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

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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%.

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So, when you're past the
equivalence point, so you've

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converted all of your weak, in
this case, acid to its

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conjugate base, and because it
was a weak acid, the conjugate

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base is going to be a weak
based and so it's not

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contributing a whole lot it'll
make the solution basic, but

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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.

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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

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moles that there are, and
divide by the total volume.

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So this was like one of the
problems on the exam, and one

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thing that I thought was
interesting on the exam is that

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more people seemed to get the
hard problem right than this,

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which was the easy problem.

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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

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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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00:02:51,000 --> 00:02:59,000
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

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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,

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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

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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

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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

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geometries and how many
unpaired or paired electrons

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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.

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And so, over here we have --
oh, actually it says gum drops

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-- you don't have gum drops
this year, I changed up here, I

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forgot to change it down here.

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We have mini marshmallows.

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Dr. Taylor went out and tried
to purchase enough gum drops to

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do this experiment, and
discovered that Cambridge only

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had 300 gum drops, so we have
mini marshmallows

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instead today.

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But this gives you the idea.

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You can take one toothpick and
you can make d z squared,

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00:08:02,000 --> 00:08:06,000
putting on your orbitals, you
have your donut in the middle,

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and then your two lobes,
which run along the z-axis.

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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

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handily, you can just have one
for all of the other d

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orbitals, because depending on
how you hold it, it can

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represent all of the other d
orbitals just very well.

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So, you can just have one of
these for all the others

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and then your d z squared.

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So what we're going to do when
we have our orbitals set up,

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then we can think about how
ligands in particular

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positions, in particular
geometries would clash with our

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00:08:53,000 --> 00:08:55,000
orbitals -- where there'd be
big repulsions or

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small repulsions.

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So, any other people missing
their jelly beans or

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00:09:03,000 --> 00:09:05,000
their marshmallows?

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00:09:05,000 --> 00:09:34,000
Please, raise your
hand, we have extras.

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So, those of you who have
them, go ahead and start

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making your d orbitals.

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00:10:08,000 --> 00:10:54,000
All right, so if you're
finished with your two d

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00:10:54,000 --> 00:11:01,000
orbitals, you can start making
an octahedral complex.

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00:11:01,000 --> 00:11:05,000
So in your geometries set,
you'll have a big gum which can

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00:11:05,000 --> 00:11:11,000
be your center metal -- you'll
have a big jelly bean -- sorry,

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00:11:11,000 --> 00:11:14,000
big jelly beans and small jelly
beans are our ligands, or our

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00:11:14,000 --> 00:11:18,000
negative point charges, and
you can set up and make an

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00:11:18,000 --> 00:13:05,000
octahedral geometry here.

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00:13:05,000 --> 00:13:10,000
OK, so as you're finishing this
up, I'm going to review what we

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00:13:10,000 --> 00:13:13,000
talked about before the exam --
so this isn't in today's

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00:13:13,000 --> 00:13:15,000
lecture handouts, it was in
last time, which we

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already went over.

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But sometimes I've discovered
that when there's an exam in

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the middle, there needs to be a
bit of a refresher, it's hard

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00:13:23,000 --> 00:13:28,000
to remember what happened
before the exam, and you

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have your models to
think about this.

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00:13:31,000 --> 00:13:34,000
So, before the exam, we had
talked about the octahedral

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00:13:34,000 --> 00:13:38,000
case, and how compared to a
spherical situation where the

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ligands are everywhere
distributed around the metals

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00:13:41,000 --> 00:13:45,000
where all d orbitals would be
affected/repulsed by the

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00:13:45,000 --> 00:13:50,000
ligands in a symmetric fashion
equally, when you have them put

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00:13:50,000 --> 00:13:54,000
as particular positions in
geometry, then they're going to

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affect the different d
orbitals differently.

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00:13:57,000 --> 00:14:00,000
And so, if you have your d z
squared made, and you have your

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00:14:00,000 --> 00:14:04,000
octahedral made, you can sort
of hold these up and realize

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00:14:04,000 --> 00:14:09,000
that you would have repulsion
from your ligands along the

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00:14:09,000 --> 00:14:14,000
z-axis directly toward your
orbitals from d z squared.

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00:14:14,000 --> 00:14:16,000
So that would be
highly repulsive.

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00:14:16,000 --> 00:14:20,000
The ligands are along the
z-axis, the d orbitals are

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00:14:20,000 --> 00:14:23,000
along the z-axis, so the
ligands, the negative point

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00:14:23,000 --> 00:14:25,000
charge ligands are going
to be pointing right

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00:14:25,000 --> 00:14:27,000
toward your orbitals.

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00:14:27,000 --> 00:14:34,000
And if you hold up this as a d
x squared y squared orbital

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00:14:34,000 --> 00:14:38,000
where the orbitals are right
along the x-axis and right

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00:14:38,000 --> 00:14:41,000
along the y-axis and you hold
that up, remember, your ligands

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00:14:41,000 --> 00:14:45,000
are right along the x-axis
and right along the y-axis.

