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

0:00:48.000,0:01:02.000
the clicker question.

0:01:02.000,0:01:09.000
OK, 76, I think that says,[br]%, which is not bad, but

0:01:09.000,0:01:12.000
we should be at 100%.

0:01:12.000,0:01:17.000
So, when you're past the[br]equivalence point, so you've

0:01:17.000,0:01:20.000
converted all of your weak, in[br]this case, acid to its

0:01:20.000,0:01:25.000
conjugate base, and because it[br]was a weak acid, the conjugate

0:01:25.000,0:01:28.000
base is going to be a weak[br]based and so it's not

0:01:28.000,0:01:31.000
contributing a whole lot it'll[br]make the solution basic, but

0:01:31.000,0:01:35.000
it's nothing compared to adding[br]strong base in there.

0:01:35.000,0:01:38.000
So even though you have[br]the weak base around, at

0:01:38.000,0:01:41.000
this point it's really[br]a strong base problem.

0:01:41.000,0:01:45.000
So you would calculate this by[br]looking at how many mils of the

0:01:45.000,0:01:50.000
strong base you've added past,[br]and figure out the number of

0:01:50.000,0:01:54.000
moles that there are, and[br]divide by the total volume.

0:01:54.000,0:01:57.000
So this was like one of the[br]problems on the exam, and one

0:01:57.000,0:02:00.000
thing that I thought was[br]interesting on the exam is that

0:02:00.000,0:02:03.000
more people seemed to get the[br]hard problem right than this,

0:02:03.000,0:02:05.000
which was the easy problem.

0:02:05.000,0:02:10.000
So we'll see on the final,[br]there will be an acid based

0:02:10.000,0:02:14.000
titration problem on the[br]final, at least one.

0:02:14.000,0:02:18.000
So let's see if we can[br]get, then, the easy and

0:02:18.000,0:02:20.000
the hard ones right.

0:02:20.000,0:02:22.000
So you've mastered the hard[br]ones and let's see if you can

0:02:22.000,0:02:29.000
learn how to do the easy ones[br]as well for the final exam.

0:02:29.000,0:02:33.000
OK, so we're going to continue[br]with transition metals.

0:02:33.000,0:02:37.000
We were talking about crystal[br]field theory and magnetism, and

0:02:37.000,0:02:42.000
you should have a handout for[br]today, and you should also have

0:02:42.000,0:02:48.000
some equipment to make models[br]of orbitals and coordination

0:02:48.000,0:02:51.000
complexes -- these[br]are not snacks.

0:02:51.000,0:02:59.000
They can be snacks later, right[br]now they're a model kit.

0:02:59.000,0:03:05.000
All right, so I'm going to[br]introduce you to some terms

0:03:05.000,0:03:09.000
that we're going to come back[br]you at the end of today's

0:03:09.000,0:03:12.000
lecture, and then we're going[br]to talk about the shapes of

0:03:12.000,0:03:14.000
coordination complexes.

0:03:14.000,0:03:18.000
So, magnetism.

0:03:18.000,0:03:21.000
So we talked last time, before[br]the exam, if you remember,

0:03:21.000,0:03:25.000
about high spin and low spin,[br]unpaired electrons and

0:03:25.000,0:03:26.000
paired electrons.

0:03:26.000,0:03:29.000
Well, compounds that have[br]unpaired electrons are

0:03:29.000,0:03:33.000
paramagnetic, they're attracted[br]by a magnetic field, and those

0:03:33.000,0:03:36.000
where the electrons are paired[br]are diamagnetic are repelled

0:03:36.000,0:03:38.000
by a magnetic field.

0:03:38.000,0:03:43.000
So you can tell whether a[br]coordination complex is

0:03:43.000,0:03:46.000
paramagnetic or diamagnetic,[br]you can test the magnetism,

0:03:46.000,0:03:51.000
and that'll give you some[br]information about the electron

0:03:51.000,0:03:55.000
configuration of the d orbitals[br]in that coordination complex.

0:03:55.000,0:03:59.000
And that can tell you[br]about the geometry.

0:03:59.000,0:04:02.000
And so you'll see that by the[br]end we're going to talk about

0:04:02.000,0:04:06.000
different types of energy[br]orbitals when you have

0:04:06.000,0:04:07.000
different geometries.

0:04:07.000,0:04:11.000
So why might you care about the[br]geometry of a metal center.

0:04:11.000,0:04:15.000
Well, people who study proteins[br]that have metal centers care a

0:04:15.000,0:04:17.000
lot about the geometry of them.

0:04:17.000,0:04:20.000
So let me just give[br]you one example.

0:04:20.000,0:04:25.000
We talked a lot about energy in[br]the course this semester, so we

0:04:25.000,0:04:28.000
need catalysts for removing[br]carbon monoxide and carbon

0:04:28.000,0:04:31.000
dioxide from the environment.

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

0:04:35.000,0:04:38.000
proteins that can do this, and[br]people have been interested in

0:04:38.000,0:04:41.000
mimicking that chemistry[br]to remove these gases

0:04:41.000,0:04:43.000
from the environment.

0:04:43.000,0:04:46.000
So let me tell you these[br]enzymes are organisms.

0:04:46.000,0:04:52.000
And this is pretty amazing,[br]some of these microorganisms.

0:04:52.000,0:04:55.000
So, over here there's one[br]-- it basically lives

0:04:55.000,0:04:57.000
on carbon monoxide.

0:04:57.000,0:05:00.000
I mean that's -- you know[br]alternative sources of energy

0:05:00.000,0:05:02.000
are one thing, but that's[br]really quite a crazy thing

0:05:02.000,0:05:03.000
that this guy does.

0:05:03.000,0:05:07.000
So, you can grow it up in these[br]big vats and pump in carbon

0:05:07.000,0:05:11.000
monoxide and it's like oh,[br]food, and they grow and

0:05:11.000,0:05:14.000
multiply, and they're very,[br]very happy in this carbon

0:05:14.000,0:05:16.000
monoxide environment.

