00:18:40.050
1 s -- we don't have to
hybridize it, it already has

00:18:40.050 --> 00:18:43.290
only one unpaired electron
in a 1 s orbital.

00:18:43.290 --> 00:18:47.060
All right, so that's how
we describe ethane.

00:18:47.060 --> 00:18:49.540
We don't have to just stick
with carbon, we can think

00:18:49.540 --> 00:18:52.960
about describing other types
of atoms as well using this

00:18:52.960 --> 00:18:54.170
hybridization.

00:18:54.170 --> 00:18:57.260
For example, we can talk about
nitrogen, and nitrogen has

00:18:57.260 --> 00:19:00.100
five valence electrons
shown here.

00:19:00.100 --> 00:19:03.410
Would you expect to see electron
promotion in nitrogen

00:19:03.410 --> 00:19:05.300
where we pull one of these
2 s electrons into

00:19:05.300 --> 00:19:06.950
one of the 2 p orbitals?

00:19:06.950 --> 00:19:08.640
STUDENT: [INAUDIBLE]

00:19:08.640 --> 00:19:09.330
PROFESSOR: No, good.

00:19:09.330 --> 00:19:12.770
So, electron promotion does
not happen in terms of

00:19:12.770 --> 00:19:15.250
nitrogen, because it would not
increased our number of

00:19:15.250 --> 00:19:16.670
unpaired electrons.

00:19:16.670 --> 00:19:19.380
No matter what we do in terms
of promotion, we're always

00:19:19.380 --> 00:19:22.460
going to have three unpaired
electrons.

00:19:22.460 --> 00:19:25.700
We can still hybridize all these
orbitals, however, so we

00:19:25.700 --> 00:19:31.290
can still form four hybrid
orbitals, which are again, 2 s

00:19:31.290 --> 00:19:35.060
p 3 hybrid orbitals.

00:19:35.060 --> 00:19:38.150
So if we take a look at nitrogen
here, what you'll

00:19:38.150 --> 00:19:40.400
notice is we have thre available
for bonding, and we

00:19:40.400 --> 00:19:42.890
already have our lone pair
-- one of our orbitals is

00:19:42.890 --> 00:19:45.210
already filled up.

00:19:45.210 --> 00:19:49.010
So we can add three hydrogen
atoms here, and fill in our

00:19:49.010 --> 00:19:50.900
other orbitals right here.

00:19:50.900 --> 00:19:54.230
So if we do this and we form
the molecule ammonia, let's

00:19:54.230 --> 00:19:57.040
switch to a clicker question,
and have you tell me what the

00:19:57.040 --> 00:19:59.510
bond angle is going to
be in ammonia --

00:19:59.510 --> 00:20:02.490
the h n h bond angle.

00:20:02.490 --> 00:20:05.520
Actually, let me draw it on
the board as you look --

00:20:05.520 --> 00:20:08.220
actually, can you put the class
notes on, since you

00:20:08.220 --> 00:20:10.000
don't actually have your
notes to refer to.

00:20:10.000 --> 00:20:11.710
So there's the class
notes there.

00:20:11.710 --> 00:20:17.830
All right, this should be a
pretty quick thing for you to

00:20:17.830 --> 00:20:32.640
figure out, so let's just
take 10 seconds on this.

00:20:32.640 --> 00:20:33.270
OK, great.

00:20:33.270 --> 00:20:36.060
Even thinking quickly, most
of you got it correct.

00:20:36.060 --> 00:20:40.410
So what we see is on ammonia
here, we know that it's less

00:20:40.410 --> 00:20:41.730
than a 109 .

00:20:41.730 --> 00:20:46.400
5, it's actually 107, so
it's less than a 109 .

00:20:46.400 --> 00:20:48.810
5, because of that lone
pair pushing down

00:20:48.810 --> 00:20:50.430
in the bonding electrons.

00:20:50.430 --> 00:20:52.460
And what is the shape,
for one more

00:20:52.460 --> 00:20:59.450
clicker question on ammonia?

00:20:59.450 --> 00:21:14.790
Let's take 10 seconds again,
this should be pretty quick.

00:21:14.790 --> 00:21:15.810
All right, pretty good.

00:21:15.810 --> 00:21:17.090
So, 70% of you.

00:21:17.090 --> 00:21:19.180
We'd like to get
this up higher.

00:21:19.180 --> 00:21:21.740
The shape is actually
trigonal pyramidal.

00:21:21.740 --> 00:21:23.940
And you need to just remember
your shapes.

00:21:23.940 --> 00:21:26.460
If they're not obvious to you
what they're called, you need

00:21:26.460 --> 00:21:28.170
to just study them
and learn them.

00:21:28.170 --> 00:21:31.780
So it's trigonal because we have
these three atoms that

00:21:31.780 --> 00:21:35.330
are bound to the central atom
here, and if you picture it,

00:21:35.330 --> 00:21:37.060
it's actually shaped
like a pyramid.

