Orbitals: Crash Course Chemistry #25


In this episode of Crash Course Chemistry, Hank discusses what Molecules actually look like and why, some quantum-mechanical three dimensional wave functions are explored, he touches on hybridization, and delves into sigma and pi bonds.


Transcript Provided by YouTube:

00:00
We spend a lot of time thinking about atoms as looking like this.
00:03
There’s a ball and there’s a stick, and there’s another ball and another stick.
00:07
It’s just a bunch of balls stuck together by these little wooden bonds. Simple.
00:13
Pretty easy to understand, and thus — as you have probably come to expect — it is entirely incorrect.
00:18
Nuclei really can be understood as little balls, and that’s more or less correct,
00:23
though when you get to some of the bigger, less stable ones they start looking more oblong and weird like a rugby ball.
00:29
Atoms are basically ball-like as well, with electrons and a spherical cloud around the nucleus.
00:34
But molecules, as we discussed last time, do not look like balls on sticks.
00:37
Bonds don’t form into neat little lines.
00:39
They form from overlapping electron clouds or shells, flowing around the nuclei of bonded atoms.
00:45
If you really get down there and understand what they look like,
00:47
they’re like lumpy, clumpy globs of probable electron locations.
00:52
And these lumpy, clumps of probable electron locations do not behave the way you might initially expect them to behave.
00:58
Oh no. That would be far too simple.
01:01
They behave based on quantum mechanical, 3-dimensional wave functions,
01:05
probabilistic distributions of electrons in space.
01:07
And yeah, by the end of this episode, you’re going to understand what I just said and it’s gonna be awesome!
01:13
[Theme Music]
01:23
Let’s start with water, because all the interesting things on our planet start with water.
01:27
It’s also universally common, not just on our planet but in our galaxy and our universe.
01:32
Case in point: In 2011, astronomers discovered a cloud of water-ice surrounding a black hole
01:36
that contains 140 trillion times more water than we have here on Earth.
01:41
And while we don’t have any confirmed worlds covered in water outside of our solar system,
01:45
we do have some right here in our solar system.
01:49
Europa contains so much water, probably salt water, that its entire surface is just ice.
01:54
What did any of that have to do with atomic orbitals? Nothing.
01:57
I just felt like maybe I scared you with all that quantum mechanics talk before the intro
02:01
and I wanted to chill you out for a second.
02:03
Okay, so water. We did its Lewis structure last week, remember?
02:06
Each hydrogen bonding to the oxygen atom, and voilà!
02:09
But that drawing is linear, just a straight line through all the nuclei,
02:13
and we know, just instinctually at this point, that water is a bent molecule.
02:18
But why? Why is water crooked?
02:20
Unbonded atoms within a molecule generally like to be as far away from each other as possible,
02:25
especially if they have the same partial charge as the 2 hydrogens do with their partial positives.
02:31
But something is keeping those hydrogens closer together than they would like to be.
02:36
So why on earth are they not stretched out as far away from each other as possible?
02:39
I ask this because if they were, the water molecule wouldn’t be polar,
02:44
and if water was suddenly non-polar we would all instantly die, as would all life on Earth.
02:50
And suddenly, we realize that this seemingly normal thing that we knew about the world is really weird.
02:56
And weird stuff is my favorite stuff because it means interesting questions.
03:00
Interesting questions I want to know the answer to.
03:03
It’s an even more compelling question than,
03:04
“What the heck is a quantum mechanical 3-dimensional wave function?”
03:06
Well, of course, the answer to this question has a great deal to do with
03:09
quantum mechanical 3-dimensional wave functions, so let’s start there.
03:12
Oh, look! I’ve got a telephone cord!
03:14
This is what old people used to use to get their voices into wires
03:18
so they could be transmitted across the world before cell phones,
03:21
but today it’s pretty much only useful for demonstrating electron fields.
03:25
Electrons are both particles and waves, which is not an easy thing to imagine.
03:29