0:05:16.000,0:05:19.000
There are also microorganisms[br]that live on carbon dioxide as

0:05:19.000,0:05:23.000
their energy and[br]a carbon source.

0:05:23.000,0:05:27.000
And so these organisms have[br]enzymes in them that have metal

0:05:27.000,0:05:30.000
centers, and those metal[br]centers are responsible for the

0:05:30.000,0:05:35.000
ability of these organisms to[br]live on these kind of bizarre

0:05:35.000,0:05:37.000
greenhouse gases[br]and pollutants.

0:05:37.000,0:05:41.000
So people would like to[br]understand how this works.

0:05:41.000,0:05:44.000
So microbes have been estimated[br]to remove hundred, a million

0:05:44.000,0:05:48.000
tons of carbon monoxide from[br]the environment every year,

0:05:48.000,0:05:52.000
producing about one trillion[br]kilograms of acetate from

0:05:52.000,0:05:53.000
these greenhouse gases.

0:05:53.000,0:05:57.000
And so, what do these catalysts[br]look like and these enzymes,

0:05:57.000,0:05:59.000
what do these metal clusters[br]look like that do

0:05:59.000,0:06:00.000
this chemistry.

0:06:00.000,0:06:03.000
And this was sort of a rough[br]model of what they look like,

0:06:03.000,0:06:07.000
and they thought it had iron[br]and sulfur and then a nickel in

0:06:07.000,0:06:10.000
some geometry, but they had no[br]idea sort of where the nickel

0:06:10.000,0:06:12.000
was and how it was coordinated.

0:06:12.000,0:06:15.000
And so before there was any[br]kind of three dimensional

0:06:15.000,0:06:18.000
information, they used[br]spectroscopy, and they

0:06:18.000,0:06:21.000
considered whether it was[br]paramagnetic or diamagnetic to

0:06:21.000,0:06:24.000
get a sense of what the[br]geometry around the metal was.

0:06:24.000,0:06:26.000
So we're going to talk about[br]different coordination

0:06:26.000,0:06:30.000
geometries and how many[br]unpaired or paired electrons

0:06:30.000,0:06:33.000
you would expect, depending[br]on those geometries today.

0:06:33.000,0:06:38.000
And so, crystal field theory,[br]again, can help you help

0:06:38.000,0:06:42.000
explain/rationalize the[br]properties of these transition

0:06:42.000,0:06:46.000
metal complexes or[br]coordination complexes.

0:06:46.000,0:06:50.000
So, to help us think about[br]geometry, I always find

0:06:50.000,0:06:54.000
for myself that it's[br]helpful to have models.

0:06:54.000,0:07:01.000
So not everyone can have such[br]large models as these, but you

0:07:01.000,0:07:06.000
can all have your own little[br]models of these geometries.

0:07:06.000,0:07:12.000
So, what we have available to[br]you are some mini marshmallows,

0:07:12.000,0:07:15.000
which, of course, as we all[br]know, are representative of d

0:07:15.000,0:07:20.000
orbitals, and jelly beans,[br]which we all know are useful

0:07:20.000,0:07:22.000
for making coordination[br]complexes.

0:07:22.000,0:07:27.000
So, what you can do with your[br]mini marshmallows is you can

0:07:27.000,0:07:30.000
put together to make[br]your different sets.

0:07:30.000,0:07:37.000
And so, over here we have --[br]oh, actually it says gum drops

0:07:37.000,0:07:39.000
-- you don't have gum drops[br]this year, I changed up here, I

0:07:39.000,0:07:41.000
forgot to change it down here.

0:07:41.000,0:07:42.000
We have mini marshmallows.

0:07:42.000,0:07:47.000
Dr. Taylor went out and tried[br]to purchase enough gum drops to

0:07:47.000,0:07:50.000
do this experiment, and[br]discovered that Cambridge only

0:07:50.000,0:07:55.000
had 300 gum drops, so we have[br]mini marshmallows

0:07:55.000,0:07:56.000
instead today.

0:07:56.000,0:07:57.000
But this gives you the idea.

0:07:57.000,0:08:02.000
You can take one toothpick and[br]you can make d z squared,

0:08:02.000,0:08:06.000
putting on your orbitals, you[br]have your donut in the middle,

0:08:06.000,0:08:09.000
and then your two lobes,[br]which run along the z-axis.

0:08:09.000,0:08:16.000
And then for your other sets of[br]orbitals, you can take these

0:08:16.000,0:08:23.000
two toothpicks and put on these[br]sets of mini marshmallows, and

0:08:23.000,0:08:27.000
handily, you can just have one[br]for all of the other d

0:08:27.000,0:08:30.000
orbitals, because depending on[br]how you hold it, it can

0:08:30.000,0:08:35.000
represent all of the other d[br]orbitals just very well.

0:08:35.000,0:08:37.000
So, you can just have one of[br]these for all the others

0:08:37.000,0:08:40.000
and then your d z squared.

0:08:40.000,0:08:44.000
So what we're going to do when[br]we have our orbitals set up,

0:08:44.000,0:08:49.000
then we can think about how[br]ligands in particular

0:08:49.000,0:08:53.000
positions, in particular[br]geometries would clash with our

0:08:53.000,0:08:55.000
orbitals -- where there'd be[br]big repulsions or

0:08:55.000,0:08:59.000
small repulsions.

0:08:59.000,0:09:03.000
So, any other people missing[br]their jelly beans or

0:09:03.000,0:09:05.000
their marshmallows?

0:09:05.000,0:09:34.000
Please, raise your[br]hand, we have extras.

0:09:34.000,0:09:36.000
So, those of you who have[br]them, go ahead and start

0:09:36.000,0:10:08.000
making your d orbitals.