00:21:37.060 --> 00:21:38.700
So it's trigonal pyramidal.

00:21:38.700 --> 00:21:42.490
That's what we call when we have
three bonding atoms and

00:21:42.490 --> 00:21:46.860
one lone pair.

00:21:46.860 --> 00:21:47.190
All right.

00:21:47.190 --> 00:21:50.630
So we can switch all the way
back to our notes here.

00:21:50.630 --> 00:21:53.200
And the last thing we can think
about is how do we name

00:21:53.200 --> 00:21:56.030
this n h bond, and again,
we just name

00:21:56.030 --> 00:21:57.380
it based on it symmetry.

00:21:57.380 --> 00:22:01.380
It's a sigma bond, and it's
going to be -- no.

00:22:01.380 --> 00:22:05.860
OK, it's going to be nitrogen
2 s p 3, because it's a

00:22:05.860 --> 00:22:09.930
nitrogen atom, and then
hydrogen 1 s.

00:22:09.930 --> 00:22:11.520
So, I don't even have to worry
because you're not writing

00:22:11.520 --> 00:22:14.040
this down, so I can just fix it
when I post the notes and

00:22:14.040 --> 00:22:17.160
no one will ever know, except
that this is not

00:22:17.160 --> 00:22:17.410
OpenCourseWare.

00:22:17.410 --> 00:22:22.500
So let's switch to thinking
about oxygen

00:22:22.500 --> 00:22:23.990
hybridization here.

00:22:23.990 --> 00:22:27.570
So in oxygen we have a similar
situation where, in fact, we

00:22:27.570 --> 00:22:30.050
are not going to promote any
of the electrons because we

00:22:30.050 --> 00:22:33.680
have two lone pair electrons
no matter what we do.

00:22:33.680 --> 00:22:37.460
So when we hybridize our
orbitals, we're going to end

00:22:37.460 --> 00:22:42.840
up with again, four hybrid
orbitals, 4 s p 3 orbitals,

00:22:42.840 --> 00:22:45.890
and what we'll see is that two
of these are already going to

00:22:45.890 --> 00:22:49.590
be filled up with a paired
electrons, so we're only going

00:22:49.590 --> 00:22:51.750
to have 2 orbitals with an
unpaired electron available

00:22:51.750 --> 00:22:53.780
for bonding.

00:22:53.780 --> 00:22:56.750
So let's think about water here
as our simplest example

00:22:56.750 --> 00:22:57.970
with oxygen.

00:22:57.970 --> 00:23:02.260
So we can have our two hydrogen
atoms come in here,

00:23:02.260 --> 00:23:05.260
and what we will find is now
that we have all of our

00:23:05.260 --> 00:23:08.870
orbitals filled up -- so
thinking about what this angle

00:23:08.870 --> 00:23:13.120
is here, would you expect it
to be less than or greater

00:23:13.120 --> 00:23:16.770
than what we saw for
ammonia before?

00:23:16.770 --> 00:23:17.730
STUDENT: Less than.

00:23:17.730 --> 00:23:18.810
PROFESSOR: Good, good, it's
going to be less than, and

00:23:18.810 --> 00:23:20.320
it's going to be less
than because now we

00:23:20.320 --> 00:23:22.470
have two lone pairs.

00:23:22.470 --> 00:23:24.220
So since we have two lone
pairs, we're going to be

00:23:24.220 --> 00:23:27.210
pushing down even further on
the bonding electrons, so

00:23:27.210 --> 00:23:29.900
we're going to smoosh those
bonds even closer together.

00:23:29.900 --> 00:23:31.980
The bond, it turns
out, is 104 .

00:23:31.980 --> 00:23:36.040
5 degrees, that h o h bond.

00:23:36.040 --> 00:23:40.590
So in terms of naming our o h
bond, good, it's right here.

00:23:40.590 --> 00:23:45.610
So it's going to be a sigma
bond, and we have oxygen 2 s p

00:23:45.610 --> 00:23:51.770
3 and hydrogen 1 s.

00:23:51.770 --> 00:23:54.650
And the geometry, which I didn't
ask you, is going to be

00:23:54.650 --> 00:23:56.030
bent for this molecule.

00:23:56.030 --> 00:23:59.300
All right, so that's s p 3
hybridization, but those

00:23:59.300 --> 00:24:02.300
aren't the only type of hybrid
orbitals that we can form.

00:24:02.300 --> 00:24:04.800
Let's take a look at what
happens if instead of

00:24:04.800 --> 00:24:07.940
combining all four orbitals, we
just combine three of those

00:24:07.940 --> 00:24:10.660
orbitals, and what we'll
end up with is s p 2

00:24:10.660 --> 00:24:12.120
hybridization.

