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PROFESSOR: OK, let's just
take 10 more seconds on

00:00:48.000 --> 00:01:02.000
the clicker question.

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OK, 76, I think that says,
%, which is not bad, but

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we should be at 100%.

00:01:12.000 --> 00:01:17.000
So, when you're past the
equivalence point, so you've

00:01:17.000 --> 00:01:20.000
converted all of your weak, in
this case, acid to its

00:01:20.000 --> 00:01:25.000
conjugate base, and because it
was a weak acid, the conjugate

00:01:25.000 --> 00:01:28.000
base is going to be a weak
based and so it's not

00:01:28.000 --> 00:01:31.000
contributing a whole lot it'll
make the solution basic, but

00:01:31.000 --> 00:01:35.000
it's nothing compared to adding
strong base in there.

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So even though you have
the weak base around, at

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this point it's really
a strong base problem.

00:01:41.000 --> 00:01:45.000
So you would calculate this by
looking at how many mils of the

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strong base you've added past,
and figure out the number of

00:01:50.000 --> 00:01:54.000
moles that there are, and
divide by the total volume.

00:01:54.000 --> 00:01:57.000
So this was like one of the
problems on the exam, and one

00:01:57.000 --> 00:02:00.000
thing that I thought was
interesting on the exam is that

00:02:00.000 --> 00:02:03.000
more people seemed to get the
hard problem right than this,

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which was the easy problem.

00:02:05.000 --> 00:02:10.000
So we'll see on the final,
there will be an acid based

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titration problem on the
final, at least one.

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So let's see if we can
get, then, the easy and

00:02:18.000 --> 00:02:20.000
the hard ones right.

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So you've mastered the hard
ones and let's see if you can

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learn how to do the easy ones
as well for the final exam.

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OK, so we're going to continue
with transition metals.

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We were talking about crystal
field theory and magnetism, and

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you should have a handout for
today, and you should also have

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some equipment to make models
of orbitals and coordination

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complexes -- these
are not snacks.

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They can be snacks later, right
now they're a model kit.

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All right, so I'm going to
introduce you to some terms

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that we're going to come back
you at the end of today's

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lecture, and then we're going
to talk about the shapes of

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coordination complexes.

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So, magnetism.

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So we talked last time, before
the exam, if you remember,

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about high spin and low spin,
unpaired electrons and

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paired electrons.

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Well, compounds that have
unpaired electrons are

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paramagnetic, they're attracted
by a magnetic field, and those

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where the electrons are paired
are diamagnetic are repelled

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by a magnetic field.

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So you can tell whether a
coordination complex is

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paramagnetic or diamagnetic,
you can test the magnetism,

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and that'll give you some
information about the electron

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configuration of the d orbitals
in that coordination complex.

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And that can tell you
about the geometry.

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And so you'll see that by the
end we're going to talk about

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different types of energy
orbitals when you have

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different geometries.

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So why might you care about the
geometry of a metal center.

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Well, people who study proteins
that have metal centers care a

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lot about the geometry of them.

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So let me just give
you one example.

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We talked a lot about energy in
the course this semester, so we

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need catalysts for removing
carbon monoxide and carbon

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dioxide from the environment.

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And nature has some of these --
they have metal cofactors and

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proteins that can do this, and
people have been interested in

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mimicking that chemistry
to remove these gases

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from the environment.

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So let me tell you these
enzymes are organisms.

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And this is pretty amazing,
some of these microorganisms.

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So, over here there's one
-- it basically lives

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on carbon monoxide.

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I mean that's -- you know
alternative sources of energy

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are one thing, but that's
really quite a crazy thing

00:05:02.000 --> 00:05:03.000
that this guy does.

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So, you can grow it up in these
big vats and pump in carbon

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monoxide and it's like oh,
food, and they grow and

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multiply, and they're very,
very happy in this carbon

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monoxide environment.

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There are also microorganisms
that live on carbon dioxide as

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their energy and
a carbon source.

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And so these organisms have
enzymes in them that have metal

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centers, and those metal
centers are responsible for the

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ability of these organisms to
live on these kind of bizarre

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greenhouse gases
and pollutants.

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So people would like to
understand how this works.

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So microbes have been estimated
to remove hundred, a million

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tons of carbon monoxide from
the environment every year,

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producing about one trillion
kilograms of acetate from

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these greenhouse gases.

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And so, what do these catalysts
look like and these enzymes,

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what do these metal clusters
look like that do

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this chemistry.

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And this was sort of a rough
model of what they look like,

00:06:03.000 --> 00:06:07.000
and they thought it had iron
and sulfur and then a nickel in

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some geometry, but they had no
idea sort of where the nickel

00:06:10.000 --> 00:06:12.000
was and how it was coordinated.

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And so before there was any
kind of three dimensional

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information, they used
spectroscopy, and they

00:06:18.000 --> 00:06:21.000
considered whether it was
paramagnetic or diamagnetic to

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get a sense of what the
geometry around the metal was.

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So we're going to talk about
different coordination

00:06:26.000 --> 00:06:30.000
geometries and how many
unpaired or paired electrons

00:06:30.000 --> 00:06:33.000
you would expect, depending
on those geometries today.

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And so, crystal field theory,
again, can help you help

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explain/rationalize the
properties of these transition

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metal complexes or
coordination complexes.

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So, to help us think about
geometry, I always find

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for myself that it's
helpful to have models.

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So not everyone can have such
large models as these, but you

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can all have your own little
models of these geometries.

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So, what we have available to
you are some mini marshmallows,

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which, of course, as we all
know, are representative of d

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orbitals, and jelly beans,
which we all know are useful

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for making coordination
complexes.