0:10:08.000,0:10:54.000
All right, so if you're[br]finished with your two d

0:10:54.000,0:11:01.000
orbitals, you can start making[br]an octahedral complex.

0:11:01.000,0:11:05.000
So in your geometries set,[br]you'll have a big gum which can

0:11:05.000,0:11:11.000
be your center metal -- you'll[br]have a big jelly bean -- sorry,

0:11:11.000,0:11:14.000
big jelly beans and small jelly[br]beans are our ligands, or our

0:11:14.000,0:11:18.000
negative point charges, and[br]you can set up and make an

0:11:18.000,0:13:05.000
octahedral geometry here.

0:13:05.000,0:13:10.000
OK, so as you're finishing this[br]up, I'm going to review what we

0:13:10.000,0:13:13.000
talked about before the exam --[br]so this isn't in today's

0:13:13.000,0:13:15.000
lecture handouts, it was in[br]last time, which we

0:13:15.000,0:13:17.000
already went over.

0:13:17.000,0:13:20.000
But sometimes I've discovered[br]that when there's an exam in

0:13:20.000,0:13:23.000
the middle, there needs to be a[br]bit of a refresher, it's hard

0:13:23.000,0:13:28.000
to remember what happened[br]before the exam, and you

0:13:28.000,0:13:31.000
have your models to[br]think about this.

0:13:31.000,0:13:34.000
So, before the exam, we had[br]talked about the octahedral

0:13:34.000,0:13:38.000
case, and how compared to a[br]spherical situation where the

0:13:38.000,0:13:41.000
ligands are everywhere[br]distributed around the metals

0:13:41.000,0:13:45.000
where all d orbitals would be[br]affected/repulsed by the

0:13:45.000,0:13:50.000
ligands in a symmetric fashion[br]equally, when you have them put

0:13:50.000,0:13:54.000
as particular positions in[br]geometry, then they're going to

0:13:54.000,0:13:57.000
affect the different d[br]orbitals differently.

0:13:57.000,0:14:00.000
And so, if you have your d z[br]squared made, and you have your

0:14:00.000,0:14:04.000
octahedral made, you can sort[br]of hold these up and realize

0:14:04.000,0:14:09.000
that you would have repulsion[br]from your ligands along the

0:14:09.000,0:14:14.000
z-axis directly toward your[br]orbitals from d z squared.

0:14:14.000,0:14:16.000
So that would be[br]highly repulsive.

0:14:16.000,0:14:20.000
The ligands are along the[br]z-axis, the d orbitals are

0:14:20.000,0:14:23.000
along the z-axis, so the[br]ligands, the negative point

0:14:23.000,0:14:25.000
charge ligands are going[br]to be pointing right

0:14:25.000,0:14:27.000
toward your orbitals.

0:14:27.000,0:14:34.000
And if you hold up this as a d[br]x squared y squared orbital

0:14:34.000,0:14:38.000
where the orbitals are right[br]along the x-axis and right

0:14:38.000,0:14:41.000
along the y-axis and you hold[br]that up, remember, your ligands

0:14:41.000,0:14:45.000
are right along the x-axis[br]and right along the y-axis.

0:14:45.000,0:14:49.000
So, you should also have[br]significant repulsion for d x

0:14:49.000,0:14:53.000
squared minus y squared, and[br]octahedrally oriented ligands.

0:14:53.000,0:15:01.000
In contrast, the ligands set[br]that are 45 degrees off-axis,

0:15:01.000,0:15:08.000
so d y z, d x z, and d x y,[br]they're all 45 degrees off.

0:15:08.000,0:15:11.000
Your ligands are along the[br]axis, but your orbitals

0:15:11.000,0:15:14.000
are 45 degrees off-axis.

0:15:14.000,0:15:16.000
So if you look at that[br]together, you'll see that

0:15:16.000,0:15:19.000
whichever one you look at, the[br]ligands are not going to be

0:15:19.000,0:15:22.000
pointing directly toward[br]those d orbitals.

0:15:22.000,0:15:24.000
The orbitals are off-axis,[br]ligands are on-axis.

0:15:24.000,0:15:29.000
So there will be much[br]smaller repulsions there.

0:15:29.000,0:15:37.000
And that we talked about the[br]fact that for d x squared minus

0:15:37.000,0:15:40.000
y squared and d z squared,[br]they're both have experienced

0:15:40.000,0:15:44.000
large repulsions, they're both[br]degenerate in energy, they go

0:15:44.000,0:15:48.000
up in energy, whereas these[br]three d orbitals, smaller

0:15:48.000,0:15:52.000
repulsion, and they're also[br]degenerate with respect to each

0:15:52.000,0:15:55.000
other, and they're stabilized[br]compared to these guys up here.

0:15:55.000,0:15:58.000
So you can try to hold those up[br]and convince yourself that

0:15:58.000,0:16:01.000
that's true for the[br]octahedral case.

0:16:01.000,0:16:04.000
So, that's what we talked about[br]last time, and now we want to

0:16:04.000,0:16:08.000
-- oh, and I'll just remind you[br]we looked at these splitting

0:16:08.000,0:16:09.000
diagrams as well.

0:16:09.000,0:16:13.000
We looked at the average energy[br]of the d orbitals -- d z

0:16:13.000,0:16:17.000
squared and d x squared minus[br]y squared go up in energy,

0:16:17.000,0:16:24.000
and then the other three d[br]orbitals go down in energy.

0:16:24.000,0:16:27.000
So now we want to consider[br]what happens with

0:16:27.000,0:16:31.000
different geometries.

0:16:31.000,0:16:35.000
So now you can turn your[br]octahedral case into a

0:16:35.000,0:16:42.000
square planar case, and[br]how am I going to do that?

0:16:42.000,0:16:45.000
Yeah, so we can just take off[br]the top and the bottom and we

0:16:45.000,0:16:51.000
have our nice square planar[br]case, and try to make a

0:16:51.000,0:16:57.000
tetrahedral complex as well.