Very basically, you can think of them as an excitation of the electron field, which exists everywhere.
03:35
When energy is dumped into the electron field, electrons exist inside a wave function.
03:40
What’s a wave function?
03:41
It’s a mathematical function that describes the probability that an electron is in a certain place at any given moment.
03:46
So, this telephone cord is an electron field.
03:48
I dump some energy into it and we create what’s called a standing wave.
03:53
The wave function is the mathematical function that describes it.
03:55
Electrons function the same way.
03:58
They exist as excitations in the electron field around the nucleus in a standing wave.
04:03
The simplest of these wave functions is the s orbital,
04:06
which can contain 2 electrons and is a spherical pattern of standing waves around the nucleus.
04:11
This standing wave can have different numbers of nodes,
04:14
allowing patterns to repeat themselves when there are more electrons around the nucleus.
04:18
Every orbital can contain, and indeed is at its lowest energy when it contains, 2 electrons.
04:23
Hydrogen has one electron in its s orbital.
04:26
Helium, an ultra-stable, very low-energy noble gas, has 2.
04:31
It’s happy cause it has its shell filled.
04:33
But, of course, there are other sorts of orbitals as well.
04:35
After we fill the first and second s orbitals, we move on to filling the p orbital.
04:40
Or rather, I should say p orbitals, because we’re talking about 3 dimensional space here,
04:45
so there can be one on the x axis, and one on the y axis, and one on the z axis.
04:49
Each of those can contain 2 electrons for a total of 8
04:52
with 2 in the s orbital and 6 in the 3 p orbitals.
04:55
And yes, those 8 electrons are the reason for whole the octet rule thing.
04:58
Remember now, the periodic table is a map of the orbitals as they fill.
05:02
Elements in the s block are filling their s orbitals.
05:04
Elements in the p block are filling their p’s.
05:06
Same with the d’s and the f’s.
05:08
So, s orbitals, very simple, spherical, p orbitals a little bit weirder, d and f orbitals, so crazy.
05:13
Some of the f orbitals in particular have just ridiculously cool geometries.
05:17
Lots of fancy math is involved in writing out these wave functions and understanding them.
05:22
So, with hydrogen, we’ve just got the one s orbital.
05:24
It’s a sphere. Marvelously uncomplicated.
05:27
But, in the second shell, we have an s orbital and 3 p orbitals.
05:31
The p orbitals, if they were all by themselves, look like this.
05:33
But, when you actually stick them around an atom, the s and p orbitals start to interact with each other,
05:39
doing their best not to overlap and changing each other.
05:42
The s and the p orbitals can merge into hybrid sp orbitals.
05:46
Instead of being 2 different kinds of orbitals, they become 4 identical orbitals trying their best not to overlap.
05:52
This is called orbital hybridization.
05:54
When the s orbital hybridizes with all 3 p orbitals it’s called sp3 hybridization and
05:59
it forms a tetrahedral shape.
06:01
And this is that tetrahedral shape.
06:03
It’s the easiest way for all the orbitals to form something like a sphere around the atom, but not interact too much.
06:09
I didn’t do anything fancy to make these balloons take this shape.
06:12
I just tied them together at the base.
06:14
They naturally formed this shape because they can’t overlap with each other.
06:18
And yes, this is exactly what’s going on with water.
06:21
In water, oxygen’s 8 electrons are arranged with 2 in each sp3 hybridized orbital.
06:26
2 of those electrons are from hydrogen.
06:29
6 are from oxygen, including 2 lone pairs.
06:32
Those lone pairs, even though they’re not participating in any bonds, still have their orbitals.
06:36
And so water is locked into that tetrahedral structure.
06:39
No matter which orbital you stick the hydrogen atoms to, you’re stuck with an asymmetrical molecule.
06:44
That, along with the difference in electronegativities of oxygen and hydrogen,
06:48
leads to the polarity of water and the existence of life.
06:52
But s and p orbitals can hybridize in other ways as well.
06:55
How, for example, could you imagine sp3 orbitals forming a double bond?
07:00
You can’t have 2 orbitals mashing together in the same space,
07:03
and sp3 orbitals are pretty much stuck in their tetrahedral structure.