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So, what you can do with your
mini marshmallows is you can

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put together to make
your different sets.

00:07:30.000 --> 00:07:37.000
And so, over here we have --
oh, actually it says gum drops

00:07:37.000 --> 00:07:39.000
-- you don't have gum drops
this year, I changed up here, I

00:07:39.000 --> 00:07:41.000
forgot to change it down here.

00:07:41.000 --> 00:07:42.000
We have mini marshmallows.

00:07:42.000 --> 00:07:47.000
Dr. Taylor went out and tried
to purchase enough gum drops to

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do this experiment, and
discovered that Cambridge only

00:07:50.000 --> 00:07:55.000
had 300 gum drops, so we have
mini marshmallows

00:07:55.000 --> 00:07:56.000
instead today.

00:07:56.000 --> 00:07:57.000
But this gives you the idea.

00:07:57.000 --> 00:08:02.000
You can take one toothpick and
you can make d z squared,

00:08:02.000 --> 00:08:06.000
putting on your orbitals, you
have your donut in the middle,

00:08:06.000 --> 00:08:09.000
and then your two lobes,
which run along the z-axis.

00:08:09.000 --> 00:08:16.000
And then for your other sets of
orbitals, you can take these

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two toothpicks and put on these
sets of mini marshmallows, and

00:08:23.000 --> 00:08:27.000
handily, you can just have one
for all of the other d

00:08:27.000 --> 00:08:30.000
orbitals, because depending on
how you hold it, it can

00:08:30.000 --> 00:08:35.000
represent all of the other d
orbitals just very well.

00:08:35.000 --> 00:08:37.000
So, you can just have one of
these for all the others

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and then your d z squared.

00:08:40.000 --> 00:08:44.000
So what we're going to do when
we have our orbitals set up,

00:08:44.000 --> 00:08:49.000
then we can think about how
ligands in particular

00:08:49.000 --> 00:08:53.000
positions, in particular
geometries would clash with our

00:08:53.000 --> 00:08:55.000
orbitals -- where there'd be
big repulsions or

00:08:55.000 --> 00:08:59.000
small repulsions.

00:08:59.000 --> 00:09:03.000
So, any other people missing
their jelly beans or

00:09:03.000 --> 00:09:05.000
their marshmallows?

00:09:05.000 --> 00:09:34.000
Please, raise your
hand, we have extras.

00:09:34.000 --> 00:09:36.000
So, those of you who have
them, go ahead and start

00:09:36.000 --> 00:10:08.000
making your d orbitals.

00:10:08.000 --> 00:10:54.000
All right, so if you're
finished with your two d

00:10:54.000 --> 00:11:01.000
orbitals, you can start making
an octahedral complex.

00:11:01.000 --> 00:11:05.000
So in your geometries set,
you'll have a big gum which can

00:11:05.000 --> 00:11:11.000
be your center metal -- you'll
have a big jelly bean -- sorry,

00:11:11.000 --> 00:11:14.000
big jelly beans and small jelly
beans are our ligands, or our

00:11:14.000 --> 00:11:18.000
negative point charges, and
you can set up and make an

00:11:18.000 --> 00:13:05.000
octahedral geometry here.

00:13:05.000 --> 00:13:10.000
OK, so as you're finishing this
up, I'm going to review what we

00:13:10.000 --> 00:13:13.000
talked about before the exam --
so this isn't in today's

00:13:13.000 --> 00:13:15.000
lecture handouts, it was in
last time, which we

00:13:15.000 --> 00:13:17.000
already went over.

00:13:17.000 --> 00:13:20.000
But sometimes I've discovered
that when there's an exam in

00:13:20.000 --> 00:13:23.000
the middle, there needs to be a
bit of a refresher, it's hard

00:13:23.000 --> 00:13:28.000
to remember what happened
before the exam, and you

00:13:28.000 --> 00:13:31.000
have your models to
think about this.

00:13:31.000 --> 00:13:34.000
So, before the exam, we had
talked about the octahedral

00:13:34.000 --> 00:13:38.000
case, and how compared to a
spherical situation where the

00:13:38.000 --> 00:13:41.000
ligands are everywhere
distributed around the metals

00:13:41.000 --> 00:13:45.000
where all d orbitals would be
affected/repulsed by the

00:13:45.000 --> 00:13:50.000
ligands in a symmetric fashion
equally, when you have them put

00:13:50.000 --> 00:13:54.000
as particular positions in
geometry, then they're going to

00:13:54.000 --> 00:13:57.000
affect the different d
orbitals differently.

00:13:57.000 --> 00:14:00.000
And so, if you have your d z
squared made, and you have your

00:14:00.000 --> 00:14:04.000
octahedral made, you can sort
of hold these up and realize

00:14:04.000 --> 00:14:09.000
that you would have repulsion
from your ligands along the

00:14:09.000 --> 00:14:14.000
z-axis directly toward your
orbitals from d z squared.

00:14:14.000 --> 00:14:16.000
So that would be
highly repulsive.

00:14:16.000 --> 00:14:20.000
The ligands are along the
z-axis, the d orbitals are

00:14:20.000 --> 00:14:23.000
along the z-axis, so the
ligands, the negative point

00:14:23.000 --> 00:14:25.000
charge ligands are going
to be pointing right

00:14:25.000 --> 00:14:27.000
toward your orbitals.

00:14:27.000 --> 00:14:34.000
And if you hold up this as a d
x squared y squared orbital

00:14:34.000 --> 00:14:38.000
where the orbitals are right
along the x-axis and right

00:14:38.000 --> 00:14:41.000
along the y-axis and you hold
that up, remember, your ligands

00:14:41.000 --> 00:14:45.000
are right along the x-axis
and right along the y-axis.

