AP Chemistry Hybrid Orbitals

Hello, and welcome back to Educator.com; welcome back to AP Chemistry.0000

Today, we are going to close out our discussion by talking about hybrid orbitals.0004

Well, let's just jump right on in.0011

OK, so Lewis structures--they showed shared electron pairs; so let me write this down: "Lewis structures showed shared electron pairs."0014

I shouldn't say "showed"--they actually show...OK, "show electron pairs."0035

Now, the VSEPR, the Valence Shell Electron Pair Repulsion--that predicts geometry in space.0040

Now, we are going to discuss the structure of the atomic orbitals that actually do the sharing.0055

We are going to show where these orbitals actually come from, what it is that they actually look like, and why it is that they do what they do.0062

Now, a word of warning, a word of caution regarding this particular chapter and this particular topic: bonding is one of those things--I had mentioned earlier that there are certain things where you run the danger of actually saying too much about a topic.0075

Hybridization is one of those things that you actually do run the risk of saying too much.0095

What I'm going to do is: I'm just going to present it in its most basic form; and the reason I do that is because what I want to give you is the basic outline of how to look at hybrid orbitals.0101

Once you have that knowledge (which is actually only a handful of bits of information), you want to take that, and you definitely want to look at the chapter, the respective chapter, in your book.0113

Then, everything will make sense.0125

What I am going to do is tell you what is going on; once you know what is going on, all of the other little bits of information, you should be able to gather for yourself; it's very, very important, because there are little bits of information, but I myself can't really go through them in a list, because it would be just that--it would just be a list.0127

That is available in your book: but as long as you understand what is happening, which is what I am hoping to do with the presentation that I give, everything else should be as clear as day.0145

You should be able to just go to any page in your book and say, "Yes, that is what that means; that is what that means; that is what that means."0156

OK, I just wanted to make you aware of that; I'm not going to give you a whole bunch of detailed information--just a broad outline of what is actually happening.0161

OK, now, when atoms bond, they mix (literally mix) their s and p, and sometimes d (if they need to), orbitals, to produce an equal number of equivalent orbitals called hybrid orbitals.0169

And again, you know what hybrid means: hybrid just means a mixing.0231

Now, what that means is this: that, if I take one s orbital and three p orbitals, that consists of four orbitals altogether.0237

I mix them up; well, the number of orbitals that I started off with (4) should be the number that I end up with.0246

I end up with four hybrid orbitals, and I give them new names: I call them sp³.0253

That is the idea: the number of orbitals that I start with has to equal the number of orbitals that I end up with; that is actually the most important thing.0259

This is where most kids actually get messed up: they lose orbitals along the way, or they add some.0267

The mathematics (because orbitals are just functions: remember the wave equation? It's just trigonometric functions, really)...well, math is such that, when you add something, you have to end up with that same amount.0273

Things don't just disappear: if you start with 7 orbitals, you had better end with 7 hybrid orbitals.0287

They may look different--obviously, they are going to look different; they are going to look like hybrid orbitals; but the number has to match; so bear that in mind.0294

All right, so before we dive into that, let's just take a quick look at CH₄.0302

Now, we said the bonding here...a carbon has the following in its valence shell (because again, valence shell is the one that is involved in bonding).0308

It has a 2s orbital, and it has three 2p's; so it is 2s² and 2p²; so these three are available.0319

And hydrogen, well, hydrogen just has its 1s, with 1 electron in it.0333

OK, in order to come up with...so carbon brings these 4 electrons, and hydrogen brings this 1 electron, but since we have 4 of them, it's going to be 1 times 4, right?0342

We have 2, 4, 6, 8; we have done the Lewis structure bit; everything works out fine.0364

Well, here is what is kind of interesting: well, notice: if they just interacted orbital-to-orbital--one of these p orbitals with one s from one hydrogen; another p from another s from another hydrogen; there are going to be some problems.0371