07:06
Well, if a molecule is going to be at its lowest energy state by forming a double bond,
07:10
it has a nice simple solution.
07:11
It only hybridizes 2 p orbitals with the s orbital, forming 3 sp2 hybridized orbitals
07:17
with an unhybridized p orbital sticking up from the center.
07:21
Tie balloons together like that, and you get what we call a trigonal plane.
07:24
Each sp2 orbital is 120° away from the other, drawing a line straight through their centers,
07:30
and you get an equilateral triangle.
07:32
One of the 2 bonds in the double bond has sp2 orbitals merging together nicely in line with the nuclei.
07:37
This straightforward sort of bond is called a sigma bond.
07:41
A second and weirder bond forms,
07:43
this one from the unhybridized p orbital sticking out above and below the nucleus.
07:47
These atoms merge to form a pi bond.
07:50
That’s your nice symmetrical double bond that you see in molecules like ethylene.
07:54
And, yes, sp orbitals, where the s only hybridizes with one p orbital, are also all over the place.
08:00
These occur when an atom is either triple bonded to another atom or is double bonded to 2 atoms.
08:05
The sp orbital, the one that forms the sigma bonds here, is linear.
08:09
There are just 2 of them, balloons, easy, see? Straight line.
08:13
The trick is to have those 2 unhybridized p orbitals that can engage in 2 pi bonds,
08:18
either to form a single triple bond or to form 2 double bonds like in carbon dioxide.
08:23
Carbon dioxide’s orbital structure is actually really cool, so let’s take a look at it as an example.
08:27
The carbon is going to have 2 double bonds,
08:29
so it has to have 2 un-hybridized p orbitals and one sp hybridized orbital.
08:34
The oxygens are going to have one double bond,
08:36
so they need to set up as sp2 hybridized with one un-hybridized p orbital, for the double bonding.
08:41
As they come together for the bond, the sigma bonds will occur between the hybridized orbitals.
08:45
Very simple.
08:46
One oxygen will line up to form a pi bond with the vertically oriented p orbital from the carbon
08:50
and the other will line up with the horizontally oriented one.
08:53
There you have it. Bond, bond, bond, bond.
08:56
But, of course, as will always be the case in your unrelenting search for more knowledge, there is yet more to learn.
09:02
d and f orbitals can hybridize with sp hybridized orbitals
09:05
and with each other, forming some gorgeously peculiar geometries,
09:09
and when 2 d orbitals hybridize with sp3 orbitals, you get d2sp3, an octahedral structure,
09:15
which those of you who play role playing games will recognize as an 8-sided die.
09:19
These orbital configurations determine the shape of molecules,
09:21
and the shape of molecules determines how they behave, what forms they take, what properties they have.
09:27
It’s pretty dang amazing, really, that wave functions determining the probable locations of electrons keep water bent,
09:34
and thus polar, and thus able to dissolve nutrients and form a stable home for ourselves
09:39
so that we can walk around as weird bags of mostly water thinking about stuff,
09:44
making YouTube videos, trying to learn more about the world, or maybe just trying to pass a test.
09:50
Thanks for watching this episode of Crash Course Chemistry.
09:52
If you were paying attention today, you learned that molecules are clumpy globs of probable electron locations
09:58
determined by wave functions that are a bit more complicated than waves on a telephone cord,
10:03
that water is an asymmetrical molecule because of oxygen’s sp3 hybridized orbitals forcing
10:07
the electrons into a tetrahedral structure,
10:10
and that s and p orbitals can also hybridize other ways as sp2 or sp
10:15
and how those hybridizations allow for double and triple bonds using both sigma and pi bond types.
10:20
Finally, you learned that d orbitals can get involved too,
10:23
allowing for hybridizations that form even cooler 3-dimensional shapes.
10:27
This episode of Crash Course Chemistry was written by me and edited by Blake de Pastino,
10:31
and our chemistry consultants are Dr. Heiko Langner and Edi Gonzales.
10:35
It was filmed, edited, and directed by Nicholas Jenkins.
10:37
Our sound designer is Michael Aranda, and our graphics team is Thought Café.


This post was previously published on YouTube.

Photo credit: Screenshot from video