00:14:45.000 --> 00:14:49.000
So, you should also have
significant repulsion for d x

00:14:49.000 --> 00:14:53.000
squared minus y squared, and
octahedrally oriented ligands.

00:14:53.000 --> 00:15:01.000
In contrast, the ligands set
that are 45 degrees off-axis,

00:15:01.000 --> 00:15:08.000
so d y z, d x z, and d x y,
they're all 45 degrees off.

00:15:08.000 --> 00:15:11.000
Your ligands are along the
axis, but your orbitals

00:15:11.000 --> 00:15:14.000
are 45 degrees off-axis.

00:15:14.000 --> 00:15:16.000
So if you look at that
together, you'll see that

00:15:16.000 --> 00:15:19.000
whichever one you look at, the
ligands are not going to be

00:15:19.000 --> 00:15:22.000
pointing directly toward
those d orbitals.

00:15:22.000 --> 00:15:24.000
The orbitals are off-axis,
ligands are on-axis.

00:15:24.000 --> 00:15:29.000
So there will be much
smaller repulsions there.

00:15:29.000 --> 00:15:37.000
And that we talked about the
fact that for d x squared minus

00:15:37.000 --> 00:15:40.000
y squared and d z squared,
they're both have experienced

00:15:40.000 --> 00:15:44.000
large repulsions, they're both
degenerate in energy, they go

00:15:44.000 --> 00:15:48.000
up in energy, whereas these
three d orbitals, smaller

00:15:48.000 --> 00:15:52.000
repulsion, and they're also
degenerate with respect to each

00:15:52.000 --> 00:15:55.000
other, and they're stabilized
compared to these guys up here.

00:15:55.000 --> 00:15:58.000
So you can try to hold those up
and convince yourself that

00:15:58.000 --> 00:16:01.000
that's true for the
octahedral case.

00:16:01.000 --> 00:16:04.000
So, that's what we talked about
last time, and now we want to

00:16:04.000 --> 00:16:08.000
-- oh, and I'll just remind you
we looked at these splitting

00:16:08.000 --> 00:16:09.000
diagrams as well.

00:16:09.000 --> 00:16:13.000
We looked at the average energy
of the d orbitals -- d z

00:16:13.000 --> 00:16:17.000
squared and d x squared minus
y squared go up in energy,

00:16:17.000 --> 00:16:24.000
and then the other three d
orbitals go down in energy.

00:16:24.000 --> 00:16:27.000
So now we want to consider
what happens with

00:16:27.000 --> 00:16:31.000
different geometries.

00:16:31.000 --> 00:16:35.000
So now you can turn your
octahedral case into a

00:16:35.000 --> 00:16:42.000
square planar case, and
how am I going to do that?

00:16:42.000 --> 00:16:45.000
Yeah, so we can just take off
the top and the bottom and we

00:16:45.000 --> 00:16:51.000
have our nice square planar
case, and try to make a

00:16:51.000 --> 00:16:57.000
tetrahedral complex as well.

00:16:57.000 --> 00:16:59.000
And here's an example
of a tetrahedral one.

00:16:59.000 --> 00:17:02.000
Again, you can take a jelly
bean in the middle, and big

00:17:02.000 --> 00:17:05.000
jelly bean, and then the
smaller ones on the outside.

00:17:05.000 --> 00:17:08.000
So what angles am I going for
here in the tetrahedral case?

00:17:08.000 --> 00:17:10.000
109 .

00:17:10.000 --> 00:17:11.000
5.

00:17:11.000 --> 00:17:15.000
So you can go ahead and make
your tetrahedral complex,

00:17:15.000 --> 00:17:17.000
and don't worry so
much about the 0 .

00:17:17.000 --> 00:18:36.000
5, but we'll see if people can
do a good job with the 109.

00:18:36.000 --> 00:18:40.000
OK, how are your tetrahedral
complexes coming?

00:18:40.000 --> 00:18:46.000
Do they look like this sort of?

00:18:46.000 --> 00:18:49.000
So let me define for you how
we're going to consider

00:18:49.000 --> 00:18:52.000
the tetrahedral case.

00:18:52.000 --> 00:18:56.000
So, in the tetrahedral case,
we're going to have the x-axis

00:18:56.000 --> 00:19:00.000
comes out of the plane, the
y-axis is this way, z-axis

00:19:00.000 --> 00:19:02.000
again, up and down.

00:19:02.000 --> 00:19:05.000
We're going to have one ligand
coming out here, another going

00:19:05.000 --> 00:19:07.000
back, and then these two
are pretty much in the

00:19:07.000 --> 00:19:09.000
plane of the screen.

00:19:09.000 --> 00:19:12.000
So this is sort of how I'm
holding the tetrahedral complex

00:19:12.000 --> 00:19:18.000
with respect to the x, z,
and y coordinate system.

00:19:18.000 --> 00:19:21.000
So, there is a splitting,
energy splitting, associated

00:19:21.000 --> 00:19:25.000
with tetrahedral, and it's
going to be smaller than

00:19:25.000 --> 00:19:29.000
octahedral because none of
these ligands will be pointing

00:19:29.000 --> 00:19:31.000
directly toward the orbitals.

00:19:31.000 --> 00:19:36.000
But let's consider which
orbitals are going to be most

00:19:36.000 --> 00:19:42.000
affected by a tetrahedral case.

00:19:42.000 --> 00:19:48.000
So, let's consider d z squared.

00:19:48.000 --> 00:19:49.000
What do you think?

00:19:49.000 --> 00:19:52.000
Is that going to be
particularly -- are the ligands

00:19:52.000 --> 00:19:55.000
pointing toward d z squared?

