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## Organic chemistry

### Course: Organic chemistry > Unit 1

Lesson 2: Hybridization# sp³ hybridized orbitals and sigma bonds

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*sp*³ hybridized orbitals and sigma bonds. Created by Sal Khan.## Want to join the conversation?

- Why do s-orbitals and p-orbitals take different shapes? Is ist because of the energy?(101 votes)
- As you study further into chemistry, you will learn about the four quantum numbers. As stated, a quantum number for a "s" orbital, "p" orbital and so on exists and falls out of solving something known as the Schrodinger wave equation. Essentially, the shapes are related to how dependent a certain function will be on radial versus angular dependance. For example, a "s" orbital has absolutely no angular dependence, so it is spherically symmetrical, where "p" orbitals do have angular dependence and are not spherically symmetrical. It becomes more complicated as you consider the magnetic orientation of orbitals as well. Hopefully that did not confuse anybody further.(142 votes)

- During the hybridization talk about methane at7:50, why is the reality of carbon bond actually 4 of the sp3 hybrid orbitals? Why can't they just have two electrons filling in the two lone 2p orbitals of Carbon?(20 votes)
- Orbitals are not "real" things, they are a book keeping method chemists use. The electrons do what they do, and we try and shoehorn them into these orbitals to make it easier to keep up with. Apparently forming the four bonds, in the configuration we call the sp3 hybrid orbitals, is a low energy state of the carbon in that situation. "It's a low energy state" is the explanation in one way or another for just about everything in chemistry/physics. The explanation of why some state is low energy can get pretty intense however. In this case we need four areas of electron density, cause that's how many single bonds it takes to fill carbon's valence shell. Areas of electron density try to get as far away from each other as possible (VESPR theory). It turns out that the tripod shape sal mentioned maximizes the distance between the orbitals, which is apparently why that shape is lowest energy.(44 votes)

- At11:30, why is one lobe of the sp3 orbital smaller than the other?(17 votes)
- The larger lobe is the bonding lobe and the smaller is the antibonding lobe. It's because when you add two orbitals, they add in two manners. One result (the bigger lobe) comes about when they reinforce each other. The other result (the smaller lobe) comes about when they interfere with each other. Remember that orbitals describe the motion of electrons behaving as waves. Waves interact to constructively and destructively interfere with each other. When you combine two orbital wave*functions* together, you get two new orbital wave functions - one from the addition of them and one from the difference between them.(35 votes)

- What is the meaning of 3 in sp3 orbitals.(13 votes)
- 3 denotes the fact all three parts of the p-orbital, ie. the px axis, the py axis and the pz axis (I presume, you know that P has 3 sub-orbitals, x, y and z) participate in the sp3 hybridization.

sp3 also may denote the fact that 1 s-orbital and 3-p orbitals take part in hybridization, thus an sp3 orbital has 25% of s-orbital characteristics and 75% of p-orbital characteristics :)(8 votes)

- As the carbon needs energy to make the electron jump from "s" to "p", would the nature of this hybridization remain the same at absolute zero? I know electrons still orbit at 0 K but what would happen?(12 votes)
- We can only speculate. At 0 K all motion of atoms ceases, except for a very small amount of so-called zero-point vibrational energy. Since, for example, H atoms cannot move towards a C atom in order to form bonds, there would be no reason for the C atom to hybridize for bond formation. Also, a jump from one electronic energy level to another takes much more energy than from one vibrational energy level to another. So I do not think hybridization will occur.(14 votes)

- Is there any special reason why the orbitals looks the way they do? also, how is the spin of an electron determined?(7 votes)
- The orbitals are just mathematical solutions to the Schrodinger equation. They tell you where you are most likely to find an electron in the space around a nucleus. When you plot the orbitals in three dimensions, they look like the pictures you see in the texts.

You can't determine the spin of an individual electron. But you can demonstrate that electrons have spin. If you pass a beam if silver atoms (one unpaired electron each) through a magnetic field, the atoms that have electrons with one type of spin will be deflected in one direction. Those with the other type of spin will be deflected in the opposite direction.

We give these two types of spin the quantum numbers +½ and -½. There is no way to tell which spin corresponds to which number. It is customary to assign +½ to "up" and -½ to "down", and to list "up" first when describing electron configurations, but this choice is completely arbitrary.(19 votes)

- Why do the electrons organize themselves into orbitals?(5 votes)
- Electrons do not exactly organize themselves in orbitals . Electrons are most probably to be found inside the orbitals. Orbitals are just the areas where electrons are most probably to be found. The charge exerted by the nucleus makes the electrons revolve around it and most probably these electrons are found within the orbitals....(11 votes)

- While drawing the structure of the CH4 molecule ,why doesn`t Sal draw the 1s2 orbital?(4 votes)
- Because the 1s2 orbital of carbon doesn't take part in any of the bonds with hydrogen. It is a filled orbital and thus not looking to partner with any of the hydrogens. It is unnecessary to draw it since he was only talking about the orbitals involved in bonding.(12 votes)

- What is the Schrödinger equation?(2 votes)
- The Schrödinger equation treats a particle as if it were a wave.