0:16:57.000,0:16:59.000
And here's an example[br]of a tetrahedral one.

0:16:59.000,0:17:02.000
Again, you can take a jelly[br]bean in the middle, and big

0:17:02.000,0:17:05.000
jelly bean, and then the[br]smaller ones on the outside.

0:17:05.000,0:17:08.000
So what angles am I going for[br]here in the tetrahedral case?

0:17:08.000,0:17:10.000
109 .

0:17:10.000,0:17:11.000
5.

0:17:11.000,0:17:15.000
So you can go ahead and make[br]your tetrahedral complex,

0:17:15.000,0:17:17.000
and don't worry so[br]much about the 0 .

0:17:17.000,0:18:36.000
5, but we'll see if people can[br]do a good job with the 109.

0:18:36.000,0:18:40.000
OK, how are your tetrahedral[br]complexes coming?

0:18:40.000,0:18:46.000
Do they look like this sort of?

0:18:46.000,0:18:49.000
So let me define for you how[br]we're going to consider

0:18:49.000,0:18:52.000
the tetrahedral case.

0:18:52.000,0:18:56.000
So, in the tetrahedral case,[br]we're going to have the x-axis

0:18:56.000,0:19:00.000
comes out of the plane, the[br]y-axis is this way, z-axis

0:19:00.000,0:19:02.000
again, up and down.

0:19:02.000,0:19:05.000
We're going to have one ligand[br]coming out here, another going

0:19:05.000,0:19:07.000
back, and then these two[br]are pretty much in the

0:19:07.000,0:19:09.000
plane of the screen.

0:19:09.000,0:19:12.000
So this is sort of how I'm[br]holding the tetrahedral complex

0:19:12.000,0:19:18.000
with respect to the x, z,[br]and y coordinate system.

0:19:18.000,0:19:21.000
So, there is a splitting,[br]energy splitting, associated

0:19:21.000,0:19:25.000
with tetrahedral, and it's[br]going to be smaller than

0:19:25.000,0:19:29.000
octahedral because none of[br]these ligands will be pointing

0:19:29.000,0:19:31.000
directly toward the orbitals.

0:19:31.000,0:19:36.000
But let's consider which[br]orbitals are going to be most

0:19:36.000,0:19:42.000
affected by a tetrahedral case.

0:19:42.000,0:19:48.000
So, let's consider d z squared.

0:19:48.000,0:19:49.000
What do you think?

0:19:49.000,0:19:52.000
Is that going to be[br]particularly -- are the ligands

0:19:52.000,0:19:55.000
pointing toward d z squared?

0:19:55.000,0:19:57.000
No.

0:19:57.000,0:20:01.000
And d x squared minus y[br]squared, we can think of,

0:20:01.000,0:20:04.000
what about that one?

0:20:04.000,0:20:06.000
No, not really.

0:20:06.000,0:20:12.000
What about d x y,[br]d y z, and d x y?

0:20:12.000,0:20:17.000
Moreso.

0:20:17.000,0:20:20.000
So, if you try holding up your[br]tetrahedral in our coordinate

0:20:20.000,0:20:25.000
system, and then hold your d[br]orbitals 45 degrees off-axis,

0:20:25.000,0:20:28.000
it's not perfect, they're not[br]pointing directly toward them,

0:20:28.000,0:20:31.000
but it's a little closer than[br]for the d orbitals that

0:20:31.000,0:20:36.000
are directly on-axis.

0:20:36.000,0:20:41.000
So, if we look at this, we see[br]that the orbitals are going to

0:20:41.000,0:20:46.000
be split in the exact opposite[br]way of the octahedral system.

0:20:46.000,0:20:50.000
In the octahedral system, the[br]ligands are on-axis, so the

0:20:50.000,0:20:53.000
orbitals that are on-axis, d x[br]squared minus y squared and d

0:20:53.000,0:20:56.000
z squared are going to[br]be the most affected.

0:20:56.000,0:20:59.000
But with tetrahedral, the[br]ligands are off-axis, so the

0:20:59.000,0:21:02.000
d orbitals that are also[br]off-axis are going to

0:21:02.000,0:21:03.000
be the most affected.

0:21:03.000,0:21:06.000
But they're not going to be as[br]dramatically affected, so the

0:21:06.000,0:21:09.000
splitting is actually[br]smaller in this case.

0:21:09.000,0:21:13.000
So here, with tetrahedral,[br]you have the opposite of

0:21:13.000,0:21:16.000
the octahedral system.

0:21:16.000,0:21:19.000
And you can keep these and[br]try to convince yourself

0:21:19.000,0:21:25.000
of that later if you have[br]trouble visualizing it.

0:21:25.000,0:21:29.000
So, you'll have more repulsion[br]between the ligands as negative

0:21:29.000,0:21:32.000
point charges, and the d[br]orbitals that are 45 degrees

0:21:32.000,0:21:36.000
off-axis than you do with[br]the two d orbitals

0:21:36.000,0:21:39.000
that are on-axis.

0:21:39.000,0:21:44.000
So here, d x squared minus y[br]squared and d z squared have

0:21:44.000,0:21:47.000
the same energy with respect to[br]each other, they're degenerate.

0:21:47.000,0:21:54.000
And we have our d y z, x z,[br]and x y have the same energy

0:21:54.000,0:21:58.000
with respect to each other,[br]they are also degenerate.

0:21:58.000,0:22:01.000
So it's the same sets that[br]are degenerate as with

0:22:01.000,0:22:08.000
octahedral, but they're[br]all affected differently.

0:22:08.000,0:22:13.000
So now let's look at the energy[br]diagrams and compare the

0:22:13.000,0:22:17.000
octahedral system with[br]the tetrahedral system.

0:22:17.000,0:22:20.000
Remember an octahedral, we[br]had the two orbitals going

0:22:20.000,0:22:22.000
up and three going down.