00:24:12.120 --> 00:24:16.920
So in s p 2 hybridization,
instead of combining all four,

00:24:16.920 --> 00:24:18.460
we're just combining
two of the p

00:24:18.460 --> 00:24:20.540
orbitals with the s orbital.

00:24:20.540 --> 00:24:22.630
So what we're going to
end up with now is

00:24:22.630 --> 00:24:24.480
three hybrid orbitals.

00:24:24.480 --> 00:24:28.240
And what happens to this last
p orbital is nothing at all,

00:24:28.240 --> 00:24:29.540
we just get it back.

00:24:29.540 --> 00:24:32.990
So we end up with 1 p orbital
completely untouched, and

00:24:32.990 --> 00:24:36.960
three hybrid s p 2 orbitals.

00:24:36.960 --> 00:24:39.550
So again, we can think
of an example here.

00:24:39.550 --> 00:24:44.170
So let's take boron, for
example, and this has -- it

00:24:44.170 --> 00:24:46.690
starts off with three
valence electrons.

00:24:46.690 --> 00:24:49.350
Would you expect to see electron
promotion for boron?

00:24:49.350 --> 00:24:50.790
STUDENT: Yes.

00:24:50.790 --> 00:24:53.890
PROFESSOR: Yeah, absolutely.
if we move up one of our

00:24:53.890 --> 00:24:56.150
electrons into an empty p
orbital, what were going to

00:24:56.150 --> 00:24:56.440
see is now we have three
unpaired electrons that are

00:24:56.440 --> 00:24:57.910
ready for bonding.

00:24:57.910 --> 00:25:05.880
So, if we hybridize just these
three orbitals, what we're

00:25:05.880 --> 00:25:10.240
going to end up with is our
s p 2 hybrid orbitals.

00:25:10.240 --> 00:25:12.860
Again, the name is very
straightforward, it comes from

00:25:12.860 --> 00:25:17.130
1 s and 2 p orbital, so
it will be s p 2.

00:25:17.130 --> 00:25:20.250
And again, you might be thinking
well, why didn't we

00:25:20.250 --> 00:25:23.010
actually hybridize this
2 p y orbital.

00:25:23.010 --> 00:25:26.180
It doesn't actually have an
electron in it, so we don't

00:25:26.180 --> 00:25:28.720
have to worry about whether it's
very high in energy or

00:25:28.720 --> 00:25:30.720
not, we don't care that
it's high in energy.

00:25:30.720 --> 00:25:33.930
What we do care about is the
energy of our orbitals that

00:25:33.930 --> 00:25:37.680
have electrons in them, and if
we combined all four of the

00:25:37.680 --> 00:25:40.480
orbitals, then our hybrid
orbitals would have more p

00:25:40.480 --> 00:25:43.930
character to them, so they'd
actually be higher in energy.

00:25:43.930 --> 00:25:46.240
So if we don't have to hybridize
one of the p

00:25:46.240 --> 00:25:49.150
orbitals, we can actually end
up with a lower energy

00:25:49.150 --> 00:25:53.320
situation, because now these
s p 2 orbitals are 1/3 s

00:25:53.320 --> 00:25:59.660
character, and only 2/3 p
character, instead of 3/4.

00:25:59.660 --> 00:26:04.690
So we end up with 3 s p 2 hybrid
orbitals, so we can

00:26:04.690 --> 00:26:09.420
think about what would happen
here in terms of bonding, and

00:26:09.420 --> 00:26:14.880
if we think about how to get
our bonds as far away as

00:26:14.880 --> 00:26:16.860
possible from each other, what
we're going to have is the

00:26:16.860 --> 00:26:18.600
trigonal planer situation.

00:26:18.600 --> 00:26:21.950
So if you picture, for example,
b h 3, it's going to

00:26:21.950 --> 00:26:23.750
look like this.

00:26:23.750 --> 00:26:26.610
All of our electrons are in our
bonds, we want to got them

00:26:26.610 --> 00:26:29.960
a 120 degrees away from each
other, that's as far away as

00:26:29.960 --> 00:26:31.220
we can get them.

00:26:31.220 --> 00:26:34.310
Keep in mind we do have this p
orbital here and it's coming

00:26:34.310 --> 00:26:35.620
right out at us.

00:26:35.620 --> 00:26:38.350
And this p orbital is here,
but it's empty, it doesn't

00:26:38.350 --> 00:26:41.220
have any electrons in it, that's
why we don't have to

00:26:41.220 --> 00:26:43.720
worry about it in terms of
getting our electrons as far

00:26:43.720 --> 00:26:45.810
away from each other
as possible.

00:26:45.810 --> 00:26:49.060
So what we'll have here is a
trigonal planar case, and you

00:26:49.060 --> 00:26:52.330
can see that we only have three
electrons that are set

00:26:52.330 --> 00:26:55.950
for bonding, so we'll add three
hydrogens, and for b h

00:26:55.950 --> 00:26:58.650
3, we'll get a stable
structure here.