00:19:55.000 --> 00:19:57.000
No.

00:19:57.000 --> 00:20:01.000
And d x squared minus y
squared, we can think of,

00:20:01.000 --> 00:20:04.000
what about that one?

00:20:04.000 --> 00:20:06.000
No, not really.

00:20:06.000 --> 00:20:12.000
What about d x y,
d y z, and d x y?

00:20:12.000 --> 00:20:17.000
Moreso.

00:20:17.000 --> 00:20:20.000
So, if you try holding up your
tetrahedral in our coordinate

00:20:20.000 --> 00:20:25.000
system, and then hold your d
orbitals 45 degrees off-axis,

00:20:25.000 --> 00:20:28.000
it's not perfect, they're not
pointing directly toward them,

00:20:28.000 --> 00:20:31.000
but it's a little closer than
for the d orbitals that

00:20:31.000 --> 00:20:36.000
are directly on-axis.

00:20:36.000 --> 00:20:41.000
So, if we look at this, we see
that the orbitals are going to

00:20:41.000 --> 00:20:46.000
be split in the exact opposite
way of the octahedral system.

00:20:46.000 --> 00:20:50.000
In the octahedral system, the
ligands are on-axis, so the

00:20:50.000 --> 00:20:53.000
orbitals that are on-axis, d x
squared minus y squared and d

00:20:53.000 --> 00:20:56.000
z squared are going to
be the most affected.

00:20:56.000 --> 00:20:59.000
But with tetrahedral, the
ligands are off-axis, so the

00:20:59.000 --> 00:21:02.000
d orbitals that are also
off-axis are going to

00:21:02.000 --> 00:21:03.000
be the most affected.

00:21:03.000 --> 00:21:06.000
But they're not going to be as
dramatically affected, so the

00:21:06.000 --> 00:21:09.000
splitting is actually
smaller in this case.

00:21:09.000 --> 00:21:13.000
So here, with tetrahedral,
you have the opposite of

00:21:13.000 --> 00:21:16.000
the octahedral system.

00:21:16.000 --> 00:21:19.000
And you can keep these and
try to convince yourself

00:21:19.000 --> 00:21:25.000
of that later if you have
trouble visualizing it.

00:21:25.000 --> 00:21:29.000
So, you'll have more repulsion
between the ligands as negative

00:21:29.000 --> 00:21:32.000
point charges, and the d
orbitals that are 45 degrees

00:21:32.000 --> 00:21:36.000
off-axis than you do with
the two d orbitals

00:21:36.000 --> 00:21:39.000
that are on-axis.

00:21:39.000 --> 00:21:44.000
So here, d x squared minus y
squared and d z squared have

00:21:44.000 --> 00:21:47.000
the same energy with respect to
each other, they're degenerate.

00:21:47.000 --> 00:21:54.000
And we have our d y z, x z,
and x y have the same energy

00:21:54.000 --> 00:21:58.000
with respect to each other,
they are also degenerate.

00:21:58.000 --> 00:22:01.000
So it's the same sets that
are degenerate as with

00:22:01.000 --> 00:22:08.000
octahedral, but they're
all affected differently.

00:22:08.000 --> 00:22:13.000
So now let's look at the energy
diagrams and compare the

00:22:13.000 --> 00:22:17.000
octahedral system with
the tetrahedral system.

00:22:17.000 --> 00:22:20.000
Remember an octahedral, we
had the two orbitals going

00:22:20.000 --> 00:22:22.000
up and three going down.

00:22:22.000 --> 00:22:25.000
The splitting, the energy
difference between

00:22:25.000 --> 00:22:26.000
them was abbreviated.

00:22:26.000 --> 00:22:29.000
The octahedral crystal field
splitting energy, with a

00:22:29.000 --> 00:22:31.000
little o for octahedral.

00:22:31.000 --> 00:22:35.000
We now have a t for
tetrahedral, so we have

00:22:35.000 --> 00:22:37.000
a different name.

00:22:37.000 --> 00:22:41.000
And so here is now
our tetrahedral set.

00:22:41.000 --> 00:22:44.000
You notice it's the opposite of
octahedral, so the orbitals

00:22:44.000 --> 00:22:49.000
that were most destabilized in
the octahedral case are now

00:22:49.000 --> 00:22:54.000
more stabilized down here, so
we've moved down in energy.

00:22:54.000 --> 00:22:58.000
And the orbitals that are
off-axis, 45 degrees off-axis,

00:22:58.000 --> 00:23:02.000
which were stabilized in the
octahedral system, because none

00:23:02.000 --> 00:23:05.000
of ligands were pointing right
toward them, now those ligands

00:23:05.000 --> 00:23:09.000
are a bit closer so they jump
up in energy, and so we have

00:23:09.000 --> 00:23:15.000
this swap between the two.

00:23:15.000 --> 00:23:18.000
So, we have some new
labels as well.

00:23:18.000 --> 00:23:24.000
So, we had e g up here as an
abbreviation for these sets

00:23:24.000 --> 00:23:27.000
of orbitals, and now that's
just referred to as e.

00:23:27.000 --> 00:23:32.000
Notice the book in one place
has an e 2, but uses e in all

00:23:32.000 --> 00:23:35.000
the other places, so just
use e, the e 2 was a

00:23:35.000 --> 00:23:36.000
mistake in the book.

00:23:36.000 --> 00:23:42.000
And then we have t 2 g
becomes t 2 up here.

00:23:42.000 --> 00:23:45.000
So we have this slightly
different nomenclature and we

00:23:45.000 --> 00:23:49.000
have this flip in direction.