0:22:22.000,0:22:25.000
The splitting, the energy[br]difference between

0:22:25.000,0:22:26.000
them was abbreviated.

0:22:26.000,0:22:29.000
The octahedral crystal field[br]splitting energy, with a

0:22:29.000,0:22:31.000
little o for octahedral.

0:22:31.000,0:22:35.000
We now have a t for[br]tetrahedral, so we have

0:22:35.000,0:22:37.000
a different name.

0:22:37.000,0:22:41.000
And so here is now[br]our tetrahedral set.

0:22:41.000,0:22:44.000
You notice it's the opposite of[br]octahedral, so the orbitals

0:22:44.000,0:22:49.000
that were most destabilized in[br]the octahedral case are now

0:22:49.000,0:22:54.000
more stabilized down here, so[br]we've moved down in energy.

0:22:54.000,0:22:58.000
And the orbitals that are[br]off-axis, 45 degrees off-axis,

0:22:58.000,0:23:02.000
which were stabilized in the[br]octahedral system, because none

0:23:02.000,0:23:05.000
of ligands were pointing right[br]toward them, now those ligands

0:23:05.000,0:23:09.000
are a bit closer so they jump[br]up in energy, and so we have

0:23:09.000,0:23:15.000
this swap between the two.

0:23:15.000,0:23:18.000
So, we have some new[br]labels as well.

0:23:18.000,0:23:24.000
So, we had e g up here as an[br]abbreviation for these sets

0:23:24.000,0:23:27.000
of orbitals, and now that's[br]just referred to as e.

0:23:27.000,0:23:32.000
Notice the book in one place[br]has an e 2, but uses e in all

0:23:32.000,0:23:35.000
the other places, so just[br]use e, the e 2 was a

0:23:35.000,0:23:36.000
mistake in the book.

0:23:36.000,0:23:42.000
And then we have t 2 g[br]becomes t 2 up here.

0:23:42.000,0:23:45.000
So we have this slightly[br]different nomenclature and we

0:23:45.000,0:23:49.000
have this flip in direction.

0:23:49.000,0:23:53.000
So, the other thing that is[br]important to emphasize is that

0:23:53.000,0:23:58.000
the tetrahedral splitting[br]energy is smaller, because none

0:23:58.000,0:24:00.000
of those ligands are pointing[br]directly toward any

0:24:00.000,0:24:01.000
of the d orbitals.

0:24:01.000,0:24:05.000
So here there is a much larger[br]difference, here there is a

0:24:05.000,0:24:09.000
smaller difference, so that's[br]why it's written much closer

0:24:09.000,0:24:14.000
together, so that's smaller.

0:24:14.000,0:24:19.000
And because of that, many[br]tetrahedral complexes are high

0:24:19.000,0:24:21.000
spin, and in this course, you[br]can assume that they're

0:24:21.000,0:24:23.000
all high spin.

0:24:23.000,0:24:25.000
So that means there's a weak[br]field, there's not a big

0:24:25.000,0:24:31.000
energy difference between[br]those orbital sets.

0:24:31.000,0:24:35.000
And again, we're going to --[br]since we're going to consider

0:24:35.000,0:24:38.000
how much they go up and down[br]in energy, the overall

0:24:38.000,0:24:40.000
energy is maintained.

0:24:40.000,0:24:45.000
So here we had two orbitals[br]going up by 3/5, three

0:24:45.000,0:24:47.000
orbitals going down by 2/5.

0:24:47.000,0:24:50.000
So here, we have three orbitals[br]going up, so they'll go up in

0:24:50.000,0:24:54.000
energy by 2/5, two orbitals go[br]down, so they'll be going

0:24:54.000,0:24:57.000
down in energy by 3/5.

0:24:57.000,0:25:01.000
So again, it's the opposite[br]of the octahedral system.

0:25:01.000,0:25:03.000
It's opposite pretty much in[br]every way except that the

0:25:03.000,0:25:06.000
splitting energy is much[br]smaller, it's not as large

0:25:06.000,0:25:11.000
for the tetrahedral complex.

0:25:11.000,0:25:15.000
All right, so let's look at an[br]example, and we're going to

0:25:15.000,0:25:20.000
consider a chromium, and like[br]we did before, we have to first

0:25:20.000,0:25:26.000
figure out the d count, so[br]we have chromium plus 3.

0:25:26.000,0:25:32.000
So what is our d count here?

0:25:32.000,0:25:36.000
You know where chromium is,[br]what its group number --

0:25:36.000,0:25:42.000
here is a periodic table.

0:25:42.000,0:25:45.000
So what is the d count?

0:25:45.000,0:25:46.000
3.

0:25:46.000,0:25:53.000
So we have 6 minus 3,[br]3 -- a d 3 system.

0:25:53.000,0:25:58.000
And now, why don't you tell me[br]how you would fill in those

0:25:58.000,0:26:02.000
three electrons in a[br]tetrahedral case.

0:26:02.000,0:26:56.000
Have a clicker question there.

0:26:56.000,0:27:00.000
So, notice that in addition to[br]having electron configurations

0:27:00.000,0:27:02.000
that are different, the d[br]orbitals are labelled

0:27:02.000,0:27:29.000
differently.

0:27:29.000,0:27:44.000
OK, 10 more seconds.

0:27:44.000,0:27:47.000
OK, very good, 80%.

0:27:47.000,0:27:49.000
So, let's take a look at that.

0:27:49.000,0:27:53.000
So down here, we're going to[br]have then our d x squared minus

0:27:53.000,0:27:58.000
y squared, d z squared orbitals[br]up in the top, we have

0:27:58.000,0:28:05.000
x y and x z and y z.

0:28:05.000,0:28:10.000
Again, the orbitals that are[br]on-axis are repelled a little

0:28:10.000,0:28:14.000
less than the orbitals that are[br]off-axis in a tetrahedral case.

0:28:14.000,0:28:18.000
And then we put in our[br]electrons, we start down here.