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00:14:45,000 --> 00:14:49,000
So, you should also have
significant repulsion for d x

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00:14:49,000 --> 00:14:53,000
squared minus y squared, and
octahedrally oriented ligands.

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00:14:53,000 --> 00:15:01,000
In contrast, the ligands set
that are 45 degrees off-axis,

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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.

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00:15:08,000 --> 00:15:11,000
Your ligands are along the
axis, but your orbitals

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are 45 degrees off-axis.

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So if you look at that
together, you'll see that

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whichever one you look at, the
ligands are not going to be

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pointing directly toward
those d orbitals.

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The orbitals are off-axis,
ligands are on-axis.

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So there will be much
smaller repulsions there.

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And that we talked about the
fact that for d x squared minus

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00:15:37,000 --> 00:15:40,000
y squared and d z squared,
they're both have experienced

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large repulsions, they're both
degenerate in energy, they go

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up in energy, whereas these
three d orbitals, smaller

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repulsion, and they're also
degenerate with respect to each

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00:15:52,000 --> 00:15:55,000
other, and they're stabilized
compared to these guys up here.

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So you can try to hold those up
and convince yourself that

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00:15:58,000 --> 00:16:01,000
that's true for the
octahedral case.

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00:16:01,000 --> 00:16:04,000
So, that's what we talked about
last time, and now we want to

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00:16:04,000 --> 00:16:08,000
-- oh, and I'll just remind you
we looked at these splitting

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00:16:08,000 --> 00:16:09,000
diagrams as well.

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00:16:09,000 --> 00:16:13,000
We looked at the average energy
of the d orbitals -- d z

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00:16:13,000 --> 00:16:17,000
squared and d x squared minus
y squared go up in energy,

208
00:16:17,000 --> 00:16:24,000
and then the other three d
orbitals go down in energy.

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00:16:24,000 --> 00:16:27,000
So now we want to consider
what happens with

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00:16:27,000 --> 00:16:31,000
different geometries.

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00:16:31,000 --> 00:16:35,000
So now you can turn your
octahedral case into a

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00:16:35,000 --> 00:16:42,000
square planar case, and
how am I going to do that?

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00:16:42,000 --> 00:16:45,000
Yeah, so we can just take off
the top and the bottom and we

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00:16:45,000 --> 00:16:51,000
have our nice square planar
case, and try to make a

215
00:16:51,000 --> 00:16:57,000
tetrahedral complex as well.

216
00:16:57,000 --> 00:16:59,000
And here's an example
of a tetrahedral one.

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00:16:59,000 --> 00:17:02,000
Again, you can take a jelly
bean in the middle, and big

218
00:17:02,000 --> 00:17:05,000
jelly bean, and then the
smaller ones on the outside.

219
00:17:05,000 --> 00:17:08,000
So what angles am I going for
here in the tetrahedral case?

220
00:17:08,000 --> 00:17:10,000
109 .

221
00:17:10,000 --> 00:17:11,000
5.

222
00:17:11,000 --> 00:17:15,000
So you can go ahead and make
your tetrahedral complex,

223
00:17:15,000 --> 00:17:17,000
and don't worry so
much about the 0 .

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00:17:17,000 --> 00:18:36,000
5, but we'll see if people can
do a good job with the 109.

225
00:18:36,000 --> 00:18:40,000
OK, how are your tetrahedral
complexes coming?

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00:18:40,000 --> 00:18:46,000
Do they look like this sort of?

227
00:18:46,000 --> 00:18:49,000
So let me define for you how
we're going to consider

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00:18:49,000 --> 00:18:52,000
the tetrahedral case.

229
00:18:52,000 --> 00:18:56,000
So, in the tetrahedral case,
we're going to have the x-axis

230
00:18:56,000 --> 00:19:00,000
comes out of the plane, the
y-axis is this way, z-axis

231
00:19:00,000 --> 00:19:02,000
again, up and down.

232
00:19:02,000 --> 00:19:05,000
We're going to have one ligand
coming out here, another going

233
00:19:05,000 --> 00:19:07,000
back, and then these two
are pretty much in the

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00:19:07,000 --> 00:19:09,000
plane of the screen.

235
00:19:09,000 --> 00:19:12,000
So this is sort of how I'm
holding the tetrahedral complex

236
00:19:12,000 --> 00:19:18,000
with respect to the x, z,
and y coordinate system.

237
00:19:18,000 --> 00:19:21,000
So, there is a splitting,
energy splitting, associated

238
00:19:21,000 --> 00:19:25,000
with tetrahedral, and it's
going to be smaller than

239
00:19:25,000 --> 00:19:29,000
octahedral because none of
these ligands will be pointing

240
00:19:29,000 --> 00:19:31,000
directly toward the orbitals.

241
00:19:31,000 --> 00:19:36,000
But let's consider which
orbitals are going to be most

242
00:19:36,000 --> 00:19:42,000
affected by a tetrahedral case.

243
00:19:42,000 --> 00:19:48,000
So, let's consider d z squared.