The problems are a couple: one of them--this 2s orbital is already filled; well, we know that when a 2s orbital is filled (or when any orbital itself is actually filled), it's not going to want to interact; it already has the 2 electrons that it needs.0385

This might form a bond with a hydrogen s, and this might form one, but that is only 2 bonds.0397

Well, there is no electron in here; so if this one interacts with a hydrogen...you know what, let me actually draw out four different ones, because I have 1 carbon; let me draw out each 1s; that way, I think it will make more sense.0404

I have a 1s, a 1s, a 1s, a 1s, because I have 4 hydrogens, right?0420

There we go; so this and this might match, or this and this might go; this and this might go; but what about these two?--they are not going to interact with this.0424

How does this actually bond?0434

Well, one possibility is: one of these electrons can jump over to this p orbital, and then you will have a p and an s, a p and an s, a p and an s, and then a 2s and a 1s interaction, but a p and an s, a p and an s, and a p and an s--those are equivalent, but they are going to be different types of bonds from a 2s and a 1s.0437

But, as it turns out, all of these bonds are equivalent, so what is it that is going on?0457

Well, here is what is going on: we take the s orbital in carbon; we add the p, the p, and the p (this is just the carbon here now, OK?--this is just the carbon); we take the 2s orbital, and we take the 2p, the 2p, the 2p (right?--there are three 2p orbitals).0462

We mix them; we started off with 4 orbitals; we ended up with 4 hybrid orbitals.0487

We call them sp³, sp³, sp³, sp³; this is a symbol for an orbital.0495

Be very, very clear about that: when we say sp³, what that means is that we have taken an s orbital; we have taken three p orbitals; we have mixed them all together; and then, we divide that mixture into four equal parts: sp³, sp³, sp³, sp³.0505

These are all equivalent hybrid orbitals.0523

This is what we call the hybrid orbitals.0527

Now, we need to know where these hybrid orbitals came from.0530

Well, this hybrid orbital...75% of it is p character; 25% of it is s character.0535

This hybrid orbital: 75% p character, 25% s character--which is why we say sp³; we used one s orbital; we used 2 p orbitals to create 4 sp³ orbitals.0544

Four orbitals to start with that are atomic: these are hybrid orbitals that are atomic.0559

They are on the carbon atom; that is what they are.0565

Now, each sp³ orbital has 75% p character, because again, we used 3 p orbitals to actually come up with it--but only one s orbital, so it has 3 times as much p character as s character...75% p character and 25% s character.0568

But they are equivalent--the hybrid orbitals.0612

Here, these are not equivalent orbitals; I have three orbitals that are p; one is s; if these were to bond, just directly, with the s orbitals of the hydrogen, I would have three bonds that are the same, but one bond that wouldn't be the same.0614

However, experimentally, we know that all bonds in the methane molecule are the same: literally, what happens is that the orbitals rearrange themselves, they mix themselves up, and then they divide equally, and then they go to their respective places, as far away as possible from each other, because they are going to be involved in bonding, and the electrons are electron pairs in bonding, and they want to be as far away as possible from each other.0626

So, for molecules...now, when we...well, OK, that is fine.0651

For molecules containing 4 (I shouldn't say that) objects around a central atom, and single bonds only, only sp³ hybridization is active.0658

In other words, if I have a molecule where the central atom has 4 objects around it, and of those objects, the atoms--if the atoms are single-bonded to that central atom, that means that that central atom is sp³ hybridized--always.0709

For example, the CH₄--we just did that one; well, what about NH₃?0728

Well, we know that the NH₃ molecule looks like this, right?--we know it has 4 objects around it.0733

Well, of those 4 objects, three of them are H's; one of them is a lone pair; but the objects that are atoms are single-bonded to the nitrogen, so that means the nitrogen itself is sp³ hybridized.0741

That means that the 2s orbital and the three p orbitals on nitrogen--they mix together, and then they separated; they separated out as four orbitals, each of those orbitals having 75%...each of those orbitals being sp³.0753

So now, I have four sp³ orbitals around a nitrogen; in other words, what it looks like is this.0771