00:26:58.650 --> 00:27:02.070
So, remember, boron was one of
those exceptions to our Lewis

00:27:02.070 --> 00:27:04.780
structure rules where it was
perfectly happy not having a

00:27:04.780 --> 00:27:05.760
full octet.

00:27:05.760 --> 00:27:09.660
So this can tell you why it's so
happy with only having six

00:27:09.660 --> 00:27:10.830
electrons around it.

00:27:10.830 --> 00:27:16.830
All right, so if we think about
b h bond here, again,

00:27:16.830 --> 00:27:20.000
it's the sigma bond, and we're
going to say it's a boron 2 s

00:27:20.000 --> 00:27:26.470
p 2 hybrid orbital interacting
with a hydrogen 1 s orbital.

00:27:26.470 --> 00:27:29.400
So let's take a look at another
case where we have s p

00:27:29.400 --> 00:27:31.510
2 hybridization, we can
actually also have

00:27:31.510 --> 00:27:33.190
it happen in carbon.

00:27:33.190 --> 00:27:35.970
So if we think about having
it happen in carbon, we're

00:27:35.970 --> 00:27:38.630
starting with the situation
where we've already promoted

00:27:38.630 --> 00:27:42.500
our electron into a 2 p orbital
here, and what we're

00:27:42.500 --> 00:27:46.340
going to do is just combine the
s and two of the p's, so

00:27:46.340 --> 00:27:50.470
we'll end up with electrons
in one of each three

00:27:50.470 --> 00:27:52.090
s p 2 hybrid orbitals.

00:27:52.090 --> 00:27:55.890
But unlike the case with boron
where we had an empty p

00:27:55.890 --> 00:27:59.520
orbital, we're actually going
to have an electron in the p

00:27:59.520 --> 00:28:02.920
orbital of carbon as well.

00:28:02.920 --> 00:28:05.790
So again, if we think about
that shape of that carbon

00:28:05.790 --> 00:28:08.110
atom, it's going to be trigonal
planar, it's going to

00:28:08.110 --> 00:28:12.500
have bond angles of 120 degrees,
because we have this

00:28:12.500 --> 00:28:16.350
set up of having three
hybrid orbitals.

00:28:16.350 --> 00:28:18.790
So let's take a look at what
actually happens if we're

00:28:18.790 --> 00:28:22.990
talking about a carbon-carbon
double bond, such as in

00:28:22.990 --> 00:28:27.060
ethene, c 2 h 4, we're going
to have a double bond.

00:28:27.060 --> 00:28:30.310
If we have a double bond, we
know we need to have only one

00:28:30.310 --> 00:28:33.180
sigma bond, and we're also going
to have one pi bond.

00:28:33.180 --> 00:28:35.080
So it already should make
sense why we have that p

00:28:35.080 --> 00:28:37.350
orbital there, in order to form
a pi bond, we're going to

00:28:37.350 --> 00:28:38.770
need a p orbital.

00:28:38.770 --> 00:28:42.740
So if you picture this as our
s p 2 carbon atom where we

00:28:42.740 --> 00:28:47.510
have three hybrid orbitals,
and then one p y orbital

00:28:47.510 --> 00:28:49.090
coming right out at us.

00:28:49.090 --> 00:28:51.840
So again, we picture the same
thing as we pictured with the

00:28:51.840 --> 00:28:53.770
boron there.

00:28:53.770 --> 00:28:57.600
If we have, coming along this
z axis, another carbon atom,

00:28:57.600 --> 00:29:00.060
we can actually form one
bond between the two

00:29:00.060 --> 00:29:01.670
carbon atoms there.

00:29:01.670 --> 00:29:07.850
So if we picture how this
happens, what we have here if

00:29:07.850 --> 00:29:19.680
these are our 2 s p 2 carbon
atoms -- so here we have s p 2

00:29:19.680 --> 00:29:25.410
hybrid carbon, and here we have
s p 2 hybrid carbon atom.

00:29:25.410 --> 00:29:29.180
These 2 are going to come
together like this, and the

00:29:29.180 --> 00:29:31.450
first bond that we're going to
form is going to be a sigma

00:29:31.450 --> 00:29:32.950
bond, right, so we
see that here.

00:29:32.950 --> 00:29:36.020
If we're looking head on, we
see they form a sigma bond.

00:29:36.020 --> 00:29:38.440
We can also look at them coming
in from the side, and

00:29:38.440 --> 00:29:40.770
that's what I tried to depict
here where you can actually

00:29:40.770 --> 00:29:43.250
see in pink is the p orbital.

00:29:43.250 --> 00:29:45.850
So we can also show them coming
together this way, so

00:29:45.850 --> 00:29:48.460
now you're looking at it where
you can see the p orbital, and

00:29:48.460 --> 00:29:52.430
maybe just see well one
of the hydrogen atoms.