00:23:49.000 --> 00:23:53.000
So, the other thing that is
important to emphasize is that

00:23:53.000 --> 00:23:58.000
the tetrahedral splitting
energy is smaller, because none

00:23:58.000 --> 00:24:00.000
of those ligands are pointing
directly toward any

00:24:00.000 --> 00:24:01.000
of the d orbitals.

00:24:01.000 --> 00:24:05.000
So here there is a much larger
difference, here there is a

00:24:05.000 --> 00:24:09.000
smaller difference, so that's
why it's written much closer

00:24:09.000 --> 00:24:14.000
together, so that's smaller.

00:24:14.000 --> 00:24:19.000
And because of that, many
tetrahedral complexes are high

00:24:19.000 --> 00:24:21.000
spin, and in this course, you
can assume that they're

00:24:21.000 --> 00:24:23.000
all high spin.

00:24:23.000 --> 00:24:25.000
So that means there's a weak
field, there's not a big

00:24:25.000 --> 00:24:31.000
energy difference between
those orbital sets.

00:24:31.000 --> 00:24:35.000
And again, we're going to --
since we're going to consider

00:24:35.000 --> 00:24:38.000
how much they go up and down
in energy, the overall

00:24:38.000 --> 00:24:40.000
energy is maintained.

00:24:40.000 --> 00:24:45.000
So here we had two orbitals
going up by 3/5, three

00:24:45.000 --> 00:24:47.000
orbitals going down by 2/5.

00:24:47.000 --> 00:24:50.000
So here, we have three orbitals
going up, so they'll go up in

00:24:50.000 --> 00:24:54.000
energy by 2/5, two orbitals go
down, so they'll be going

00:24:54.000 --> 00:24:57.000
down in energy by 3/5.

00:24:57.000 --> 00:25:01.000
So again, it's the opposite
of the octahedral system.

00:25:01.000 --> 00:25:03.000
It's opposite pretty much in
every way except that the

00:25:03.000 --> 00:25:06.000
splitting energy is much
smaller, it's not as large

00:25:06.000 --> 00:25:11.000
for the tetrahedral complex.

00:25:11.000 --> 00:25:15.000
All right, so let's look at an
example, and we're going to

00:25:15.000 --> 00:25:20.000
consider a chromium, and like
we did before, we have to first

00:25:20.000 --> 00:25:26.000
figure out the d count, so
we have chromium plus 3.

00:25:26.000 --> 00:25:32.000
So what is our d count here?

00:25:32.000 --> 00:25:36.000
You know where chromium is,
what its group number --

00:25:36.000 --> 00:25:42.000
here is a periodic table.

00:25:42.000 --> 00:25:45.000
So what is the d count?

00:25:45.000 --> 00:25:46.000
3.

00:25:46.000 --> 00:25:53.000
So we have 6 minus 3,
3 -- a d 3 system.

00:25:53.000 --> 00:25:58.000
And now, why don't you tell me
how you would fill in those

00:25:58.000 --> 00:26:02.000
three electrons in a
tetrahedral case.

00:26:02.000 --> 00:26:56.000
Have a clicker question there.

00:26:56.000 --> 00:27:00.000
So, notice that in addition to
having electron configurations

00:27:00.000 --> 00:27:02.000
that are different, the d
orbitals are labelled

00:27:02.000 --> 00:27:29.000
differently.

00:27:29.000 --> 00:27:44.000
OK, 10 more seconds.

00:27:44.000 --> 00:27:47.000
OK, very good, 80%.

00:27:47.000 --> 00:27:49.000
So, let's take a look at that.

00:27:49.000 --> 00:27:53.000
So down here, we're going to
have then our d x squared minus

00:27:53.000 --> 00:27:58.000
y squared, d z squared orbitals
up in the top, we have

00:27:58.000 --> 00:28:05.000
x y and x z and y z.

00:28:05.000 --> 00:28:10.000
Again, the orbitals that are
on-axis are repelled a little

00:28:10.000 --> 00:28:14.000
less than the orbitals that are
off-axis in a tetrahedral case.

00:28:14.000 --> 00:28:18.000
And then we put in our
electrons, we start down here.

00:28:18.000 --> 00:28:21.000
And then one of the questions
is do we keep down here and

00:28:21.000 --> 00:28:26.000
pair up or go up here, and the
answer is that you

00:28:26.000 --> 00:28:27.000
would go up here.

00:28:27.000 --> 00:28:31.000
Does someone want to tell me
why they think that's true?

00:28:31.000 --> 00:28:31.000
Yeah.

00:28:31.000 --> 00:28:33.000
STUDENT: [INAUDIBLE]

00:28:33.000 --> 00:28:36.000
PROFESSOR: Right, because it
has a smaller splitting energy.

00:28:36.000 --> 00:28:38.000
So, the way that we were
deciding before with the weak

00:28:38.000 --> 00:28:41.000
field and the strong field, if
it's a weak field, it doesn't

00:28:41.000 --> 00:28:43.000
take much energy to
put it up there.

00:28:43.000 --> 00:28:45.000
So you go they don't want to
be paired, there's energy

00:28:45.000 --> 00:28:47.000
associated with pairing.

00:28:47.000 --> 00:28:51.000
But if there's a really huge
splitting energy, then it takes

00:28:51.000 --> 00:28:54.000
less energy to pair them up
before you go that big

00:28:54.000 --> 00:28:55.000
distance up there.

00:28:55.000 --> 00:28:58.000
But in tetrahedral cases, the
splitting energy's always

00:28:58.000 --> 00:29:02.000
small, so you're just going to
always fill them up singly

00:29:02.000 --> 00:29:05.000
to the fullest extent
possible before you pair.