0:28:18.000,0:28:21.000
And then one of the questions[br]is do we keep down here and

0:28:21.000,0:28:26.000
pair up or go up here, and the[br]answer is that you

0:28:26.000,0:28:27.000
would go up here.

0:28:27.000,0:28:31.000
Does someone want to tell me[br]why they think that's true?

0:28:31.000,0:28:31.000
Yeah.

0:28:31.000,0:28:33.000
STUDENT: [INAUDIBLE]

0:28:33.000,0:28:36.000
PROFESSOR: Right, because it[br]has a smaller splitting energy.

0:28:36.000,0:28:38.000
So, the way that we were[br]deciding before with the weak

0:28:38.000,0:28:41.000
field and the strong field, if[br]it's a weak field, it doesn't

0:28:41.000,0:28:43.000
take much energy to[br]put it up there.

0:28:43.000,0:28:45.000
So you go they don't want to[br]be paired, there's energy

0:28:45.000,0:28:47.000
associated with pairing.

0:28:47.000,0:28:51.000
But if there's a really huge[br]splitting energy, then it takes

0:28:51.000,0:28:54.000
less energy to pair them up[br]before you go that big

0:28:54.000,0:28:55.000
distance up there.

0:28:55.000,0:28:58.000
But in tetrahedral cases, the[br]splitting energy's always

0:28:58.000,0:29:02.000
small, so you're just going to[br]always fill them up singly

0:29:02.000,0:29:05.000
to the fullest extent[br]possible before you pair.

0:29:05.000,0:29:09.000
So this is like a weak field[br]case for the octahedral system,

0:29:09.000,0:29:12.000
and all tetrahedral complexes[br]are sort of the equivalent of

0:29:12.000,0:29:14.000
the weak field, because the[br]splitting energy is always

0:29:14.000,0:29:18.000
small in an octahedral case,[br]because none of the ligands'

0:29:18.000,0:29:21.000
negative point charges are[br]really pointing toward any of

0:29:21.000,0:29:25.000
those orbitals that much, so[br]it's not that big a difference.

0:29:25.000,0:29:30.000
So, here we have this and now[br]we can practice writing our d

0:29:30.000,0:29:33.000
to the n electron[br]configuration.

0:29:33.000,0:29:38.000
So what do I put here?

0:29:38.000,0:29:42.000
What do I put first?

0:29:42.000,0:29:46.000
So we put the e and then what?

0:29:46.000,0:29:47.000
Yup.

0:29:47.000,0:29:51.000
There are two electrons in the[br]e set of orbitals, and in the

0:29:51.000,0:29:55.000
t 2 orbitals, there's one.

0:29:55.000,0:29:59.000
So that is our d n[br]electron configuration.

0:29:59.000,0:30:03.000
And then we're also asked how[br]many unpaired electrons.

0:30:03.000,0:30:16.000
Unpaired electrons[br]and that is three.

0:30:16.000,0:30:16.000
All right.

0:30:16.000,0:30:21.000
So that's not too bad, that's[br]the tetrahedral case.

0:30:21.000,0:30:23.000
The hardest part is[br]probably making your

0:30:23.000,0:30:27.000
tetrahedral complex.

0:30:27.000,0:30:31.000
Now square planar.

0:30:31.000,0:30:34.000
So again, with the square[br]planar set you have your square

0:30:34.000,0:30:38.000
planar model -- we have[br]a bigger one down here.

0:30:38.000,0:30:43.000
And the axes is defined such[br]that we have ligands right

0:30:43.000,0:30:46.000
along x -- one coming out at[br]you and one going back, and

0:30:46.000,0:30:50.000
also ligands right[br]along the y-axis.

0:30:50.000,0:30:53.000
So as defined then, we've[br]gotten rid of our ligands

0:30:53.000,0:30:56.000
along the z-axis.

0:30:56.000,0:30:57.000
So, what do you predict?

0:30:57.000,0:31:04.000
Which two of these will be[br]the most destabilized now?

0:31:04.000,0:31:06.000
What would be the most[br]destabilized, what

0:31:06.000,0:31:09.000
do you guess?

0:31:09.000,0:31:13.000
You can hold up your[br]little sets here.

0:31:13.000,0:31:15.000
What's the most destabilized,[br]what's going to go up

0:31:15.000,0:31:19.000
the most in energy here?

0:31:19.000,0:31:22.000
Yeah, d z squared[br]minus y squared.

0:31:22.000,0:31:26.000
What do you predict might[br]be next, in terms of

0:31:26.000,0:31:29.000
most unfavorable?

0:31:29.000,0:31:30.000
Yeah, the x y one.

0:31:30.000,0:31:35.000
So these two now are going to[br]be the most destabilized, with

0:31:35.000,0:31:39.000
d x squared minus y squared[br]being a lot more destabilized

0:31:39.000,0:31:42.000
than just the x y, because[br]again, those d orbitals

0:31:42.000,0:31:47.000
are on-axis and these[br]ligands are on-axis.

0:31:47.000,0:31:51.000
So, let's take a look[br]at all of these again.

0:31:51.000,0:31:55.000
So in the octahedral case,[br]these were degenerate.

0:31:55.000,0:31:58.000
That's no longer true,[br]because there are no ligands

0:31:58.000,0:32:00.000
along the z-axis anymore.

0:32:00.000,0:32:03.000
So we took those off in going[br]from the octahedral to the

0:32:03.000,0:32:07.000
square planar, so you have much[br]less repulsion, but with the d

0:32:07.000,0:32:12.000
x squared minus y squared, you[br]still have a lot repulsion.

0:32:12.000,0:32:17.000
so then if we start building up[br]our case, and this diagram is,

0:32:17.000,0:32:19.000
I think, on the next page of[br]your handout, but I'm going to

0:32:19.000,0:32:21.000
start building it[br]all up together.