244
00:19:48,000 --> 00:19:49,000
What do you think?

245
00:19:49,000 --> 00:19:52,000
Is that going to be
particularly -- are the ligands

246
00:19:52,000 --> 00:19:55,000
pointing toward d z squared?

247
00:19:55,000 --> 00:19:57,000
No.

248
00:19:57,000 --> 00:20:01,000
And d x squared minus y
squared, we can think of,

249
00:20:01,000 --> 00:20:04,000
what about that one?

250
00:20:04,000 --> 00:20:06,000
No, not really.

251
00:20:06,000 --> 00:20:12,000
What about d x y,
d y z, and d x y?

252
00:20:12,000 --> 00:20:17,000
Moreso.

253
00:20:17,000 --> 00:20:20,000
So, if you try holding up your
tetrahedral in our coordinate

254
00:20:20,000 --> 00:20:25,000
system, and then hold your d
orbitals 45 degrees off-axis,

255
00:20:25,000 --> 00:20:28,000
it's not perfect, they're not
pointing directly toward them,

256
00:20:28,000 --> 00:20:31,000
but it's a little closer than
for the d orbitals that

257
00:20:31,000 --> 00:20:36,000
are directly on-axis.

258
00:20:36,000 --> 00:20:41,000
So, if we look at this, we see
that the orbitals are going to

259
00:20:41,000 --> 00:20:46,000
be split in the exact opposite
way of the octahedral system.

260
00:20:46,000 --> 00:20:50,000
In the octahedral system, the
ligands are on-axis, so the

261
00:20:50,000 --> 00:20:53,000
orbitals that are on-axis, d x
squared minus y squared and d

262
00:20:53,000 --> 00:20:56,000
z squared are going to
be the most affected.

263
00:20:56,000 --> 00:20:59,000
But with tetrahedral, the
ligands are off-axis, so the

264
00:20:59,000 --> 00:21:02,000
d orbitals that are also
off-axis are going to

265
00:21:02,000 --> 00:21:03,000
be the most affected.

266
00:21:03,000 --> 00:21:06,000
But they're not going to be as
dramatically affected, so the

267
00:21:06,000 --> 00:21:09,000
splitting is actually
smaller in this case.

268
00:21:09,000 --> 00:21:13,000
So here, with tetrahedral,
you have the opposite of

269
00:21:13,000 --> 00:21:16,000
the octahedral system.

270
00:21:16,000 --> 00:21:19,000
And you can keep these and
try to convince yourself

271
00:21:19,000 --> 00:21:25,000
of that later if you have
trouble visualizing it.

272
00:21:25,000 --> 00:21:29,000
So, you'll have more repulsion
between the ligands as negative

273
00:21:29,000 --> 00:21:32,000
point charges, and the d
orbitals that are 45 degrees

274
00:21:32,000 --> 00:21:36,000
off-axis than you do with
the two d orbitals

275
00:21:36,000 --> 00:21:39,000
that are on-axis.

276
00:21:39,000 --> 00:21:44,000
So here, d x squared minus y
squared and d z squared have

277
00:21:44,000 --> 00:21:47,000
the same energy with respect to
each other, they're degenerate.

278
00:21:47,000 --> 00:21:54,000
And we have our d y z, x z,
and x y have the same energy

279
00:21:54,000 --> 00:21:58,000
with respect to each other,
they are also degenerate.

280
00:21:58,000 --> 00:22:01,000
So it's the same sets that
are degenerate as with

281
00:22:01,000 --> 00:22:08,000
octahedral, but they're
all affected differently.

282
00:22:08,000 --> 00:22:13,000
So now let's look at the energy
diagrams and compare the

283
00:22:13,000 --> 00:22:17,000
octahedral system with
the tetrahedral system.

284
00:22:17,000 --> 00:22:20,000
Remember an octahedral, we
had the two orbitals going

285
00:22:20,000 --> 00:22:22,000
up and three going down.

286
00:22:22,000 --> 00:22:25,000
The splitting, the energy
difference between

287
00:22:25,000 --> 00:22:26,000
them was abbreviated.

288
00:22:26,000 --> 00:22:29,000
The octahedral crystal field
splitting energy, with a

289
00:22:29,000 --> 00:22:31,000
little o for octahedral.

290
00:22:31,000 --> 00:22:35,000
We now have a t for
tetrahedral, so we have

291
00:22:35,000 --> 00:22:37,000
a different name.

292
00:22:37,000 --> 00:22:41,000
And so here is now
our tetrahedral set.

293
00:22:41,000 --> 00:22:44,000
You notice it's the opposite of
octahedral, so the orbitals

294
00:22:44,000 --> 00:22:49,000
that were most destabilized in
the octahedral case are now

295
00:22:49,000 --> 00:22:54,000
more stabilized down here, so
we've moved down in energy.