00:29:05.000 --> 00:29:09.000
So this is like a weak field
case for the octahedral system,

00:29:09.000 --> 00:29:12.000
and all tetrahedral complexes
are sort of the equivalent of

00:29:12.000 --> 00:29:14.000
the weak field, because the
splitting energy is always

00:29:14.000 --> 00:29:18.000
small in an octahedral case,
because none of the ligands'

00:29:18.000 --> 00:29:21.000
negative point charges are
really pointing toward any of

00:29:21.000 --> 00:29:25.000
those orbitals that much, so
it's not that big a difference.

00:29:25.000 --> 00:29:30.000
So, here we have this and now
we can practice writing our d

00:29:30.000 --> 00:29:33.000
to the n electron
configuration.

00:29:33.000 --> 00:29:38.000
So what do I put here?

00:29:38.000 --> 00:29:42.000
What do I put first?

00:29:42.000 --> 00:29:46.000
So we put the e and then what?

00:29:46.000 --> 00:29:47.000
Yup.

00:29:47.000 --> 00:29:51.000
There are two electrons in the
e set of orbitals, and in the

00:29:51.000 --> 00:29:55.000
t 2 orbitals, there's one.

00:29:55.000 --> 00:29:59.000
So that is our d n
electron configuration.

00:29:59.000 --> 00:30:03.000
And then we're also asked how
many unpaired electrons.

00:30:03.000 --> 00:30:16.000
Unpaired electrons
and that is three.

00:30:16.000 --> 00:30:16.000
All right.

00:30:16.000 --> 00:30:21.000
So that's not too bad, that's
the tetrahedral case.

00:30:21.000 --> 00:30:23.000
The hardest part is
probably making your

00:30:23.000 --> 00:30:27.000
tetrahedral complex.

00:30:27.000 --> 00:30:31.000
Now square planar.

00:30:31.000 --> 00:30:34.000
So again, with the square
planar set you have your square

00:30:34.000 --> 00:30:38.000
planar model -- we have
a bigger one down here.

00:30:38.000 --> 00:30:43.000
And the axes is defined such
that we have ligands right

00:30:43.000 --> 00:30:46.000
along x -- one coming out at
you and one going back, and

00:30:46.000 --> 00:30:50.000
also ligands right
along the y-axis.

00:30:50.000 --> 00:30:53.000
So as defined then, we've
gotten rid of our ligands

00:30:53.000 --> 00:30:56.000
along the z-axis.

00:30:56.000 --> 00:30:57.000
So, what do you predict?

00:30:57.000 --> 00:31:04.000
Which two of these will be
the most destabilized now?

00:31:04.000 --> 00:31:06.000
What would be the most
destabilized, what

00:31:06.000 --> 00:31:09.000
do you guess?

00:31:09.000 --> 00:31:13.000
You can hold up your
little sets here.

00:31:13.000 --> 00:31:15.000
What's the most destabilized,
what's going to go up

00:31:15.000 --> 00:31:19.000
the most in energy here?

00:31:19.000 --> 00:31:22.000
Yeah, d z squared
minus y squared.

00:31:22.000 --> 00:31:26.000
What do you predict might
be next, in terms of

00:31:26.000 --> 00:31:29.000
most unfavorable?

00:31:29.000 --> 00:31:30.000
Yeah, the x y one.

00:31:30.000 --> 00:31:35.000
So these two now are going to
be the most destabilized, with

00:31:35.000 --> 00:31:39.000
d x squared minus y squared
being a lot more destabilized

00:31:39.000 --> 00:31:42.000
than just the x y, because
again, those d orbitals

00:31:42.000 --> 00:31:47.000
are on-axis and these
ligands are on-axis.

00:31:47.000 --> 00:31:51.000
So, let's take a look
at all of these again.

00:31:51.000 --> 00:31:55.000
So in the octahedral case,
these were degenerate.

00:31:55.000 --> 00:31:58.000
That's no longer true,
because there are no ligands

00:31:58.000 --> 00:32:00.000
along the z-axis anymore.

00:32:00.000 --> 00:32:03.000
So we took those off in going
from the octahedral to the

00:32:03.000 --> 00:32:07.000
square planar, so you have much
less repulsion, but with the d

00:32:07.000 --> 00:32:12.000
x squared minus y squared, you
still have a lot repulsion.

00:32:12.000 --> 00:32:17.000
so then if we start building up
our case, and this diagram is,

00:32:17.000 --> 00:32:19.000
I think, on the next page of
your handout, but I'm going to

00:32:19.000 --> 00:32:21.000
start building it
all up together.

00:32:21.000 --> 00:32:26.000
So now d x squared, y squared
is really high up, it's very

00:32:26.000 --> 00:32:29.000
much more destabilized
than anybody else.

00:32:29.000 --> 00:32:32.000
D z squared, on the
other hand, is down.

00:32:32.000 --> 00:32:35.000
It's not -- it would be
stabilized compared -- it's

00:32:35.000 --> 00:32:40.000
not nearly as destabilized
as the other system.

00:32:40.000 --> 00:32:44.000
So then we go back
and look at these.

00:32:44.000 --> 00:32:48.000
You told me that d x y would
probably be next, and

00:32:48.000 --> 00:32:50.000
that's a very good guess.

00:32:50.000 --> 00:32:53.000
You see you have more repulsion
than in the other two, because

00:32:53.000 --> 00:32:56.000
the other orbitals have
some z component in them.

00:32:56.000 --> 00:33:00.000
So you have less repulsion than
d x squared minus y squared,

00:33:00.000 --> 00:33:04.000
because it's 45 degrees off,
but still that one is probably

00:33:04.000 --> 00:33:07.000
going to be up a little bit
more in energy than

00:33:07.000 --> 00:33:08.000
the other set.