Now, this sp³ orbital contains the lone pair; this sp³ orbital is interacting with an s orbital on hydrogen; this sp³ orbital is interacting with an s orbital on hydrogen; and this sp³ orbital is interacting with an s orbital on hydrogen.0782

All of these are equivalent: each has a pair of electrons.0801

This is a single bond; that is a single bond; that is a single bond; this is not a single bond, but it does have a lone pair in it--that lone pair is occupying an sp³ hybridized orbital.0806

All of these are actually equivalent; so any time you have a molecule that has 4 objects, and the atoms that constitute those objects are single-bonded, you have sp³ hybridization--always.0820

OK, so now, let's move on to the next possibility.0835

That is it: basically, what happens is that any time an atom comes together to bond with another atom, it is going to mix its orbitals the way it needs to mix its orbitals, in order to achieve what the Lewis structure says that it has achieved.0841

So, sp³ hybridization is one possibility; well, what if you have s and p and p, and we know we have three p's, but what if s decides to only mix with two p orbitals?0857

Well, what you end up having is: well, they do--they mix--but this time, s mixes with two p's.0877

You have three orbitals to start, so you are going to end up with three hybrid orbitals, and they are sp², sp², sp², and then this p orbital that is off to the side.0886

You have four orbitals to start; you have four orbitals that ended; except this time, s only mixed with two of the p orbitals; the third p didn't involve in the mixing--it stayed separate.0900

You ended up with an sp², an sp², an sp², and a p.0912

OK, any time you have three objects around a central atom, and one of the bonds is a double bond, you have sp² hybridization.0919

That is it: at the end of this lesson, when we do some examples, that is what we are going to ask: we are going to give you a particular atom, a particular molecule to a species, and we are going to ask you what the hybridization is of the particular atoms that are involved.0957

This is how you decide.0970

An example of this would be something like CHO, formaldehyde.0972

This actually...the Lewis structure of this looks like this.0985

What you have is a carbon, double-bonded to an oxygen that has a couple of lone pairs on it; and you have the hydrogen here, and the hydrogen here; you have the central atom.0992

Now notice: this one--it has three objects around it, and so it is sp² hybridized; this one has...well, actually, you know what, let's do it one at a time; so let's draw this out.1001

We have the C; we have the O; and we have H, H.1016

I'm going to draw the lone p orbital here; and then, this one has lone pair, lone pair, and another p orbital.1028

So here, we actually have 2 atoms that are going to be sp² hybridized.1044

This carbon atom--three of the sp² orbitals are involved in single bonds: single bond, single bond, single bond.1048

The p orbital on this carbon, the lone p orbital, is just there, as is.1057

Well, here, the oxygen itself is also...notice, it has three objects around it...actually...yes, it has three objects around it, except one of them is a double bond.1062

As it turns out, you have: this is one sp² orbital; this is another sp² orbital; this is another sp² orbital.1074

As it turns out, let me draw this this way.1085

This sp² orbital and this sp² orbital form a single bond; this sp² orbital on oxygen and this one carry the electron pairs; these sp² orbitals over here end up being bonded to...they end up interacting with s orbitals on hydrogen.1088

Now, I have a p orbital, and I have a p orbital; as it turns out, the p orbitals themselves (the p orbital on carbon and the p orbital on oxygen)--they interact, and they form the second bond.1108

There we go: OK, now, we want to define something.1120

Any bond that is along the centers of two atoms, right down the middle--that is called a sigma bond.1126

Any bond that forms between the interaction of a pi orbital and another pi orbital is called a pi bond.1138

OK, let me actually write that down: OK, a sigma bond is a single bond that runs along the line joining the centers of the two atoms involved in the bonding.1148

A pi bond is a bond between the p orbitals of adjacent atoms.1209

So now, I'm going to draw this again: I have a C, which is sp² hybridized; one sp² orbital, one sp² orbital, one sp² orbital; and this is going to be a free p orbital.1230