296
00:22:54,000 --> 00:22:58,000
And the orbitals that are
off-axis, 45 degrees off-axis,

297
00:22:58,000 --> 00:23:02,000
which were stabilized in the
octahedral system, because none

298
00:23:02,000 --> 00:23:05,000
of ligands were pointing right
toward them, now those ligands

299
00:23:05,000 --> 00:23:09,000
are a bit closer so they jump
up in energy, and so we have

300
00:23:09,000 --> 00:23:15,000
this swap between the two.

301
00:23:15,000 --> 00:23:18,000
So, we have some new
labels as well.

302
00:23:18,000 --> 00:23:24,000
So, we had e g up here as an
abbreviation for these sets

303
00:23:24,000 --> 00:23:27,000
of orbitals, and now that's
just referred to as e.

304
00:23:27,000 --> 00:23:32,000
Notice the book in one place
has an e 2, but uses e in all

305
00:23:32,000 --> 00:23:35,000
the other places, so just
use e, the e 2 was a

306
00:23:35,000 --> 00:23:36,000
mistake in the book.

307
00:23:36,000 --> 00:23:42,000
And then we have t 2 g
becomes t 2 up here.

308
00:23:42,000 --> 00:23:45,000
So we have this slightly
different nomenclature and we

309
00:23:45,000 --> 00:23:49,000
have this flip in direction.

310
00:23:49,000 --> 00:23:53,000
So, the other thing that is
important to emphasize is that

311
00:23:53,000 --> 00:23:58,000
the tetrahedral splitting
energy is smaller, because none

312
00:23:58,000 --> 00:24:00,000
of those ligands are pointing
directly toward any

313
00:24:00,000 --> 00:24:01,000
of the d orbitals.

314
00:24:01,000 --> 00:24:05,000
So here there is a much larger
difference, here there is a

315
00:24:05,000 --> 00:24:09,000
smaller difference, so that's
why it's written much closer

316
00:24:09,000 --> 00:24:14,000
together, so that's smaller.

317
00:24:14,000 --> 00:24:19,000
And because of that, many
tetrahedral complexes are high

318
00:24:19,000 --> 00:24:21,000
spin, and in this course, you
can assume that they're

319
00:24:21,000 --> 00:24:23,000
all high spin.

320
00:24:23,000 --> 00:24:25,000
So that means there's a weak
field, there's not a big

321
00:24:25,000 --> 00:24:31,000
energy difference between
those orbital sets.

322
00:24:31,000 --> 00:24:35,000
And again, we're going to --
since we're going to consider

323
00:24:35,000 --> 00:24:38,000
how much they go up and down
in energy, the overall

324
00:24:38,000 --> 00:24:40,000
energy is maintained.

325
00:24:40,000 --> 00:24:45,000
So here we had two orbitals
going up by 3/5, three

326
00:24:45,000 --> 00:24:47,000
orbitals going down by 2/5.

327
00:24:47,000 --> 00:24:50,000
So here, we have three orbitals
going up, so they'll go up in

328
00:24:50,000 --> 00:24:54,000
energy by 2/5, two orbitals go
down, so they'll be going

329
00:24:54,000 --> 00:24:57,000
down in energy by 3/5.

330
00:24:57,000 --> 00:25:01,000
So again, it's the opposite
of the octahedral system.

331
00:25:01,000 --> 00:25:03,000
It's opposite pretty much in
every way except that the

332
00:25:03,000 --> 00:25:06,000
splitting energy is much
smaller, it's not as large

333
00:25:06,000 --> 00:25:11,000
for the tetrahedral complex.

334
00:25:11,000 --> 00:25:15,000
All right, so let's look at an
example, and we're going to

335
00:25:15,000 --> 00:25:20,000
consider a chromium, and like
we did before, we have to first

336
00:25:20,000 --> 00:25:26,000
figure out the d count, so
we have chromium plus 3.

337
00:25:26,000 --> 00:25:32,000
So what is our d count here?

338
00:25:32,000 --> 00:25:36,000
You know where chromium is,
what its group number --

339
00:25:36,000 --> 00:25:42,000
here is a periodic table.

340
00:25:42,000 --> 00:25:45,000
So what is the d count?

341
00:25:45,000 --> 00:25:46,000
3.

342
00:25:46,000 --> 00:25:53,000
So we have 6 minus 3,
3 -- a d 3 system.

343
00:25:53,000 --> 00:25:58,000
And now, why don't you tell me
how you would fill in those

344
00:25:58,000 --> 00:26:02,000
three electrons in a
tetrahedral case.

345
00:26:02,000 --> 00:26:56,000
Have a clicker question there.

346
00:26:56,000 --> 00:27:00,000
So, notice that in addition to
having electron configurations

347
00:27:00,000 --> 00:27:02,000
that are different, the d
orbitals are labelled

348
00:27:02,000 --> 00:27:29,000
differently.

349
00:27:29,000 --> 00:27:44,000
OK, 10 more seconds.

350
00:27:44,000 --> 00:27:47,000
OK, very good, 80%.

351
00:27:47,000 --> 00:27:49,000
So, let's take a look at that.