0:32:21.000,0:32:26.000
So now d x squared, y squared[br]is really high up, it's very

0:32:26.000,0:32:29.000
much more destabilized[br]than anybody else.

0:32:29.000,0:32:32.000
D z squared, on the[br]other hand, is down.

0:32:32.000,0:32:35.000
It's not -- it would be[br]stabilized compared -- it's

0:32:35.000,0:32:40.000
not nearly as destabilized[br]as the other system.

0:32:40.000,0:32:44.000
So then we go back[br]and look at these.

0:32:44.000,0:32:48.000
You told me that d x y would[br]probably be next, and

0:32:48.000,0:32:50.000
that's a very good guess.

0:32:50.000,0:32:53.000
You see you have more repulsion[br]than in the other two, because

0:32:53.000,0:32:56.000
the other orbitals have[br]some z component in them.

0:32:56.000,0:33:00.000
So you have less repulsion than[br]d x squared minus y squared,

0:33:00.000,0:33:04.000
because it's 45 degrees off,[br]but still that one is probably

0:33:04.000,0:33:07.000
going to be up a little bit[br]more in energy than

0:33:07.000,0:33:08.000
the other set.

0:33:08.000,0:33:13.000
These two here are stabilized[br]compared to the others, so

0:33:13.000,0:33:14.000
they're somewhere down here.

0:33:14.000,0:33:18.000
Now the exact sort of[br]arrangement can vary a little

0:33:18.000,0:33:22.000
bit, but the important points[br]are that the d x squared minus

0:33:22.000,0:33:26.000
y squared is the most[br]destabilized, d x y would be

0:33:26.000,0:33:31.000
next, and the other are[br]much lower in energy.

0:33:31.000,0:33:34.000
And we're not going to do this[br]how much up and down thing,

0:33:34.000,0:33:38.000
like the 3/5 and the[br]2/5 because it's more

0:33:38.000,0:33:40.000
complicated in this case.

0:33:40.000,0:33:43.000
So just the basic rationale you[br]need to know here, not the

0:33:43.000,0:33:52.000
exact energy differences[br]in this particular case.

0:33:52.000,0:33:58.000
OK, so now we've thought about[br]three different kinds of

0:33:58.000,0:34:01.000
geometries -- octahedral,[br]tetrahedral, and

0:34:01.000,0:34:02.000
the square planar.

0:34:02.000,0:34:07.000
You should be able to[br]rationalize, for any

0:34:07.000,0:34:10.000
geometry that I give[br]you, what would be true.

0:34:10.000,0:34:14.000
If I tell you the geometry and[br]how it compares with our frame,

0:34:14.000,0:34:19.000
with our axis frame of where[br]the z-axis is, you should be

0:34:19.000,0:34:21.000
able to tell me which[br]orbital sets would be

0:34:21.000,0:34:24.000
the most destabilized.

0:34:24.000,0:34:28.000
And to give you practice,[br]why don't you try

0:34:28.000,0:34:29.000
this one right here.

0:34:29.000,0:34:35.000
So we have a square pyramidal[br]case as drawn here with the

0:34:35.000,0:34:40.000
axes labeled z, y and x,[br]coming in and coming out.

0:34:40.000,0:34:46.000
Tell me which of the following[br]statements are true.

0:34:46.000,0:34:51.000
And if you want, you can take[br]your square planar and turn it

0:34:51.000,0:35:54.000
into the geometry[br]to help you out.

0:35:54.000,0:36:10.000
Let's just take[br]10 more seconds.

0:36:10.000,0:36:11.000
All right.

0:36:11.000,0:36:13.000
That was good.

0:36:13.000,0:36:15.000
People did well on[br]that question.

0:36:15.000,0:36:25.000
So, if we consider that we[br]had the top two are correct.

0:36:25.000,0:36:29.000
So, if we consider the d z[br]squared, now we've put a ligand

0:36:29.000,0:36:33.000
along z, so that is going to[br]cause that to be more

0:36:33.000,0:36:37.000
destabilized for this geometry[br]rather than square planar,

0:36:37.000,0:36:42.000
which doesn't have anything in[br]the z direction. ah And then in

0:36:42.000,0:36:47.000
terms, also, other orbitals[br]that have a component along z

0:36:47.000,0:36:52.000
are going to be affected a[br]little bit by that, but our

0:36:52.000,0:36:56.000
other one here is not going to[br]be true, so we just have all of

0:36:56.000,0:36:58.000
the above is not correct,[br]so we have this one.

0:36:58.000,0:37:02.000
So if we had up those, that's[br]actually a pretty good score.

0:37:02.000,0:37:07.000
And so you could think about,[br]say, what would be true of a

0:37:07.000,0:37:11.000
complex that was linear along[br]z, what would be the most

0:37:11.000,0:37:13.000
stabilized, for example.

0:37:13.000,0:37:16.000
So these are the kinds of[br]questions you can get, and

0:37:16.000,0:37:20.000
I think there are a few[br]on the problem-set.

0:37:20.000,0:37:24.000
All right, so let's come[br]back together now and talk

0:37:24.000,0:37:26.000
about magnetism again.

0:37:26.000,0:37:30.000
So, we said in the beginning[br]that magnetism can be used to

0:37:30.000,0:37:35.000
figure out geometry in, say, a[br]metal cluster in an enzyme, and

0:37:35.000,0:37:39.000
let's give an example of[br]how that could be true.

0:37:39.000,0:37:44.000
So, suppose you have a nickel[br]plus 2 system, so that would be

0:37:44.000,0:37:49.000
a d 8 system, so we have group[br]10 minus 2 or d 8, and it was

0:37:49.000,0:37:51.000
found to be diamagnetic.

0:37:51.000,0:37:56.000
And from that, we may be able[br]to guess, using these kinds of

0:37:56.000,0:37:59.000
diagrams, whether it has[br]square planar geometry,

0:37:59.000,0:38:03.000
tetrahedral geometry,[br]or octahedral geometry.