Oxygen: oxygen has an sp², an sp², an sp²; and it has a free p orbital.1245

One of the sp²s on this carbon interacts with the sp² on this oxygen, right along the line that joins them; this is a sigma bond.1256

Well, this p orbital here interacts with this p orbital, and it forms a pi bond.1268

So, a double bond actually consists of one sigma bond and one pi bond.1275

This sp² orbital on the carbon interacts with the s orbital on hydrogen; this one interacts with another s on hydrogen, giving us that; this sp² actually contains that lone pair; and this sp² on oxygen contains that lone pair.1281

Each of these central atoms is actually sp² hybridized; that means two of the p's have mixed with one of the s to create a situation where you end up with a double bond.1298

When you see a double bond in a molecule, those two atoms are going to be sp² hybridized.1309

That is what you have to know; that is it.1315

OK, let's try another kind of hybridization.1319

What happens when...so I have s, and I have p, and I have p, and I have p...what happens when only one s interacts with one p?1327

We mix, and we end with an sp; we end up with an sp; we end up with a free p; and we end up with another free p.1337

Here is what it looks like: let's take nitrogen: sp³ hybridization--triple bond; any time you see a triple bond, you are dealing with atoms, adjacent atoms, that are sp hybridized.1346

Nitrogen is going to be sp hybridized; it has one sp orbital, another sp orbital; this is a p; this is a p; and then, perpendicular to that...nitrogen is here.1362

One sp hybrid orbital; one sp hybrid orbital; one p up here--that is this (right?--this is a p); and the other p is that way, that way: it's coming out and going back.1377

OK, in fact, I'm not even going to...well, that is fine.1393

And then, I'm going to draw another nitrogen; that is one sp; that is one sp; this whole thing is one p orbital.1398

That is a p orbital.1411

The first bond that they make, when one sp orbital reacts with an sp of the other, is a sigma bond.1413

One p orbital reacts with another p orbital on the adjacent nitrogen to form a pi bond.1422

This p orbital reacts with this p orbital to form a pi bond.1433

So, what you end up with is 1, 2, 3--you end up with a triple bond.1438

Then, the lone pair on this nitrogen is on that sp orbital; the lone pair on this nitrogen is on that sp orbital; what you end up with is a triple bond, N...1444

If I were to take this molecule, the N and the N, and if I were to turn it around this way or this way, so that you are looking at it (N in front, N in back), here is what it would look like.1456

N, and there is another N directly behind it (right?--let me make it a big N, so think about it that way; there is one N in front and one N in back); there is one bond that is right down the center of them: that is the sigma bond.1470

There is another bond out here, and there is another bond out here, going one end-one end.1489

There is a bond that is connecting them; that is the sigma bond--that is the bond that takes place between the two sp hybridized orbitals.1497

There is another bond up here; it is parallel to the sigma bond, but it is up above it.1506

This is the pi bond, formed from the free p on this nitrogen and the free p on this nitrogen.1511

And then, there is another bond here: it is parallel to the sigma.1519

It is formed from the free p on this nitrogen and the free p on this nitrogen; this is what the triple bond actually looks like in space--the electrons actually are above (there is an electron cloud above and an electron cloud over here, and there is an electron cloud in between).1524

So, any time you see a triple bond, think sp hybridization.1542

Any time you see a double bond, think sp² hybridization.1546

Any time you see a single bond, 4 objects, think sp³ hybridization.1550

Let me do another example of an sp³ here.1556

Let's do this ethyne molecule...H, H...what you have is: carbon, carbon; you have an sp² and an sp², sp², sp²; you have a p; you have a p here; and you have another p; you have another p here.1560

Now, don't get confused with what it is that I have drawn: this is one sp, and this is another one of the sp's, but these p orbitals that are free--I have drawn in both lobes.1585

It is true that the sp and the sp² and the sp³--there is a second lobe on the other end; I haven't drawn it, because they are very tiny.1597