352
00:27:49,000 --> 00:27:53,000
So down here, we're going to
have then our d x squared minus

353
00:27:53,000 --> 00:27:58,000
y squared, d z squared orbitals
up in the top, we have

354
00:27:58,000 --> 00:28:05,000
x y and x z and y z.

355
00:28:05,000 --> 00:28:10,000
Again, the orbitals that are
on-axis are repelled a little

356
00:28:10,000 --> 00:28:14,000
less than the orbitals that are
off-axis in a tetrahedral case.

357
00:28:14,000 --> 00:28:18,000
And then we put in our
electrons, we start down here.

358
00:28:18,000 --> 00:28:21,000
And then one of the questions
is do we keep down here and

359
00:28:21,000 --> 00:28:26,000
pair up or go up here, and the
answer is that you

360
00:28:26,000 --> 00:28:27,000
would go up here.

361
00:28:27,000 --> 00:28:31,000
Does someone want to tell me
why they think that's true?

362
00:28:31,000 --> 00:28:31,000
Yeah.

363
00:28:31,000 --> 00:28:33,000
STUDENT: [INAUDIBLE]

364
00:28:33,000 --> 00:28:36,000
PROFESSOR: Right, because it
has a smaller splitting energy.

365
00:28:36,000 --> 00:28:38,000
So, the way that we were
deciding before with the weak

366
00:28:38,000 --> 00:28:41,000
field and the strong field, if
it's a weak field, it doesn't

367
00:28:41,000 --> 00:28:43,000
take much energy to
put it up there.

368
00:28:43,000 --> 00:28:45,000
So you go they don't want to
be paired, there's energy

369
00:28:45,000 --> 00:28:47,000
associated with pairing.

370
00:28:47,000 --> 00:28:51,000
But if there's a really huge
splitting energy, then it takes

371
00:28:51,000 --> 00:28:54,000
less energy to pair them up
before you go that big

372
00:28:54,000 --> 00:28:55,000
distance up there.

373
00:28:55,000 --> 00:28:58,000
But in tetrahedral cases, the
splitting energy's always

374
00:28:58,000 --> 00:29:02,000
small, so you're just going to
always fill them up singly

375
00:29:02,000 --> 00:29:05,000
to the fullest extent
possible before you pair.

376
00:29:05,000 --> 00:29:09,000
So this is like a weak field
case for the octahedral system,

377
00:29:09,000 --> 00:29:12,000
and all tetrahedral complexes
are sort of the equivalent of

378
00:29:12,000 --> 00:29:14,000
the weak field, because the
splitting energy is always

379
00:29:14,000 --> 00:29:18,000
small in an octahedral case,
because none of the ligands'

380
00:29:18,000 --> 00:29:21,000
negative point charges are
really pointing toward any of

381
00:29:21,000 --> 00:29:25,000
those orbitals that much, so
it's not that big a difference.

382
00:29:25,000 --> 00:29:30,000
So, here we have this and now
we can practice writing our d

383
00:29:30,000 --> 00:29:33,000
to the n electron
configuration.

384
00:29:33,000 --> 00:29:38,000
So what do I put here?

385
00:29:38,000 --> 00:29:42,000
What do I put first?

386
00:29:42,000 --> 00:29:46,000
So we put the e and then what?

387
00:29:46,000 --> 00:29:47,000
Yup.

388
00:29:47,000 --> 00:29:51,000
There are two electrons in the
e set of orbitals, and in the

389
00:29:51,000 --> 00:29:55,000
t 2 orbitals, there's one.

390
00:29:55,000 --> 00:29:59,000
So that is our d n
electron configuration.

391
00:29:59,000 --> 00:30:03,000
And then we're also asked how
many unpaired electrons.

392
00:30:03,000 --> 00:30:16,000
Unpaired electrons
and that is three.

393
00:30:16,000 --> 00:30:16,000
All right.

394
00:30:16,000 --> 00:30:21,000
So that's not too bad, that's
the tetrahedral case.

395
00:30:21,000 --> 00:30:23,000
The hardest part is
probably making your

396
00:30:23,000 --> 00:30:27,000
tetrahedral complex.

397
00:30:27,000 --> 00:30:31,000
Now square planar.

398
00:30:31,000 --> 00:30:34,000
So again, with the square
planar set you have your square

399
00:30:34,000 --> 00:30:38,000
planar model -- we have
a bigger one down here.

400
00:30:38,000 --> 00:30:43,000
And the axes is defined such
that we have ligands right

401
00:30:43,000 --> 00:30:46,000
along x -- one coming out at
you and one going back, and

402
00:30:46,000 --> 00:30:50,000
also ligands right
along the y-axis.

403
00:30:50,000 --> 00:30:53,000
So as defined then, we've
gotten rid of our ligands

404
00:30:53,000 --> 00:30:56,000
along the z-axis.

405
00:30:56,000 --> 00:30:57,000
So, what do you predict?

406
00:30:57,000 --> 00:31:04,000
Which two of these will be
the most destabilized now?