00:29:52.430 --> 00:29:57.630
So we can have four total
hydrogens bonding here, and we

00:29:57.630 --> 00:29:59.340
can think about how
to describe these

00:29:59.340 --> 00:30:01.000
carbon-carbon bonds.

00:30:01.000 --> 00:30:05.050
So in the first case of this
first bond here that I've put

00:30:05.050 --> 00:30:07.460
in a square, what type
of a bond is this, is

00:30:07.460 --> 00:30:08.650
the sigma or pi?

00:30:08.650 --> 00:30:10.210
STUDENT: Sigma.

00:30:10.210 --> 00:30:11.210
PROFESSOR: Yup, it's
a sigma bond.

00:30:11.210 --> 00:30:12.870
We're having two
orbitals coming

00:30:12.870 --> 00:30:15.530
together on the bond axis.

00:30:15.530 --> 00:30:20.210
So we'll call this sigma, and
it's between two s p 2 hybrid

00:30:20.210 --> 00:30:26.560
carbon atoms. So it's stigma
carbon s p 2, carbon s p 2.

00:30:26.560 --> 00:30:29.750
What about this second bond here
where we're going to have

00:30:29.750 --> 00:30:32.470
interaction of 2 p orbitals,
is that sigma or pi?

00:30:32.470 --> 00:30:34.140
STUDENT: Pi.

00:30:34.140 --> 00:30:34.820
PROFESSOR: Pi, great.

00:30:34.820 --> 00:30:38.040
So our second bond is going
to be a pi bond.

00:30:38.040 --> 00:30:40.990
And again, this is between the
p orbitals, these are not

00:30:40.990 --> 00:30:43.940
hybrid orbitals, so when we name
this bond we're going to

00:30:43.940 --> 00:30:47.770
name it as a pi bond here,
because it's between two p

00:30:47.770 --> 00:30:51.150
orbitals, and it's going to be
between the carbon 2 p y

00:30:51.150 --> 00:30:54.280
orbital, and the other
carbon 2 p y orbital.

00:30:54.280 --> 00:30:57.740
Remember, we didn't hybridize
the 2 p y orbital, so that's

00:30:57.740 --> 00:31:00.490
what we have left over to
form these pi bonds.

00:31:00.490 --> 00:31:03.430
All right.

00:31:03.430 --> 00:31:07.160
So in addition to having these
two carbon bonds, we actually

00:31:07.160 --> 00:31:11.890
also have four carbon hydrogen
bonds in addition to our

00:31:11.890 --> 00:31:13.370
carbon-carbon bonds.

00:31:13.370 --> 00:31:17.280
So why don't you tell me what
the valence bond description

00:31:17.280 --> 00:31:19.520
would be of these carbon
hydrogen bonds?

00:31:19.520 --> 00:31:45.280
So let's take 10 seconds
on that.

00:31:45.280 --> 00:31:45.880
OK, great.

00:31:45.880 --> 00:31:48.660
So most and you got it, so we
can switch to the notes and

00:31:48.660 --> 00:31:50.860
let's talk about this here.

00:31:50.860 --> 00:31:55.230
So in terms of the carbon
hydrogen bond, it's a sigma

00:31:55.230 --> 00:31:59.520
bond, because we define it --
any time we are bonding to an

00:31:59.520 --> 00:32:01.940
atom, we have to keep redefining
our bond axis to

00:32:01.940 --> 00:32:04.040
whatever two atoms we're
talking about.

00:32:04.040 --> 00:32:07.540
So it's along the bond axis and
it's between a carbon s p

00:32:07.540 --> 00:32:10.950
2 hybrid, and then the hydrogen
is just a 1 s orbital

00:32:10.950 --> 00:32:12.680
that we're combining here.

00:32:12.680 --> 00:32:17.290
So those are our three types
of bonds in ethene.

00:32:17.290 --> 00:32:19.340
One thing that I want to
mention that is really

00:32:19.340 --> 00:32:22.690
important is once you have
double bonds, what happens

00:32:22.690 --> 00:32:25.900
between those two atoms in the
molecule is they can no longer

00:32:25.900 --> 00:32:28.380
rotate in relation
to each other.

00:32:28.380 --> 00:32:29.950
So you can think about
why that is.

00:32:29.950 --> 00:32:33.170
When we have just a single bond
in them molecule, you

00:32:33.170 --> 00:32:35.780
have all the free rotation you
want, you can just spin it

00:32:35.780 --> 00:32:37.930
around, there's nothing
keeping it in place.

00:32:37.930 --> 00:32:41.010
But once you have a double
bond here, we have our pi

00:32:41.010 --> 00:32:43.050
bond, as well as
our sigma bond.

00:32:43.050 --> 00:32:46.710
So there's electron density
above the bond

00:32:46.710 --> 00:32:47.940
and below the bond.

