So far, we have focused on the properties of atoms and seen how they can bond by sharing valence electrons for covalent bonds, or stealing them completely in the case of ionic bonds. If we want to investigate further into the properties of molecules, we will need to understand how they are arranged in three-dimensional space. In this video, we will consider how the two-dimensional representations we have used can be visualized in three dimensions, and We will see how to predict the geometry of molecules around a central atom.
Once we can see the geometry around these central atoms, we can visualize how larger and more complex molecules will look in future courses. Atoms in a molecule will share their unpaired electrons in order to achieve a full octet. For Lewis diagrams, we write atoms so that each of the four sides of the atomic symbol can hold up to two electrons.
Additionally, We don't pair up electrons on a side until we absolutely have to. Consider how this reveals the number of covalent bonds an atom prefers to make. Carbon easily makes four bonds. Nitrogen makes three bonds. Oxygen makes two bonds.
And hydrogen can only ever make one bond. We can visualize this in two dimensions using Lewis structures. However, these molecules are not all flat. When determining the three-dimensional geometry around an atom that is bonded into a molecule, we need to know two pieces of information. The first is how many electron domains it has around it.
An electron domain is defined as either a lone electron pair or a bond. Single, double, and triple bonds all count as a single electron domain. The second thing we need to know is how many of those electron domains are involved in bonding. So if an atom has one lone electron pair, a double bond, and a single bond, Then it has three electron domains, and two of them are bonding domains.
The shape of a molecule is determined by the number and types of bonds around the central atom. This means that lone electron pairs will contribute to the shape, but they are not counted as part of the geometry. Only bonds with atoms attached to them are part of the overall geometry.
Here is a chart showing all the possible combinations of electron domains and bonding domains. Let's go over each geometry and see how it is formed in actual molecules, and how you can predict each using a Lewis structure for that molecule. We know that atoms like to have a full valence shell. For all rows after the first, this would be 8 electrons around each atom.
Hence, we have 2 on each side for a total of 8. Before, we saw that valence electrons consist of s and p orbitals, sometimes referred to as px, py, and pz. These are called atomic orbitals because these orbitals are formed by the electrons found in a single atom. Hybrid orbitals happen when those electrons create new orbitals that are part of a bond. Since hybrid orbitals are just a rearrangement of these orbitals, we can only end up with a maximum of four orbitals once they are combined.
Each of the rearranged orbitals can hold two electrons. For a total of eight valence electrons, hybrid orbitals have designations, just as atomic orbitals do. These designations represent which atomic orbitals have been combined to create them.
Because the s orbital is the lowest energy, it is always used when creating a hybrid orbital. It can be combined with one, two, or all three p orbitals. When the s orbital is combined with a single p orbital, the hybrid orbitals that they make are called sp orbitals.
Because we use two orbitals to make it, we get two sp orbitals as a result. We have two p orbitals left over. These can also participate in bonding. to make double and triple bonds, but we'll discuss that a little later.
Hybrid orbitals can also be made by combining the s orbital with two p orbitals. These hybrids are called sp2 orbitals. Since we combine the three atomic orbitals, s, p, and p, we get three sp2 orbitals out of it.
This leaves us with a single p orbital that can be used for making double bonds. Finally, we can combine all four atomic orbitals in four new hybrid orbitals called sp3 orbitals. Here, we combine s, p, p, and p to get four sp3 hybrid orbitals. This leaves us with no p orbitals left over.
Atoms that bond using sp3 orbitals do not have any double or triple bonds. For bonding with sp3 hybrid orbitals, we can fill each of these hybrid orbitals with up to two electrons. When sharing, they generally contain one electron that will be shared.
However, If a hybrid orbital contains two electrons already, it will not share and will not form a bond. These are what we have drawn as lone electron pairs. They fill up the hybrid orbital and leave no room for bonding. We can relate this to Lewis structures pretty easily.
All atoms like to have eight electrons in their valence shells. They will share what they need to and pair up when they don't need to. Since they need eight and each orbital holds two electrons, we can say that each atom will have up to four electron domains.
Those domains can either hold a lone electron pair or an electron in its shared partner. Let's look at water to demonstrate this idea. Water has the chemical formula H2O. Oxygen has six valence electrons.