But the p orbitals...this whole thing is one p orbital, right here.1607

OK, one p orbital has 2 lobes; but an sp--the hybrid orbitals--I am only drawing them with single lobes; so this is one orbital; this is another orbital; this is another orbital; this is another orbital.1613

There is one bond between them; there is another pi bond that is interacting; and then, there is another pi bond here.1632

This is interacting with an H; this is interacting with an H; single bond, single bond; that gives us that.1642

When I see the triple bond, I know that I am looking at sp hybridization.1651

OK, now, let's do some mixes with the d's.1656

d plus s plus p plus p plus p: we know that third-row elements and beyond have d orbitals available to them, which is why sometimes phosphorus and sulfur have 5 things around it, or 6 things around it--because they can accommodate.1661

Well, how do we come up with 5 or 6 equivalent orbitals that bond?--well, here is how we do it.1678

They take the three p's; they take an s; in other words, these are the 3p orbitals; this is the 3s orbital; and this is one of the 3d orbitals.1685

They mix: 1, 2, 3, 4, 5; and you get 5 hybrid orbitals.1697

dsp³; dsp³; dsp³; dsp³; dsp³.1702

20, 40...60% p character; 20% s character; 20% d character: that is the distribution.1714

This orbital is a mix; most of it will look like p, but 20% of it will look like an s; 20% of it will look like a d; 5 orbitals to start; 5 orbitals that way.1725

PCl₅ is a molecule where the phosphorus is dsp³ hybridized.1740

OK, so it looks like this: P; one of the orbitals is here; one of the orbitals is here; one of the orbitals is here; one of the orbitals is behind the page; one of the orbitals is in front of the page.1754

Now, here is what is interesting: the chlorine...well, if we look at PCl₅, one of the bonds, one of the P-Cls, is like this, right?1769

Well, look at the chlorine: the chlorine has 1, 2, 3, 4 objects around it, and it is single-bonded, so the chlorine itself is sp³ hybridized.1781

The chlorine has an sp³, an sp³, an sp³, and an sp³.1795

Lone pairs are in three of the sp³s; this sp³ interacts with this dsp³ to form a single bond; and the same thing with the other chlorines.1803

I'll just put chlorine here, chlorine here, chlorine here, and chlorine here; so in this case, the phosphorus is dsp³ hybridized; the chlorine is sp³ hybridized.1816

Each atom attains its own hybridization to make it do what it can do.1829

OK, I have one more: now, I have d, plus d, plus s, plus p, plus p, plus p: when I mix those, I get d²sp³.1836

I have 6 of these: d²sp³, d²sp³, d²sp³, d²sp³, and d²sp³.1856

When you see a central atom that has 6 things around it, whether it's lone pairs or 6 actual atoms (like SF⁶), the hybridization on sulfur is d²sp³, because all of the bonds are equivalent.1869

Let's actually take SF₆: we know that it looks like this in terms of a Lewis structure, right?1884

We draw it like this; it looks like this: s; it has 1, 2, 3, 4, 5, 6; and I'll just take one of the fluorines: it is going to be 1, 2, 3, 4: this is--each of these orbitals is--a d²sp³ orbital.1894

It interacts with fluorine, which is sp³ hybridized.1923

It has lone pairs on three of the sp³ hybrid; this orbital interacts with this orbital to form a single bond; so we have an sp³ on fluorine single-bonded to a d²sp³ on sulfur; and then, of course, the other fluorines are the same.1927

OK, so let's do some examples.1952

Now, example: For each molecule or ion, predict the hybridization of each atom and describe the molecular geometry.1956

OK, A: we will take CO; well, we need to take a look at the Lewis structure for this--that is how we decide.2000

As it turns out, when you do the Lewis structure for CO (let me see...well, you know what, let's actually do it), carbon brings 4; oxygen brings 6, for a total of 10.2008

Let's do CO; that is 2, 4, 6, 8, 10; that is not going to do it, so let's do C...as it turns out, if I do three of those, that works out just fine; so my Lewis structure is O, this, and this.2019