00:32:47.940 --> 00:32:51.310
So if I try to rotate my 2
atoms, you see that I have to

00:32:51.310 --> 00:32:54.470
break that pi bond, because they
need to be lined up so

00:32:54.470 --> 00:32:56.680
that the electron density
can overlap.

00:32:56.680 --> 00:33:00.550
So in order to rotate a double
bond, you have to actually

00:33:00.550 --> 00:33:02.980
break the pi bond, so
essentially what you're doing

00:33:02.980 --> 00:33:04.420
is breaking the double bond.

00:33:04.420 --> 00:33:07.880
So really, you can not ever
rotate a double bond, it makes

00:33:07.880 --> 00:33:09.820
your molecule very rigid.

00:33:09.820 --> 00:33:13.470
This is incredibly important
because if you picture having

00:33:13.470 --> 00:33:16.780
a double bond in a very large
molecule, you could have all

00:33:16.780 --> 00:33:19.920
sorts of other atoms off this
way and all sorts of other

00:33:19.920 --> 00:33:22.710
atoms off this way, and you can
picture the shape would be

00:33:22.710 --> 00:33:26.300
very different if you have one
confirmation versus another

00:33:26.300 --> 00:33:27.600
confirmation.

00:33:27.600 --> 00:33:31.280
So it's very important that the
double bond locks it in a

00:33:31.280 --> 00:33:32.610
particular conformation.

00:33:32.610 --> 00:33:35.980
This completely could change if
you were to flip from one

00:33:35.980 --> 00:33:37.350
to the other conformation
which can

00:33:37.350 --> 00:33:39.240
happen in chemical reactions.

00:33:39.240 --> 00:33:41.550
If you were to make that change
you would find that the

00:33:41.550 --> 00:33:44.460
molecule now has completely
different biological and

00:33:44.460 --> 00:33:46.390
chemical properties.

00:33:46.390 --> 00:33:48.880
So it's very important to be
keeping in mind that any time

00:33:48.880 --> 00:33:51.650
you see a double bond, you
have a pi bond there, so

00:33:51.650 --> 00:33:56.160
you're not going to see any
rotation around the bond axis.

00:33:56.160 --> 00:33:59.620
All right, so let's think of a
more complicated example of

00:33:59.620 --> 00:34:01.590
having a double bond, and
maybe a more interesting

00:34:01.590 --> 00:34:03.960
example, and this is talking
about benzene.

00:34:03.960 --> 00:34:06.380
I think most and you have talked
a little bit about

00:34:06.380 --> 00:34:09.550
benzene over this past
week in recitation.

00:34:09.550 --> 00:34:13.520
Benzene is a ring that's made up
of six carbon atoms and six

00:34:13.520 --> 00:34:16.760
hydrogen atoms. So let's picture
what this looks like

00:34:16.760 --> 00:34:18.660
here, and we'll start
with four and we'll

00:34:18.660 --> 00:34:19.430
add in our last two.

00:34:19.430 --> 00:34:23.480
So essentially, we have two
ethene or ethylene molecules

00:34:23.480 --> 00:34:28.690
here to start with where these
blue are our 2 s p 2 hybrid

00:34:28.690 --> 00:34:32.000
orbitals, so you can see that
for each carbon atom, one is

00:34:32.000 --> 00:34:35.150
already used up binding to
another carbon atom.

00:34:35.150 --> 00:34:39.160
If we think about bringing in
those last two carbons, what

00:34:39.160 --> 00:34:43.220
you can see is that for every
carbon, two of its hybrid

00:34:43.220 --> 00:34:48.500
orbitals are being used to
bond to other carbons.

00:34:48.500 --> 00:34:50.750
So that leaves each carbon
with only one

00:34:50.750 --> 00:34:53.370
hybrid orbital left.

00:34:53.370 --> 00:34:56.320
And if we think about the six
hydrogens, now each of those

00:34:56.320 --> 00:34:59.380
are going to bind by combining
one of the carbon hybrid

00:34:59.380 --> 00:35:03.160
orbitals to a 1 s orbital
of hydrogen.

00:35:03.160 --> 00:35:07.400
So, if we think about what bonds
are in this molecule, we

00:35:07.400 --> 00:35:11.960
actually have six of these
sigma carbon s p 2,

00:35:11.960 --> 00:35:14.160
carbon s p 2 bonds.

00:35:14.160 --> 00:35:18.660
We also have carbon s p
2 hydrogen 1 s bonds.

00:35:18.660 --> 00:35:21.370
How many of those do we have?

00:35:21.370 --> 00:35:23.980
Yup, we also have six of these,
because we have six

00:35:23.980 --> 00:35:25.770
carbon hydrogen bonds.