We have seen already that it wants to form two bonds, allowing it to share two electrons and then it has a full octet. It also has two sets of lone electron pairs. The Lewis structure for it looks like this. We can also notice that there are four domains of electrons around oxygen.
Two lone electron pair domains and two bonding domains. Each contains two electrons, giving oxygen a total of eight electrons on a full valence shell. According to the chart, We can have two, three, or four electron domains around atoms that follow the octet rule.
Let's start with four electron domains and work our way down to two, looking at the geometry of each set. sp3 hybrid orbitals part one. Four electron domains and four bonding domains.
Methane has four electron domains and four of them are bonding domains. In 3D, the electron domains around carbon would look like this. This is called a tetrahedron.
It is a shape with four sides. The hydrogen is attached to the ends of each orbital, forming methane. It doesn't have to be the hydrogen, of course, but for now, that is easiest to visualize.
The four electron domains will automatically arrange themselves as far apart as possible, because the individual domains are all negatively charged. When this happens, each electron domain is approximately 109 degrees from the other domains. This is called a bond angle, and it will change depending on the geometry. Because methane has four of the combined orbitals around it, they must be sp3, which are formed from the hybridization of an s-orbital and 3p orbitals. We can say that any atom with four electron domains that has all four of them as bonding domains will have this shape.
The shape of a molecule is determined by the atoms that surround the central atom. sp3 hybrid orbitals, part 2 Four electron domains and three bonding domains. Let's look at ammonia.
Ammonia has the formula NH3, and we know that nitrogen has five valence electrons. So the Lewis structure of ammonia looks like this. It has four electron domains, and three of them are bonding.
One is a lone electron pair. Since it has four domains, these domains will form a tetrahedron. Three bonding, and one holding the lone electron pair.
However... The molecule only has atoms at three of those points. So what shape would the molecule have? Since the molecule's final appearance is determined only by looking at the bonded atoms, and not at the lone electron pairs, the molecule looks like this. This shape is called trigonal pyramidal, because the nitrogen looks like the top of a three-sided pyramid.
These orbitals are still sp3 because there are four orbitals, but we only see those with atoms attached. sp3 hybrid orbitals part 3 four electron domains and two bonding domains let's take another look at water h2o has four electron domains around the oxygen two bonding and two lone electron pair domains because it has four domains these domains will need sp3 hybrid orbitals two of them are bonding domains so what we see is this the shape of this molecule is bent because the two lone electron pairs take two of the four sides and leave us with this bent molecule. Again, these are still sp3 hybrid orbitals because there are four of them. However, we only see the two bonded domains.
sp3 hybrid orbitals part four. Four electron domains and one bonding domain. Finally. We can finish off this natural progression of removing one bonding domain at a time and considering the shape of what is produced.
For the last sp3 hybrid orbital shape, we will look at the halogens. Halogens have seven valence electrons and thus only need a single bond to complete their shell. We can consider hydrogen fluoride or hydrofluoric acid.
It has four electron domains, but only one of them is bonding. What is the only shape possible between two objects? That's right, it's a straight line or linear. So, we can notice a pattern forming. If we know the number of electron domains and the number of bonding domains, we can determine the shape.
All of these molecules will be using sp3 hybrid orbitals because they have a total of four electron domains. So to summarize what we have found. For four electron domains and four bonding domains, we have tetrahedral.
For four electron domains and three bonding domains, we have trigonal pyramidal. For four electron domains and two bonding domains, we have bent. And finally, for four electron domains and one bonding domain, we have linear. Now, let's consider sp2 hybrid orbitals, three electron domains. For these molecules, there are only three sp2 hybrid orbitals, because they are made of an s orbital and two p orbitals.
Boron is a weirdo. It only has three valence electrons and is usually happy with only three bonds, or six total shared electrons. With three electron domains, boron has sp2 hybrid orbitals, as we can see with borane, BH3. Boron forms three sp2 hybrid orbitals and makes what is called a trigonal planar geometry. We can see that if we remove one of the hydrogens, we will have a bent geometry.
We can also see that if we have removed two hydrogens, we would again have a linear molecule since two atoms must be linear. So for sp2 hybrid orbitals, we have the following summary. Three electron domains and three bonding domains equals trigonal planar.
For three electron domains, two bonding domains equals bent. And for three electron domains with one bonding domain, it equals linear. We should take a moment to consider another way to get sp2 hybrid orbital geometry.