00:33:08.000 --> 00:33:13.000
These two here are stabilized
compared to the others, so

00:33:13.000 --> 00:33:14.000
they're somewhere down here.

00:33:14.000 --> 00:33:18.000
Now the exact sort of
arrangement can vary a little

00:33:18.000 --> 00:33:22.000
bit, but the important points
are that the d x squared minus

00:33:22.000 --> 00:33:26.000
y squared is the most
destabilized, d x y would be

00:33:26.000 --> 00:33:31.000
next, and the other are
much lower in energy.

00:33:31.000 --> 00:33:34.000
And we're not going to do this
how much up and down thing,

00:33:34.000 --> 00:33:38.000
like the 3/5 and the
2/5 because it's more

00:33:38.000 --> 00:33:40.000
complicated in this case.

00:33:40.000 --> 00:33:43.000
So just the basic rationale you
need to know here, not the

00:33:43.000 --> 00:33:52.000
exact energy differences
in this particular case.

00:33:52.000 --> 00:33:58.000
OK, so now we've thought about
three different kinds of

00:33:58.000 --> 00:34:01.000
geometries -- octahedral,
tetrahedral, and

00:34:01.000 --> 00:34:02.000
the square planar.

00:34:02.000 --> 00:34:07.000
You should be able to
rationalize, for any

00:34:07.000 --> 00:34:10.000
geometry that I give
you, what would be true.

00:34:10.000 --> 00:34:14.000
If I tell you the geometry and
how it compares with our frame,

00:34:14.000 --> 00:34:19.000
with our axis frame of where
the z-axis is, you should be

00:34:19.000 --> 00:34:21.000
able to tell me which
orbital sets would be

00:34:21.000 --> 00:34:24.000
the most destabilized.

00:34:24.000 --> 00:34:28.000
And to give you practice,
why don't you try

00:34:28.000 --> 00:34:29.000
this one right here.

00:34:29.000 --> 00:34:35.000
So we have a square pyramidal
case as drawn here with the

00:34:35.000 --> 00:34:40.000
axes labeled z, y and x,
coming in and coming out.

00:34:40.000 --> 00:34:46.000
Tell me which of the following
statements are true.

00:34:46.000 --> 00:34:51.000
And if you want, you can take
your square planar and turn it

00:34:51.000 --> 00:35:54.000
into the geometry
to help you out.

00:35:54.000 --> 00:36:10.000
Let's just take
10 more seconds.

00:36:10.000 --> 00:36:11.000
All right.

00:36:11.000 --> 00:36:13.000
That was good.

00:36:13.000 --> 00:36:15.000
People did well on
that question.

00:36:15.000 --> 00:36:25.000
So, if we consider that we
had the top two are correct.

00:36:25.000 --> 00:36:29.000
So, if we consider the d z
squared, now we've put a ligand

00:36:29.000 --> 00:36:33.000
along z, so that is going to
cause that to be more

00:36:33.000 --> 00:36:37.000
destabilized for this geometry
rather than square planar,

00:36:37.000 --> 00:36:42.000
which doesn't have anything in
the z direction. ah And then in

00:36:42.000 --> 00:36:47.000
terms, also, other orbitals
that have a component along z

00:36:47.000 --> 00:36:52.000
are going to be affected a
little bit by that, but our

00:36:52.000 --> 00:36:56.000
other one here is not going to
be true, so we just have all of

00:36:56.000 --> 00:36:58.000
the above is not correct,
so we have this one.

00:36:58.000 --> 00:37:02.000
So if we had up those, that's
actually a pretty good score.

00:37:02.000 --> 00:37:07.000
And so you could think about,
say, what would be true of a

00:37:07.000 --> 00:37:11.000
complex that was linear along
z, what would be the most

00:37:11.000 --> 00:37:13.000
stabilized, for example.

00:37:13.000 --> 00:37:16.000
So these are the kinds of
questions you can get, and

00:37:16.000 --> 00:37:20.000
I think there are a few
on the problem-set.

00:37:20.000 --> 00:37:24.000
All right, so let's come
back together now and talk

00:37:24.000 --> 00:37:26.000
about magnetism again.

00:37:26.000 --> 00:37:30.000
So, we said in the beginning
that magnetism can be used to

00:37:30.000 --> 00:37:35.000
figure out geometry in, say, a
metal cluster in an enzyme, and

00:37:35.000 --> 00:37:39.000
let's give an example of
how that could be true.

00:37:39.000 --> 00:37:44.000
So, suppose you have a nickel
plus 2 system, so that would be

00:37:44.000 --> 00:37:49.000
a d 8 system, so we have group
10 minus 2 or d 8, and it was

00:37:49.000 --> 00:37:51.000
found to be diamagnetic.

00:37:51.000 --> 00:37:56.000
And from that, we may be able
to guess, using these kinds of

00:37:56.000 --> 00:37:59.000
diagrams, whether it has
square planar geometry,

00:37:59.000 --> 00:38:03.000
tetrahedral geometry,
or octahedral geometry.

00:38:03.000 --> 00:38:08.000
We can predict the geometry
based on that information.

00:38:08.000 --> 00:38:11.000
Let's think about
how that's true.

00:38:11.000 --> 00:38:14.000
We have a d 8 system.

00:38:14.000 --> 00:38:17.000
Think about octahedral
for a minute.

00:38:17.000 --> 00:38:24.000
Are there two options for how
this might look in this case?

00:38:24.000 --> 00:38:26.000
Is there going to be a
difference in electron

00:38:26.000 --> 00:38:32.000
configurations if it's a weak
field or a strong field?