00:35:25.770 --> 00:35:28.900
So that's two of our types of
bonds in benzene, and we have

00:35:28.900 --> 00:35:31.610
one type left, and that's
going to actually be the

00:35:31.610 --> 00:35:35.570
double bond or the pi bond that
forms between some of

00:35:35.570 --> 00:35:37.140
these p orbitals.

00:35:37.140 --> 00:35:41.400
So we can have one bond here
between this carbon's p

00:35:41.400 --> 00:35:43.410
orbital and this carbon's
p orbital.

00:35:43.410 --> 00:35:46.180
So let's have a clicker question
here on how many

00:35:46.180 --> 00:35:50.980
total pi bonds do you expect
to see in benzene?

00:35:50.980 --> 00:35:56.950
Oh good, so it's left up -- the
notes are left up on this

00:35:56.950 --> 00:35:57.690
screen right now.

00:35:57.690 --> 00:36:16.980
All right, so let's take
10 seconds on that.

00:36:16.980 --> 00:36:17.530
All right, great.

00:36:17.530 --> 00:36:20.920
So, most of you saw that what
we would expect to see is a

00:36:20.920 --> 00:36:22.540
three bond, some of
you thought six.

00:36:22.540 --> 00:36:25.010
So let's take a look at
why three is correct.

00:36:25.010 --> 00:36:29.305
So, what we end up having
is three of these pi --

00:36:29.305 --> 00:36:32.930
2 p y 2 p y bonds, we
can have one between

00:36:32.930 --> 00:36:34.130
these two carbons here.

00:36:34.130 --> 00:36:36.260
Can we have one between
these two carbons here

00:36:36.260 --> 00:36:37.310
if we have one here?

00:36:37.310 --> 00:36:38.280
STUDENT: No.

00:36:38.280 --> 00:36:38.670
PROFESSOR: No, we can't.

00:36:38.670 --> 00:36:42.230
We're already using it up in
this pi bond here, so that

00:36:42.230 --> 00:36:45.130
means we're limited to only
two other spots on the

00:36:45.130 --> 00:36:47.250
molecule, so we have three.

00:36:47.250 --> 00:36:49.810
But, of course, what you saw in
recitation, and hopefully,

00:36:49.810 --> 00:36:53.240
what you can now think very
quickly by looking at this, is

00:36:53.240 --> 00:36:56.720
that this is not the only
configuration of pi bonds that

00:36:56.720 --> 00:36:58.670
we could have in benzene.

00:36:58.670 --> 00:37:00.770
There's absolutely no reason
I couldn't have switched it

00:37:00.770 --> 00:37:04.710
around and said that instead the
pi orbitals form between

00:37:04.710 --> 00:37:08.120
these atoms instead of those
first atoms I showed.

00:37:08.120 --> 00:37:11.390
So, let's look at this in a
more simple structure here

00:37:11.390 --> 00:37:15.110
where we have the two possible
forms of benzene, and the

00:37:15.110 --> 00:37:17.250
reality is is that it's
going to be some

00:37:17.250 --> 00:37:18.410
combination of the two.

00:37:18.410 --> 00:37:21.830
This is resonance, this is a
case of a resonance structure.

00:37:21.830 --> 00:37:25.260
So what we see is that those six
pi electrons are actually

00:37:25.260 --> 00:37:29.620
going to be de-localized around
all six of those atoms.

00:37:29.620 --> 00:37:33.330
So if you think about any one of
these carbon-carbon bonds,

00:37:33.330 --> 00:37:36.000
what type of a bond would
you expect that to be?

00:37:36.000 --> 00:37:38.460
What would the bond order
be for this bond?

00:37:38.460 --> 00:37:40.360
STUDENT: [INAUDIBLE]

00:37:40.360 --> 00:37:41.320
PROFESSOR: Yup, it's going
to be a 1 and 1/2 bond.

00:37:41.320 --> 00:37:45.510
It's a 1 and 1/2 because it's
halfway between a double bond

00:37:45.510 --> 00:37:46.590
and a single bond.

00:37:46.590 --> 00:37:49.080
So, of course, this is resonance
so we can go ahead

00:37:49.080 --> 00:37:51.980
and put our resonance notation
in there to indicate that

00:37:51.980 --> 00:37:53.680
benzene is a resonance
structure.

00:37:53.680 --> 00:37:55.420
All right.

00:37:55.420 --> 00:37:58.530
So let's quickly talk about our
last type of hybridization

00:37:58.530 --> 00:38:00.710
that we're going to discuss
today, which is s p

00:38:00.710 --> 00:38:01.160
hybridization.

00:38:01.160 --> 00:38:06.640
So s p hybridization comes now
from when we're combining an s

00:38:06.640 --> 00:38:08.180
orbital now with only
one p orbital.

00:38:08.180 --> 00:38:11.700
So let's take a look at
this with carbon.