407
00:31:04,000 --> 00:31:06,000
What would be the most
destabilized, what

408
00:31:06,000 --> 00:31:09,000
do you guess?

409
00:31:09,000 --> 00:31:13,000
You can hold up your
little sets here.

410
00:31:13,000 --> 00:31:15,000
What's the most destabilized,
what's going to go up

411
00:31:15,000 --> 00:31:19,000
the most in energy here?

412
00:31:19,000 --> 00:31:22,000
Yeah, d z squared
minus y squared.

413
00:31:22,000 --> 00:31:26,000
What do you predict might
be next, in terms of

414
00:31:26,000 --> 00:31:29,000
most unfavorable?

415
00:31:29,000 --> 00:31:30,000
Yeah, the x y one.

416
00:31:30,000 --> 00:31:35,000
So these two now are going to
be the most destabilized, with

417
00:31:35,000 --> 00:31:39,000
d x squared minus y squared
being a lot more destabilized

418
00:31:39,000 --> 00:31:42,000
than just the x y, because
again, those d orbitals

419
00:31:42,000 --> 00:31:47,000
are on-axis and these
ligands are on-axis.

420
00:31:47,000 --> 00:31:51,000
So, let's take a look
at all of these again.

421
00:31:51,000 --> 00:31:55,000
So in the octahedral case,
these were degenerate.

422
00:31:55,000 --> 00:31:58,000
That's no longer true,
because there are no ligands

423
00:31:58,000 --> 00:32:00,000
along the z-axis anymore.

424
00:32:00,000 --> 00:32:03,000
So we took those off in going
from the octahedral to the

425
00:32:03,000 --> 00:32:07,000
square planar, so you have much
less repulsion, but with the d

426
00:32:07,000 --> 00:32:12,000
x squared minus y squared, you
still have a lot repulsion.

427
00:32:12,000 --> 00:32:17,000
so then if we start building up
our case, and this diagram is,

428
00:32:17,000 --> 00:32:19,000
I think, on the next page of
your handout, but I'm going to

429
00:32:19,000 --> 00:32:21,000
start building it
all up together.

430
00:32:21,000 --> 00:32:26,000
So now d x squared, y squared
is really high up, it's very

431
00:32:26,000 --> 00:32:29,000
much more destabilized
than anybody else.

432
00:32:29,000 --> 00:32:32,000
D z squared, on the
other hand, is down.

433
00:32:32,000 --> 00:32:35,000
It's not -- it would be
stabilized compared -- it's

434
00:32:35,000 --> 00:32:40,000
not nearly as destabilized
as the other system.

435
00:32:40,000 --> 00:32:44,000
So then we go back
and look at these.

436
00:32:44,000 --> 00:32:48,000
You told me that d x y would
probably be next, and

437
00:32:48,000 --> 00:32:50,000
that's a very good guess.

438
00:32:50,000 --> 00:32:53,000
You see you have more repulsion
than in the other two, because

439
00:32:53,000 --> 00:32:56,000
the other orbitals have
some z component in them.

440
00:32:56,000 --> 00:33:00,000
So you have less repulsion than
d x squared minus y squared,

441
00:33:00,000 --> 00:33:04,000
because it's 45 degrees off,
but still that one is probably

442
00:33:04,000 --> 00:33:07,000
going to be up a little bit
more in energy than

443
00:33:07,000 --> 00:33:08,000
the other set.

444
00:33:08,000 --> 00:33:13,000
These two here are stabilized
compared to the others, so

445
00:33:13,000 --> 00:33:14,000
they're somewhere down here.

446
00:33:14,000 --> 00:33:18,000
Now the exact sort of
arrangement can vary a little

447
00:33:18,000 --> 00:33:22,000
bit, but the important points
are that the d x squared minus

448
00:33:22,000 --> 00:33:26,000
y squared is the most
destabilized, d x y would be

449
00:33:26,000 --> 00:33:31,000
next, and the other are
much lower in energy.

450
00:33:31,000 --> 00:33:34,000
And we're not going to do this
how much up and down thing,

451
00:33:34,000 --> 00:33:38,000
like the 3/5 and the
2/5 because it's more

452
00:33:38,000 --> 00:33:40,000
complicated in this case.

453
00:33:40,000 --> 00:33:43,000
So just the basic rationale you
need to know here, not the

454
00:33:43,000 --> 00:33:52,000
exact energy differences
in this particular case.

455
00:33:52,000 --> 00:33:58,000
OK, so now we've thought about
three different kinds of

456
00:33:58,000 --> 00:34:01,000
geometries -- octahedral,
tetrahedral, and

457
00:34:01,000 --> 00:34:02,000
the square planar.

458
00:34:02,000 --> 00:34:07,000
You should be able to
rationalize, for any

459
00:34:07,000 --> 00:34:10,000
geometry that I give
you, what would be true.

460
00:34:10,000 --> 00:34:14,000
If I tell you the geometry and
how it compares with our frame,

461
00:34:14,000 --> 00:34:19,000
with our axis frame of where
the z-axis is, you should be

462
00:34:19,000 --> 00:34:21,000
able to tell me which
orbital sets would be

463
00:34:21,000 --> 00:34:24,000
the most destabilized.