00:38:32.000 --> 00:38:36.000
So, write it out on your
handout and tell me whether

00:38:36.000 --> 00:38:54.000
it would be true, think
about it both ways.

00:38:54.000 --> 00:38:58.000
Is there a difference?

00:38:58.000 --> 00:39:00.000
So, you would end up
getting the same thing

00:39:00.000 --> 00:39:01.000
in this particular case.

00:39:01.000 --> 00:39:05.000
So if it's a weak field and
you put in 1, 2, 3, then jump

00:39:05.000 --> 00:39:09.000
up here, 4, 5, and then you
have to come back, 6, 7, 8.

00:39:09.000 --> 00:39:13.000
Or you could pair up all the
ones on the bottom first and

00:39:13.000 --> 00:39:16.000
then go up there, but you
actually get the same result no

00:39:16.000 --> 00:39:21.000
matter which way you put them
in, the diagram looks the same.

00:39:21.000 --> 00:39:24.000
So it doesn't matter in this
case if it is a weak or strong

00:39:24.000 --> 00:39:27.000
field, you end up with those
number of electrons with the

00:39:27.000 --> 00:39:31.000
exact same configuration.

00:39:31.000 --> 00:39:33.000
So, we know what
that looks like.

00:39:33.000 --> 00:39:36.000
Well, what about square planar.

00:39:36.000 --> 00:39:38.000
So let's put our
electrons in there.

00:39:38.000 --> 00:39:41.000
We'll start at the bottom,
we'll just put them in.

00:39:41.000 --> 00:39:44.000
I'm not going to worry too much
about whether we can jump up or

00:39:44.000 --> 00:39:48.000
not, we'll just go and pair
them up as we go down here, and

00:39:48.000 --> 00:39:52.000
then go up here, and now we've
put in our eight electrons.

00:39:52.000 --> 00:39:56.000
So, how close these are, we're
just going to put them all in.

00:39:56.000 --> 00:39:59.000
We're just going to be very
careful not to bump up any

00:39:59.000 --> 00:40:04.000
electrons there unless we
absolutely have to, because d x

00:40:04.000 --> 00:40:08.000
squared minus y squared is very
much more destabilized in the

00:40:08.000 --> 00:40:11.000
square planar system, so we're
going to want to pair all

00:40:11.000 --> 00:40:15.000
our electrons up in those
lower energy orbitals.

00:40:15.000 --> 00:40:18.000
So even if we sort of
did it a different way,

00:40:18.000 --> 00:40:19.000
that's what we would get.

00:40:19.000 --> 00:40:22.000
So we're going to want to pair
everything up before we go

00:40:22.000 --> 00:40:25.000
up to that top one there.

00:40:25.000 --> 00:40:26.000
So there's our square planar.

00:40:26.000 --> 00:40:28.000
Well, what about tetrahedral.

00:40:28.000 --> 00:40:31.000
How are we going
to fill these up?

00:40:31.000 --> 00:40:37.000
Do we want to pair first, or
we do want to put them to the

00:40:37.000 --> 00:40:40.000
full extent possible singly?

00:40:40.000 --> 00:40:43.000
Single, right, it's going to be
a weak field, there's not a big

00:40:43.000 --> 00:40:46.000
splitting here between these,
so we'll put them in, there's

00:40:46.000 --> 00:40:53.000
1, 2, 3, 4, 5, 6, 7, 8.

00:40:53.000 --> 00:40:55.000
All right, so now we can
consider which of these will

00:40:55.000 --> 00:40:58.000
be paramagnetic and which
will be diamagnetic.

00:40:58.000 --> 00:41:01.000
What's octahedral?

00:41:01.000 --> 00:41:05.000
It's paramagnetic, we
have unpaired electrons.

00:41:05.000 --> 00:41:08.000
What about square planar?

00:41:08.000 --> 00:41:10.000
Square planar's diamagnetic.

00:41:10.000 --> 00:41:11.000
And what about tetrahedral?

00:41:11.000 --> 00:41:14.000
Paramagnetic.

00:41:14.000 --> 00:41:20.000
So, if the experimental data
told us that a nickel center in

00:41:20.000 --> 00:41:23.000
an enzyme was diamagnetic, and
we were trying to decide

00:41:23.000 --> 00:41:27.000
between those three geometries,
it really seems like square

00:41:27.000 --> 00:41:31.000
planar is going to
be our best guess.

00:41:31.000 --> 00:41:34.000
And so, let me show
you an example of a

00:41:34.000 --> 00:41:39.000
square planar system.

00:41:39.000 --> 00:41:44.000
And so this particular nickel
is in a square planar system.

00:41:44.000 --> 00:41:50.000
It has four ligands that are
all in the same plane, and it

00:41:50.000 --> 00:41:54.000
is a square planar center for a
nickel, so that's one example.

00:41:54.000 --> 00:41:58.000
And this is a cluster
that's involved in life

00:41:58.000 --> 00:42:01.000
on carbon dioxide.

00:42:01.000 --> 00:42:04.000
All right, so that's
different geometries,

00:42:04.000 --> 00:42:05.000
you're set with that.

00:42:05.000 --> 00:42:09.000
Monday we're going to talk
about colors of coordination

00:42:09.000 --> 00:42:12.000
complexes, which all have to do
with the different geometries,

00:42:12.000 --> 00:42:16.000
paired and unpaired electrons,
high field, low spin,

00:42:16.000 --> 00:42:19.000
strong field, weak field.

00:42:19.000 --> 00:42:21.000
Have a nice weekend.

00:42:21.000 --> 00:42:22.000