This is my Lewis structure: what kind of hybridization does carbon have? what kind of hybridization does oxygen have?2039

Very simple: you have a carbon triple-bonded to an oxygen, and oxygen triple-bonded to a carbon; each of these is sp hybridized.2045

sp: oxygen is sp; remember, we said if you see a triple bond, it is immediately sp hybridized--both of the atoms.2056

OK, one of the bonds is sigma (the single bond); one of the bonds has 1 sigma bond, and then it has 2 pi bonds, right?2065

The sigma bond comes from the interaction of the sp and sp; the other ones are a p interacting with a p, a p interacting with a p; this is the arrangement of the bonds.2083

Two of the bonds are p-p interactions between the carbon and the oxygen; the single bond is the sigma bond; this is σ; this is π; this is π.2098

The sigma--the bond in the middle--that is the one that is an interaction between the sp orbital hybridization on carbon and the hybrid sp orbital on the oxygen.2107

OK, now, let's try BF₄^-: OK, when I do the Lewis structure for this, I end up with this thing.2116

BF₄^-...and then, of course, lone pairs on the fluorines; OK.2137

Well, look at boron: I have four objects around it, single-bonded; this is sp³ hybridized.2147

Fluorine: I have 1, 2, 3, 4 objects around it; fluorine--single bond--it is sp³ hybridized.2154

So, that is it: for the boron, I have an sp³ hybrid orbital interacting with one of the sp³s on fluorine to form a sigma bond.2162

On fluorine, the other three sp³s are filled with lone pairs; on boron, the other sp³s are involved in bonding.2172

I have four objects around a central atom; there are no lone pairs on the central atom; I have a tetrahedral geometry--hybridization and geometry; OK.2180

Now, let's actually...let me draw this out, so you can see the actual shape of it; we are going to use our notation.2197

This is going to be B, F, F...this is the shape of a tripod (I never do my wedges properly).2205

There you go: this is...I have a little triangle; it's a tripod and an F on top.2219

This is the three-dimensional structure: it looks like this, with another F right on top.2223

OK, and now, let us close it out with xenon F₂, difluoride: we have 8 electrons from xenon; F brings 7, so 2 times 7 is 14; we have a total of 22 electrons.2230

Xenon is going to look like: F...it's going to be F, and then we are going to have 1, 2, 3, 4, 5, 6; and I think, if you do the electron count...2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22...yes; so what we have is a Lewis structure that is F, F...2248

We have 5 objects around xenon; 5 objects is sp...no; 5 objects is dsp³: 3, 4, 5: three p's, one s, one d, gives me that kind of hybridization.2273

My fluorine...well, the fluorine just has single bonds, and it is four objects, so my fluorines are sp³ hybridized.2296

One of the dsp³...let's look at this bond over here: a dsp³ hybrid orbital on xenon is interacting with an sp³ orbital on fluorine to form a sigma bond.2306

That is this single sigma bond; OK.2321

Another: this is the same thing on this side: a dsp³ on xenon is interacting with an sp³ on fluorine for this single bond.2329

The lone pairs on fluorine occupy the other sp³ hybrid orbitals on fluorine, and the three lone pairs on xenon occupy the last three dsp³ hybrid orbitals on the xenon atom.2340

That is it: it is just a question of how many objects you have around a central atom: the number of objects will actually tell you what kind of hybridization you have.2358

If you have four objects and single bonds, sp³; if you have a double bond anywhere, it's sp² automatically; if you have a triple bond, it's sp hybridization.2370

If you have 5 objects, it's dsp³, and if you have 6 objects, it's d²sp³.2382

Everything else is just little, little bits of details that we definitely don't want to get into here, because I think it will complicate the matter; but I absolutely encourage you to take a look at this chapter to make sure you have those little bit of details.2388

What I have presented here is really all that you need to know about hybridization and atomic orbitals and molecular geometry.2401

Thank you for joining us here at Educator.com.2409

We'll see each other again, and we are going to start practicing for the AP exam; take care; goodbye.2412