464
00:34:24,000 --> 00:34:28,000
And to give you practice,
why don't you try

465
00:34:28,000 --> 00:34:29,000
this one right here.

466
00:34:29,000 --> 00:34:35,000
So we have a square pyramidal
case as drawn here with the

467
00:34:35,000 --> 00:34:40,000
axes labeled z, y and x,
coming in and coming out.

468
00:34:40,000 --> 00:34:46,000
Tell me which of the following
statements are true.

469
00:34:46,000 --> 00:34:51,000
And if you want, you can take
your square planar and turn it

470
00:34:51,000 --> 00:35:54,000
into the geometry
to help you out.

471
00:35:54,000 --> 00:36:10,000
Let's just take
10 more seconds.

472
00:36:10,000 --> 00:36:11,000
All right.

473
00:36:11,000 --> 00:36:13,000
That was good.

474
00:36:13,000 --> 00:36:15,000
People did well on
that question.

475
00:36:15,000 --> 00:36:25,000
So, if we consider that we
had the top two are correct.

476
00:36:25,000 --> 00:36:29,000
So, if we consider the d z
squared, now we've put a ligand

477
00:36:29,000 --> 00:36:33,000
along z, so that is going to
cause that to be more

478
00:36:33,000 --> 00:36:37,000
destabilized for this geometry
rather than square planar,

479
00:36:37,000 --> 00:36:42,000
which doesn't have anything in
the z direction. ah And then in

480
00:36:42,000 --> 00:36:47,000
terms, also, other orbitals
that have a component along z

481
00:36:47,000 --> 00:36:52,000
are going to be affected a
little bit by that, but our

482
00:36:52,000 --> 00:36:56,000
other one here is not going to
be true, so we just have all of

483
00:36:56,000 --> 00:36:58,000
the above is not correct,
so we have this one.

484
00:36:58,000 --> 00:37:02,000
So if we had up those, that's
actually a pretty good score.

485
00:37:02,000 --> 00:37:07,000
And so you could think about,
say, what would be true of a

486
00:37:07,000 --> 00:37:11,000
complex that was linear along
z, what would be the most

487
00:37:11,000 --> 00:37:13,000
stabilized, for example.

488
00:37:13,000 --> 00:37:16,000
So these are the kinds of
questions you can get, and

489
00:37:16,000 --> 00:37:20,000
I think there are a few
on the problem-set.

490
00:37:20,000 --> 00:37:24,000
All right, so let's come
back together now and talk

491
00:37:24,000 --> 00:37:26,000
about magnetism again.

492
00:37:26,000 --> 00:37:30,000
So, we said in the beginning
that magnetism can be used to

493
00:37:30,000 --> 00:37:35,000
figure out geometry in, say, a
metal cluster in an enzyme, and

494
00:37:35,000 --> 00:37:39,000
let's give an example of
how that could be true.

495
00:37:39,000 --> 00:37:44,000
So, suppose you have a nickel
plus 2 system, so that would be

496
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

497
00:37:49,000 --> 00:37:51,000
found to be diamagnetic.

498
00:37:51,000 --> 00:37:56,000
And from that, we may be able
to guess, using these kinds of

499
00:37:56,000 --> 00:37:59,000
diagrams, whether it has
square planar geometry,

500
00:37:59,000 --> 00:38:03,000
tetrahedral geometry,
or octahedral geometry.

501
00:38:03,000 --> 00:38:08,000
We can predict the geometry
based on that information.

502
00:38:08,000 --> 00:38:11,000
Let's think about
how that's true.

503
00:38:11,000 --> 00:38:14,000
We have a d 8 system.

504
00:38:14,000 --> 00:38:17,000
Think about octahedral
for a minute.

505
00:38:17,000 --> 00:38:24,000
Are there two options for how
this might look in this case?

506
00:38:24,000 --> 00:38:26,000
Is there going to be a
difference in electron

507
00:38:26,000 --> 00:38:32,000
configurations if it's a weak
field or a strong field?

508
00:38:32,000 --> 00:38:36,000
So, write it out on your
handout and tell me whether

509
00:38:36,000 --> 00:38:54,000
it would be true, think
about it both ways.

510
00:38:54,000 --> 00:38:58,000
Is there a difference?

511
00:38:58,000 --> 00:39:00,000
So, you would end up
getting the same thing

512
00:39:00,000 --> 00:39:01,000
in this particular case.

513
00:39:01,000 --> 00:39:05,000
So if it's a weak field and
you put in 1, 2, 3, then jump

514
00:39:05,000 --> 00:39:09,000
up here, 4, 5, and then you
have to come back, 6, 7, 8.

515
00:39:09,000 --> 00:39:13,000
Or you could pair up all the
ones on the bottom first and

516
00:39:13,000 --> 00:39:16,000
then go up there, but you
actually get the same result no

517
00:39:16,000 --> 00:39:21,000
matter which way you put them
in, the diagram looks the same.