For a particle, Kinetic Energy + Potential Energy = Total Energy

or T + U = E

For a wave, the Schrödinger equation becomes

(-h²/4π²m)(d²ψ/d²x + d²ψ/d²y + d²ψ/d²z) + Uψ = Eψ

h = Planck's constant;

m = mass;

U = the potential energy (it also depends on x, y, and z —the distance from the nucleus)

ψ = the wave function [analogous to y = sin(x)cos(x)]

This is a hairy differential equation that requires advanced calculus to solve.

You can solve it only by assuming that there must be only certain allowed quantum numbers n, l, and m.

For a 1s orbital, ψ = ke^(-r), where r is the distance from the nucleus and k is a constant made from several other constants.

The electron density is given by ψ².

The probability of finding an electron at a given distance from the nucleus is

P = 4πr²ψ² = 4πr²k²e^(-2r) ∝ r²e^(-r)

Notice that P → 0 when r → 0 and when r → ∞. But there is some distance (r) from the nucleus at which the probability of finding an electron is the greatest.

This is just what we know about 1s orbitals.(10 votes)

- what is hybridisation.and why does hybridization takes place(3 votes)
- In chemistry, hybridization is the mixing of atomic orbitals into new hybrid orbitals (with different energies, shapes, etc., than the actual orbitals that are hybridizing) that are suitable for the pairing of electrons to form chemical bonds. Hybrid orbitals are very useful in the explanation of molecular geometry and atomic bonding properties.

Hybridization take place so that the electron pairs in the new orbitals are as far apart from each other as they can get, Since electrons repel each other, this leads to the lowest possible energy state for the molecule.(4 votes)