0:38:03.000,0:38:08.000
We can predict the geometry[br]based on that information.

0:38:08.000,0:38:11.000
Let's think about[br]how that's true.

0:38:11.000,0:38:14.000
We have a d 8 system.

0:38:14.000,0:38:17.000
Think about octahedral[br]for a minute.

0:38:17.000,0:38:24.000
Are there two options for how[br]this might look in this case?

0:38:24.000,0:38:26.000
Is there going to be a[br]difference in electron

0:38:26.000,0:38:32.000
configurations if it's a weak[br]field or a strong field?

0:38:32.000,0:38:36.000
So, write it out on your[br]handout and tell me whether

0:38:36.000,0:38:54.000
it would be true, think[br]about it both ways.

0:38:54.000,0:38:58.000
Is there a difference?

0:38:58.000,0:39:00.000
So, you would end up[br]getting the same thing

0:39:00.000,0:39:01.000
in this particular case.

0:39:01.000,0:39:05.000
So if it's a weak field and[br]you put in 1, 2, 3, then jump

0:39:05.000,0:39:09.000
up here, 4, 5, and then you[br]have to come back, 6, 7, 8.

0:39:09.000,0:39:13.000
Or you could pair up all the[br]ones on the bottom first and

0:39:13.000,0:39:16.000
then go up there, but you[br]actually get the same result no

0:39:16.000,0:39:21.000
matter which way you put them[br]in, the diagram looks the same.

0:39:21.000,0:39:24.000
So it doesn't matter in this[br]case if it is a weak or strong

0:39:24.000,0:39:27.000
field, you end up with those[br]number of electrons with the

0:39:27.000,0:39:31.000
exact same configuration.

0:39:31.000,0:39:33.000
So, we know what[br]that looks like.

0:39:33.000,0:39:36.000
Well, what about square planar.

0:39:36.000,0:39:38.000
So let's put our[br]electrons in there.

0:39:38.000,0:39:41.000
We'll start at the bottom,[br]we'll just put them in.

0:39:41.000,0:39:44.000
I'm not going to worry too much[br]about whether we can jump up or

0:39:44.000,0:39:48.000
not, we'll just go and pair[br]them up as we go down here, and

0:39:48.000,0:39:52.000
then go up here, and now we've[br]put in our eight electrons.

0:39:52.000,0:39:56.000
So, how close these are, we're[br]just going to put them all in.

0:39:56.000,0:39:59.000
We're just going to be very[br]careful not to bump up any

0:39:59.000,0:40:04.000
electrons there unless we[br]absolutely have to, because d x

0:40:04.000,0:40:08.000
squared minus y squared is very[br]much more destabilized in the

0:40:08.000,0:40:11.000
square planar system, so we're[br]going to want to pair all

0:40:11.000,0:40:15.000
our electrons up in those[br]lower energy orbitals.

0:40:15.000,0:40:18.000
So even if we sort of[br]did it a different way,

0:40:18.000,0:40:19.000
that's what we would get.

0:40:19.000,0:40:22.000
So we're going to want to pair[br]everything up before we go

0:40:22.000,0:40:25.000
up to that top one there.

0:40:25.000,0:40:26.000
So there's our square planar.

0:40:26.000,0:40:28.000
Well, what about tetrahedral.

0:40:28.000,0:40:31.000
How are we going[br]to fill these up?

0:40:31.000,0:40:37.000
Do we want to pair first, or[br]we do want to put them to the

0:40:37.000,0:40:40.000
full extent possible singly?

0:40:40.000,0:40:43.000
Single, right, it's going to be[br]a weak field, there's not a big

0:40:43.000,0:40:46.000
splitting here between these,[br]so we'll put them in, there's

0:40:46.000,0:40:53.000
1, 2, 3, 4, 5, 6, 7, 8.

0:40:53.000,0:40:55.000
All right, so now we can[br]consider which of these will

0:40:55.000,0:40:58.000
be paramagnetic and which[br]will be diamagnetic.

0:40:58.000,0:41:01.000
What's octahedral?

0:41:01.000,0:41:05.000
It's paramagnetic, we[br]have unpaired electrons.

0:41:05.000,0:41:08.000
What about square planar?

0:41:08.000,0:41:10.000
Square planar's diamagnetic.

0:41:10.000,0:41:11.000
And what about tetrahedral?

0:41:11.000,0:41:14.000
Paramagnetic.

0:41:14.000,0:41:20.000
So, if the experimental data[br]told us that a nickel center in

0:41:20.000,0:41:23.000
an enzyme was diamagnetic, and[br]we were trying to decide

0:41:23.000,0:41:27.000
between those three geometries,[br]it really seems like square

0:41:27.000,0:41:31.000
planar is going to[br]be our best guess.

0:41:31.000,0:41:34.000
And so, let me show[br]you an example of a

0:41:34.000,0:41:39.000
square planar system.

0:41:39.000,0:41:44.000
And so this particular nickel[br]is in a square planar system.

0:41:44.000,0:41:50.000
It has four ligands that are[br]all in the same plane, and it

0:41:50.000,0:41:54.000
is a square planar center for a[br]nickel, so that's one example.

0:41:54.000,0:41:58.000
And this is a cluster[br]that's involved in life

0:41:58.000,0:42:01.000
on carbon dioxide.

0:42:01.000,0:42:04.000
All right, so that's[br]different geometries,

0:42:04.000,0:42:05.000
you're set with that.

0:42:05.000,0:42:09.000
Monday we're going to talk[br]about colors of coordination

0:42:09.000,0:42:12.000
complexes, which all have to do[br]with the different geometries,

0:42:12.000,0:42:16.000
paired and unpaired electrons,[br]high field, low spin,

0:42:16.000,0:42:19.000
strong field, weak field.

0:42:19.000,0:42:21.000
Have a nice weekend.

0:42:21.000,0:42:22.000