518
00:39:21,000 --> 00:39:24,000
So it doesn't matter in this
case if it is a weak or strong

519
00:39:24,000 --> 00:39:27,000
field, you end up with those
number of electrons with the

520
00:39:27,000 --> 00:39:31,000
exact same configuration.

521
00:39:31,000 --> 00:39:33,000
So, we know what
that looks like.

522
00:39:33,000 --> 00:39:36,000
Well, what about square planar.

523
00:39:36,000 --> 00:39:38,000
So let's put our
electrons in there.

524
00:39:38,000 --> 00:39:41,000
We'll start at the bottom,
we'll just put them in.

525
00:39:41,000 --> 00:39:44,000
I'm not going to worry too much
about whether we can jump up or

526
00:39:44,000 --> 00:39:48,000
not, we'll just go and pair
them up as we go down here, and

527
00:39:48,000 --> 00:39:52,000
then go up here, and now we've
put in our eight electrons.

528
00:39:52,000 --> 00:39:56,000
So, how close these are, we're
just going to put them all in.

529
00:39:56,000 --> 00:39:59,000
We're just going to be very
careful not to bump up any

530
00:39:59,000 --> 00:40:04,000
electrons there unless we
absolutely have to, because d x

531
00:40:04,000 --> 00:40:08,000
squared minus y squared is very
much more destabilized in the

532
00:40:08,000 --> 00:40:11,000
square planar system, so we're
going to want to pair all

533
00:40:11,000 --> 00:40:15,000
our electrons up in those
lower energy orbitals.

534
00:40:15,000 --> 00:40:18,000
So even if we sort of
did it a different way,

535
00:40:18,000 --> 00:40:19,000
that's what we would get.

536
00:40:19,000 --> 00:40:22,000
So we're going to want to pair
everything up before we go

537
00:40:22,000 --> 00:40:25,000
up to that top one there.

538
00:40:25,000 --> 00:40:26,000
So there's our square planar.

539
00:40:26,000 --> 00:40:28,000
Well, what about tetrahedral.

540
00:40:28,000 --> 00:40:31,000
How are we going
to fill these up?

541
00:40:31,000 --> 00:40:37,000
Do we want to pair first, or
we do want to put them to the

542
00:40:37,000 --> 00:40:40,000
full extent possible singly?

543
00:40:40,000 --> 00:40:43,000
Single, right, it's going to be
a weak field, there's not a big

544
00:40:43,000 --> 00:40:46,000
splitting here between these,
so we'll put them in, there's

545
00:40:46,000 --> 00:40:53,000
1, 2, 3, 4, 5, 6, 7, 8.

546
00:40:53,000 --> 00:40:55,000
All right, so now we can
consider which of these will

547
00:40:55,000 --> 00:40:58,000
be paramagnetic and which
will be diamagnetic.

548
00:40:58,000 --> 00:41:01,000
What's octahedral?

549
00:41:01,000 --> 00:41:05,000
It's paramagnetic, we
have unpaired electrons.

550
00:41:05,000 --> 00:41:08,000
What about square planar?

551
00:41:08,000 --> 00:41:10,000
Square planar's diamagnetic.

552
00:41:10,000 --> 00:41:11,000
And what about tetrahedral?

553
00:41:11,000 --> 00:41:14,000
Paramagnetic.

554
00:41:14,000 --> 00:41:20,000
So, if the experimental data
told us that a nickel center in

555
00:41:20,000 --> 00:41:23,000
an enzyme was diamagnetic, and
we were trying to decide

556
00:41:23,000 --> 00:41:27,000
between those three geometries,
it really seems like square

557
00:41:27,000 --> 00:41:31,000
planar is going to
be our best guess.

558
00:41:31,000 --> 00:41:34,000
And so, let me show
you an example of a

559
00:41:34,000 --> 00:41:39,000
square planar system.

560
00:41:39,000 --> 00:41:44,000
And so this particular nickel
is in a square planar system.

561
00:41:44,000 --> 00:41:50,000
It has four ligands that are
all in the same plane, and it

562
00:41:50,000 --> 00:41:54,000
is a square planar center for a
nickel, so that's one example.

563
00:41:54,000 --> 00:41:58,000
And this is a cluster
that's involved in life

564
00:41:58,000 --> 00:42:01,000
on carbon dioxide.

565
00:42:01,000 --> 00:42:04,000
All right, so that's
different geometries,

566
00:42:04,000 --> 00:42:05,000
you're set with that.

567
00:42:05,000 --> 00:42:09,000
Monday we're going to talk
about colors of coordination

568
00:42:09,000 --> 00:42:12,000
complexes, which all have to do
with the different geometries,

569
00:42:12,000 --> 00:42:16,000
paired and unpaired electrons,
high field, low spin,

570
00:42:16,000 --> 00:42:19,000
strong field, weak field.

571
00:42:19,000 --> 00:42:21,000
Have a nice weekend.

572
00:42:21,000 --> 00:42:22,000