## Video transcript

Let's remind ourselves a little
bit of what we already know about orbitals and I've
gone over this early on in the regular chemistry playlist.
Let's say that this is the nucleus of our atom, super
small, and around that we have our first orbital,
the 1s orbital. The 1s orbital, you can kind
of just view it as a cloud around the nucleus. So you have your 1s orbital and
it can fit two electrons, so the first electron will go
into the 1s orbital and then the second electron will also
go into the 1s orbital. For example, hydrogen has
only one electron, so it would go into 1s. Helium has one more,
so that will also go into the 1s orbital. After that is filled, then you
move onto the 2s orbital. The 2s orbital, you can view
it as a shell around the 1s orbital, and all of these, you
can't really view it in our conventional way of thinking. You can kind of view it as a
probability cloud of where you might find the electrons. But for visualization purposes,
just imagine it's kind of a shell cloud around
the 1s orbital. So imagine that it's kind of
a fuzzy shell around the 1s orbital, so it's around the
1s orbital, and your next electron will go there. Then the fourth electron will
also go there, and I drew these arrows upward and downward
because the first electron that goes into the 1s
orbital has one spin and then the next electron to go into
1s orbital will have the opposite spin, and so they keep
pairing up in that way. They have opposite spins. Now, if we keep adding
electrons, now we move to the 2p orbitals. Actually, you can view it as
there are three 2p orbitals and each of them can hold two
electrons, so it can hold a total of six electrons
in the 2p orbitals. Let me draw them for you just
so you can visualize it. So if we were to label our axis
here, so think in three dimensions. So imagine that that right
there is the x-axis. Let me do this in different
colors. Let's say that this right
here is our y-axis and then we have a z-axis. I'll do that in blue. Let's say we have a z-axis
just like that. You actually have a p orbital
that goes along each of those axes. So you could have your
two-- let me do it in the same color. So you have your 2p sub x
orbital, and so what that'll look like is a dumbbell shape
that's going in the x-direction. So let me try my best attempt
at drawing this. It's a dumbbell shape that goes
in the x-direction, in kind of both directions, and
it's actually symmetric. I'm drawing this end bigger than
that end so it looks like it's coming out at you a little
bit, but let me draw it a little bit better than that. I can do a better job. And maybe it comes
out like that. Remember, these are really just
probability clouds, but it's helpful to kind of
visualize them as maybe a little bit more things that we
would see in our world, but I think probability cloud is the
best way to think about it. So that is the 2px orbital,
and then I haven't talked about how they get filled yet,
but then you also have your 2py orbital, which'll go in this
axis, but same idea, kind of a dumbbell shape in the
y-direction, going in both along the y-axis, going in that direction and in that direction. Then, of course, so let me do
this 2py, and then you also have your 2pz, and that goes
in the z-direction up like that and then downwards
like that. So when you keep adding
electrons, the first-- so far, we've added four electrons. If you add a fifth electron, you
would expect it to go into the 2px orbital right there. So even though this 2px orbital
can fit two electrons, the first one goes there. The very next one won't
go into that one. It actually wants to separate
itself within the p orbital, so the very next electron that
you add won't go into 2px, it'll go into 2py. And then the one after that
won't go into 2py or 2px, it'll go into 2pz. They try to separate
themselves. Then if you add another
electron, if you add-- let's see, we've added one, two,
three, four, five, six, seven. If you add an eighth electron,
that will then go into the 2px orbital, so the eighth electron
would go there, but it would have the
opposite spin. So this is just a little bit of
review with a little bit of visualization. Now, given what we just
reviewed, let's think about what's happening with carbon. Carbon has six electrons. Its electron configuration, it
is 1s2, two electrons in the 1s orbital. Then 2s2, then 2p2, right? It only has two left,
because it has a total of six electrons. Two go here, then there,
then two are left to fill the p orbitals. If you go based on what we just
drew and what we just talked about here, what you
would expect for carbon-- let me just draw it out the
way I did this. So you have your 1s orbital,
your 2s orbital, and then you have your 2px orbital, your 2py
orbital, and then you have your 2pz orbital. If you just go straight from
the electron configuration, you would expect carbon, so the
1s orbital fills first, so that's our first electron,
our second electron, our third electron. Then we go to our 2s orbital,
That fills next, third electron, then fourth
electron. Then you would expect maybe
your fifth electron to go in the 2px. We could have said 2py or 2z. It just depends on how
you label the axis. But you would have your fifth
electron go into one of the p orbitals, and then you
would expect your sixth to go into another. So you would expect that
to be kind of the configuration for carbon. And if we were to draw it--
let me draw our axes. That is our y-axis and then
this is our x-axis. Let me draw it a little
bit better than that. So that is the x-axis and, of
course, you have your z-axis. You have to think in three
dimensions a little bit. Then you have your z-axis,
just like that. So first we fill the 1s orbital,
so if our nucleus is sitting here, our
1s orbital gets filled with two electrons. You can imagine that
as a little cloud around the nucleus. Then we fill the 2s orbital
and that would be a cloud around that, kind of a
shell around that. Then we would put one electron
in the 2px orbital, so one electron would start kind of
jumping around or moving around, depending how you want
to think about it, in that orbital over there, 2px. Then you'd have the next
electron jumping around or moving around in the 2py
orbital, so it would be moving around like this. If you went just off of this,
you would say, you know what? These guys, this guy over
here and that guy over there is lonely. He's looking for a opposite
spin partner. This would be the only places
that bonds would form. You would expect some type of
bonding to form with the x-orbitals or the y-orbitals. Now, that's what you would
expect if you just straight-up kind of stayed with this model
of how things fill and how orbitals look. The reality of carbon, and I
guess the simplest reality of carbon, is if you look at a
methane molecule, is very different than what you
would expect here. First of all, what you would
expect here is that carbon would probably-- maybe it
would form two bonds. But we know carbon forms four