00:38:11.700 --> 00:38:15.450
And if we hybridize these
orbitals in carbon, what we

00:38:15.450 --> 00:38:19.060
end up with is having two hybrid
orbitals, and then

00:38:19.060 --> 00:38:21.750
we're going to be left with two
of our p orbitals that are

00:38:21.750 --> 00:38:25.770
each going to have an electron
associated in them.

00:38:25.770 --> 00:38:28.350
So again, looking at the
shapes, now we're just

00:38:28.350 --> 00:38:32.720
combining two, we've got these
two equal hybrid orbitals plus

00:38:32.720 --> 00:38:34.540
these 2 p orbitals here.

00:38:34.540 --> 00:38:38.830
So let's take the case of
acetylene where we have two

00:38:38.830 --> 00:38:41.430
carbon atoms that are going to
be triple bonded to each

00:38:41.430 --> 00:38:43.420
other, each are bonded
to a carbon

00:38:43.420 --> 00:38:45.290
and then to one hydrogen.

00:38:45.290 --> 00:38:47.660
So this is a little bit trickier
to look at and see

00:38:47.660 --> 00:38:50.290
what it means, but essentially
we have two hybrid orbitals,

00:38:50.290 --> 00:38:53.870
which are shown in blue here,
and then we have one p orbital

00:38:53.870 --> 00:38:56.590
that's left alone that's going
up and down on the page.

00:38:56.590 --> 00:38:58.820
And then that second p orbital's
actually coming

00:38:58.820 --> 00:39:01.650
right out at you, it's coming
out of the screen at you.

00:39:01.650 --> 00:39:05.070
So, if we think about this z
bonding axis between the two

00:39:05.070 --> 00:39:09.170
carbon atoms, we can picture
overlap of those s p hybrid

00:39:09.170 --> 00:39:13.400
orbitals, and then we can also
picture bonding to hydrogen.

00:39:13.400 --> 00:39:19.380
So, in a settling, what is
the bond angle here?

00:39:19.380 --> 00:39:21.700
This is the easiest question
all day, what is the bond

00:39:21.700 --> 00:39:24.760
angle between all of these?

00:39:24.760 --> 00:39:26.130
Great, so it's 180 degrees.

00:39:26.130 --> 00:39:30.800
So, if we think about the bonds
that are forming -- oh I

00:39:30.800 --> 00:39:33.870
see our TAs are here, so you
can start handing them out,

00:39:33.870 --> 00:39:37.530
because we have two minutes
left to go.

00:39:37.530 --> 00:39:44.530
So, as they're very quietly
handing out your class notes,

00:39:44.530 --> 00:39:47.670
let's think about what this bond
is here, this boxed bond,

00:39:47.670 --> 00:39:50.380
is it a pi bond or
a sigma bond?

00:39:50.380 --> 00:39:51.860
It's going to be a sigma bond.

00:39:51.860 --> 00:39:56.120
So, we have sigma 2
s p, carbon 2 s p.

00:39:56.120 --> 00:39:59.070
So they're two s p
bonds combining.

00:39:59.070 --> 00:40:01.740
Now let's think about this first
pi bond, which will be

00:40:01.740 --> 00:40:04.500
above and below the
bonding axis.

00:40:04.500 --> 00:40:07.330
Is this pi or sigma?

00:40:07.330 --> 00:40:08.540
This is pi.

00:40:08.540 --> 00:40:13.080
So we're talking about pi carbon
2 p x, because it's the

00:40:13.080 --> 00:40:17.720
x axes combining to
carbon 2 p x.

00:40:17.720 --> 00:40:22.830
And the last bond that we have
here is a carbon-carbon bond,

00:40:22.830 --> 00:40:25.530
and this is our last p orbitals

00:40:25.530 --> 00:40:26.470
that are coming together.

00:40:26.470 --> 00:40:29.200
These are the ones that are
coming right out at you, so

00:40:29.200 --> 00:40:32.470
this is going to be on
a second pi orbital.

00:40:32.470 --> 00:40:36.580
So this will be pi carbon
2 p y, carbon 2 p y.

00:40:36.580 --> 00:40:38.880
All right.

00:40:38.880 --> 00:40:42.000
So, we'll stop here today.

00:40:42.000 --> 00:40:44.520
Just stay in your seats for
another 30 seconds as they're

00:40:44.520 --> 00:40:46.040
handing out your notes.

00:40:46.040 --> 00:40:48.830
I want to mention that you're
going to get problem-set five

00:40:48.830 --> 00:40:52.060
is posted today, and I'll
write which ones you can

00:40:52.060 --> 00:40:55.430
already do so far, because you
don't have class on Monday.

00:40:55.430 --> 00:40:58.760
But remember that you do have
recitation on Tuesday, so that

00:40:58.760 --> 00:41:02.660
could be very helpful with the
problem-set, so be sure to go

00:41:02.660 --> 00:41:06.090
to recitation on Tuesday, and
have a great long weekend.