It's time to consider double bond. Let's use carbon because it is the basis of all life and an interesting atom for bonding. Carbon has four valence electrons.
If they all bond to a single atom, we have sp3 orbitals. Let's consider what happens when carbon forms double bonds. Let's take formaldehyde as an example. What is the geometry around this carbon? Let's count the electron domains around carbon and see what we get.
Believe it or not, there are only three of them. The double bond counts as a single domain of electrons. The best way to discuss what is happening here is to consider some new terminology.
Single bonds are called sigma bonds. Anytime two atoms are sharing one electron each between them, it is a sigma bond. If we add additional electrons to the bond, as in double bonds, we get what is called a pi bond.
So, in formaldehyde, we have three single bonds and one pi bond. In the Lewis structure below, sigma bonds are colored red and the single pi bond is green. We can say that the carbon has three sigma bonds and a pi bond.
These three sigma bonds are made with sp2 hybrid orbitals. They create a 3d structure that is trigonal planar, just as boron trihydride. It has three electron domains and three bonding domains. Now we know that double and triple bonds count as one bonding domain. Remember that with four orbitals s, px, py, and pz, We can make three sp2 hybrid orbitals and have one p orbital left over.
The p orbital contains one electron that can be shared with oxygen. So, the second bond in the double bond is that p orbital being shared along with a sigma bond. This works because p orbitals are perpendicular to the molecule which is flat, or planar.
Let's consider ethylene, the molecule that helps ripen fruit. The formula for ethylene is C2H4. Each of the carbons here are using sp2 hybrid orbitals for all of the sigma bonds. They are also sharing electrons in their p orbitals to form the pi bond between them. Each carbon has the geometry of trigonal planar because they have three electron domains and three bonding domains.
This is a flat geometry. The p orbital is dumbbell shaped so it sticks up above and below the structure. It is still only one orbital even though it has two lobes.
The electrons in these p orbitals bond across the space between the carbon atoms like the diagram below. The key to understanding double bonds is to recognize that the first of these two bonds is a sigma bond, and the bond represented in purple is a one pi bond. Imagine the electrons that are being shared racing around the purple area like a racetrack. It's all one big pi bond.
So we have three sigma bonds which are in sp2 hybrid orbitals, and we have one pi bond formed by the remaining p orbitals. Carbons with one double bond and two single bonds have a trigonal planar geometry. SP hybrid orbitals, one electron domain and one or two bonding domains.
Lastly, we will look at SP hybrid orbitals. Because they are a combination of an s-orbital and a single p-orbital, there are only two of them. The geometry for all sp-orbital molecules is linear. You can't make a straight line between two atoms and get any other shape.
So, if there are two electron domains and one or two bonding domains, the geometry is linear. Consider nitrogen gas, N2. It has a triple bond and a lone electron pair.
The first bond of the triple bond is the sp-sigma bond. So it has two electron domains and one bonding domain. Two electron domains with one bonding domain equals linear. However, we should look at carbon again. Carbon can also triple bond with itself.
We can consider acetylene, which has the molecular formula of C2H2. Each carbon has two electron domains and two bonding domains. The red dots represent the sp hybrid orbital sigma bonds, and the green dots represent the two additional pi bonds. These pi bonds, again, are created from electrons in p orbitals.
Because this molecule is linear, it can have a pi bond above and to the side. The two pi bonds look like this. Now, we have discussed all the options in this chart. You will need to know how to identify geometries based on the number of electron domains and the number of these domains that are participating in bonding.
You will need to do this either by seeing the molecule's Lewis structure or being told the number of electron domains and bonding domains around a central atom. Molecular orbital theory. Hybrid orbital theory is not the only theory of bonding that exists.
It is a great idea, and it has a lot of predictive power. A lot of organic chemistry is built on hybrid orbital theory. As discussed, hybrid orbital theory is the idea that orbitals on each atom hybridize, then bond. The shapes of the orbitals are mathematically built from each atom by itself, then combined in bonds with other atoms. Molecular orbital theory uses wave equation mathematics to combine orbitals from different atoms to form molecular orbitals that only exist when those two atoms are bonded.
This sounds similar, but in practice it is not. In order to predict the molecular orbitals for anything larger than water, it requires some crazy supercomputers. You should be aware that it exists. But you will not need to use it in this class.