bonds and it wants to pretend like it has eight electrons. Frankly, almost every atom wants
to pretend like it has eight electrons. So in order for that to happen,
you have to think about a different reality. This isn't really what's
happening when carbon bonds, so not what happens
when carbon bonds. What's really happening when
carbon bonds, and this will kind of go into the discussion
of sp3 hybridization, but what you're going to see
is it's not that complicated of a topic. It sounds very daunting, but
it's actually pretty straightforward. What really happens when carbon
bonds, because it wants to form four bonds with things,
is its configuration, you could imagine, looks
more like this. So you have 1s. We have two electrons there. Then you have your 2s,
2px, 2py and 2pz. Now what you can imagine is it
wants to form four bonds. It has four electrons that are
willing to pair up with electrons from other
molecules. In the case of methane, that
other molecule is a hydrogen. So what you could imagine is
that the electrons actually-- maybe the hydrogen brings this
electron right here into a higher energy state and
puts it into 2z. That's one way to
visualize it. So this other guy here maybe
ends up over there, and then these two guys are over
there and over there. Now, all of a sudden, it looks
like you have four lonely guys and they are ready to bond,
and that's actually more accurate of how carbon bonds. It likes to bond with
four other people. Now, it's a little bit arbitrary
which electron ends up in each of these things, and
even if you had this type of bonding, you would expect
things to bond along the x, y, and z axis. The reality is, the reality of
carbon, is that these four electrons in its second shell
don't look like they're in just-- the first one doesn't
look like it's just in the s orbital and then the p and y
and z for the other three. They all look like they're a
little bit in the s and a little bit in the p orbitals. Let me make that clear. So instead of this being a 2s,
what it really looks like for carbon is that this looks
like a 2sp3 orbital. This looks like a 2sp3 orbital,
that looks like a 2sp3 orbital, that looks
like a 2sp3 orbital. They all look like they're kind
of in the same orbital. This special type of--
it sounds very fancy. This sp3 hybridized orbital,
what it actually looks like is something that's in between
an s and a p orbital. It has a 25% s nature
and a 75% p nature. You can imagine it as being a
mixture of these four things. That's the behavior
that carbon has. So when you mix them all,
instead of having an s orbital, so if this is
a nucleus and we do a cross-section, an s orbital
looks like that and the p orbital looks something like
that in cross-section. So this is a an s
and that is a p. When they get mixed up, the
orbital looks like this. An sp3 orbital looks something
like this. This is a hybridized
sp3 orbital. Hybrid just means a combination
of two things. A hybrid car is a combination
of gas and electric. A hybridized orbital is a
combination of s and p. Hybridized sp3 orbitals are the
orbitals when carbon bonds with things like hydrogen
or really when it bonds with anything. So if you looked at a molecule
of methane, and people talk about sp3 hybridized orbitals,
all they're saying is that you have a carbon in the center. Let's say that's the carbon
nucleus right there. And instead of having one s and
three p orbitals, it has four sp3 orbitals. So let me try my best at drawing
the four sp3 orbitals. Let's say this is the big lobe
that is kind of pointing near us, and then it has a small
lobe in the back. Then you have another one that
has a big lobe like that and a small lobe in the back. Then you have one that's going
back behind the page, so let me draw that. You can kind of imagine a
three-legged stool, and then its small lobe will come
out like that. And then you have one where
the big lobe is pointing straight up, and it has a
small lobe going down. You can imagine it as kind
of a three-legged stool. One of them is behind like
that and it's pointing straight up, So a three-legged
stool with something-- it's kind of like a tripod, I
guess is the best way to think about it. So that's the carbon nucleus
in the center and then you have the hydrogens, so that's
our carbon right there. Then you have your hydrogens. You have a hydrogen here. A hydrogen just has one electron
in the 1s orbital, so the hydrogen has a 1s orbital. You have a hydrogen here that
just has a 1s orbital. It has a hydrogen here,
1s orbital, hydrogen here, 1s orbital. So this is how the hydrogen
orbital and the carbon orbitals get mixed. The hydrogens 1s orbital bonds
with-- well, each of the hydrogen's 1s orbital bonds
with each of the carbon's sp3 orbitals. Just so you get a little bit
more notation, so when people talk about hybridized sp3
orbitals, all they're saying is, look, carbon doesn't bond. Once carbon-- this
right here is a molecule of methane, right? This is CH4, or methane, and it
doesn't bond like you would expect if you just want
with straight vanilla s and p orbitals. If you just went with straight
vanilla s and p orbitals, the bonds would form. Maybe the hydrogen might be
there and there, and if it had four hydrogens, maybe there and
there, depending on how you want to think about it. But the reality is it doesn't
look like that. It looks more like a tripod. It has a tetrahedral shape. The best way that that can be
explained, I guess the shape of the structure, is if you have
four equally-- four of the same types of orbital
shapes, and those four types of orbital shapes are hybrids
between s's and p's. One other piece of notation to
know, sometimes people think it's a very fancy term, but when
you have a bond between two molecules, where the
orbitals are kind of pointing at each other, so you can
imagine right here, this hydrogen orbital is pointing
in that direction. This sp3 orbital is pointing
that direction, and they're overlapping right around here. This is called a sigma bond,
where the overlap is along the same axis as if you connected
the two molecules. Over here, you connect the two
molecules, the overlap is on that same axis. This is the strongest form of
covalent bonds, and this'll be a good basis for discussion
maybe in the next video when we talk a little bit
about pi bonds. The big takeaway of this video
is to just understand what does it mean? What is an sp3 hybridized
orbital? Nothing fancy, just a combination of s and p orbitals. It has 25% s character, 75% p
character, which makes sense. It's what exists when carbon
forms bonds, especially in the case of methane. That's what describes it's
tetrahedral structure. That's why we have an angle
between the various branches of a 109.5 degrees, which some
teachers might want you know, so it's useful to know. If you take this angle right
here, 109.5, that's the same thing as that angle, or if you
were to go behind it, that angle right there, 109.5
degrees, explained by sp3 hybridization. The bonds themselves
are sigma bonds. The overlap is along the axis
connecting the hydrogen.